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[Illustration: _VOL. I. MODERN MACHINE-SHOP PRACTICE FRONTISPIECE_
_Copyright, 1887 by Charles Scribner's Sons._
=MODERN AMERICAN FREIGHT LOCOMOTIVE.=]
MODERN
MACHINE-SHOP PRACTICE
BY
JOSHUA ROSE, M.E.
ILLUSTRATED WITH MORE THAN 3000 ENGRAVINGS
VOLUME I.
NEW YORK
CHARLES SCRIBNER'S SONS
1887
COPYRIGHT, 1887, BY
CHARLES SCRIBNER'S SONS
Press of J. J. Little & Co.
Astor Place, New York.
PREFACE.
MODERN MACHINE-SHOP PRACTICE is presented to American mechanics as a
complete guide to the operations of the best equipped and best managed
workshops, and to the care and management of engines and boilers.
The materials have been gathered in part from the author's experience of
thirty-one years as a practical mechanic; and in part from the many
skilled workmen and eminent mechanics and engineers who have generously
aided in its preparation. Grateful acknowledgment is here made to all
who have contributed information about improved machines and details of
new methods.
The object of the work is practical instruction, and it has been written
throughout from the point of view, not of theory, but of approved
practice. The language is that of the workshop. The mathematical
problems and tables are in simple arithmetical terms, and involve no
algebra or higher mathematics. The method of treatment is strictly
progressive, following the successive steps necessary to becoming an
intelligent and skilled mechanic.
The work is designed to form a complete manual of reference for all who
handle tools or operate machinery of any kind, and treats exhaustively
of the following general topics: I. The construction and use of
machinery for making machines and tools; II. The construction and use of
work-holding appliances and tools used in machines for working metal or
wood; III. The construction and use of hand tools for working metal or
wood; IV. The construction and management of steam engines and boilers.
The reader is referred to the TABLE OF CONTENTS for a view of the
multitude of special topics considered.
The work will also be found to give numerous details of practice never
before in print, and known hitherto only to their originators, and aims
to be useful as well to master-workmen as to apprentices, and to owners
and managers of manufacturing establishments equally with their
employees, whether machinists, draughtsmen, wood-workers, engineers, or
operators of special machines.
The illustrations, over three thousand in number, are taken from modern
practice; they represent the machines, tools, appliances and methods now
used in the leading manufactories of the world, and the typical steam
engines and boilers of American manufacture.
The new PRONOUNCING AND DEFINING DICTIONARY at the end of the work, aims
to include all the technical words and phrases of the machine shop, both
those of recent origin and many old terms that have never before
appeared in a vocabulary of this kind.
The wide range of subjects treated, their convenient arrangement and
thorough illustration, with the exhaustive TABLE OF CONTENTS of each
volume and the full ANALYTICAL INDEX to both, will, the author hopes,
make the work serve as a fairly complete ready reference library and
manual of self-instruction for all practical mechanics, and will
lighten, while making more profitable, the labor of his fellow-workmen.
CONTENTS.
VOLUME I.
CHAPTER I.
=THE TEETH OF GEAR-WHEELS.=
PAGE
=Gear-Wheels.= Spur-wheels, bevel-wheels, mitre-wheels,
crown-wheels, annular or internal wheels 1
Trundle-wheels, rack and pinion-wheel and tangent screw, or
worm and worm-wheel 1
The diameter of the pitch circle of 1
=Gear-Wheel Teeth.= The face, the flank, the depth or height 1
The space, the pitch line, the point, the arc pitch, the chord
pitch, the line of centres 2
Rules for finding the chord pitch from the arc pitch; table of
natural sines; diametral pitch; finding the arc from the
diametral pitch; table of arc and diametral pitches 3
=Gear-Wheels.= The driver and follower, a train of gears 3
Intermediate gears 3
The velocity of compounded wheels 4
Finding the diameters of the pitch circles of 4
Considered as revolving levers 5
Calculating the revolutions of, and power transmitted by 5
The angular velocity of 6
=Gear-Wheels.= Hunting tooth in, stop motion of 7
=Gear-Wheel Teeth.= The requirements and nature of the teeth
curves 7
Cycloidal curves for the faces of; epicycloidal and involute
curves; the hypocycloidal curve; method of forming or
generating the epicycloidal and hypocycloidal curves for the
faces and flanks of gear teeth 8
Applications of the epicycloidal and hypocycloidal curves in
the formation of gear teeth 9
The diameter of the circle for generating the epicycloidal and
hypocycloidal curves; graphical demonstration that the flank
curves are correctly formed to work with the face curves of the
other wheel 10
Graphical demonstration that the curves are correct independent
of either the respective sizes of the wheels, or of the curve
generating circles 11
=Gear-Wheels.= Hand applications of the rolling or
generating circle to mark the tooth curves for a pair of wheels 12
=Gear-Wheel Teeth.= The variation of curve due to different
diameters of wheels or of rolling circles 12
Tracing the path of contact of tooth upon tooth in a pair of
gear-wheels; definition of the "arc of approach;" definition of
the "arc of recess;" demonstration that the flanks of the teeth
on the driver or driving-wheel have contact with the faces of
the driven wheel during the arc of approach, and with the
flanks of the driven wheel during the arc of recess 13
Confining the action of the teeth to one side only of the line
of centres, when motion rather than power is to be conveyed 13
Demonstration that the appearance or symmetry of a tooth has no
significance with regard to its action 14
Finding how many teeth will be in constant action, the diameter
of the wheels, the pitch of the teeth, and the diameter of the
rolling circle being given 15
Example of the variation of tooth form due to variation of
wheel diameter 15
=Gear Teeth.= Variation of shape from using different
diameters of rolling circles 16
Thrust on the wheel shafts caused by different shapes of teeth 16
=Gear-Wheels.= Willis' system of one size of rolling circle for
trains of interchangeable gearing 16
Conditions necessary to obtain a uniform velocity of 16
=Gear Teeth.= The amount of rolling and of sliding motion of 16
The path of the point of contact of 16
The arcs of approaching and of receding contact 16
Lengths of the arcs of approach and of recess 16
The influence of the sizes of the wheels upon the arcs of
contact 17
Influence of the size of the rolling circle upon the amount of
flank contact 18
Demonstration that incorrectly formed teeth cannot correct
themselves by wear 18
The smaller the diameter of the rolling circle, the less the
sliding motion 18
Influence of the size of the rolling upon the number of teeth
in contact in a given pair of wheels 19
Demonstration that the degrees of angle the teeth move through
exceed those of the path of contact, unless the tooth faces
meet in a point 19
Influence of the height of the teeth upon the number of teeth
in contact 20
Increasing the arc of recess without increasing the arc of
approach 20
Wheels for transmitting motion rather than power 21
Clock wheels 21
Forms of teeth having generating or rolling circles, as large
or nearly as large as the diameters of the wheels 21
=Gear-Wheels.= Bevel 21
The principles governing the formation of the teeth of bevel-
wheels 22
Demonstration that the faces of the wheels must be in line with
the point of intersection of the axis of the two shafts 22
=Gear Teeth.= Method of finding the curves of, for bevel
gear 22
=Gear-Wheels.= Internal or annular 23 to 27
Demonstration that the teeth of annular wheels correspond to
the spaces of spur-wheels 23
=Gear-Wheels Internal.= Increase in the length of the path
of contact on spur-wheels of the same diameter, and having the
same diameter of generating or rolling circle 23
Demonstration that the teeth of internal wheels may interfere
when spur-wheels would not do so 23
Methods of avoiding the above interference 23
Comparison of, with spur-wheels 23
The teeth of: demonstration that it is practicable to so form
the teeth faces that they will have contact together as well as
with the flanks of the other wheel 24
Intermediate rolling circle for accomplishing the above result 24
The application of two rolling circles for accomplishing the
above result 24
Demonstration that the result reached by the employment of two
rolling circles of proper diameter is theoretically and
practically perfect 24
Limits of the diameters of the two rolling circles 25
Increase in the arc of contact obtained by using two rolling
circles 25
Demonstration that the above increase is on the arc of recess
or receding contact, and therefore gives a smooth action 25
Demonstration that by using two rolling circles each tooth has
for a certain period two points of contact 25
The laws governing the diameters of the two rolling circles 25
Practical application of two rolling circles 26
Demonstration that by using two rolling circles the pinion may
contain but one tooth less than the wheel 26
The sliding and rolling motion of the teeth of 27
CHAPTER II.
=THE TEETH OF GEAR-WHEELS (Continued).=
=Worm and Worm-Wheel=, or wheel and tangent screw 28 to 31
General description of 28
Qualifications of 28
The wear of 28
=Worm-Wheel Teeth=, the sliding motion of 28
When straight have contact on the centres only of the tooth
sides 28
That envelop a part of the worm circumference 28
The location of the pitch line of the worm 28
The proper number of teeth in the worm-wheel 29
Locating the pitch line of the worm so as to insure durability 29
Rule for finding the best location for the pitch line of the
worm 29
Increasing the face of the worm to obtain a smoother action 29
=Worms=, to work with a square thread 29
=Worm-Wheels=, applications of 30
=Gear-Wheels= with involute teeth 31 to 34
=Gear Teeth.= Generating the involute curve 31
Templates for marking the involute curve 32
=Involute Teeth=, the advantages of 34
=Gear Teeth=, Pratt and Whitney's machine for cutting
templates for 35
CHAPTER III.
=THE TEETH OF GEAR-WHEELS (Continued).=
=Gear Teeth=, revolving cutters for 37
Pantagraph engine for dressing the cutters for 38
Numbers of cutters used for a train of wheels 39
=Gear-Wheel Teeth.= Table of equidistant value of cutters 41
Depth of, in the Brown and Sharpe system 42
Cutting the teeth of worm-wheels 42
Finding the angle of the cutter for cutting worm-wheels 43
The construction of templates for rolling the tooth curves 43
Rolling the curves for gear teeth 43
Forms of templates for gear teeth 44
Pivoted arms for tooth templates 44
Marking the curves by hand 45
Former or Template of the Corliss bevel gear-wheel engine or
cutting machine 45
The use of extra circles in marking the curves with compasses 46
Finding the face curves by geometrical constructions 47
The Willis odontograph for finding the radius for striking the
curves by hand 47
The method of using the Willis odontograph 48
Professor Robinson's odontograph 49
Method of using Professor Robinson's odontograph 49
Application of Professor Robinson's odontograph for trains of
gearing 51
Tabular values and setting numbers for Professor Robinson's
odontograph 51
Walker's patent wheel scale for marking the curves of cast
teeth 51
The amount of side clearance in cast teeth 53
Filleting the roots of epicycloidal teeth with radial flanks 53
Scale of tooth proportions given by Professor Willis 54
The construction of a pattern for a spur-wheel that is to be
cast with the teeth on 54
Template for planing the tooth to shape 54
Method of marking the curves on teeth that are to be glued on 55
Method of getting out the teeth of 56
Spacing the teeth on the wheel rim 56
Methods of accurately spacing the pattern when it has an even
number of teeth 58
Method of spacing the wheel rim when it has an odd number of
teeth 58
=Gear-Wheels, Bevel Pinion=, drawings for 59
Getting out the body for a bevel-wheel 59
Template for marking the division lines on the face of the
wheel 59
Marking the lines of the division on the wheel 60
=Gear-Wheels, Pinion=, with dovetail teeth 60
Testing the angle of bevel-wheels while in the lathe 60
=Gear-Wheels, Skew Bevel.= Finding the line of contact 61
Marking the inclination of the teeth 61
=Gear-Wheels, Bevel=, drawing for built up 61
=Gear-Wheels, Worm=, or endless screw 62
Constructing a pattern from which the worm is to be cast 62
Tools for cutting the worm in a lathe 62
Cutting the teeth by hand 62
=Gear-Wheels, Mortise= or cogged 63
Methods of fastening cogs 63
Methods of getting out cogs for 63
=Gear-Wheel Teeth=, calculating the strength of epicycloidal 64
Factors of safety for 64
Tredgold's rule for calculating the strength of 65
Cut, calculating the strength of 65
=Gear-Wheel Teeth.= The strength of cogs 66
The thickness of cogs 66
The durability of cogs 66
Table for calculating the strength of different kinds of 67
The contact of cast teeth 67
Table for determining the relation between pitch diameter,
pitch, and number of teeth in gear-wheels 68
Examples of the use of the above table 68
With stepped teeth 69
Angular or helical teeth 69
End thrust of angular teeth 69
Herring-bone angular teeth 69
For transmitting motion at a right angle by means of angular or
helical teeth 69
Cutting helical teeth in the lathe 69
For wheels whose shaft axes are neither parallel nor meeting 70
Elliptical 70
Elliptical, marking the pitch lines of 70
Elliptical, drawing the teeth curves of 73
For variable motion 74
Form of worm to give a period of rest 74
Various applications of 74
=Gear-Wheels=, arrangement of, for periodically reversing
the direction of motion 75
Watt's sun and planet motion 75
Arrangements for the rapid multiplication of motion 75
Arrangement of, for the steering gear of steam fire-engines 75
Various forms of mangle gearing 79
=Gear-Wheel and Rack=, for reciprocating motion 77
=Friction Wheels.= 77
The material for 77
Paper 78
For the feed motion of machines 78
The unequal wear upon grooved 79
Form of, for relieving the journals of strain 79
=Cams=, for irregular motion 80
Finding the pitch line of 80
Finding the working face of 80
The effect the diameter roller has upon the motion produced by
a cam 80
Demonstration of the different motion produced by different
diameters of rollers upon the same cam 80
Diagram of motion produced from the same cam with different
diameters of rollers 81
Return or backing 82
Methods of finding the shape of return or backing 82
=Cam Motion=, for an engine slide valve without steam lap 83
For a slide valve with steam lap 83
=Groove Cams=, proper construction of 84
The wear of 84
Brady's improved groove cam with rolling motion and adjustment
for wear 84
CHAPTER IV.
=SCREW-THREADS.=
=Screw Threads=, the various forms of 85
The pitch of 85
Self-locking 85
The Whitworth 86
The United States standard 86
The Common V 86
The requirements of 86
Tools for cutting 87
Variation of pitch from hardening 87
The wear of thread-cutting tools 88
Methods of producing 88
Alteration of shape of, from the wear of the tools they are cut
by 89
=Screw Thread Cutting Tools.= The wear of the tap and the die 89
Improved form of chaser to equalize the wear 90
Form of, to eliminate the effects of the wear in altering the
fit 90
Originating standard angles for 91
Standard micrometer gauge for the United States standard screw
thread 91
Standard plug and collar gauges for 91
Producing gauges for 92
Table of United States standard for bolts and nuts 93
Table of standard for the V-thread 93
United States standard for gas and steam pipes 93
Taper for standard pipe threads 95
Tables of the pitches and diameters at root of thread, of the
Whitworth thread 95
Table of Whitworth's screw threads for gas, water, and
hydraulic piping 96
Whitworth's standard gauges for watch and instrument makers 96
Screw-cutting hand tools 96
=Thread-Cutting Tools.= American and English forms of stocks
and dies 97
Adjustable or jamb dies 98
The friction of jamb dies 98
The sizes of hobs that should be used on jamb dies 99
Cutting right or left-hand thread with either single, double,
or treble threads with the same dies 99
Hobs for hobbing or threading dies 100
Various forms of stocks with dies adjustable to take up the
wear 101
Dies for gas and steam pipes 101
=Thread-Cutting Tool Taps.= The general forms of taps 102
Reducing the friction of 102
Giving clearance to 102
The friction of taper 103
Improved forms of 103
Professor J. E. Sweet's form of tap 104
Adjustable standard 104
The various shapes of flutes employed on taps 105
The number of flutes a tap should have 105
Demonstration that a tap should have four cutting edges rather
than three 106
The position of the square or driving end, with relation to the
cutting edges 106
Taper taps for blacksmiths 106
Collapsing taps for use in tapping machines 107
Collapsing tap for use in a screw machine 107
The alteration of pitch that occurs in hardening 108
Gauging the pitch after the hardening 108
Correcting the errors of pitch caused by the hardening 109
For lead 109
Elliptical in cross section 109
For very straight holes 109
Tap wrenches solid and adjustable 110
=Thread-Cutting.= Tapping 110
Appliances for tapping standard work 111
CHAPTER V.
=FASTENING DEVICES.=
=Bolts=, classification of, from the shapes of their heads 112
Classification of, from the shapes of their bodies 112
Countersunk 112
Holes for, classification of 112
For foundations, various forms of 113
Hook bolts 113
The United States standard for finished bolts and nuts 113
The United States standard for rough bolts and nuts, or black
bolts 114
The Whitworth standard for bolts and nuts 114
=Screws= 114
=Studs= 115
=Set Screws= 115
=Bolts= for quick removal 116
That do not pass through the work 117
That self-lock in grooves and are readily removable 117
Heads and their bedding 117
=Nuts=, the forms of, when they are to be steam tight 118
Various forms of 118
Jamb nuts and lock nuts 119
=Differential Threads= for locking purposes 119
For fine adjustments 119
=Nuts=, taking up the wear of 120
Securing devices 120
Securing by taper pins 121
Securing by cotters 121
Securing by notched plates 121
=Pins.= Securing for exact adjustments 121
And double eyes fitting 121
Fixed 122
Working 122
=Bolts=, removing corroded 122
=Nuts=, removing corroded 122
=Washers=, standard sizes of 122
=Wrench=, the proper angles of 123
Box 124
Monkey 125
Adjustable, various forms of 125
Sockets 125
Novel for carriage bolts 125
Pin 126
Improved form of 126
=Keys=, the various kinds of 126
The bearing surfaces of 126
=Set Screws=, application of, to hubs or bosses 127
=Keys=, with set-screws 127
The draught of 127
=Feathers=, and their applications 127
=Keys=, for parallel rods 128
=Taper Pins=, proper position of, for locking purposes 128
Improved method of fitting 128
CHAPTER VI.
=THE LATHE.=
=Lathe=, the importance and advantages of 129
Classification of lathes 129
Foot 130
Methods of designating the sizes of 130
Bench 130
Power 130
Hand 130
Slide Rest for 131
American form of, their advantages and disadvantages 132
English forms of 132
For spherical work 132
Methods of taking up lost motion of 133
=Engine Lathe=, general construction of 133
The construction of the shears of 134
Construction of the headstock 134
Construction of the bearings 134
Construction of the back gear 135
Means of giving motion to the feed spindle 135
Construction of the tailstock 135
Method of rapidly securing and releasing the tailstock 136
=Lathe Tailstock=, setting over for turning tapers 136
=Engine Lathe=, construction of carriage 137
Feed motion for carriage or saddle 137
=Lathe Apron=, Construction of the feed traverse 138
Construction of the cross-feed motion 138
=Engine Lathe=, lead screw and change wheels of 139
Feed spindle and lead screw bearings 139
Swing frame for lead screw 139
Lead screw nuts 140
With compound slide rest 140
Construction of compound slide rest 141
Advantages of compound slide rest 141
For taper turning 142
Taper-turning attachments 142
With compound duplex slide rest 143
Detachable slide rest 143
Three-tool slide rest for turning shafting 143
With flat saddle for chucking work on 143
=The Sellers Lathe= 143
Construction of the headstock and treble gear 144
Construction of the tailstock and method of keeping it in line 145
Construction of the carriage and slide rest 145
Methods of engaging and disengaging the feed motions 146
=Car Axle Lathe=, with central driving motion and two slide
rests 147
The feed motions of 148
=Self-Acting Lathe=, English form of 148
=Pattern Maker's Lathe= 148
Brake for cone pulley 149
With wooden bed 149
Slide rest for 149
=Chucking Lathe=, English 149
Feed motions of 150
=Pulley Lathe= 150
=Gap or Break Lathe= 151
=Extension Lathe= 151
=Wheel Lathe= 151
=Chucking Lathe= for boring purposes 152
=Lathe= for turning crank axles 152
Construction of the headstock 153
Construction of the feed motions 154
For turning crank, Arrangements of the slide rests 154
Application of the slide rest to a crank 155
CHAPTER VII.
=DETAILS IN LATHE CONSTRUCTION.=
=Live Spindle= of a lathe, the fit of 157
With coned journals 157
Methods of taking up the end motion of 158
Arranging the swing frame for the change gears 158
Taking up the wear of the back bearing 158
The wear of the front bearing of 158
=The Taper= for the live centre 159
=Methods= of removing the lathe centres 159
=Tapers= for the live centres 159
=Methods= of removing the dead centre 159
=Driving Cone=, arranging the steps of 159
Requirements of proportioning the steps of 159
Rules for proportioning the diameters of the steps of, when the
two pulleys are exactly alike and are connected by an open
belt 159 to 161
When the two pulleys are unlike 161 to 164
=Back Gear=, methods of throwing in and out 165
=Conveying= motion to the lead screw 165
=Attaching= the swing frame 166
=Feed Gear.= Arrangement for cutting worm threads or tangent
screws 167
=Feed Motion= for reversing the direction of tool traverse
in screw cutting 168
For lathe aprons 168
=Slide Rest=, weighted elevated 168
Double tool holder for 169
Gibbed elevating 169
=Examples= of feed motions 170
=Feed Regulators= for screw cutting 171
The star feed 172
=Ratchet Feeds= 173
=Tool Holding= devices, the various kinds of 173
=Tool Rest= swiveling 174
=Tool Holder= for compound slide rests 174
For octagon boring tools 175
=Lathe Lead and Feed Screws= 175
Lead screws, supporting, long 176
Position of the feed nut 177
Form of threads of lead screws 177
The effect the form of thread has in causing the nut to lock
properly or improperly 177
Example of a lead screw with a pitch of three threads per inch 177
Example of a lead screw with five threads per inch 178
Example with a lead screw of five threads per inch 179
Device for correcting the errors of pitch of 179
=Table= for finding the change wheels for screw cutting when
the teeth in the change wheels advance by four 180
For finding the change wheels when the teeth in the wheels
advance by six 180
Constructing a table to cut fractional threads on any lathe 181
Finding the change wheels necessary to enable the lathe to cut
threads of any given pitches 181
Finding the change wheels necessary to cut fractional pitches 181
=Determining= the pitches of the teeth for change wheels 182
=Lathe Shears= or beds 182
Advantages and disadvantages of, with raised V-guide-ways 182
Examples of various forms of 183
=Lathe Shears= with one V and one flat side 183
Methods of ribbing 184
The arrangement of the legs of 184
=Lathe Tailblock= 185
With rapid spindle motion 185
With rapid fastenings and releasing devices 185
The wear of the spindles of 185
Spindles, the various methods of locking 186
Testing, various methods of 187
CHAPTER VIII.
=SPECIAL FORMS OF THE LATHE.=
=Watchmaker's Lathes= 188
Construction of the headstock 188
Construction of chucks for 188
Expanding chucks for 188
Contracting chucks for 188
Construction of the tailblock 189
Open spindle tailstocks for 189
Filing fixture for 189
Fixture for wheel and pinion cutting 189
Jewelers' rest for 189
=Watch Manufacturers' Lathe= 190
Special chucks for 190
Pump centre rest 190
=Lathe=, hand 191
Screw slotting 192
With variable speed for facing purposes 192
Cutting-off machine 193
Grinding Lathes 193
With elevating rest 194
Universal 195
Special chucks for 196
The Morton Poole calender roll grinding lathe 196
The construction of the bed and carriages 197
Principles of action of the carriages 197, 198
Construction of the emery-wheel arbors and the driving
motion 198, 199
The advantages of 199
The method of driving the roll 200
Construction of the headstock 200
The transverse motion 200
=The Brown and Sharpe Screw Machine=, or screw-making lathe 200
Threading tools for 203
Examples of the use of 203
=The Secor Screw Machine=, construction of the headstock 204
The chuck 205
The feed gear 205
The turret 205
The cross slide 205
The stop motions 206
=Pratt and Whitney's Screw Machine= 206
Parkhurst's wire feed, construction of the headstock, chuck and
feed motion 207
Box tools for 208
Applications of box tools 208
Threading tool for 208
Cutting-off tool for 208
=Special Lathe= for wood working 208
The construction of the carriage and reducing knife 209
Construction of the various feed motions 209
Construction of the tailstock 209
=Lathes for irregular forms= 210
Axe-handle 210
Back knife gauge 210
Special, for pulley turning 211
=Boring and Turning= mill or lathe 211
Construction of the feed motions 213
Construction of the framing and means of grinding the lathe 214
Construction of the vertical feed motions 215
=The Morton Poole= roll turning lathe 215
Construction of the slide rest 216
The tools for 216
=Special Lathes= for brass work 216, 217
=Boring Lathe= with traversing spindle 218
For engine cylinders 219
Cylinder, with facing slide rests 219
With double heads and facing rests 220
=Lathe for turning Wheel= hubs 221
CHAPTER IX.
=DRIVING WORK IN THE LATHE.=
=Drivers=, carriers, dogs, or clamps, and their defects 222
Lathe clamps 222
Equalizing drivers 223
The Clements driver 223
Driver and face plate for screw cutting 223
Forms of, for bolt heads 224
Adjustable, for bolt heads 224
For threaded work 225
For steady rest work 225
For cored work 225
For wood 225
=Centres= for hollow work 226
For taper work 226
=Lathe Mandrels=, or arbors 227
Drivers for 227
For tubular work 227
Expanding mandrels 227
With expanding cones 228
With expanding pieces 228
Expanding, for large work 228
For threaded work 228
For nuts, various forms of 229
For eccentric work 229
=Centring devices= for crank axles 230
=The Steady Rest= or back rest 231
Steady rest, improved form of 232
Cone chuck 232
Steady rest for square and taper work 233
The cat head 233
Clamps for 233
Follower rests 234
=Chucks and Chucking= 234
Simple forms of chucks 234
Adjustable chucks for true work 235
Two-jawed chucks 236
Box body chucks 237
Reversible jawed chucks 237
Three and four-jawed chucks 237
Combination chucks 237
The wear of scroll chuck threads 237
Universal chucks 238
The wear of chucks 240
Special forms of chucks 241
Expanding chucks for ring-work 241
Cement chuck 241
Chucks for wood-working lathes 242
=Lathe Face Plates= 243
Face plates, errors in, and their effects 243
Work-holding straps 244
Face plate, clamping work on 245
Forms of clamps for 245
Examples of chucking work on 246, 247
For wood work 247
=Special Lathe Chuck= for cranks 248
=Face Plate Work=, examples of 249
Errors in chucking 250
Movable dogs for 250
The angle plate 251
Applications of 251
Angle plate chucking, examples of 251
Cross-head chucking 251-253
CHAPTER X.
=CUTTING TOOLS FOR LATHES.=
=Principles= governing the shapes of lathe tools 254
=Diamond-pointed=, or front tool 254
=Principles= governing use of tools 254
Front rake and clearance of front tools 254
Influence of the height of a tool upon its clearance and
keenness 255
Tools with side rake in various directions 256
The effect of side rake 256
The angle of clearance in lathe tools 257
Variation of clearance from different rates of feed and
diameters of work 257
=Round-nosed= tools 258
=Utmost Duty= of cutting tools 258
Judging the quantity of the tool from the shape of its cutting 259
=Square-nosed= tools 260
The height of lathe tools 260
Side tools for lathe work 261
Cutting-off or grooving tools 262
Facing tools or knife tools 262
Spring tools 263
=Brass Work=, front tools for 264
Side tools for 264
=Threading= tools 264
Internal threading tools 264
The length of threading tools 265
The level of threading tools 265
Gauges for threading tools 266
Setting threading tools 266
Circular threading tools 267
Threading tool holders 267
=Chasers= 268
Chaser holders 268
Setting chasers 268
=Square Threads=, clearance of tools for 269
Diameter at the roots of threads 269
Cutting coarse pitch square threads 269
Dies for finishing square threads 269
=Tool Holders= for outside work 270
For circular cutters 272
Swiveled 273
Combined tool holders and cutting-off tools 273
=Power Required= to drive cutting tools 273
CHAPTER XI.
=DRILLING AND BORING IN THE LATHE.=
=The Twist Drill= 274
Twist drill holders 274
The diametral clearance of twist drills 274
The front rake of twist drills 275
The variable clearance on twist drills as usually ground 275
Demonstration of the common error in grinding twist drills 276
The effects of improper grinding upon twist drills 276
Table of speeds and feeds for twist drills 277
Grinding twist drills by hand 279
Twist drills for wood work 279
=Tailstock Chucks= for drilled work 279
=Flat Drills= for lathe work 280
Holders for lathe work 281
=Half-round= bit or pod auger 281
With front rake for wrought iron or steel 281
With adjustable cutter 281
For very true work 281
=Chucking Reamer= 281
The number of teeth for reamers 282
Spacing the teeth of reamers 282
Spiral teeth for reamers 282
Grinding the teeth of reamers 282
Various positions of emery-wheel in grinding reamers 282
Chucking reamers for true work 283
Shell reamers 283
Arbor for shell reamers 283
Rose-bit or rose reamers 283
Shell rose reamers 284
Adjustable reamers 284
Stepped reamers for taper work 285
Half-round reamers 285
Reamers for rifle barrels 285
=Boring Tools= for lathe work 285
Countersinks 285
Shapes of lathe boring tools 285
Boring tools for brass work 286
The spring of boring tools 286
Boring tools for small work 287
Boring tool holders 287
=Boring Devices for Lathes= 288
=Boring Heads= 288
=Boring Bars= 289
Boring bar cutters 289
Three _versus_ four cutters for boring bars 290
Boring bars with fixed heads 290
With sliding heads 290
Bar cutters, the shapes of 291
Boring head with nut feed 291
Boring bars for taper work, various forms of 292
Boring double-coned work 293
Boring bar, centres for 293
=Cutting Speeds= and feeds for wrought iron 294
Examples of speeds taken from practice 295
CHAPTER XII.
=EXAMPLES IN LATHE WORK.=
=Technical Terms= used in the work 296
=Lathe Centres= 296
Devices for truing 297
Tools for testing the truth of, for fine work 298
Shapes of, for light and heavy work 299
=Centre Drilling=, attachment for lathes 300
The error induced by straightening work after 300
Machine 300
Combined centre-drill and countersink 300
Countersink with adjustable drill 300
Centring square 300
Centre-punch 300
Centre-punch guide 301
Centring work with the scribing block 301
Finding the centre of very rough work 301
Centre-drill chuck 302
The proper form of countersink for lathe work 302
Countersinks for lathe work 302
Various forms of square centres 303
The advantage of the square centre for countersinking 303
Novel form of countersink for hardened work 303
Chucks for centre-drilling and countersinking 303
Recentring turned work 304
=Straightening Work.= Straightening machine for bar iron 304
Hand device for straightening lathe work 305
Chuck for straightening wire 305
=Cutting Rods= into small pieces of exact length, tools for 305
=Roughing cuts=, the change of shape of work that occurs
from removing the surface by 306
Feeds for 306
Rates of feed for 307
=Finishing Work=, the position of the tool for 307
Finishing cast-iron with water 307
Specks in finished cast-iron work 307
Scrapers for finishing cast-iron work 307
Method of polishing lathe work 308
Filing lathe work 308
The use of emery paper on lathe work 308
The direction of tool feed in finishing long work 309
Forms of laps for finishing gauges or other cylindrical lathe
work 310
Forms of laps for finishing internal work 311
Grinding and polishing clamps for lathe work 311
Burnishing lathe work 311
=Taper Work=, turning 312
The wear of the centres of 312
Setting over the tailstock to turn 312
Gauge for setting over 313
Fitting 313
Grinding 313
The order of procedure in turning 313
The influence of the height of the tool in producing true 314
=Special Forms.= Curved work 314, 315
Standard gauges for taper work 316
Methods of turning an eccentric 317
Turning a cylinder cover 318
Turning pulleys 318
Chucking device for pulleys 318
=Cutting Screws= in the lathe 319
The arrangement of the change gears 319
The intermediate wheels 319
The compounded gears 320
Finding the change wheels to cut a given thread 320
Finding the change wheels for a lathe whose gears are
compounded 321
Finding the change gears for cutting fractional pitches 321
To find what pitch of thread the wheels already on the lathe
will cut 322
Cutting left-hand threads 322
Cutting double threads 322
Cutting screws whose pitches are given in the terms of the
metric system 322
Cutting threads on taper work 323
Errors in cutting threads on taper work 324
CHAPTER XIII.
=EXAMPLES IN LATHE WORK (Continued).=
=Ball Turning= with tubular saw 325
With a single tooth on the end of a revolving tube 325
With a removable tool on an arbor 325
Tool holder with worm feed 325
By hand 325
=Cams=, cutting in the lathe 326
Improved method of originating cams in the lathe 326
Motions for turning cams in the lathe 326, 327
Application of cam motions to special work 327
Cam chuck for irregular work 328
=Milling= or knurling tool 328
Improved forms of 328
=Winding Spiral Springs= in the lathe 329
=Hand Turning= 330
The heel tool 330
The graver and its applications 330, 331
Hand side tools 331
Hand round-nosed tools for iron 331
Hand finishing tool 331
=Hand Tools=, for roughing out brass work 332
Various forms and applications of scrapers 332, 333
Clockmakers' hand tool for special or standard work 334
Screw cutting with hand tools 334
Outside and inside chasers 334
Hobs and their uses 335
The application of chasers, and errors that may arise from
the position in which they are presented to the work 336
Errors commonly made in cutting up inside chasers 337
V-tool for starting outside threads 337
Starting outside threads 338
Cutting taper threads 338
Wood turning hand tools 338
The gauge and how to use it 338
The chisel and its use 339
The skew chisel and how to use it 339
Wood turners' boring tools for lathe work 340
CHAPTER XIV.
=MEASURING MACHINES, TOOLS AND DEVICES.=
=Standards of Measurements=, in various countries 341
Use of, by sight and by the sense of feeling 341
Variations in standard gauges 341
The necessity for accurate standards 341
The Rogers Bond standard measuring machine 342
Details of construction of 343, 344
The principle of construction of 344
The methods of using 345
The Whitworth measuring machine 345
The Betts Machine Company's measuring machine 346
Professor Sweet's measuring machine 347
Measuring machine for sheet metal 348
=Circle=, division of the 348
Troughton's method of dividing the circle 348, 349
Ramsden's dividing engine 349
The construction of 350, 351
Pratt and Whitney's dividing device 352
Practical application of 353
Index wheel, method of originating, by R. Hoe & Co. 353
Application of the index wheel (Hoe & Co.'s system) 353
=Classification= of the measuring tools used by workmen 354
=Micrometer Caliper= and its principle of construction 354, 355
=Gauges.= Standard plug and collar gauges 356
Methods of comparing standard plug and collar gauges 356
The effects of variations of temperature upon standard gauges 356
Plug and collar gauges for taper work 357
The Baldwin standards for taper bolts 359
Workmen's gauges for lathe work 359
=Calipers=, outside, the various forms of 360
Inside calipers 360
Calipers with locking devices 360
Spring calipers 360
The methods of holding and using 361, 362
Keyway calipers 363
The advantages of calipers 363
=Fitting.= The four kinds of fit in machine work 363
The influence of the diameter of the work in limiting the
application of standard gauges 363
The wear of tools and its influence upon the application of the
standard gauge system 364
The influence of the smoothness of the surface upon the
allowance to be made for drilling or hydraulic fits 365
Examples of allowance for hydraulic fits 365
Parallel holes and taper plugs for hydraulic fits 365
=Fitting.= Practicable methods of testing the fit of axle
brasses forced in by hydraulic pressure 366
Shrinkage or contraction fits 366
Allowances for 366
Gauge for 367
The shrinkage system at the Royal Gun Factory at Woolwich 367
Experiments by Thomas Wrightson upon the shrinkage of iron
under repeated heatings and coolings 368 to 374
Shrinking work, to refit it 374, 375
CHAPTER XV.
=MEASURING TOOLS.=
=End Measurements= of large lathe work 376
Template gauges for 376
Trammels or Trains 377
Adjustable gauges for 377
=Compasses=--Dividers 377
Compass calipers 378
=Key Seating= rule 378
=Surface Gauge= 378
Pattern makers' pipe gauge 379
=Squares.= The try square 379
The T square 379
Various methods of testing squares 379, 380
Bevel squares 380
=Bevel Protractors= 380
=Hexagon Gauge= 381
=Straight Edge= and its applications 381, 382
Winding strips and their application 382
=Surface Plate= or planimeter 383
=Templates= for curves 384
=Wire Gauges=, notch 384
Standard gauges for wire, &c. 384, 386
Gauge for music wire 386
Brown and Sharpe wire gauge 387
Birmingham wire gauge for rolled shell silver and gold 387
Sheet iron gauge, Russian 387
Galvanized iron 387
Belgian sheet zinc 387
American sheet zinc 387
=Rifle Bore= gauge 387
=Strength of Wire=, Kirkaldy's experiments 387, 388
CHAPTER XVI.
=SHAPING AND PLANING MACHINES.=
=General description= of a shaping machine 389
=Construction= of swivel head 389
Slide 390
Vice chuck 390
Feed motion 390
=Hand= shaping machine 392
=Quick Return Motion=, Whitworth's 392
=Vice Chucks=, the principles of construction of plain, for
planing machine 392
The proper methods of chucking work in 393
Holding taper work in 394
Various forms of 394
Swiveling 395
Rapid motion 396
For vice work 396
=Centres= for shaping machines 397
=Traveling Head= in shaping machine 397
=Planer Shapers= or shaping machines, having a tappet motion
for reversing the direction of motion 398, 399
=Quick Return Motion= shaping machines, link 399
The Whitworth 400
Comparisons of the link motion and Whitworth 401
=Simple Crank=, investigating the motion of 401
=Planing Machines=, or planer 402
The various motions of 402, 403
The table driving gear 404
Planing machine with double heads 404
Rotary planing machine 405
CHAPTER XVII.
=PLANING MACHINERY.=
=The Sellers= planing machine 406
The belt shifting mechanism 406, 407
The automatic feed motions 408
=Sliding Head= 408
=Cross Bar= 409
=Slides of Planers=, the various forms of construction of 410
=Wear of the Slides= of planer heads, various methods of
taking up the 410
=Swivel Heads= 411
=Tool Aprons= 411
=Swivel Tool-holding devices= for planers 411
=Planer Heads=, graduations of 412
Safety devices for 413
Feed motions for 414
V-guideways for 414
Flat guideways for 415
Oiling devices for 415
=Planing Machine Tables= 415
Slots and holes in planing machine tables 416
Forms of bolts for planer tables 417
Supplementary tables for planer tables 417
Angle plates for planer tables 418
Chucking devices for planer tables 418
=Planer Centres= 418
=Planer Chucks= 419
For spiral grooved work 419
For curved work 420
Chucking machine beds on planer tables 420
For large planing machines 422
Chucking the halves of large pulleys on a planer 423
=Gauges= for planing V-guideways in machine beds 421
Planing guideways in machine beds 422
Gauge for planer tools 424
=Planer Tools=, the shapes of 424
For coarse finishing feeds 424
The clearance of 424
For slotted work 424
=Planer Tool Holder=, with tool post 425
Various applications of 425
Simple and advantageous form of 426
Examples of application of 426
CHAPTER XVIII.
=DRILLING MACHINES.=
=Drilling Machines.= General description of a power drilling
machine 428
Lever feed 428
With automatic and quick return feed motions 428
Improved, with simple belt and uniform motion, two series of
rates of automatic feed, and guide for boring bar 429, 430
Radial 430, 431
For boiler shells 436
Cotter or keyway 438
Drilling Machine, three-spindle 434
Four-spindle 434
=Drilling and Boring= machine 431
Feed motion of 432
=Combined Drilling Machine= and lathe 433
=Boring Machine=, horizontal 433
For car wheels 438
For pulleys 438
=Quartering Machine= 434
=Drilling and Turning Machine= for boiler makers 435
Feed motions of 436
CHAPTER XIX.
=DRILLS AND CUTTERS FOR DRILLING MACHINES.=
=Jigs or Fixtures= for drilling machines 439
Limits of error in 439
Examples of, for simple work, as for links, &c. 440
Considerations in designing 440
For drilling engine cylinders 440 to 441
For cutting out steam ports 441
=Drills and Cutters= for drilling machines 442
Table of sizes of twist drills, and their shanks 442
Flat drills for drilling machines 442
Errors in grinding flat drills 443
The tit-drill 443
The lip drill 443
Cotter or keyway drills 446
=Drilling holes= true to location with flat drills 444
Drilling hard metal 444
Table of sizes of tapping holes 445
=Drill Shanks= and sockets 445
Improved form of drill shank 446
Square shanked drills and their disadvantages 446
=Drill Chucks= 446
=Stocks and Cutters= for drilling machines 447
Tube plate cutters 448
=Stocks and Cutters.= Adjustable stock and cutter 448
Facing tool with reamer pin 449
Counterbores for drilling machines 449
Drill and counterbore for wood work 449
Facing and countersink cutters 449
Device for drilling square holes 450
Device for drilling taper holes in a drilling machine 451
CHAPTER XX.
=HAND-DRILLING AND BORING TOOLS, AND DEVICES.=
=The Brad-awl= 452
=Bits.= The gimlet bit 452
The German bit 452
The nail bit 452
The spoon bit 452
The nose bit 453
The auger bit 453
Cook's auger bit 453
Principles governing the shapes of the cutting edges of auger
bits 453
Auger bit for boring end grain wood 453
The centre bit 454
The expanding bit 454
=Drills.= Drill for stone 454
The fiddle drill 455
The fiddle drill with feeding device 455
Drill with cord and spring motion 455
Drill stock with spiral grooves 455
Drill brace 455
Drill brace with ratchet motion 456
Universal joint for drill brace 456
Drill brace with multiplying gear and ratchet motion 456
Breast drill with double gear 456
Drilling levers for blacksmiths 457
Drill cranks 457
Ratchet brace 457
Flexible shaft for driving drills 458
Drilling device for lock work 459
Hand drilling machine 459
=Slotting Machine= 459
Sectional view of 460
Tool holders 460, 461
Tools 461, 462
CHAPTER XXI.
=THREAD-CUTTING MACHINERY AND BROACHING PRESS.=
=Pipe Threading=, die stock for, by hand 463
Die stock for, by power 463
Pipe threading machines, general construction of 463
=Bolt Threading= hand machine 464
With revolving head 465
Power threading machine 465
With automatic stop motion 466
Construction of the head 466
Construction of the chasers 466
Bolt threading machine with back gear 467
Single rapid bolt threading machine 467
Double rapid bolt threading machine 467
Construction of the heads of the rapid machines 468
Bolt threading machinery, the Acme 468
Construction of the head of 468 to 470
Capacity of 470
=Cutting Edges= for taps, the number of 471
Examples when three and when four cutting edges are used, and
the results upon bolts that are not round 471, 472
Demonstration that four cutting edges are correct for bar iron 472
=Positions of Dies=, or chasers in the heads of bolt cutting
machine 473
=Dies=, methods of hobbing, to avoid undue friction 473
The construction of, for bolt threading machines 473
Method of avoiding friction in thread cutting 474
Hob for threading 474
Cutting speeds for threading 474
=Nut Tapping= machine 475
Automatic socket for 475
Rotary 475
Three-spindle 475
=Pipe Threading Machine= 475 to 477
=Tapping Machine= for steam pipe fittings 478
=Broaching Press= 478
Principles of broaching 478
Examples in the construction of broaches 479
FULL-PAGE PLATES.
Volume I.
_Facing_
_Frontispiece._ MODERN LOCOMOTIVE ENGINE. TITLE PAGE
PLATE I. TEMPLATE-CUTTING MACHINES FOR GEAR TEETH. 34
" II. FORMS OF SCREW THREADS. 85
" III. MEASURING AND GAUGING SCREW THREADS. 93
" IV. END-ADJUSTMENT AND LOCKING DEVICES. 120
" V. EXAMPLES IN LATHE CONSTRUCTION. 148
" VI. CHUCKING LATHES. 150
" VII. TOOL-HOLDING AND ADJUSTING APPLIANCES. 174
" VIII. WATCHMAKER'S LATHE. 188
" IX. DETAILS OF WATCHMAKER'S LATHE. 188
" X. EXAMPLES OF SCREW MACHINES. 200
" XI. ROLL-TURNING LATHE. 215
" XII. EXAMPLES IN ANGLE-PLATE CHUCKING. 252
" XIII. METHODS OF BALL-TURNING. 325
" XIV. STANDARD MEASURING MACHINES. 341
" XV. DIVIDING ENGINE AND MICROMETER. 354
" XVI. SHAPING MACHINES AND TABLE-SWIVELING DEVICES. 398
" XVII. EXAMPLES OF PLANING MACHINES. 404
" XVIII. EXAMPLES IN PLANING WORK. 422
" XIX. LIGHT DRILLING MACHINES. 428
" XX. HEAVY DRILLING MACHINES. 430
" XXI. EXAMPLES IN BORING MACHINERY. 434
" XXII. BOILER-DRILLING MACHINERY. 436
" XXIII. NUT-TAPPING MACHINERY. 475
MODERN
MACHINE SHOP PRACTICE.
CHAPTER I.--THE TEETH OF GEAR-WHEELS.
A wheel that is provided with teeth to mesh, engage, or gear with
similar teeth upon another wheel, so that the motion of one may be
imparted to the other, is called, in general terms, a gear-wheel.
[Illustration: Fig. 1.]
When the teeth are arranged to be parallel to the wheel-axis, as in Fig.
1, the wheel is termed a spur-wheel. In the figure, A represents the
axial line or axis of the wheel or of its shaft, to which the teeth are
parallel while spaced equidistant around the rim, or face, as it is
termed, of the wheel.
[Illustration: Fig. 2.]
[Illustration: Fig. 3.]
When the wheel has its teeth arranged at an angle to the shaft, as in
Fig. 2, it is termed a bevel-wheel, or bevel gear; but when this angle
is one of 45°, as in Fig. 3, as it must be if the pair of wheels are of
the same diameter, so as to make the revolutions of their shafts equal,
then the wheel is called a mitre-wheel. When the teeth are arranged upon
the radial or side face of the wheel, as in Fig. 4, it is termed a
crown-wheel. The smallest wheel of a pair, or of a train or set of
gear-wheels, is termed the pinion; and when the teeth are composed of
rungs, as in Fig. 5, it is termed a lantern, trundle, or wallower; and
each cylindrical piece serving as a tooth is termed a _stave_,
_spindle_, or _round_, and by some a _leaf_.
[Illustration: Fig. 4.]
An annular or internal gear-wheel is one in which the faces of the teeth
are within and the flanks without, or outside the pitch-circle, as in
Fig. 6; hence the pinion P operates within the wheel.
[Illustration: Fig. 5.]
[Illustration: Fig. 6.]
When the teeth of a wheel are inserted in mortises or slots provided in
the wheel-rim, it is termed a mortised-wheel, or a cogged-wheel, and the
teeth are termed cogs.
When the teeth are arranged along a plane surface or straight line, as
in Fig. 7, the toothed plane is termed a _rack_, and the wheel is termed
a pinion.
A wheel that is driven by a revolving screw, or worm as it is termed, is
called a worm-wheel, the arrangement of a worm and worm-wheel being
shown in Fig. 8. The screw or worm is sometimes also called an endless
screw, because its action upon the wheel does not come to an end as it
does when it is revolved in one continuous direction and actuates a nut.
So also, since the worm is tangent to the wheel, the arrangement is
sometimes called a wheel and tangent screw.
The diameter of a gear-wheel is always taken at the pitch circle, unless
otherwise specially stated as "diameter over all," "diameter of
addendum," or "diameter at root of teeth," &c., &c.
[Illustration: Fig. 7.]
When the teeth of wheels engage to the proper distance, which is when
the pitch circles meet, they are said to be in gear, or geared together.
It is obvious that if two wheels are to be geared together their teeth
must be the same distance apart, or the same _pitch_, as it is called.
The designations of the various parts or surfaces of a tooth of a
gear-wheel are represented in Fig. 9, in which the surface A is the face
of the tooth, while the dimension F is the width of face of the wheel,
when its size is referred to. B is the flank or distance from the pitch
line to the root of the tooth, and C the point. H is the _space_, or
the distance from the side of one tooth to the nearest side of the next
tooth, the width of space being measured on the pitch circle P P. E is
the depth of the tooth, and G its thickness, the latter also being
measured on the pitch circle P P. When spoken of with reference to a
tooth, P P is called the pitch line, but when the whole wheel is
referred to it becomes the pitch circle.
[Illustration: Fig. 8.]
The points C and the surface H are true to the wheel axis.
The teeth are designated for measurement by the pitch; the height or
depth above and below pitch line; and the thickness.
The pitch, however, may be measured in two ways, to wit, around the
pitch circle A, in Fig. 10, which is called the arc or circular pitch,
and across B, which is termed the chord pitch.
[Illustration: Fig. 9.]
In proportion as the diameter of a wheel (having a given pitch) is
increased, or as the pitch of the teeth is made finer (on a wheel of a
given diameter) the arc and chord pitches more nearly coincide in
length. In the practical operations of marking out the teeth, however,
the arc pitch is not necessarily referred to, for if the diameter of the
pitch circle be made correct for the required number of teeth having the
necessary arc pitch, and the wheel be accurately divided off into the
requisite number of divisions with compasses set to the chord pitch, or
by means of an index plate, then the arc pitch must necessarily be
correct, although not referred to, save in determining the diameter of
the wheel at the pitch circle.
The difference between the width of a space and the thickness of the
tooth (both being measured on the pitch circle or pitch line) is termed
the clearance or side clearance, which is necessary to prevent the teeth
of one wheel from becoming locked in the spaces of the other. The amount
of clearance is, when the teeth are cut to shape in a machine, made just
sufficient to prevent contact on one side of the teeth when they are in
proper gear (the pitch circles meeting in the line of centres). But when
the teeth are cast upon the wheel the clearance is increased to allow
for the slight inequalities of tooth shape that is incidental to casting
them. The amount of clearance given is varied to suit the method
employed to mould the wheels, as will be explained hereafter.
The line of centres is an imaginary line from the centre or axis of one
wheel to the axis of the other when the two are in gear; hence each
tooth is most deeply engaged, in the space of the other wheel, when it
is on the line of centres.
There are three methods of designating the sizes of gear-wheels. First,
by their diameters at the pitch circle or pitch diameter and the number
of teeth they contain; second, by the number of teeth in the wheel and
the pitch of the teeth; and third, by a system known as diametral pitch.
[Illustration: Fig. 10.]
The first is objectionable because it involves a calculation to find the
pitch of the teeth; furthermore, if this calculation be made by dividing
the circumference of the pitch circle by the number of teeth in the
wheel, the result gives the arc pitch, which cannot be measured
correctly by a lineal measuring rule, especially if the wheel be a small
one having but few teeth, or of coarse pitch, as, in that case, the arc
pitch very sensibly differs from the chord pitch, and a second
calculation may become necessary to find the chord pitch from the arc
pitch.
The second method (the number and pitch of the teeth) possesses the
disadvantage that it is necessary to state whether the pitch is the arc
or the chord pitch.
If the arc pitch is given it is difficult to measure as before, while if
the chord pitch is given it possesses the disadvantage that the
diameters of the wheels will not be exactly proportional to the numbers
of teeth in the respective wheels. For instance, a wheel with 20 teeth
of 2 inch chord pitch is not exactly half the diameter of one of 40
teeth and 2 inch chord pitch.
To find the chord pitch of a wheel take 180 (= half the degrees in a
circle) and divide it by the number of teeth in the wheel. In a table of
natural sines find the sine for the number so found, which multiply by
2, and then by the radius of the wheel in inches.
Example.--What is the chord pitch of a wheel having 12 teeth and a
diameter (at pitch circle) of 8 inches? Here 180 ÷ 12 = 15; (sine of 15
is .25881). Then .25881 × 2 = .51762 × 4 (= radius of wheel) = 2.07048
inches = chord pitch.
TABLE OF NATURAL SINES.
+--------+--------++--------+--------++--------+--------+
|Degrees.| Sine. ||Degrees.| Sine. ||Degrees.| Sine. |
+--------+--------++--------+--------++--------+--------+
| 1 | .01745 || 16 | .27563 || 31 | .51503 |
| 2 | .03489 || 17 | .29237 || 32 | .52991 |
| 3 | .05233 || 18 | .30901 || 33 | .54463 |
| 4 | .06975 || 19 | .32556 || 34 | .55919 |
| 5 | .08715 || 20 | .34202 || 35 | .57357 |
| 6 | .10452 || 21 | .35836 || 36 | .58778 |
| 7 | .12186 || 22 | .37460 || 37 | .60181 |
| 8 | .13917 || 23 | .39073 || 38 | .61566 |
| 9 | .15643 || 24 | .40673 || 39 | .62932 |
| 10 | .17364 || 25 | .42261 || 40 | .64278 |
| 11 | .19080 || 26 | .43837 || 41 | .65605 |
| 12 | .20791 || 27 | .45399 || 42 | .66913 |
| 13 | .22495 || 28 | .46947 || 43 | .68199 |
| 14 | .24192 || 29 | .48480 || 44 | .69465 |
| 15 | .25881 || 30 | .50000 || 45 | .70710 |
+--------+--------++--------+--------++--------+--------+
The principle upon which diametral pitch is based is as follows:--
The diameter of the wheel at the pitch circle is supposed to be divided
into as many equal parts or divisions as there are teeth in the wheel,
and the length of one of these parts is the diametral pitch. The
relationship which the diametral bears to the arc pitch is the same as
the diameter to the circumference, hence a diametral pitch which
measures 1 inch will accord with an arc pitch of 3.1416; and it becomes
evident that, for all arc pitches of less than 3.1416 inches, the
corresponding diametral pitch must be expressed in fractions of an inch,
as 1/2, 1/3, 1/4, and so on, increasing the denominator until the
fraction becomes so small that an arc with which it accords is too fine
to be of practical service. The numerators of these fractions being 1,
in each case, they are in practice discarded, the denominators only
being used, so that, instead of saying diametral pitches of 1/2, 1/3, or
1/4, we say diametral pitches of 2, 3, or 4, meaning that there are 2,
3, or 4 teeth on the wheel for every inch in the diameter of the pitch
circle.
Suppose now we are given a diametral pitch of 2. To obtain the
corresponding arc pitch we divide 3.1416 (the relation of the
circumference to the diameter) by 2 (the diametral pitch), and 3.1416 ÷
2 = 1.57 = the arc pitch in inches and decimal parts of an inch. The
reason of this is plain, because, an arc pitch of 3.1416 inches being
represented by a diametral pitch of 1, a diametral pitch of 1/2 (or 2 as
it is called) will be one half of 3.1416. The advantage of discarding
the numerator is, then, that we avoid the use of fractions and are
readily enabled to find any arc pitch from a given diametral pitch.
Examples.--Given a 5 diametral pitch; what is the arc pitch? First
(using the full fraction 1/5) we have 1/5 × 3.1416 = .628 = the arc
pitch. Second (discarding the numerator), we have 3.1416 ÷ 5 = .628 =
arc pitch. If we are given an arc pitch to find a corresponding
diametral pitch we again simply divide 3.1416 by the given arc pitch.
Example.--What is the diametral pitch of a wheel whose arc pitch is
1-1/2 inches? Here 3.1416 ÷ 1.5 = 2.09 = diametral pitch. The reason of
this is also plain, for since the arc pitch is to the diametral pitch as
the circumference is to the diameter we have: as 3.1416 is to 1, so is
1.5 to the required diametral pitch; then 3.1416 × 1 ÷ 1.5 = 2.09 = the
required diametral pitch.
To find the number of teeth contained in a wheel when the diameter and
diametral pitch is given, multiply the diameter in inches by the
diametral pitch. The product is the answer. Thus, how many teeth in a
wheel 36 inches diameter and of 3 diametral pitch? Here 36 × 3 = 108 =
the number of teeth sought. Or, per contra, a wheel of 36 inches
diameter has 108 teeth. What is the diametral pitch? 108 ÷ 36 = 3 = the
diametral pitch. Thus it will be seen that, for determining the relative
sizes of wheels, this system is excellent from its simplicity. It also
possesses the advantage that, by adding two parts of the diametral pitch
to the pitch diameter, the outside diameter of the wheel or the diameter
of the addendum is obtained. For instance, a wheel containing 30 teeth
of 10 pitch would be 3 inches diameter on the pitch circle and 3-2/10
outside or total diameter.
Again, a wheel having 40 teeth of 8 diametral pitch would have a pitch
circle diameter of 5 inches, because 40 ÷ 8 = 5, and its full diameter
would be 5-1/4 inches, because the diametral pitch is 1/8, and this
multiplied by 2 gives 1/4, which added to the pitch circle diameter of 5
inches makes 5-1/4 inches, which is therefore the diameter of the
addendum, or, in other words, the full diameter of the wheel.
Suppose now that a pair of wheels require to have pitch circles of 5 and
8 inches diameter respectively, and that the arc pitch requires to be,
say, as near as may be 4/10 inch; to find a suitable pitch and the
number of teeth by the diametral pitch system we proceed as follows:
In the following table are given various arc pitches, and the
corresponding diametral pitch.
+----------------+----------+----------+----------------+
|Diametral Pitch.|Arc Pitch.|Arc Pitch.|Diametral Pitch.|
+----------------+----------+----------+----------------+
| | | Inch. | |
| 2 | 1.57 | 1.75 | 1.79 |
| 2.25 | 1.39 | 1.5 | 2.09 |
| 2.5 | 1.25 | 1.4375 | 2.18 |
| 2.75 | 1.14 | 1.375 | 2.28 |
| 3 | 1.04 | 1.3125 | 2.39 |
| 3.5 | .890 | 1.25 | 2.51 |
| 4 | .785 | 1.1875 | 2.65 |
| 5 | .628 | 1.125 | 2.79 |
| 6 | .523 | 1.0625 | 2.96 |
| 7 | .448 | 1.0000 | 3.14 |
| 8 | .392 | 0.9375 | 3.35 |
| 9 | .350 | 0.875 | 3.59 |
| 10 | .314 | 0.8125 | 3.86 |
| 11 | .280 | 0.75 | 4.19 |
| 12 | .261 | 0.6875 | 4.57 |
| 14 | .224 | 0.625 | 5.03 |
| 16 | .196 | 0.5625 | 5.58 |
| 18 | .174 | 0.5 | 6.28 |
| 20 | .157 | 0.4375 | 7.18 |
| 22 | .143 | 0.375 | 8.38 |
| 24 | .130 | 0.3125 | 10.00 |
| 26 | .120 | 0.25 | 12.56 |
+----------------+----------+----------+----------------+
From this table we find that the nearest diametral pitch that will
correspond to an arc pitch of 4/10 inch is a diametral pitch of 8, which
equals an arc pitch of .392, hence we multiply the pitch circles (5 and
8,) by 8, and obtain 40 and 64 as the number of teeth, the arc pitch
being .392 of an inch. To find the number of teeth and pitch by the arc
pitch and circumference of the pitch circle, we should require to find
the circumference of the pitch circle, and divide this by the nearest
arc pitch that would divide the circumference without leaving a
remainder, which would entail more calculating than by the diametral
pitch system.
The designation of pitch by the diametral pitch system is, however, not
applied in practice to coarse pitches, nor to gears in which the teeth
are cast upon the wheels, pattern makers generally preferring to make
the pitch to some measurement that accords with the divisions of the
ordinary measuring rule.
Of two gear-wheels that which impels the other is termed the driver, and
that which receives motion from the other is termed the driven wheel or
follower; hence in a single pair of wheels in gear together, one is the
driver and the other the driven wheel or follower. But if there are
three wheels in gear together, the middle one will be the follower when
spoken of with reference to the first or prime mover, and the driver,
when mentioned with reference to the third wheel, which will be a
follower. A series of more than two wheels in gear together is termed a
train of wheels or of gearing. When the wheels in a train are in gear
continuously, so that each wheel, save the first and last, both receives
and imparts motion, it is a simple train, the first wheel being the
driver, and the last the follower, the others being termed intermediate
wheels. Each of these intermediates is a follower with reference to the
wheel that drives it, and a driver to the one that it drives. But the
velocity of all the wheels in the train is the same in fact per second
(or in a given space of time), although the revolutions in that space
of time may vary; hence a simple train of wheels transmits motion
without influencing its velocity. To alter the velocity (which is always
taken at a point on the pitch circle) the gearing must be compounded, as
in Fig. 11, in which A, B, C, E are four wheels in gear, B and C being
compounded, that is, so held together on the shaft D that both make an
equal number of revolutions in a given time. Hence the velocity of C
will be less than that of B in proportion as the diameter,
circumference, radius, or number of teeth in C, varies from the
diameter, radius, circumference, or number of teeth (all the wheels
being supposed to have teeth of the same pitch) in B, although the
rotations of B and C are equal. It is most convenient, and therefore
usual, to take the number of teeth, but if the teeth on C (and therefore
those on E also) were of different pitch from those on B, the radius or
diameters of the wheels must be taken instead of the pitch, when the
velocities of the various wheels are to be computed. It is obvious that
the compounded pair of wheels will diminish the velocity when the driver
of the compounded pair (as C in the figure) is of less radius than the
follower B, and conversely that the velocity will be increased when the
driver is of greater radius than the follower of the compound pair.
[Illustration: Fig. 11.]
The diameter of the addendum or outer circle of a wheel has no influence
upon the velocity of the wheel. Suppose, for example, that we have a
pair of wheels of 3 inch arc or circular pitch, and containing 20 teeth,
the driver of the two making one revolution per minute. Suppose the
driven wheel to have fast upon its shaft a pulley whose diameter is one
foot, and that a weight is suspended from a line or cord wound around
this pulley, then (not taking the thickness of the line into account)
each rotation of the driven wheel would raise the weight 3.1416 feet
(that being the circumference of the pulley). Now suppose that the
addendum circle of either of the wheels were cut off down to the pitch
circle, and that they were again set in motion, then each rotation of
the driven wheel would still raise the weight 3.1416 feet as before.
It is obvious, however, that the addendum circle must be sufficiently
larger than the pitch circle to enable at least one pair of teeth to be
in continuous contact; that is to say, it is obvious that contact
between any two teeth must not cease before contact between the next two
has taken place, for otherwise the motion would not be conveyed
continuously. The diameter of the pitch circle cannot be obtained from
that of the addendum circle unless the pitch of the teeth and the
proportion of the pitch allowed for the addendum be known. But if these
be known the diameter of the pitch circle may be obtained by subtracting
from that of the addendum circle twice the amount allowed for the
addendum of the tooth.
Example.--A wheel has 19 teeth of 3 inch arc pitch; the addendum of the
tooth or teeth equals 3/10 of the pitch, and its addendum circle
measures 19.943 inches; what is the diameter of the pitch circle? Here
the addendum on each side of the wheel equals (3/10 of 3 inches) = .9
inches, hence the .9 must be multiplied by 2 for the two sides of the
wheel, thus, .9 × 2 = 1.8. Then, diameter of addendum circle 19.943
inches less 1.8 inches = 18.143 inches, which is the diameter of the
pitch circle.
Proof.--Number of teeth = 19, arc pitch 3, hence 19 × 3 = 57 inches,
which, divided by 3.1416 (the proportion of the circumference to the
diameter) = 18.143 inches.
If the distance between the centres of a pair of wheels that are in gear
be divided into two parts whose lengths are in the same proportion one
to the other as are the numbers of teeth in the wheels, then these two
parts will represent the radius of the pitch circles of the respective
wheels. Thus, suppose one wheel to contain 100 and the other 50 teeth,
and that the distance between their centres is 18 inches, then the pitch
radius or pitch diameter of one will be twice that of the other, because
one contains twice as many teeth as the other. In this case the radius
of pitch circle for the large wheel will be 12 inches, and that for the
small one 6 inches, because 12 added to 6 makes 18, which is the
distance between the wheel centres, and 12 is in the same proportion to
6 that 100 is to 50.
A simple rule whereby to find the radius of the pitch circles of a pair
of wheels is as follows:--
Rule.--Divide number of teeth in the large wheel by the number in the
small one, and to the sum so obtained add 1. Take this amount and divide
it into the distance between the centres of the wheels, and the result
will be the radius of the smallest wheel. To obtain the radius of the
largest wheel subtract the radius of the smallest wheel from the
distance between the wheel centres.
Example.--Of a pair of wheels, one has 100 and the other 50 teeth, the
distance between their centres is 18 inches; what is the pitch radius of
each wheel?
Here 100 ÷ 50 = 2, and 2 + 1 = 3. Then 18 ÷ 3 = 6, hence the pitch
radius of the small wheel is 6 inches. Then 18 - 6 = 12 = pitch radius
of large wheel.
Example 2.--Of a pair of wheels one has 40 and the other 90 teeth. The
distance between the wheel centres is 32-1/2 inches; what are the radii
of the respective pitch circles? 90 ÷ 40 = 2.25 and 2.25 + 1 = 3.25.
Then 32.5 ÷ 3.25 = 10 = pitch radius of small wheel, and 32.5 - 10 =
22.5, which is the pitch radius of the large wheel.
To prove this we may show that the pitch radii of the two wheels are in
the same proportion as their numbers of teeth, thus:--
Proof.--Radius of small wheel = 10 × 4 = 40
---- ----
radius of large wheel = 22.5 × 4 = 90.0
Suppose now that a pair of wheels are constructed, having respectively
50 and 100 teeth, and that the radii of their true pitch circles are 12
and 6 respectively, but that from wear in their journals or journal
bearings this 18 inches (12 + 6 = 18) between centres (or line of
centres, as it is termed) has become 18-3/8 inches. Then the acting
effective or operative radii of the pitch circles will bear the same
proportion to the 18-3/8 as the numbers of teeth in the respective
wheels, and will be 12.25 for the large, and 6.125 for the small wheel,
instead of 12 and 6, as would be the case were the wheels 18 inches
apart. Working this out under the rule given we have 100 ÷ 50 = 2, and 2
+ 1 = 3. Then 18.375 ÷ 3 = 6.125 = pitch radius of small wheel, and
18.375 - 6.125 = 12.25 = pitch radius of the large wheel.
The true pitch line of a tooth is the line or point where the face curve
joins the flank curve, and it is essential to the transmission of
uniform motion that the pitch circles of epicycloidal wheels exactly
coincide on the line of centres, but if they do not coincide (as by not
meeting or by overlapping each other), then a false pitch circle becomes
operative instead of the true one, and the motion of the driven wheel
will be unequal at different instants of time, although the revolutions
of the wheels will of course be in proportion to the respective numbers
of their teeth.
If the pitch circle is not marked on a single wheel and its arc pitch is
not known, it is practically a difficult matter to obtain either the arc
pitch or diameter of the pitch circle. If the wheel is a new one, and
its teeth are of the proper curves, the pitch circle will be shown by
the junction of the curves forming the faces with those forming the
flanks of the teeth, because that is the location of the pitch circle;
but in worn wheels, where from play or looseness between the journals
and their bearings, this point of junction becomes rounded, it cannot be
defined with certainty.
In wheels of large diameter the arc pitch so nearly coincides with the
chord pitch, that if the pitch circle is not marked on the wheel and the
arc pitch is not known, the chord pitch is in practice often assumed to
represent the arc pitch, and the diameter of the wheel is obtained by
multiplying the number of teeth by the chord pitch. This induces no
error in wheels of coarse pitches, because those pitches advance by 1/4
or 1/2 inch at a step, and a pitch measuring about, say, 1-1/4 inch
chord pitch, would be known to be 1-1/4 arc pitch, because the
difference between the arc and chord pitch would be too minute to cause
sensible error. Thus the next coarsest pitch to 1 inch would be 1-1/8,
or more often 1-1/4 inch, and the difference between the arc and chord
pitch of the smallest wheel would not amount to anything near 1/8 inch,
hence there would be no liability to mistake a pitch of 1-1/8 for 1 inch
or _vice versâ_. The diameter of wheel that will be large enough to
transmit continuous motion is diminished in proportion as the pitch is
decreased; in proportion, also, as the wheel diameter is reduced, the
difference between the arc and chord pitch increases, and further the
steps by which fine pitches advance are more minute (as 1/4, 9/32, 5/16,
&c.). From these facts there is much more liability to err in estimating
the arc from the measured chord pitch in fine pitches, hence the
employment of diametral pitch for small wheels of fine pitches is on
this account also very advantageous. In marking out a wheel the chord
pitch will be correct if the pitch circle be of correct diameter and be
divided off into as many points of equal division (with compasses) as
there are to be teeth in the wheel. We may then mark from these points
others giving the thickness of the teeth, which will make the spaces
also correct. But when the wheel teeth are to be cut in a machine out of
solid metal, the mechanism of the machine enables the marking out to be
dispensed with, and all that is necessary is to turn the wheel to the
required addendum diameter, and mark the pitch circle. The following are
rules for the purposes they indicate.
The circumference of a circle is obtained by multiplying its diameter by
3.1416, and the diameter may be obtained by dividing the circumference
by 3.1416.
The circumference of the pitch circle divided by the arc pitch gives the
number of teeth in the wheel.
The arc pitch multiplied by the number of teeth in the wheel gives the
circumference of the pitch circle.
Gear-wheels are simply rotating levers transmitting the power they
receive, less the amount of friction necessary to rotate them under the
given conditions. All that is accomplished by a simple train of gearing
is, as has been said, to vary the number of revolutions, the speed or
velocity measured in feet moved through per minute remaining the same
for every wheel in the train. But in a compound train of gears the speed
in feet per minute, as well as the revolutions, may be varied by means
of the compounded pairs of wheels. In either a simple or a compound
train of gearing the power remains the same in amount for every wheel in
the train, because what is in a compound train lost in velocity is
gained in force, or what is gained in velocity is lost in force, the
word force being used to convey the idea of strain, pressure, or pull.
In Fig. 12, let A, B, and C represent the pitch circles of three gears
of which A and B are in gear, while C is compounded with B; let E be the
shaft of A, and G that for B and C. Let A be 60 inches, B = 30 inches,
and C = 40 inches in diameter. Now suppose that shaft E suspends from
its perimeter a weight of 50 lbs., the shaft being 4 inches in diameter.
Then this weight will be at a leverage of 2 inches from the centre of E
and the 50 must be multiplied by 2, making 100 lbs. at the centre of E.
Then at the perimeter of A this 100 will become one-thirtieth of one
hundred, because from the centre to the perimeter of A is 30.
One-thirtieth of 100 is 3-33/100 lbs., which will be the force exerted
by A on the perimeter of B. Now from the perimeter of B to its centre
(or in other words its radius) is 15 inches, hence the 3-33/100 lbs. at
its perimeter will become fifteen times as much at the centre G of B,
and 3-33/100 × 15 = 49-95/100 lbs. From the centre G to the perimeter of
C being 20 inches, the 49-95/100 lbs. at the centre will be only
one-twentieth of that amount at the perimeter of C, hence 49-95/100 ÷ 20
= 2-49/100 lbs., which is the amount of force at the perimeter of C.
Here we have treated the wheels as simple levers, dividing the weight by
the length of the levers in all cases where it is transmitted from the
shaft to the perimeter, and multiplying it by the length of the lever
when it is transmitted from the perimeter of the wheel to the centre of
the shaft. The precise same result will be reached if we take the
diameter of the wheels or the number of the teeth, providing the pitch
of the teeth on all the wheels is alike.
Suppose, for example, that A has 60 teeth, B has 30 teeth, and C has 40
teeth, all being of the same pitch. Suppose the 50 lb. weight be
suspended as before, and that the circumference of the shaft be equal to
that of a pinion having 4 teeth of the same pitch as the wheels. Then
the 50 multiplied by the 4 becomes 200, which divided by 60 (the number
of teeth on A) becomes 3-33/100, which multiplied by 30 (the number of
teeth on B) becomes 99-90/100, which divided by 40 (the number of teeth
on C) becomes 2-49/100 lbs. as before.
[Illustration: Fig. 12.]
It may now be explained why the shaft was taken as equal to a pinion
having 4 teeth. Its diameter was taken as 4 inches and the wheel
diameter was taken as being 60 inches, and it was supposed to contain 60
teeth, hence there was 1 tooth to each inch of diameter, and the 4
inches diameter of shaft was therefore equal to a pinion having 4 teeth.
From this we may perceive the philosophy of the rule that to obtain the
revolutions of wheels we multiply the given revolutions by the teeth in
the driving wheels and divide by the teeth in the driven wheels.
Suppose that A (Fig. 13) makes 1 revolution per minute, how many will C
make, A having 60 teeth, B 30 teeth, and C 40 teeth? In this case we
have but one driving wheel A, and one driven wheel B, the driver having
60 teeth, the driven 30, hence 60 ÷ 30 = 2, equals revolutions of B and
also of C, the two latter being on the same shaft.
It will be observed then that the revolutions are in the same proportion
as the numbers of the teeth or the radii of the wheels, or what is the
same thing, in the same proportion as their diameters. The number of
teeth, however, is usually taken as being easier obtained than the
diameter of the pitch circles, and easier to calculate, because the
teeth will be represented by a whole number, whereas the diameter,
radius, or circumference, will generally contain fractions.
Suppose that the 4 wheels in Fig. 14 have the respective numbers of
teeth marked beside them, and that the upper one having 40 teeth makes
60 revolutions per minute, then we may obtain the revolutions of the
others as follows:--
Revolu- Teeth Teeth Teeth Teeth
tions. in first in first in second in second
driver. driven. driver. driven.
60 × 40 ÷ 60 × 20 ÷ 120 = 6-66/100
and a remainder of the reciprocating decimals. We may now prove this by
reversing the question, thus. Suppose the 120 wheel to make 6-66/100
revolutions per minute, how many will the 40 wheel make?
Revolu- Teeth Teeth Teeth Teeth
tions. in first in first in second in second
driver. driven. driver. driven.
6.66 × 120 ÷ 20 × 60 ÷ 40 = 59-99/100 =
revolutions of the 40 wheel, the discrepancy of 1/100 being due to the
6.66 leaving a remainder and not therefore being absolutely correct.
That the amount of power transmitted by gearing, whether compounded or
not, is equal throughout every wheel in the train, may be shown as
follows:--
[Illustration: Fig. 13.]
Referring again to Fig. 10, it has been shown that with a 50 lb. weight
suspended from a 4 inch shaft E, there would be 30-33/100 lbs. at the
perimeter of A. Now suppose a rotation be made, then the 50 lb. weight
would fall a distance equal to the circumference of the shaft, which is
(3.1416 × 4 = 12-56/100) 12-56/100 inches. Now the circumference of the
wheel is (60 dia. × 3.1416 = 188-49/100 cir.) 188-49/100 inches, which
is the distance through which the 3-33/100 lbs. would move during one
rotation of A. Now 3.33 lbs. moving through 188.49 inches represents the
same amount of power as does 50 lbs. moving through a distance of 12.56
inches, as may be found by converting the two into inch lbs. (that is to
say, into the number of inches moved by 1 lb.), bearing in mind that
there will be a slight discrepancy due to the fact that the fractions
.33 in the one case, and .56 in the other are not quite correct. Thus:
188.49 inches × 3.33 lbs. = 627.67 inch lbs., and
12.56 " × 50 " = 628 " "
Taking the next wheels in Fig. 12, it has been shown that the 3.33 lbs.
delivered from A to the perimeter of B, becomes 2.49 lbs. at the
perimeter of C, and it has also been shown that C makes two revolutions
to one of A, and its diameter being 40 inches, the distance this 2.49
lbs. will move through in one revolution of A will therefore be equal to
twice its circumference, which is (40 dia. × 3.1416 = 125.666 cir., and
125.666 × 2 = 251.332) 251.332 inches. Now 2.49 lbs. moving through
251.332 gives when brought to inch lbs. 627.67 inch lbs., thus 251.332 ×
2.49 = 627.67. Hence the amount of power remains constant, but is
altered in form, merely being converted from a heavy weight moving a
short distance, into a lighter one moving a distance exactly as much
greater as the weight or force is lessened or lighter.
[Illustration: Fig. 14.]
Gear-wheels therefore form a convenient method of either simply
transmitting motion or power, as when the wheels are all of equal
diameter, or of transmitting it and simultaneously varying its velocity
of motion, as when the wheels are compounded either to reduce or
increase the speed or velocity in feet per second of the prime mover or
first driver of the train or pair, as the case may be.
[Illustration: Fig. 15.]
In considering the action of gear-teeth, however, it sometimes is more
convenient to denote their motion by the number of degrees of angle they
move through during a certain portion of a revolution, and to refer to
their relative velocities in terms of the ratio or proportion existing
between their velocities. The first of these is termed the angular
velocity, or the number of degrees of angle the wheel moves through
during a given period, while the second is termed the velocity ratio of
the pair of wheels. Let it be supposed that two wheels of equal diameter
have contact at their perimeters so that one drives the other by
friction without any slip, then the velocity of a point on the perimeter
of one will equal that of a point on the other. Thus in Fig. 15 let A
and B represent the pitch circles of two wheels, and C an imaginary line
joining the axes of the two wheels and termed the line of centres. Now
the point of contact of the two wheels will be on the line of centres
as at D, and if a point or dot be marked at D and motion be imparted
from A to B, then when each wheel has made a quarter revolution the dot
on A will have arrived at E while that on B will have arrived at F. As
each wheel has moved through one quarter revolution, it has moved
through 90° of angle, because in the whole circle there is 360°, one
quarter of which is 90°, hence instead of saying that the wheels have
each moved through one quarter of a revolution we may say they have
moved through an angle of 90°, or, in other words, their angular
velocity has, during this period, been 90°. And as both wheels have
moved through an equal number of degrees of angle their velocity ratio
or proportion of velocity has been equal.
Obviously then the angular velocity of a wheel represents a portion of a
revolution irrespective of the diameter of the wheel, while the velocity
ratio represents the diameter of one in proportion to that of the other
irrespective of the actual diameter of either of them.
[Illustration: Fig. 16.]
Now suppose that in Fig. 16 A is a wheel of twice the diameter of B;
that the two are free to revolve about their fixed centres, but that
there is frictional contact between their perimeters at the line of
centres sufficient to cause the motion of one to be imparted to the
other without slip or lost motion, and that a point be marked on both
wheels at the point of contact D. Now let motion be communicated to A
until the mark that was made at D has moved one-eighth of a revolution
and it will have moved through an eighth of a circle, or 45°. But during
this motion the mark on B will have moved a quarter of a revolution, or
through an angle of 90° (which is one quarter of the 360° that there are
in the whole circle). The angular velocities of the two are, therefore,
in the same ratio as their diameters, or two to one, and the velocity
ratio is also two to one. The angular velocity of each is therefore the
number of degrees of angle that it moves through in a certain portion of
a revolution, or during the period that the other wheel of the pair
makes a certain portion of a revolution, while the velocity ratio is the
proportion existing between the velocity of one wheel and that of the
other; hence if the diameter of one only of the wheels be changed, its
angular velocity will be changed and the velocity ratio of the pair will
be changed. The velocity ratio may be obtained by dividing either the
radius, pitch, diameter, or number of teeth of one wheel into that of
the other.
Conversely, if a given velocity ratio is to be obtained, the radius,
diameter, or number of teeth of the driver must bear the same relation
to the radius, diameter, or number of teeth of the follower, as the
velocity of the follower is desired to bear to that of the driver.
If a pair of wheels have an equal number of teeth, the same pairs of
teeth will come into action at every revolution; but if of two wheels
one is twice as large as the other, each tooth on the small wheel will
come into action twice during each revolution of the large one, and will
work during each successive revolution with the same two teeth on the
large wheel; and an application of the principle of the hunting tooth is
sometimes employed in clocks to prevent the overwinding of their
springs, the device being shown in Fig. 17, which is from "Willis'
Principles of Mechanism."
For this purpose the winding arbor C has a pinion A of 19 teeth fixed to
it close to the front plate. A pinion B of 18 teeth is mounted on a stud
so as to be in gear with the former. A radial plate C D is fixed to the
face of the upper wheel A, and a similar plate F E to the lower wheel B.
These plates terminate outward in semicircular noses D, E, so
proportioned as to cause their extremities to abut against each other,
as shown in the figure, when the motion given to the upper arbor by the
winding has brought them into the position of contact. The clock being
now wound up, the winding arbor and wheel A will begin to turn in the
opposite direction. When its first complete rotation is effected the
wheel B will have gained one tooth distance from the line of centres, so
as to place the stop D in advance of E and thus avoid a contact with E,
which would stop the motion. As each turn of the upper wheel increases
the distance of the stops, it follows from the principle of the hunting
cog, that after eighteen revolutions of A and nineteen of B the stops
will come together again and the clock be prevented from running down
too far. The winding key being applied, the upper wheel A will be
rotated in the opposite direction, and the winding repeated as above.
[Illustration: Fig. 17.]
Thus the teeth on one wheel will wear to imbed one upon the other. On
the other hand the teeth of the two wheels may be of such numbers that
those on one wheel will not fall into gear with the same teeth on the
other except at intervals, and thus an inequality on any one tooth is
subjected to correction by all the teeth in the other wheel. When a
tooth is added to the number of teeth on a wheel to effect this purpose
it is termed a hunting cog, or hunting tooth, because if one wheel have
a tooth less, then any two teeth which meet in the first revolution are
distant, one tooth in the second, two teeth in the third, three in the
fourth, and so on. The odd tooth is on this account termed a hunting
tooth.
It is obvious then that the shape or form to be given to the teeth must,
to obtain correct results, be such that the motion of the driver will be
communicated to the follower with the velocity due to the relative
diameters of the wheels at the pitch circles, and since the teeth move
in the arc of a circle it is also obvious that the sides of the teeth,
which are the only parts that come into contact, must be of same curve.
The nature of this curve must be such that the teeth shall possess the
strength necessary to transmit the required amount of power, shall
possess ample wearing surface, shall be as easily produced as possible
for all the varying conditions, shall give as many teeth in constant
contact as possible, and shall, as far as possible, exert a pressure in
a direction to rotate the wheels without inducing undue wear upon the
journals of the shafts upon which the wheels rotate. In cases, however,
in which some of these requirements must be partly sacrificed to
increase the value of the others, or of some of the others, to suit the
special circumstances under which the wheels are to operate, the
selection is left to the judgment of the designer, and the
considerations which should influence his determinations will appear
hereafter.
[Illustration: Fig. 18.]
Modern practice has accepted the curve known in general terms as the
cycloid, as that best filling all the requirements of wheel teeth, and
this curve is employed to produce two distinct forms of teeth,
epicycloidal and involute. In epicycloidal teeth the curve forming the
face of the tooth is designated an epicycloid, and that forming the
flank an hypocycloid. An epicycloid may be traced or generated, as it is
termed, by a point in the circumference of a circle that rolls without
slip upon the circumference of another circle. Thus, in Fig. 18, A and B
represent two wooden wheels, A having a pencil at P, to serve as a
tracing or marking point. Now, if the wheels are laid upon a sheet of
paper and while holding B in a fixed position, roll A in contact with B
and let the tracing point touch the paper, the point P will trace the
curve C C. Suppose now the diameter of the base circle B to be
infinitely large, a portion of its circumference may be represented by a
straight line, and the curve traced by a point on the circumference of
the generating circle as it rolls along the base line B is termed a
cycloid. Thus, in Fig. 19, B is the base line, A the rolling wheel or
generating circle, and C C the cycloidal curve traced or marked by the
point D when A is rolled along B. If now we suppose the base line B to
represent the pitch line of a rack, it will be obvious that part of the
cycloid at one end is suitable for the face on one side of the tooth,
and a part at the other end is suitable for the face of the other side
of the tooth.
[Illustration: Fig. 19.]
A hypocycloid is a curve traced or generated by a point on the
circumference of a circle rolling within and in contact (without slip)
with another circle. Thus, in Fig. 20, A represents a wheel in contact
with the internal circumference of B, and a point on its circumference
will trace the two curves, C C, both curves starting from the same
point, the upper having been traced by rolling the generating circle or
wheel A in one direction and the lower curve by rolling it in the
opposite direction.
[Illustration: Fig. 20.]
To demonstrate that by the epicycloidal and hypocycloidal curves,
forming the faces and flanks of what are known as epicycloidal teeth,
motion may be communicated from one wheel to another with as much
uniformity as by frictional contact of their circumferential surfaces,
let A, B, in Fig. 21, represent two plain wheel disks at liberty to
revolve about their fixed centres, and let C C represent a margin of
stiff white paper attached to the face of B so as to revolve with it.
Now suppose that A and B are in close contact at their perimeters at the
point G, and that there is no slip, and that rotary motion commenced
when the point E (where as tracing point a pencil is attached), in
conjunction with the point F, formed the point of contact of the two
wheels, and continued until the points E and F had arrived at their
respective positions as shown in the figure; the pencil at E will have
traced upon the margin of white paper the portion of an epicycloid
denoted by the curve E F; and as the movement of the two wheels A, B,
took place by reason of the contact of their circumferences, it is
evident that the length of the arc E G must be equal to that of the arc
G F, and that the motion of A (supposing it to be the driver) would be
communicated uniformly to B.
[Illustration: Fig. 21.]
Now suppose that the wheels had been rotated in the opposite direction
and the same form of curve would be produced, but it would run in the
opposite direction, and these two curves may be utilized to form teeth,
as in Fig. 22, the points on the wheel A working against the curved
sides of the teeth on B.
To render such a pair of wheels useful in practice, all that is
necessary is to diminish the teeth on B without altering the nature of
the curves, and increase the diameter of the points on A, making them
into rungs or pins, thus forming the wheels into what is termed a wheel
and lantern, which are illustrated in Fig. 23.
[Illustration: Fig. 22.]
A represents the pinion (or lantern), and B the wheel, and C, C, the
primitive teeth reduced in thickness to receive the pins on A. This
reduction we may make by setting a pair of compasses to the radius of
the rung and describing half-circles at the bottom of the spaces in B.
We may then set a pair of compasses to the curve of C, and mark off the
faces of the teeth of B to meet the half-circles at the pitch line, and
reduce the teeth heights so as to leave the points of the proper
thickness; having in this operation maintained the same epicycloidal
curves, but brought them closer together and made them shorter. It is
obvious, however, that such a method of communicating rotary motion is
unsuited to the transmission of much power; because of the weakness of,
and small amount of wearing surface on, the points or rungs in A.
[Illustration: Fig. 23.]
[Illustration: Fig. 24.]
In place of points or rungs we may have radial lines, these lines,
representing the surfaces of ribs, set equidistant on the radial face of
the pinion, as in Fig. 24. To determine the epicycloidal curves for the
faces of teeth to work with these radial lines, we may take a generating
circle C, of half the diameter of A, and cause it to roll in contact
with the internal circumference of A, and a tracing point fixed in the
circumference of C will draw the radial lines shown upon A. The
circumstances will not be altered if we suppose the three circles, A, B,
C, to be movable about their fixed centres, and let their centres be in
a straight line; and if, under these circumstances, we suppose rotation
to be imparted to the three circles, through frictional contact of their
perimeters, a tracing point on the circumference of C would trace the
epicycloids shown upon B and the radial lines shown upon A, evidencing
the capability of one to impart uniform rotary motion to the other.
[Illustration: Fig. 25.]
To render the radial lines capable of use we must let them be the
surfaces of lugs or projections on the face of the wheel, as shown in
Fig. 25 at D, E, &c., or the faces of notches cut in the wheel as at F,
G, H, &c., the metal between F and G forming a tooth J, having flanks
only. The wheel B has the curves of each tooth brought closer together
to give room for the reception of the teeth upon A. We have here a pair
of gears that possess sufficient strength and are capable of working
correctly in either direction.
[Illustration: Fig. 26.]
But the form of tooth on one wheel is conformed simply to suit those on
the other, hence, neither two of the wheels A, nor would two of B, work
correctly together.
They may be qualified to do so, however, by simply adding to the tops
of the teeth on A, teeth of the form of those on B, and adding to those
on B, and within the pitch circle, teeth corresponding to those on A, as
in Fig. 26, where at K´ and J´ teeth are provided on B corresponding to
J and K on A, while on A there are added teeth O´, N´, corresponding to
O, N, on B, with the result that two wheels such as A or two such as B
would work correctly together, either being the driver or either the
follower, and rotation may occur in either direction. In this operation
we have simply added faces to the teeth on A, and flanks to those on B,
the curves being generated or obtained by rolling the generating, or
curve marking, circle C upon the pitch circles P and P´. Thus, for the
flanks of the teeth of A, C is rolled upon, and within the pitch circle
P of A; while for the face curves of the same teeth C is rolled upon,
but without or outside of P. Similarly for the teeth of wheel B the
generating circle C is rolled within P´ for the flanks and without for
the faces. With the curves rolled or produced with the same diameter of
generating circle the wheels will work correctly together, no matter
what their relative diameter may be, as will be shown hereafter.
[Illustration: Fig. 27.]
In this demonstration, however, the curves for the faces of the teeth
being produced by an operation distinct from that employed to produce
the flank curves, it is not clearly seen that the curves for the flanks
of one wheel are the proper curves to insure a uniform velocity to the
other. This, however, may be made clear as follows:--
In Fig. 27 let _a_ _a_ and _b_ _b_ represent the pitch circles of two
wheels of equal diameters, and therefore having the same number of
teeth. On the left, the wheels are shown with the teeth in, while on the
right-hand side of the line of centres A B, the wheels are shown blank;
_a_ _a_ is the pitch line of one wheel, and _b_ _b_ that for the other.
Now suppose that both wheels are capable of being rotated on their
shafts, whose centres will of course be on the line A B, and suppose a
third disk, Q, be also capable of rotation upon its centre, C, which is
also on the line A B. Let these three wheels have sufficient contact at
their perimeters at the point _n_, that if one be rotated it will rotate
both the others (by friction) without any slip or lost motion, and of
course all three will rotate at an equal velocity. Suppose that there is
fixed to wheel Q a pencil whose point is at _n_. If then rotation be
given to _a_ _a_ in the direction of the arrow _s_, all three wheels
will rotate in that direction as denoted by their respective arrows _s_.
Assume, then, that rotation of the three has occurred until the pencil
point at _n_ has arrived at the point _m_, and during this period of
rotation the point _n_ will recede from the line of centres A B, and
will also recede from the arcs or lines of the two pitch circles _a_
_a_, _b_ _b_. The pencil point being capable of marking its path, it
will be found on reaching _m_ to have marked inside the pitch circle _b_
_b_ the curve denoted by the full line _m_ _x_, and simultaneously with
this curve it has marked another curve outside of _a_ _a_, as denoted by
the dotted line _y_ _m_. These two curves being marked by the pencil
point at the same time and extending from _y_ to _m_, and _x_ also to
_m_. They are prolonged respectively to _p_ and to K for clearness of
illustration only.
The rotation of the three wheels being continued, when the pencil point
has arrived at O it will have continued the same curves as shown at O
_f_, and O _g_, curve O _f_ being the same as _m_ _x_ placed in a new
position, and O _g_ being the same as _m_ _y_, but placed in a new
position. Now since both these curves (O _f_ and O _g_) were marked by
the one pencil point, and at the same time, it follows that at every
point in its course that point must have touched both curves at once.
Now the pencil point having moved around the arc of the circle Q from
_n_ to _m_, it is obvious that the two curves must always be in contact,
or coincide with each other, at some point in the path of the pencil or
describing point, or, in other words, the curves will always touch each
other at some point on the curve of Q, and between _n_ and O. Thus when
the pencil has arrived at _m_, curve _m_ _y_ touches curve K _x_ at the
point _m_, while when the pencil had arrived at point O, the curves O
_f_ and O _g_ will touch at O. Now the pitch circles _a_ _a_ and _b_
_b_, and the describing circle Q, having had constant and uniform
velocity while the traced curves had constant contact at some point in
their lengths, it is evident that if instead of being mere lines, _m_
_y_ was the face of a tooth on _a_ _a_, and _m_ _x_ was the flank of a
tooth on _b_ _b_, the same uniform motion may be transmitted from _a_
_a_, to _b_ _b_, by pressing the tooth face _m_ _y_ against the tooth
flank _m_ _x_. Let it now be noted that the curve _y_ _m_ corresponds to
the face of a tooth, as say the face E of a tooth on _a_ _a_, and that
curve _x_ _m_ corresponds to the flank of a tooth on _b_ _b_, as say to
the flank F, short portions only of the curves being used for those
flanks. If the direction of rotation of the three wheels was reversed,
the same shape of curves would be produced, but they would lie in an
opposite direction, and would, therefore, be suitable for the other
sides of the teeth. In this case, the contact of tooth upon tooth will
be on the other side of the line of centres, as at some point between
_n_ and Q.
[Illustration: Fig. 28.]
In this illustration the diameter of the rolling or describing circle Q,
being less than the radius of the wheels _a_ _a_ or _b_ _b_, the flanks
of the teeth are curves, and the two wheels being of the same diameter,
the teeth on the two are of the same shape. But the principles governing
the proper formation of the curve remain the same whatever be the
conditions. Thus in Fig. 28 are segments of a pair of wheels of equal
diameter, but the describing, rolling, or curve-generating circle is
equal in diameter to the radius of the wheels. Motion is supposed to
have occurred in the direction of the arrows, and the tracing point to
have moved from _n_ to _m_. During this motion it will have marked a
curve _y_ _m_, a portion of the _y_ end serving for the face of a tooth
on one wheel, and also the line _k_ _x_, a continuation of which serves
for the flank of a tooth on the other wheel. In Fig. 29 the pitch
circles only of the wheels are marked, _a_ _a_ being twice the diameter
of _b_ _b_, and the curve-generating circle being equal in diameter to
the radius of wheel _b_ _b_. Motion is assumed to have occurred until
the pencil point, starting from _n_, had arrived at _o_, marking curves
suitable for the face of the teeth on one wheel and for the flanks of
the other as before, and the contact of tooth upon tooth still, at every
point in the path of the teeth, occurring at some point of the arc _n_
_o_. Thus when the point had proceeded as far as point _m_ it will have
marked the curve _y_ and the radial line _x_, and when the point had
arrived at _o_, it will have prolonged _m_ _y_ into _o_ _g_ and _x_ into
_o_ _f_, while in either position the point is marking both lines. The
velocities of the wheels remain the same notwithstanding their different
diameters, for the arc _n_ _g_ must obviously (if the wheels rotate
without slip by friction of their surfaces while the curves are traced)
be equal in length to the arc _n_ _f_ or the arc _n_ _o_.
[Illustration: Fig. 29.]
[Illustration: Fig. 30.]
In Fig. 30 _a_ _a_ and _b_ _b_ are the pitch circles of two wheels as
before, and _c_ _c_ the pitch circle of an annular or internal gear, and
D is the rolling or describing circle. When the describing point arrived
at _m_, it will have marked the curve _y_ for the face of a tooth on _a_
_a_, the curve _x_ for the flank of a tooth on _b_ _b_, and the curve
_e_ for the face of a tooth on the internal wheel _c_ _c_. Motion being
continued _m_ _y_ will be prolonged to _o_ _g_, while simultaneously _x_
will be extended into _o_ _f_ and _e_ into _h_ _v_, the velocity of all
the wheels being uniform and equal. Thus the arcs _n_ _v_, _n_ _f_, and
_n_ _g_, are of equal length.
[Illustration: Fig. 31.]
In Fig. 31 is shown the case of a rack and pinion; _a_ _a_ is the pitch
line of the rack, _b_ _b_ that of the pinion, A B at a right angle to
_a_ _a_, the line of centres, and D the generating circle. The wheel and
rack are shown with teeth _n_ on one side simply for clearness of
illustration. The pencil point _n_ will, on arriving at _m_, have traced
the flank curve _x_ and the curve _y_ for the face of the rack teeth.
[Illustration: Fig. 32.]
It has been supposed that the three circles rotated together by the
frictional contact of their perimeters on the line of centres, but the
circumstances will remain the same if the wheels remain at rest while
the generating or describing circle is rolled around them. Thus in Fig.
32 are two segments of wheels as before, _c_ representing the centre of
a tooth on _a_ _a_, and _d_ representing the centre of a tooth on _b_
_b_. Now suppose that a generating or rolling circle be placed with its
pencil point at _e_, and that it then be rolled around _a_ _a_ until it
had reached the position marked 1, then it will have marked the curve
from _e_ to _n_, a part of this curve serving for the face of tooth _c_.
Now let the rolling circle be placed within the pitch circle _a_ _a_ and
its pencil point _n_ be set to _e_, then, on being rolled to position 2,
it will have marked the flank of tooth _c_. For the other wheel suppose
the rolling wheel or circle to have started from _f_ and rolled to the
line of centres as in the cut, it will have traced the curve forming the
face of the tooth _d_. For the flank of _d_ the rolling circle or wheel
is placed within _b_ _b_, its tracing point set at _f_ on the pitch
circle, and on being rolled to position 3 it will have marked the flank
curve. The curves thus produced will be precisely the same as those
produced by rotating all three wheels about their axes, as in our
previous demonstrations.
The curves both for the faces and for the flanks thus obtained will vary
in their curvature with every variation in either the diameter of the
generating circle or of the base or pitch circle of the wheel. Thus it
will be observable to the eye that the face curve of tooth _c_ is more
curved than that of _d_, and also that the flank curve of _d_ is more
spread at the root than is that for _c_, which has in this case resulted
from the difference between the diameter of the wheels _a_ _a_ and _b_
_b_. But the curves obtained by a given diameter of rolling circle on a
given diameter of pitch circle will be correct for any pitch of teeth
that can be used upon wheels having that diameter of pitch circle. Thus,
suppose we have a curve obtained by rolling a wheel of 20 inches
circumference on a pitch circle of 40 inches circumference--now a wheel
of 40 inches in circumference may contain 20 teeth of 2 inch arc pitch,
or 10 teeth of 4 inch arc pitch, or 8 teeth of 5 inch arc pitch, and the
curve may be used for either of those pitches.
If we trace the path of contact of each tooth, from the moment it takes
until it leaves contact with a tooth upon the other wheel, we shall find
that contact begins at the point where the flank of the tooth on the
wheel that drives or imparts motion to the other wheel, meets the face
of the tooth on the driven wheel, which will always be where the point
of the driven tooth cuts or meets the generating or rolling circle of
the driving tooth. Thus in Fig. 33 are represented segments of two
spur-wheels marked respectively the driver and the driven, their
generating circles being marked at G and G´, and X X representing the
line of centres. Tooth A is shown in the position in which it commences
its contact with tooth B at B. Secondly, we shall find that as these
two teeth approach the line of centres X, the point of contact between
them moves or takes place along the thickened arc or curve C X, or along
the path of the generating circle G.
Thus we may suppose tooth D to be another position of tooth A, the
contact being at F, and as motion was continued the contact would pass
along the thickened curve until it arrived at the line of centres X. Now
since the teeth have during this path of contact approached the line of
centres, this part of the whole arc of action or of the path of contact
is termed the arc of approach. After the two teeth have passed the line
of centres X, the path of contact of the teeth will be along the dotted
arc from X to L, and as the teeth are during this period of motion
receding from X this part of the contact path is termed the arc of
recess.
That contact of the teeth would not occur earlier than at C nor later
than at L, is shown by the dotted teeth sides; thus A and B would not
touch when in the position denoted by the dotted teeth, nor would teeth
I and K if in the position denoted by their dotted lines.
[Illustration: Fig. 33.]
If we examine further into this path of contact we find that throughout
its whole path the face of the tooth of one wheel has contact with the
flank only of the tooth of the other wheel, and also that the flank only
of the driving-wheel tooth has contact before the tooth reaches the line
of centres, while the face of only the driving tooth has contact after
the tooth has passed the line of centres.
Thus the flanks of tooth A and of tooth D are in driving contact with
the faces of teeth B and E, while the face of tooth H is in contact with
the flank of tooth I.
These conditions will always exist, whatever be the diameters of the
wheels, their number of teeth or the diameter of the generating circle.
That is to say, in fully developed epicycloidal teeth, no matter which
of two wheels is the driver or which the driven wheel, contact on the
teeth of the driver will always be on the tooth flank during the arc of
approach and on the tooth face during the arc of recess; while on the
driven wheel contact during the arc of approach will be on the tooth
face only, and during the arc of recess on the tooth flank only, it
being borne in mind that the arcs of approach and recess are reversed in
location if the direction of revolution be reversed. Thus if the
direction of wheel motion was opposite to that denoted by the arrows in
Fig. 33 then the arc of approach would be from M to X, and the arc of
recess from X to N.
It is laid down by Professor Willis that the motion of a pair of
gear-wheels is smoother in cases where the path of contact begins at the
line of centres, or, in other words, when there is no arc of approach;
and this action may be secured by giving to the driven wheel flanks
only, as in Fig. 34, in which the driver has fully developed teeth,
while the teeth on the driven have no faces.
In this case, supposing the wheels to revolve in the direction of arrow
P, the contact will begin at the line of centres X, move or pass along
the thickened arc and end at B, and there will be contact during the arc
of recess only. Similarly, if the direction of motion be reversed as
denoted by arrow Q, the driver will begin contact at X, and cease
contact at H, having, as before, contact during the arc of recess only.
But if the wheel W were the driver and V the driven, then these
conditions would be exactly reversed. Thus, suppose this to be the case
and the direction of motion be as denoted by arrow P, the contact would
occur during the arc of approach, from H to X, ceasing at X.
Or if W were the driver, and the direction of motion was as denoted by
Q, then, again, the path of contact would be during the arc of approach
only, beginning at B and ceasing at X, as denoted by the thickened arc B
X.
The action of the teeth will in either case serve to give a
theoretically perfect motion so far as uniformity of velocity is
concerned, or, in other words, the motion of the driver will be
transmitted with perfect uniformity to the driven wheel. It will be
observed, however, that by the removal of the faces of the teeth, there
are a less number of teeth in contact at each instant of time; thus, in
Fig. 33 there is driving contact at three points, C, F, and J, while in
Fig. 34 there is driving contact at two points only. From the fact that
the faces of the teeth work with the flanks only, and that one side only
of the teeth comes into action, it becomes apparent that each tooth may
have curves formed by four different diameters of rolling or generating
circles and yet work correctly, no matter which wheel be the driver, or
which the driven wheel or follower, or in which direction motion occurs.
Thus in Fig. 35, suppose wheel V to be the driver, having motion in the
direction of arrow P, then faces a on the teeth of V will work with
flanks B of the teeth on W, and so long as the curves for these faces
and flanks are obtained with the same diameter of rolling circle, the
action of the teeth will be correct, no matter what the shapes of the
other parts of the teeth. Now suppose that V still being the driver,
motion occurs in the other direction as denoted by Q, then the faces C
of the teeth on V will drive the flanks C of the teeth on W, and the
motion will again be correct, providing that the same diameter (whatever
it may be) of rolling circle be used for these faces and flanks,
irrespective, of course, of what diameter of rolling circle is used for
any other of the teeth curves. Now suppose that W is the driver, motion
occurring in the direction of P, then faces E will drive flanks F, and
the motion will be correct as before if the curves E and F are produced
with the same diameter of rolling circle. Finally, let W be the driving
wheel and motion occur in the direction of Q, and faces G will drive
flanks H, and yet another diameter of rolling circle may be used for
these faces and flanks. Here then it is shown that four different
diameters of rolling circles may be used upon a pair of wheels, giving
teeth-forms that will fill all the requirements so far as correctly
transmitting motion is concerned. In the case of a pair of wheels having
an equal number of teeth, so that each tooth on one wheel will always
fall into gear with the same tooth on the other wheel, every tooth may
have its individual curves differing from all the others, providing that
the corresponding teeth on the other wheel are formed to match them by
using the same size of rolling circle for each flank and face that work
together.
[Illustration: Fig. 34.]
[Illustration: Fig. 35.]
It is obvious, however, that such teeth would involve a great deal of
labor in their formation and would possess no advantage, hence they are
not employed. It is not unusual, however, in a pair of wheels that are
to gear together and that are not intended to interchange with other
wheels, to use such sizes as will give to for the face of the teeth on
the largest wheel of the pair and for the flanks of the teeth of the
smallest wheel, a generating circle equal in diameter to the radius of
the smallest wheel, and for the faces of the teeth of the small wheel
and the flanks of the teeth of the large one, a generating circle whose
diameter equals the radius of the large wheel.
[Illustration: Fig. 36.]
It will now be evident that if we have planned a pair or a train of
wheels we may find how many teeth will be in contact for any given
pitch, as follows. In Fig. 36 let A, B, and C, represent three blanks
for gear-wheels whose addendum circles are M, N and O; P representing
the pitch circles, and Q representing the circles for the roots of the
teeth. Let X and Y represent the lines of centres, and A, H, I and K the
generating or rolling circle, whose centres are on the respective lines
of centres--the diameter of the generating circle being equal to the
radius of the pinion, as in the Willis system, then, the pinion M being
the driver, and the wheels revolving in the direction denoted by the
respective arrows, the arc or path of contact for the first pair will be
from point D, where the generating circle G crosses circle N to E, where
generating circle H crosses the circle M, this path being composed of
two arcs of a circle. All that is necessary, therefore, is to set the
compasses to the pitch the teeth are to have and step them along these
arcs, and the number of steps will be the number of teeth that will be
in contact. Similarly, for the second pair contact will begin at R and
end at S, and the compasses applied as before (from R to S) along the
arc of generating circle I to the line of centres, and thence along the
arc of generating circle K to S, will give in the number of steps, the
number of teeth that will be in contact. If for any given purpose the
number of teeth thus found to be in contact is insufficient; the pitch
may be made finer.
[Illustration: Fig. 37.]
When a wheel is intended to be formed to work correctly with any other
wheel having the same pitch, or when there are more than two wheels in
the train, it is necessary that the same size of generating circle be
used for all the faces and all the flanks in the set, and if this be
done the wheels will work correctly together, no matter what the number
of the teeth in each wheel may be, nor in what way they are
interchanged. Thus in Fig. 37, let A represent the pitch line of a rack,
and B and C the pitch circles of two wheels, then the generating circle
would be rolled within B, as at 1, for the flank curves, and without it,
as at 2, for the face curves of B. It would be rolled without the pitch
line, as at 3, for the rack faces, and within it, as at 4, for the rack
flanks, and without C, as at 5, for the faces, and within it, as at 6,
for flanks of the teeth on C, and all the teeth will work correctly
together however they be placed; thus C might receive motion from the
rack, and B receive motion from C. Or if any number of different
diameters of wheels are used they will all work correctly together and
interchange perfectly, with the single condition that the same size of
generating circle be used throughout. But the curves of the teeth so
formed will not be alike. Thus in Fig. 38 are shown three teeth, all
struck with the same size of generating circle, D being for a wheel of
12 teeth, E for a wheel of 50 teeth, and F a tooth of a rack; teeth E,
F, being made wider so as to let the curves show clearly on each side,
it being obvious that since the curves are due to the relative sizes of
the pitch and generating circles they are equally applicable to any
pitch or thickness of teeth on wheels having the same diameters of pitch
circle.
[Illustration: Fig. 38.]
In determining the diameter of a generating circle for a set or train
of wheels, we have the consideration that the smaller the diameter of
the generating circle in proportion to that of the pitch circle the more
the teeth are spread at the roots, and this creates a pressure tending
to thrust the wheels apart, thus causing the axle journals to wear. In
Fig. 39, for example, A A is the line of centres, and the contact of the
curves at B C would cause a thrust in the direction of the arrows D, E.
This thrust would exist throughout the whole path of contact save at the
point F, on the line of centres. This thrust is reduced in proportion as
the diameter of the generating circle is increased; thus in Fig. 40, is
represented a pair of pinions of 12 teeth and 3 inch pitch, and C being
the driver, there is contact at E, and at G, and E being a radial line,
there is obviously a minimum of thrust.
[Illustration: Fig. 39.]
[Illustration: Fig. 40.]
What is known as the Willis system for interchangeable gearing, consists
of using for every pitch of the teeth a generating circle whose diameter
is equal to the radius of a pinion having 12 teeth, hence the pinion
will in each pitch have radial flanks, and the roots of the teeth will
be more spread as the number of teeth in the wheel is increased. Twelve
teeth is the least number that it is considered practicable to use;
hence it is obvious that under this system all wheels of the same pitch
will work correctly together.
[Illustration: Fig. 41.]
Unless the faces of the teeth and the flanks with which they work are
curves produced from the same size of generating circle, the velocity of
the teeth will not be uniform. Obviously the revolutions of the wheels
will be proportionate to their numbers of teeth; hence in a pair of
wheels having an equal number of teeth, the revolutions will per force
be equal, but the driver will not impart uniform motion to the driven
wheel, but each tooth will during the path of contact move irregularly.
The velocity of a pair of wheels will be uniform at each instant of
time, if a line normal to the surfaces of the curves at their point of
contact passes through the point of contact of the pitch circles on the
line of centres of the wheels. Thus in Fig. 41, the line A A is tangent
to the teeth curves where they touch, and D at a right angle to A A, and
meets it at the point of the tooth curves, hence it is normal to the
point of contact, and as it meets the pitch circles on the line of
centres the velocity of the wheels will be uniform.
The amount of rolling motion of the teeth one upon the other while
passing through the path of contact, will be a minimum when the tooth
curves are correctly formed according to the rules given. But
furthermore the sliding motion will be increased in proportion as the
diameter of the generating circle is increased, and the number of teeth
in contact will be increased because the arc, or path, of contact is
longer as the generating circle is made larger.
[Illustration: Fig. 42.]
Thus in Fig. 42 is a pair of wheels whose tooth curves are from a
generating circle equal to the radius of the wheels, hence the flanks
are radial. The teeth are made of unusual depth to keep the lines in the
engraving clear. Suppose V to be the driver, W the driven wheel or
follower, and the direction of motion as at P, contact upon tooth A will
begin at C, and while A is passing to the line of centres the path of
contact will pass along the thickened line to X. During this time the
whole length of face from C to R will have had contact with the length
of flank from C to N, and it follows that the length of face on A that
rolled on C N can only equal the length of C N, and that the amount of
sliding motion must be represented by the length of R N on A, and the
amount of rolling motion by the length N C. Again, during the arc of
recess (marked by dots) the length of flank that will have had contact
is the depth from S to Ls, and over this depth the full length of tooth
face on wheel V will have swept, and as L S equals C N, the amount of
rolling and of sliding motion during the arc of recess is equal to that
during the arc of approach, and the action is in both cases partly a
rolling and partly a sliding one. The two wheels are here shown of the
same diameter, and therefore contain an equal number of teeth, hence the
arcs of approach and of recess are equal in length, which will not be
the case when one wheel contains more teeth than the other. Thus in Fig.
43, let A represent a segment of a pinion, and B a segment of a
spur-wheel, both segments being blank with their pitch circles, the
tooth height and depth being marked by arcs of circles. Let C and D
represent the generating circles shown in the two respective positions
on the line of centres. Let pinion A be the driver moving in the
direction of P, and the arc of approach will be from E to X along the
thickened arc, while the arc of recess will be as denoted by the dotted
arc from X to F. The distance E X being greater than distance X F,
therefore the arc of approach is longer than that of recess.
But suppose B to be the driver and the reverse will be the case, the arc
of approach will begin at G and end at X, while the arc of recess will
begin at X and end at H, the latter being farther from the line of
centres than G is. It will be found also that, one wheel being larger
than the other, the amount of sliding and rolling contact is different
for the two wheels, and that the flanks of the teeth on the larger wheel
B, have contact along a greater portion of their depths than do the
flanks of those on the smaller, as is shown by the dotted arc I being
farther from the pitch circle than the dotted arc J is, these two dotted
arcs representing the paths of the lowest points of flank contact,
points F and G, marking the initial lowest contact for the two
directions of revolution.
[Illustration: Fig. 43.]
Thus it appears that there is more sliding action upon the teeth of the
smaller than upon those of the larger wheel, and this is a condition
that will always exist.
In Fig. 44 is represented portion of a pair of wheels corresponding to
those shown in Fig. 42, except that in this case the diameter of the
generating circle is reduced to one quarter that of the pitch diameter
of the wheels. V is the driver in the direction the teeth of V that
will have contact is C N, which, the wheels, being of equal diameter,
will remain the same whichever wheel be the driver, and in whatever
direction motion occurs. The amount of rolling motion is, therefore, C
N, and that of sliding is the difference between the distance C N and
the length of the tooth face.
[Illustration: Fig. 44.]
If now we examine the distance C N in Fig. 42, we find that reducing the
diameter of generating circle in Fig. 44 has increased the depth of
flank that has contact, and therefore increased the rolling motion of
the tooth face along the flank, and correspondingly diminished the
sliding action of the tooth contact. But at the same time we have
diminished the number of teeth in contact. Thus in Fig. 42 there are
three teeth in driving contact, while in Fig. 44 there are but two,
viz., D and E.
[Illustration: Fig. 45.]
In an article by Professor Robinson, attention is called to the fact
that if the teeth of wheels are not formed to have correct curves when
new, they cannot be improved by wear; and this will be clearly perceived
from the preceding remarks upon the amount of rolling and sliding
contact. It will also readily appear that the nearer the diameter of the
generating to that of the base circle the more the teeth wear out of
correct shape; hence, in a train of gearing in which the generating
circle equals the radius of the pinion, the pinion will wear out of
shape the quickest, and the largest wheel the least; because not only
does each tooth on the pinion more frequently come into action on
account of its increased revolutions, but furthermore the length of
flank that has contact is less, while the amount of sliding action is
greater. In Fig. 45, for example, are a wheel and pinion, the latter
having radial flanks and the pinion being the driver, the arc of
approach is the thickened arc from C to the line of centres, while the
arc of recess is denoted by the dotted arc. As contact on the pinion
flank begins at point C and ends at the line of centres, the total depth
of flank that suffers wear from the contact is that from C to N; and as
the whole length of the wheel tooth face sweeps over this depth C N, the
pinion flanks must wear faster than the wheel faces, and the pinion
flanks will wear underneath, as denoted by the dotted curve on the
flanks of tooth W. In the case of the wheel, contact on its tooth flanks
begins at the line of centres and ends at L, hence that flank can only
wear between point L and the pitch line L; and as the whole length of
pinion face sweeps on this short length L S, the pinion flank will wear
most, the wear being in the direction of the dotted arc on the left-hand
side V of the tooth. Now the pinion flank depth C N, being less than the
wheel flank depth S L, and the same length of tooth face sweeping
(during the path of contact) over both, obviously the pinion tooth will
wear the most, while both will, as the wear proceeds, lose their proper
flank curve. In Fig. 46 the generating arcs, G and G´, and the wheel are
the same, but the pinion is larger. As a result the acting length C N,
of pinion flank is increased, as is also the acting length S L, of wheel
flank; hence, the flanks of both wheels would wear better, and also
better preserve their correct and original shapes.
It has been shown, when referring to Figs. 42 and 44, when treating of
the amount of sliding and of rolling motion, that the smaller the
diameter of rolling circle in proportion to that of pitch circle, the
longer the acting length of flank and the more the amount of rolling
motion; and it follows that the teeth would also preserve their original
and true shape better. But the wear of the teeth, and the alteration of
tooth form by reason of that wear, will, in any event, be greater upon
the pinion than upon the wheel, and can only be equal when the two
wheels are of equal diameter, in which case the tooth curves will be
alike on both wheels, and the acting depths of flank will be equal, as
shown in Fig. 47, the flanks being radial, and the acting depths of
flank being shown at J K. In Fig. 48 is shown a pair of wheels with a
generating circle, G and G´, of one quarter the diameter of the base
circle or pitch diameter, and the acting length of flank is shown at L
M. The wear of the teeth would, therefore, in this latter case, cause it
in time to assume the form shown in Fig. 49. But it is to be noted that
while the acting depth of flank has been increased the arcs of contact
have been diminished, and that in Fig. 47 there are two teeth in
contact, while in Fig. 48 there is but one, hence the pressure upon each
tooth is less in proportion as the diameter of the generating circle is
increased. If a train of wheels are to be constructed, or if the wheels
are to be capable of interchanging with other combinations of wheels of
the same pitch, the diameter of the generating circle must be equal to
the smallest wheel or pinion, which is, under the Willis system, a
pinion of 12 teeth; under the Pratt and Whitney, and Brown and Sharpe
systems, a pinion of 15 teeth.
[Illustration: Fig. 46.]
[Illustration: Fig. 47.]
But if a pair or a particular train of gears are to be constructed, then
a diameter of generating circle may be selected that is considered most
suitable to the particular conditions; as, for example, it may be equal
to the radius of the smallest wheel giving it radial flanks, or less
than that radius giving parallel or spread flanks. But in any event, in
order to transmit continuous motion, the diameter of generating circle
must be such as to give arcs of action that are equal to the pitch, so
that each pair of teeth will come into action before the preceding pair
have gone out of action.
[Illustration: Fig. 48.]
It may now be pointed out that the degrees of angle that the teeth move
through always exceeds the number of degrees of angle contained in the
paths of contact, or, in other words, exceeds the degrees contained in
the arcs of approach and recess combined.
[Illustration: Fig. 49.]
In Fig. 50, for example, are a wheel A and pinion B, the teeth on the
wheel being extended to a point. Suppose that the wheel A is the driver,
and contact will begin between the two teeth D and F on the dotted arc.
Now suppose tooth D to have moved to position C, and F will have been
moved to position H. The degrees of angle the pinion has been moved
through are therefore denoted by I, whereas the degrees of angle the
arcs of contact contain are therefore denoted by J.
The degrees of angle that the wheel A has moved through are obviously
denoted by E, because the point of tooth D has during the arcs of
contact moved from position D to position C. The degrees of angle
contained in its path of contact are denoted by K, and are less than E,
hence, in the case of teeth terminating in a point as tooth D, the
excess of angle of action over path of contact is as many degrees as are
contained in one-half the thickness of the tooth, while when the points
of the teeth are cut off, the excess is the number of degrees contained
in the distance between the corner and the side of the tooth as marked
on a tooth at P.
[Illustration: Fig. 50.]
With a given diameter of pitch circle and pitch diameter of wheel, the
length of the arc of contact will be influenced by the height of the
addendum from the pitch circle, because, as has been shown, the arcs of
approach and of recess, respectively, begin and end on the addendum
circle.
If the height of the addendum on the follower be reduced, the arc of
approach will be reduced, while the arc of recess will not be altered;
and if the follower have no addendum, contact between the teeth will
occur on the arc of recess only, which gives a smoother motion, because
the action of the driver is that of dragging rather than that of pushing
the follower. In this case, however, the arc of recess must, to produce
continuous motion, be at least equal to the pitch.
It is obvious, however, that the follower having no addendum would, if
acting as a driver to a third wheel, as in a train of wheels, act on its
follower, or the fourth wheel of the train, on the arc of approach only;
hence it follows that the addendum might be reduced to diminish, or
dispensed with to eliminate action, on the arc of approach in the
follower of a pair of wheels only, and not in the case of a train of
wheels.
To make this clear to the reader it may be necessary to refer again to
Fig. 33 or 34, from which it will be seen that the action of the teeth
of the driver on the follower during the arc of approach is produced by
the flanks of the driver on the faces of the follower. But if there are
no such faces there can be no such contact.
On the arc of recess, however, the faces of the driver act on the flanks
of the follower, hence the absence of faces on the follower is of no
import.
From these considerations it also appears that by giving to the driver
an increase of addendum the arc of recess may be increased without
affecting the arc of approach. But the height of addendum in machinists'
practice is made a constant proportion of the pitch, so that the wheel
may be used indiscriminately, as circumstances may require, as either a
driver or a follower, the arcs of approach and of recess being equal.
The height of addendum, however, is an element in determining the number
of teeth in contact, and upon small pinions this is of importance.
[Illustration: Fig. 51.]
In Fig. 51, for example, is shown a section of two pinions of equal
diameters, and it will be observed that if the full line A determined
the height of the addendum there would be contact either at C or B only
(according to the direction in which the motion took place).
With the addendum extended to the dotted circle, contact would be just
avoided, while with the addendum extended to D there would be contact
either at E or at F, according to which direction the wheel had motion.
This, by dividing the strain over two teeth instead of placing it all
upon one tooth, not only doubles the strength for driving capacity, but
decreases the wear by giving more area of bearing surface at each
instant of time, although not increasing that area in proportion to the
number of teeth contained in the wheel.
In wheels of larger diameter, short teeth are more permissible, because
there are more teeth in contact, the number increasing with the
diameters of the wheels. It is to be observed, however, that from having
radial flanks, the smallest wheel is always the weakest, and that from
making the most revolutions in a given time, it suffers the most from
wear, and hence requires the greatest attainable number of teeth in
constant contact at each period of time, as well as the largest possible
area of bearing or wearing surface on the teeth.
It is true that increasing the "depth of tooth to pitch line" increases
the whole length of tooth, and, therefore, weakens it; but this is far
more than compensated for by distributing the strain over a greater
number of teeth. This is in practice accomplished, _when circumstances
will permit_, by making the pitch finer, giving to a wheel, of a given
diameter, a greater number of teeth.
[Illustration: Fig. 52.]
When the wheels are required to transmit motion rather than power (as in
the case of clock wheels), to move as frictionless as possible, and to
place a minimum of thrust on the journals of the shafts of the wheels,
the generating circle may be made nearly as large as the diameter of the
pitch circle, producing teeth of the form shown in Fig. 52. But the
minimum of friction is attained when the two flanks for the tooth are
drawn into one common hypocycloid, as in Fig. 53. The difference between
the form of tooth shown in Fig. 52 and that shown in Fig. 53, is merely
due to an increase in the diameter of the generating circle for the
latter. It will be observed that in these forms the acting length of
flank diminishes in proportion as the diameter of the generating circle
is increased, the ultimate diameter of generating circle being as large
as the pitch circles.
[Illustration: Fig. 53.]
[1]This form is undesirable in that there is contact on one side only
(on the arc of approach) of the line of centres, but the flanks of the
teeth may be so modified as to give contact on the arc of recess also,
by forming the flanks as shown in Fig. 54, the flanks, or rather the
parts within the pitch circles, being nearly half circles, and the parts
without with peculiarly formed faces, as shown in the figure. The pitch
circles must still be regarded as the rolling circles rolling upon each
other. Suppose _b_ a tracing point on B, then as B rolls on A it will
describe the epicycloid _a_ _b_. A parallel line _c_ _d_ will work at a
constant distance as at _c_ _d_ from _a_ _b_, and this distance may be
the radius of that part of D that is within the pitch line, the same
process being applied to the teeth on both wheels. Each tooth is thus
composed of a spur based upon a half cylinder.
[1] From an article by Professor Robinson.
[Illustration: Fig. 54.]
Comparing Figs. 53 and 54, we see that the bases in 53 are flattest, and
that the contact of faces upon them must range nearer the pitch line
than in 54. Hence, 53 presents a more favorable obliquity of the line of
direction of the pressures of tooth upon tooth. In seeking a still more
favorable direction by going outside for the point of contact, we see by
simply recalling the method of generating the tooth curves, that tooth
contacts outside the pitch lines have no possible existence; and hence,
Fig. 53 may be regarded as representing that form of toothed gear which
will operate with less friction than any other known form.
[Illustration: Fig. 55.]
This statement is intended to cover fixed teeth only, and not that
complicated form of the trundle wheel in which the cylinder teeth are
friction rollers. No doubt such would run still easier, even with their
necessary one-sided contacts. Also, the statement is supposed to be
confined to such forms of teeth as have good practical contacts at and
near the line of centres.
Bevel-gear wheels are employed to transmit motion from one shaft to
another when the axis of one is at an angle to that of the other. Thus
in Fig. 55 is shown a pair of bevel-wheels to transmit motion from
shafts at a right angle. In bevel-wheels all the lines of the teeth,
both at the tops or points of the teeth, at the bottoms of the spaces,
and on the sides of the teeth, radiate from the centre E, where the axes
of the two shafts would meet if produced. Hence the depth, thickness,
and height of the tooth decreases as the point E is approached from the
diameter of the wheel, which is always measured on the pitch circle at
the largest end of the cone, or in other words, at the largest pitch
diameter.
The principles governing the practical construction of the curves for
the teeth of the bevel-wheels may be explained as follows:--
In Fig. 56 let F and G represent two shafts, rotating about their
respective axes; and having cones whose greatest diameters are at A and
B, and whose points are at E. The diameter A being equal to that of B
their circumferences will be equal, and the angular and velocity ratios
will therefore be equal.
[Illustration: Fig. 56.]
Let C and D represent two circles about the respective cones, being
equidistant from E, and therefore of equal diameters and circumferences,
and it is obvious that at every point in the length of each cone the
velocity will be equal to a point upon the other so long as both points
are equidistant from the points of intersection of the axes of the two
shafts; hence if one cone drive the other by frictional contact of
surfaces, both shafts will be rotated at an equal speed of rotation, or
if one cone be fixed and the other moved around it, the contact of the
surfaces will be a rolling contact throughout. The line of contact
between the two cones will be a straight line, radiating at all times
from the point E. If such, however, is not the case, then the contact
will no longer be a rolling one. Thus, in Fig. 57 the diameters or
circumferences at A and B being equal, the surfaces would roll upon each
other, but on account of the line of contact not radiating from E (which
is the common centre of motion for the two shafts) the circumference C
is less than that of D, rendering a rolling contact impossible.
[Illustration: Fig. 57.]
We have supposed that the diameters of the cones be equal, but the
conditions will remain the same when their diameters are unequal; thus,
in Fig. 58 the circumference of A is twice that of B, hence the latter
will make two rotations to one of the former, and the contact will still
be a rolling one. Similarly the circumference of D is one half that of
C, hence D will also make two rotations to one of C, and the contact
will also be a rolling one; a condition which will always exist
independent of the diameters of the wheels so long as the angles of the
faces, or wheels, or (what is the same thing, the line of contact
between the two,) radiates from the point E, which is located where the
axes of the shafts would meet.
[Illustration: Fig. 58.]
[Illustration: Fig. 59.]
The principles governing the forms of the cones on which the teeth are
to be located thus being explained, we may now consider the curves of
the teeth. Suppose that in Fig. 59 the cone A is fixed, and that the
cone whose axis is F be rotated upon it in the direction of the arrow.
Then let a point be fixed in any part of the circumference of B (say at
_d_), and it is evident that the path of this point will be as B rolls
around the axis F, and at the same time around A from the centre of
motion, E. The curve so generated or described by the point _d_ will be
a spherical epicycloid. In this case the exterior of one cone has rolled
upon the coned surface of the other; but suppose it rolls upon the
interior, as around the walls of a conical recess in a solid body; then
a point in its circumference would describe a curve known as the
spherical hypocycloid; both curves agreeing (except in their spherical
property) to the epicycloid and hypocycloid of the spur-wheel. But this
spherical property renders it very difficult indeed to practically
delineate or mark the curves by rolling contact, and on account of this
difficulty Tredgold devised a method of construction whereby the curves
may be produced sufficiently accurate for all practical purposes, as
follows:--
[Illustration: Fig. 60.]
In Fig. 60 let A A represent the axis of one shaft, and B the axis of
the other, the axes of the two meeting at W. Mark E, representing the
diameter of one wheel, and F that of the other (both lines representing
the pitch circles of the respective wheels). Draw the line G G passing
through the point W, and the point T, where the pitch circles E, F meet,
and G G will be the line of contact between the cones. From W as a
centre, draw on each side of G G dotted lines as _p_, representing the
height of the teeth above and below the pitch line G G. At a right angle
to G G mark the line J K, and from the junction of this line with axis B
(as at Q) as a centre, mark the arc _a_, which will represent the pitch
circle for the large diameter of pinion D; mark also the arc _b_ for the
addendum and _c_ for the roots of the teeth, so that from _b_ to _c_
will represent the height of the tooth at that end.
[Illustration: Fig. 61.]
Similarly from P, as a centre, mark (for the large diameter of wheel C,)
the pitch circle _g_, root circle _h_, and addendum _i_. On these arcs
mark the curves in the same manner as for spur-wheels. To obtain these
arcs for the small diameters of the wheels, draw M M parallel to J K.
Set the compasses to the radius R L, and from P, as a centre, draw the
pitch circle _k_. To obtain the depth for the tooth, draw the dotted
line _p_, meeting the circle _h_, and the point W. A similar line from
circle _i_ to W will show the height of the addendum, or extreme
diameter; and mark the tooth curves on _k_, _l_, _m_, in the same manner
as for a spur-wheel.
Similarly for the pitch circle of the small end of the pinion teeth, set
the compasses to the radius S L, and from Q as a centre, mark the pitch
circle _d_, outside of _d_ mark _e_ for the height of the addendum and
inside of _d_ mark _f_ for the roots of the teeth at that end. The
distance between the dotted lines (as _p_) represents the full height of
the teeth, hence _h_ meets line _p_, being the root of tooth for the
large wheel, and to give clearance, the point of the pinion teeth is
marked below, thus arc _b_ does not meet _h_ or _p_. Having obtained
these arcs the curves are rolled as for a spur-wheel.
A tooth thus marked out is shown at _x_, and from its curves between _b_
_c_, a template for the large diameter of the pinion tooth may be made,
while from the tooth curves between the arcs _e_ _f_, a template for the
smallest tooth diameter of the pinion can be made.
Similarly for the wheel C the outer end curves are marked on the lines
_g_, _h_, _i_, and those for the inner end on the lines _k_, _l_, _m_.
[Illustration: Fig. 62.]
Internal or annular gear-wheels have their tooth curves formed by
rolling the generating circle upon the pitch circle or base circle, upon
the same general principle as external or spur-wheels. But the tooth of
the annular wheel corresponds with the space in the spur-wheel, as is
shown in Fig. 61, in which curve A forms the flank of a tooth on a
spur-wheel P, and the face of a tooth on the annular wheel W. It is
obvious then that the generating circle is rolled within the pitch
circle for the face of the wheel and without for its flank, or the
reverse of the process for spur-wheels. But in the case of internal or
annular wheels the path of contact of tooth upon tooth with a pinion
having a given number of teeth increases in proportion as the number of
teeth in the wheel is diminished, which is also the reverse of what
occurs in spur-wheels; as will readily be perceived when it is
considered that if in an internal wheel the pinion have as many teeth as
the wheel the contact would exist around the whole pitch circles of the
wheel and pinion and the two would rotate together without any motion of
tooth upon tooth. Obviously then we have, in the case of internal
wheels, a consideration as to what is the greatest number (as well as
what is the least number) of teeth a pinion may contain to work with a
given wheel, whereas in spur-wheels the reverse is again the case, the
consideration being how few teeth the wheel may contain to work with a
given pinion. Now it is found that although the curves of the teeth in
internal wheels and pinions may be rolled according to the principles
already laid down for spur-wheels, yet cases may arise in which internal
gears will not work under conditions in which spur-wheels would work,
because the internal wheels will not engage together. Thus, in Fig. 62,
is a pinion of 12 teeth and a wheel of 22 teeth, a generating circle
having a diameter equal to the radius of the pinion having been used for
all the tooth curves of both wheel and pinion. It will be observed that
teeth A, B, and C clearly overlap teeth D, E, and F, and would therefore
prevent the wheels from engaging to the requisite depth. This may of
course be remedied by taking the faces off the pinion, as in Fig. 63,
and thus confining the arc of contact to an arc of recess if the pinion
drives, or an arc of approach if the wheel drives; or the number of
teeth in the pinion may be reduced, or that in the wheel increased;
either of which may be carried out to a degree sufficient to enable the
teeth to engage and not interfere one with the other. In Fig. 64 the
number of teeth in the pinion P is reduced from 12 to 6, the wheel W
having 22 as before, and it will be observed that the teeth engage and
properly clear each other.
[Illustration: Fig. 63.]
By the introduction into the figure of a segment of a spur-wheel also
having 22 teeth and placed on the other side of the pinion, it is shown
that the path of contact is greater, and therefore the angle of action
is greater, in internal than in spur gearing. Thus suppose the pinion to
drive in the direction of the arrows and the thickened arcs A B will be
the arcs of approach, A measuring longer than B. The dotted arcs C D
represent the arcs of receding contact and C is found longer than D, the
angles of action being 66° for the spur-wheels and 72° for the annular
wheel.
On referring again to Fig. 62 it will be observed that it is the faces
of the teeth on the two wheels that interfere and will prevent them from
engaging, hence it will readily occur to the mind that it is possible to
form the curves of the pinion faces correct to work with the faces of
the wheel teeth as well as with the flanks; or it is possible to form
the wheel faces with curves that will work correctly with the faces, as
well as with the flanks of the pinion teeth, which will therefore
increase the angle of action, and Professor McCord has shown in an
article in the London _Engineering_ how to accomplish this in a simple
and yet exceedingly ingenious manner which may be described as
follows:--
[Illustration: Fig. 64.]
It is required to find a describing circle that will roll the curves for
the flanks of the pinion and the faces of the wheels, and also a
describing circle for the flanks of the wheel and the faces of the
pinion; the curve for the wheel faces to work correctly with the faces
as well as with the flanks of the pinion, and the curve for the pinion
faces to work correctly with both the flanks and faces of the internal
wheel.
[Illustration: Fig. 65.]
[Illustration: Fig. 66.]
In Fig. 65 let P represent the pitch circle of an annular or internal
wheel whose centre is at A, and Q the pitch circle of a pinion whose
centre is at B, and let R be a describing circle whose centre is at C,
and which is to be used to roll all the curves for the teeth. For the
flanks of the annular wheel we may roll R within P, while for the faces
of the wheel we may roll R outside of P, but in the case of the pinion
we cannot roll R within Q, because R is larger than Q, hence we must
find some other rolling circle of less diameter than R, and that can be
used in its stead (the radius of R always being greater than the radius
of the axis of the wheel and pinion for reasons that will appear
presently). Suppose then that in Fig. 66 we have a ring whose bore R
corresponds in diameter to the intermediate describing circle R, Fig. 65
and that Q represents the pinion. Then we may roll R around and in
contact with the pinion Q, and a tracing point in R will trace the curve
M N O, giving a curve a portion of which may be used for the faces of
the pinion. But suppose that instead of rolling the intermediate
describing circle R around P, we roll the circle T around P, and it will
trace precisely the same curve M N O; hence for the faces of the pinion
we have found a rolling circle T which is a perfect substitute for the
intermediate circle Q, and which it will always be, no matter what the
diameters of the pinion and of the intermediate describing circle may
be, providing that the diameter of T is equal to the difference between
the diameters of the pinion and that of the intermediate describing
circle as in the figure. If now we use this describing circle to roll
the flanks of the annular wheel as well as the faces of the pinion,
these faces and flanks will obviously work correctly together. Since
this describing circle is rolled on the outside of the pinion and on the
outside of the annular wheel we may distinguish it as the exterior
describing circle.
[Illustration: Fig. 67.]
Now instead of rolling the intermediate describing circle R within the
annular wheel P for the face curves of the teeth upon P, we may find
some other circle that will give the same curve and be small enough to
be rolled within the pinion Q for its teeth flanks. Thus in Fig. 67 P
represents the pitch circle of the annular wheel and R the intermediate
circle, and if R be rolled within P, a point on the circumference of R
will trace the curve V W. But if we take the circle S, having a diameter
equal to the difference between the diameter of R and that of P, and
roll it within P, a point in its circumference will trace the same curve
V W; hence S is a perfect substitute for R, and a portion of the curve V
W may be used for the faces of the teeth on the annular wheel. The
circle S being used for the pinion flanks, the wheel faces and pinion
flanks will work correctly together, and as the circle S is rolled
within the pinion for its flanks and within the wheel for its faces, it
may be distinguished as the interior describing circle.
To prove the correctness of the construction it may be noted that with
the particular diameter of intermediate describing circle used in Fig.
65, the interior and exterior describing circles are of equal diameters;
hence, as the same diameter of describing circle is used for all the
faces and flanks of the pair of wheels they will obviously work
correctly together, in accordance with the rules laid down for spur
gearing. The radius of S in Fig. 69 is equal to the radius of the
annular wheel, less the radius of the intermediate circle, or the radius
from A to C. The radius of the exterior describing circle T is the
radius of the intermediate circle less the radius of the pinion, or
radius C B in the figure.
[Illustration: Fig. 68.]
[Illustration: Fig. 69.]
Now the diameter of the intermediate circle may be determined at will,
but cannot exceed that of the annular wheel or be less than the pinion.
But having been selected between these two limits the interior and
exterior describing circles derived from it give teeth that not only
engage properly and avoid the interference shown in Fig. 62, but that
will also have an additional arc of action during the recess, as is
shown in Fig. 68, which represents the wheel and pinion shown in Fig.
62, but produced by means of the interior and exterior describing
circles. Supposing the pinion to be the driver the arc of approach will
be along the thickened arc of the interior describing circle, while
during the arc of recess there will be an arc of contact along the
dotted portion of the exterior describing circle as in ordinary gearing.
But in addition there will be an arc of recess along the dotted portion
of the intermediate circle R, which arc is due to the faces of the
pinion acting upon the faces as well as upon the flanks of the wheel
teeth. It is obvious from this that as soon as a tooth passes the line
of centres it will, during a certain period, have two points of contact,
one on the arc of the exterior describing circle, and another along the
arc of R, this period continuing until the addendum circle of the pinion
crosses the dotted arc of the exterior describing circle at Z.
The diameters of the interior and exterior describing circles obviously
depend upon the diameter of the intermediate circle, and as this may, as
already stated, be selected, within certain limits, at will, it is
evident that the relative diameters of the interior and exterior
describing circles will vary in proportion, the interior becoming
smaller and the exterior larger, while from the very mode of
construction the radius of the two will equal that of the axes of the
wheel and pinion. Thus in Fig. 69 the radii of S, T, equal A B, or the
line of centres, and their diameters, therefore, equal the radius of the
annular wheel, as is shown by dotting them in at the upper half of the
figure. But after their diameters have been determined by this
construction either of them may be decreased in diameter and the teeth
of the wheels will clear (and not interfere as in Fig. 62), but the
action will be the same as in ordinary gear, or in other words there
will be no arc of action on the circle R. But S cannot be increased
without correspondingly decreasing T, nor can T be increased without
correspondingly decreasing S.
[Illustration: Fig. 70.]
Fig. 70 shows the same pair of gears as in Fig. 68 (the wheel having 22
and the pinion 12 teeth), the diameter of the intermediate circle having
been enlarged to decrease the diameter of S and increase that of T, and
as these are left of the diameter derived from the construction there is
receding action along R from the line of centres to T.
[Illustration: Fig. 71.]
In Fig. 71 are represented a wheel and pinion, the pinion having but
four teeth less than the wheel, and a tooth, J, being shown in position
in which it has contact at two places. Thus at _k_ it is in contact with
the flank of a tooth on the annular wheel, while at L it is in contact
with the face of the same tooth.
As the faces of the teeth on the wheel do not have contact higher than
point _t_, it is obvious that instead of having them 3/10 of the pitch
as at the bottom of the figure, we may cut off the portion X without
diminishing the arc of contact, leaving them formed as at the top of the
figure. These faces being thus reduced in height we may correspondingly
reduce the depth of flank on the pinion by filling in the portion G,
leaving the teeth formed as at the top of the pinion. The teeth faces of
the wheel being thus reduced we may, by using a sufficiently large
intermediate circle, obtain interior and exterior describing circles
that will form teeth that will permit of the pinion having but one tooth
less than the wheel, or that will form a wheel having but one tooth more
than the pinion.
The limits to the diameter of the intermediate describing circle are as
follows: in Fig. 72 it is made equal in diameter to the pitch diameter
of the pinion, hence B will represent the centre of the intermediate
circle as well as of the pinion, and the pitch circle of the pinion will
also represent the intermediate circle R. To obtain the radius for the
interior describing circle we subtract the radius of the intermediate
circle from the radius of the annular wheel, which gives A P, hence the
pitch circle of the pinion also represents the interior circle R. But
when we come to obtain the radius for the exterior describing circle
(T), by subtracting the radius of the pinion from that of the
intermediate circle, we find that the two being equal give O for the
radius of (T), hence there could be no flanks on the pinion.
[Illustration: Fig. 72.]
Now suppose that the intermediate circle be made equal in diameter to
the pitch circle of the annular wheel, and we may obtain the radius for
the exterior describing circle T; by subtracting the radius of the
pinion from that of the intermediate circle, we shall obtain the radius
A B; hence the radius of (T) will equal that of the pinion. But when we
come to obtain the radius for the interior describing circle by
subtracting the radius of the intermediate circle from that of the
annular wheel, we find these two to be equal, hence there would be no
interior describing circle, and, therefore, no faces to the pinion.
[Illustration: Fig. 73.]
The action of the teeth in internal wheels is less a sliding and more a
rolling one than that in any other form of toothed gearing. This may be
shown as follows: In Fig. 73 let A A represent the pitch circle of an
external pinion, and B B that of an internal one, and P P the pitch
circle of an external wheel for A A or an internal one for B B, the
point of contact at the line of centres being at C, and the direction of
rotation P P being as denoted by the arrow; the two pinions being
driven, we suppose a point at C, on the pitch circle P P, to be
coincident with a point on each of the two pinions at the line of
centres. If P P be rotated so as to bring this point to the position
denoted by D, the point on the external pinion having moved to E, while
that on the internal pinion has moved to F, both having moved through an
arc equal to C D, then the distance from E to D being greater than from
D to F, more sliding motion must have accompanied the contact of the
teeth at the point E than at the point F; and the difference in the
length of the arc E D and that of F D, may be taken to represent the
excess of sliding action for the teeth on E; for whatever, under any
given condition, the amount of sliding contact may be, it will be in the
proportion of the length of E D to that of F D. Presuming, then, that
the amount of power transmitted be equal for the two pinions, and the
friction of all other things being equal--being in proportion to the
space passed (or in this case slid) over--it is obvious that the
internal pinion has the least friction.
CHAPTER II.--THE TEETH OF GEAR-WHEELS.--CAMS.
WHEEL AND TANGENT SCREW OR WORM AND WORM GEAR.
In Fig. 74 are shown a worm and worm gear partly in section on the line
of centres. The worm or tangent screw W is simply one long tooth wound
around a cylinder, and its form may be determined by the rules laid down
for a rack and pinion, the tangent screw or worm being considered as a
rack and the wheel as an ordinary spur-wheel.
[Illustration: Fig. 74.]
Worm gearing is employed for transmitting motion at a right angle, while
greatly reducing the motion. Thus one rotation of the screw will rotate
the wheel to the amount of the pitch of its teeth only. Worm gearing
possesses the qualification that, unless of very coarse pitch, the worm
locks the wheel in any position in which the two may come to a state of
rest, while at the same time the excess of movement of the worm over
that of the wheel enables the movement of the latter, through a very
minute portion of a revolution. And it is evident that, when the plane
of rotation of the worm is at a right angle to that of the wheel, the
contact of the teeth is wholly a sliding one. The wear of the worm is
greater than that of the wheel, because its teeth are in continuous
contact, whereas the wheel teeth are in contact only when passing
through the angle of action. It may be noted, however, that each tooth
upon the worm is longer than the teeth on the wheel in proportion as the
circumference of the worm is to the length of wheel tooth.
[Illustration: Fig. 75.]
If the teeth of the wheel are straight and are set at an angle equal to
the angle of the worm thread to its axis, as in Fig. 75, P P
representing the pitch line of the worm, C D the line of centres, and
_d_ the worm axis, the contact of tooth upon tooth will be at the centre
only of the sides of the wheel teeth. It is generally preferred,
however, to have the wheel teeth curved to envelop a part of the
circumference of the worm, and thus increase the line of contact of
tooth upon tooth, and thereby provide more ample wearing surface.
[Illustration: Fig. 76.]
In this case the form of the teeth upon the worm wheel varies at every
point in its length as the line of centres is departed from. Thus in
Fig. 76 is shown an end view of a worm and a worm gear in section, _c_
_d_ being the line of centres, and it will be readily perceived that the
shape of the teeth if taken on the line _e_ _f_, will differ from that
on the line of centres _c_ _d_; hence the form of the wheel teeth must,
if contact is to occur along the full length of the tooth, be conformed
to fit to the worm, which may be done by taking a series of section of
the worm thread at varying distances from, and parallel to, the line of
centres and joining the wheel teeth to the shape so obtained. But if the
teeth of the wheel are to be cut to shape, then obviously a worm may be
provided with teeth (by serrating it along its length) and mounted in
position upon the wheel so as to cut the teeth of the wheel to shape as
the worm rotates. The pitch line of the wheel teeth, whether they be
straight and are disposed at an angle as in Fig. 75, or curved as in
Fig. 76, is at a right angle to the line of centres _c_ _d_, or in other
words in the plane of _g_ _h_, in Fig. 76. This is evident because the
pitch line must be parallel to the wheel axis, being at an equal radius
from that axis, and therefore having an equal velocity of rotation at
every point in the length of the pitch line of the wheel tooth.
If we multiply the number of teeth by their pitch to obtain the
circumference of the pitch circle we shall obtain the circumference due
to the radius of _g_ _h_, from the wheel axis, and so long as _g_ _h_ is
parallel to the wheel axis we shall by this means obtain the same
diameter of pitch circle, so long as we measure it on a line parallel to
the line of centres _c_ _d_. The pitch of the worm is the same at
whatever point in the tooth depth it may be measured, because the teeth
curves are parallel one to the other, thus in Fig. 77 the pitch measures
are equal at _m_, _n_, or _o_.
But the action of the worm and wheel will nevertheless not be correct
unless the pitch line from which the curves were rolled coincides with
the pitch line of the wheel on the line of centres, for although, if the
pitch lines do not so coincide, the worm will at each revolution move
the pitch line of the wheel through a distance equal to the pitch of the
worm, yet the motion of the wheel will not be uniform because,
supposing the two pitch lines not to meet, the faces of the pinion teeth
will act against those of the wheel, as shown in Fig. 78, instead of
against their flanks, and as the faces are not formed to work correctly
together the motion will be irregular.
[Illustration: Fig. 77.]
The diameter of the worm is usually made equal to four times the pitch
of the teeth, and if the teeth are curved as in figure 76 they are made
to envelop not more than 30° of the worm.
The number of teeth in the wheel should not be less than thirty, a
double worm being employed when a quicker ratio of wheel to worm motion
is required.
[Illustration: Fig. 78.]
[Illustration: Fig. 79.]
When the teeth of the wheel are curved to partly envelop the worm
circumference it has been found, from experiments made by Robert Briggs,
that the worm and the wheel will be more durable, and will work with
greatly diminished friction, if the pitch line of the worm be located to
increase the length of face and diminish that of the flank, which will
decrease the length of face and increase the length of flank on the
wheel, as is shown in Fig. 79; the location for the pitch line of the
worm being determined as follows:--
[Illustration: Fig. 80.]
The full radius of the worm is made equal to twice the pitch of its
teeth, and the total depth of its teeth is made equal to .65 of its
pitch. The pitch line is then drawn at a radius of 1.606 of the pitch
from the worm axis. The pitch line is thus determined in Fig. 76, with
the result that the area of tooth face and of worm surface is equalized
on the two sides of the pitch line in the figure. In addition to this,
however, it may be observed that by thus locating the pitch line the
arcs both of approach and of recess are altered. Thus in Fig. 80 is
represented the same worm and wheel as in Fig. 79, but the pitch lines
are here laid down as in ordinary gearing. In the two figures the arcs
of approach are marked by the thickened part of the generating circle,
while the arcs of recess are denoted by the dotted arc on the generating
circle, and it is shown that increasing the worm face, as in Fig. 79,
increases the arc of recess, while diminishing the worm flank diminishes
the arc of approach, and the action of the worm is smoother because the
worm exerts more pulling than pushing action, it being noted that the
action of the worm on the wheel is a pushing one before reaching, and a
pulling one after passing, the line of centres.
[Illustration: Fig. 81.]
It may here be shown that a worm-wheel may be made to work correctly
with a square thread. Suppose, for example, that the diameter of the
generating circle be supposed to be infinite, and the sides of the
thread may be accepted as rolled by the circle. On the wheel we roll a
straight line, which gives a cycloidal curve suitable to work with the
square thread. But the action will be confined to the points of the
teeth, as is shown in Fig. 81, and also to the arc of approach. This is
the same thing as taking the faces off the worm and filling in the
flanks of the wheel. Obviously, then, we may reverse the process and
give the worm faces only, and the wheel, flanks only, using such size of
generating circle as will make the spaces of the wheel parallel in their
depths and rolling the same generating circle upon the pitch line of the
worm to obtain its face curve. This would enable the teeth on the wheel
to be cut by a square-threaded tap, and would confine the contact of
tooth upon tooth to the recess.
The diameter of generating circle used to roll the curves for a worm and
worm-wheel should in all cases be larger than the radius of the
worm-wheel, so that the flanks of the wheel teeth may be at least as
thick at the root as they are at the pitch circle.
To find the diameter of a wheel, driven by a tangent-screw, which is
required to make one revolution for a given number of turns of the
screw, it is obvious, in the first place, that when the screw is
single-threaded, the number of teeth in the wheel must be equal to the
number of turns of the screw. Consequently, the pitch being also given,
the radius of the wheel will be found by multiplying the pitch by the
number of turns of the screw during one turn of the wheel, and dividing
the product by 6.28.
[Illustration: Fig. 82.]
When a wheel pattern is to be made, the first consideration is the
determination of the diameter to suit the required speed; the next is
the pitch which the teeth ought to have, so that the wheel may be in
accordance with the power which it is intended to transmit; the next,
the number of the teeth in relation to the pitch and diameter; and,
lastly, the proportions of the teeth, the clearance, length, and
breadth.
[Illustration: Fig. 83.]
When the amount of power to be transmitted is sufficient to cause
excessive wear, or when the velocity is so great as to cause rapid wear,
the worm instead of being made parallel in diameter from end to end, is
sometimes given a curvature equal to that of the worm-wheel, as is shown
in Fig. 82.
[Illustration: Fig. 84.]
[Illustration: Fig. 85.]
The object of this design is to increase the bearing area, and thus, by
causing the power transmitted to be spread over a larger area of
contact, to diminish the wear. A mechanical means of cutting a worm to
the required form for this arrangement is shown in Fig. 83, which is
extracted from "Willis' Principles of Mechanism." "A is a wheel driven
by an endless screw or worm-wheel, B, C is a toothed wheel fixed to the
axis of the endless screw B and in gear with another and equal toothed
gear D, upon whose axis is mounted the smooth surfaced solid E, which it
is desired to cut into Hindley's[2] endless screw. For this purpose a
cutting tooth F is clamped to the face of the wheel A. When the handle
attached to the axis of B C is turned round, the wheel A and solid wheel
E will revolve with the same relative velocity as A and B, and the tool
F will trace upon the surface of the solid E a thread which will
correspond to the conditions. For from the very mode of its formation
the section of every thread through the axis will point to the centre of
the wheel A. The axis of E lies considerably higher than that of B to
enable the solid E to clear the wheel A.
[2] The inventor of this form of endless screw.
"The edges of the section of the solid E along its horizontal centre
line exactly fit the segment of the toothed wheel, but if a section be
made by a plane parallel to this the teeth will no longer be equally
divided as they are in the common screw, and therefore this kind of
screw can only be in contact with each tooth along a line corresponding
to its middle section. So that the advantage of this form over the
common one is not so great as appears at first sight.
"If the inclination of the thread of a screw be very great, one or more
intermediate threads may be added, as in Fig. 84, in which case the
screw is said to be double or triple according to the number of separate
spiral threads that are so placed upon its surface. As every one of
these will pass its own wheel-tooth across the line of centres in each
revolution of the screw, it follows that as many teeth of the wheel will
pass that line during one revolution of the screw as there are threads
to the screw. If we suppose the number of these threads to be
considerable, for example, equal to those of the wheel teeth, then the
screw and wheel may be made exactly alike, as in Fig. 85; which may
serve as an example of the disguised forms which some common
arrangements may assume."
[Illustration: Fig. 86.]
In Fig. 86 is shown Hawkins's worm gearing. The object of this ingenious
mechanical device is to transmit motion by means of screw or worm
gearing, either by a screw in which the threads are of equal diameter
throughout its length, or by a spiral worm, in which the threads are not
of equal diameter throughout, but increase in diameter each way from the
centre of its length, or about the centre of its length outwardly.
Parallel screws are most applicable to this device when rectilinear
motions are produced from circular motions of the driver, and spiral
worms are applied when a circular motion is given by the driver, and
imparted to the driven wheel. The threads of a spiral worm instead of
gearing into teeth like those of an ordinary worm-wheel, actuate a
series of rollers turning upon studs, which studs are attached to a
wheel whose axis is not parallel to that of the worm, but placed at a
suitable inclination thereto. When motion is given to the worm then
rotation is produced in the roller wheel at a rate proportionable to the
pitch of worm and diameter of wheel respectively.
In the arrangement for transmitting rectilinear motion from a screw,
rollers may be employed whose axes are inclined to the axis of the
driving screw, or else at right angles to or parallel to the same. When
separate rollers are employed with inclined axes, or axes at right
angles with that of the main driving screw, each thread in gear touches
a roller at one part only; but when the rollers are employed with axes
parallel to that of the driving screw a succession of grooves are turned
in these rollers, into which the threads of the driving screw will be in
gear throughout the entire length of the roller. These grooves may be
separate and apart from each other, or else form a screw whose pitch is
equal to that of the driving screw or some multiple thereof.
In Fig. 86 the spiral worm is made of such a length that the edge of one
roller does not cease contact until the edge of the next comes into
contact; a wheel carries four rollers which turn on studs, the latter
being secured by cottars; the axis of the worm is at right angles with
that of the wheel. The edges of the rollers come near together, leaving
sufficient space for the thread of the worm to fit between any two
contiguous rollers. The pitch line of the screw thread forms an arc of a
circle, whose centre coincides with that of the wheel, therefore the
thread will always bear fairly against the rollers and maintain rolling
contact therewith during the whole of the time each roller is in gear,
and by turning the screw in either direction the wheel will rotate.
[Illustration: Fig. 87.]
To prevent end thrust on a worm shaft it may have a right-hand worm A,
and a left-hand one C (Fig. 87), driving two wheels B and D which are in
gear, and either of which may transmit the power. The thrust of the two
worms A and C, being in opposite directions, one neutralizes the other,
and it is obvious that as each revolution of the worm shaft moves both
wheels to an amount equal to the pitch of the worms, the two wheels B D
may, if desirable, be of different diameters.
[Illustration: Fig. 88.]
[Illustration: Fig. 89.]
Involute teeth.--These are teeth having their whole operative surfaces
formed of one continuous involute curve. The diameter of the generating
circle being supposed as infinite, then a portion of its circumference
may be represented by a straight line, such as A in Fig. 88, and if this
straight line be made to roll upon the circumference of a circle, as
shown, then the curve traced will be involute P. In practice, a piece of
flat spring steel, such as a piece of clock spring, is used for tracing
involutes. It may be of any length, but at one end it should be filed so
as to leave a scribing point that will come close to the base circle or
line, and have a short handle, as shown in Fig. 89, in which S
represents the piece of spring, having the point P´, and the handle H.
The operation is, to make a template for the base circle, rest this
template on drawing paper and mark a circle round its edge to represent
on the paper the pitch circle, and to then bend the spring around the
circle B, holding the point P´ in contact with the drawing paper,
securing the other end of the piece of steel, so that it cannot slip
upon B, and allowing the steel to unwind from the cylinder or circle B.
The point P´ will mark the involute curve P. Another way to mark an
involute is to use a piece of twine in place of the spring and a pencil
instead of the tracing point; but this is not so accurate, unless,
indeed, a piece of wood be laid on the drawing-board and the pencil held
firmly against it, so as to steady the pencil point and prevent the
variation in the curve that would arise from variation in the vertical
position of the pencil.
The flanks being composed of the same curve as the faces of the teeth,
it is obvious that the circle from which the tracing point starts, or
around which the straight line rolls, must be of less diameter than the
pitch circle, or the teeth would have no flanks.
A circle of less diameter than the pitch circle of the wheel is,
therefore, introduced, wherefrom to produce the involute curves forming
the full side of the tooth.
[Illustration: Fig. 90.]
The depth below pitch line or the length of flank is, therefore, the
distance between the pitch circle and the base circle. Now even
supposing a straight line to be a portion of the circumference of a
circle of infinite diameter or radius, the conditions would here appear
to be imperfect, because the generating circle is not rolled upon the
pitch circle but upon a circle of lesser diameter. But it can be shown
that the requirements of a proper velocity ratio will be met,
notwithstanding the employment of the base instead of the pitch circle.
Thus, in Fig. 90, let A and B represent the respective centres of the
two pitch circles, marked in dotted lines. Draw the base circle for B as
E Q, which may be of any radius less than that of the pitch circle of
B. Draw the straight line Q D R touching this base circle at its
perimeter and passing through the point of contact on the pitch circles
as at D. Draw the circle whose radius is A R forming the base circle for
wheel A. Thus the line R P Q will meet the perimeters of the two circles
while passing through the point of contact D at the line of centres (a
condition which the relative diameters of the base circles must always
be so proportioned as to attain).
If now we take any point on R Q, as P in the figure, as a tracing point,
and suppose the radius or distance P Q to represent the steel spring
shown in Fig. 89, and move the tracing point back to the base circle of
B, it will trace the involute E P. Again we may take the tracing point P
(supposing the line P R to represent the steel spring), and trace the
involute P F, and these two involutes represent each one side of the
teeth on the respective wheels.
[Illustration: Fig. 91.]
The line R P Q is at a right angle to the curves P E and P F, at their
point of contact, and, therefore, fills the conditions referred to in
Fig. 41. Now the line R P Q denotes the path of contact of tooth upon
tooth as the wheels revolve; or, in other words, the point of contact
between the side of a tooth on one wheel, and the side of a tooth on the
other wheel, will always move along the line Q R, or upon a similar line
passing through D, but meeting the base circles upon the opposite sides
of the line of centres, and since line Q R always cuts the line of
centres at the point of contact of the pitch circles, the conditions
necessary to obtain a correct angular velocity are completely fulfilled.
The velocity ratio is, therefore, as the length of B Q is to that of A
R, or, what is the same thing, as the radius of the base circle of one
wheel is to that of the other. It is to be observed that the line Q R
will vary in its angle to the line of centres A B, according to the
diameter of the base circle from which it is struck, and it becomes a
consideration as to what is its most desirable angle to produce the
least possible amount of thrust tending to separate the wheels, because
this thrust (described in Fig. 39) tends to wear the journals and
bearings carrying the wheel shafts, and thus to permit the pitch circles
to separate. To avoid, as far as possible, this thrust the proportions
between the diameters of the base circles D and E, Fig. 91, must be such
that the line D E passes through the point of contact on the line of
centres, as at C, while the angles of the straight line D E should be as
nearly 90° to a radial line, meeting it from the centres of the wheels
(as shown in the figure, by the lines B E and D E), as is consistent
with the length of D E, which in order to impart continuous motion must
at least equal the pitch of the teeth. It is obvious, also, that, to
give continuous motion, the length of D E must be more than the pitch in
proportion, as the points of the teeth come short of passing through the
base circles at D and E, as denoted by the dotted arcs, which should
therefore represent the addendum circles. The least possible obliquity,
or angle of D E, will be when the construction under any given
conditions be made such by trial, that the base circles D and E coincide
with the addendum circles on the line of centres, and thus, with a given
depth of both beyond, the pitch circle, or addenda as it is termed, will
cause the tooth contacts to extend over the greatest attainable length
of line between the limits of the addendum circles, thus giving a
maximum number of teeth in contact at any instant of time. These
conditions are fulfilled in Fig. 92,[3] the addendum on the small wheel
being longer than the depth below pitch line, while the faces of the
teeth are the narrowest.
[3] From an article by Prof. Robinson.
[Illustration: Fig. 92.]
In seeking the minimum obliquity or angle of D E in the figure, it is to
be observed that the less it is, the nearer the base circle approaches
the pitch circle; hence, the shorter the operative length of tooth flank
and the greater its wear.
In comparing the merits of involute with those of epicycloidal teeth,
the direction of the line of pressure at each point of contact must
always be the common perpendicular to the surfaces at the point of
contact, and these perpendiculars or normals must pass through the pitch
circles on the line of centres, as was shown in Fig. 41, and it follows
that a line drawn from C (Fig. 91) to any point of contact, is in the
direction of the pressure on the surfaces at that point of contact. In
involute teeth, the contact will always be on the line D E (Fig. 92),
but in epicycloidal, on the line of the generating circle, when that
circle is tangent at the line of centres; hence, the direction of
pressure will be a chord of the circle drawn from the pitch circle at
the line of centres to the position of contact considered. Comparing
involute with radial flanked epicycloidal teeth, let C D A (Fig. 91)
represent the rolling circle for the latter, and D C will be the
direction of pressure for the contact at D; but for point of contact
nearer C, the direction will be much nearer 90°, reaching that angle as
the point of contact approaches C. Now, D is the most remote legitimate
contact for involute teeth (and considering it so far as epicycloidal
struck with a generating circle of infinite diameter), we find that the
aggregate directions of the pressures of the teeth upon each other is
much nearer perpendicular in epicycloidal, than in involute gearing;
hence, the latter exert a greater pressure, tending to force the wheels
apart. Hence, the former are, in this respect, preferable.
It is to be observed, however, that in some experiments made by Mr.
Hawkins, he states that he found "no tendency to press the wheels apart,
which tendency would exist if the angle of the line D E (Fig. 92)
deviated more than 20° from the line of centres A B of the two wheels."
A method commonly employed in practice to strike the curves of involute
teeth, is as follows:--
In Fig. 93 let C represent the centre of a wheel, D D the full diameter,
P P the pitch circle, and E the circle of the roots of the teeth, while
R is a radial line. Divide on R, the distance between the pitch circle
and the wheel centre, into four equal parts, by 1, 2, 3, &c. From point
or division 2, as a centre, describe the semicircle S, cutting the wheel
centre and the pitch circle at its junction with R (as at A). From A,
with compasses set to the length of one of the parts, as A 3, describe
the arc B, cutting S at F, and F will be the centre from which one side
of the tooth may be struck; hence from F as a centre, with the compasses
set to the radius A B, mark the curve G. From the centre C strike,
through F, a circle T T, and the centres wherefrom to strike all the
teeth curves will fall on T T. Thus, to strike the other curve of the
tooth, mark off from A the thickness of the tooth on the pitch circle P
P, producing the point H. From H as a centre (with the same radius as
before,) mark on T T the point I, and from I, as a centre, mark the
curve J, forming the other side of the tooth.
[Illustration: Fig. 93.]
[Illustration: Fig. 94.]
In Fig. 94 the process is shown carried out for several teeth. On the
pitch circle P P, divisions 1, 2, 3, 4, &c., for the thickness of teeth
and the width of the spaces are marked. The compasses are set to the
radius by the construction shown in Fig. 93, then from _a_, the point
_b_ on T is marked, and from _b_ the curve _c_ is struck.
In like manner, from _d_, _g_, _j_, the centres _e_, _h_, _k_, wherefrom
to strike the respective curves, _f_, _i_, _l_, are obtained.
Then from _m_ the point _n_, on T T, is marked, giving the centre
wherefrom to strike the curve at _h_ _m_, and from _o_ is obtained the
point _p_, on T T, serving as a centre for the curve _e_ _o_.
A more simple method of finding point F is to make a sheet metal
template, C, as in Fig. 95, its edges being at an angle one to the other
of 75° and 30'. One of its edges is marked off in quarters of an inch,
as 1, 2, 3, 4, &c. Place one of its edges coincident with the line R,
its point touching the pitch circle at the side of a tooth, as at A, and
the centre for marking the curve on that side of the tooth will be found
on the graduated edge at a distance from A equal to one-fourth the
length of R.
[Illustration: Fig. 95.]
The result obtained in this process is precisely the same as that by the
construction in Fig. 93, as will be plainly seen, because there are
marked on Fig. 93 all the circles by which point F was arrived at in
Fig. 95; and line 3, which in Fig. 95 gives the centre wherefrom to
strike curve _o_, is coincident with point F, as is shown in Fig. 95. By
marking the graduated edge of C in quarter-inch divisions, as 1, 2, 3,
&c., then every division will represent the distance from A for the
centre for every inch of wheel radius. Suppose, for example, that a
wheel has 3 inches radius, then with the scale C set to the radial line
R, the centre therefrom to strike the curve _o_ will be at 3; were the
radius of the wheel 4 inches, then the scale being set the same as
before (one edge coincident with R), the centre for the curve _o_ would
be at 4, and arc T would require to meet the edge of C at 4. Having
found the radius from the centre of the wheel of point F for one tooth,
we may mark circle T, cutting point F, and mark off all the teeth by
setting one point of the compasses (set to radius A F) on one side of
the tooth and marking on circle T the centre wherefrom to mark the curve
(as _o_), continuing the process all around the wheel and on both sides
of the tooth.
This operation of finding the location for the centre wherefrom to
strike the tooth curves, must be performed separately for each wheel,
because the distance or radius of the tooth curves varies with the
radius of each wheel.
In Fig. 96 this template is shown with all the lines necessary to set
it, those shown in Fig. 95 to show the identity of its results with
those given in Fig. 93 being omitted.
The principles involved in the construction of a rack to work correctly
with a wheel or pinion, having involute teeth, are as in Fig. 97, in
which the pitch circle is shown by a dotted circle and the base circle
by a full line circle. Now the diameter of the base circle has been
shown to be arbitrary, but being assumed the radius B Q will be
determined (since it extends from the centre B to the point of contact
of D Q, with the base circle); B D is a straight line from the centre B
of the pinion to the pitch line of the rack, and (whatever the angle of
Q D to B D) the sides of the rack teeth must be straight lines inclined
to the pitch line of the rack at an angle equal to that of B D Q.
Involute teeth possess four great advantages--1st, they are thickest at
the roots, where they should be to have a maximum of strength, which is
of great importance in pinions transmitting much power; 2nd, the action
of the teeth will remain practically perfect, even though the wheels are
spread apart so that the pitch circles do not meet on the line of
centres; 3rd, they are much easier to mark, and truth in the marking is
easier attained; and 4th, they are much easier to cut, because the full
depth of the teeth can, on spur-wheels, in all cases be cut with one
revolving cutter, and at one passage of the cutter, if there is
sufficient power to drive it, which is not the case with epicycloidal
teeth whenever the flank space is wider below than it is at the pitch
circle. On account of the first-named advantage, they are largely
employed upon small gears, having their teeth cut true in a gear-cutting
machine; while on account of the second advantage, interchangeable
wheels, which are merely required to transmit motion, may be put in gear
without a fine adjustment of the pitch circle, in which case the wear of
the teeth will not prove destructive to the curves of the teeth. Another
advantage is, that a greater number of teeth of equal strength may be
given to a wheel than in the epicycloidal form, for with the latter the
space must at least equal the thickness of the tooth, while in involute
the space may be considerably less in width than the tooth, both
measured, of course, at the pitch circle. There are also more teeth in
contact at the same time; hence, the strain is distributed over more
teeth.
[Illustration: Fig. 96.]
These advantages assume increased value from the following
considerations.
In a train of epicycloidal gearing in which the pinion or smallest wheel
has radial flanks, the flanks of the teeth will become spread as the
diameters of the wheels in the train increase. Coincident with spread at
the roots is the thrust shown with reference to Fig. 39, hence under the
most favorable conditions the wear on the journals of the wheel axles
and the bearings containing them will take place, and the pitch circles
will separate. Now so soon as this separation takes place, the motion of
the wheels will not be as uniformly equal as when the pitch circles were
in contact on the line of centres, because the conditions under which
the tooth curves, necessary to produce a uniform velocity of motion,
were formed, will have become altered, and the value of those curves to
produce constant regularity of motion will have become impaired in
proportion as the pitch circles have separated.
[Illustration: Fig. 97.]
In a single pair of epicycloidal wheels in which the flanks of the teeth
are radial, the conditions are more favorable, but in this case the
pinion teeth will be weaker than if of involute form, while the wear of
the journals and bearings (which will take place to some extent) will
have the injurious effect already stated, whereas in involute teeth, as
has been noted, the separation of the pitch circles does not affect the
uniformity of the motion or the correct working of the teeth.
If the teeth of wheels are to be cut to shape in a gear-cutting machine,
either the cutters employed determine from their shapes the shapes or
curves of the teeth, or else the cutting tool is so guided to the work
that the curves are determined by the operations of the machine. In
either case nothing is left to the machine operator but to select the
proper tools and set them, and the work in proper position in the
machine. But when the teeth are to be cast upon the wheel the pattern
wherefrom the wheel is to be moulded must have the teeth proportioned
and shaped to proper curve and form.
Wheels that require to run without noise or jar, and to have uniformity
of motion, must be finished in gear-cutting machines, because it is
impracticable to cast true wheels.
When the teeth are to be cast upon the wheels the pattern-maker makes
templates of the tooth curves (by some one of the methods to be
hereafter described), and carefully cuts the teeth to shape. But the
production of these templates is a tedious and costly operation, and one
which is very liable to error unless much experience has been had. The
Pratt and Whitney Company have, however, produced a machine that will
produce templates of far greater accuracy than can be made by hand work.
These templates are in metal, and for epicycloidal teeth from 15 to a
rack, and having a diametral pitch ranging from 1-1/2 to 32.
The principles of action of the machine are that a segment of a ring
(representing a portion of the pitch circle of the wheel for whose teeth
a template is to be produced) is fixed to the frame of the machine. Upon
this ring rolls a disk representing the rolling, generating, or
describing circle, this disk being carried by a frame mounted upon an
arm representing the radius of the wheel, and therefore pivoted at a
point central to the ring. The describing disk is rolled upon the ring
describing the epicycloidal curve, and by suitable mechanical devices
this curve is cut upon a piece of steel, thus producing a template by
actually rolling the generating upon the base circle, and the rolling
motion being produced by positive mechanical motion, there cannot
possibly be any slip, hence the curves so produced are true epicycloids.
The general construction of the machine is shown in the side view, Fig.
98 (Plate I.), and top view, Fig. 99 (Plate I.), details of construction
being shown in Figs. 100, 101 (Plate I.), 102, 103, 104, 105, and 106. A
A is the segment of a ring whose outer edge represents a part of the
pitch circle. B is a disk representing the rolling or generating circle
carried by the frame C, which is attached to a rod pivoted at D. The
axis of pivot D represents the axis of the base circle or pitch circle
of the wheel, and D is adjustable along the rod to suit the radius of A
A, or what is the same thing, to equal the radius of the wheel for whose
teeth a template is to be produced.
When the frame C is moved its centre or axis of motion is therefore at D
and its path of motion is around the circumference of A A, upon the edge
of which it rolls. To prevent B from slipping instead of rolling upon A
A, a flexible steel ribbon is fastened at one end upon A A, passes
around the edge of A A and thence around the circumference of B, where
its other end is fastened; due allowance for the thickness of this
ribbon being made in adjusting the radii of A A and of B.
E´ is a tubular pivot or stud fixed on the centre line of pivots E and
D, and distant from the edge of A A to the same amount that E is. These
two studs E and E´ carry two worm-wheels F and F´ in Fig. 102, which
stand above A and B, so that the axis of the worm G is vertically over
the common tangent of the pitch and describing circles.
[Illustration: _VOL. I._ =TEMPLATE-CUTTING MACHINES FOR GEAR TEETH.=
_PLATE I._
Fig. 98.
Fig. 99.
Fig. 100.
Fig. 101.]
The relative positions of these and other parts will be most clearly
seen by a study of the vertical section, Fig. 102.[4] The worm G is
supported in bearings secured to the carrier C and is driven by another
small worm turned by the pulley I, as seen in Fig. 101 (Plate I.); the
driving cord, passing through suitable guiding pulleys, is kept at
uniform tension by a weight, however C moves; this is shown in Figs. 98
and 99 (Plate I.).
[4] From "The Teeth of Spur Wheels," by Professor McCord.
[Illustration: Fig. 102.]
Upon the same studs, in a plane still higher than the worm-wheels turn
the two disks H, H´, Figs. 103, 104, 105. The diameters of these are
equal, and precisely the same as those of the describing circles which
they represent, with due allowance, again, for the thickness of a steel
ribbon, by which these also are connected. It will be understood that
each of these disks is secured to the worm-wheel below it, and the outer
one of these, to the disk B, so that as the worm G turns, H and H´ are
rotated in opposite directions, the motion of H being identical with
that of B; this last is a rolling one upon the edge of A, the carrier C
with all its attached mechanism moving around D at the same time.
Ultimately, then, the motions of H, H´, are those of two equal
describing circles rolling in external and internal contact with a fixed
pitch circle.
[Illustration: Fig. 103.]
[Illustration: Fig. 104.]
In the edge of each disk a semicircular recess is formed, into which is
accurately fitted a cylinder J, provided with flanges, between which the
disks fit so as to prevent end play. This cylinder is perforated for the
passage of the steel ribbon, the sides of the opening, as shown in Fig.
103, having the same curvature as the rims of the disks. Thus when these
recesses are opposite each other, as in Fig. 104, the cylinder J fills
them both, and the tendency of the steel ribbon is to carry it along
with H when C moves to one side of this position, as in Fig. 105, and
along with H´ when C moves to the other side, as in Fig. 103.
This action is made positively certain by means of the hooks K, K´,
which catch into recesses formed in the upper flange of J, as seen in
Fig. 104. The spindles, with which these hooks turn, extend through the
hollow studs, and the coiled springs attached to their lower ends, as
seen in Fig. 102, urge the hooks in the directions of their points;
their motions being limited by stops _o_, _o´_, fixed, not in the disks
H, H´, but in projecting collars on the upper ends of the tubular studs.
The action will be readily traced by comparing Fig. 104 with Fig. 105;
as C goes to the left, the hook K´ is left behind, but the other one, K,
cannot escape from its engagement with the flange of J; which,
accordingly, is carried along with H by the combined action of the hook
and the steel ribbon.
On the top of the upper flange of J, is secured a bracket, carrying the
bearing of a vertical spindle L, whose centre line is a prolongation of
that of J itself. This spindle is driven by the spur-wheel N, keyed on
its upper end, through a flexible train of gearing seen in Fig. 99; at
its lower end it carries a small milling cutter M, which shapes the edge
of the template T, Fig. 105, firmly clamped to the framing.
[Illustration: Fig. 105.]
When the machine is in operation, a heavy weight, seen in Fig. 98 (Plate
I.), acts to move C about the pivot D, being attached to the carrier by
a cord guided by suitably arranged pulleys; this keeps the cutter M up
to its work, while the spindle L is independently driven, and the duty
left for the worm G to perform is merely that of controlling the motions
of the cutter by the means above described, and regulating their speed.
The centre line of the cutter is thus automatically compelled to travel
in the path R S, Fig. 105, composed of an epicycloid and a hypocycloid
if A A be the segment of a circle as here shown; or of two cycloids, if
A A be a straight bar. The radius of the cutter being constant, the edge
of the template T is cut to an outline also composed of two curves;
since the radius M is small, this outline closely resembles R S, but
particular attention is called to the fact that it is _not identical
with it, nor yet composed of truly epicycloidal curves of any generation
whatever:_ the result of which will be subsequently explained.
NUMBER AND SIZES OF TEMPLATES.
With a given pitch every additional tooth increases the diameter of the
wheel, and changes the form of the epicycloid; so that it would appear
necessary to have as many different cutters, as there are wheels to be
made, of any one pitch.
But the proportional increment, and the actual change of form, due to
the addition of one tooth, becomes less as the wheel becomes larger; and
the alteration in the outline soon becomes imperceptible. Going still
farther, we can presently add more teeth without producing a sensible
variation in the contour. That is to say, several wheels can be cut with
the same cutter, without introducing a perceptible error. It is obvious
that this variation in the form is least near the pitch circle, which is
the only part of the epicycloid made use of; and Prof. Willis many years
ago deduced theoretically, what has since been abundantly proved by
practice, that instead of an infinite number of cutters, 24 are
sufficient of one pitch, for making all wheels, from one with 12 teeth
up to a rack.
[Illustration: Fig. 106.]
Accordingly, in using the epicycloidal milling engine, for forming the
template, segments of pitch circles are provided of the following
diameters (in inches):
12, 16, 20, 27, 43, 100,
13, 17, 21, 30, 50, 150,
14, 18, 23, 34, 60, 300.
15, 19, 25, 38, 75,
In Fig. 106, the edge T T is shaped by the cutter T T, whose centre
travels in the path R S, therefore these two lines are at a constant
normal distance from each other. Let a roller P, of any reasonable
diameter, be run along T T, its centre will trace the line U V, which is
at a constant normal distance from T T, and therefore from R S. Let the
normal distance between U V and R S be the radius of another milling
cutter N, having the same axis as the roller P, and carried by it, but
in a different plane as shown in the side view; then whatever N cuts
will have R S for its contour, if it lie upon the same side of the
cutter as the template.
The diameter of the disks which act as describing circles is 7-1/2
inches, and that of the milling cutter which shapes the edge of the
template is 1/8 of an inch.
Now if we make a set of 1-pitch wheels with the diameters above given,
the smallest will have twelve teeth, and the one with fifteen teeth will
have radial flanks. The curves will be the same whatever the pitch; but
as shown in Fig. 106, the blank should be adjusted in the epicycloidal
engine, so that its lower edge shall be 1/16th of an inch (the radius of
the cutter M) above the bottom of the space; also its relation to the
side of the proposed tooth should be as here shown. As previously
explained, the depth of the space depends upon the pitch. In the system
adopted by the Pratt & Whitney Company, the whole height of the tooth is
2-1/8 times the diametral pitch, the projection outside the pitch circle
being just equal to the pitch, so that diameter of blank = diameter of
pitch circle + 2 × diametral pitch.
We have now to show how, from a single set of what may be called 1-pitch
templates, complete sets of cutters of the true epicycloidal contour may
be made of the same or any less pitch.
Now if T T be a 1-pitch template as above mentioned, it is clear that N
will correctly shape a cutting edge of a gear cutter for a 1-pitch
wheel. The same figure, reduced to half size, would correctly represent
the formation of a cutter for a 2-pitch wheel of the same number of
teeth; if to quarter size, that of a cutter for a 4-pitch wheel, and so
on.
But since the actual size and curvature of the contour thus determined
depend upon the dimensions and motion of the cutter N, it will be seen
that the same result will practically be accomplished, if these only be
reduced; the size of the template, the diameter and the path of the
roller remaining unchanged.
The nature of the mechanism by which this is effected in the Pratt &
Whitney system of producing epicycloidal cutters will be hereafter
explained in connection with cutters.
CHAPTER III.--THE TEETH OF GEAR-WHEELS (continued).
The revolving cutters employed in gear-cutting machines, gear-cutters,
or cutting engines (as the machines for cutting the teeth of gear-wheels
to shape are promiscuously termed), are of the form shown in Fig. 107,
which represents what is known as a Brown and Sharpe patent cutter,
whose peculiarities will be explained presently. This class of cutters
is made as follows:--
[Illustration: Fig. 107.]
A cast steel disk is turned in the lathe to the required form and
outline. After turning, its circumference is serrated as shown, so as to
provide protuberances, or teeth, on the face of which the cutting edges
may be formed. To produce a cutting edge it is necessary that the metal
behind that edge should slope or slant away leaving the cutting edge to
project. Two methods of accomplishing this are employed: in the first,
which is that embodied in the Brown and Sharpe system, each tooth has
the curved outline, forming what may be termed its circumferential
outline, of the same curvature and shape from end to end, and from front
to back, as it may more properly be termed, the clearance being given by
the back of the tooth approaching the centre of the cutter, so that if a
line be traced along the circumference of a tooth, from the cutting edge
to the back, it will approach the centre of the cutter as the back is
approached, but the form of the tooth will be the same at every point in
the line. It follows then that the radial faces of the teeth may be
ground away to sharpen the teeth without affecting the shape of the
tooth, which being made correct will remain correct.
This not only saves a great deal of labor in sharpening the teeth, but
also saves the softening and rehardening process, otherwise necessary at
each resharpening.
The ordinary method of producing the cutting edges after turning the
cutter and serrating it, is to cut away the metal with a file or rotary
cutter of some kind forming the cutting edge to correct shape, but
paying no regard to the shape of the back of the tooth more than to give
it the necessary amount of clearance. In this case the cutter must be
softened and reset to sharpen it. To bring the cutting edge up to a
sharp edge all around its profile, while still preserving the shape to
which it was turned, the pantagraphic engine, shown in Fig. 108, has
been made by the Pratt and Whitney Company. Figs. 109 and 110 show some
details of its construction.[5] "The milling cutter N is driven by a
flexible train acting upon the wheel O, whose spindle is carried by the
bracket B, which can slide from right to left upon the piece B, and this
again is free to slide in the frame F. These two motions are in
horizontal planes, and perpendicular to each other.
[5] From "The Teeth of Spur Wheels," by Professor McCord.
[Illustration: Fig. 108.]
"The upper end of the long lever P C is formed into a ball, working in a
socket which is fixed to P C. Over the cylindrical upper part of this
lever slides an accurately fitted sleeve D, partly spherical externally,
and working in a socket which can be clamped at any height on the frame
F. The lower end P of this lever being accurately turned, corresponds to
the roller P in Fig. 109, and is moved along the edge of the template T,
which is fastened in the frame in an invariable position.
"By clamping D at various heights, the ratio of the lever arms P D, P D,
may be varied at will, and the axis of N made to travel in a path
similar to that of the axis of P, but as many times smaller as we
choose; and the diameter of N must be made less than that of P in the
same proportion.
"The template being on the left of the roller, the cutter to be shaped
is placed on the right of N, as shown in the plan view at Z, because the
lever reverses the movement.
"This arrangement is not mathematically perfect, by reason of the
angular vibration of the lever. This is, however, very small, owing to
the length of the lever; it might have been compensated for by the
introduction of another universal joint, which would practically have
introduced an error greater than the one to be obviated, and it has,
with good judgment, been omitted.
"The gear-cutter is turned nearly to the required form, the notches are
cut in it, and the duty of the pantagraphic engine is merely to give the
finishing touch to each cutting edge, and give it the correct outline.
It is obvious that this machine is in no way connected with, or
dependent upon, the epicycloidal engine; but by the use of proper
templates it will make cutters for any desired form of tooth; and by its
aid exact duplicates may be made in any numbers with the greatest
facility.
[Illustration: Fig. 109.]
"It forms no part of our plan to represent as perfect that which is not
so, and there are one or two facts, which at first thought might seem
serious objections to the adoption of the epicycloidal system. These
are:
"1. It is physically impossible to mill out a _concave_ cycloid, by any
means whatever, because at the pitch line its radius of curvature is
zero, and a milling cutter must have a sensible diameter.
"2. It is impossible to mill out even a _convex_ cycloid or epicycloid,
by the means and in the manner above described.
[Illustration: Fig. 110.]
"This is on account of a hitherto unnoticed peculiarity of the curve at
a constant normal distance from the cycloid. In order to show this
clearly, we have, in Fig. 110, enormously exaggerated the radius C D, of
the milling cutter (M of Figs. 105 and 106). The outer curve H L,
evidently, could be milled out by the cutter, whose centre travels in
the cycloid C A; it resembles the cycloid somewhat in form, and presents
no remarkable features. But the inner one is quite different; it starts
at D, and at first goes down, _inside the circle whose radius is_ C D,
forms a cusp at E, then begins to rise, crossing this circle at G, and
the base line at F. It will be seen, then, that if the centre of the
cutter travel in the cycloid A C, its edge will cut away the part G E D,
leaving the template of the form O G I. Now if a roller of the same
radius C D, be rolled along this edge, its centre will travel in the
cycloid from A, to the point P, where a normal from G, cuts it; then the
roller will turn upon G as a fulcrum, and its centre will travel from P
to C, in a circular arc whose radius G P = C D.
"That is to say even a roller of the same size as the original milling
cutter, will not retrace completely the cycloidal path in which the
cutter travelled.
"Now in making a rack template, the cutter, after reaching C, travels in
the reversed cycloid C R, its left-hand edge, therefore, milling out a
curve D K, similar to H L. This curve lies wholly _outside_ the circle D
I, and therefore cuts O G at a point between F and G, but very near to
G. This point of intersection is marked S in Fig. 110, where the actual
form of the template O S K is shown. The roller which is run along this
template is _larger_, as has been explained, than the milling cutter.
When the point of contact reaches S (which so nearly corresponds to G
that they practically coincide), this roller cannot now swing about S
through an angle so great as P G C of Fig. 110; because at the root D,
the radius of curvature of D K is only equal to that of the cutter, and
G and S are so near the root that the curvature of S K, near the latter
point, is greater than that of the roller. Consequently there must be
some point U in the path of the centre of the roller, such, that when
the centre reaches it, the circumference will pass through S, and be
also tangent to S K. Let T be the point of tangency; draw S U and T U,
cutting the cycloidal path A R in X and Y. Then, U Y being the radius of
the new milling cutter (corresponding to N of Fig. 109), it is clear
that in the outline of the gear cutter shaped by it, the circular arc X
Y will be substituted for the true cycloid.
[Illustration: Fig. 111.]
THE SYSTEM PRACTICALLY PERFECT.
"The above defects undeniably exist; now, what do they amount to? The
diagram is drawn purposely with these sources of error greatly
exaggerated, in order to make their nature apparent and their existence
sensible. The diameters used in practice, as previously stated, are:
describing circle, 7-1/2 inches; cutter for shaping template, 1/8 of an
inch; roller used against edge of template, 1-1/8 inches; cutter for
shaping a 1-pitch gear cutter, 1 inch.
"With these data the writer has found that the _total length_ of the arc
X Y of Fig. 110, which appears instead of the cycloid in the outline of
a cutter for a 1-pitch rack, is less than 0.0175 inch; the real
_deviation_ from the true form, obviously, must be much less than that.
It need hardly be stated that the effect upon the velocity ratio of an
error so minute, and in that part of the contour, is so extremely small
as to defy detection. And the best proof of the practical perfection of
this system of making epicycloidal teeth is found in the smoothness and
precision with which the wheels run; a set of them is shown in gear in
Fig. 111, the rack gearing as accurately with the largest as with the
smallest. To which is to be added, finally, that objection taken, on
whatever grounds, to the epicycloidal form of tooth, has no bearing upon
the method above described of producing duplicate cutters for teeth of
any form, which the pantagraphic engine will make with the same facility
and exactness, if furnished with the proper templates.
"The front faces of the teeth of rotary cutters for gear-cutting are
usually radial lines, and are ground square across so as to stand
parallel with the axis of the cutter driving spindle, so that to
whatever depth the cutter may have entered the wheel, the whole of the
cutting edge within the wheel will meet the cut simultaneously. If this
is not the case the pressure of the cut will spring the cutter, and also
the arbor driving it, to one side. Suppose, for example, that the tooth
faces not being square across, one side of the teeth meets the work
first, then there will be as each tooth meets its cut an endeavour to
crowd away from the cut until such time as the other side of the tooth
also takes its cut."
It is obvious that rotating cutters of this class cannot be used to cut
teeth having the width of the space wider below than it is at the pitch
line. Hence, if such cutters are required to be used upon epicycloidal
teeth, the curves to be theoretically correct must be such as are due to
a generating circle that will give at least parallel flanks. From this
it becomes apparent that involute teeth being always thicker at the root
than at the pitch line, and the spaces being, therefore, narrower at the
root, may be cut with these cutters, no matter what the diameter of the
base circle of the involute.
To produce with revolving cutters teeth of absolutely correct
theoretical curvature of face and flank, it is essential that the cutter
teeth be made of the exact curvature due to the diameter of pitch circle
and generating circle of the wheel to be cut; while to produce a tooth
thickness and space width, also theoretically correct, the thickness of
the cutter must also be made to exactly answer the requirements of the
particular wheel to be cut; hence, for every different number of teeth
in wheels of an equal pitch a separate cutter is necessary if
theoretical correctness is to be attained.
This requirement of curvature is necessary because it has been shown
that the curvatures of the epicycloid and hypocycloid, as also of the
involute, vary with every different diameter of base circle, even
though, in the case of epicycloidal teeth, the diameter of the
generating circle remain the same. The requirement of thickness is
necessary because the difference between the arc and the chord pitch is
greater in proportion as the diameter of the base or pitch circle is
decreased.
But the difference in the curvature on the short portions of the curves
used for the teeth of fine pitches (and therefore of but little height)
due to a slight variation in the diameter of the base circle is so
minute, that it is found in practice that no sensible error is produced
if a cutter be used within certain limits upon wheels having a different
number of teeth than that for which the cutter is theoretically correct.
The range of these limits, however, must (to avoid sensible error) be
more confined as the diameter of the base circle (or what is the same
thing, the number of the teeth in the wheel) is decreased, because the
error of curvature referred to increases as the diameters of either the
base or the generating circles decrease. Thus the difference in the
curve struck on a base circle of 20 inches diameter, and one of 40
inches diameter, using the same diameter of generating circle, would be
very much less than that between the curves produced by the same
diameter of generating circle on base circles respectively 10 and 5
inches diameter.
For these reasons the cutters are limited to fewer wheels according as
the number of teeth decreases, or, per contra, are allowed to be used
over a greater range of wheels as the number of teeth in the wheels is
increased.
Thus in the Brown and Sharpe system for involute teeth there are 8
cutters numbered numerically (for convenience in ordering) from 1 to 8,
and in the following table the range of the respective cutters is shown,
and the number of teeth for which the cutter is theoretically correct is
also given.
BROWN AND SHARPE SYSTEM.
No. of cutter. Involute teeth. Teeth.
1 Used upon all wheels having from 135 teeth to a rack correct for 200
2 " " " " " 55 " to 134 teeth, 68
3 " " " " " 35 " to 54 " 40
4 " " " " " 26 " to 34 " 29
5 " " " " " 21 " to 25 " 22
6 " " " " " 17 " to 20 " 18
7 " " " " " 14 " to 16 " 16
8 " " " " " 12 " to 14 " 13
Suppose that it was required that of a pair of wheels one make twice the
revolutions of the other; then, knowing the particular number of teeth
for which the cutters are made correct, we may obtain the nearest
theoretically true results as follows: If we select cutters Nos. 8 and 4
and cut wheels having respectively 13 and 26 teeth, the 13 wheel will be
theoretically correct, and the 26 will contain the minute error due to
the fact that the cutter is used upon a wheel having three less teeth
than the number it is theoretically correct for. But we may select the
cutters that are correct for 16 and 29 teeth respectively, the 16th
tooth being theoretically correct, and the 29th cutter (or cutter No. 4
in the table) being used to cut 32 teeth, this wheel will contain the
error due to cutting 3 more teeth than the cutter was made correct for.
This will be nearer correct, because the error is in a larger wheel,
and, therefore, less in actual amount. The pitch of teeth may be
selected so that with the given number of teeth the diameters of the
wheels will be that required.
We may now examine the effect of the variation of curvature in
combination with that of the thickness, upon a wheel having less and
upon one having more teeth than the number in the wheel for which the
cutter is correct.
First, then, suppose a cutter to be used upon a wheel having less teeth
and it will cut the spaces too wide, because of the variation of
thickness, and the curves too straight or insufficiently curved because
of the error of curvature. Upon a wheel having more teeth it will cut
the spaces too narrow, and the curvature of the teeth too great; but, as
before stated, the number of wheels assigned to each cutter may be so
apportioned that the error will be confined to practically unappreciable
limits.
If, however, the teeth are epicycloidal, it is apparent that the spaces
of one wheel must be wide enough to admit the teeth of the other to a
depth sufficient to permit the pitch lines to coincide on the line of
centres; hence it is necessary in small diameters, in which there is a
sensible difference between the arc and the chord pitches, to confine
the use of a cutter to the special wheel for which it is designed, that
is, having the same number of teeth as the cutter is designed for.
Thus the Pratt and Whitney arrangement of cutters for epicycloidal teeth
is as follows:--
PRATT AND WHITNEY SYSTEM.
EPICYCLOIDAL TEETH.
[All wheels having from 12 to 21 teeth have a special cutter for each
number of teeth.][6]
Cutter correct for
No. of teeth.
23 Used on wheels having from 22 to 24 teeth.
25 " " " " 25 to 26 "
27 " " " " 26 to 29 "
30 " " " " 29 to 32 "
34 " " " " 32 to 36 "
38 " " " " 36 to 40 "
43 " " " " 40 to 46 "
50 " " " " 46 to 55 "
60 " " " " 55 to 67 "
76 " " " " 67 to 87 "
100 " " " " 87 to 123 "
150 " " " " 123 to 200 "
300 " " " " 200 to 600 "
Rack " " " " 600 to rack.
[6] For wheels having less than 12 teeth the Pratt and Whitney Co. use
involute cutters.
Here it will be observed that by a judicious selection of pitch and
cutters, almost theoretically perfect results may be obtained for
almost any conditions, while at the same time the cutters are so
numerous that there is no necessity for making any selection with a view
to taking into consideration for what particular number of teeth the
cutter is made correct.
For epicycloidal cutters made on the Brown and Sharpe system so as to
enable the grinding of the face of the tooth to sharpen it, the Brown
and Sharpe company make a separate cutter for wheels from 12 to 20
teeth, as is shown in the accompanying table, in which the cutters are
for convenience of designation denoted by an alphabetical letter.
24 CUTTERS IN EACH SET.
Letter A cuts 12 teeth.
B " 13 "
C " 14 "
D " 15 "
E " 16 "
F " 17 "
G " 18 "
H " 19 "
I " 20 "
J " 21 to 22 "
K " 23 " 24 "
L " 25 " 26 "
M " 27 " 29 "
N " 30 " 33 "
O " 34 " 37 "
P " 38 " 42 "
Q " 43 " 49 "
R " 50 " 59 "
S " 60 " 74 "
T " 75 " 99 "
U " 100 " 149 "
V " 150 " 249 "
W " 250 " Rack.
X " Rack.
In these cutters a shoulder having no clearance is placed on each side
of the cutter, so that when the cutter has entered the wheel until the
shoulder meets the circumference of the wheel, the tooth is of the
correct depth to make the pitch circles coincide.
In both the Brown and Sharpe and Pratt and Whitney systems, no side
clearance is given other than that quite sufficient to prevent the teeth
of one wheel from jambing into the spaces of the other. Pratt and
Whitney allow 1/8 of the pitch for top and bottom clearance, while Brown
and Sharpe allow 1/10 of the thickness of the tooth for top and bottom
clearance.
It may be explained now, why the thickness of the cutter if employed
upon a wheel having more teeth than the cutter is correct for,
interferes with theoretical exactitude.
[Illustration: Fig. 112.]
[Illustration: Fig. 113.]
First, then, with regard to the thickness of tooth and width of space.
Suppose, then, Fig. 112 to represent a section of a wheel having 12
teeth, then the pitch circle of the cutter will be represented by line
A, and there will be the same difference between the arc and chord pitch
on the cutter as there is on the wheel; but suppose that this same
cutter be used on a wheel having 24 teeth, as in Fig. 113, then the
pitch circle on the cutter will be more curved than that on the wheel as
denoted at C, and there will be more difference between the arc and
chord pitches on the cutter than there is on the wheel, and as a result
the cutter will cut a groove too narrow.
The amount of error thus induced diminishes as the diameter of the pitch
circle of the cutter is increased.
But to illustrate the amount. Suppose that a cutter is made to be
theoretically correct in thickness at the pitch line for a wheel to
contain 12 teeth, and having a pitch circle diameter of 8 inches, then
we have
3.1416 = ratio of circumference to diameter.
8 = diameter.
-------
Number of teeth = 12 ) 25.1328 = circumference.
-------
2.0944 = arc pitch of wheel.
If now we subtract the chord pitch from the arc pitch, we shall obtain
the difference between the arc and the chord pitches of the wheel; here
2.0944 = arc pitch.
2.0706 = chord pitch.
------
.0238 = difference between the arc and the chord pitch.
Now suppose this cutter to be used upon a wheel having the same pitch,
but containing 18 teeth; then we have
2.0944 = arc pitch.
2.0836 = chord pitch.
------
.0108 = difference between the arc and the chord pitch.
Then
.0238 = difference on wheel with 12 teeth.
.0108 = " " " 18 "
-----
.0130 = variation between the differences.
And the thickness of the tooth equalling the width of the space, it
becomes obvious that the thickness of the cutter at the pitch line being
correct for the 12 teeth, is one half of .013 of an inch too thin for
the 18 teeth, making the spaces too narrow and the teeth too thick by
that amount.
Now let us suppose that a cutter is made correct for a wheel having 96
teeth of 2.0944 arc pitch, and that it be used upon a wheel having 144
teeth. The proportion of the wheels one to the other remains as before
(for 96 bears the proportion to 144 as 12 does to 18).
Then we have for the 96 teeth
2.0944 = arc pitch.
2.0934 = chord pitch.
------
.0010 = difference.
For the 144 teeth we have
2.0944 = arc pitch.
2.0937 = chord pitch.
------
.0007 = difference.
We find, then, that the variation decreases as the size of the wheels
increases, and is so small as to be of no practical consequence.
If our examples were to be put into practice, and it were actually
required to make one cutter serve for wheels having, say, from 12 to 18
teeth, a greater degree of correctness would be obtained if the cutter
were made to some other wheel than the smallest. But it should be made
for a wheel having less than the mean diameter (within the range of 12
and 18), that is, having less than 15 teeth; because the difference
between the arc and chord pitch increases as the diameter of the pitch
circle increases, as already shown.
A rule for calculating the number of wheels to be cut by each cutter
when the number of cutters in the set and the number of teeth in the
smallest and largest wheel in the train are given is as follows:--
Rule.--Multiply the number of teeth in the smallest wheel of the train
by the number of cutters it is proposed to have in the set, and divide
the amount so obtained by a sum obtained as follows:--
From the number of cutters in the set subtract the number of the cutter,
and to the remainder add the sum obtained by multiplying the number of
the teeth in the smallest wheel of the set or train by the number of the
cutter and dividing the product by the number of teeth in the largest
wheel of the set or train.
Example.--I require to find how many wheels each cutter should cut,
there being 8 cutters and the smallest wheel having 12 teeth, while the
largest has 300.
Number of teeth in Number of cutters
smallest wheel. in the set.
12 × 8 = 96
Then
Number of cutters Number of
in set. cutter.
8 - 7 = 1
Then
Number of teeth in The number of the The number of the teeth
smallest wheel. cutter. in largest wheel.
12 × 8 ÷ 300
12
8
---
300 ) 960 ( 0.32
900
---
600
600
Now add the 1 to the .32 and we have 1.32, which we must divide into the
96 first obtained.
Thus
1.32 ) 96.00 ( 72
924
----
360
264
---
96
Hence No. 8 cutter may be used for all wheels that have between 72 teeth
and 300 teeth.
To find the range of wheels to be cut by the next cutter, which we will
call No. 7, proceed again as before, but using 7 instead of 8 as the
number of the cutter.
Thus
Number of teeth in Number of cutters in
smallest wheel. the set.
12 × 8 = 96
Then
Number of cutters Number of
in the set. cutters.
8 - 6 = 2
And
Number of teeth in The number of the The number of teeth
smallest wheel. cutter. in the largest wheel.
12 × 8 ÷ 300
Here
12
8
---
300 ) 960 ( 0.32
900
---
600
600
Add the 2 to the .32 and we have 2.32 to divide into the 96.
Thus
2.32 ) 96.00 ( 41
928
---
320
232
---
88
Hence this cutter will cut all wheels having not less than the 41 teeth,
and up to the 72 teeth where the other cutter begins. For the range of
the next cutter proceed the same, using 6 as the number of the cutter,
and so on.
By this rule we obtain the lowest number of teeth in a wheel for which
the cutter should be used, and it follows that its range will continue
upwards to the smallest wheel cut by the cutter above it.
Having by this means found the range of wheels for each cutter, it
remains to find for what particular number of teeth within that range
the cutter teeth should be made correct, in order to have whatever error
there may be equal in amount on the largest and smallest wheel of its
range. This is done by using precisely the same rule, but supposing
there to be twice as many cutters as there actually are, and then taking
the intermediate numbers as those to be used.
Applying this plan to the first of the two previous examples we have--
Number of teeth in the Number of cutters in
smallest wheel. the set.
12 × 16 = 192
Then
Number of cutters Number of the
in the set. cutter.
16 - 15 = 1
And
Number of teeth in The number of the The number of the teeth in
smallest wheel. cutter. the largest wheel.
12 × 15 ÷ 300
12
15
---
60
12
-----
300 ) 180.0 ( 0.6
1800
Then add the 1 to the .6 = 1.6, and this divided into 192 = 120.
By continuing this process for each of the 16 cutters we obtain the
following table:--
Number of Number of
Cutter. Teeth.
1 12
*2 13
3 14
*4 15
5 17
*6 18
7 20.61
*8 23
9 26
*10 30
11 35
*12 42
13 54
*14 75
15 120
*16 300
Suppose now we take for our 8 cutters those marked by an asterisk, and
use cutter 2 for all wheels having either 12, 13, or 14 teeth, then the
next cutter would be that numbered 4, cutting 14, 15, or 16 toothed
wheels, and so on.
A similar table in which 8 cutters are required, but 16 are used in the
calculation, the largest wheel having 200 teeth in the set, is given
below.
Number of Number of
Cutter. Teeth.
1 12.7
2 13.5
3 14.5
4 15.6
5 16.9
6 18
7 21
8 23.5
9 26.5
10 29
11 35
12 40.6
13 52.9
14 67.6
15 101
16 200
To assist in the selections as to what wheels in a given set the
determined number of cutters should be made correct for, so as to obtain
the least limit of error, Professor Willis has calculated the following
table, by means of which cutters may be selected that will give the same
difference of form between any two consecutive numbers, and this table
he terms the table of equidistant value of cutters.
TABLE OF EQUIDISTANT VALUE OF CUTTERS.
Number of Teeth.
Rack--300, 150, 100, 76, 60, 50, 43, 38, 34, 30, 27, 25, 23, 21, 20, 19,
17, 16, 15, 14, 13, 12.
The method of using the table is as follows:--Suppose it is required to
make a set of wheels, the smallest of which is to contain 50 teeth and
the largest 150, and it is determined to use but one cutter, then that
cutter should be made correct for a wheel containing 76; because in the
table 76 is midway between 50 and 150.
But suppose it were determined to employ two cutters, then one of them
should be made correct for a wheel having 60 teeth, and used on all the
wheels having between 50 and 76 teeth, while the other should be made
correct for a wheel containing 100 teeth, and used on all wheels
containing between 76 and 150 teeth.
In the following table, also arranged by Professor Willis, the most
desirable selection of cutters for different circumstances is given, it
being supposed that the set of wheels contains from 12 teeth to a rack.
+-----------+------------------------------------------------------+
|Number of | |
|cutters in | Number of Teeth in Wheel for which the Cutter is to |
|the set. | be made correct. |
+-----------+----+----+--------------------------------------------+
| 2 | 50 | 16 | |
| --+----+----+----+ |
| 3 | 75 | 25 | 15 | |
| --+----+----+----+----+ |
| 4 | 100| 34 | 20 | 14 | |
| --+----+----+----+----+----+----+ |
| 6 | 150| 50 | 30 | 21 | 16 | 13 | |
| --+----+----+----+----+----+----+----+----+ |
| 8 | 200| 67 | 40 | 29 | 22 | 18 | 15 | 13 | |
| --+----+----+----+----+----+----+----+----+----+----+ |
| 10 | 200| 77 | 50 | 35 | 27 | 22 | 19 | 16 | 14 | 13 | |
| --+----+----+----+----+----+----+----+----+----+----+----+
| | 300| 100| 60 | 43 | 34 |27 | 23 | 20 | 17 | 15 | 14 |
| 12 +----+----+----+----+----+----+----+----+----+----+----+
| | 13 | |
| --+----+----+----+----+----+----+----+----+----+----+----+
| | 300| 150| 100| 70 | 50 | 40 | 30 | 26 | 24 | 22 | 20 |
| 18 +----+----+----+----+----+----+----+----+----+----+----+
| | 18 | 16 | 15 | 14 | 13 | 12 | |
| --+----+----+----+----+----+----+----+----+----+----+----+
| |Rack| 300| 150| 100| 76 | 60 | 50 | 43 | 38 | 34 | 30 |
| +----+----+----+----+----+----+----+----+----+----+----+
| 24 | 27 | 25 | 23 | 21 | 20 | 19 | 18 | 17 | 16 | 15 | 14 |
| +----+----+----+----+----+----+----+----+----+----+----+
| | 13 | 12 | |
+-----------+----+----+--------------------------------------------+
Suppose now we take the cutters, of a given pitch, necessary to cut all
the wheels from 12 teeth to a rack, then the thickness of the teeth at
the pitch line will for the purposes of designation be the thickness of
the teeth of all the wheels, which thickness may be a certain proportion
of the pitch.
But in involute teeth while the depth of tooth on the cutter may be
taken as the standard for all the wheels in the range, and the actual
depth for the wheel for which the cutter is correct, yet the depth of
the teeth in the other wheels in the range may be varied sufficiently on
each wheel to make the thickness of the teeth equal the width of the
spaces (notwithstanding the variation between the arc and chord
pitches), so that by a variation in the tooth depth the error induced by
that variation may be corrected. The following table gives the
proportions in the Brown and Sharpe system.
+------------+-----------------+-----------------+
| Arc Pitch. | Depth of Tooth. | Depth in terms |
| | |of the arc pitch.|
+------------+-----------------+-----------------+
| inches. | inches. | inches. |
| 1.570 | 1.078 | .686 |
| 1.394 | .958 | .687 |
| 1.256 | .863 | .686 |
| 1.140 | .784 | .697 |
| 1.046 | .719 | .687 |
| .896 | .616 | .686 |
| .786 | .539 | .685 |
| .628 | .431 | .686 |
| .524 | .359 | .685 |
| .448 | .307 | .685 |
| .392 | .270 | .686 |
| .350 | .240 | .686 |
| .314 | .216 | .687 |
+------------+-----------------+-----------------+
To avoid the trouble of measuring, and to assist in obtaining accuracy
of depth, a gauge is employed to mark on the wheel face a line denoting
the depth to which the cutter should be entered.
Suppose now that it be required to make a set of cutters for a certain
range of wheels, and it be determined that the cutters be so constructed
that the greatest permissible amount of error in any wheel of the set be
1/100 inch. Then the curves for the smallest wheel, and those for the
largest in the set, and the amount of difference between them
ascertained, and assuming this difference to amount to 1/16 inch, which
is about 6/100, then it is evident that 6 cutters must be employed for
the set.
It has been shown that on bevel-wheels the tooth curves vary at every
point in the tooth breadth; hence it is obvious that the cutter being of
a fixed curve will make the tooth to that curve. Again, the thickness of
the teeth and breadth of the spaces vary at every point in the breadth,
while with a cutter of fixed thickness the space cut will be parallel
from end to end. To overcome these difficulties it is usual to give to
the cutter a curve corresponding to the curve required at the middle of
the wheel face and a thickness equal to the required width of space at
its smallest end, which is at the smallest face diameter.
The cutter thus formed produces, when passed through the wheel once, and
to the required depth, a tooth of one curve from end to end, having its
thickness and width of space correct at the smaller face diameter only,
the teeth being too thick and the spaces too narrow as the outer
diameter of the wheel is approached. But the position and line of
traverse of the cutter may be altered so as to take a second cut,
widening the space and reducing the tooth thickness at the outer
diameter.
By moving the cutter's position two or three times the points of contact
between the teeth may be made to occur at two or three points across the
breadth of the teeth and their points of contact; the wear will soon
spread out so that the teeth bear all the way across.
Another plan is to employ two or three cutters, one having the correct
curve for the inner diameter, and of the correct thickness for that
diameter, another having the correct curve for the pitch circle, and
another having the correct curve at the largest diameter of the teeth.
The thickness of the first and second cutters must not exceed the
required width of space at the small end, while that for the third may
be the same as the others, or equal to the thickness of the smallest
space breadth that it will encounter in its traverse along the teeth.
The second cutter must be so set that it will leave the inner end of the
teeth intact, but cut the space to the required width in the middle of
the wheel face. The third cutter must be so set as to leave the middle
of the tooth breadth intact, and cut the teeth to the required thickness
at the outer or largest diameter.
CUTTING WORM-WHEELS.
The most correct method of cutting the teeth of a worm-wheel is by means
of a worm-cutter, which is a worm of the pitch and form of tooth that
the working worm is intended to be, but of hardened steel, and having
grooves cut lengthways of the worm so as to provide cutting edges
similar to those on the cutter shown in Fig. 107.
The wheel is mounted on an arbor or mandril free to rotate on its axis
and at a right angle to the cutter worm, which is rotated and brought to
bear upon the perimeter of the worm-wheel in the same manner as the
working worm-wheel when in action. The worm-cutter will thus cut out the
spaces in the wheel, and must therefore be of a thickness equal to those
spaces. The cutter worm acting as a screw causes the worm-wheel to
rotate upon its axis, and therefore to feed to the cutter.
In wheels of fine pitch and small diameter this mode of procedure is a
simple matter, especially if the form of tooth be such that it is
thicker, as the root of the tooth is approached from the pitch line,
because in that case the cutter worm may be entered a part of the depth
in the worm-wheel and a cut be taken around the wheel. The cutter may
then be moved farther into the wheel and a second cut taken around the
wheel, so that by continuing the process until the pitch line of the
cutter worm coincides with that of the worm-cutter, the worm-wheel may
be cut with a number of light cuts, instead of at one heavy cut.
But in the case of large wheels the strain due to such a long line of
cutting edge as is possessed by the cutter worm-teeth springs or bends
the worm-wheel, and on account of the circular form of the breadth of
the teeth this bending or spring causes that part of the tooth arc above
the centre of the wheel thickness to lock against the cutter.
To prevent this, several means may be employed. Thus the grooves forming
the cutting edges of the worm-cutter may wind spirally along instead of
being parallel to the axis of the cutter.
The distance apart of these grooves may be greater than the breadth of
tooth a width of worm-wheel face, in which case the cutting edge of one
tooth only will meet the work at one time. In addition to this two
stationary supports may be placed beneath the worm-wheel (one on each
side of the cutter). But on coarse pitches with their corresponding
depth of tooth, the difficulty presents itself, that the arbor driving
the worm-cutter will spring, causing the cutter to lift and lock as
before; hence it is necessary to operate on part of the space at a time,
and shape it out to so nearly the correct form that the finishing cut
may be a very light one indeed, in which case the worm-cutter will
answer for the final cut.
The removal of the surplus metal preparatory to the introduction of the
worm-cutter to finish, may be made with a cutter-worm that will cut out
a narrow groove being of the thickness equal to the bottom of the tooth
space and cutting on its circumference only. This cutter may be fed into
the wheel to the permissible depth of cut, and after the cut is taken
all around the wheel, it may be entered deeper and a second cut taken,
and so on until it has entered the wheel to the necessary depth of
tooth. A second cutter-worm may then be used, it being so shaped as to
cut the face curve only of the teeth. A third may cut the flank curve
only, and finally a worm-cutter of correct form may take a finishing cut
over both the faces and the flanks. In this manner teeth of any pitch
and depth may be cut. Another method is to use a revolving cutter such
as shown in Fig. 107, and to set it at the required angle to the wheel,
and then take a succession of cuts around the wheel, the first cut
forming a certain part of the tooth depth, the second increasing this
depth, and so on until the final cut forms the tooth to the requisite
depth. In this case the cutter operates on each space separately, or on
one space only at a time, and the angle at which to set the cutter may
be obtained as follows in Fig. 114. Let the length of the line A A equal
the diameter of the worm at the pitch circle, and B B (a line at a right
angle to A A) represent the axial line of the worm. Let the distance C
equal the pitch of the teeth, and the angle of the line D with A A or B
B according to circumstances, will be that to which the cutter must be
set with reference to the tooth.
[Illustration: Fig. 114.]
If then a piece of sheet metal be cut to the lines A, D, and the cutter
so set that with the edge D of the piece held against the side face of
the cutter (which must be flat or straight across), the edge A will
stand truly vertical, and the cutter will be at the correct angle
supposing the wheel to be horizontal.
[Illustration: Fig. 115.]
[Illustration: Fig. 116.]
In making patterns wherefrom gear-wheels may be cast in a mould, the
true curves are frequently represented by arcs of circles struck from
the requisite centres and of the most desirable radius with compasses,
and this will be treated after explaining the pattern maker's method of
obtaining true curves by rolling segments by hand. If, then, the wheels
are of small diameter, as say, less than 12 inches in diameter, and
precision is required, it is best to turn in the lathe wooden disks
representing in their diameters the base and generating circles. But
otherwise, wooden segments to answer the same purpose may be made as
from a piece of soft wood, such as pine or cedar, about three-eighths
inch thick, make two pieces A and B, in Fig. 115, and trim the edges C
and D to the circle of the pitch line of the required wheel. If the
diameter of the pitch circle is marked on a drawing, the pieces may be
laid on the drawing and sighted for curvature by the eye. In the absence
of a drawing, strike a portion of the pitch circle with a pair of
sharp-pointed compasses on a piece of zinc, which will show a very fine
line quite clear. After the pieces are filed to the circle, try them
together by laying them flat on a piece of board, bringing the curves in
contact and sweeping A against B, and the places of contact will plainly
show, and may be filed until continuous contact along the curves is
obtained. Take another similar piece of wood and form it as shown in
Fig. 116, the edge E representing a portion of the rolling circle. In
preparing these segments it is an excellent plan to file the convex
edges, as shown in Fig. 117, in which P is a piece of iron or wood
having its surface S trued; F is a file held firmly to S, while its
surface stands vertical, and T is the template laid flat on S, while
swept against the file. This insures that the edge shall be square
across or at least at the same angle all around, which is all that is
absolutely necessary. It is better, however, that the edges be square.
So likewise in fitting A and B (Fig. 115) together, they should be laid
flat on a piece of board. This will insure that they will have contact
clear across the edge, which will give more grip and make slip less
likely when using the segments. Now take a piece of stiff drawing paper
or of sheet zinc, lay segment A upon it, and mark a line coincident with
the curved edge. Place the segment representing the generating circle
flat on the paper or zinc, hold its edge against segment A, and roll it
around a sufficient distance to give as much of the curve as may be
required; the operation being illustrated in Fig. 118, in which A is the
segment representing the pitch or base circle, E is the segment
representing the generating circle, P is the paper, C the curve struck
by the tracing point or pencil O.
[Illustration: Fig. 117.]
[Illustration: Fig. 118.]
This tracing point should be, if paper be used to trace on, a piece of
the _hardest_ pencil obtainable, and should be filed so that its edge,
if flat, shall stand as near as may be in the line of motion when
rolled, thus marking a fine line. If sheet zinc be used instead of paper
a needle makes an excellent tracing point. Several of the curves, C,
should be struck, moving the position of the generating segment a little
each time.
[Illustration: Fig. 119.]
On removing the segments from the paper, there will appear the lines
shown in Fig. 119; A representing the pitch circle, and O O O the curves
struck by the tracing point.
Cut out a piece of sheet zinc so that its edge will coincide with the
curve A and the epicycloid O, trying it with all four of the epicycloids
to see that no slip has occurred when marking them; shape a template as
shown in Fig. 120. Cutting the notches at _a_ _b_, acts to let the file
clear well when filing the template, and to allow the scriber to go
clear into the corner. Now take the segment A in Fig. 118, and use it as
a guide to carry the pitch circle across the template as at P, in Fig.
120. A zinc template for the flank curve is made after the same manner,
using the rolling segment in conjunction with the segment B in Fig. 115.
[Illustration: Fig. 120.]
But the form of template for the flank should be such as shown in Fig.
121, the curve P representing, and being of the same radius as the pitch
circle, and the curve F being that of the hypocycloid. Both these
templates are set to the pitch circles and to coincide with the marks
made on the wheel teeth to denote the thickness, and with a hardened
steel point a line is traced on the tooth showing the correct curve for
the same.
[Illustration: Fig. 121.]
An experienced hand will find no difficulty in producing true templates
by this method, but to avoid all possibility of the segments slipping on
coarse pitches, and with large segments, the segments may be connected,
as shown in Fig. 122, in which O represents a strip of steel fastened at
one end into one segment and at the other end to the other segment.
Sometimes, indeed, where great accuracy is requisite, two pieces of
steel are thus employed, the second one being shown at P P, in the
figure. The surfaces of these pieces should exactly coincide with the
edge of the segments.
[Illustration: Fig. 122.]
[Illustration: Fig. 123.]
[Illustration: Fig. 124.]
[Illustration: Fig. 125.]
[Illustration: Fig. 126.]
The curve templates thus produced being shaped to apply to the pitch
circle may be correctly applied to that circle independently of its
concentricity to the wheel axis or of the points of the teeth, but if
the points of the teeth are turned in the lathe so as to be true (that
is, concentric to the wheel axis) the form of the template may be such
as shown in Fig. 123, the radius of the arc A A equalling that of the
addendum circle or circumference at the points of the teeth, and the
width at B (the pitch circle) equaling the width of a space instead of
the thickness of a tooth. The curves on each side of the template may in
this case be filed for the full side of a tooth on each side of the
template so that it will completely fill the finished space, or the
sides of two contiguous teeth may be marked at one operation. This
template may be set to the marks made on the teeth at the pitch circle
to denote their requisite thickness, or for greater accuracy, a similar
template made double so as to fill two finished tooth spaces may be
employed, the advantage being that in this case the template also serves
to mark or test the thickness of the teeth. Since, however, a double
template is difficult to make, a more simple method is to provide for
the thickness of a tooth, the template shown in Fig. 124, the width from
A to B being either the thickness of tooth required or twice the
thickness of a tooth plus the width of a space, so that it may be
applied to the outsides of two contiguous teeth. The arc C may be made
both in its radius and distance from the pitch circle D D to equal that
of the addendum circle, so as to serve as a gauge for the tooth points,
if the latter are not turned true in the lathe, or to rest on the
addendum circle (if the teeth points are turned true), and adjust the
pitch circle D D to the pitch circle on the wheel.
The curves for the template must be very carefully filed to the lines
produced by the rolling segments, because any error in the template is
copied on every tooth marked from it. Furthermore, instead of drawing
the pitch circle only, the addendum circle and circle for the roots of
the teeth or spaces should also be drawn, so that the template may be
first filed to them, and then adjusted to them while filing the edges to
the curves.
Another form of template much used is shown in Fig. 125. The curves A
and B are filed to the curve produced by rolling segments as before, and
the holes C, D, E, are for fastening the template to an arm, such as
shown in Fig. 126, which represents a section of a wheel W, with a plug
P, fitting tightly into the hub H of the wheel. This plug carries at its
centre a cylindrical pin on which pivots the arm A. The template T is
fastened to the arm by screws, and set so that its pitch circle
coincides with the pitch circle P on the wheel, when the curves for one
side of all the teeth may be marked. The template must then be turned
over to mark the other side of the teeth.
The objection to this form of template is that the length of arc
representing the pitch circle is too short, for it is absolutely
essential that the pitch line on the template (or line representing the
arc of the addendum if that be used) be greater than the width of a
single tooth, because an error of the thickness of a line (in the
thickness of a tooth), in the coincidence of the pitch line of the
template with that of the tooth, would throw the tooth curves out to an
extent altogether inadmissible where true work is essential.
[Illustration: Fig. 127.]
To overcome this objection the template may be made to equal half the
thickness of a tooth and its edge filed to represent a radial line on
the wheel. But there are other objections, as, for example, that the
template can only be applied to the wheel when adjusted on the arm shown
in Fig. 126, unless, indeed, a radial line be struck on every tooth of
the wheel. Again, to produce the template a radial line representing the
radius of the wheel must be produced, which is difficult where segments
only are used to produce the curves. It is better, therefore, to form
the template as shown in Fig. 127, the projections at A B having their
edges filed to coincide with the pitch circle P, so that they may be
applied to a length of one arc of pitch circle at least equal to the
pitch of the teeth.
The templates for the tooth curves being obtained, the wheel must be
divided off on the pitch circle for the thickness of the teeth and the
width of the spaces, and the templates applied to the marks or points of
division to serve as guides to mark the tooth curves. Since, however, as
already stated, the tooth curves are as often struck by arcs of circles
as by templates, the application of such arcs and their suitability may
be discussed.
MARKING THE CURVES BY HAND.
In the employment of arcs of circles several methods of finding the
necessary radius are found in practice.
[Illustration: Fig. 128.]
In the best practice the true curve is marked by the rolling segments
already described, and the compass points are set by trial to that
radius which gives an arc nearest approaching to the true face and flank
curves respectively. The degree of curve error thus induced is
sufficient that the form of tooth produced cannot with propriety be
termed epicycloidal teeth, except in the case of fine pitches in which
the arc of a circle may be employed to so nearly approach the true curve
as to be permissible as a substitute. But in coarse pitches the error is
of much importance. Thus in Fig. 128 is shown the curve of the _former_
or _template_ attachment used on the celebrated Corliss Bevel Gear
Cutting Machine, to cut the teeth on the bevel-wheels employed upon the
line shafting at the Centennial Exhibition. These gears, it may be
remarked, were marvels of smooth and noiseless running, and attracted
wide attention both at home and abroad. The engraving is made from a
drawing marked direct from the _former_ itself, and kindly furnished me
by Mr. George H. Corliss. A A is the face and B B the flank of the
tooth, C C is the arc of a circle nearest approaching to the face curve,
and D D the arc of a circle nearest approaching the flank curve. In the
face curve, there are but two points where the circle coincides with the
true curve, while in the flank there are three such points; a circle of
smaller radius than C C would increase the error at _b_, but decrease it
at _a_; one of a greater radius would decrease it at _b_, and increase
it at _a_. Again, a circle larger in radius than D D would decrease the
error at _e_ and increase it at _f_; while one smaller would increase it
at _e_ and decrease it at _f_. Only the working part of the tooth is
given in the illustration, and it will be noted that the error is
greatest in the flank, although the circle has three points of
coincidence.
[Illustration: Fig. 129.]
In this case the depth of the _former_ tooth is about three and
three-quarter times greater than the depth of tooth cut on the
bevel-wheels; hence, in the figure the actual error is magnified three
and three-quarter times. It demonstrates, however, the impropriety of
calling coarsely pitched teeth that are found by arcs of circles
"epicycloidal" teeth.
When, however, the pitches of the teeth are fine as, say an inch or
less, the coincidence of an arc of a circle with the true curve is
sufficiently near for nearly all practical purposes, and in the case of
cast gear the amount of variation in a pitch of 2 inches would be
practically inappreciable.
To obtain the necessary set of the compasses to mark the curves, the
following methods may be employed.
First by rolling the true curves with segments as already described, and
the setting the compass points (by trial) to that radius which gives an
arc nearest approaching the true curves. In this operation it is not
found that the location for the centre from which the curve must be
struck always falls on the pitch circle, and since that location will
for every tooth curve lie at the same radius from the wheel centre it is
obvious that after the proper location for one of the curves, as for the
first tooth face or tooth flank as the case may be, is found, a circle
may be struck denoting the radius of the location for all the teeth. In
Fig. 129, for example, P P represents the pitch circle, A B the radius
that will produce an arc nearest approaching the true curve produced by
rolling segments, and A the location of the centre from which the face
arc B should be struck. The point A being found by trial with the
compasses applied to the curve B, the circle A C may be struck, and the
location for the centres from which the face arcs of each tooth must be
struck will also fall on this circle, and all that is necessary is to
rest one point of the compasses on the side of the tooth as, say at E,
and mark on the second circle A C the point C, which is the location
wherefrom to mark the face arc D.
If the teeth flanks are not radial, the locations of the centre
wherefrom to strike the flank curves are found in like manner by trial
of the compasses with the true curves, and a third circle, as I in Fig.
130, is struck to intersect the first point found, as at G in the
figure. Thus there will be upon the wheel face three circles, P P the
pitch circle, J J wherefrom to mark the face curves, and I wherefrom to
mark the flank curves.
When this method is pursued a little time may be saved, when dividing
off the wheel, by dividing it into as many divisions as there are teeth
in the wheel, and then find the locations for the curves as in Fig. 131,
in which 1, 2, 3 are points of divisions on the pitch circle P P, while
A, B, struck from point 2, are centres wherefrom to strike the arcs E,
F; C, D, struck also from point 2 are centres wherefrom to strike the
flank curves G, H.
[Illustration: Fig. 130.]
It will be noted that all the points serving as centres for the face
curves, in Fig. 130, fall within a space; hence if the teeth were rudely
cast in the wheel, and were to be subsequently cut or trimmed to the
lines, some provision would have to be made to receive the compass
points.
To obviate the necessity of finding the necessary radius from rolling
segments various forms of construction are sometimes employed.
[Illustration: Fig. 131.]
Thus Rankine gives that shown in Fig. 132, which is obtained as follows.
Draw the generating circle D, and A D the line of centres. From the
point of contact at C, mark on circle D, a point distance from C
one-half the amount of the pitch, as at P, and draw the line P C of
indefinite length beyond C. Draw a line from P, passing through the line
of centres at E, which is equidistant between C and A. Then multiply
the length from P to C by the distance from A to D, and divide by the
distance between D and E. Take the length and radius so found, and mark
it upon P C, as at F, and the latter will be the location of centre for
compasses to strike the face curve.
[Illustration: Fig. 132.]
Another method of finding the face curve, with compasses, is as follows:
In Fig. 133, let P P represent the pitch circle of the wheel to be
marked, and B C the path of the centre of the generating or describing
circle as it rolls outside of P P. Let the point B represent the centre
of the generating circle when that circle is in contact with the pitch
circle at A. Then from B, mark off on B C any number of equidistant
points, as D, E, F, G, H, and from A, mark on the pitch circle, points
of division, as 1, 2, 3, 4, 5, at the intersection of radial lines from
D, E, F, G, and H. With the radius of the generating circle, that is, A
B, from B, as a centre, mark the arc I, from D the arc J, from E the arc
K, &c., to M, marking as many arcs as there are points of division on B
C. With the compasses set to the radius of divisions 1, 2, step off on
arc M the five divisions, N, O, S, T, V, and V will be a point in the
epicycloidal curves. From point of division 4, step off on L four points
of division, as _a_, _b_, _c_, _d_, and _d_ will be another point in the
epicycloidal curve. From point 3 set off three divisions on K, from
point 2 two dimensions on L, and so on, and through the points so
obtained, draw by hand or with a scroll the curve represented in the cut
by curve A V.
[Illustration: Fig. 133.]
Hypocycloids for the flanks of the teeth may be traced in a similar
manner. Thus in Fig. 134 P P is the pitch circle, and B C the line of
motion of the centre of the generating circle to be rolled within P P,
and R a radial line. From 1 to 6 are points of equal division on the
pitch circle, and D to I are arc locations for the centre of the
generating circle. Starting from A, which represents the supposed
location for the centre of the generating circle, the point of contact
between the generating and base circles will be at B. Then from 1 to 6
are points of equal division on the pitch circle, and from D to I are
the corresponding locations for the centres of the generating circle.
From these centres the arcs J, K, L, M, N, O, are struck. From 6 mark
the six points of division from _a_ to _f_, and _f_ is a point in the
curve. Five divisions on N, four on M, and so on, give respectively
points in the curve which is marked in the figure from A to _f_.
There is this, however, to be noted concerning the constructions of the
last two figures. Since the circle described by the centre of the
generating circle is of different arc or curve to that of the pitch
circle, the chord of an arc having an equal length on each will be
different. The amount is so small as to be practically correct. The
direction of the error is to give to the curves a less curvature, as
though they had been produced by a generating circle of larger diameter.
Suppose, for example, that the difference between the arc N 5 (Fig. 133)
and its chord is .1, and that the difference between the arc 4 5, and
its chord is .01, then the error in one step is .09, and, as the point V
is formed in 5 steps, it will contain this error multiplied five times.
Point _d_ would contain it multiplied four times, because it has 4
steps, and so on.
The error will increase in proportion as the diameter of the generating
is less than that of the pitch circle, and though in large wheels,
working with large wheels (so that the difference between the radius of
the generating circle and that of the smallest wheel is not excessive),
it is so small as to be practically inappreciable, yet in small wheels,
working with large ones, it may form a sensible error.
[Illustration: Fig. 134.]
An instrument much employed in the best practice to find the radius
which will strike an arc of a circle approximating the true epicycloidal
curve, _and for finding at the same time_ the location of the centre
wherefrom that curve should be struck, is found in the Willis'
odontograph. This is, in reality, a scale of centres or radii for
different and various diameters of wheels and generating circles. It
consists of a scale, shown in Fig. 135, and is formed of a piece of
sheet metal, one edge of which is marked or graduated in divisions of
one-twentieth of an inch. The edge meeting the graduated edge at O is at
angle of 75° to the graduated edge.
On one side of the odontograph is a table (as shown in the cut), for the
flanks of the teeth, while on the other is the following table for the
faces of the teeth:
TABLE SHOWING THE PLACE OF THE CENTRES UPON THE SCALE.
CENTRES FOR THE FACES OF THE TEETH.
Pitch in Inches and Parts.
+------+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|No. of|1/4|3/8|1/2|5/8|3/4| 1|1- |1- |1- | 2|2- |2- | 3|3- |
|Teeth | | | | | | |1/4|1/2|3/4| |1/4|1/2| |1/2|
|------+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 12 | 1| 2| 2| 3| 4| 5| 6| 7| 9| 10| 11| 12| 15| 17|
| 15 | ..| ..| 3| ..| ..| ..| 7| 8| 10| 11| 12| 14| 17| 19|
| 20 | 2| ..| ..| 4| 5| 6| 8| 9| 11| 12| 14| 15| 18| 21|
| 30 | ..| 3| 4| ..| ..| 7| 9| 10| 12| 14| 16| 18| 21| 25|
| 40 | ..| ..| ..| ..| 6| 8| ..| 11| 13| 15| 17| 19| 23| 26|
| | | | | | | | | | | | | | | |
| 60 | ..| ..| ..| 5| ..| ..| 10| 12| 14| 16| 18| 20| 25| 29|
| 80 | ..| ..| ..| ..| ..| 9| 11| 13| 15| 17| 19| 21| 26| 30|
| 100 | ..| ..| ..| ..| 7| ..| ..| ..| ..| 18| 20| 22| ..| 31|
| 150 | ..| ..| 5| 6| ..| ..| ..| 14| 16| 19| 21| 23| 27| 32|
|Rack. | ..| 4| ..| ..| ..| 10| 12| 15| 17| 20| 22| 25| 30| 34|
+------+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
The method of using the instrument is as follows: In Fig. 136, let C
represent the centre, and P the pitch circle of a wheel to contain 30
teeth of 3 inch arc pitch. Draw the radial line L, meeting the pitch
circle at A. From A mark on the pitch circle, as at B, a radius equal to
the pitch of the teeth, and the thickness of the tooth as A _k_. Draw
from B to C the radial line E. Then for the flanks place the slant edge
of the odontograph coincident and parallel with E, and let its corners
coincide with the pitch circle as shown. In the table headed _centres
for the flanks of the teeth_, look down the column of 3 inch pitch, and
opposite to the 30 in the column of numbers of teeth, will be found the
number 49, which indicates that the centre from which to draw an arc for
the flank is at 49 on the graduated edge of the odontograph, as denoted
in the cut by _r_. Thus from _r_ to the side _k_ of the tooth is the
radius for the compasses, and at _r_, or 49, is the location for the
centre to strike the flank curve _f_. For the face curve set the slant
edge of the odontograph coincident with the radial line L, and in the
table of centres for the faces of teeth, look down the column of 3-inch
pitch, and opposite to 30 in the number of teeth column will be found
the number 21, indicating that at 21 on the graduated edge of the
odontograph, is the location of the centre wherefrom to strike the curve
_d_ for the face of the tooth, this location being denoted in the cut at
R.
[Illustration: Fig. 135.
TABLE SHOWING THE PLACE OF THE CENTRES UPON THE SCALE.
+--------------------------------------------------------------+
| CENTRES FOR THE FLANKS OF THE TEETH. |
+--------------------------------------------------------------+
| PITCH IN INCHES AND PARTS. |
+------+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|Number| | | | | | | | | | | | | | |
| of | | | | | | 1 | 1-| 1-| 1-| 2 | 2-| 2-| 3 | 3-|
|teeth.|1/4|3/8|1/2|5/8|3/4| |1/4|1/2|3/4| |1/4|1/2| |1/2|
+------+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 13| 32| 48| 64| 80| 96|129|160|193|225|257|289|321|386|450|
| 14| 17| 26| 35| 43| 52| 69| 87|104|121|139|156|173|208|242|
| 15| 12| 18| 25| 31| 37| 49| 62| 74| 86| 99|111|123|148|173|
| 16| 10| 15| 20| 25| 30| 40| 50| 59| 69| 79| 89| 99|119|138|
| 17| 8| 13| 17| 21| 25| 34| 43| 50| 59| 67| 75| 84|101|117|
| 18| 7| 11| 15| 19| 22| 30| 37| 45| 52| 59| 67| 74| 89|104|
| 19|...| 10| 13| 17| 20| 27| 35| 40| 47| 54| 60| 67| 80| 94|
| 20| 6| 9| 12| 16| 19| 25| 31| 37| 43| 49| 56| 62| 74| 86|
| 22| 5| 8| 11| 14| 16| 22| 27| 33| 39| 43| 49| 54| 65| 76|
| 24|...| 7| 10| 12| 15| 20| 25| 30| 35| 40| 45| 49| 59| 69|
| 26|...|...| 9| 11| 14| 18| 23| 27| 32| 37| 41| 46| 55| 64|
| 28| 4| 6|...|...| 13|...| 22| 26| 30| 35| 40| 43| 52| 60|
| 30|...|...| 8| 10| 12| 17| 21| 25| 29| 33| 37| 41| 49| 58|
| 35|...|...|...| 9| 11| 16| 19| 23| 26| 30| 34| 38| 45| 53|
| 40|...| 5| 7|...|...| 15| 18| 21| 25| 28| 32| 35| 42| 49|
| 60| 3|...| 6| 8| 9| 13| 15| 19| 22| 25| 28| 31| 37| 43|
| 80|...| 4|...| 7|...| 12|...| 17| 20| 23| 26| 29| 35| 41|
| 100|...|...|...|...| 8| 11| 14|...|...| 22| 25| 28| 34| 39|
| 150|...|...| 5|...|...|...| 13| 16| 19| 21| 24| 27| 32| 38|
| Rack.| 2|...|...| 6| 7| 10| 12| 15| 17| 20| 22| 25| 30| 34|
+------+---+---+---+---+---+---+---+---+---+---+---+---+---+---+]
The requisite number on the graduated edge for pitches beyond 3-1/2 (the
greatest given in the tables), may be obtained by direct proportion from
those given in the tables. Thus for 4 inch pitch, by doubling the
numbers given for a 2 inch pitch, containing the same number of teeth,
for 4-1/2 inch pitch by doubling the numbers given for a 2-1/4 inch
pitch. If the pitch be a fraction that cannot be so obtained, no serious
error will be induced if the nearest number marked be taken.
[Illustration: Fig. 136.]
An improved form of template odontograph, designed by Professor Robinson
of the Illinois School of Industry, is shown in Fig. 137.
In this instrument the curved edge, having graduated lines, approaches
more nearly to the curves produced by rolling circles than can be
obtained from any system in which an arc of a circle is taken to
represent the curve; hence, that edge is applied direct to the teeth and
used as a template wherefrom to mark the curve. The curve is a
logarithmic spiral, and the use of the instrument involves no other
labor than that of setting it in position. The applicability of this
curve, for the purpose, arises from two of its properties: first, that
the involute of the logarithmic spiral is another like spiral with poles
in common; and, second, that the obliquity or angle between a normal and
radius sector is constant, the latter property being possessed by this
curve only. By the first property it is known that a line, lying tangent
to the curve C E H, will be normal or perpendicular to the curve C D B;
so that when the line D E F is tangent to the pitch line, the curve A D
B will coincide very closely with the true epicycloidal curve, or,
rather, with that portion of it which is applied to the tooth curve of
the wheel. By the second quality, all sectors of the spiral, with given
angle at the poles, are similar figures which admit of the same degree
of coincidence for all similar epicycloids, whether great or small, and
nearly the same for epicycloids in general; thus enabling the
application of the instrument to epicycloids in general.
To set the instrument in position for drawing a tooth face a table which
accompanies the instrument is used. From this table a numerical value is
taken, which value depends upon the diameters of the wheels, and the
number of teeth in the wheel for which the curve is sought. This tabular
value, when multiplied by the pitch of the teeth, is to be found on the
graduated edge on the instrument A D B in Fig. 137. This done, draw the
line D E F tangent to the pitch line at the middle of the tooth, and
mark off the half thickness of the tooth, as E, D, either on the tangent
line or the pitch line. Then place the graduated edge of the odontograph
at D, and in such a position that the number and division found as
already stated shall come precisely on the tangent line at D, and at the
same time so set the curved edge H F C so that it shall be tangent to
the tangent line, that is to say, the curved edge C H must just meet the
tangent line at some one point, as at F in the figure. A line drawn
coincident with the graduated edge will then mark the face curve
required, and the odontograph may be turned over, and the face on the
other side of the tooth marked from a similar setting and process.
For the flanks of the teeth setting numbers are obtained from a separate
table, and the instrument is turned upside down, and the tangent line D
F, Fig. 137, is drawn from the side of the tooth (instead of from the
centre), as shown in Fig. 138.
It is obvious that this odontograph may be set upon a radial arm and
used as a template, as shown in Fig. 126, in which case the instrument
would require but four settings for the whole wheel, while rolling
segments and the making of templates are entirely dispensed with, and
the degree of accuracy is greater than is obtainable by means of the
employment of arcs of circles.
The tables wherefrom to find the number or mark on the graduated edge,
which is to be placed coincident with the tangent line in each case, are
as follows:--
TABLE OF TABULAR VALUES WHICH, MULTIPLIED BY THE ARC PITCH OF THE TEETH,
GIVES THE SETTING NUMBER ON THE GRADUATED EDGE OF THE INSTRUMENT.
+--------------------+-----------------------------------------------------+
| | Number of Teeth in Wheel Sought; or, Wheel for |
| | Which Teeth are Sought. |
| +-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | 8 | 12 | 16 | 20 | 30 | 40 | 50 | 60 | 70 |
| +-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | _For Faces: Flanks Radial or Curved._ |
| RATIOS.[7] | Draw Setting Tangent at Middle of Tooth.-- |
| | Epicycloidal Spur or Bevel Gearing. |
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 1/12 = .083 | .32 | .39 | .46 | .51 | | | | | |
| 1/4 = .250 | .31 | .37 | .44 | .49 | .61 | .70 | .78 | .85 | .92 |
| 1/2 = .500 | .28 | .34 | .41 | .46 | .57 | .66 | .73 | .80 | .87 |
| 2/3 = .667 | .27 | .32 | .38 | .43 | .54 | .62 | .70 | .77 | .83 |
| 1 | .23 | .28 | .34 | .39 | .49 | .58 | .65 | .72 | .78 |
| 3/2 = 1.50 | .19 | .25 | .29 | .34 | .44 | .51 | .58 | .64 | .69 |
| 2 | .17 | .22 | .26 | .30 | .38 | .46 | .53 | .59 | .63 |
| 3 | | .16 | .19 | .23 | .31 | .38 | .44 | .49 | .53 |
| 4 | | .14 | .17 | .20 | .26 | .33 | .38 | .42 | .46 |
| 6 | | | | | .22 | .26 | .30 | .34 | .37 |
| 12 | | | | | | .20 | .23 | .25 | .28 |
| 24 | | | | | | | | | |
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | Number of Teeth in Wheel Sought; or, Wheel for|
| | Which Teeth are Sought. |
| +-----+-----+-----+-----+-----+-----+-----+-----+
| | 80 | 90 | 100 | 120 | 150 | 200 | 300 | 500 |
| +-----+-----+-----+-----+-----+-----+-----+-----+
| | _For Faces: Flanks Radial or Curved._ |
| RATIOS.[7] | Draw Setting Tangent at Middle of Tooth.-- |
| | Epicycloidal Spur or Bevel Gearing. |
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+
| 1/12 = .083 | | | | | | | | |
| 1/4 = .250 | .99 | 1.05| 1.11| 1.22| 1.36| 1.55| 1.94| 2.54|
| 1/2 = .500 | .93 | 1.00| 1.06| 1.15| 1.29| 1.50| 1.86| 2.41|
| 2/3 = .667 | .89 | .95| 1.01| 1.11| 1.24| 1.45| 1.79| 2.32|
| 1 | .83 | .89| .94| 1.03| 1.15| 1.36| 1.65| 2.10|
| 3/2 = 1.50 | .74 | .79| .84| .93| 1.05| 1.25| 1.53| 1.94|
| 2 | .68 | .72| .76| .84| .95| 1.13| 1.40| 1.81|
| 3 | .57 | .60| .63| .71| .82| .97| 1.23| 1.60|
| 4 | .49 | .53| .56| .63| .73| .87| 1.08| 1.42|
| 6 | .41 | .44| .47| .53| .61| .71| .90| 1.20|
| 12 | .30 | .32| .34| .37| .42| .49| .60| .82|
| 24 | | .19| .21| .23| .26| .31| .40| .57|
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+
+--------------------+-----------------------------------------------------+
| | Number of Teeth in Wheel Sought; or, Wheel for |
| | Which Teeth are Sought. |
| +-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | 8 | 12 | 16 | 20 | 30 | 40 | 50 | 60 | 70 |
| +-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | _For Flanks, when Curved._ |
| | Draw Setting Tangent at Side of Tooth.-- |
| | Epicycloidal Spur and Bevel Gearing. |
|D C | Faces of Internal, and Flanks of Pinion Teeth. |
|e u +-----+-----+-----+-----+-----+-----+-----+-----+-----+
|g F r { 1.5 slight.| .77 | .98 | 1.18| 1.36| 1.75| 2.05| 2.31| 2.56| 2.75|
|r l v { 2 good. | .44 | .54 | .63| .72 | .92| 1.09| 1.24| 1.38| 1.49|
|e a a { 3 more. | .20 | .28 | .35| .40 | .54| .65| .76| .86| .95|
|e n t { 4 much. | | .20 | .23| .25 | .34| .42| .51| .59| .66|
| k u { 6 | | | .16| .17 | .26| .32| .38| .43| .48|
|o r {12 | | | | | .19| .24| .28| .31| .34|
|f e {24 | | | | | | | | | |
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | Number of Teeth in Wheel Sought; or, Wheel for|
| | Which Teeth are Sought. |
| +-----+-----+-----+-----+-----+-----+-----+-----+
| | 80 | 90 | 100 | 120 | 150 | 200 | 300 | 500 |
| +-----+-----+-----+-----+-----+-----+-----+-----+
| | _For Flanks, when Curved._ |
| | Draw Setting Tangent at Side of Tooth.-- |
| | Epicycloidal Spur and Bevel Gearing. |
|D C | Faces of Internal, and Flanks of Pinion Teeth.|
|e u +-----+-----+-----+-----+-----+-----+-----+-----+
|g F r { 1.5 slight.| 2.92| 3.08| 3.24| 3.52| 3.87| 4.51| 5.50| 7.20|
|r l v { 2 good. | 1.59| 1.79| 1.79| 1.98| 2.23| 2.67| 3.22| 4.50|
|e a a { 3 more. | 1.02| 1.10| 1.18| 1.31| 1.46| 1.67| 2.08| 2.76|
|e n t { 4 much. | .71| .77| .82| .92| 1.06| 1.25| 1.64| 2.15|
| k u { 6 | .52| .56| .60| .66| .76| .93| 1.20| 1.54|
|o r {12 | .36| .38| .40| .45| .52| .63| .80| .98|
|f e {24 | | | .22| .25| .28| .33| .47| .60|
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+
+--------------------+-----------------------------------------------------+
| | Number of Teeth in Wheel Sought; or, Wheel for |
| | Which Teeth are Sought. |
| +-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | 8 | 12 | 16 | 20 | 30 | 40 | 50 | 60 | 70 |
| +-----+-----+-----+-----+-----+-----+-----+-----+-----+
| _For Faces of Racks; and of Pinions for Racks and Internal Gears; for |
| Flanks of Internal and Sides of Involute Teeth._ |
| Draw Setting Tangent at Middle of Tooth, regarding Space as Tooth in |
| Internal Teeth. For Rack use Number of Teeth in Pinion. |
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| Pinion. | .31 | .39 | .48 | .57 | .73 | .88 | 1.00| 1.10| 1.20|
| Rack. | .32 | .38 | .44 | .50 | .62 | .72 | .80| .87| .93|
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| | Number of Teeth in Wheel Sought; or, Wheel for|
| | Which Teeth are Sought. |
| +-----+-----+-----+-----+-----+-----+-----+-----+
| | 80 | 90 | 100 | 120 | 150 | 200 | 300 | 500 |
| +-----+-----+-----+-----+-----+-----+-----+-----+
| _For Faces of Racks; and of Pinions for Racks and Internal Gears; |
| for Flanks of Internal and Sides of Involute Teeth._ |
|Draw Setting Tangent at Middle of Tooth, regarding Space as Tooth in|
| Internal Teeth. For Rack use Number of Teeth in Pinion. |
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+
| Pinion. | 1.30| 1.40| 1.48| 1.65| 1.85| 2.15| 2.65| 3.50|
| Rack. | .99| 1.03| 1.08| 1.16| 1.27| 1.49| 1.86| 2.44|
+--------------------+-----+-----+-----+-----+-----+-----+-----+-----+
[7] These ratios are obtained by dividing the radius of the wheel
sought by the diameter of the generating circle.
From these tables may be found a tabular value which, multiplied by the
pitch of the wheel to be marked (as stated at the head of the table),
will give the setting number on the graduated edge of the instrument,
the procedure being as follows:--
For the teeth of a pair of wheels intended to gear together only (and
not with other wheels having a different number of teeth).
For the face of such teeth where the flanks are to be radial lines.
Rule.--Divide the pitch circle radius of the wheel to have its teeth
marked by the pitch circle radius of the wheel with which it is to gear:
or, what is the same thing, divide the number of teeth in the wheel to
have its teeth marked by the number of teeth in the wheel with which it
is to gear, and the quotient is the "ratio." In the ratio column find
this number, and look along that line, and in the column at the head of
which is the number of teeth contained in the wheel to be marked, is a
number termed the tabular value, which, multiplied by the arc pitch of
the teeth, will give the number on the graduated edge by which to set
the instrument to the tangent line.
Example.--What is the setting number for the face curves of a wheel to
contain 12 teeth, of 3-inch arc pitch, and to gear with a wheel having
24 teeth?
Here number of teeth in wheel to be marked = 12, divided by the number
of teeth (24) with which it gears; 12 ÷ 24 = .5. Now in column of ratios
may be found 1/2 = .500 (which is the same thing as .5), and along the
same horizontal line in the table, and in the column headed 12 (the
number of teeth in the wheel) is found .34. This is the tabular value,
which, multiplied by 3 (the arc pitch of the teeth), gives 1.02, which
is the setting number on the graduated edge. It will be noted, however,
that the graduated edge is marked 1, 2, 3, &c., and that between each
consecutive division are ten subdivisions; hence, for the decimal .02 an
allowance may be made by setting the line 1 a proportionate amount below
the tangent line marked on the wheel to set the instrument by.
[Illustration: Fig. 137. NEW ODONTOGRAPH Full Size]
Required now the setting number for the wheel to have the 24 teeth.
Here number of teeth on the wheel = 24, divided by the number of teeth
(12) on the wheel with which it gears; 24 ÷ 12 = 2. Now, there is no
column in the "number of teeth sought" for 24 teeth; but we may find the
necessary tabular value from the columns given for 20 teeth and 30
teeth, thus:--opposite ratio 2, and under 20 teeth is given .30, and
under 30 teeth is given .38--the difference between the two being .08.
Now the difference between 20 teeth and 24 teeth is 4/10; hence, we take
4/10 of the .08 and add it to the tabular value given for 20 teeth,
thus: .08 × 4 ÷ 10 = .032, and this added to .30 (the tabular value
given for 20 teeth = .33, which is the tabular value for 24 teeth). The
.33 multiplied by arc pitch (3) gives .99. This, therefore, is the
setting number for the instrument, being sufficiently near to the 1 on
the graduated edge to allow that 1 to be used instead of .99.
[Illustration: Fig. 138.]
It is to be noted here that the pinion, having radial lines, the other
wheel must have curved flanks; the rule for which is as follows:--
CURVED FLANKS FOR A PAIR OF WHEELS.
Note.--When the flanks are desired to be curved instead of radial, it is
necessary to the use of the instrument to select and assume a value for
the degree of curve, as is done in the table in the column marked
"Degree for flank curving;" in which
1.5 slight--a slight curvature of flank.
2 good--an increased curvature of flank.
3 more--a degree of pronounced spread at root.
4 much--spread at root is a distinguishing feature of tooth form.
6--still increased spread in cases where the strength at root of
pinion is of much importance to give strength.
12--as above, under aggravated conditions.
24--undesirable (unless requirement of strength compels this degree),
because of excessive strain on pinion.
Rule.--For faces of teeth to have curved flanks.
Divide the number of teeth in the wheel to be marked by the number of
teeth in the wheel with which it gears, and multiply by the degree of
flank curve selected for the wheel with which that to be marked is to
gear, and this will give the ratio. Find this number in ratio column,
and the tabular number under the column of number of teeth of wheel to
be marked; multiply tabular number so found by arc pitch of wheel to be
marked, and the product will be the setting number for the instrument.
Example.--What is the setting number on the graduated edge of the
odontograph for the faces of a wheel (of a pair) to contain 12 teeth of
2-inch arc pitch, and to gear with a wheel having 24 teeth and a flank
curvature represented by 3 in "Degree of flank curving" column?
Here teeth in wheel to be marked (12) divided by number of teeth in the
wheel it is to gear with (24), 12 ÷ 24 = .5, which multiplied by 3
(degree of curvature selected for flanks of 24-teeth wheel), .5 × 3 =
1.5. In column of ratio numbers find 1.5, and in 12-teeth column is .25,
which multiplied by pitch (2) gives .5 as the setting number for the
instrument; this being the fifth line on the instrument, and half way
between the end and mark 1.
FOR CURVED FLANKS.
Rule.--Assume the degree of curve desired for the flanks to be marked,
select the corresponding value in the column of "Degrees of flank
curving," and find the tabular value under the number of teeth column.
Multiply tabular value so found by the arc pitch of the teeth, and the
product is the setting number on the instrument.
Example.--What is the setting number on the odontograph for the flanks
of a wheel to contain 12 teeth and gear with one having 24 teeth, the
degree of curvature for the flanks being represented by 4 in the column
of "Degree of flank curvature?"
Here in column of degrees of flank curvature on the 3 line and under 12
teeth is .20, which multiplied by pitch of teeth (2) is .20 × 2 = 40, or
4/10; hence, the fourth line of division on the curved corner is the
setting line, it representing 4/10 of 1.
FOR INTERCHANGEABLE GEARING (THAT IS, A TRAIN OF GEARS ANY ONE OF WHICH
WILL WORK CORRECTLY WITH ANY OTHER OF THE SAME SET).
Rule--both for the faces and for the flanks. For each respective wheel
divide the number of teeth in that wheel by some one number not greater
than the number of teeth in the smallest wheel in the set, which gives
the ratio number for the wheel to be marked. On that line of ratio
numbers, and in the column of numbers of teeth, find the tabular value
number; multiply this by the arc pitch of the wheel to be marked, and
the product is the setting number of the instrument.
Example.--A set of wheels is to contain 10 wheels; the smallest is to
contain 12 teeth; the arc pitch of the wheels is four inches. What is
the setting number for the smallest wheel?
Here number of teeth in smallest wheel of set is 10; divide this by any
number smaller than itself (as say 5), 10 ÷ 5 = 2 = the ratio number on
ratio line for 2; and under column for 12 is .17, which is the tabular
value, which multiplied by pitch (4) is .17 × 4 = 68, or 6/10 and 8/100;
hence, the instrument must be set with its seventh line of division just
above the tangent line marked on the wheel. It will be noted that, if
the seventh line were used as the setting, the adjustment would be only
the 2/100 of a division out, an amount scarcely practically appreciable.
Both for the faces and flanks, the second number is obtained in
_precisely_ the same manner for every wheel in the set, except that
instead of 10 the number of teeth in each wheel must be substituted.
RACK AND PINION.--_For radial flanks_ use for faces the two lower lines
of table. _For curved flanks_ find tabular value for pinion faces in
lowest line. For flanks of pinion choose degree of curving, and find
tabular value under "flanks," as for other wheels. For faces of rack
divide number of teeth in pinion by degree of curving, which take for
number of teeth in looking opposite "rack." Flanks of rack are still
parallel, but may be arbitrarily curved beyond half way below pitch
line.
INTERNAL GEARS.--For tooth curves within the pitch lines, divide radius
of each wheel by any number not greater than radius of pinion, and look
in the table under "flanks." For curves outside pitch line use lower
line of table; or, divide radii by any number and look under "faces." In
applying instrument draw tangents at middle and side of _space_, for
internal teeth.
INVOLUTE TEETH.--For tabular values look opposite "Pinion," under proper
number of teeth, for each wheel. Draw setting tangent from "base circle"
of involute, at middle of tooth. For this the instrument gives the whole
side of tooth at once.
In all cases multiply the tabular value by the pitch in inches.
BEVEL-WHEELS.--Apply above rules, using the developed normal cone bases
as pitch lines. For right-angled axes this is done by using in place of
the actual ratio of radii, or of teeth numbers, the square of that
ratio; and for number of teeth, the actual number multiplied by the
square root of one plus square of ratio or radii; the numerator of
ratio, and number of teeth, belonging to wheel sought.
When the first column ratio and teeth numbers fall between those given
in the table, the tabular values are found by interpolating as seen in
the following examples:
EXAMPLES OF TABULAR VALUES AND SETTING NUMBERS.
_Take a pair of 16 and 56 teeth; radii 5.09 and 17.82 inches
respectively; and 2 inches pitch._
+----------------+------+----------------+------+---------------+-------+
| |Number} | | First Column | Tab. |
|Kind of Gearing.| of } Kind of Flank. |Ratio | Ratio. | Val. |
| |Teeth.} |Radii.+--------+------+---+---+
| | | | | Flank. |Face. |[A]|[B]|
+----------------+------+----------------+------+--------+------+---+---+
|Epicycloidal, }|Small |Radial | .29 |Radial | .29 |.. |.44|
|Radial Flanks }|Large |Radial | 3.5 |Radial | 3.5 |.. |.44|
|Epicycloidal, } |Small |Curved 2 deg. | .29 | 2 | .87 |.63|.36|
|Curved Flanks.} |Large |Curved 3 deg. } | 3.5 | 3 | 7. |.82|.30|
|Epicycloidal, }|Small |"Sets," Divide} | 2. | 2 | 2. |.63|.26|
|Interchange'bl.}|Large |Radii by 2.55 } | 7. | 7 | 7. |.40|.30|
|Epicycloidal, } |Pinion|Curved 2 deg. | | 2 |Pinion|.63|.44|
|Internal. } |Wheel |Int. face 7 deg.| 3.5 |Pinion | 7[8] |.84|.39|
|Epicycloidal, }|Pinion|Curved 2 deg. | | 2 |Pinion|.63|.44|
|Rack & Pinion. }|Rack |Parallel | |Parallel|Rack |.. |.31|
|Involute } |Small |Face and Flank | | Pinion. | .44 |
|Gearing. } |Large |One Curve | | Pinion. | .84 |
+----------------+------+----------------+------+--------+------+-------+
Legend: A = Flank.
B = Face.
[8] The face being here internal, the tabular value is to be found
under "flanks." If bevels, use ratio radii .082 and 12.25; and teeth
numbers 16.6 and 203.8 respectively.
WALKER'S PATENT WHEEL SCALE.--This scale is used in many manufactories
in the United States to mark off the teeth for patterns, wherefrom to
mould cast gears, and consists of a diagram from which the compasses may
be set to the required radius to strike the curves of the teeth.
[Illustration: Fig. 139.]
The general form of this diagram is shown in Fig. 139. From the portion
A the length of the teeth, according to the pitch, is obtained. From the
portion B half the thickness of the tooth at the pitch line is obtained.
From the part C half the thickness at the root is obtained, and from the
part D half the thickness at the point is obtained.
[Illustration: Fig. 140.]
Each of these parts is marked with the number of teeth the wheel is to
contain, and with the pitch of the teeth as shown in Fig. 140, which
represents part C full size. Now suppose it is required to find the
thickness at the root, for a tooth of a wheel having 60 teeth of one
inch pitch, the circles from the point A, pitch line B and root C being
drawn, and a radial line representing the middle of the tooth being
marked, as is shown in Fig. 142, the compass points are set to the
distance F B, Fig. 140--F being at the junction of line 1 with line 60;
the compasses are then rested at G, and the points H I are marked. Then,
from the portion B, Fig. 139 of the diagram, which is shown full-size in
Fig. 141, the compasses may be set to half the thickness at the pitch
circle, as in this case (for ordinary teeth) from E to E, and the points
J K, Fig. 142, are marked. By a reference to the portion D of the
diagram, half the thickness of the tooth at the point is obtained, and
marked as at L M in Fig. 142. It now remains to set compasses to the
radius for the face and that for the flank curves, both of which may be
obtained from the part A of the diagram. The locations of the centres,
wherefrom to strike these curves, are obtained as in Fig. 142. The
compasses set for the face curve are rested at H, and the arc N is
struck; they are then rested at J and the arc O struck; and from the
intersection of N O, as a centre, the face curve H J is marked. By a
similar process, reference to the portion D of the diagram, half the
thickness of the tooth at the point is obtained, and marked as at L M in
Fig. 142. It now remains to set the compasses to the radius to strike
the respective face and flank curves, and for this purpose the operator
turns to the portion A, Fig. 139, of the diagram or scale, and sets the
compasses from the marks on that portion to the required radii.
[Illustration: Fig. 141.]
It now remains to find the proper location from which to strike the
curves.
[Illustration: Fig. 142.]
The face curve on the other side of the tooth is struck. The compasses
set to the flank radius is then rested at M, and the arc P is marked and
rested at K to mark the arc Q; and from the intersection of P Q, as a
centre, the flank curve K M is marked: that on the other side of the
tooth being marked in a similar manner.
Additional scales or diagrams, not shown in Fig. 139, give similar
distances to set the compasses for the teeth of internal wheels and
racks.
It now remains to explain the method whereby the author of the scale has
obtained the various radii, which is as follows: A wheel of 200 teeth
was given the form of tooth curve that would be obtained by rolling it
upon another wheel, containing 200 teeth of the same pitch. It was next
given the form of tooth that would be obtained by rolling upon it a
wheel having 10 teeth of the same pitch, and a line intermediate between
the two curves was taken as representing the proper curve for the large
wheel. The wheel having 10 teeth was then given the form of tooth that
would be obtained by rolling upon it another wheel of the same diameter
of pitch circle and pitch of teeth. It was next given the form of tooth
that would be given by rolling upon it a wheel having 200 teeth, and a
curve intermediate between the two curves thus obtained was taken as
representing the proper curve for the pinion of 10 teeth. By this means
the inventor does not claim to produce wheels having an exactly equal
velocity ratio, but he claims that he obtains a curve that is the
nearest approximation to the proper epicycloidal curve. The radii for
the curves for all other numbers of teeth (between 10 and 200) are
obtained in precisely the same manner, the pinion for each pitch being
supposed to contain 10 teeth. Thus the scale is intended for
interchangeable cast gears.
The nature of the scale renders it necessary to assume a constant height
of tooth for all wheels of the same pitch, and this Mr. Walker has
assumed as .40 of the pitch, from the pitch line to the base, and .35
from the pitch line to the point.
The curves for the faces obtained by this method have rather more
curvature than would be due to the true epicycloid, which causes the
points to begin and leave contact more easily than would otherwise be
the case.
For a pair of wheels Mr. Walker strikes the face curve by a point on the
pitch rolling circle, and the flanks by a point on the addendum circle,
fastening a piece of wood to the pitch circle to carry the tracing
point. The flank of each wheel is struck with a tracing point, thus
attached to the pitch circle of the other wheel.
The proportions of teeth and of the spaces between them are usually
given in turns of the pitch, so that all teeth of a given pitch shall
have an equal thickness, height, and breadth, with an equal addendum and
flank, and the same amount of clearance.
The term "clearance" as applied to gear-wheel teeth means the amount of
space left between the teeth of one wheel, and the spaces in the other,
or, in other words, the difference between the width of the teeth and
that of the spaces between the teeth.
This clearance exists at the sides of the teeth, as in Fig. 143, at A,
and between the tops of the teeth and the bottoms or roots of the spaces
as at B. When, however, the simple term clearance is employed it implies
the side clearance as at A, the clearance at B being usually designated
as _top and bottom clearance_. Clearance is necessary for two purposes;
first, in teeth cut in a machine to accurate form and dimensions, to
prevent the teeth of one wheel from binding in the spaces of the other,
and second, in cast teeth, to allow for the imperfections in the teeth
which are incidental to casting in a founder's mould. In machine-cut
teeth the amount of clearance is a minimum.
In wheels which are cast with their teeth complete and on the pattern,
the amount of clearance must be a maximum, because, in the first place,
the teeth on the pattern must be made taper to enable the extraction of
the pattern from the mould without damage to the teeth in the mould, and
the amount of this taper must be greater than in machine-moulded teeth,
because the pattern cannot be lifted so truly vertical by hand as to
avoid, in all cases, damage to the mould; in which case the moulder
repairs the mould either with his moulding tools and by the aid of the
eye, or else with a tooth and a space made on a piece of wood for the
purpose. But even in this case the concentricity of the teeth is
scarcely likely to be preserved.
It is obvious that by reason of this taper each wheel is larger in
diameter on one side than on the other, hence to preserve the true
curves to the teeth the pitch circle is made correspondingly smaller.
But if in keying the wheels to their shafts the two large diameters of a
pair of wheels be placed to work together, the teeth of the pair would
have contact on that side of the wheel only, and to avoid this and give
the teeth contact across their full breadth the wheels are so placed on
their shafts that the large diameter of one shall work with the small
one of the other, the amount of taper being the same in each wheel
irrespective of their relative diameters. This also serves to keep the
clearance equal in amount both top, and bottom, and sideways.
A second imperfection is that in order to loosen the pattern in the sand
or mould, and enable its extraction by hand from the mould, the pattern
requires to be _rapped_ in the mould, the blows forcing back the sand of
the mould and thus loosening the pattern. In ordinary practice the
amount of this rapping is left entirely to the judgment of the moulder,
who has nothing to guide him in securing an equal amount of pattern
movement in each direction in the mould; hence, the finished mould may
be of increased radius at the circumference in the direction in which
the wheel moved most during the rapping. Again, the wood pattern is apt
in time to shrink and become _out of round_, while even iron patterns
are not entirely free from warping. Again, the cast metal is liable to
contract in cooling more in one direction than in another. The amount of
clearance usually allowed for pattern-moulded cast gearing is given by
Professor Willis as follows:--Whole depth of tooth 7/10, of the pitch
working depth 6/10; hence 1/10 of the pitch is allowed for top and
bottom clearance, and this is the amount shown at B in Fig. 143. The
amount of side clearance given by Willis as that ordinarily found in
practice is as follows:--"Thickness of tooth 5/11 of the pitch; breadth
of space 6/11; hence, the side clearance equals 1/11 of the pitch, which
in a 3-inch pitch equals .27 of an inch in each wheel." Calling this in
round figures, which is near enough for our purpose, 1/4 inch, we have
thickness of tooth 1-1/4, width of space 1-3/4, or 1/2 inch of clearance
in a 3-inch pitch, an amount which on wheels of coarse pitch is
evidently more than that necessary in view of the accuracy of modern
moulding, however suitable it may have been for the less perfect
practice of Professor Willis's time. It is to be observed that the
rapping of the pattern in the founder's mould reduces the thickness of
the teeth and increases the width of the spaces somewhat, and to that
extent augments the amount of side clearance allowed on the pattern, and
the amount of clearance thus obtained would be nearly sufficient for a
small wheel, as say of 2 inches diameter. It is further to be observed
that the amount of rapping is not proportionate to the diameter of the
wheel; thus, in a wheel of 2 inches diameter, the rapping would increase
the size of the mould about 1/32 inch. But in the proportion of 1/32
inch to every 2 inches of diameter, the rapping on a 6-foot wheel would
amount to 1-1/16 inches, whereas, in actual practice, a 6-foot wheel
would not enlarge the mould more than at most 1/8 inch from the rapping.
[Illustration: Fig. 143.]
It is obvious, then, that it would be more in accordance with the
requirements to proportion the amount of clearance to the diameter of
the wheel, so as to keep the clearance as small as possible. This will
possess the advantage that the teeth will be stronger, it being obvious
that the teeth are weakened both from the loss of thickness and the
increase of height due to the clearance.
It is usual in epicycloidal teeth to fill in the corner at the root of
the tooth with a fillet, as at C, D, in Fig. 143, to strengthen it.
This is not requisite when the diameter of the generating circle is so
small in proportion to the base circle as to produce teeth that are
spread at the roots; but it is especially advantageous when the teeth
have radial flanks, in which case the fillets may extend farther up the
flanks than when they are spread; because, as shown in Fig. 47, the
length of operative flank is a minimum in teeth having radial flanks,
and as the smallest pinion in the set is that with radial flanks, and
further as it has the least number of teeth in contact, it is the
weakest, and requires all the strengthening that the fillets in the
corners will give, and sometimes the addition of the flanges on the
sides of the pinion, such gears being termed "shrouded."
The proportion of the teeth to the pitch as found in ordinary practice
is given by Professor Willis as follows:--
Depth to pitch line 3/10 of the pitch.
Working depth 6/10 " "
Whole depth 7/10 " "
Thickness of tooth 5/11 " "
Breadth of space 6/11 " "
The depth to pitch line is, of course, the same thing as the height of
the addendum, and is measured through the centre of the tooth from the
point to the pitch line in the direction of a radial line and not
following the curve of tooth face.
Referring to the working depth, it was shown in Figs. 42 and 44 that the
height of the addendum remaining constant, it varies with the diameter
of the generating circle.
[Illustration: Fig. 144. Scale of Proportions given by Willis]
From these proportions or such others as may be selected, in which the
proportions bear a fixed relation to the pitch, a scale may be made and
used as a gauge, to set the compasses by, and in marking off the teeth
for any pitch within the capacity of the scale. A vertical line A B in
Fig. 144, is drawn and marked off in inches and parts of an inch, to
represent the pitches of the teeth; at a right angle to A B, the line B
C is drawn, its length equalling the whole depth of tooth, which since
the coarsest pitch in the scale is 4 inches will be 7/10 of 4 inches.
From the end of line C we draw a diagonal line to A, and this gives us
the whole depth of tooth for any pitch up to 4 inches: thus the whole
depth for a 4-inch pitch is the full length of the horizontal line B C;
the whole depth for a 3-inch pitch will be the length of the horizontal
line running from the 3 on line A B, to line A C on the right hand of
the figure; similarly for the full depth of tooth for a 2-inch pitch is
the length of the horizontal line running from 2 to A C. The working
depth of tooth being 6/10 of the pitch a diagonal is drawn from A
meeting line C at a distance from B of 6/10 of 4 inches and we get the
working depth for any other pitch by measuring (along the horizontal
line corresponding to that pitch), from the line of pitches to the
diagonal line for working depth of tooth. The thickness of tooth is 5/11
of the pitch and its diagonal is distant 5/11 of 4 (from B) on line B C,
the thickness for other pitches being obtained on the horizontal line
corresponding to those pitches as before.
[Illustration: Fig. 145.]
The construction of a pattern wherefrom to make a foundry mould, in
which to cast a spur gear-wheel, is as shown in section, and in plan of
Fig. 145. The method of constructing these patterns depends somewhat on
their size. Large patterns are constructed with the teeth separate, and
the body of the wheel is built of separate pieces, forming the arms, the
hub, the rim, and the teeth respectively. Pinion patterns, of six inches
and less in diameter, are usually made out of a solid piece, in which
case the grain of the wood must lie in the direction of the teeth
height. The chuck or face plate of the lathe, for turning the piece,
must be of smaller diameter than the pinion, so that it will permit
access to a tool applied on both sides, so as to strike the pitch circle
on both sides. A second circle is also struck for the roots or depths of
the teeth, and also, if required, an extra circle for striking the
curves of the teeth with compasses, as was described in Fig. 130. All
these circles are to be struck on both sides of the pattern, and as the
pattern is to be left slightly taper, to permit of its leaving the
mould easily, they must be made of smaller diameter on one side than on
the other of the pattern; the reduction in diameter all being made on
the same side of the pattern. The pinion body must then be divided off
on the pitch line into as many equal divisions as there are to be teeth
in it; the curves of the teeth are then marked by some one of the
methods described in the remarks on curves of gear-teeth. The top of the
face curves are then marked along the points of the teeth by means of a
square and scribe, and from these lines the curves are marked in on the
other side of the pinion, and the spaces cut out, leaving the teeth
projecting. For a larger pinion, without arms, the hub or body is built
up of courses of quadrants, the joints of the second course _breaking
joint_ with those of the first.
[Illustration: Fig. 146.]
The quadrants are glued together, and when the whole is formed and the
glue dry, it is turned in the lathe to the diameter of the wheel at the
roots of the teeth. Blocks of wood, to form the teeth, are then planed
up, one face being a hollow curve to fit the circle of the wheel. The
circumference of the wheel is divided, or pitched off, as it is termed,
into as many points of equal division as there are to be teeth, and at
these points lines are drawn, using a square, having its back held
firmly against the radial face of the pinion, while the blade is brought
coincidal with the point of division, so as to act as a guide in
converting that point into a line running exactly true with the pinion.
All the points of division being thus carried into lines, the blocks for
the teeth are glued to the body of the pinion, as denoted by A, in Fig.
145. Another method is to dovetail the teeth into the pinion, as in Fig.
145 at B. After the teeth blocks are set, the process is, as already
described, for a solid pinion.
[Illustration: Fig. 147.]
The construction of a wheel, such as shown in Fig. 145, is as follows:
The rim R must be built up in segments, but when the courses of segments
are high enough to reach the flat sides of the arms they should be
turned in the lathe to the diameter on the inside, and the arms should
be let in, as shown in the figure at O. The rest of the courses of
segments should then be added. The arms are then put in, and the inside
of the segments last added may then be turned up, and the outside of the
rim turned. The hub should then be added, one-half on each side of the
arms, as in the figure. The ribs C of the arms are then added, and the
body is completed (ready to receive the teeth), by filleting in the
corners. An excellent method of getting out the teeth is as follows:
Shape A piece of hard wood, as in Fig. 146, making it some five or six
inches longer than the teeth, and about three inches deeper, the
thickness being not less than the thickness of the required teeth at the
pitch line. Parallel to the edge B C, mark the line A D, distant from B
C to an amount equal to the required depth of tooth. Mark off, about
midway of the piece, the lines A B and C D, distant from each other to
an amount equal to the breadth of the wheel rim, and make two saw cuts
to those lines. Take a piece of board an inch or two longer than the
radius of the gear-wheel and insert a piece of wood (which is termed a
box) tightly into the board, as shown in Fig. 147, E representing the
box. Let the point F on the board represent the centre of the wheel, and
draw a radial line R from F through the centre of the box. From the
centre F, with a trammel, mark the addendum line G G, pitch line H I,
and line J K for the depth of the teeth (and also a line wherefrom to
strike the teeth curves, as shown in Fig. 129 if necessary). From the
radial line R, as a centre, mark off on the pitch circle, points of
division for several teeth, so as to be able to test the accuracy of the
spacing across the several points, as well as from one point to the
next, and mark the curves for the teeth on the end of the box, as shown.
Turn the box end for end in the board, and mark out a tooth by the same
method on the other end of the box. The box being removed from the board
must now have its sides planed to the lines, when it will be ready to
shape the teeth in. The teeth are got out for length, breadth, and
thickness at the pitch line as follows: The lumber from which they are
cut should be very straight grained, and should be first cut into strips
of a width and thickness slightly greater than that of the teeth at the
pitch line. These strips (which should be about two feet long) should
then be planed down on the sides to very nearly the thickness of the
tooth at the pitch line, and hollow on one edge to fit the curvature of
the wheel rim. From these strips, pieces a trifle longer than the
breadth of the wheel rim are cut, these forming the teeth. The pieces
are then planed on the ends to the exact width of the wheel rim. To
facilitate this planing a number of the pieces or blank teeth may be set
in a frame, as in Figs. 148 and 149, in which A is a piece having the
blocks B B affixed to it. C is a clamp secured by the screws at S S, and
1, 2, 3, 4, 5, 6 are the ends of the blank teeth. The clamp need not be
as wide as the teeth, as in Fig. 148, but it is well to let the pieces
A and B B equal the breadth of the wheel rim, so that they will act as a
template to plane the blank teeth ends to. The ends of B B may be
blackleaded, so as to show plainly if the plane blade happens to shave
them, and hence to prevent planing B B with the teeth. The blank teeth
may now be separately placed in the box (Fig. 146) and secured by a
screw, as shown in that figure, in which S is the screw, and T the blank
tooth. The sides of the tooth must be carefully planed down equal and
level with the surface of the box. The rim of the wheel, having been
divided off into as many divisions as there are to be teeth in the
wheel, as shown in Fig. 150, at _a_, _a_, _a_, &c., the finished teeth
are glued so that the same respective side of each tooth exactly meets
one of the lines _a_. Only a few spots of glue should be applied, and
these at the middle of the root thickness, so that the glue shall not
exude and hide the line _a_, which would make it difficult to set the
teeth true to the line. When the teeth are all dry they must be
additionally secured to the rim by nails. Wheels sufficiently large to
incur difficulty of transportation are composed of a number of sections,
each usually consisting of an arm, with an equal length of the rim arc
on each side of it, so that the joint where the rim segments are bolted
together will be midway between the two arms.
[Illustration: Fig. 148.]
This, however, is not absolutely necessary so long as the joints are so
arranged as to occur in the middle of tooth spaces, and not in the
thickness of the tooth. This sometimes necessitates that the rim
sections have an unequal length of arc, in which event the pattern is
made for the longest segment, and when these are cast the teeth
superfluous for the shorter segments are stopped off by the foundry
moulder. This saves cutting or altering the pattern, which, therefore,
remains good for other wheels when required.
[Illustration: Fig. 149.]
When the teeth of wheels are to be cut in a gear-cutting machine the
accurate spacing of the teeth is determined by the index plate and
gearing of the machine itself; but when the teeth are to be cast upon
the wheel and a pattern is to be made, wherefrom to cast the wheel the
points of division denoting the thickness of the teeth and the width of
the spaces are usually marked by hand. This is often rendered necessary
from the wheels being of too large a diameter to go into dividing
machines of the sizes usually constructed.
To accurately divide off the pitch circle of a gear-wheel by hand,
requires both patience and skilful manipulation, but it is time and
trouble that well repays its cost, for in the accuracy of spaces lies
the first requisite of a good gear-wheel.
It is a very difficult matter to set the compasses so that by commencing
at any one point and stepping the compasses around the circle
continuously in one direction, the compass point shall fall into the
precise point from which it started, for if the compass point be set the
1-200th inch out, the last space will come an inch out in a circle
having 200 points of divisions. It is, therefore, almost impossible and
quite impracticable to accurately mark or divide off a circle having
many points of division in this manner, not only on account of the
fineness of the adjustment of the compass points, but because the
frequent trials will leave so many marks upon the circle that the true
ones will not be distinguishable from the false. Furthermore, the
compass points are apt to spring and fall into the false marks when
those marks come close to the true ones.
[Illustration: Fig. 150.]
In Fig. 151 is shown a construction by means of which the compass points
may be set more nearly than by dividing the circumference of the circle
by the number of divisions it is required to be marked into and setting
the compasses to the quotient, because such a calculation gives the
length of the division measured around the arc of the circle, instead of
the distance measured straight from point of division to point of
division.
[Illustration: Fig. 151.]
The construction of Fig. 151 is as follows: P P is a portion of the
circle to be divided, and A B is a line at a tangent to the point C of
the circle P P. The point D is set off distant from C, to an amount
obtained by dividing the circumference of P P by the number of divisions
it is to have. Take one-quarter of this distance C D, and mark it from
C, giving the point E, set one point of the compass at E and the other
at D, and draw the arc D F, and the distance from F to C, as denoted by
G, is the distance to which to set the compasses to divide the circle
properly. The compasses being set to this distance G, we may rest one
compass point at C, and mark the arc F H, and the distance between arc H
and arc D, measured on the line A B, is the difference between the
points C, F when measured around the circle P P, and straight across, as
at G.
[Illustration: Fig. 152.]
A pair of compasses set even by this construction will not, however, be
entirely accurate, because there will be some degree of error, even
though it be in placing the compass points on the lines and on the
points marked, hence it is necessary to step the compasses around the
circle, and the best method of doing this is as follows: Commencing at
A, Fig. 152, we mark off continuously one from the other, and taking
care to be very exact to place the compass point exactly coincident with
the line of the circle, the points B, C, D, &c., continuing until we
have marked half as many divisions as the circle is to contain, and
arriving at E, starting again at A, we mark off similar divisions (one
half of the total number), F, G, H, arriving at I, and the centre K,
between the two lines E, I, will be the true position of the point
diametrally opposite to point A, whence we started. These points are all
marked inside the circle to keep them distinct from those subsequently
marked.
[Illustration: Fig. 153.]
It will be, perhaps, observed by the reader that it would be more
expeditious, and perhaps cause less variation, were we to set the
compasses to the radius of the circle and mark off the point K, as shown
in Fig. 153, commencing at the point A, and marking off on the one side
the lines B, C, and D, and on the other side E, F, and G, the junction
or centre, between G and D, at the circle being the true position of the
point K. For circles struck upon flat surfaces, this plan may be
advantageous; and in cases where there are not at hand compasses large
enough, a pair of trammels may be used for the purpose; but our
instructions are intended to apply also to marking off equidistant
points on such circumferences as the faces of pulleys or on the outsides
of small rings or cylinders, in which cases the use of compasses is
impracticable. The experienced hand may, it is true, adjust the
compasses as instructed, and mark off three or four of the marks B, C,
&c., in Fig. 152, and then open out the compasses to the distance
between the two extreme marks, and proceed as before to find the centre
K, but as a rule, the time saved will scarcely repay the trouble; and
all that can be done to save time in such cases is, if the holes come
reasonably close together, to mark off, after the compasses are
adjusted, three or four spaces, as shown in Fig. 154. Commencing at the
point A, and marking off the points B, C, and D, we then set another
pair of compasses to the distance between A and D, and then mark, from D
on one side and from A on the other, the marks from F to L and from M to
T, thus obtaining the point K. This method, however expeditious and
correct for certain work, is not applicable to circumferential work of
small diameter and in which the distance between two of the adjacent
points is, at the most, 1/20 of the circumference of the circle; because
the angle of the surface of the metal to the compass point causes the
latter to spring wider open in consequence of the pressure necessary to
cause the compass point to mark the metal. This will be readily
perceived on reference to Fig. 155 in which A represents the stationary,
and B the scribing or marking point of the compasses.
[Illustration: Fig. 154.]
The error in the set of the compasses as shown by the distance apart of
the two marks E and I on the circle in Fig. 152 is too fine to render it
practicable to remedy it by moving the compass legs, hence we effect the
adjustment by oilstoning the points on the outside, throwing them closer
together as the figure shows is necessary.
[Illustration: Fig. 155.]
Having found the point K, we mark (on the outside of the circle, so as
to keep the marks distinct from those first marked) the division B, C,
D, Fig. 156, &c., up to G, the number of divisions between B and G being
one quarter of those in the whole circle. Then, beginning at K, we mark
off also one quarter of the number of divisions arriving at M in the
figure and producing the point 3. By a similar operation on the other
side of the circle, we get the true position of point No. 4. If, in
obtaining points 3 and 4, the compasses are not found to be set dead
true, the necessary adjustment must be made; and it will be seen that,
so far, we have obtained four true positions, and the process of
obtaining each of them has served as a justification of the distance of
the compass points. From these four points we may proceed in like
manner to mark off the holes or points between them; and the whole will
be as true as it is practicable to mark them off upon that size of
circle. In cases, however, where mathematical precision is required upon
flat and not circumferential surfaces, the marking off may be performed
upon a circle of larger diameter, as shown in Fig. 157. If it is
required to mark off the circle A, Fig. 157, into any even number of
equidistant points, and if, in consequence of the closeness together of
the points, it becomes difficult to mark them (as described) with the
compasses, we mark a circle B B of larger diameter, and perform our
marking upon it, carrying the marks across the smaller circle with a
straightedge placed to intersect the centres of the circles and the
points marked on each side of the diameter. Thus, in Fig. 157, the lines
1 and 2 on the smaller circle would be obtained from a line struck
through 1 and 4 on the outer circle; and supposing the larger circle to
be three times the size of the smaller, the deviation from truth in the
latter will be only 1/3 of whatever it is in the former.
[Illustration: Fig. 156.]
[Illustration: Fig. 157.]
In this example we have supposed the number of divisions to be an even
one, hence the point K, Fig. 152, falls diametrically opposite to A,
whereas in an odd number of points of division this would not be the
case, and we must proceed by either of the two following methods:--
[Illustration: Fig. 158.]
In Fig. 158 is shown a circle requiring to be divided by 17 equidistant
points. Starting from point 1 we mark on the outside of the
circumference points 2, 3, 4, &c., up to point 9. Starting again from
point 1 we mark points 10, 11, &c., up to 17. If, then, we try the
compasses to 17 and 9 we shall find they come too close together, hence
we take another pair of compasses (so as not to disturb the set of our
first pair) and find the centre between 9 and 17 as shown by the point
A. We then correct the set of our first pair of compasses, as near as
the judgment dictates, and from point A, we mark with the second
compasses (set to one half the new space of the first compasses) the
points B, C. With the first pair of compasses, starting from B, we mark
D, E, &c., to G; and from I, we mark divisions H, I, &c., to K, and if
the compasses were set true, K and G would meet at the circle. We may,
however, mark a point midway between K and G, as at 5. Starting again
from points C and I, we mark the other side of the circle in a similar
manner, producing the lines P and Q, midway between which (the compasses
not being set quite correct as yet) is the true point for another
division. After again correcting the compasses, we start from B and 5
respectively, and mark point 7, again correcting the compasses. Then
from C and the point between P and Q, we may mark an intermediate point,
and so on until all the points of division are made. This method is
correct enough for most practical purposes, but the method shown in Fig.
159 is more correct for an odd number of points of division. Suppose
that we have commenced at the point marked I, we mark off half the
required number of holes on one side and arrive at the point 2; and
then, commencing at the point I again, we mark off the other half of the
required number of holes, arriving at the point 3. We then apply our
compasses to the distance between the points 2 and 3; and if that
distance is not exactly the same to which the compasses are set, we make
the necessary adjustment, and try again and again until correct
adjustment is secured.
[Illustration: Fig. 159.]
It is highly necessary, in this case, to make the lines drawn at each
trial all on the same side of the circle and of equal length, but of a
different length to those marked on previous trials. For example, left
the lines A, B, C, D, in Fig. 159 represent those made on the first
trial, and E, F, G, H, those made on the second trial; and when the
adjustment is complete, let the last trial be made upon the outside or
other side of the circle, as shown by the lines I, J, K, L. Having
obtained the three true points, marked 1, 2, 3, we proceed to mark the
intermediate divisions, as described for an even number of divisions,
save that there will be a space, 2 and 3, opposite point 1, instead of a
point, as in case of a circle having an even number of divisions.
[Illustration: Fig. 160.]
The equal points of division thus obtained may be taken for the centres
of the tooth at the pitch circle or for one side of the teeth, as the
method to be pursued to mark the tooth curves may render most desirable.
If, for example, a template be used to mark off the tooth curves, the
marks may be used to best advantage as representing the side of a tooth,
and from them the thickness of the tooth may be marked or not as the
kind of template used may require. Thus, if the template shown in Fig.
21 be used, no other marks will be used, because the sides of a tooth on
each side of a space may be marked at one setting of the template to the
lines or marks of division. If, however, a template, such as shown in
Fig. 81 be used, a second set of lines marked distant from the first to
a radius equal to the thickness of a tooth becomes necessary so that the
template may be set to each line marked. If the Willis odontograph or
the Robinson template odontograph be used the second set of lines will
also be necessary. In using the Walker scale a radial line, as G in Fig.
142, will require to be marked through the points of equal division, and
the thickness of the tooth at the points on the pitch circle and at the
root must be marked as was shown in Fig. 142.
But if the arcs for the tooth curves are to be marked by compasses, the
location for the centres wherefrom to strike these arcs may be marked
from the points of division as was shown in Fig. 130.
To construct a pattern wherefrom to cast a bevel gear-wheel.--When a
pair of bevel-wheels are in gear and upon their respective shafts all
the teeth on each wheel incline, as has been shown, to a single point,
hence the pattern maker draws upon a piece of board a sketch
representing the conditions under which the wheels are to operate. A
sketch of this kind is shown in Fig. 160, in which A, B, C, D, represent
in section the body of a bevel pinion. F G is the point of a tooth on
one side, and E the point of a tooth on the other side of the pinion,
while H I are pitch lines for the two teeth. Thus, the cone surface, the
points, the pitch lines and the bottom of the spaces, projected as
denoted by the dotted lines, would all meet at X, which represents the
point where the axes of the shafts would meet.
[Illustration: Fig. 161.]
In making wooden patterns wherefrom to cast the wheels, it is usual,
therefore, to mark these lines on a drawing-board, so that they may be
referred to by the workman in obtaining the degree of cone necessary for
the body A B C D, to which the teeth are to be affixed. Suppose, then,
that the diameter of the pinion is sufficiently small to permit the body
A B C D to be formed of one piece instead of being put together in
segments, the operation is as follows: The face D C is turned off on the
lathe, and the piece is reversed on the lathe chuck, and the face A B is
turned, leaving a slight recess at the centre to receive and hold the
cone point true with the wheel. A bevel gauge is then set to the angle A
B C, and the cone of the body is turned to coincide in angle with the
gauge and to the required diameter, its surface being made true and
straight so that the teeth may bed well. While turning the face D C in
the lathe a fine line circle should be struck around the circumference
of the cone and near D C, on which line the spacing for the teeth may be
stepped off with the compasses. After this circle or line is divided off
into as many equidistant points as there are to be teeth on the wheel,
the points of division require to be drawn into lines, running across
the cone surface of the wheel, and as the ordinary square is
inapplicable for the purpose, a suitable square is improvised as
follows: In Fig. 161 let the outline in full lines denote the body of a
pinion ready to receive the teeth, and A B the circle referred to as
necessary for the spacing or dividing with the compasses. On A B take
any point, as C, as a centre, and with a pair of compasses mark
equidistant on each side of it two lines, as D, D. From D, D as
respective centres mark two lines, crossing each other as at F, and draw
a line, joining the intersection of the lines at F with C, and the last
line, so produced, will be in the place in which the teeth are to lie;
hence the wheel will require as many of these lines as it is to contain
teeth, and the sides of the teeth, being set to these lines all around
the pinion, will be in their proper positions, with the pitch lines
pointing to X, in Fig. 160.
[Illustration: Fig. 162.]
To avoid, however, the labor involved in producing these lines for each
tooth, two other plans may be adopted. The first is to make a square,
such as shown in Fig. 162, the face _f_ _f_ being fitted to the surface
C, in Fig. 161, while the edges of its blade coincide with the line
referred to; hence the edge of the blade may be placed coincident
successively with each point of division, as D D, and the lines for the
place of the length of each tooth be drawn. The second plan is to divide
off the line A B before removing the body of the pinion from the lathe,
and produce, as described, a line for one tooth. A piece of wood may
then be placed so that when it lies on the surface of the hand-rest its
upper surface will coincide with the line as shown in Fig. 163, in which
W is the piece of wood, and A, B, C, &c., the lines referred to. If the
teeth are to be glued and bradded to the body, they are first cut out in
blocks, left a little larger every way than they are to be when
finished, and the surfaces which are to bed on the cone are hollowed to
fit it. Then blocks are glued to the body, one and the same relative
side of each tooth being set fair to the lines. When the glue is dry,
the pinion is again turned on the lathe, the gauge for the cone of the
teeth being set in this case to the lines E, F, G in Fig. 160. The pitch
circles must then be struck at the ends of the teeth. The turned wheel
is then ready to have the curves of the teeth marked. The wheel must now
again be divided off on the pitch circle at the large end of the cone
into as many equidistant points as there are to be teeth on the wheel,
and from these points, and on the same relative side of them, mark off a
second series of points, distant from the points of division to an
amount equal to the thickness the teeth are required to be. From these
points draw in the outline of the teeth (upon the ends of the blocks to
form the teeth) at the large end of the cone. Then, by use of the
square, shown in Fig. 162, transfer the points of the teeth to the small
end of the cone, and trace the outline of the teeth at the small end,
taking centres and distances proportionate to the reduced diameter of
the pitch circle at the small end, as shown in Fig. 160, where at J are
three teeth so marked for the large end, and at K three for the small
end, P P representing the pitch circle, and R R a circle for the compass
points. The teeth for bevel pinions are sometimes put on by dovetails,
as shown in Fig. 164, a plan which possesses points of advantage and
disadvantage. Wood shrinks more across the grain than lengthwise with
it, hence when the grain of the teeth crosses that of the body with
every expansion or contraction of the wood (which always accompanies
changes in the humidity of the atmosphere) there will be a movement
between the two, because of the unequal expansion and contraction,
causing the teeth to loosen or to move. In the employment of dovetails,
however, a freedom of movement lengthways of the tooth is provided to
accommodate the movement, while the teeth are detained in their proper
positions. Again, if in making the founders' mould, one of the mould
teeth should break or fall down when the pattern is withdrawn, a tooth
may be removed from the pattern and used by the moulder to build up the
damaged part of the mould again. And if the teeth of a bevel pinion are
too much undercut on the flank curves to permit the whole pattern from
being extracted from the mould without damaging it, dovetailed teeth may
be drawn, leaving the body of the pattern to be extracted from the mould
last. On the other hand, the dovetail is a costly construction if
applied to large wheels. If the teeth are to be affixed by dovetails,
the construction varies as follows: Cut out a wooden template of the
dovetail, leaving it a little narrower than the thickness of the tooth
at the root, and set the template on the cone at a distance from one of
the lines A, B, C, Fig. 163, equal to the margin allowed between the
edge of the dovetail and the side of the root of the tooth, and set it
true by the employment of the square, shown in Fig. 162, and draw along
the cone surface of the body lines representing the location of the
dovetail grooves. The lines so drawn will give a taper toward X (Fig.
160), providing that, the template sides being parallel, each side is
set to the square. While the body is in the lathe, a circle on each end
may be struck for the depth of the dovetails, which should be cut out to
gauge and to template, so that the teeth will interchange to any
dovetail. The bottom of the dovetails need not be circular, but flat,
which is easier to make. Dovetail pieces or strips are fitted to the
grooves, being left to project slightly above the face of the cone or
body. They are drawn in tight enough to enable them to keep their
position while being turned in the lathe when the projecting points are
turned down level with the cone of the body. The teeth may then be got
out as described for glued teeth, and the dovetails added, each being
marked to its place, and finally the teeth are cut to shape.
[Illustration: Fig. 163.]
[Illustration: Fig. 164.]
[Illustration: Fig. 165.]
In wheels too large to have their cones tested by a bevel gauge, a
wooden gauge may be made by nailing two pieces of wood to stand at the
required angle as shown in Fig. 165, which is extracted from _The
American Machinist_, or the dead centre C and a straightedge may be used
as follows. In the figure the other wheel of the pair is shown dotted in
at B, and the dead centre is set at the point where the axes of A and B
would meet; hence if the largest diameter of the cone of A is turned to
correct size, the cone will be correct when a straightedge applied as
shown lies flat on the cone and meets the point of the dead centre E.
The pinion B, however, is merely introduced to explain the principle,
and obviously could not be so applied practically, the distance to set
_e_, however, is the radius _a_.
Skew Bevel.[9]--When the axles of the shaft are inclined to each other
instead of being in a straight line, and it is proposed to connect and
communicate motion to the shafts by means of a single pair of
bevel-gears, the teeth must be inclined to the base of the frustra to
allow them to come into contact.
[9] From the "Engineer and Machinists' Assistant."
[Illustration: Fig. 166.]
To find the line of contact upon a given frustrum of the tangent-cone;
let the Fig. 166 be the plane of the frustrum; _a_ the centre. Set off
_a_ _e_ equal to the shortest distance between the axes (called the
_eccentricity_), and divide it in _c_, so that _a_ _c_ is to _e_ _c_ as
the mean radius of the frustrum to the mean radius of that with which it
is to work; draw _c_ _p_ perpendicular to _a_ _e_, and meeting the
circumference of the conical surface at _m_; perform a similar operation
on the base of the frustrum by drawing a line parallel to _c_ _m_ and at
the same distance _a_ _c_ from the centre, meeting the circumference in
_p_.
The line _p_ _c_ is then plainly the line of direction of the teeth. We
are also at liberty to employ the equally inclined line _c_ _q_ in the
opposite direction, observing only that, in laying out the two wheels,
the pair of directions be taken, of which the inclinations correspond.
[Illustration: Fig. 167.]
Fig. 167 renders this mode of laying off the outlines of the wheels at
once obvious. In this figure the line _a_ _e_ corresponds to the line
marked by the same letters in Fig. 166; and the division of it at _c_ is
determined in the manner directed. The line _c_ _m_ being thus found in
direction, it is drawn indefinitely to _d_. Parallel to this line and
from the point _c_ draw _e_ to _e_, and in this line take the centre of
the second wheel. The line _c_ _m_ _d_ gives the direction of the teeth;
and if from the centre _a_ with radius at _c_ a circle be described, the
direction of any tooth of the wheel will be a tangent to it, as at _c_,
and similarly if a centre _e_ be taken in the line _e_ _d_, and with
radius _e_ _d_, _c_ _e_ a circle be drawn, the direction of the teeth of
the second wheel will be tangents to this last, as at _d_.
Having thus found the direction of the teeth, these outlines may be
formed as in the case of ordinary bevel-wheels and with equal exactness
and facility, all that is necessary being to find the curves for the
teeth as described for bevel-wheels, and follow precisely the same
construction, except that the square, Fig. 162, marking the lines across
the cones, requires to be set to the angle for the tooth instead of at a
right angle, and this angle may be found by the construction shown in
Fig. 167, it being there represented by line _d_ _c_. It is obvious,
however, that the bottoms of the blocks to form the teeth must be curved
to bed on the cone along the line _d_ _c_, Fig. 167, and this may best
be done by bedding two teeth, testing them by trial of the actual
surfaces.
[Illustration: Fig. 168.]
Then two teeth may be set in as No. 1 and No. 6 in the box shown in Fig.
148, the intermediate ones being dressed down to them.
Where a bevel-wheel pattern is too large to be constructed in one piece
and requires to be built up in pieces, the construction is as in Fig.
168, in which on the left is shown the courses of segments 1, 2, 3, 4,
5, &c., of which the rim is built up (as described for spur wheels), and
on the right is shown the finished rim with a tooth, _c_, in position.
The tooth proper is of the length of face of the wheel as denoted by _b
b´_; now all the lines bounding the teeth must converge to the point X.
Suppose, then, that the teeth are to be shaped for curve of face and
flank in a box as described for spur-wheel teeth in Fig. 146, then in
Fig. 168 let _a_, _a_ represent the bottom and _b b´_ the top of the
box, and _c_ a tooth in the box, its ends filling the opening in the box
at _b b´_ then the curve on the sides of the box at _b´_ must be of the
form shown at F, and the curve on the sides of the box (at the point _b_
of its length) must be as shown at G, the teeth shown in profile at G
and U representing the forms of the teeth at their ends, on the outside
of the wheel rim at _b´_, and on the inside at _b_; having thus made a
box of the correct form on its sides, the teeth may be placed in it and
planed down to it, thus giving all the teeth the same curve.
The spacing for the teeth and their fixing may be done as described for
the bevel pinion.
[Illustration: Fig. 169.]
To construct a pattern wherefrom to cast an endless screw, worm, or
tangent screw, which is to have the worm or thread cut in a lathe.--Take
two pieces, each to form one longitudinal half of the pattern; peg and
screw them together at the ends, an excess of stuff being allowed at
each end for the accommodation of two screws to hold the two halves
together while turning them in the lathe, or dogs, if the latter are
more convenient, as they might be in a large pattern. Turn the piece
down to the size over the top of the thread, after which the core prints
are turned. The body thus formed will be ready to have the worm or
thread cut, and for this purpose the tools shown in Figs. 169 and 140
are necessary.
That shown in Fig. 169 should be flat on the face similar to a parting
tool for cast iron, but should have a great deal more bottom rake, as
strength is not so much an object, and the tool is more easily
sharpened. It has also in addition two little projections A B like the
point of a penknife, formed by filing away the steel in the centre;
these points are to cut the fibres of the wood, the severed portion
being scraped away by the flat part of the tool.
[Illustration: Fig. 170.]
The degree of side rake given to the tool must be sufficient to let the
tool sides well clear the thread or worm, and will therefore vary with
the pitch of the worm.
The width of the tool must be a shade narrower than the narrowest part
of the space in the worm. Having suitably adjusted the change wheels of
the lathe to cut the pitch required the parting tool is fed in until the
extreme points reach the bottom of the spaces, and a square nosed
parting tool without any points or spurs will finish the worm to the
required depth. This will have left a square thread, and this we have
now to cut to the required curves on the thread or worm sides, and as
the cutting will be performed on the end grain of the wood, the top face
of the tool must be made keen by piercing through the tool a slot A,
Fig. 170, and filing up the bevel faces B, C and D, and then carefully
oilstoning them. This tool should be made slightly narrower than the
width of the worm space, so that it may not cut on both sides at once,
as it would have too great a length of cutting edge.
[Illustration: Fig. 171.]
Furthermore, if the pattern is very large, it will be necessary to have
two tools for finishing, one to cut from the pitch line inwards and the
other to complete the form from the pitch line outwards. It is advisable
to use hard wood for the pattern.
If it is decided to cut the thread by hand instead of with these lathe
tools, then, the pattern being turned as before, separate the two halves
by taking out the screws at the ends; select the half that has not the
pegs, as being a little more convenient for tracing lines across. Set
out the sections of the thread, A, B, C, and D, Fig. 171, similar to a
rack; through the centres of A, B, C, and D, square lines across the
piece; these lines, where they intersect the pitch line, will give the
centres of teeth on that side: or if we draw lines, as E, F, through the
centres of the spaces, they will pass through the centres of the teeth
(so to speak) on the other side; in this position complete the outline
on that side. It will be found, in drawing these outlines, that the
centres of some of the arcs will lie outside the pattern. To obtain
support for the compasses, we must fit over the pattern a piece of board
such as shown by dotted lines at G H.
[Illustration: Fig. 172.]
It now remains to draw in the top of the thread upon the curved surface
of the half pattern; for this purpose take a piece of stiff card or
other flexible material, wrap it around the pattern and fix it
temporarily by tacks, we then trim off the edges true to the pattern,
and mark upon the edges of the card the position of the tops of the
thread upon each side; we remove the card and spread it out on a flat
surface, join the points marked on the edges by lines as in Fig. 172,
replace the card exactly as before upon the pattern, and with a fine
scriber we prick through the lines. The cutting out is commenced by
sawing, keeping, of course, well within the lines; and it is facilitated
by attaching a stop to the saw so as to insure cutting at all parts
nearly to the exact depth. This stop is a simple strip of wood and may
be clamped to the saw, though it is much more convenient to have a
couple of holes in the saw blade for the passage of screws. For
finishing, a pair of templates, P and Q, Fig. 173, right and left, will
be found useful; and finally the work should be verified and slight
imperfections corrected by the use of a form or template taking in three
spaces, as shown at R in Fig. 173. In drawing the lines on the card, we
must consider whether it is a right or left-handed worm that we desire.
In the engraving the lines are those suitable for a right-handed thread.
Having completed one half of the pattern, place the two halves together,
and trace off the half that is uncut, using again the card template for
drawing the lines on the curved surface. The cutting out will be the
same as before.
[Illustration: Fig. 173.]
As the teeth of cast wheels are, from their deviation from accuracy in
the tooth curves and the concentricity of the teeth to the wheel centre,
apt to create noise in running, it is not unusual to cast one or both
wheels with mortises in the rim to receive wooden teeth. In this case
the wheel is termed a mortise wheel, and the teeth are termed _cogs_. If
only one of a pair of wheels is to be cogged, the largest of the pair is
usually selected, because there are in that case more teeth to withstand
the wear, it being obvious that the wear is greatest upon the wheel
having the fewest teeth, and that the iron wheel or pinion can better
withstand the wear than the mortise wheel. The woods most used for cogs
are hickory, maple, hornbeam and locust. The blocks wherefrom the teeth
are to be formed are usually cut out to nearly the required dimensions,
and kept in stock, so as to be thoroughly well-seasoned when required
for use, and, therefore less liable to come loose from shrinkage after
being fitted to the mortise in the wheel. The length of the shanks is
made sufficient to project through the wheel rim and receive a pin, as
shown in Fig. 174, in which B is a blank tooth, and C a finished tooth
inserted in the wheel, the pin referred to being at P. But, if a mortise
should fall in an arm of the wheel, this pin-hole must pass through the
rim, as shown in the mortise A. The wheel, however, should be designed
so that the mortises will not terminate in the arms of the wheel.
[Illustration: Fig. 174.]
[Illustration: Fig. 175.]
Another method of securing the teeth in the mortises is to dovetail them
at the small end and drive wedges between them, as shown in Fig. 175, in
which C C are two contiguous teeth, R the wheel rim and W W two of the
wedges. On account of the dovetailing the wedges exert A pressure
pressing the teeth into the mortises. This plan is preferable to that
shown in the Fig. 174 inasmuch as from the small bearing area of the
pins they become loose quicker, and furthermore there is more elasticity
to take up the wear in the case of the wedges.
[Illustration: Fig. 176.]
The mortises are first dressed out to a uniform size and taper, using
two templates to test them with, one of which is for the breadth and the
other for the width of the mortise. The height above the wheel requires
to be considerably more than that due to the depth of the teeth, so that
the surface bruised by driving the cogs or when fitting them into the
mortises may be cut off. To avoid this damage as much as possible, a
broad-face hammer should be employed--a copper, lead, lignum vitæ, or a
raw hide hammer being preferable, and the last the best. The teeth are
got out in a box and two guides, such as shown in Figs. 176, 177, and
178, similar letters of reference denoting the same parts in all three
illustrations.
In Fig. 176, X is a frame or box containing and holding the operative
part of the tooth, and resting on two guides C D. The height of D from
the saw table is sufficiently greater than that of C to give the shank G
the correct taper, E F representing the circular saw. T is a plain piece
of the full size of the box or frame, and serving simply to close up on
that side the mortise in the frame. The grain of T should run at a right
angle to the other piece of the frame so as to strengthen it. S is a
binding screw to hold the cog on the frame, and H is a guide for the
edge of the frame to slide against. It is obvious, now, that if the
piece D be adjusted at a proper distance from the circular saw E F, and
the edge of the frame be moved in contact with the guide H, one side of
the tooth shank will be sawn. Then, by reversing the frame end for end,
the other side of the shank may be sawn. Turning the frame to a right
angle the edges of the cog shank can be sawn from the same box or frame,
and pieces C, D, as shown in Fig. 177.
[Illustration: Fig. 177.]
The frame is now stood on edge, as in Fig. 178, and the underneath
surfaces sawed off to the depth the saw entered when the shank taper was
sawn. This operation requires to be performed on all four sides of the
tooth.
After this operation is performed on one cog, it should be tried in the
wheel mortises, to test its correctness before cutting out the shanks on
all the teeth.
[Illustration: Fig. 178.]
The shanks, being correctly sawn, may then be fitted to the mortises,
and let in within 1/8 of butting down on the face of the wheel, this
amount being left for the final driving. The cogs should be numbered to
their places, and two of the mortises must be numbered to show the
direction in which the numbers proceed. To mark the shoulders (which are
now square) to the curvature of the rim, a fork scriber should be used,
and the shanks of the cogs should have marked on them a line coincident
with the inner edge of the wheel rim. This line serves as a guide in
marking the pin-holes and for cutting the shanks to length; but it is to
be remembered that the shanks will pass farther through to the amount of
the distance marked by the fork scriber. The holes for the pins which
pass through the shanks should be made slightly less in their distances
(measured from the nearest edge of the pin-hole) from the shoulders of
the cogs than is the thickness of the rim of the wheel, so that when the
cogs are driven fully home the pin-holes will appear not quite full
circles on the inside of the wheel rim; hence, the pins will bind
tightly against the inside of the wheel rim, and act somewhat as keys,
locking and drawing the shanks to their seats in the mortises.
In cases where quietness of running is of more consequence than the
durability of the teeth, or where the wear is not great, both wheels may
be cogged, but as a rule the larger wheel is cogged, the smaller being
of metal. This is done because the teeth of the smaller wheel are the
most subject to wear. The teeth of the cogged wheel are usually made the
thickest, so as to somewhat equalise the strength of the teeth on the
two wheels.
Since the power transmitted by a wheel in a given time is composed of
the pressure or weight upon the wheel, and the space a point on the
pitch circle moves through in the given time, it is obvious that in a
train of wheels single geared, the velocities of all the wheels in the
train being equal at the pitch circle, the teeth require to be of equal
pitch and thickness throughout the train. But when the gearing is
compounded the variation of velocity at the pitch circle, which is due
to the compounding, has an important bearing upon the necessary strength
of the teeth.
Suppose, for example, that a wheel receives a tooth pressure of 100 lbs.
at the pitch circle, which travels at the velocity of 100 feet per
minute, and is keyed to the same shaft with another wheel whose velocity
is 50 feet per minute. Now, in the power transmitted by the two wheels
the element of time is 50 for one wheel and 100 for the other, hence the
latter (supposing both wheels to have an equal number of teeth in
contact with their driver or follower as the case may be) will be twice
as strong in proportion to the duty, and it appears that in compounded
gearing the strength in proportion to the duty may be varied in
proportion as the velocity is modified by compounding of the wheels.
Thus, when the velocity at the pitch circle is increased its strength is
increased, and per contra when its velocity is decreased its strength is
decreased, when considered in proportion to the duty. When, however, the
wheels are upon long shafts, or when they overhang the bearing of the
shaft, the corner contact will from tension of the shaft, continue much
longer than when the shaft is maintained rigid.
It is obvious that if a wheel transmits a certain amount of power, the
pressure of tooth upon tooth will depend upon the number of teeth in
contact, but since, in the case of very small wheels, that is to say,
pinions of the smallest diameter of the given pitch that will transmit
continuous motion, it occurs that only one tooth is in continuous
contact, it is obvious that each single tooth must have sufficient
strength to withstand the whole of the pressure when worn to the limits
to which the teeth are supposed to wear. But when the pinion is so small
that it has but one tooth in continuous contact, that contact takes
place nearer the line of centres and to the root of the tooth, and
therefore at a less leverage to the line of fracture, hence the ultimate
strength of the tooth is proportionately increased. On the other hand,
however, the whole stress of the wheel being concentrated on the arc of
contact of one tooth only (instead of upon two or more teeth as in
larger wheels), the wear is proportionately greater; hence, in a short
time the teeth of the pinion are found to be thinner than those on the
other wheel or wheels. The multiplicity of conditions under which small
wheels may work with relation to the number of teeth in contact, the
average leverage of the point of contact from the root of the tooth, the
shape of the tooth, &c., renders it desirable in a general rule to
suppose that the whole strain falls upon one tooth, so that the
calculation shall give results to meet the requirements when a single
tooth only is in continuous contact.
It follows, then, that the thickness of tooth arrived at by calculation
should be that which will give to a tooth, when worn to the extreme
thinness allowed, sufficient strength (with a proper margin of safety)
to transmit the whole of the power transmitted by the wheel.
The margin (or factor) of safety, or in other words, the number of times
the strength of the tooth should exceed the amount of power transmitted,
varies (according to the conditions under which the wheels work) between
5 and 10.
The lesser factor may be used for slow speeds when the power is
continuously and uniformly transmitted. The greater factor is necessary
when the wheels are subjected to violent shocks and the direction of
revolution requires to be reversed.
[Illustration: Fig. 179.]
In pattern-cast teeth, contact between the teeth of one wheel and those
of the other frequently occurs at one corner only, as shown in Fig. 179,
and the line of fracture is in the direction denoted by the diagonal
dotted lines. The causes of this corner contact have been already
explained, but it may be added that as the wheels wear, the contact
extends across the full breadths of the teeth, and the strength in
proportion to the duty, therefore, steadily increases from the time the
new wheels have action until the wear has caused contact fully across
the breadth. Tredgold's rule for finding the proper thickness of tooth
for a given stress upon cast-iron teeth loaded at the corner as in Fig.
179 and supposed to have a velocity of three feet per second of time, is
as follows:--
Rule.--Divide the stress in pounds at the pitch circle by 1500, and the
square root of the quotient is the required thickness of tooth in inches
or parts of an inch.
In the results obtained by the employment of this rule, an allowance of
one-third the thickness for wear, and the margin for safety is included,
so that the thickness of tooth arrived at is that to be given to the
actual tooth. Further, the rule supposes the breadth of the tooth to be
not less than twice the height of the same, any extra breadth not
affecting the result (as already explained), when the pressure falls on
a corner of the tooth.
In practical application, however, the diameter of the wheel at the
pitch circle is generally, or at least often a fixed quantity, as well
as the amount of stress, and it will happen as a rule that taking the
stress as a fixed element and arriving at the thickness of the tooth by
calculation, the required diameter of wheel, or what is the same thing,
its circumference, will not be such as to contain the exact number of
teeth of the thickness found by the calculation, and still give the
desired amount of side clearance. It is desirable, therefore, to deal
with the stress upon the tooth at the pitch circle, and the diameter,
radius, or circumference of the pitch circle, and its velocity, and
deduce therefrom the required thickness for the teeth, and conform the
pitch to the requirements as to clearance from the tooth thickness thus
obtained.
To deduce the thickness of the teeth from these elements we have
Robertson Buchanan's rule, which is as follows:--
Find the amount of horse-power employed to move the wheel, and divide
such horse-power by the velocity in feet per second of the pitch line of
the wheel. Extract the square root of the quotient, and three-fourths of
this root will be the least thickness of the tooth. To the result thus
obtained, there must be added the allowance for wear of the teeth and
the width of the space including the clearance which will determine the
number of teeth in the wheel.
In conforming strictly to this rule the difficulty is met with that it
would give fractional pitches not usually employed and difficult to
measure on an existing wheel. Cast wheels kept on hand or in stock by
machinists have usually the following standard:--
Beginning with an inch pitch, the pitches increase by 1/8 inch up to
3-inch pitch, from 3 to 4-inch pitches the increase is by 1/4 inch, and
from 4-inch pitch and upwards the increase is by 1/2 inch. Now, under
the rule the pitches would, with the clearance made to bear a certain
proportion to the pitch, be in odd fractions of an inch.
It appears then, that, if in a calculation to obtain the necessary
thickness of tooth, the diameter of the pitch circle is not an element,
the rule cannot be strictly adhered to unless the diameter of the pitch
circle be varied to suit the calculated thickness of tooth; or unless
either the clearance, factor of safety, or amount of tooth thickness
allowed for wear be varied to admit of the thickness of tooth arrived at
by the calculation. But if the diameter of the pitch circle is one of
the elements considered in arriving at the thickness of tooth requisite
under given conditions, the pitch must, as a rule, either be in odd
fractions, or else the allowance for wear, factor of safety, or amount
of side clearance cannot bear a definite proportion to the pitch. But
the allowance for clearance is in practice always a constant proportion
of the pitch, and under these circumstances, all that can be done when
the circumstances require a definite circumference of pitch circle, is
to select such a pitch as will nearest meet the requirements of tooth
thickness as found by calculation, while following the rule of making
the clearance a constant proportion of the pitch. When following this
plan gives a thinner tooth than the calculation calls for, the factor of
safety and the allowance for wear are reduced. But this is of little
consequence whenever more than one tooth on each wheel is in contact,
because the rules provide for all the stress falling on one tooth. When,
however, the number of teeth in the pinion is so small that one tooth
only is in contact, it is better to select a pitch that will give a
thicker rather than a thinner tooth than called for by the calculation,
providing, of course, that the pitch be less than the arc of contact, so
that the motion shall be continuous.
But when the pinions are shrouded, that is, have flanges at each end,
the teeth are strengthened; and since the wear will continue greater
than in wheels having more teeth in contact, the shrouding may be
regarded as a provision against breakage in consequence of the reduction
of tooth thickness resulting from wear.
In the following table is given the thickness of the tooth for a given
stress at the pitch circle, calculated from Tredgold's rule for teeth
supposed to have contact when new at one corner only.
+-------------------+--------------------+---------------------+
| Stress in lbs. at | Thickness of tooth | Actual pitches to |
| pitch circle. | in inches. | which wheels may be |
| | | made. |
+-------------------+--------------------+---------------------+
| 400 | .52 | 1-1/8 to 1-1/4 |
| 800 | .75 | 1-1/2 " 1-5/8 |
| 1,200 | .90 | 1-7/8 " 2 |
| 1,600 | 1.03 | 2 " 2-1/8 |
| 2,000 | 1.15 | 2-1/4 " 2-3/8 |
| 2,400 | 1.26 | 2-1/2 " 2-5/8 |
| 2,800 | 1.36 | 2-5/8 " 2-3/4 |
| 3,200 | 1.43 | 2-7/8 " 3 |
| 3,600 | 1.56 | 3-1/8 " 3-1/4 |
| 4,000 | 1.63 | 3-1/4 " 3-3/8 |
| 4,400 | 1.70 | 3-3/8 " 3-1/2 |
| 4,800 | 1.78 | 3-1/2 " 3-5/8 |
| 5,200 | 1.86 | 3-5/8 " 3-3/4 |
| 5,600 | 1.93 | 3-3/4 " 4 |
| 6,000 | 2.00 | 4 " 4-1/4 |
+-------------------+--------------------+---------------------+
In wheels that have their teeth cut to form in a gear-cutting machine
the thickness of tooth at any point in the depth is equal at any point
across the breadth; hence, supposing the wheels to be properly keyed to
their shafts so that the pitch line across the breadth of the wheel
stands parallel to the axis of the shaft, the contact of tooth upon
tooth occurs across the full breadth of the tooth.
As the practical result of these conditions we have three important
advantages: first, that the stress being exerted along the full breadth
of the tooth instead of on one corner only, the tooth is stronger (with
a given breadth and thickness) in proportion to the duty; second, that
with a given pitch, the thickness and therefore the margin for safety
and allowance for wear are increased, because the tooth may be increased
in thickness at the expense of the clearance, which need be merely
sufficient to prevent contact on both sides of the spaces so as to
prevent the teeth from locking in the spaces; and thirdly, because the
teeth will not be subject to sudden impacts or shocks of tooth upon
tooth by reason of back lash.
[Illustration: Fig. 180.]
In determining the strength of cut gear-teeth we may suppose the weight
to be disposed along the face at the extreme height of the tooth, in
which case the theoretical shape of the tooth to possess equal strength
at every point from the addendum circle to the root would be a parabola,
as shown by the dotted lines in Fig. 180, which represents a tooth
having radial flanks. In this case it is evident that the ultimate
strength of the tooth is that due to the thickness at the root, because
it is less than that at the pitch circle, and the strength, as a whole,
is not greater than that at the weakest part. But since teeth with
radial flanks are produced, as has been shown, with a generating circle
equal in diameter to the radius of the pinion, and since with a
generating circle bearing that ratio of diameter to diameter of pitch
circle the acting part of the flank is limited, it is usual to fill in
the corners with fillets or rounded corners, as shown in Fig. 129;
hence, the weakest part of the tooth will be where the radial line of
the flank joins the fillet and, therefore, nearer the pitch circle than
is the root. But as only the smallest wheel of the set has radial flanks
and the flanks thicken as the diameter of the wheels increase, it is
usual to take the thickness of the tooth at the pitch circle as
representing the weakest part of the tooth, and, therefore, that from
which the strength of the tooth is to be computed. This, however, is not
actually the case even in teeth which have considerable spread at the
roots, as is shown in Fig. 181, in which the shape of the tooth to
possess equal strength throughout its depth is denoted by the parabolic
dotted lines.
[Illustration: Fig. 181.]
Considering a tooth as simply a beam supporting the strain as a weight
we may calculate its strength as follows:--
Multiply the breadth of the tooth by the square of its thickness, and
the product by the strength of the material, per square inch of section,
of which the teeth are composed, and divide this last product by the
distance of the pitch line from the root, and the quotient will give a
tooth thickness having a strength equal to the weight of the load, but
having no margin for safety, and no allowance for wear; hence, the
result thus obtained must be multiplied by the factor of safety (which
for this class of tooth may be taken as 6), and must have an additional
thickness added to allow for wear, so that the factor of safety will be
constant notwithstanding the wear.
Another, and in some respects more convenient method, for obtaining the
strength of a tooth, is to take the strength of a tooth having 1-inch
pitch, and 1 inch of breadth, and multiply this quantity of strength by
the pitch and the face of the tooth it is required to find the strength
of, both teeth being of the same material.
Example.--The safe working pressure for a cast-iron tooth of an inch
pitch, and an inch broad will transmit, being taken as 400 lbs., what
pressure will a tooth of 3/4-inch pitch and 3 inches broad transmit with
safety?
Here 400 lbs. × 3/4 pitch × 3 breadth = 900 = safe working pressure of
tooth 3/4-inch pitch and 3 inches broad.
Again, the safe working pressure of a cast-iron tooth, 1 inch in breadth
and of 1-inch pitch, being considered as 400 lbs., what is the safe
working pressure of a tooth of 1-inch pitch and 4-inch breadth?
Here 400 × 1 × 4 = 1600.
The philosophy of this is apparent when we consider that four wheels of
1-inch pitch and an inch face, placed together side by side, would
constitute, if welded together, one wheel of an inch pitch and 4 inches
face. (The term _face_ is applied to the wheel, and the term breadth to
the tooth, because such is the custom of the workshop, both terms,
however, mean, in the case of spur-wheels, the dimension of the tooth in
a direction parallel to the axis of the wheel shaft or wheel bore.)
The following table gives the safe working pressures for wheels having
an inch pitch and an inch face when working at the given velocities,
S.W.P. standing for "safe working pressure:"--
+------------+------------+------------+------------+--------------+
| Velocity of| | | | |
|pitch circle| S.W.P. for | S.W.P. for |S.W.P. for | S.W.P. |
| in feet | cast-iron |spur mortise| cast-iron | for bevel |
|per second. |spur gears. | gears. |bevel gears.|mortise gears.|
+------------+------------+------------+------------+--------------+
| 2 | 368 | 178 | 258 | 178 |
| 3 | 322 | 178 | 225 | 157 |
| 6 | 255 | 178 | 178 | 125 |
| 12 | 203 | 142 | 142 | 99 |
| 18 | 177 | 124 | 124 | 87 |
| 24 | 161 | 113 | 113 | 79 |
| 30 | 150 | 105 | 105 | 74 |
| 36 | 140 | 98 | 98 | 69 |
| 42 | 133 | 93 | 93 | 65 |
| 48 | 127 | 88 | 88 | 62 |
+------------+------------+------------+------------+--------------+
For velocities less than 2 feet per second, use the same value as for 2
feet per second.
The proportions, in terms of the pitch, upon which this table is based,
are as follows:--
Thickness of iron teeth .395 of the pitch.
" wooden " .595 "
Height of addendum .28 "
Depth below pitch line .32 "
The table is based upon 400 lbs. per inch of face for an inch pitch, as
the safe working pressure of mortise wheel teeth or cogs; it may be
noted that there is considerable difference of opinion. They are claimed
by some to be in many cases practically stronger than teeth of cast
iron. This may be, and probably is, the case when the conditions are
such that the teeth being rigid and rigidly held (as in the case of
cast-iron teeth), there is but one tooth on each wheel in contact. But
when there is so nearly contact between two teeth on each wheel that but
little elasticity in the teeth would cause a second pair of teeth to
have contact, then the elasticity of the wood would cause this second
contact. Added to this, however, we have the fact that under conditions
where violent shock occurs the cog would have sufficient elasticity to
give, or spring, and thus break the shock which cast iron would resist
to the point of rupture. It is under these conditions, which mainly
occur in high velocities with one of the wheels having cast teeth, that
mortise wheels, or cogging, is employed, possessing the advantage that a
broken or worn-out tooth, or teeth, may be readily replaced. It is
usual, however, to assign to wooden teeth a value of strength more
nearly equal to that of its strength in proportion to that of cast iron;
hence, Thomas Box allows a wood tooth a value of about 3/10ths the
strength of cast iron; a value as high as 7/10ths is, however, assigned
by other authorities. But the strength of the tooth cannot exceed that
at the top of the shank, where it fits into the mortise of the wheel,
and on account of the leverage of the pressure the width of the mortise
should exceed the thickness of the tooth.
In some practice, the mortise teeth, or cogs, are made thicker in
proportion to the pitch than the teeth on the iron wheel; thus Professor
Unwin, in his "Elements of Machine Design," gives the following as "good
proportions":--
Thickness of iron teeth 0.395 of the pitch.
" wood cogs 0.595 " "
which makes the cogs 2/10ths inch thicker than the teeth.
The mortises in the wheel rim are made taper in both the breadth and the
width, which enables the tooth shank to be more accurately fitted, and
also of being driven more tightly home, than if parallel. The amount of
this taper is a matter of judgment, but it may be observed that the
greater the taper the more labor there is involved in fitting, and the
more strain there is thrown upon the pins when locking the teeth with a
given amount of strain. While the less the taper, the more care required
to obtain an accurate fit. Taking these two elements into consideration,
1/8th inch of taper in a length of 4 inches may be given as a desirable
proportion.
[Illustration: Fig. 182.]
As an evidence of the durability of wooden teeth, there appeared in
_Engineering_ of January 7th, 1879, the illustration shown in Fig. 182,
which represents a cog from a wheel of 14 ft. 1/2 in. diameter, and
having a 10-inch face, its pinion being 4 ft. in diameter. This cog had
been running for 26-1/2 years, day and night; not a cog in the wheel
having been touched during that time. Its average revolutions were 38
per minute, the power developed by the engine being from 90 to 100
indicated horse-power. The teeth were composed of beech, and had been
greased twice a week, with tallow and plumbago ore.
Since the width of the face of a wheel influences its wear (by providing
a larger area of contact over which the pressure may be distributed, as
well as increasing the strength), two methods of proportioning the
breadth may be adopted. First, it may be made a certain proportion of
the pitch; and secondly, it may be proportioned to the pressure
transmitted and the number of revolutions. The desirability of the
second is manifest when we consider that each tooth will pass through
the arcs of contact (and thus be subjected to wear) once during each
revolution; hence, by making the number of revolutions an element in the
calculation to find the breadth, the latter is more in proportion to the
wear than it would be if proportioned to the pitch.
It is obvious that the breadth should be sufficient to afford the
required degree of strength with a suitable factor of safety, and
allowance for wear of the smallest wheel in the pair or set, as the case
may be.
According to Reuleaux, the face of a wheel should never be less than
that obtained by multiplying the gross pressure, transmitted in lbs., by
the revolutions per minute, and dividing the product by 28,000.
In the case of bevel-wheels the pitch increases, as the perimeter of
the wheel is approached, and the maximum pitch is usually taken as the
designated pitch of the wheel. But the mean pitch is that which should
be taken for the purposes of calculating the strength, it being in the
middle of the tooth breadth. The mean pitch is also the diameter of the
pitch circle, used for ascertaining the velocity of the wheel as an
element in calculating the safe pressure, or the amount of power the
wheel is capable of transmitting, and it is upon this basis that the
values for bevel-wheels in the above table are computed.
In many cases it is required to find the amount of horse-power a wheel
will transmit, or the proportions requisite for a wheel to transmit a
given horse-power; and as an aid to the necessary calculations, the
following table is given of the amount of horse-power that may be
transmitted with safety, by the various wheels at the given velocities,
with a wheel of an inch pitch and an inch face, from which that for
other pitches and faces may be obtained by proportion.
TABLE SHOWING THE HORSE-POWER WHICH DIFFERENT KINDS OF GEAR-WHEELS OF
ONE INCH PITCH AND ONE INCH FACE WILL SAFELY TRANSMIT AT VARIOUS
VELOCITIES OF PITCH CIRCLE.
+------------+------------+------------+-------------+-------------+
|Velocity of | | | | |
|Pitch Circle|Spur-Wheels.|Spur Mortise|Bevel-Wheels.|Bevel Mortise|
|in Feet per | H.P. | Wheels. | H.P. | Wheels. |
|Second. | | H.P. | | H.P. |
+------------+------------+------------+-------------+-------------+
| 2 | 1.338 | .647 | .938 | .647 |
| 3 | 1.756 | .971 | 1.227 | .856 |
| 6 | 2.782 | 1.76 | 1.76 | 1.363 |
| 12 | 4.43 | 3.1 | 3.1 | 2.16 |
| 18 | 5.793 | 4.058 | 4.058 | 2.847 |
| 24 | 7.025 | 4.931 | 4.931 | 3.447 |
| 30 | 8.182 | 5.727 | 5.727 | 4.036 |
| 36 | 9.163 | 6.414 | 6.414 | 4.516 |
| 42 | 10.156 | 7.102 | 7.102 | 4.963 |
| 48 | 11.083 | 7.680 | 7.680 | 5.411 |
+------------+------------+------------+-------------+-------------+
In this table, as in the preceding one, the safe working pressure for
1-inch pitch and 1-inch breadth of face is supposed to be 400 lbs.
In cast gearing, the mould for which is made by a gear moulding machine,
the element of draft to permit the extraction of the pattern is reduced:
hence, the pressure of tooth upon tooth may be supposed to be along the
full breadth of the tooth instead of at one corner only, as in the case
of pattern-moulded teeth. But from the inaccuracies which may occur from
unequal contraction in the cooling of the casting, and from possible
warping of the casting while cooling, which is sure to occur to some
extent, however small the amount may be, it is not to be presumed that
the contact of the teeth of one wheel will be in all the teeth as
perfect across the full breadth as in the case of machine-cut teeth.
Furthermore, the clearance allowed for machine-moulded teeth, while
considerably less than that allowed for pattern-moulded teeth, is
greater than that allowed for machine-cut teeth; hence, the strength of
machine-moulded teeth in proportion to the pitch lies somewhere between
that of pattern-moulded and machine-cut teeth--but exactly where, it
would be difficult to determine in the absence of experiments made for
the purpose of ascertaining.
It is not improbable, however, that the contact of tooth upon tooth
extends in cast gears across at least two-thirds of the breadth of the
tooth, in which case the rules for ascertaining the strength of cut
teeth of equal thickness may be employed, substituting 2/3rds of the
actual tooth breadth as the breadth for the purposes of the calculation.
If instead of supposing all the strain to fall upon one tooth and
calculating the necessary strength of the teeth upon that basis (as is
necessary in interchangeable gearing, because these conditions may exist
in the case of the smallest pinion that can be used in pitch), the
actual working condition of each separate application of gears be
considered, it will appear that with a given diameter of pitch circle,
all other things being equal, the arc of contact will remain constant
whatever the pitch of the teeth, or in other words is independent of the
pitch, and it follows that when the thickness of iron necessary to
withstand (with the allowances for wear and factor of safety) the given
stress under the given velocity has been determined, it may be disposed
in a coarse pitch that will give one tooth always in contact, or a finer
pitch that will give two or more teeth always in contact, the strength
in proportion to the duty remaining the same in both cases.
In this case the expense of producing the wheel patterns or in trimming
the teeth is to be considered, because if there are a train of wheels
the finer pitch would obviously involve the construction and dressing to
shape of a much greater number of teeth on each wheel in the train, thus
increasing the labor. When, however, it is required to reduce the pinion
to a minimum diameter, it is obvious that this may be accomplished by
selecting the finer pitch, because the finer the pitch, the less the
diameter of the wheel may be. Thus with a given diameter of pitch circle
it is possible to select a pitch so fine that motion from one wheel may
be communicated to another, whatever the diameter of the pitch circle
may be, the limit being bounded by the practicability of casting or
producing teeth of the necessary fineness of pitch. The durability of a
wheel having a fine pitch is greater for two reasons: first, because the
metal nearest the cast surface of cast iron is stronger than the
internal metal, and the finer pitch would have more of this surface to
withstand the wear; and second, because in a wheel of a given width
there would be two points, or twice the area of metal, to withstand the
abrasion, it being remembered that the point of contact is a line which
partly rolls and partly slides along the depth of the tooth as the wheel
rotates, and that with two teeth in contact on each wheel there are two
of such lines. There is also less sliding or rubbing action of the
teeth, but this is offset by the fact that there are more teeth in
contact, and that there are therefore a greater number of teeth
simultaneously rubbing or sliding one upon the other.
But when we deal with the number of teeth the circumstances are altered;
thus with teeth of epicycloidal form it is manifestly impossible to
communicate constant motion with a driving wheel having but one tooth,
or to receive motion on a follower having but one tooth. The number of
teeth must always be such that there is at all times a tooth of each
wheel within the arc of action, or in contact, so that one pair of teeth
may come into contact before the contact of the preceding teeth has
ceased.
In the construction of wheels designed to transmit power as well as
simple motion, as is the case with the wheels employed in machine work,
however, it is not considered desirable to employ wheels containing a
less number of teeth than 12. The diameter of the wheel bearing such a
relation to the pitch that both wheels containing the same number of
teeth (12), the motion will be communicated from one to the other
continuously.
It is obvious that as the number of teeth in one of the wheels (of a
pair in gear) is increased the number of teeth in the other may be
(within certain limits) diminished, and still be capable of transmitting
continuous motion. Thus a pinion containing, say 8 teeth, may be capable
of receiving continuous motion from a rack in continuous motion, while
it would not be capable of receiving continuous motion from a pinion
having 4 teeth; and as the requirements of machine construction often
call for the transmission of motion from one pinion to another of equal
diameters, and as small as possible, 12 teeth are the smallest number it
is considered desirable for a pinion to contain, except it be in the
case of an internal wheel, in which the arc of contact is greater in
proportion to the diameters than in spur-wheels, and continuous motion
can therefore be transmitted either with coarser pitches or smaller
diameters of pinion.
For convenience in calculating the pitch diameter at pitch circle, or
pitch diameter as it is termed, and the number of teeth of wheels, the
following rules and table extracted from the _Cincinnati Artisan_ and
arranged from a table by D. A. Clarke, are given. The first column gives
the pitch, the following nine columns give the pitch diameters of wheels
for each pitch from 1 tooth to 9. By multiplying these numbers by 10 we
have the pitch diameters from 10 to 90 teeth, increasing by _tens_; by
multiplying by 100 we likewise have the pitch diameters from 100 to 900,
increasing by _hundreds_.
TABLE FOR DETERMINING THE RELATION BETWEEN PITCH DIAMETER, PITCH, AND
NUMBER OF TEETH IN GEAR-WHEELS.
+-----+------------------------------------------------------------------+
| | NUMBER OF TEETH. |
|Pitch.------+------+------+------+------+-------+-------+-------+-------+
| | 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. | 9. |
+-----+------+------+------+------+------+-------+-------+-------+-------+
|1 | .3183| .6366| .9549|1.2732|1.5915| 1.9099| 2.2282| 2.5465| 2.8648|
|1-1/8| .3581| .7162|1.0743|1.4324|1.7905| 2.1486| 2.5067| 2.8648| 3.2229|
|1-1/4| .3979| .7958|1.1937|1.5915|1.9894| 2.3873| 2.7852| 3.1831| 3.5810|
|1-3/8| .4377| .8753|1.3130|1.7507|2.1884| 2.6260| 3.0637| 3.5014| 3.9391|
| | | | | | | | | | |
|1-1/2| .4775| .9549|1.4324|1.9099|2.3873| 2.8648| 3.3422| 3.8197| 4.2971|
|1-5/8| .5173|1.0345|1.5517|2.0690|2.5862| 3.1035| 3.6207| 4.1380| 4.6552|
|1-3/4| .5570|1.1141|1.6711|2.2282|2.7852| 3.3422| 3.8993| 4.4563| 5.0134|
|1-7/8| .5968|1.1937|1.7905|2.3873|2.9841| 3.5810| 4.1778| 4.7746| 5.3714|
| | | | | | | | | | |
|2 | .6366|1.2732|1.9099|2.5465|3.1831| 3.8197| 4.4563| 5.0929| 5.7296|
|2-1/8| .6764|1.3528|2.0292|2.7056|3.3820| 4.0584| 4.7348| 5.4112| 6.0877|
|2-1/4| .7162|1.4324|2.1486|2.8648|3.5810| 4.2972| 5.0134| 5.7296| 6.4457|
|2-3/8| .7560|1.5120|2.2679|3.0239|3.7799| 4.5359| 5.2919| 6.0479| 6.8038|
| | | | | | | | | | |
|2-1/2| .7958|1.5915|2.3873|3.1831|3.9789| 4.7746| 5.5704| 6.3662| 7.1619|
|2-5/8| .8355|1.6711|2.5067|3.3422|4.1778| 5.0133| 5.8499| 6.6845| 7.5200|
|2-3/4| .8753|1.7507|2.6260|3.5014|4.3767| 5.2521| 6.1274| 7.0028| 7.8781|
|2-7/8| .9151|1.8303|2.7454|3.6605|4.5757| 5.4908| 6.4059| 7.3211| 8.2362|
| | | | | | | | | | |
|3 | .9549|1.9099|2.8648|3.8197|4.7746| 5.7296| 6.6845| 7.6394| 8.5943|
|3-1/4|1.0345|2.0690|3.1035|4.1380|5.1725| 6.2070| 7.2415| 8.2760| 9.3105|
|3-1/2|1.1141|2.2282|3.3422|4.4563|5.5704| 6.6845| 7.7986| 8.9126|10.0268|
|3-3/4|1.1937|2.3873|3.5810|4.7746|5.9683| 7.1619| 8.3556| 9.5493|10.7429|
| | | | | | | | | | |
|4 |1.2732|2.5465|3.8197|5.0929|6.3662| 7.6394| 8.9127|10.1839|11.4591|
|4-1/2|1.4324|2.8648|4.2972|5.7296|7.1619| 8.5943|10.0267|11.4591|12.8915|
|5 |1.5915|3.1831|4.7746|6.3662|7.9577| 9.5493|11.1408|12.7324|14.3240|
|5-1/2|1.7507|3.5014|5.2521|7.0028|8.7535|10.5042|12.2549|14.0056|15.7563|
|6 |1.9099|3.8196|5.7295|7.6394|9.5493|11.4591|13.3690|15.2788|17.1887|
+-----+------+------+------+------+------+-------+-------+-------+-------+
The following rules and examples show how the table is used:
Rule 1.--Given ---- number of teeth and pitch; to find ---- pitch
diameter.
Select from table in columns opposite the given pitch--
First, the value corresponding to the number of units in the number of
teeth.
Second, the value corresponding to the number of tens, and multiply this
by 10.
Third, the value corresponding to the number of hundreds, and multiply
this by 100. Add these together, and their sum is the pitch diameter
required.
Example.--What is the pitch diameter of a wheel with 128 teeth, 1-1/2
inches pitch?
We find in line corresponding to 1-1/2 inch pitch--
Pitch diameter for 8 teeth 3.8197
" " 20 " 9.549
" " 100 " 47.75
--- -------
" " 128 " 61.1187
Or about 61-1/8". Answer.
Rule 2.--Given ---- pitch diameter and number of teeth; to find
---- pitch.
First, ascertain by Rule 1 the pitch diameter for a wheel of 1-_inch
pitch_, and the given _number of teeth_.
Second, divide _given pitch diameter_ by the _pitch diameter_ for
1-_inch pitch_.
The quotient is the pitch desired.
Example.--What is the pitch of a wheel with 148 teeth, the pitch
diameter being 72"?
First, pitch diameter for 148 teeth, 1-inch pitch, is--
8 teeth 2.5465
40 " 12.732
100 " 31.83
--- -------
148 " 47.1085
Second, 72/47.1 = 1.53 inch equal to the pitch.
This is nearly 1-1/2-inch pitch, and if possible the diameter would be
reduced or the number of teeth increased so as to make the wheel exactly
1-1/2-inch pitch.
Rule 3.--Given ---- pitch and pitch diameter; to find ---- number of
teeth.
First, ascertain from table the _pitch diameter_ for 1 _tooth_ of the
given _pitch_.
Second, divide the _given pitch diameter_ by the _value_ found in table.
The quotient is the number required.
Example.--What is the number of teeth in a wheel whose pitch diameter is
42 inches, and pitch is 2-1/2 inches?
First, the pitch diameter, 1 tooth, 2-1/2-inch pitch, is 0.7958 inches.
42
Second. ------ = 52.8. Answer.
0.7958
This gives a fractional number of teeth, which is impossible; so the
pitch diameter will have to be increased to correspond to 53 teeth, or
the pitch changed so as to have the number of teeth come an even number.
Whenever two parallel shafts are connected together by gearing, the
distance between centres being a fixed quantity, and the speeds of the
shafts being of a fixed ratio, then the pitch is generally the best
proportion to be changed, and necessarily may not be of standard size.
Suppose there are two shafts situated in this manner, so that the
distance between their centres is 84 inches, and the speed of one is
2-1/2 times that of the other, what size wheels shall be used? In this
case the pitch diameter and number of teeth of the wheel on the
slow-running shaft have to be 2-1/2 times those of the wheel on the
fast-running shaft; so that 84 inches must be divided into two parts,
one of which is 2-1/2 times the other, and these quantities will be the
pitch radii of the wheels; that is, 84 inches are to be divided into
3-1/2 equal parts, 1 of which is the radius of one wheel, and 2-1/2 of
which the radius of the other, thus 84"/3-1/2 = 24 inches. So that 24
inches is the pitch radius of pinion, pitch diameter = 48 inches; and
2-1/2 × 24 inches = 60 inches is the pitch radius of the wheel, pitch
diameter = 120 inches. The pitch used depends upon the power to be
transmitted; suppose that 2-5/8 inches had been decided as about the
pitch to be used, it is found by Rule 3 that the number of teeth are
respectively 143.6, and 57.4 for wheel and pinion. As this is
impossible, some whole number of teeth, nearest these in value, have to
be taken, one of which is 2-1/2 times the other; thus 145 and 58 are the
nearest, and the pitch for these values is found by Rule 2 to be 2.6
inches, being the best that can be done under the circumstances.
[Illustration: Fig. 183.]
[Illustration: Fig. 184.]
The forms of spur-gearing having their teeth at an angle to the axis, or
formed in advancing steps shown in Figs. 183 and 184, were designed by
Dr. Hooke, and "were intended," says the inventor, "first to make a
piece of wheel work so that both the wheel and pinion, though of never
so small a size, shall have as great a number of teeth as shall be
desired, and yet neither weaken the wheels nor make the teeth so small
as not to be practicable by any ordinary workman. Next that the motion
shall be so equally communicated from the wheel to the pinion that the
work being well made there can be no inequality of force or motion
communicated.
"Thirdly, that the point of touching and bearing shall be always in the
line that joins the two centres together.
"Fourthly, that it shall have _no manner of rubbing_, nor be more
difficult to make than common wheel work."
The objections to this form of wheel lies in the difficulty of making
the pattern and of moulding it in the foundry, and as a result it is
rarely employed at the present day. For racks, however, two or more
separate racks are cast and bolted together to form the full width of
rack as shown in Fig. 185. This arrangement permits of the adjustment of
the width of step so as to take up the lost motion due to the wear of
the tooth curves.
Another objection to the sloping of the teeth, as in Fig. 183, is that
it induces an end pressure tending to force the wheels apart
_laterally_, and this causes _end_ wear on the journals and bearings.
[Illustration: Fig. 185.]
[Illustration: Fig. 186.]
To obviate this difficulty the form of gear shown in Fig. 186 is
employed, the angles of the teeth from each side of the wheel to its
centre being made equal so as to equalize the lateral pressure. It is
obvious that the stepped gear, Fig. 184, is simply equivalent to a
number of thin wheels bolted together to form a thick one, but
possessing the advantage that with a sufficient number of steps, as in
the figure, there is always contact on the line of centres, and that the
condition of constant contact at the line of centres will be approached
in proportion to the number of steps in the wheel, providing that the
steps progress in one continuous direction across the wheel as in Fig.
184. The action of the wheels will, in this event, be smoother, because
there will be less pressure tending to force the wheels apart.
But in the form of gearing shown in Fig. 183, the contact of the teeth
will bear every instant at a single point, which, as the wheels revolve,
will pass from one end to the other of the tooth, a fresh contact always
beginning on the first side immediately before the preceding contact has
ceased on the opposite side. The contact, moreover, being always in the
plane of the centres of the pair, the action is reduced to that of
rolling, and as there is no sliding motion there is consequently no
rubbing friction between the teeth.
[Illustration: Fig. 187.]
[Illustration: Fig. 188.]
A further modification of Dr. Hooke's gearing has been somewhat
extensively adopted, especially in cotton-spinning machines. This
consists, when the direction of the motion is simply to be changed to an
angle of 90°, in forming the teeth upon the periphery of the pair at an
angle of 45° to the respective axes of the wheels, as in Figs. 187 and
188; it will then be perceived that if the sloped teeth be presented to
each other in such a way as to have exactly the same horizontal angle,
the wheels will gear together, and motion being communicated to one axis
the same will be transmitted to the other at a right angle to it, as in
a common bevel pair. Thus if the wheel A upon a horizontal shaft have
the teeth formed upon its circumference at an angle of 45° to the plane
of its axis it can gear with a similar wheel B upon a vertical axis. Let
it be upon the driving shaft and the motion will be changed in direction
as if A and B were a pair of bevel-wheels of the ordinary kind, and, as
with bevels generally, the direction of motion will be changed through
an equal angle to the sum of the angles which the teeth of the wheels of
the pair form with their respective axes. The objection in respect of
lateral or end pressure, however, applies to this form equally with that
shown in Fig. 183, but in the case of a vertical shaft the end pressure
may be (by sloping the teeth in the necessary direction) made to tend to
lift the shaft and not force it down into the step bearing. This would
act to keep the wheels in close contact by reason of the weight of the
vertical shaft and at the same time reduce the friction between the end
of that shaft and its step bearing. This renders this form of gearing
preferable to skew bevels when employed upon vertical shafts.
It is obvious that gears, such as shown in Figs. 187 and 188 may be
turned up in the lathe, because the teeth are simply portions of spirals
wound about the circumference of the wheel. For a pair of wheels of
equal diameter a cylindrical piece equal in length to the required
breadth of the two wheels is turned up in the lathe, and the teeth may
be cut in the same manner as cutting a thread in the lathe, that is to
say, by traversing the tool the requisite distance per lathe revolution.
In pitches above about 1/4 inch, it will be necessary to shape one side
of the tooth at a time on account of the broadness of the cutting edges.
After the spiral (for the teeth are really spirals) is finished the
piece may be cut in two in the lathe and each half will form a wheel.
To find the full diameter to which to turn a cylinder for a pair of
these wheels we proceed as in the following example: Required to cut a
spiral wheel 5 inches in diameter and to have 30 teeth. First find the
diametral pitch, thus 30 (number of teeth) ÷ 5 (diameter of wheel at
pitch circle) = 6; thus there are 6 teeth or 6 parts to every inch of
the wheel's diameter at the pitch circle; adding 2 of these parts to the
diameter of the wheel, at the pitch circle we have 5 and 2/6 of another
inch, or 5-2/6 inches, which is the full diameter of the wheel, or the
diameter of the addendum, as it is termed.
[Illustration: Fig. 189.]
[Illustration: Fig. 190.]
It is now necessary to find what change wheels to put on the lathe to
cut the teeth out the proper angle. Suppose then the axes of the shafts
are at a right angle one to the other, and that the teeth therefore
require to be at an angle of 45° to the axes of the respective wheels,
then we have the following considerations. In Fig. 189 let the line A
represent the circumference of the wheel, and B a line of equal length
but at a right angle to it, then the line C, joining A, B, is at an
angle of 45°. It is obvious then that if the traverse of the lathe tool
be equal at each lathe revolution to the circumference of the wheel at
the pitch circle, the angle of the teeth will be 45° to the axis of the
wheel.
Hence, the change wheels on the lathe must be such as will traverse the
tool a distance equal to the circumference at pitch circle of the wheel,
and the wheels may be found as for ordinary screw cutting.
If, however, the axes of the shafts are at any other angle we may find
the distance the lathe tool must travel per lathe revolution to give
teeth of the required angle (or in other words the pitch of the spiral)
by direct proportion, thus: Let it be required to find the angle or
pitch for wheels to connect shafts at an angle of 25°, the wheels to
have 20 teeth, and to be of 10 diametral pitch.
Here, 20 ÷ 10 = 2 = diameter of wheel at the pitch circle. The
circumference of 2 inches being 6.28 inches we have, as the degrees of
angle of the axes of the shafts are to 45°, so is 6.28 inches (the
circumference of the wheels, to the pitch sought).
Here, 6.28 inches × 45° ÷ 25° = 11.3 inches, which is the required pitch
for the spiral.
When the axes of the shafts are neither parallel nor meeting, motion
from one shaft to another may be transmitted by means of a double gear.
Thus (taking rolling cones of the diameters of the respective pitch
circles as representing the wheels) in Fig. 190, let A be the shaft of
gear _h_, and B _b_ that of wheel _e_. Then a double gear-wheel having
teeth on _f_, _g_ may be placed as shown, and the face _f_ will gear
with _e_, while face _g_ will gear with _h_, the cone surfaces meeting
in a point as at C and D respectively, hence the velocity will be equal.
When the axial line of the shafts for two gear-wheels are nearly in line
one with the other, motion may be transmitted by gearing the wheels as
in Fig. 191. This is a very strong method of gearing, because there are
a large number of teeth in contact, hence the strain is distributed by a
larger number of teeth and the wear is diminished.
[Illustration: Fig. 191.]
[Illustration: Fig. 192.]
Fig. 192 (from Willis's "Principles of Mechanism") is another method of
constructing the same combination, which admits of a steady support for
the shafts at their point of intersection, A being a spherical bearing,
and B, C being cupped to fit to A.
Rotary motion variable at different parts of a rotation may be obtained
by means of gear-wheels varied in form from the true circle.
[Illustration: Fig. 193.]
The commonest form of gearing for this purpose is elliptical gearing,
the principles governing the construction of which are thus given by
Professor McCord. "It is as well to begin at the foundation by defining
the ellipse as a closed plane-curve, generated by the motion of a point
subject to the condition that the sum of its distances from two fixed
points within shall be constant: Thus, in Fig. 193, A and B are the two
fixed points, called the _foci_; L, E, F, G, P are points in the curve;
and A F + F B = A E + E B. Also, A L + L B = A P + P B = A G + G B. From
this it follows that A G = L O, O being the centre of the curve, and G
the extremity of the minor axis, whence the foci may be found if the
axes be assumed, or, if the foci and one axis be given, the other axis
may be determined. It is also apparent that if about either focus, as B,
we describe an arc with a radius greater than B P and less than B L, for
instance B E, and about A another arc with radius A E = L P-B E, the
intersection, E, of these arcs will be on the ellipse; and in this
manner any desired number of points may be found, and the curve drawn by
the aid of sweeps.
"Having completed this ellipse, prolong its major axis, and draw a
similar and equal one, with its foci, C, D, upon that prolongation, and
tangent to the first one at P; then B D = L P. About B describe an arc
with any radius, cutting the first ellipse at Y and the line L at Z;
about D describe an arc with radius D Z, cutting the second ellipse in
X; draw A Y, B Y, C X, and D X. Then A Y = D X, and B Y = C X, and
because the ellipses are alike, the arcs P Y and P X are equal. If then
B and D are taken as fixed centres, and the ellipses turn about them as
shown by the arrows, X and Y will come together at Z on the line of
centres; and the same is true of any points equally distant from P on
the two curves. But this is the condition of rolling contact. We see,
then, that in order that two ellipses may roll together, and serve as
the pitch-lines of wheels, they must be equal and similar, the fixed
centres must be at corresponding foci, and the distance between these
centres must be equal to the major axis. Were they to be toothless
wheels, if would evidently be essential that the outlines should be
truly elliptical; but the changes of curvature in the ellipse are
gradual, and circular arcs may be drawn so nearly coinciding with it,
that when teeth are employed, the errors resulting from the substitution
are quite inappreciable. Nevertheless, the rapidity of these changes
varies so much in ellipses of different proportions, that we believe it
to be practically better to draw the curve accurately first, and to find
the radii of the approximating arcs by trial and error, than to trust to
any definite rule for determining them; and for this reason we give a
second and more convenient method of finding points, in connection with
the ellipse whose centre is R, Fig. 193. About the centre describe two
circles, as shown, whose diameters are the major and minor axes; draw
any radius, as R T, cutting the first circle in T, and the second in S;
through T draw a parallel to one axis, through S a parallel to the
other, and the intersection, V, will lie on the curve. In the left hand
ellipse, the line bisecting the angle A F B is normal to the curve at F,
and the perpendicular to it is tangent at the same point, and bisects
the angles adjacent to A F B, formed by prolonging A F, B F.
[Illustration: Fig. 194.]
"To mark the pitch line we proceed as follows:--
"In Fig. 194, A A and B B are centre lines passing through the major and
minor axes of the ellipse, of which _a_ is the axis or centre, _b_ _c_
is the major and _a_ _e_ half of the minor axis. Draw the rectangle _b_
_f_ _g_ _c_, and then the diagonal line _b_ _e_; at a right angle to _b_
_e_ draw line _f_ _h_ cutting B B at _i_. With radius _a_ _e_ and from
_a_ as a centre draw the dotted arc _e_ _j_, giving the point _j_ on the
line B B. From centre _k_, which is on line B B, and central between _b_
and _j_, draw the semicircle _b_ _m_ _j_, cutting A A at _l_. Draw the
radius of the semicircle _b_ _m_ _j_ cutting _f_ _g_ at _n_. With radius
_m_ _n_ mark on A A, at and from _a_ as a centre, the point _o_. With
radius _h_ _o_ and from centre _h_ draw the arc _p_ _o_ _q_. With radius
_a_ _l_ and from _b_ and _c_ as centres draw arcs cutting _p_ _o_ _q_ at
the points _p_ _q_. Draw the lines _h_ _p_ _r_ and _h_ _q_ _s_, and also
the lines _p_ _i_ _t_ and _q_ _v_ _w_. From _h_ as centre draw that part
of the ellipse lying between _r_ and _s_. With radius _p_ _r_ and from
_p_ as a centre draw that part of the ellipse lying between _r_ and _t_.
With radius _q_ _s_ and from _q_ draw the ellipse from _s_ to _w_. With
radius _i_ _t_ and from _i_ as a centre draw the ellipse from _t_ to
_b_. With radius _v_ _w_ and from _v_ as a centre draw the ellipse from
_w_ to _c_, and one half the ellipse will be drawn. It will be seen that
the whole construction has been performed to find the centres _h_ _p_
_q_ _i_ and _v_, and that while _v_ and _i_ may be used to carry the
curve around the other side or half of the ellipse, new centres must be
provided for _h_ _p_ and _q_; these new centres correspond in position
to _h_ _p_ _q_.
"If it were possible to subdivide the ellipse into equal parts it would
be unnecessary to resort to these processes of approximately
representing the two curves by arcs of circles; but unless this be done,
the spacing of the teeth can only be effected by the laborious process
of stepping off the perimeter into such small subdivisions that the
chords may be regarded as equal to the arcs, which after all is but an
approximation; unless, indeed, we adopt the mechanical expedient of
cutting out the ellipse in metal or other substance, measuring and
subdividing it with a strip of paper or a steel tape, and wrapping back
the divided measure in order to find the points of division on the
curve.
"But these circular arcs may be rectified and subdivided with great
facility and accuracy by a very simple process, which we take from Prof.
Rankine's "Machinery and Mill Work," and is illustrated in Fig. 195. Let
O B be tangent at O to the arc O D, of which C is the centre. Draw the
chord D O, bisect it in E, and produce it to A, making O A = O E; with
centre A and radius A D describe an arc cutting the tangent in B; then O
B will be very nearly equal in length to the arc O D, which, however,
should not exceed about 60°; if it be 60°, the error is theoretically
about 1/900 of the length of the arc, O B being so much too short; but
this error varies with the fourth power of the angle subtended by the
arc, so that for 30° it is reduced to 1/16 of that amount, that is, to
1/14400. Conversely, let O B be a tangent of given length; make O F =
1/4 O B; then with centre F and radius F B describe an arc cutting the
circle O D G (tangent to O B at O) in the point D; then O D will be
approximately equal to O B, the error being the same as in the other
construction and following the same law.
[Illustration: Fig. 195.]
"The extreme simplicity of these two constructions and the facility with
which they may be made with ordinary drawing instruments make them
exceedingly convenient, and they should be more widely known than they
are. Their application to the present problem is shown in Fig. 196,
which represents a quadrant of an ellipse, the approximate arcs C D, D
E, E F, F A having been determined by trial and error. In order to space
this off, for the positions of the teeth, a tangent is drawn at D, upon
which is constructed the rectification of D C, which is D G, and also
that of D E in the opposite direction, that is, D H, by the process just
explained. Then, drawing the tangent at F, we set off in the same manner
F I = F E, and F K = F A, and then measuring H L = I K, we have finally
G L, equal to the whole quadrant of the ellipse.
[Illustration: Fig. 196.]
"Let it now be required to lay out 24 teeth upon this ellipse; that is,
6 in each quadrant; and for symmetry's sake we will suppose that the
centre of one tooth is to be at A, and that of another at C, Fig. 196.
We therefore divide L G into six equal parts at the points 1, 2, 3, &c.,
which will be the centres of the teeth upon the rectified ellipse. It is
practically necessary to make the spaces a little greater than the
teeth; but if the greatest attainable exactness in the operation of the
wheel is aimed at, it is important to observe that backlash, in
elliptical gearing, has an effect quite different from that resulting in
the case of circular wheels. When the pitch-curves are circles, they are
always in contact; and we may, if we choose, make the tooth only half
the breadth of the space, so long as its outline is correct. When the
motion of the driver is reversed, the follower will stand still until
the backlash is taken up, when the motion will go on with a perfectly
constant velocity ratio as before. But in the ease of two elliptical
wheels, if the follower stand still while the driver moves, which must
happen when the motion is reversed if backlash exists, the pitch-curves
are thrown out of contact, and, although the continuity of the motion
will not be interrupted, the velocity ratio will be affected. If the
motion is never to be reversed, the perfect law of the velocity ratio
due to the elliptical pitch-curve may be preserved by reducing the
thickness of the tooth, not equally on each side, as is done in circular
wheels, but wholly on the side not in action. But if the machine must be
capable of acting indifferently in both directions, the reduction must
be made on both sides of the tooth: evidently the action will be
slightly impaired, for which reason the backlash should be reduced to a
minimum. Precisely what _is_ the minimum is not so easy to say, as it
evidently depends much upon the excellence of the tools and the skill of
the workmen. In many treatises on constructive mechanism it is variously
stated that the backlash should be from one-fifteenth to one-eleventh of
the pitch, which would seem to be an ample allowance in reasonably good
castings not intended to be finished, and quite excessive if the teeth
are to be cut; nor is it very obvious that its amount should depend upon
the pitch any more than upon the precession of the equinoxes. On paper,
at any rate, we may reduce it to zero, and make the teeth and spaces
equal in breadth, as shown in the figure, the teeth being indicated by
the double lines. Those upon the portion L H are then laid off upon K I,
after which these divisions are transferred to curves. And since under
that condition the motion of this third line, relatively to each of the
others, is the same as though it rolled along each of them separately
while they remained fixed, the process of constructing the generated
curves becomes comparatively simple. For the describing line, we
naturally select a circle, which, in order to fulfil the condition, must
be small enough to roll within the pitch ellipse; its diameter is
determined by the consideration, that if it be equal to A P, the radius
of the arc A F, the flanks of the teeth in that region will be radial.
We have, therefore, chosen a circle whose diameter, A B, is
three-fourths of A P, as shown, so that the teeth, even at the ends of
the wheels, will be broader at the base than on the pitch line. This
circle ought strictly to roll upon the true elliptical curve, and
assuming as usual the tracing-point upon the circumference, the
generated curves would vary slightly from true epicycloids, and no two
of those used in the same quadrant of the ellipse would be exactly
alike. Were it possible to divide the ellipse accurately, there would be
no difficulty in laying out these curves; but having substituted the
circular arcs, we must now roll the generating circle upon these as
bases, thus forming true epicycloidal teeth, of which those lying upon
the same approximating arc will be exactly alike. Should the junction
of two of these arcs fall within the breadth of a tooth, as at D,
evidently both the face and the flank on one side of that tooth will be
different from those on the other side; should the junction coincide
with the edge of a tooth, which is very nearly the case at F, then the
face on that side will be the epicycloid belonging to one of the arcs,
its flank a hypocycloid belonging to the other; and it is possible that
either the face or the flank on one side should be generated by the
rolling of the describing circle partly on one arc, partly on the one
adjacent, which, upon a large scale and where the best results are aimed
at, may make a sensible change in the form of the curve.
[Illustration: Fig. 197.]
"The convenience of the constructions given in Fig. 194 is nowhere more
apparent than in the drawing of the epicycloids, when, as in the case
in hand, the base and generating circles may be of incommensurable
diameters; for which reason we have, in Fig. 197, shown its application
in connection with the most rapid and accurate mode yet known of
describing those curves. Let C be the centre of the base circle;
B that of the rolling one; A the point of contact. Divide the
semi-circumference of B into six equal parts at 1, 2, 3, &c.; draw the
common tangent at A, upon which rectify the arc A2 by process No. 1,
then by process No. 2 set out an equal arc A2 on the base circle, and
stepping it off three times to the right and left, bisect these spaces,
thus making subdivisions on the base circle equal in length to those on
the rolling one. Take in succession as radii the chords A1, A2, A3, &c.,
of the describing circle, and with centres 1, 2, 3, &c., on the base
circle, strike arcs either externally or internally, as shown
respectively on the right and left; the curve tangent to the external
arcs is the epicycloid, that tangent to the internal ones the
hypocycloid, forming the face and flank of a tooth for the base circle.
"In the diagram, Fig. 196, we have shown a part of an ellipse whose
length is 10 inches and breadth 6, the figure being half size. In order
to give an idea of the actual appearance of the combination when
complete, we show in Fig. 198 the pair in gear, on a scale of 3 inches
to the foot. The excessive eccentricity was selected merely for the
purpose of illustration. Fig. 198 will serve also to call attention to
another serious circumstance, which is that although the ellipses are
alike, the wheels are not; nor can they be made so if there be an even
number of teeth, for the obvious reason that a tooth upon one wheel must
fit into a space on the other; and since in the first wheel, Fig. 196,
we chose to place a tooth at the extremity of each axis, we must in the
second one place there a space instead; because at one time the major
axes must coincide, at another the minor axis, as in Fig. 191. If then
we use even numbers, the distribution and even the forms of the teeth
are not the same in the two wheels of the pair. But this complication
may be avoided by using an odd number of teeth, since, placing a tooth
at one extremity of the major axis, a space will come at the other.
"It is not, however, always necessary to cut teeth all round these
wheels, as will be seen by an examination of Fig. 199, C and D being the
fixed centres of the two ellipses in contact at P. Now P must be on the
line C D, whence, considering the free foci, we see P B is equal to P C,
and P A to P D; and the common tangent at P makes equal angles with C P
and P A, as is also with P B and P D; therefore, C D being a straight
line, A B is also a straight line and equal to C D. If then the wheels
be overhung, that is, fixed on the ends of the shafts outside the
bearings, leaving the outer faces free, the moving foci may be connected
by a rigid link A B, as shown.
[Illustration: Fig. 198.]
"This link will then communicate the same motion that would result from
the use of the complete elliptical wheels, and we may therefore dispense
with most of the teeth, retaining only those near the extremities of the
major axes which are necessary in order to assist and control the motion
of the link at and near the dead-points. The arc of the pitch-curves
through which the teeth must extend will vary with their eccentricity:
but in many cases it would not be greater than that which in the
approximation may be struck about one centre, so that, in fact, it would
not be necessary to go through the process of rectifying and subdividing
the quarter of the ellipse at all, as in this case it can make no
possible difference whether the spacing adopted for the teeth to be cut
would "come out even" or not if carried around the curve. By this
expedient, then, we may save not only the trouble of drawing, but a
great deal of labor in making, the teeth round the whole ellipse. We
might even omit the intermediate portions of the pitch ellipses
themselves; but as they move in rolling contact their retention can do
no harm, and in one part of the movement will be beneficial, as they
will do part of the work; for if, when turning, as shown by the arrows,
we consider the wheel whose axis is D as the driver, it will be noted
that its radius of contact, C P, is on the increase; and so long as this
is the case the other wheel will be compelled to move by contact of the
pitch lines, although the link be omitted. And even if teeth be cut all
round the wheels, this link is a comparatively inexpensive and a useful
addition to the combination, especially if the eccentricity be
considerable. Of course the wheels shown in Fig. 198 might also have
been made alike, by placing a tooth at one end of the major axis and a
space at the other, as above suggested. In regard to the variation in
the velocity ratio, it will be seen, by reference to Fig. 199, that if D
be the axis of the driver, the follower will in the position there shown
move faster, the ratio of the angular velocities being PD/PB; if the
driver turn uniformly the velocity of the follower will diminish, until
at the end of half a revolution, the velocity ratio will be PB/PD; in
the other half of the revolution these changes will occur in a reverse
order. But P D = L B; if then the centres B D are given in position, we
know L P, the major axis; and in order to produce any assumed maximum or
minimum velocity ratio, we have only to divide L P into segments whose
ratio is equal to that assumed value, which will give the foci of the
ellipse, whence the minor axis may be found and the curve described. For
instance, in Fig. 198 the velocity ratio being nine to one at the
maximum, the major axis is divided into two parts, of which one is nine
times as long as the other; in Fig. 199 the ratio is as one to three, so
that, the major axis being divided into four parts, the distance A C
between the foci is equal to two of them, and the distance of either
focus from the nearer extremity of the major axis equal to one, and from
the more remote extremity equal to three of these parts."
[Illustration: Fig. 199.]
Another example of obtaining a variable motion is given in Fig. 200. The
only condition necessary to the construction of wheels of this class is
that the sum of the radii of the pitch circles on the line of centres
shall equal the distance between the axes of the two wheels. The pitch
curves are to be considered the same as pitch circles, "so that," says
Willis, "if any given circle or curve be assumed as a describing (or
generating) curve, and if it be made to roll on the inside of one of
these pitch curves and on the outside of the corresponding portion of
the other pitch curve, then the motion communicated by the pressure and
sliding contact of one of the curved teeth so traced upon the other will
be exactly the same as that effected by the rolling contact (by
friction) of the original pitch curves."
[Illustration: Fig. 200.]
It is obvious that on B the corner sections are formed of simple
segments of a circle of which the centre is the axis of the shaft, and
that the sections between them are simply racks. The corners of A are
segments of a circle of which the axis of A is the centre, and the
sections between the corners curves meeting the pitch circles of the
rack at every point as it passes the line of centres.
Intermittent motion may also be obtained by means of a worm-wheel
constructed as in Fig. 201, the worm having its teeth at a right angle
to its axis for a distance around the circumference proportioned to the
required duration of the period of rest; or the motion may be made
variable by giving the worm teeth different degrees of inclination (to
the axis), on different portions of the circumference.
In addition to the simple operation of two or more wheels transmitting
motion by rotating about their fixed centres and in fixed positions, the
following examples of wheel motion may be given.
[Illustration: Fig. 201.]
[Illustration: Fig. 202.]
In Fig. 202 are two gear-wheels, A, which is fast upon its stationary
shaft, and B, which is free to rotate upon its shaft, the link C
affording journal bearing to the two shafts. Suppose that A has 40
teeth, while B has 20 teeth, and that the link C is rotated once around
the axis of A, how many revolutions will B make? By reason of there
being twice as many teeth in A as in B the latter will make two
rotations, and in addition to this it will, by reason of its connection
to the arm C, also make a revolution, these being two distinct motions,
one a rotation of B about the axis of A, and the other two rotations of
B upon its own axis.
A simple arrangement of gearing for reversing the direction of rotation
of a shaft is shown in Fig. 203. I and F are fast and loose pulleys for
the shaft D, A and C are gears free to rotate upon D, N is a clutch
driven by D; hence if N be moved so as to engage with C the latter will
act as a driver to rotate the shaft B, the wheel upon B rotating A in
an opposite direction to the rotation of D. But if N be moved to engage
with A the latter becomes the driving wheel, and B will be caused to
rotate in the opposite direction. Since, however, the engagement of the
clutch N with the clutch on the nut of the gear-wheels is accompanied
with a violent shock and with noise, a preferable arrangement is shown
in Fig. 204, in which the gears are all fast to their shafts, and the
driving shaft for C passes through the core or bore of that for A, which
is a sleeve, so that when the driving belt acts upon pulley F the shaft
B rotates in one direction, while when the belt acts upon E, B rotates
in the opposite direction, I being a loose pulley.
[Illustration: Fig. 203.]
If the speed of rotation of B require to be greater in one direction
than in the other, then the bevel-wheel on B is made a double one, that
is to say, it has two annular toothed surfaces on its radial face, one
of larger diameter than the other; A gearing with one of these toothed
surfaces, and C with the other. It is obvious that the pinions A C,
being of equal diameters, that gearing with the surface or gear of
largest diameter will give to B the slowest speed of rotation.
[Illustration: Fig. 204.]
Fig. 205 represents Watt's sun-and-planet motion for converting
reciprocating into rotary motion; B D is the working beam of the engine,
whose centre of motion is at D. The gear A is so connected to the
connecting rod that it cannot rotate, and is kept in gear with the wheel
C on the fly-wheel shaft by means of the link shown. The wheel A being
prevented from rotation on its axis causes rotary motion to the wheel C,
which makes two revolutions for one orbit of A.
[Illustration: Fig. 205.]
An arrangement for the rapid increase of motion by means of gears is
shown in Fig. 206, in which A is a stationary gear, B is free to rotate
upon its shaft, and being pivoted upon the shaft of A, at D, is capable
of rotation around A while remaining in gear with C. Suppose now that
the wheel A were absent, then if B were rotated around C with D as a
centre of motion, C and its shaft E would make a revolution even though
B would have no rotation upon its axis. But A will cause B to rotate
upon its axis and thus communicate a second degree of motion to C, with
the result that one revolution of B causes two rotations of C.
The relation of motion between B and C is in this case constant (2 to
1), but this relation may be made variable by a construction such as
shown in Fig. 207, in which the wheel B is carried in a gear-wheel H,
which rides upon the shaft D. Suppose now that H remains stationary
while A revolves, then motion will be transmitted through B to C, and
this motion will be constant and in proportion to the relative diameters
of A and C. But suppose by means of an independent pinion the wheel H be
rotated upon its axis, then increased motion will be imparted to C, and
the amount of the increase will be determined by the speed of rotation
of H, which may be made variable by means of cone pulleys or other
suitable mechanical devices.
[Illustration: Fig. 206.]
Fig. 208 represents an arrangement of gearing used upon steam
fire-engines and traction engines to enable them to turn easily in a
short radius, as in turning corners in narrow streets. The object is to
enable the driving wheel on either side of the engine to increase or
diminish its rotation to suit the conditions caused by the leading or
front pair of steering wheels.
[Illustration: Fig. 207.]
In the figures A is a plate wheel having the lugs L, by means of which
it may be rotated by a chain. A is a working fit on the shaft S, and
carries three pinions E pivoted upon their axes P. F is a bevel-gear, a
working fit on S, while C is a similar gear fast to S. The pinions B, D
are to drive gears on the wheels of the engine, the wheels being a
working fit on the axle. Let it now be noted that if S be rotated, C and
F will rotate in opposite directions and A will remain stationary. But
if A be rotated, then all the gears will rotate with it, but E will not
rotate upon P unless there be an unequal resistance to the motion of
pinions D and B. So soon, however, as there exists an inequality of
resistance between D and B then pinions E operate. For example, let B
have more resistance than D, and B will rotate more slowly, causing
pinion E to rotate and move C faster than is due to the motion of the
chain wheel A, thus causing the wheel on one side of the engine to
retard and the other to increase its motion, and thus enable the engine
to turn easily. From its action this arrangement is termed the
equalizing gear.
[Illustration: Fig. 208.]
In Figs. 209 to 214 are shown what are known as mangle-wheels from their
having been first used in clothes mangling machines.
[Illustration: Fig. 209.]
[Illustration: Fig. 210.]
The mangle-wheel[10] in its simplest form is a revolving disc of metal
with a centre of motion C (Fig. 209). Upon the face of the disc is fixed
a projecting annulus _a_ _m_, the outer and inner edges of which are cut
into teeth. This annulus is interrupted at _f_, and the teeth are
continued round the edges of the interrupted portion so as to form a
continued series passing from the outer to the inner edge and back
again.
[10] From Willis's "Principles of Mechanism."
A pinion B, whose teeth are of the same pitch as those of the wheel, is
fixed to the end of an axis, and this axis is mounted so as to allow of
a short travelling motion in the direction B C. This may be effected by
supporting this end of it either in a swing-frame moving upon a centre
as at D, or in a sliding piece, according to the nature of the train
with which it is connected. A short pivot projects from the centre of
the pinion, and this rests in and is guided by a groove B S _f_ _t_ _b_
_h_ K, which is cut in the surface of the disc, and made concentric to
the pitch circles of the inner and outer rays of teeth, and at a normal
distance from them equal to the pitch radius of the pinion.
Now when the pinion revolves it will, if it be on the outside, as in
Fig. 209, act upon the spur teeth and turn the wheel in the opposite
direction to its own, but when the interrupted portion _f_ of the teeth
is thus brought to the pinion the groove will guide the pinion while it
passes from the outside to the inside, and thus bring its teeth into
action with the annular or internal teeth. The wheel will then receive
motion in the same direction as that of the pinion, and this will
continue until the gap _f_ is again brought to the pinion, when the
latter will be carried outwards and the motion again be reversed. The
_velocity ratio_ in either direction will remain constant, but the ratio
when the pinion is inside will differ slightly from the ratio when it is
outside, because the pitch radius of the annular or internal teeth is
necessarily somewhat less than that of the spur teeth. However, the
change of direction is not instantaneous, for the form of the groove S
_f_ _t_, which connects the inner and outer grooves, is a semicircle,
and when the axis of the pinion reaches S the velocity of the
mangle-wheel begins to diminish gradually until it is brought to rest at
_f_, and is again gradually set in motion from _f_ to _t_, when the
constant ratio begins; and this retardation will be increased by
increasing the difference between the radius of the inner and outer
pitch circles.
The teeth of a mangle-wheel are, however, most commonly formed by pins
projecting from the face of the disc as in Fig. 210. In this manner the
pitch circles for the inner and outer wheels coincide, and therefore the
velocity ratio is the same within and without, also the space through
which the pinion moves in shifting is reduced.
[Illustration: Fig. 211.]
[Illustration: Fig. 212.]
This space may be still further reduced by arranging the teeth as in
Fig. 211, that is, by placing the spur-wheel within the annular or
internal one; but at the same time the difference of the two velocity
ratios is increased.
If it be required that the velocity ratio vary, then the pitch lines of
the mangle-wheel must no longer be concentric.
Thus in Fig. 212 the groove _k_ _l_ is directed to the centre of the
mangle-wheel, and therefore the pinion will proceed during this portion
of its path without giving any motion to the wheel, and in the other
lines of teeth the pitch radius varies, hence the angular velocity ratio
will vary.
In Figs. 209, 210, and 211 the curves of the teeth are readily obtained
by employing the same describing circle for the whole of them. But when
the form Fig. 212 is adopted, the shape of the teeth requires some
consideration.
Every tooth of such a mangle-wheel may be considered as formed of two
ordinary teeth set back to back, the pitch line passing through the
middle. The outer half, therefore, appropriated to the action of the
pinion on the outside of the wheel, resembles that portion of an
ordinary spur-wheel tooth that lies beyond its pitch line, and the inner
half which receives the inside action of the pinion resembles the half
of an annular wheel that lies within the pitch circle. But the
consequence of this arrangement is, that in both positions the action of
the driving teeth must be confined to the approach of its teeth to the
line of centres, and consequently these teeth must be wholly within
their pitch line.
To obtain the forms of the teeth, therefore, take any convenient
describing circle, and employ it to describe the teeth of the pinion by
rolling within its pitch circle, and to describe the teeth of the wheel
by rolling within and without its pitch circle, and the pinion will then
work truly with the teeth of the wheel in both positions. The tooth at
each extremity of the series must be a circular one, whose centre lies
on the pitch line and whose diameter is equal to half the pitch.
[Illustration: Fig. 213.]
If the reciprocating piece move in a straight line, as it very often
does, then the mangle-_wheel_ is transformed into a _mangle-rack_ (Fig.
213) and its teeth may be simply made cylindrical pins, which those of
the mangle-wheel do not admit of on correct principle. B _b_ is the
sliding piece, and A the driving pinion, whose axis must have the power
of shifting from A to _a_ through a space equal to its own diameter, to
allow of the change from one side of the rack to the other at each
extremity of the motion. The teeth of the mangle-rack may receive any of
the forms which are given to common rack-teeth, if the arrangement be
derived from either Fig. 210 or Fig. 211.
But the mangle-rack admits of an arrangement by which the shifting
motion of the driving pinion, which is often inconvenient, may be
dispensed with.
[Illustration: Fig. 214.]
B _b_ Fig. 214, is the piece which receives the reciprocating motion,
and which may be either guided between rollers, as shown, or in any
other usual way; A the driving pinion, whose axis of motion is fixed;
the mangle rack C _c_ is formed upon a separate plate, and in this
example has the teeth upon the inside of the projecting ridge which
borders it, and the guide-groove formed within the ring of teeth,
similar to Fig. 211.
This rack is connected with the piece B _b_ in such a manner as to allow
of a short transverse motion with respect to that piece, by which the
pinion, when it arrives at either end of the course, is enabled by
shifting the rack to follow the course of the guide-groove, and thus to
reverse the motion by acting upon the opposite row of teeth.
The best mode of connecting the rack and its sliding piece is that
represented in the figure, and is the same which is adopted in the
well-known cylinder printing-engines of Mr. Cowper. Two guide-rods K C,
_k_ _c_ are jointed at one end K _k_ to the reciprocating piece B _b_,
and at the other end C _c_ to the shifting-rack; these rods are moreover
connected by a rod M _m_ which is jointed to each midway between their
extremities, so that the angular motion of these guide-rods round their
centres K _k_ will be the same; and as the angular motion is small and
the rods nearly parallel to the path of the slide, their extremities C
_c_ may be supposed to move at a right angle to that path, and
consequently the rack which is jointed to those extremities will also
move upon B _b_ in a direction at a right angle to its path, which is
the thing required, and admits of no other motion with respect to B _b_.
[Illustration: Fig. 215.]
To multiply plane motion the construction shown in Fig. 215 is
frequently employed. A and B are two racks, and C is a wheel between
them pivoted upon the rod R. A crank shaft or lever D is pivoted at E
and also (at P) to R. If D be operated C traverses along A and also
rotates upon its axis, thus giving to B a velocity equal to twice that
of the lateral motion of C.
The diameter of the wheel is immaterial, for the motion of B will always
be twice that of C.
Friction gearing-wheels which communicate motion one to the other by
simple contact of their surfaces are termed friction-wheels, or
friction-gearing. Thus in Fig. 216 let A and B be two wheels that touch
each other at C, each being suspended upon a central shaft; then if
either be made to revolve, it will cause the other to revolve also, by
the friction of the surfaces meeting at C. The degree of force which
will be thus conveyed from one to the other will depend upon the
character of the surface and the length of the line of contact at C.
[Illustration: Fig. 216.]
These surfaces should be made as concentric to the axis of the wheel and
as flat and smooth as possible in order to obtain a maximum power of
transmission. Mr. E. S. Wicklin states that under these conditions and
proper forms of construction as much as 300 horse-power may be (and is
in some of the Western States) transmitted.
In practice, small wheels of this class are often covered with some
softer material, as leather; sometimes one wheel only is so covered, and
it is preferred that the covered wheel drive the iron one, because, if a
slip takes place and the iron wheel was the driver, it would be apt to
wear a concave spot in the wood covered one, and the friction between
the two would be so greatly diminished that there would be difficulty in
starting them when the damaged spot was on the line of centre.
If, however, the iron wheel ceased motion, the wooden one continuing to
revolve, the damage would be spread over that part of the circumference
of the wooden one which continued while the iron one was at rest, and if
this occurred throughout a whole revolution of the wooden wheel its
roundness would not be apt to be impaired, except in so far as
differences in the hardness of the wood and similar causes might effect.
"To select the best material for driving pulleys in friction-gearing has
required considerable experience; nor is it certain that this object
has yet been attained. Few, if any, well-arranged and careful
experiments have been made with a view of determining the comparative
value of different materials as a frictional medium for driving iron
pulleys. The various theories and notions of builders have, however,
caused the application to this use of several varieties of wood, and
also of leather, india-rubber, and paper; and thus an opportunity has
been given to judge of their different degrees of efficiency. The
materials most easily obtained, and most used, are the different
varieties of wood, and of these several have given good results.
"For driving light machinery, running at high speed, as in sash, door,
and blind factories, basswood, the linden of the Southern and Middle
States (_Tilia Americana_) has been found to possess good qualities,
having considerable durability and being unsurpassed in the smoothness
and softness of its movement. Cotton wood (_Populus monilifera_) has
been tried for small machinery with results somewhat similar to those of
basswood, but is found to be more affected by atmospheric changes. And
even white pine makes a driving surface which is, considering the
softness of the wood, of astonishing efficiency and durability. But for
all heavy work, where from twenty to sixty horse-power is transmitted by
a single contact, soft maple (_Acer rubrum_) has, at present, no rival.
Driving pulleys of this wood, if correctly proportioned and well built,
will run for years with no perceptible wear.
"For very small pulleys, leather is an excellent driver and is very
durable; and rubber also possesses great adhesion as a driver; but a
surface of soft rubber undoubtedly requires more power than one of a
less elastic substance.
"Recently paper has been introduced as a driver for small machinery, and
has been applied in some situations where the test was most severe; and
the remarkable manner in which it has thus far withstood the severity of
these tests appears to point to it as the most efficient material yet
tried.
"The proportioning, however, of friction-pulleys to the work required
and their substantial and accurate construction are matters of perhaps
more importance than the selection of material.
"Friction-wheels must be most accurately and substantially made and kept
in perfect line so that the contact between the surfaces may not be
diminished. The bodies are usually of iron lagged or covered with wooden
segments.
"All large drivers, say from four to ten feet diameter and from twelve
to thirty inch face, should have rims of soft maple six or seven inches
deep. These should be made up of plank, one and a half or two inches
thick, cut into 'cants,' one-sixth, eighth, or tenth of the circle, so
as to place the grain of the wood as nearly as practicable in the
direction of the circumference. The cants should be closely fitted, and
put together with white lead or glue, strongly nailed and bolted. The
wooden rim, thus made up to within about three inches of the width
required for the finished pulley, is mounted upon one or two heavy iron
'spiders,' with six or eight radial arms. If the pulley is above six
feet in diameter, there should be eight arms, and two spiders when the
width of face is more than eighteen inches.
"Upon the ends of the arms are flat 'pads,' which should be of just
sufficient width to extend across the inner face of the wooden rim, as
described; that is, three inches less than the width of the finished
pulley. These pads are gained into the inner side of the rim; the gains
being cut large enough to admit keys under and beside the pads. When the
keys are well driven, strong 'lag' screws are put through the ends of
the arm into the rim. This done, an additional 'round' is put upon each
side of the rim to cover bolt heads and secure the keys from ever
working out. The pulley is now put to its place on the shaft and keyed,
the edges trued up, and the face turned off with the utmost exactness.
"For small drivers, the best construction is to make an iron pulley of
about eight inches less diameter and three inches less face than the
pulley required. Have four lugs, about an inch square, cast across the
face of this pulley. Make a wooden rim, four inches deep, with face
equal to that of the iron pulley, and the inside diameter equal to the
outer diameter of the iron. Drive this rim snugly on over the rim of the
iron pulley having cut gains to receive the lugs, together with a hard
wood key beside each. Now add a round of cants upon each side, with
their inner diameter less than the first, so as to cover the iron rim.
If the pulley is designed for heavy work, the wood should be maple, and
should be well fastened by lag screws put through the iron rim; but for
light work, it may be of basswood or pine, and the lag screws omitted.
But in all cases, the wood should be thoroughly seasoned.
"In the early use of friction-gearing, when it was used only as backing
gear in saw-mills, and for hoisting in grist-mills, the pulleys were
made so as to present the head of the wood to the surface; and we
occasionally yet meet with an instance where they are so made. But such
pulleys never run so smoothly nor drive so well as those made with the
fibre more nearly in a line with the work."[11]
[11] By E. S. Wicklin.
[Illustration: Fig. 217.]
[Illustration: Fig. 218.]
The driving friction may be obtained from contact of the radial surfaces
in two ways: thus, Fig. 217 represents three discs, A, B, and C; the
edge of A being gripped by and between B and C, which must be held
together by a spiral spring S or other equivalent device. These wheels
may be made to give a variable speed of rotation by curving the surfaces
of the pair B C as in the figure. By means of suitable lever-motion A
may be made to advance towards or recede from the centre of B and C,
giving to their shaft an increased or diminished speed of revolution.
[Illustration: Fig. 219.]
A similar result may be obtained by the construction shown in Fig. 218,
in which D and E are two discs fast upon their respective shafts, and C
are discs of leather clamped in E. It is obvious that if D be the driver
the speed of revolution of E will be diminished in proportion as it is
moved nearer to the centre of D, and also that the direction of
revolution of D remaining constant, that of E will be in one direction
if on the side B of the centre of D, and in the other direction if it is
on the side A of the centre of D, thus affording means of reversing the
motion as well as of varying its speed. A similar arrangement is
sometimes employed to enable the direction of rotation of the driver
shaft to be reversed, or its motion to cease. Thus, in Fig. 219, R is a
driving rope driving the discs A, B, and _c_, _d_, _e_, _f_, _g_ are
discs of yellow pine clamped between the flanges _h_ _i_; when these
five discs are forced (by lifting shaft H), against the face of a motion
occurs in one direction, while if forced against B the direction of
motion of H is reversed.
For many purposes, such as hoisting, for example, where considerable
power requires to be transmitted, the form of friction wheels shown in
Fig. 220 is employed, the object being to increase the line of contact
between wheels of a given width of face. In this case the strain due to
the length of the line of contact partly counteracts itself, thus
relieving to that extent the journals from friction. Thus in Fig. 221 is
shown a single wedge and groove of a pair of wheels. The surface
pressure on each side will be at a right angle to the face, or in the
direction described by the arrows A and B. The surface contact acts to
thrust the bearings of the two shafts apart. The effective length of
surface acting to thrust the bearings apart being denoted by the dotted
line C. The relative efficiency of this class of wheel, however, is not
to be measured by the length of the line C, as compared to that of the
two contacting sides of the groove, because it is increased from the
wedge shape of the groove, and furthermore, no matter how solid the
wheels may be, there will be some elasticity which will operate to
increase the driving power due to the contact. It is to preserve the
wedge principle that the wedges are made flat at the top, so that they
shall not bottom in the grooves even after considerable wear has taken
place. The object of employing this class of gear is to avoid noise and
jar and to insure a uniform motion. The motion at the line of contact of
such wheels is not a rolling, but, in part, a sliding one, which may
readily be perceived from a consideration of the following. The
circumference of the top of each wedge is greater than that of the
bottom, and, in the case of the groove, the circumference of the top is
greater than that of the bottom; and since the top or largest
circumference of one contacts with the smallest circumference of the
other, it follows that the difference between the two represents the
amount of sliding motion that occurs in each revolution. Suppose, for
example, we take two of such wheels 10 inches in diameter, having wedges
and grooves 1/4 inch high and deep respectively; then the top of the
groove will travel 31.416 inches in a revolution, and it will contact
with the bottom of the wedge which travels (on account of its lesser
diameter) 29.845 inches per revolution.
[Illustration: Fig. 220.]
[Illustration: Fig. 221.]
Fig. 222 shows the construction for a pair of bevel wheels on the same
principle.
[Illustration: Fig. 222.]
[Illustration: Fig. 223.]
[Illustration: Fig. 224.]
A form of friction-gearing in which the journals are relieved of the
strain due to the pressure of contact, and in which slip is impossible,
is shown in Fig. 223. It consists of projections on one wheel and
corresponding depressions or cavities on the other. These projections
and cavities are at opposite angles on each half of each wheel, so as to
avoid the end pressure on the journals which would otherwise ensue.
Their shapes may be formed at will, providing that the tops of the
projections are narrower than their bases, which is necessary to enable
the projections to enter and leave the cavities. In this class of
positive gear great truth or exactness is possible, because both the
projections and cavities may be turned in a lathe. Fig. 224 represents a
similar kind of gear with the projections running lengthways of the
cylinder approaching more nearly in its action to toothed gearing, and
in this case the curves for the teeth and groves should be formed by the
rules already laid down for toothed gearing. The action of this latter
class may be made very smooth, because a continuous contact on the line
of centres may be maintained by reason of the longitudinal curve of the
teeth.
[Illustration: Fig. 225.]
Cams may be employed to impart either a uniform, an irregular, or an
intermittent motion, the principles involved in their construction being
as follows:--Let it be required to construct a cam that being revolved
at a uniform velocity shall impart a uniform reciprocating motion. First
draw an inner circle O, Fig. 225, whose radius must equal the radius of
the shaft that is to drive it, plus the depth of the cam at its
shallowest part, plus the radius of the roller the cam is to actuate.
Then from the same centre draw an outer circle S, the radius between
these two circles being equal to the amount the cam is to move the
roller. Draw a line O P, and divide it into any convenient numbers of
divisions (five being shown in the figure), and through these points
draw circles. Divide the outer circle S into twice as many equal
divisions as the line O P is divided into (as from 1 to 10 in the
figure), and where these lines pass through the circles will be points
through which the pitch line of the cam may be drawn.
[Illustration: Fig. 226.]
Thus where circle 1 meets line 1, or at point A, is one point in the
pitch line of the cam; where circle 2 meets line 2, or at B, is another
point in the pitch line of the cam, and so on until we reach the point
E, where circle 5 meets line 5. From this point we simply repeat the
process, the point E where line 6 cuts circle 4, being a point on the
pitch line, and so on throughout the whole 10 divisions, and through the
points so obtained we draw the pitch line.
[Illustration: Fig. 227.]
[Illustration: Fig. 228.]
If we were to cut out a cam to the outline thus obtained, and revolve it
at a uniform velocity, it would move a point held against its perimeter
at a uniform velocity throughout the whole of the cam revolution. But
such a point would rapidly become worn away and dulled, which would, as
the point broadened, vary the motion imparted to it, as will be seen
presently. To avoid this wear a roller is used in place of a point, and
the diameter of the roller affects the action of the cam, causing it to
accelerate the cam action at one and retard it at another part of the
cam revolution, hence the pitch line obtained by the process in Fig. 225
represents the path of the centre of the roller, and from this pitch
line we may mark out the actual cam by the construction shown in Fig.
226. A pair of compasses are set to the radius of the roller R, and from
points (such as at A, B, E, F), as the pitch line, arcs of circles are
struck, and a line drawn to just meet the crowns of these arcs will give
the outline of the actual cam. The motion of the roller, however, in
approaching and receding from the cam centre C, must be in a straight
line G G that passes through the centre C of the cam. Suppose, for
example, that instead of the roller lifting and falling in the line G G
its arm is horizontal, as in Fig. 227, and that this arm being pivoted
the roller moves in an arc of a circle as D D, and the motion imparted
to the arm will no longer be uniform. Furthermore, different diameters
of roller require different forms of cam to accomplish the same motion,
or, in other words, with a given cam the action will vary with different
diameters of roller. Suppose, for example, that in Fig. 228 we have a
cam that is to operate a roller along the line A A, and that B
represents a large and C a small roller, and with the cam in the
position shown in the figure, C will have contact with the cam edge at
point D, while B will have contact at the point E, and it follows that
on account of the enlarged diameter of roller B over roller C, its
action is at this point quicker under a given amount of cam motion,
which has occurred because the point of contact has advanced upon the
roller surface--rolling along it, as it were. In Fig. 229 we find that
as the cam moves forward this action continues on both the large and the
small roller, its effect being greater upon the large than upon the
small one, and as this rolling motion of the point of contact evidently
occurs easily, a quick roller motion is obtained without shock or
vibration. Continuing the cam motion, we find in Fig. 230 that the point
of contact is receding toward the line of motion on the large roller and
advancing upon the small one, while in Fig. 231 the two have contact at
about the same point, the forward motion being about completed.
[Illustration: Fig. 229.]
[Illustration: Fig. 230.]
[Illustration: Fig. 231.]
[Illustration: Fig. 232.]
To compare the motions of the respective rollers along the line of
motion A A we proceed as in Fig. 232, in which the two dots M and N are
the same distance apart as are the centres of the two rollers B and C
when in the positions they occupy in Fig. 228; hence a pair of compasses
set to the radius from the axis of the cam to that of roller B will, if
rested at N, strike the arc marked 1 above the line of motion A A, while
a pair of compasses set to the radius from the axis of the cam to that
of roller C in Fig. 228 will, if rested at M in Fig. 232, mark the arc 1
below the line of motion A A. Continuing this process, we set the
compasses to the radius from the axis of the cam to that of roller B in
Fig. 229, and mark this radius at arc 2 above the line A A in Fig. 232;
hence the distance apart of these two arcs is the amount the roller
travelled along the line A A while the cam moved from its position in
Fig. 228 to its position in Fig. 229. Next we set the compasses from the
axis of the cam to that of the large roller in Fig. 230, and then mark
arc 3 above the line in Fig. 232, and repeat the process for Fig. 233,
thus using the centre N for all the positions of the large roller and
marking its motion above the line A A. To get the motion of the small
roller C, we set the compasses to the radius from the axis of the cam to
the small roller in Fig. 228, and then resting one point of these
compasses on centre M in Fig. 232, we mark arc 1 below the line A A.
Turning to Fig. 229 we set the compasses from the cam axis to the centre
of roller C, and from centre N in Fig. 232 mark arc 2 below line A. From
Figs. 230 and 231 proceed in the same way to get lines 3 and 4 below
line A in Fig. 232, and we may at once compare the two motions. Thus we
find that while the cam moved from the position in Fig. 228 to that in
Fig. 229, the large roller moved twice as far as the small one, while at
230 the motions were rapidly equalizing again, the equalization being
completed at 231.
[Illustration: Fig. 233.]
[Illustration: Fig. 234.]
[Illustration: Fig. 235.]
We may now consider the return motion, and in Fig. 233 we find that the
order of things is reversed, for the small roller has contact at O,
while the large one has contact at P; hence the small one leads and
gives the most rapid motion, which it continues to do, as is shown in
Figs. 234, 235, and 236, and we may plot out the two motions as in Fig.
237--that for the large roller being above and that for the small one
below the line A A. First we set a pair of compasses to the radius from
the axis of the large and small roller when in the position shown in
Fig. 231 (which corresponds to the same radius in Fig. 228), and mark
two centres, M and N, as we did in Fig. 232. Of these N is the centre
for plotting the motion of the large roller and M the centre for
plotting the motion of the small one. We set a pair of compasses to the
radius from the axis of the cam and that of the large roller in Fig.
231, and then resting the compasses at N we mark arc 5 above the line A
A, Fig. 237. The compasses are then set from the cam to the roller axis
in Fig. 233, and arc 6 is marked above line A A. From Figs. 234, 235,
and 236 we get the radii to mark arcs 7, 8, 9 above A A, and the motion
of the large roller is plotted. We proceed in the same way for the small
one, but use the centre M, Fig. 237, to mark the arcs 5, 6, 7, 8, and 9
below the line A A, and find that the small roller has moved quickest
throughout. It appears, then, that the larger the roller the quicker the
forward motion and the slower the return one, which is advantageous,
because the object is to move the roller out quickly and close it
slowly, so that under a quick speed the cam shall not run away from the
roller as it is apt to do in the absence of a return or backing cam,
which consists of a separate cam for moving the roller on its return
stroke, thus dispensing with the use of springs or weights to keep the
roller upon the cam and making the motion positive.
[Illustration: Fig. 236.]
[Illustration: Fig. 237.]
[Illustration: Fig. 238.]
The return or backing cam obviously depends for its shape upon the
forward cam, and the latter having been determined, the requisite form
for the return cam may be found as follows. In Fig. 238 let A represent
the forward cam fastened in any suitable or convenient way to a disc of
paper, or, what is better, sheet zinc, B. The cam is pivoted by a pin
passing through it and the zinc, and driven into the drawing-board. A
frame F is made to carry two rollers R and R´, whose width apart exactly
equals the extreme length of the forward cam. The faces D D of the frame
F are in a line with a line passing through the centres of the rolls R
R´, and the cam is also pivoted on this line, so that when the four pins
P are driven into the drawing-board, the frame F will be guided by them
to move in a line that crosses the centre of the cam A. Suppose then
that, the pieces occupying the position shown in the engraving, we slide
F so that roller R touches the edge of cam A, and we may then take a
needle and mark an arc or line around the edge of R´. We then revolve
cam A a trifle, and, being fast to B, the two will move together, and
with R against A we mark a second arc, coincident with the edge of
roller R´. By continuing this process we mark the numerous short arcs
shown upon B, and the crowns of these arcs give us the outline of the
return cam. It is obvious that, while the edge of the cam A will not let
roller R (and therefore frame F) move to the right, roller R´ being
against the edge of the backing or return cam as marked upon B, prevents
the frame F from moving to the left; hence neither roll can leave its
cam.
[Illustration: Fig. 239.]
We have in this example supposed that the frame carrying the rollers is
guided to move in a straight line, and it remains to give an example in
which the rollers are carried on a pivoted shaft or rocking arm. In Fig.
239 we have the same cam A with a sheet of paper B fastened to it, the
rollers R R´ being carried in a rock shaft pivoted at X. It is essential
in this case that the rollers R and R´ and the centre upon which the cam
revolves shall all three be in the arc of a circle whose centre is the
axis of X, as is denoted by the arc D. The cam A is fastened to the
piece of stiff paper or of sheet zinc B, and the two are pivoted by a
pin passing through the axis E of the cam and into the drawing-board,
while the lever is pivoted at X by a pin passing into the drawing-board.
The backing or return cam is obviously marked out the same way as was
described with reference to Fig. 238.
[Illustration: Fig. 240.]
In Fig. 240 we have as an example the construction of a cam to operate
the slide valve of an engine which is to have the steam supply to the
cylinder cut off at one-half the piston stroke, and that will admit the
live steam as quickly as a valve having steam lap equal to, say,
three-fourths the width of the port. In Fig. 240 let the line A
represent a piston stroke of 24 inches, the outer circle B the path of
the outer edge of the cam, and the inner circle C the inner edge of the
cam, the radius between these circles representing the full width of the
steam port. Now, in a valve having lap equal to three-fourths the width
of the steam port, and travel enough to open both ports fully, the
piston of a 24-inch-stroke engine will have moved about 2 inches before
the steam port is fully opened, and to construct a cam that will effect
the same movement we mark a dot D, distant from the end E of piston
stroke 2/26 of the length of the line A, and by erecting the line F we
get at point G, the point at which the cam must attain its greatest
throw. It is obvious, therefore, that as the roller is at R the valve
will be in mid-position, as shown at the bottom of the figure, and that
when point G of the cam arrives at E the edge P of the valve will be
moved fair with edge S of the steam port T, which will therefore be full
open. To cut off at half stroke the valve must again be closed by the
time point N of the cam meets the roller R; hence we may mark point N.
We may then mark in the cam curve from N to M, making it as short as it
will work properly without causing the roller to fail to follow the
curve or strike a blow when reaching the circle C. To accomplish this
end in a single cam, it is essential to make the curve as gradual as
possible from point M to O, so as to start the roller motion easily. But
once having fairly started, its motion may be rapidly accelerated, the
descent from O to Q being rapid. To prevent the roller from meeting
circle C with a blow, the curve from Q to N is again made gradual, so as
to ease and retard the roller motion. The same remarks apply to the
curve from R to G, the object being to cause the roller to begin and end
its passage along the cam curve as slowly as the length of cam edge
occupied by the curve will permit. There is one objection to starting
the curve slowly at G, which is that the port S will be opened
correspondingly slowly for the live steam. This, however, may be
overcome by giving the valve an increased travel, as shown in Fig. 241,
which will simply cause the valve edge to travel to a corresponding
amount over the inside edge of the port. The increased travel is shown
by the circles Y and Z, and it is seen that the cam curve from W to R is
more gradual than in Fig. 240, while the roller R will be moved much
more quickly in the position shown in Fig. 241 than it will in that
shown in Fig. 240, both positions being that when the piston is at the
end of the stroke and the port about to open. While that part of the cam
curve from G to M in Fig. 241 is moving past the roller R, the valve
will be moving over the bridge, the steam port remaining wide open, and
therefore not affecting the steam distribution. After point M, Fig. 241,
has passed the roller, we have from M to T to start the roller
gradually, so that when it has arrived at T and the port begins to close
for the cut-off it may move rapidly, and continue to do so until the
point N reaches the roller and the cut-off has occurred, after which it
does not matter how slowly the valve moves; hence we may make the curve
from N to the circle Y as gradual as we like.
[Illustration: Fig. 241.]
[Illustration: Fig. 242.]
Fig. 242 represents a cam for a valve having the amount of lap
represented by the distance between circles C and Y, the cam occupying
the position it would do with the piston at one end of the stroke, as at
E. Obviously, a full port is obtained when point G reaches the roller,
and as point N is distant from E three-quarters of the diameter of the
outer circle, the cut-off occurs at three-quarter stroke, and we have
from N to Y to make the curve as gradual as we like, and from W to R in
moving the valve to open the port. We cannot, however, give more gradual
curves at G and at M without retarding the roller motion, and therefore
opening and closing the port slower, and it would simply be a matter of
increase of speed to cause the roller to fail to follow the cam surface
at these two points unless a return cam be employed.
We have in these engine cams considered the steam supply and point of
cut-off only, and it is obvious that a second and separate cam would be
required to operate the exhaust valves.
[Illustration: Fig. 243.]
Fig. 243 represents a groove-cam, and it is to be observed that the
roller cannot be maintained in a close fit in the groove, because the
friction on its two sides endeavours to drive it in opposite directions
at the same time, causing an abrasion that soon widens the groove and
reduces the roller diameter; furthermore, when the grooves are made of
equal width all the way down (and these cams are often made in this way)
the roller cannot have a rolling action only, but must have some sliding
motion. Thus, referring to Fig. 243, the amount of sliding motion will
be equal to the differences in the circumferences of the outer circle A
and the inner one B. To obviate this the groove and roller must be made
of such a taper that the axis of the cam and of the roller will meet on
the line of the cam axes and in the middle of the width, as is shown in
Fig. 244; but even in this case the cam will grind away the roller to
some extent, on account of rubbing its sides in opposite directions. To
obviate this, Mr. James Brady, of Brooklyn, N. Y., has patented the use
of two rollers, as in Fig. 245, one acting against one side and the
other against the other side of the groove, by which means lost motion
and rapid wear are successfully avoided.
[Illustration: Fig. 244.]
[Illustration: Fig. 245.]
In making a cam of this form, the body of the cam is covered by a
sleeve. The groove is cut through the sleeve and into the body, and is
made wider than the diameter of the roller. When the rollers are in
place on the spindle or journal, the sleeve is pushed forward, or rather
endways, and fastened by a set-screw. This gives the desired bearing on
both sides of the groove, while each roller touches one side only of the
groove. The edges of the sleeve are then faced off even with the cam
body, the whole appearing as in the figure.
[Illustration: _VOL. I._ =FORMS OF SCREW THREADS.= _PLATE II._
THE [V]-THREAD.
Fig. 246.
THE UNITED STATES STANDARD THREAD.
Fig. 247.
THE WHITWORTH, OR ENGLISH STANDARD THREAD.
Fig. 248.
THE SQUARE THREAD.
Fig. 249.
THE PITCH OF A THREAD.
Fig. 250.
A DOUBLE THREAD.
Fig. 251.
A RATCHET THREAD.
Fig. 252.
A "DRUNKEN" THREAD.
Fig. 253.
RIGHT AND LEFT HAND THREAD.
Fig. 254.]
CHAPTER IV.--SCREW THREAD.
Screw threads are employed for two principal purposes--for holding or
securing, and for transmitting motion. There are in use, in ordinary
machine shop practice, four forms of screw thread. There is, first, the
sharp [V]-thread shown in Fig. 246; second, the United States standard
thread, the Sellers thread, or the Franklin Institute thread, as it is
sometimes called--all three designations signifying the same form of
thread. This thread was originally proposed by William Sellers, and was
afterward recommended by the Franklin Institute. It was finally adopted
as a standard by the United States Navy Department. This form of thread
is shown in Fig. 247. The third form is the Whitworth or English
standard thread, shown in Fig. 248. It is sometimes termed the round top
and bottom thread. The fourth form is the square thread shown in Fig.
249, which is used for coarse pitches, and usually for the transmission
of motion.
The sharp [V]-thread, Fig. 246, has its sides at an angle of 60° one to
the other, as shown; or, in other words, each side of the thread is at
an angle of 60° to the axial line of the bolt. The United States
Standard, Fig. 247, is formed by dividing the depth of the sharp
[V]-thread into 8 equal divisions and taking off one of the divisions at
the top and filling in another at the bottom, so as to leave a flat
place at the top and bottom. The Whitworth thread, Fig. 248, has its
sides at an angle of 55° to each other, or to the axial line of the
bolt. In this the depth of the thread is divided into 6 equal parts, and
the sides of the thread are joined by arcs of circles that cut off one
of these parts at the top and another at the bottom of the thread. The
centres from which these arcs are struck are located on the second lines
of division, as denoted in the figure by the dots. Screw threads are
designated by their pitch or the distance between the threads. In Fig.
250 the pitch is 1/4 inch, but it is usual to take the number of threads
in an inch of length; hence the pitch in Fig. 250 would generally be
termed a pitch of 4, or 4 to the inch. The number of threads per inch of
length does not, however, govern the true pitch of the thread, unless it
be a "single" thread.
A single thread is composed of one spiral projection, whose advance upon
the bolt is equal in each revolution to the apparent pitch. In Fig. 251
is shown a double thread, which consists of two threads. In the figure,
A denotes one spiral or thread, and B the other, the latter being
carried as far as C only for the sake of illustration. The true pitch is
in this case twice that of the apparent pitch, being, as is always the
case, the number of revolutions the thread makes around the bolt (which
gives the pitch per inch), or the distance along the bolt length that
the nut or thread advances during one rotation. Threads may be made
double, treble, quadruple and so on, the object being to increase the
motion without the use of a coarser pitch single thread, whose increased
depth would weaken the body of the bolt.
The "ratchet" thread shown in Fig. 252 is sometimes used upon bolts for
ironwork, the object being to have the sides A A of the thread at a
right angle to the axis of the bolt, and therefore in the direct line of
the strain. Modifications of this form of thread are used in coarse
pitches for screws that are to thread direct into woodwork.
A waved or drunken thread is one in which the path around the bolt is
waved, as in Fig. 253, and not a continuous straight spiral, as it
should be. All threads may be either left hand or right, according to
their direction of inclination upon the bolt; thus, Fig. 254 is a
cylinder having a right-hand thread at A and a left-hand one at B. When
both ends of a piece have either right or left-hand threads, if the
piece be rotated and the nuts be prevented from rotating, they will move
in the same direction, and, if the pitches of the threads are alike, at
the same rate of motion; but if one thread be a right and the other a
left one, then, under the above conditions, the nuts will advance toward
or recede from each other according to the direction of rotation of the
male thread.
[Illustration: Fig. 255.]
In Fig. 255 is represented a form of thread designed to enable the nut
to fit the bolt, and the thread sides to have a bearing one upon the
other, notwithstanding that the diameter of the nut and bolt may differ.
The thread in the nut is what may be termed a reversed ratchet thread,
and that in the bolt an undercut ratchet thread, the amount of undercut
being about 2°. Where this form of thread is used, the diameter of the
bolt may vary as much as 1-32d of an inch in a bolt 3/4 inch in
diameter, and yet the nut will screw home and be a tight fit. The
difference in the thread fit that ordinarily arises from differences in
the standards of measurement from wear of the threading tools, does not
in this form affect the fit of the nut to the bolt. In screwing the nut
on, the threads conform one to the other, giving a bearing area
extending over the full sides of the thread. The undercutting on the
leading face of the bolt thread gives room for the metal to conform
itself to the nut thread, which it does very completely. The result is
that the nut may be passed up and down the bolt several times and still
remain too tight a fit to be worked by hand. Experiment has demonstrated
that it may be run up and down the bolt dozens of times without becoming
as loose as an ordinary bolt and nut. On account of this capacity of the
peculiar form of thread employed, to adapt itself, the threads may be
made a tight fit when the threading tools are new. The extra tightness
that arises from the wear of these tools is accommodated in the
undercutting, which gives room for the thread to adjust itself to the
opposite part or nut.
In a second form of self-locking thread, the thread on the bolt is made
of the usual [V]-shape United States standard. The thread in the nut,
however, is formed as illustrated in Fig. 256, which is a section of a
3/4-inch bolt, greatly enlarged for the sake of clearness of
illustration. The leading threads are of the same angle as the thread on
the bolt, but their diameters are 3/4 and 1-16th inch, which allows the
nut to pass easily upon the bolt. The angle of the next thread following
is 56°, the succeeding one 52°, and so on, each thread having 4° less
angle than the one preceding, while the pitch remains the same
throughout. As a result, the rear threads are deeper than the leading
ones. As the nut is screwed home, the bolt thread is forced out or up,
and fills the rear threads to a degree depending upon the diameter of
the bolt thread. For example, if the bolt is 3/4 inch, its leading or
end thread will simply change its angle from that of 60° to that of 44°,
or if the bolt thread is 3/4 and 1-64th inch in diameter, its leading
thread will change from an angle of 60° to one of 44°. It will almost
completely fill the loose thread in the nut. The areas of spaces between
the nut threads are very nearly equal, although slightly greater at the
back end of the nut, so that if the front end will enter at all, the nut
will screw home, while the thread fit will be tight, even under a
considerable variation in the bolt itself. From this description, it is
evident that the employment of nuts threaded in this manner is only
necessary in order to give to ordinary bolts all the advantages of
tightness due to this form of thread.
The term "diameter" of a thread is understood to mean its diameter at
the top of the thread and measured at a right angle to the axis of the
bolt. When the diameter of the bottom or root of the thread is referred
to it is usually specified as diameter at the bottom or at the root of
the thread.
The depth of a thread is the vertical height of the thread upon the
bolt, measured at a right angle to the bolt axis and not along the side
of the thread.
A true thread is one that winds around the bolt in a continuous and even
spiral and is not waved or drunken as is the thread in Fig. 253. An
outside or male thread is one upon an external surface as upon a bolt;
an internal or female thread is one produced in a bore or hole as in a
nut.
[Illustration: Fig. 256.]
The Whitworth or English standard thread, shown in Fig. 248, is that
employed in Great Britain and her colonies, and to a small extent in the
United States. The [V]-thread fig. 246 is that in most common use in the
United States, but it is being displaced by the United States standard
thread. The reasons for the adoption of the latter by the Franklin
Institute are set forth in the report of a committee appointed by that
Institute to consider the matter. From that report the following
extracts are made.
"That in the course of their investigations they have become more deeply
impressed with the necessity of some acknowledged standard, the
varieties of threads in use being much greater than they had supposed
possible; in fact, the difficulty of obtaining the exact pitch of a
thread not a multiple or sub-multiple of the inch measure is sometimes a
matter of extreme embarrassment.
"Such a state of things must evidently be prejudicial to the best
interests of the whole country; a great and unnecessary waste is its
certain consequence, for not only must the various parts of new
machinery be adjusted to each other, in place of being interchangeable,
but no adequate provision can be made for repairs, and a costly variety
of screwing apparatus becomes a necessity. It may reasonably be hoped
that should a uniformity of practice result from the efforts and
investigations now undertaken, the advantages flowing from it will be so
manifest, as to induce reform in other particulars of scarcely less
importance.
"Your committee have held numerous meetings for the purpose of
considering the various conditions required in any system which they
could recommend for adoption. Strength, durability, with reference to
wear from constant use, and ease of construction, would seem to be the
principal requisites in any general system; for although in many cases,
as, for instance, when a square thread is used, the strength of the
thread and bolt are both sacrificed for the sake of securing some other
advantage, yet all such have been considered as special cases, not
affecting the general inquiry. With this in view, your committee decided
that threads having their sides at an angle to each other must
necessarily more nearly fulfil the first condition than any other form;
but what this angle should be must be governed by a variety of
considerations, for it is clear that if the two sides start from the
same point at the top, the greater the angle contained between them, the
greater will be the strength of the bolt; on the other hand, the greater
this angle, supposing the apex of the thread to be over the centre of
its base, the greater will be the tendency to burst the nut, and the
greater the friction between the nut and the bolt, so that if carried to
excess the bolt would be broken by torsional strain rather than by a
strain in the direction of its length. If, however, we should make one
side of the thread perpendicular to the axis of the bolt, and the other
at an angle to the first, we should obtain the greatest amount of
strength, together with the least frictional resistance; but we should
have a thread only suitable for supporting strains in one direction, and
constant care would be requisite to cut the thread in the nut in the
proper direction to correspond with the bolt; we have consequently
classed this form as exceptional, and decided that the two sides should
be at an angle to each other and form equal angles with the base.
"The general form of the thread having been determined upon the above
considerations, the angle which the sides should bear to each other has
been fixed at 60°, not only because this seems to fulfil the conditions
of least frictional resistance combined with the greatest strength, but
because it is an angle more readily obtained than any other, and it is
also in more general use. As this form is in common use almost to the
exclusion of any other, your committee have carefully weighed its
advantages and disadvantages before deciding to recommend any
modification of it. It cannot be doubted that the sharp thread offers us
the simplest form, and that its general adoption would require no
special tools for its construction, but its liability to accident,
always great, becomes a serious matter upon large bolts, whilst the
small amount of strength at the sharp top is a strong inducement to
sacrifice some of it for the sake of better protection to the remainder;
when this conclusion is reached, it is at once evident a corresponding
space may be filled up in the bottom of the thread, and thus give an
increased strength to the bolt, which may compensate for the reduction
in strength and wearing surface upon the thread. It is also clear that
such a modification, by avoiding the fine points and angles in the tools
of construction, will increase their durability; all of which being
admitted, the question comes up, what form shall be given to the top and
bottom of the thread? for it is evident one should be the converse of
the other. It being admitted that the sharp thread can be made
interchangeable more readily than any other, it is clear that this
advantage would not be impaired if we should stop cutting out the space
before we had made the thread full or sharp; but to give the same shape
at the bottom of the threads would require that a similar quantity
should be taken off the point of the cutting tool, thus necessitating
the use of some instrument capable of measuring the required amount, but
when this is done the thread having a flat top and bottom can be quite
as readily formed as if it was sharp. A very slight examination sufficed
to satisfy us that in point of construction the rounded top and bottom
presents much greater difficulties--in fact, all taps and screws that
are chased or cut in a lathe require to be finished or rounded by a
second process. As the radius of the curve to form this must vary for
every thread, it will be impossible to make one gauge to answer for all
sizes, and very difficult, in fact impossible, without special tools, to
shape it correctly for one.
"Your committee are of opinion that the introduction of a uniform system
would be greatly facilitated by the adoption of such a form of thread as
would enable any intelligent mechanic to construct it without any
special tools, or if any are necessary, that they shall be as few and as
simple as possible, so that although the round top and bottom presents
some advantages when it is perfectly made, as increased strength to the
thread and the best form to the cutting tools, yet we have considered
that these are more than compensated by ease of construction, the
certainty of fit, and increased wearing surface offered by the flat top
and bottom, and therefore recommend its adoption. The amount of flat to
be taken off should be as small as possible, and only sufficient to
protect the thread; for this purpose one-eighth of the pitch would seem
to be ample, and this will leave three-fourths of the pitch for bearing
surface. The considerations governing the pitch are so various that
their discussion has consumed much time.
"As in every instance the threads now in use are stronger than their
bolts, it became a question whether a finer scale would not be an
advantage. It is possible that if the use of the screw thread was
confined to wrought iron or brass, such a conclusion might have been
reached, but as cast iron enters so largely into all engineering work,
it was believed finer threads than those in general use might not be
found an improvement; particularly when it was considered that so far as
the vertical height of thread and strength of bolt are concerned, the
adoption of a flat top and bottom thread was equivalent to decreasing
the pitch of a sharp thread 25 per cent., or what is the same thing,
increasing the number of threads per inch 33 per cent. If finer threads
were adopted they would require also greater exactitude than at present
exists in the machinery of construction, to avoid the liability of
overriding, and the wearing surface would be diminished; moreover, we
are of opinion that the average practice of the mechanical world would
probably be found better adapted to the general want than any
proportions founded upon theory alone."
* * * * *
[Illustration: Fig. 257.]
[Illustration: Fig. 258.]
The principal requirements for a screw thread are as follows: 1. That it
shall possess a strength that, in the length or depth of a nut, shall be
equal to the strength of the weakest part of the bolt, which is at the
bottom of the bolt thread. 2. That the tools required to produce it
shall be easily made, and shall not alter their form by reason of wear.
3. That these tools shall (in the case of lathe work) be easily
sharpened, and set to correct position in the lathe. 4. That a minimum
of measuring and gauging shall be required to test the diameter and form
of the thread. 5. That the angles of the sides shall be as acute as is
consistent with the required strength. 6. That it shall not be unduly
liable to become loose in cases where the nut may require to be fastened
and loosened occasionally.
Referring to the first, by the term "the strength of a screw thread," is
not meant the strength of one thread, but of so many threads as are
contained in the nut. This obviously depends upon the depth or thickness
of the nut-piece. The standard thickness of nut, both in the United
States and Whitworth systems, as well as in general practice, or where
the common [V]-thread is used, is made equal to the diameter of the top
of the thread. Therefore, by the term "strength of thread" is meant the
combined strength of as many threads as are contained in a nut of the
above named depth. It is obvious, then, when it is advantageous to
increase the strength of a thread, that it may be done by increasing the
depth of the nut, or in other words, by increasing the number of threads
used in computing its strength. This is undesirable by reason of
increasing the cost and labor of producing the nuts, especially as the
threading tools used for nuts are the weakest, and are especially liable
to breakage, even with the present depth of nuts.
It has been found from experiments that have been made that our present
threads are stronger than their bolts, which is desirable, inasmuch as
it gives a margin for wear on the sides of the threads. But for threads
whose nuts are to remain permanently fastened and are not subject to
wear, it is questionable whether it were not better for the bolts to be
stronger than the threads. Suppose, for instance, that a thread strips,
and the bolt will remain in place because the nut will not come off the
bolt readily. Hence the pieces held by the bolt become loosened, but not
disconnected. If, on the other hand, the bolt breaks, it is very liable
to fall out, leaving the piece or pieces, as the case may be, to fall
apart, or at least become disconnected, so far as the bolt is concerned.
But since threads are used under conditions where the threads are liable
to wear, and since it is undesirable to have more than one standard
thread, it is better to have the threads, when new, stronger than the
bolts.
[Illustration: Fig. 259.]
Referring to the second requirement, screw threads or the tools that
produce them are originated in the lathe, and the difficulty with making
a round top and bottom thread lies in shaping the corner to cut the top
of the thread. This is shown in Fig. 257, where a Whitworth thread and a
single-toothed thread-cutting tool are represented. The rounded point A
of the tool will not be difficult to produce, but the hollow at B would
require special tools to cut it. This is, in fact, the plan pursued
under the Whitworth system, in which a hob or chaser-cutting tool is
used to produce all the thread-cutting tools. A chaser is simply a
toothed tool such as is shown in Fig. 258. Now, it would manifestly be
impracticable to produce a chaser having all the curves, A and B, at the
top and at the bottom of the teeth alike, by the grinding operations
usually employed in the workshop, and hence the employment of the hob.
Fig. 259 represents a hob, which is a threaded piece of steel with a
number of grooves such as shown at A, A, A, which divide the thread into
teeth, the edges of which will cut a chaser, of a form corresponding to
that of the thread upon the hob. The chaser is employed to produce taps
and secondary hobs to be used for cutting the threads in dies, &c., so
that the original hob is the source from which all the thread-cutting
tools are derived.
[Illustration: Fig. 260.]
For the United States standard or the common [V]-thread, however, no
standard hob is necessary, because a single-pointed tool can be ground
with the ordinary grinding appliances of the workshop. Thus, for the
United States standard, a flat-pointed tool, Fig. 260, and for the
common [V]-thread, a sharp-pointed tool, Fig. 260, may be used. So far
as the correctness of angle of pitch and of thread depth are concerned,
the United States standard and the common [V]-thread can both be
produced, under skilful operation, more correctly than is possible with
the Whitworth thread, for the following reasons:--
To enable a hob to cut, it must be hardened, and in the hardening
process the pitch of the thread alters, becoming, as a general rule
(although not always) finer. This alteration of pitch is not only
irregular in different threads, but also in different parts of the same
thread. Now, whatever error the hob thread receives from hardening it
transfers to the chaser it cuts. But the chaser also alters its form in
hardening, the pitch, as a general rule, becoming coarser. It may happen
that the error induced in the hob hardening is corrected by that induced
by hardening the chaser, but such is not necessarily the case.
[Illustration: Fig. 261.]
The single-pointed tool for the United States standard or for the common
[V]-thread is accurately ground to form after the hardening, and hence
need contain no error. On the other hand, however, the rounded top and
bottom thread preserves its form and diameter upon the thread-cutting
tools better than is the case with threads having sharp corners, for the
reason that a rounded point will not wear away so quickly as a sharp
point. To fully perceive the importance of this, it is necessary to
consider the action of a tool in cutting a thread. In Fig. 261 there is
shown a chaser, A, applied to a partly-formed thread, and it will be
observed that the projecting ends or points of the teeth are in
continuous action, cutting a groove deeper and deeper until a full
thread is developed, at which time the bottoms of the chaser teeth will
meet the perimeter of the work, but will perform no cutting duty upon
it. As a result, the chaser points wear off, which they will do more
quickly if they are pointed, and less quickly if they are rounded. This
causes the thread cut to be of increased and improper diameter at the
root.
[Illustration: Fig. 262.]
The same defect occurs on the tools for cutting internal threads, or
threads in holes or bores. In Fig. 262, for example, is shown a tool
cutting an internal thread, which tool may be taken to represent one
tooth of a tap. Here again the projecting point of the tool is in
continuous cutting action, while this, being a single-toothed tool, has
no bottom corners to suffer from wear. As a result of the wear upon the
tools for cutting internal threads, the thread grooves, when cut to
their full widths, will be too shallow in depth, or, more correctly
speaking, the full diameter of the thread will be too small to an amount
corresponding to twice the amount of wear that the tool point has
suffered. In single-pointed tools, such as are used upon lathe work,
this has but little significance, because it is the work of but a minute
or two to grind up the tool to a full point again, but in taps and solid
dies, or in chasers in heads (as in some bolt-cutting machines) it is
highly important, because it impairs the fit of the threads, and it is
difficult to bring the tools to shape after they are once worn.
[Illustration: Fig. 263.]
The internal threads for the nuts of bolts are produced by a tap formed
as at T in Fig. 263. It consists of a piece of steel having an external
thread and longitudinal flutes or grooves which cut the thread into
teeth. The end of the thread is tapered off as shown, to enable the end
of the tap to enter the hole, and as it is rotated and the nut N held
stationary, the teeth cut grooves as the tap winds through, thus forming
the thread.
[Illustration: Fig. 264.]
The threads upon bolts are usually produced either by a head containing
chasers or by a solid die such as shown at A in Fig. 264, B representing
a bolt being threaded. The bore of A is threaded and fluted to provide
cutting teeth, and the threads are chamfered off at the mouth to assist
the cutting by spreading it over several teeth, which enables the bolt
to enter the die more easily.
We may now consider the effect of continued use and its consequent wear
upon the threads or teeth of a tap and die or chaser.
The wear of the corners at the tops of the thread (as at A B in Fig.
265) of a tap is greater than the wear at the bottom corners at E F,
because the tops perform more cutting duty.
[Illustration: Fig. 265.]
First, the top has a larger circle of rotation than has the bottom, and,
therefore, its cutting speed is greater, to an amount equal to the
difference between the circumferences of the thread at the top and at
the bottom. Secondly, the tops of the teeth of tap perform nearly all
the cutting duty, because the thread in the nut is formed by the tops
and sides of the tap, which on entering cut a groove which they
gradually deepen, until a full thread is formed, while the bottoms of
the teeth (supposing the tapping hole to be of proper diameter and not
too small) simply meet the bore of the tapping hole as the thread is
finished. If, as in the case of hot punched nuts, the nut bore contains
scale, this scale is about removed by the time the bottoms of the top
teeth come into action, hence the teeth bottoms are less affected by the
hardness of the scale.
In the case of the teeth on dies and chasers, the wear at the corners C
D, in Fig. 266, is the greatest. Now, the tops of the teeth on the tap
(A B, in Fig. 265) cut the bottom or full diameter of the thread in the
nut, while the tops of the teeth (C D, in Fig. 266) in the die cut the
bottom of the thread on the bolt; hence the rounded corners cut on the
work by the tops of the teeth in the one case, meet the more square
corners left by the tops of the teeth in the other, and providing that
under these circumstances the thread in the nut were of equal diameter
to that on the bolt the latter would not enter the former.
If the bolt were made of a diameter to enable the nut to wind a close
fit upon the bolt, the corners only of the threads would fit, as shown
in Fig. 267, which represents at N a thread in a portion of a nut and at
S a portion of a thread upon a tap or bolt, the two threads being
magnified and shown slightly apart for clearness of illustration. The
corners A, B of the nut are then cut by the corners A B of the tap in
Fig. 265, and the corners C, C, D correspond to those cut by the corners
C, D of the die teeth in Fig. 266; corners E, F, Fig. 267, are cut by
corners C, D, in Fig. 266, and corners G, H are cut by corners G, H in
Fig. 266, and it is obvious that the roundness of the corners A, B, C,
and D in Fig. 267 will not permit the tops of the thread on the bolt to
meet the bottoms of the thread in the nut, but that the threads will
bear at the corners only.
[Illustration: Fig. 266.]
[Illustration: Fig. 267.]
So far, however, we have only considered the wear tending to round off
the sharp corners of the teeth, which wear is greater in proportion as
the corners are sharp, and less as they are rounded or flattened, and we
have to consider the wear as affecting the diameters of the male and
female thread at their tops and bottoms respectively.
Now, since the tops of the tap teeth wear the most, the diameter of the
thread decreases in depth, while, since the tops of the die teeth wear
most, the depth of the thread in the die also decreases. The tops of the
tap teeth cut the bottom of the thread in the nut and the tops of the
die teeth cut the bottoms of the thread upon the bolt.
Let it be supposed then that the points of the teeth of a tap have worn
off to a depth of the 1-2000th part of an inch, which they will by the
time they become sufficiently dulled to require resharpening, and that
the teeth of a die have become reduced by wear by the same amount, and
the result will be the production of threads such as shown in Fig. 268,
in which the diameter of the bolt is supposed to be an inch, and the
proper thread depth 1-10th inch. Now, the diameter at the root of the
thread on the bolt will be .802 inch in consequence of the wear, but the
smallest diameter of the nut thread is .800 inch, and hence too small to
admit the male or bolt thread. Again, the full diameter of the bolt
thread is 1 inch, whereas the full diameter of the nut thread is but
.998 inch, or, again, too small to admit the bolt thread. As a result,
it is found in practice that any standard form of thread that makes no
allowance for wear, cannot be rigidly adhered to, or if it is adhered
to, the tap must be made when new above the standard diameter, causing
the thread to be an easy fit, which fit will become closer as the
thread-cutting tools wear, until finally it becomes too tight
altogether. The fit, however, becomes too tight at the top and bottom,
where it is not required, instead of at the sides, where it should
occur. When this is the case, the nuts will soon wear loose because of
their small amount of bearing area.
[Illustration: Fig. 268.]
[Illustration: Fig. 269.]
It may be pointed out, however, that from the form in which the chasers
or solid dies for bolt machines, and also that in which taps are made,
the finishing points of the teeth are greatly relieved of cutting duty,
as is shown in Figs. 269 and 270. In the die the first two or three
threads are chamfered off, while in the tap the thread is tapered off
for a length usually equal to about two or three times the diameter for
taps to be used by hand, and six or seven times the diameter for taps to
be used in a machine. The wear of the die is, therefore, more than that
of the tap, because the amount of cutting duty to produce a given
length of thread is obviously the same, whether the thread be an
internal or an external one, and the die has less cutting edges to
perform this duty than the tap has. The main part of the cutting is, it
is true, in both cases borne by the beveled surfaces at the top of the
chamfered teeth of the cutting tools, but the fact remains that the
depth of the thread is finished by the extreme tops of the teeth, and
these, therefore, must in time suffer from the consequent wear, while
the bottoms of the teeth perform no cutting duty, providing that the
hole in the one case and the bolt in the other are of just sufficient
diameter to permit of a full thread being formed, as should be the case.
In threads cut by chasers the same thing occurs; thus in Fig. 271 is
shown at A a chaser having full teeth, as it must have when a full
thread is to pass up to a shoulder, as up to the head of a bolt. Here
the first tooth takes the whole depth of the cut, but if from wear this
point becomes rounded, the next tooth may remedy the defect. When,
however, a chaser is to be used upon a thread that terminates in a stem
of smaller diameter, as C in Fig. 271, then the chaser may have its
teeth bevelled off, as is shown on B.
[Illustration: Fig. 270.]
The evils thus pointed out as attending the wear of screw-cutting tools
for bolts and nuts, may be overcome by a slight variation in the form of
the thread. Thus in Fig. 272, at A is shown a form of thread for the
tools to cut internal threads, and at B a form of thread for dies to cut
external threads. The sides of the thread are in both cases at the same
angle, as say, 60°. The depth of the thread, supposing the angle of the
sides to meet in a point, is divided off into 11, or any number of equal
divisions. For a tap one of these divisions is taken off, forming a flat
top, while at the bottom two of these divisions are taken off, or if
desirable, 1-1/2 divisions may be taken off, since the exact amount is
not of primary importance. On the external thread cutting tool B, as say
a solid die, two divisions are taken off at the largest diameter, and
one at the smallest diameter, or, if any other proportion be selected
for the tap, the same proportion may be selected for the die, so long as
the least is taken off the largest diameter of the tap thread, and of
the smallest diameter of the die thread.
[Illustration: Fig. 271.]
The diameter of the tap may still be standard to ring or collar gauge,
as in the Franklin Institute thread, the angle at the sides being simply
carried in a less distance. In the die the largest diameter of the
thread has a flat equal to that on the bottom of the tap, while the
smallest diameter has a flat equal to that on the tops of the tap teeth,
the width or thickness of the threads remaining the same as in the
Franklin Institute thread at each corresponding diameter in its depth.
[Illustration: Fig. 272.]
The effect is to give to the threads on the work a certain amount of
clearance at the top and bottom of the thread, leaving the angles just
the same as before, and insuring that the contact shall be at the sides,
as shown in Fig. 273.
This form of thread retains the valuable features of the Franklin
Institute that it can be originated by any one, and that it can be
formed with a single-toothed or single-pointed tool. Furthermore, the
wear of the threading tools will not impair the diametral fit of the
work, while the permissible limit of error in diameter will be
increased.
By this means great accuracy in the diameters of the threads is rendered
unnecessary, and the wear of the screw-cutting tools at their corners is
rendered harmless, nor can any confusion occur, because the tools for
external threads cannot be employed upon internal ones. The sides only
of the thread will fit, and the whole contact and pressure of the fit
will be on those sides only.
[Illustration: Fig. 273.]
This is an important advantage, because if the tops of the thread are
from the wear of the dies and taps of too large or small diameter,
respectively, the threads cannot fit on the sides. Thus, suppose a bolt
thread to be loose at the sides, but to be 1-1000 of an inch larger in
diameter than the nut thread, then it cannot be screwed home until that
amount has been worn or forced off the thread diameter, or has been
bruised down by contact with the nut thread, and it would apparently be
a tight fit at the sides. Suppose a thread to have been cut in the
lathe to the correct diameter at the bottom of the thread, the sides of
the thread being at the correct angle, but let the diameter at the top
of the thread (a Franklin Institute thread is here referred to), be
1-1000 too large, then the nut cannot be forced on until that 1-1000 is
removed by some means or other, unless the nut thread be deepened to
correspond.
Now take this last bolt and turn the 1-1000 inch off, and it will fit,
turn off another 1-1000 or 1-64 inch, and it will still fit, and the fit
will remain so nearly the same with the 1-64 inch off that the
difference can scarcely be found. Furthermore, with a nut of a fit
requiring a given amount of force to screw it upon the bolt, the area of
contact will be much greater when that contact is on the sides than when
it is upon the tops and bottoms of the thread, while the contact will be
in a direction better to serve as an abutment to the thrust or strain.
In very fine pitches of thread such as are used in the manufacture of
watches, this plan of easing or keeping free the extremities of the
thread is found to be essential, and there appears every probability
that its adoption would obviate the necessity of using check nuts.
It has been observed that the threads upon tools alter in pitch from the
hardening operation, and this is an objection to the employment of
chasers cut from hobs.
Suppose, for instance, that a nut is produced having a thread of true
and uniform pitch, then after hardening, the pitch may be no longer
correct. The chasers cut from the hob will contain the error of pitch
existing in the hob, and upon being hardened may have added to it errors
of its own. If this chaser be used to produce a new hob, the latter will
contain the errors in the chaser added to whatever error it may itself
obtain in the hardening. The errors may not, it is true, all exist in
one direction, and those of one hardening may affect or correct those
caused by another hardening, but this is not necessarily the case, and
it is therefore preferable to employ a form of thread that can be cut by
a tool ground to correct shape after having been hardened, as is the
case with the [V]-thread and the United States standard.
[Illustration: Fig. 274.]
It is obvious that in originating either the sharp [V] or the United
States standard thread, the first requisite is to obtain a correct angle
of 60°, which has been done in a very ingenious manner by Mr. J. H.
Heyer for the Pratt and Whitney Company, the method being as follows.
Fig. 274 is a face and an end view of an equilateral triangle employed
as a guide in making standard triangles, and constructed as
follows:--Three bars, A, A, A, of steel were made parallel and of
exactly equal dimensions. Holes X were then pierced central in the width
of each bar and the same distance apart in each bar; the method of
insuring accuracy in this respect being shown in Figs. 275 and 276, in
which S represents the live spindle of a lathe with its face-plate on
and a plug, C, fitted into the live centre hole. The end of this plug is
turned cylindrically true, and upon it is closely fitted a bush, the
plug obviously holding the bush true by its hole. A rectangular piece
_e_ is provided with a slot closely fitting to the bush.
The rectangular piece _e_ is then bolted to the lathe face-plate and
pierced with a hole, which from this method of chucking will be exactly
central to its slot, and at a right angle to its base. The bush is now
dispensed with and the piece _e_ is chucked with its base against the
face-plate and the hole pierced as above, closely fitting to the pin on
the end of the plug _c_, which, therefore, holds _e_ true.
[Illustration: Fig. 275.]
The bars A are then chucked one at a time in the piece _e_ (the outer
end resting upon a parallel piece _f_), and a hole is pierced near one
end, this hole being from this method of chucking exactly central to the
width of the bar A, and at a right angle to its face.
[Illustration: Fig. 276.]
The parallel piece _f_ is then provided with a pin closely fitting the
hole thus pierced in the bar. The bars were turned end for end with the
hole enveloping the pin in _f_ (the latter being firmly fixed to the
face-plate), and the other end laid in the slot in _e_, while the second
hole was pierced. The holes (X, Fig. 274) must be, from this method of
chucking, exactly an equal distance apart on each bar. The bars were
then let together at their ends, each being cut half-way through and
closely fitting pins inserted in the holes X, thus producing an
equilateral triangle entirely by machine work, and therefore as correct
as it can possibly be made, and this triangle is kept as a standard
gauge whereby others for shop use may be made by the following
process:--
Into the interior walls of this triangle there is fitted a cylindrical
bush B, it being obvious that this bush is held axially true or central
to the triangle, and it is secured in place by screws _y_, _y_, _y_,
passing through its flange and into bars A.
At one end of the bush B, is a cylindrical part D, whose diameter is 2
inches or equal to the length of one side of an equilateral triangle
circumscribed about a circle whose diameter is 1.1547 inches, as shown
in Fig. 278 and through this bush B passes a pin P, having a nut N. A
small triangle is then roughed out, and its bore fitting to the stem of
pin P, and by means of nut N, the small triangle is gripped between the
under face of D and the head of P. The large triangle is then held to an
angle-plate upon a machine while resting upon the machine-table, and the
uppermost edge of the small triangle is dressed down level with the
cylindrical stem D, which thus serves as a gauge to determine how much
to take off each edge of the small triangle to bring it to correct
dimensions.
The truth of the angles of the small triangle depends, of course, also
upon the large one; thus with face H resting upon the machine-table,
face G is cut down level with stem D; with face F upon the table, face E
is cut down level with D; and with face L upon the table, face K is
dressed down level with D. And we have a true equilateral triangle
produced by a very ingenious system of chuckings, each of which may be
known to be true.
The next operation is to cut upon the small triangle the flat
representing the top and bottom of the United States standard thread,
which is done by cutting off one-eighth part of its vertical height, and
it then becomes a test piece or standard gauge of the form of thread.
The next step is to provide a micrometer by means of which tools for
various pitches may be tested both for angle and for width of flat, and
this is accomplished as follows:--
[Illustration: _VOL. I_ =MEASURING AND GAUGING SCREW THREADS.= _PLATE
III._
Fig. 279.
Fig. 280.
Fig. 281.
Fig. 282.
Fig. 285.
Fig. 286.
Fig. 283.
Fig. 284.
Fig. 287.]
In Fig. 278 F is a jaw fixed by a set screw to the bar of the
micrometer, and E is a sliding jaw; these two jaws being fitted to the
edges of the triangle or test piece T in the figure which has been made
as already described. To the sliding jaw E is attached the micrometer
screw C, which has a pitch of 40 threads per inch; the drum A upon the
screw has its circumference divided into 250 equidistant divisions,
hence if the drum be moved through a space equal to one of these
divisions the sliding jaw E will be moved the 1-250th part of 1-40th of
an inch, or in other words the 1-10,000th of an inch. To properly adjust
the position of the zero piece or pointer, the test piece T is placed in
the position shown in Fig. 278, and when the jaws were so adjusted that
light was excluded from the three edges of the test piece, the pointer
R, Fig. 277, was set opposite to the zero mark on the drum and fastened.
[Illustration: Fig. 277.]
To set the instrument for any required pitch of thread of the United
States standard form the micrometer is used to move the sliding jaw E
away from the fixed jaw F to an amount equal to the width of flat upon
the top and bottom, of the required thread, while for the sharp
[V]-thread the jaws are simply closed. The gauge being set the tool is
ground to the gauge.
[Illustration: Fig. 278.]
Referring to the third requirement, that the tools shall in the case of
lathe work be easily sharpened and set to correct position in the lathe,
it will be treated in connection with cutting screws in the lathe.
Referring to the fourth requirement, that a minimum of measuring and
gauging shall be required to test the diameter and form of thread, it is
to be observed that in a Whitworth thread the angle and depth of the
thread is determined by the chaser, which may be constantly ground to
resharpen without altering the angles or depth of the thread, hence in
cutting the tooth the full diameter of the thread is all that needs to
be gauged or measured. In cutting a sharp [V]-thread, however, the
thread top is apt to project (from the action of the single-pointed
tool) slightly above the natural diameter of the work, producing a
feather edge which it becomes necessary to file off to gauge the full
diameter of the thread. In originating a sharp [V]-thread it is
necessary first to grind the tool to correct angle; second, to set it at
the correct height in the latter, and with the tool angles at the proper
angle with the work (as is explained with reference to thread cutting in
the lathe) and to gauge the thread to the proper diameter. In the
absence of a standard cylindrical gauge or piece to measure from, a
sheet metal gauge, such as in Fig. 279, may be applied to the thread;
such gauges are, however, difficult to correctly produce.
So far as the diameter of a thread is concerned it may be measured by
calipers applied between the threads as in Figs. 280 and 281, a plan
that is commonly practised in the workshop when there is at hand a
standard thread or gauge known to be of proper diameter; and this method
of measuring may be used upon any form of thread, but if it is required
to test the form of the thread, as may occur when its form depends upon
the workman's accuracy in producing the single-pointed threading tools,
then, in the case of the United States standard thread, the top, the
bottom, and the angle must be tested. The top of the thread may (for all
threads) be readily measured, but the bottom is quite difficult to
measure unless there is some standard to refer it to, to obtain its
proper diameter, because the gauge or calipers applied to the bottom of
the thread do not stand at a right angle to the axis of the bolt on
which the thread is cut, but at an angle equal to the pitch of the
thread, as shown in Fig. 282.
Now, the same pitch of thread is necessarily used in mechanical
manipulation upon work of widely varying diameters, and as the angle of
the calipers upon the same pitch of thread would vary (decreasing as the
diameter of the thread increases), the diameter measured at the bottom
of the thread would bear a constantly varying proportion to the diameter
measured across the tops of the thread at a right angle to the axial
line of the work. Thus in Fig. 282, A A is the axial line of two
threaded pieces, B, C. D, D represents a gauge applied to B, its width
covering the tops of two threads and measuring the diameter at a right
angle to A A, as denoted by the dotted line E. The dotted line F
represents the measurement at the bottom of the thread standing at an
angle to E equal to half the pitch. The dotted line G is the measurement
of C at the bottom of the thread.
Now suppose the diameter of B to be 1-1/2 inches at the top of the
thread, and 1-1/8 inches at the bottom, while C is 1-1/8 inches on the
top and 3/4 at the bottom of the thread, the pitches of the two threads
being 1/4 inch; then the angle of F to E will be 1/8 inch (half the
pitch) in its length of 1-1/8 inches. The angle of G to E will be 1/8
inch (half the pitch) in 3/4 (the diameter at the bottom or root of the
thread).
It is obvious, then, that it is impracticable to gauge threads from
their diameters at the bottom, or root.
On account of the minute exactitude necessary to produce with lathe
tools threads of the sharp [V] and United States standard forms, the
Pratt and Whitney Company manufacture thread-cutting tools which are
made under a special system insuring accuracy, and provide standard
gauges whereby the finished threads may be tested, and since these tools
are more directly connected with the subject of lathe tools than with
that of screw thread, they are illustrated in connection with such
tools. It is upon the sides of threads that the contact should exist to
make a fit, and the best method of testing the fit of a male and female
thread is to try them together, winding them back and forth until the
bright marks of contact show. Giving the male thread a faint tint of
paint made of Venetian red mixed with lubricating oil, will cause the
bearing of the threads to show very plainly.
Figs. 283 and 284 represent standard reference gauges for the United
States standard thread. Fig. 283 is the plug or male gauge. The top of
the thread has, it will be observed, the standard flat, while the bottom
of the thread is sharp. In the collar, or female gauge, or the template,
as it may be termed, a side and a top view of which are shown in Fig.
284, and a sectional end view in Fig. 285, the flat is made on the
smallest diameter of the thread, while the largest diameter is left
sharp; hence, if we put the two together they will appear as in Fig.
286, there being clearance at both the tops and bottoms of the threads.
This enables the diameters of the threads to be in both cases tested by
standard cylindrical gauges, while it facilitates the making of the
screw gauges. The male or plug gauge is made with a plain part, A, whose
diameter is the standard size for the bottoms of the threads measured
at a right angle to the axis of the gauge and taking the flats into
account. The female gauge or template is constructed as follows:--A
rectangular piece of steel is pierced with a plain hole at B, and a
standard thread hole at A, and is split through at C. At D is a pin to
prevent the two jaws from springing, this being an important element of
the construction. E is a screw threaded through one jaw and abutting
against the face of the other, while at F is another screw passing
through one jaw and threaded into the other, and it is evident that
while by operating these two screws the size of the gauge bore A may be
adjusted, yet the screws will not move and destroy the adjustment,
because the pressure of one acts as a lock to the other. It is obvious
that in adjusting the female gauge to size, the thread of the male gauge
may be used as a standard to set it by.
To produce sheet metal templates such as was shown in Fig. 279, the
following method may be employed, it being assumed that we have a
threading tool correctly formed.
[Illustration: Fig. 288.]
[Illustration: Fig. 289.]
Suppose it is required to make a gauge for a pitch of 6 per inch, then a
piece of iron of any diameter may be put in the lathe and turned up to
the required diameter for the top of the thread. The end of this piece
should be turned up to the proper diameter for the bottom of the thread,
as at G, in Fig. 287. Now, it will be seen that the angle of the thread
to the axis A of the iron is that of line C to line A, and if we require
to find the angle the thread passes through in once winding around the
bolt, we proceed as in Fig. 288, in which D represents the circumference
of the thread measured at a right angle to the bolt axis, as denoted by
the line B in Fig. 287. F, Fig. 288 (at a right angle to D), is the
pitch of the thread, and line C therefore represents the angle of the
thread to the bolt axis, and corresponds to line C in Fig. 287. We now
take a piece of iron whose length when turned true will equal its
finished and threaded circumference, and after truing it up and leaving
it a little above its required finished diameter, we put a pointed tool
in the slide-rest and mark a line A A in Fig. 289, which will represent
its axis. At one end of this line we mark off below A A the pitch of the
thread, and then draw the line H J, its end H falling below A to an
amount equal to the pitch of the thread to be cut. The piece is then put
in a milling machine and a groove is cut along H J, this groove being to
receive a tightly-fitting piece of sheet metal of which a thread gauge
is to be made. This piece of sheet metal must be firmly secured in the
groove by set-screws. The piece of iron is then again put in the lathe
and its diameter finished to that of the required diameter of thread.
Its two ends are then turned down to the required diameter for the
bottom of the thread, leaving in the middle a section on which a full
thread can be cut, as in Fig. 290, in which F F represents the sheet
metal for the gauge. After the thread is cut, as in Fig. 290, we take
out the gauge and it will appear as in Fig. 291, and all that is
necessary is to file off the two outside teeth if only one tooth is
wanted.
[Illustration: Fig. 290.]
The philosophy of this process is that we have set the gauge at an angle
of 90°, or a right angle to the thread, as is shown in Fig. 289, the
line C representing the angle of the thread to the axis A A, and
therefore corresponding to the line C in Fig. 287. A gauge made in this
way will serve as a test of its own correctness for the following
reasons: Taking the middle tooth in Fig. 291, it is clear that one of
its sides was cut by one angle and the other by the other angle of the
tool that cut it, and as a correctly formed thread is of exactly the
same shape as the space between two threads, it follows that if the
gauge be applied to any part of the thread that was cut in forming it,
and if it fits properly when tried, and then turned end for end and
tried again, it is proof that the gauge and the thread are both correct.
Suppose, for example, that the tool was correct in its shape, but was
not set with its two angles equal to the line of lathe centres, and in
that case the two sides of the thread will not be alike and the gauge
will not reverse end for end and in both cases fit to the thread. Or
suppose the flat on the tool point was too narrow, and the flat at the
bottom of the thread will not be like that at the top, and the gauge
will show it.
[Illustration: Fig. 291.]
Referring to the fifth requirement, that the angles of the sides of the
threads shall be as acute as is consistent with the required strength,
it is obvious that the more acute the angles of the sides of the thread
one to the other the finer the pitch and the weaker the thread, but on
the other hand, the more acute the angle the better the sides of the
thread will conform one to the other. The importance of this arises from
the fact that on account of the alteration of pitch, already explained,
as accompanying the hardening of screw-cutting tools, the sides of
threads cut even by unworn tools rarely have full contact, and a nut
that is a tight fit on its first passage down its bolt may generally be
caused to become quite easy by running it up and down the bolt a few
times. Nuts that require a severe wrench force to wind them on the bolt,
may, even though they be as large as a two-inch bolt, often be made to
pass easily by hand, if while upon the bolt they are hammered on their
sides with a hand hammer. The action is in both cases to cause the sides
of the thread to conform one to the other, which they will the more
readily do in proportion as their sides are more acute. Furthermore, the
more acute the angles the less the importance of gauging the threads to
precise diameter, especially if the tops and bottoms of the male and
female thread are clear of one another, as in Fig. 273.
Referring to the sixth requirement, that the nut shall not be unduly
liable to become loose of itself in cases where it may require to be
fastened and loosened occasionally, it may be observed, that in such
cases the threads are apt from the wear to become a loose fit, and the
nuts, if under jar or vibration, are apt to turn back of themselves upon
the bolt. This is best obviated by insuring a full bearing upon the
whole area of the sides of the thread, and by the employment of as fine
pitches as is consistent with sufficient strength, since the finer the
pitch the nearer the thread stands at right angle to the bolt axis, and
the less the tendency to unscrew from the pressure on the nut face.
The pitches, diameters, and widths of flat of the United States
standard thread are as per the following table:--
UNITED STATES STANDARD SCREW THREADS.
+-------------+-----------+-----------------+----------+
| Diameter of | Threads | Diameter at | Width of |
| Screw. | per inch. | root of Thread. | Flat. |
+-------------+-----------+-----------------+----------+
| 1/4 | 20 | .1850 | .0063 |
| 5/16 | 18 | .2403 | .0069 |
| 3/8 | 16 | .2938 | .0078 |
| 7/16 | 14 | .3447 | .0089 |
| 1/2 | 13 | .4001 | .0096 |
| 9/16 | 12 | .4542 | .0104 |
| 5/8 | 11 | .5069 | .0114 |
| 3/4 | 10 | .6201 | .0125 |
| 7/8 | 9 | .7307 | .0139 |
| | | | |
| 1 | 8 | .8376 | .0156 |
| 1-1/8 | 7 | .9394 | .0179 |
| 1-1/4 | 7 | 1.0644 | .0179 |
| 1-3/8 | 6 | 1.1585 | .0208 |
| 1-1/2 | 6 | 1.2835 | .0208 |
| 1-5/8 | 5-1/2 | 1.3888 | .0227 |
| 1-3/4 | 5 | 1.4902 | .0250 |
| 1-7/8 | 5 | 1.6152 | .0250 |
| 2 | 4-1/2 | 1.7113 | .0278 |
+-------------+-----------+-----------------+----------+
The standard pitches for the sharp [V]-thread are as follows:--
SIZE OF BOLT.
---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---
1/4| 5/|3/8| 7/|1/2|5/8|3/4|7/8| 1 | 1-| 1-| 1-| 1-| 1-| 1-| 1-| 2
| 16| | 16| | | | | |1/8|1/4|3/8|1/2|5/8|3/4|7/8|
---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---
NUMBER OF THREADS TO INCH.
---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---
20| 18| 16| 14| 12| 11| 10| 9 | 8 | 7 | 7 | 6 | 6 | 5 | 5 | 4-| 4-
| | | | | | | | | | | | | | |1/2|1/2
---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---
The following table gives the threads per inch, pitches and diameters at
root of thread of the Whitworth thread. The table being arranged from
the diameter of the screw as a basis.
+----------+---------+--------+----------------+
| Diameter | Threads | | Diameter at |
| of | per | Pitch. | Root or Bottom |
| Screw. | Inch. | | of Thread. |
+----------+---------+--------+----------------+
| | | Inch. | Inch. |
| 1/8 | 40 | .025 | .0929 |
| 3/16 | 24 | .041 | .1341 |
| 1/4 | 20 | .050 | .1859 |
| 5/16 | 18 | .056 | .2413 |
| 3/8 | 16 | .063 | .2949 |
| 7/16 | 14 | .071 | .346 |
| 1/2 | 12 | .083 | .3932 |
| 9/16 | 12 | .083 | .4557 |
| 5/8 | 11 | .091 | .5085 |
| 11/16 | 11 | .095 | .571 |
| 3/4 | 10 | .100 | .6219 |
| 13/16 | 10 | .100 | .6844 |
| 7/8 | 9 | .111 | .7327 |
| 15/16 | 9 | .111 | .7952 |
| 1 | 8 | .125 | .8399 |
| 1-1/8 | 7 | .143 | .942 |
| 1-1/4 | 7 | .143 | 1.067 |
| 1-3/8 | 6 | .167 | 1.1615 |
| 1-1/2 | 6 | .167 | 1.2865 |
| 1-5/8 | 5 | .200 | 1.3688 |
| 1-3/4 | 5 | .200 | 1.4938 |
| 1-7/8 | 4-1/2 | .222 | 1.5904 |
| 2 | 4-1/2 | .222 | 1.7154 |
| 2-1/8 | 4-1/2 | .222 | 1.8404 |
| 2-1/4 | 4 | .250 | 1.9298 |
| 2-3/8 | 4 | .250 | 2.0548 |
| 2-1/2 | 4 | .250 | 2.1798 |
| 2-5/8 | 4 | .250 | 2.3048 |
| 2-3/4 | 3-1/2 | .286 | 2.384 |
| 2-7/8 | 3-1/2 | .286 | 2.509 |
| 3 | 3-1/2 | .286 | 2.634 |
| 3-1/4 | 3-1/4 | .308 | 2.884 |
| 3-1/2 | 3-1/4 | .308 | 3.106 |
| 3-3/4 | 3 | .333 | 3.356 |
| 4 | 3 | .333 | 3.574 |
| 4-1/4 | 2-7/8 | .348 | 3.824 |
| 4-1/2 | 2-7/8 | .348 | 4.055 |
| 4-3/4 | 2-3/4 | .364 | 4.305 |
| 5 | 2-3/4 | .364 | 4.534 |
| 5-1/4 | 2-5/8 | .381 | 4.764 |
| 5-1/2 | 2-5/8 | .381 | 5.014 |
| 5-3/4 | 2-1/2 | .400 | 5.238 |
| 6 | 2-1/2 | .400 | 5.488 |
+----------+---------+--------+----------------+
The standard degree of taper, both for the taps and the dies, is 1/16
inch per inch, or 3/4 inch per foot, for all sizes up to 10-inch bore.
The sockets or couplings, however, are ordinarily tapped parallel and
stretched to fit the pipe taper when forced on the pipe. For bores of
pipe over 10 inches diameter the taper is reduced to 3/8 inch per foot.
The pipes or casings for oil wells are given a taper of 3/8 inch per
foot, and their couplings are tapped taper from both ends. There is,
however, just enough difference made between the taper of the socket and
that of the pipe to give the pipe threads a bearing at the pipe end
first when tried with red marking, the threads increasing their bearing
as the pieces are screwed together.
The United States standard thread for steam, gas and water pipe is given
below, which is taken from the Report of the Committee on Standard Pipe
and Pipe Threads of The American Society of Mechanical Engineers,
submitted at the 8th Annual Meeting held in New York, November-December,
1886.
"A longitudinal section of the tapering tube end, with the screw-thread
as actually formed, is shown full size in Fig. 291_a_ for a nominal
2-1/2 inch tube, that is, a tube of about 2-1/2 inches internal
diameter, and 2-7/8 inches actual external diameter.
[Illustration: Fig. 291_a_.]
"The thread employed has an angle of 60°; it is slightly rounded off
both at the top and at the bottom, so that the height or depth of the
thread, instead of being exactly equal to the pitch, is only four fifths
of the pitch, or equal to 0.8 × 1/_n_ if _n_ be the number of threads
per inch. For the length of tube end throughout which the screw thread
continues perfect, the empirical formula used is (0.8_D_ + 4.8) × 1/_n_,
where _D_ is the actual external diameter of the tube throughout its
parallel length, and is expressed in inches. Further back, beyond the
perfect threads, come two having the same taper at the bottom, but
imperfect at the top. The remaining imperfect portion of the screw
thread, furthest back from the extremity of the tube, is not essential
in any way to this system of joint; and its imperfection is simply
incidental to the process of cutting the thread at a single operation.
The standard thicknesses of the pipes and pitches of thread are as
follows:--
STANDARD DIMENSIONS OF WROUGHT IRON WELDED TUBES.
+-----------------------------+-----------+--------------------+
| DIAMETER OF TUBE. | | SCREWED ENDS. |
+---------+---------+---------+ THICKNESS +----------+---------+
| Nominal | Actual | Actual | OF | Number |Length of|
| Inside. | Inside. | Outside.| METAL. |of Threads| Perfect |
| | | | |per Inch. | Screw. |
+---------+---------+---------+-----------+----------+---------+
| Inches. | Inches. | Inches. | Inch. | No. | Inch. |
| 1/8 | 0.270 | 0.405 | 0.068 | 27 | 0.19 |
| 1/4 | 0.364 | 0.540 | 0.088 | 18 | 0.29 |
| 3/8 | 0.494 | 0.675 | 0.091 | 18 | 0.30 |
| 1/2 | 0.623 | 0.840 | 0.109 | 14 | 0.39 |
| 3/4 | 0.824 | 1.050 | 0.113 | 14 | 0.40 |
| 1 | 1.048 | 1.315 | 0.134 | 11-1/2 | 0.51 |
| 1-1/4 | 1.380 | 1.660 | 0.140 | 11-1/2 | 0.54 |
| 1-1/2 | 1.610 | 1.900 | 0.145 | 11-1/2 | 0.55 |
| 2 | 2.067 | 2.375 | 0.154 | 11-1/2 | 0.58 |
| 2-1/2 | 2.468 | 2.875 | 0.204 | 8 | 0.89 |
| 3 | 3.067 | 3.500 | 0.217 | 8 | 0.95 |
| 3-1/2 | 3.548 | 4.000 | 0.226 | 8 | 1.00 |
| 4 | 4.026 | 4.500 | 0.237 | 8 | 1.05 |
| 4-1/2 | 4.508 | 5.000 | 0.246 | 8 | 1.10 |
| 5 | 5.045 | 5.563 | 0.259 | 8 | 1.16 |
| 6 | 6.065 | 6.625 | 0.280 | 8 | 1.26 |
| 7 | 7.023 | 7.625 | 0.301 | 8 | 1.36 |
| 8 | 8.982 | 8.625 | 0.322 | 8 | 1.46 |
| 9 | 9.000 | 9.688 | 0.344 | 8 | 1.57 |
| 10 | 10.019 | 10.750 | 0.366 | 8 | 1.68 |
+---------+---------+---------+-----------+----------+---------+
The taper of the threads is 1/16 inch in diameter for each inch of
length or 3/4 inch per foot.
WHITWORTH'S SCREW THREADS FOR GAS, WATER, AND HYDRAULIC IRON PIPING.
NOTE.--The Internal and External diameters of Pipes, as given below, are
those adopted by the firm of Messrs. JAMES RUSSELL & SONS, in Pipes of
their manufacture.
+---------------------------------------+
| GAS AND WATER PIPING. |
+-------------+-------------+-----------+
| Internal | External | No. of |
| Diameter of | Diameter of | Threads |
| Pipe. | Pipe. | per Inch. |
+-------------+-------------+-----------+
| 1/8 | .385 | 28 |
| 1/4 | .520 | 19 |
| 3/8 | .665 | 19 |
| 1/2 | .822 | 14 |
| 3/4 | 1.034 | 14 |
| 1 | 1.302 } | |
| 1-1/8 | 1.492 } | |
| 1-1/4 | 1.650 } | |
| 1-3/8 | 1.745 } | |
| 1-1/2 | 1.882 } | |
| 1-5/8 | 2.021 } | |
| 1-3/4 | 2.047 } | |
| 1-7/8 | 2.245 } | |
| 2 | 2.347 } | |
| 2-1/8 | 2.467 } | |
| 2-1/4 | 2.587 } | 11 |
| 2-3/8 | 2.794 } | |
| 2-1/2 | 3.001 } | |
| 2-5/8 | 3.124 } | |
| 2-3/4 | 3.247 } | |
| 2-7/8 | 3.367 } | |
| 3 | 3.485 } | |
| 3-1/4 | 3.698 } | |
| 3-1/2 | 3.912 } | |
| 3-3/4 | 4.125 } | |
| 4 | 4.339 } | |
+-------------+-------------+-----------+
+----------------------------------------------------+
| HYDRAULIC PIPING. |
+----------+----------+------------------+-----------+
| Internal | External | Pressure in lbs. | No. of |
| Diameter | Diameter | per Square | Threads |
| of Pipe. | of Pipe. | Inch. | per Inch. |
+----------+----------+------------------+-----------+
| | { 5/8 | 4,000} | |
| 1/4 | { 3/4 | 6,000} | 14 |
| | { 7/8 | 8,000} | |
| | {1 | 10,000} | |
| | | | |
| | { 3/4 | 4,000} | |
| 3/8 | { 7/8 | 6,000} | 14 |
| | {1 | 8,000} | |
| | {1-1/8 | 10,000} | |
| | | | |
| | {1 | 4,000} | 14 |
| 1/2 | {1-1/8 | 6,000} | |
| | {1-1/4 | 8,000 } | 11 |
| | {1-3/8 | 10,000 } | |
| | | | |
| | {1-1/8 | 4,000 | 14 |
| 5/8 | {1-1/4 | 6,000} | |
| | {1-3/8 | 8,000} | 11 |
| | {1-1/2 | 10,000} | |
| | | | |
| | {1-1/4 | 4,000} | |
| 3/4 | {1-3/8 | 6,000} | 11 |
| | {1-1/2 | 8,000} | |
| | {1-5/8 | 10,000} | |
| | | | |
| | {1-3/8 | 4,000} | |
| 7/8 | {1-1/2 | 6,000} | 11 |
| | {1-5/8 | 8,000} | |
| | {1-3/4 | 10,000} | |
| | | | |
| | {1-1/2 | 4,000} | |
| 1 | {1-5/8 | 6,000} | 11 |
| | {1-3/4 | 8,000} | |
| | {1-7/8 | 10,000} | |
| | | | |
| | {1-5/8 | 4,000} | |
| 1-1/8 | {1-3/4 | 6,000} | 11 |
| | {1-7/8 | 8,000} | |
| | {2 | 10,000} | |
| | | | |
| | {1-3/4 | 4,000} | |
| 1-1/4 | {1-7/8 | 6,000} | 11 |
| | {2 | 8,000} | |
| | {2-1/8 | 10,000} | |
| | | | |
| | {1-7/8 | 4,000} | |
| 1-3/8 | {2 | 6,000} | 11 |
| | {2-1/8 | 8,000} | |
| | {2-1/4 | 10,000} | |
| | | | |
| | {2 | 4,000} | |
| | {2-1/8 | 6,000} | |
| 1-1/2 | {2-1/4 | 8,000} | 11 |
| | {2-3/8 | 10,000} | |
| | {2-1/2 | 10,000} | |
| | | | |
| | {2-1/8 | 4,000} | |
| 1-5/8 | {2-1/4 | 6,000} | 11 |
| | {2-3/8 | 8,000} | |
| | {2-1/2 | 10,000} | |
| | | | |
| | {2-1/4 | 3,000} | |
| | {2-3/8 | 4,000} | |
| 1-3/4 | {2-1/2 | 6,000} | 11 |
| | {2-5/8 | 8,000} | |
| | {2-3/4 | 10,000} | |
| | | | |
| | {2-3/8 | 3,000} | |
| | {2-1/2 | 4,000} | |
| 1-7/8 | {2-5/8 | 6,000} | 11 |
| | {2-3/4 | 8,000} | |
| | {2-7/8 | 10,000} | |
| | | | |
| | {2-1/2 | 3,000} | |
| | {2-5/8 | 4,000} | |
| 2 | {2-3/4 | 6,000} | 11 |
| | {2-7/8 | 8,000} | |
| | {3 | 10,000} | |
+----------+----------+------------------+-----------+
The English pipe thread is a sharp [V]-thread having its sides at an
angle of 60°, and therefore corresponds to the American pipe thread
except that the pitches are different.
The standard screw thread of The Royal Microscopical Society of London,
England, is employed for microscope objectives, and the nose pieces of
the microscope into which these objectives screw.
The thread is a Whitworth one, the original standard threading tools now
in the cabinet of the society having been made especially for the
society by Sir Joseph Whitworth. The pitch of the thread is 36 per inch.
The cylinder, or male gauge, is .7626 inch in diameter.
The following table gives the Whitworth standard of thread pitches and
diameters for watch and mathematical instrument makers.
WHITWORTH'S STANDARD GAUGES FOR WATCH AND INSTRUMENT MAKERS, WITH SCREW
THREADS FOR THE VARIOUS SIZES, 1881.
+---------------------+-------------+-------------+
| No. of each | Size in | Number of |
| size in thousandths | decimals of | Threads per |
| of an inch. | an inch. | inch. |
+---------------------+-------------+-------------+
| 10 | .010 | 400 |
| 11 | .011 | " |
| 12 | .012 | 350 |
| 13 | .013 | " |
| 14 | .014 | 300 |
| 15 | .015 | " |
| 16 | .016 | " |
| 17 | .017 | 250 |
| 18 | .018 | " |
| 19 | .019 | " |
| 20 | .020 | 210 |
| 22 | .022 | " |
| 24 | .024 | " |
| 26 | .026 | 180 |
| 28 | .028 | " |
| 30 | .030 | " |
| 32 | .032 | 150 |
| 34 | .034 | " |
| 36 | .036 | " |
| 38 | .038 | 120 |
| 40 | .040 | " |
| 45 | .045 | " |
| 50 | .050 | 100 |
| 55 | .055 | " |
| 60 | .060 | " |
| 65 | .065 | 80 |
| 70 | .070 | " |
| 75 | .075 | " |
| 80 | .080 | 60 |
| 85 | .085 | " |
| 90 | .090 | " |
| 95 | .095 | " |
| 100 | .100 | 50 |
+---------------------+-------------+-------------+
For the pitches of the threads of lag screws there is no standard, but
the following pitches are largely used.
+-----------+-----------+
|Diameter of| Threads |
| Screw. | per Inch. |
+-----------+-----------+
| Inch. | |
| 1/4 | 10 |
| 5/16 | 9 |
| 3/8 | 8 |
| 7/16 | 7 |
| 1/2 | 6 |
| 9/16 | 6 |
| 5/8 | 5 |
| 11/16 | 5 |
| 3/4 | 5 |
| 7/8 | 4 |
| 1 | 4 |
+-----------+-----------+
SCREW-CUTTING HAND TOOLS.
For cutting external or male threads by hand three classes of tools are
employed.
The first is the screw plate shown in Fig. 292. It consists of a
hardened steel plate containing holes of varying diameters and threaded
with screw threads of different pitches. These holes are provided with
two diametrically opposite notches or slots so as to form cutting edges.
[Illustration: Fig. 292.]
This tool is placed upon the end of the work and slowly rotated while
under a hand pressure tending to force it upon the work, the teeth
cutting grooves to form the thread and advancing along the bolt at a
rate determined by the pitch of the thread.
The screw plate is suitable for the softer metals and upon diameters of
1/8 inch and less, in which the cutting duty is light; hence the holes
do not so rapidly wear larger.
The second class consists of a stock and dies such as shown in Fig. 293.
For each stock there are provided a set of dies having different
diameters and pitches of thread.
In this class of tool the dies are opened out and placed upon the bolt.
The set screw is tightened up, forcing the dies to their cut, and the
stock is slowly rotated and a traverse taken down the work.
[Illustration: Fig. 293.]
In some cases the dies are then again forced to the work by the set
screw, and a cut taken by winding the stocks up the bolt, the operation
being continued until the thread is fully developed and cut to the
required diameter. In other cases the cut is carried down the bolt, only
the dies being wound back to the top of the bolt after each cut is
carried down. The difference between these two operations will be shown
presently.
[Illustration: Fig. 294.]
The thread in dies which take successive cuts to form a thread may be
left full clear through the die, and will thus cut a full thread close
up to the head collar or shoulder of the work. It is usual, however, to
chamfer off the half threads at the ends of the dies, because if left of
their full _height_ they are apt to break off when in use. It is
sometimes the practice, however, to chamfer off the first two threads on
one side of the dies, leaving the teeth on the other side full, and to
use the chamfered as the leading side in all cases in which the thread
on the work does not require to be cut up to a shoulder, but turning the
dies over with the full threaded teeth as the leading ones when the
thread _does_ require to be carried up to a head or shoulder on the
work.
To facilitate the insertion and extraction of the dies in and from their
places in the stock, the Morse Twist Drill Co. employ the following
construction. In Figs. 294 and 295 the pieces A, A´ which hold the dies
are pivoted in the stock at B, so as to swing outward as in Fig. 295,
and receive the dies which are slotted to fit them. These pieces are
then swung into position in the stock. The lower die is provided with a
hole to fit the pin C, hence when that die is placed home C acts as a
detaining piece locking the pieces A, A´ through the medium of the
bottom die.
[Illustration: Fig. 295.]
[Illustration: Fig. 296.]
In other dies of this class the two side pieces or levers which hold the
dies are pivoted at the corner of the angle, as in Fig. 296. In the
bottom of the stock is a sliding piece beveled at its top and meeting
the bottom face of the levers; hence, by pressing this piece inwards the
side pieces recede into a slot provided in the stock, and leave the
opening free for the dies to pass into their places, when the pin is
released and a spring brings the side pieces back. Now, since the bottom
die rests upon the bottom angle of the side pieces the pressure of the
set screw closes the side pieces to the dies holding them firmly.
[Illustration: Fig. 297.]
In Fig. 297 is shown Whitworth's stocks and dies, the cap that holds the
guide die _a_ and the two chasers _b_, _c_ in their seats or recesses in
the stock being removed to expose the interior parts. The ends of the
chasers _b_, _c_ are beveled and abut against correspondingly beveled
recesses in the key _d_, so that by operating the nut _e_ on the end of
the key the dies are caused to move longitudinally. The principles of
action are more clearly shown in Fig. 298. The two cutting chasers B and
C move in lines that would meet at D, and therefore at a point behind
the centre or axis of the bolt being threaded; this has the effect of
preserving their clearance. It is obvious, for example, that when these
chasers cut a thread on the work it will move over toward guide A on
account of the thread on the work sinking into the threads on A, and
this motion would prevent the chasers B, C from cutting if they moved in
a line pointing to the centre of the work. This is more clearly shown in
Fig. 299, in which the guide die A and one of the cutting dies or
chasers B is shown removed from the stock, while the bolt to be threaded
is shown in two positions--one when the first cut is taken, and the
other when the thread is finished. For the first cut the centre of the
work is at E, for the last one it is at G, and this movement would, were
the line of motion as denoted by the dotted lines, prevent the chaser
from cutting, because, while the line of chaser motion would remain at
J, pointing to the centre of work for the first cut, it would require a
line at K to point to that centre for the last one; hence, when
considered with relation to the work, the line of chaser motion has been
moved forward, presenting the cutting edges at an angle that would
prevent their cutting. By having their motion as shown in Fig. 299,
however, the clearance of the chasers is preserved.
[Illustration: Fig. 298.]
[Illustration: Fig. 299.]
[Illustration: Fig. 300.]
Referring now to the die A, it acts as a guide rather than as a cutting
chaser, because it has virtually no clearance and cannot cut so freely
as B and C; hence it offers a resistance to the moving of the bolt, or
of the dies upon the bolt, in a lateral direction when the chaser teeth
meet either a projection or a depression upon the work. The guide
principle is, however, much more fully carried out in a design by
Bodmer, which is shown in Fig. 300. Here there is but one cutting chaser
C, the bush G being a guide let into a recess in the stock and secured
thereon by a pin _p_. The chaser is set in a stock, D also let into a
recess in the stock, and this recess, being circular, permits of stock D
swinging. At S are two set-screws, which are employed to limit the
amount of motion permitted to D. the handle E screws through D, and acts
upon the edge of chaser C to put on the cut. The action of the tool is
shown in Fig. 301, where it is shown upon a piece of work. Pulling the
handle E causes D to swing in the stock, thus giving the chaser
clearance, as shown. When the cut is carried down, a new cut may be put
on by means of E, and on winding the stock in the opposite direction, D
will swing in its seat, and cant or tilt the chaser in the opposite
direction, giving it the necessary clearance to enable it to cut on the
upward or back traverse. Another point of advantage is that the cutting
edges are not rubbed by the work during the back stroke, and their
sharpness is, therefore, greatly preserved. A die of this kind will
produce work almost as true as the lathe, and, in the case of long,
slender work, more true than the lathe; but it is obvious that, on
account of the friction caused by the pressure of the work to the guide
G, the tool will require more power to operate than the ordinary stock
and die or the solid die.
[Illustration: Fig. 301.]
In adjustable dies which require to take more than one cut along the
bolt to produce a fully developed thread, there is always a certain
amount of friction between the sides of the thread in the die and the
grooves being cut, because the angle of the thread at the top of a
thread is less than the angle at the bottom. Thus in Fig. 302 the pitch
at the top of thread (at A, B) is the same as at the bottom (C, D). Now
suppose that in Fig. 303 _a_ _b_ represents the axial line of a bolt,
and _c_ _d_ a line at a right angle to _a_ _b_. The radius _e_ _f_ being
equal to the circumference of the top of the thread, the pitch being
represented by _b_; then _k_ represents the angle of the top of the
thread to the axial line _a_ _b_. Now suppose that the radius _e_ _g_
represents the circumference at the bottom of the thread and to the
pitch; then _l_ is the angle of the bottom of the thread to the axial
line of the work, and the difference in angle between _k_ and _l_ is the
difference in angle between the top and bottom of the thread in the dies
and the thread to be cut on the work.
[Illustration: Fig. 302.]
Now the tops of the teeth on the die stand at the greatest angle _l_, in
Fig. 303, when taking the first cut on the bolt, but the grooves they
cut will be on the full diameter of the bolt, and will, therefore, stand
at the angle _k_, hence the lengths of the teeth do not lie in the same
planes as the grooves which they cut.
[Illustration: Fig. 303.]
In cutting [V]-threads, however, the angle of the die threads gradually
right themselves with the plane of the grooves attaining their nearest
coincidence when closed to finish the thread.
Since, however, the full width of groove is in a square thread cut at
the first cut taken by the dies, it is obvious that a square thread
cannot be cut by this class of die, because the sides of the grooves
would be cut away each time the dies were closed to take another cut.
[Illustration: Fig. 304.]
[Illustration: Fig. 305.]
Dies of this class require to have the threaded hole made of a larger
diameter than is the diameter of the bolt they are intended to thread,
the reason being as follows:--
Suppose the threaded hole in the dies to be cut by a hob or master tap
of the same diameter as the thread to be cut by the dies; when the dies
are opened out and placed upon the work as in Fig. 304, the edges A, B
will meet the work, and there will be nothing to steady the dies, which
will, therefore, wobble and start a drunken thread, that is to say, a
thread such as was shown in Fig. 253.
[Illustration: Fig. 306.]
Instances have been known in the use of dies made in this manner,
wherein the workman using a right-hand single-threaded pair of dies has
cut a right or left-hand double or treble thread; the teeth of the dies
acting as chasers well canted over, as shown in Fig. 305. It is
necessary to this operation, however, that the diameter of the work be
larger than the size of hob the dies were threaded with.
In Fig. 306 is shown a single right-hand and a treble left-hand thread
cut by the author with the same pair of dies.
All that is necessary to perform this operation is to rotate the dies
from left to right to produce a right-hand thread, and from right to
left for a left-hand thread, exerting a pressure to cause the dies to
advance more rapidly along the bolt than is due to the pitch of the
thread. A double thread is produced when the dies traverse along the
work twice as fast as is due to the pitch of the thread in the dies, and
so on.
[Illustration: Fig. 307.]
It is obvious, also, that a piece of a cylindrical thread may be used to
cut a left-hand external thread. Thus in Fig. 307 is shown a square
piece of metal having a notch cut in on one side of it and a piece of an
external thread (as a tap inserted) in the notch. By forcing a piece of
cylindrical work through the hole while rotating it, the piece of tap
would cut upon the work a thread of the pitch of the tap, but a
left-handed thread, which occurs because, as shown by the dotted lines
of the figure, the thread on one side of a bolt slopes in opposite
directions to its direction on the other, and in the above operation the
thread on one side is taken to cut the thread on the other.
These methods of cutting left-hand threads with right-handed ones are
mentioned simply as curiosities of thread cutting, and not as being of
any practical value.
To proceed, then: to avoid these difficulties it is usual to thread the
dies with a hob or master tap of a diameter equal to twice the depth of
the thread, larger than the size of bolt the dies are to thread. In this
case the dies fit to the bolt at the first cut, as shown in Fig. 308, C,
D being the cutting edges. The relation of the circle of the thread in
the dies to that of the work during the final cut is shown in Fig. 309.
[Illustration: Fig. 308.]
[Illustration: Fig. 309.]
There is yet another objection to tapping the dies with a hob of the
diameter of the bolt to be threaded, in that the teeth fit perfectly to
the thread of the bolt when the latter is threaded to the proper
diameter, producing a great deal of friction, and being difficult to
make cut, especially when the cutting edges have become slightly dulled
from use.
Referring now to taking a cut up the bolt or work as well as down, it
will be noted that supposing the dies to have a right-hand thread, and
to be rotating from left to right, they will be passing down the bolt
and the edges C, D (Fig. 308) will be the cutting ones. But when the
dies are rotated from right to left to bring them to the end of the bolt
again, C, D will be rubbed by the thread, which tends to abrade them and
thus destroy their sharpness.
[Illustration: Fig. 310.]
In some cases two or more pairs of dies are fitted to the same stock, as
shown in Fig. 310, but this is objectionable, because it is always
desirable to have the hole in the dies central to the length of the
stock, so that when placed to the work the stock shall be balanced,
which will render it easier to start the thread true with the axial line
of the bolt.
[Illustration: Fig. 311.]
From what has been said with reference to Fig. 303, it is obvious that a
square thread cannot be cut by a die that opens and closes to take
successive cuts along the work, but such threads may be cut upon work
that is of sufficient strength to withstand the twisting pressure of the
dies, by making a solid die, and tapering off the threads for some
distance at the mouth of the die, so as to enable the die to take its
bite or grip upon the work, and start itself. It is necessary, however,
to give to the die as many flutes (and therefore cutting edges), as
possible, or else to make flutes wide and the teeth as short as will
leave them sufficiently strong, both these means serving to avoid
friction.
[Illustration: Fig. 312.]
The teeth for adjustable dies, such as shown in Fig. 293, are cut as
follows:--There is inserted between the two dies a piece of metal,
separating them when set together to a distance equal to twice the depth
of the thread, added to the distance the faces of the dies are to be
apart when the dies are set to cut to this designated or proper
diameter. The tapping hole is then drilled (with the pieces in place) to
the diameter of the bolt the die is for. The form of hob used by the
Morse Twist Drill & Machine Company, to cut the thread, is shown in Fig.
311. The unthreaded part at the entering end is made to a diameter equal
to that of the work the dies are to be used in; the thread at the
entering end is made sunk in one half the height of the full thread, and
is flattened off one half the height of a full thread, so that the top
of the thread is even with the diameter of the unthreaded part at the
entering end. The thread then runs a straight taper up the hob until a
distance equal to the diameter of the nut is reached, and the length of
hob equal to its diameter is made a full and parallel thread for
finishing the die teeth with. The thread on the taper part has more
taper at the root of the thread than it has at the top of the same, and
the diameter of the full and parallel part at the shank end of the
thread is made of a diameter equal to twice the height or depth of a
full thread, larger than the diameter at the entering end of the hob.
The hob thus becomes a taper and relieved tap cutting a full thread at
one passage through the dies. If the hob is made parallel and a full
thread from end to end, as in Fig. 312, the dies must traverse up and
down the hob, or the hob through the dies to form a full thread.
The third class of stock and die is intended to cut a full thread at one
passage along the work, while at the same time provision is made,
whereby, to take up the wear due to the abrasion of the cutting edges,
which wear would cause the diameter of thread cut to be above the
standard.
In Fig. 313 is shown the Grant adjustable die made by the Pratt &
Whitney Company. It consists of four chasers or toothed cutting tools,
inserted in radial recesses or slots in an iron disc or collet encircled
by an iron ring. Each chaser is beveled at its end to fit a
corresponding bevel in the ring, and is grooved on one of its side faces
to receive the hardened point of a screw that is inserted in the collet
to hold the chaser in its adjusted position. Four screws extend up
through the central flange or body of the collet, two of which serve to
draw down the ring, and by reason of the taper on the ring move the
chasers equally towards the centre and reduce the cutting diameter of
the die, while the other two hold the ring in the desired position, or
force it upward to enlarge the cutting diameter of the die. The range of
adjustment permitted by this arrangement is 1-32 inch. The dies may be
taken out and ground up to sharpen.
[Illustration: Fig. 313.]
The object of cutting grooves in the sides of the chasers is that the
fine burrs formed by the ends of the set screws do not prevent the
chasers from moving easily in the collet during the process of
adjustment; the groove also acts as a shoulder for the screw end to
press the chaser down to its seat. These chasers are marked to their
respective places in the collet, and are so made that if one chaser
should break, a new one can be supplied to fit to its place, the teeth
of the new one falling exactly in line with the teeth on the other
three, whereas under ordinary conditions if one chaser breaks, a full
set of four new ones must be obtained.
In this die, as in all others which cut a full thread at one passage
along the work, the front teeth of the chasers are beveled off as shown
in the cut; this is necessary to enable the dies to take hold of or
"bite" the work, the chamfer giving a relief to the cutting edge, while
at the same time forming to a certain extent a wedge facilitating the
entrance of the work into the die.
Fig. 314 represents J. J. Grant's patent die, termed by its makers
(Wiley and Russel) the "lightening die." In this, as in other similar
stocks, several collets with dies of various pitches and diameters of
thread, fit to one stock. The nut of the stock is split on one side, and
is provided with lugs on that side to receive a screw, which operates to
open and enlarge the bore to release a collet, or close thereon and
grip it, as may be required when inserting or extracting the same. The
dies are formed as shown in Fig. 315, in which A, A are the dies, and B
the collet. To open the dies within the collet, the screws E are
loosened and the screws D are tightened, while to close the dies D, D
are loosened and E are tightened; thus the adjustment to size is
effected by these four screws, while the screws D also serve to hold the
dies to the collet B. The collets are provided with a collar having a
bore F, through which the work passes, so that the dies may be guided
true when starting upon the work; but if it is required to cut a thread
close up to a head or shoulder, the stock is turned upside down, not
only to have the collet out of the way of the head or shoulder, but also
because the thread of the dies on the collet side are chamfered off (as
is necessary in all solid dies, or dies which cut a full thread at one
traverse down the work) so as to enable them to grip or bite the work,
and start the thread upon it as before stated.
[Illustration: Fig. 314.]
[Illustration: Fig. 315.]
In Fig. 316 is shown Stetson's die, which cuts a full thread at one
passage, is adjustable to take up its wear, and has a guide to steady it
upon the work and assist it in cutting a true thread. The guide piece
consists of a hub (through which the work passes) having a flange
fitting into the dies and being secured thereto by the two screws shown.
The holes in the flanges are slotted to permit of the dies being closed
(to take up wear) by means of the small screws shown at the end of the
die, which screws pass through one die in a plain hole and screw into
the other.
[Illustration: Fig. 316.]
In Fig. 317 is shown Everett's stocks and dies. In this tool the dies
are set up by a cam lever, the dies being set to standard size when the
lever arm stands parallel with the arm of the stock. By turning the
straight side of the cam lever opposite to the dies, the latter may be
instantly removed and another size of die inserted. The dies may be used
to cut on their passage up and down the bolt or by operating the cam.
When the dies are at the end of a cut the dies may be opened, lifted to
the top of the work and another cut taken, thus saving the time
necessary to wind the stock back. When the final cut is taken the dies
may be opened and lifted off the work.
[Illustration: Fig. 317.]
The hardening process usually increases the thickness of these dies,
making the pitch of the thread coarser. The amount of expansion due to
hardening is variable, but increases with the thickness of the die. The
hob as a rule shortens during the tempering, but the amount being
variable, no rule for its quantity can be given.[12]
[12] See also page 108.
Stocks and dies for pipe work are made in the form shown in Fig. 318, in
which B is the stock having the detachable handles (for ease of
conveyance) A, H, the latter being shown detached. The solid
screw-cutting dies C are placed in the square recess at B, and are
secured in B by the cap D, which swings over (upon its pivoted end as a
centre) and is locked by the thumbscrew E. To guide the stocks and cause
them to cut a true thread, the bushes F are provided. These fit into the
lower end of B and are locked in position by four set screws G. The
bores of the bushes F are made an easy fit to the outside of the pipe to
be threaded, there being a separate bush for each size of pipe.
[Illustration: Fig. 318.]
The dies employed in stocks for threading steam and gas pipes by hand
are sometimes solid, as in Fig. 318 at C, and at others adjustable. In
Fig. 319 is shown Stetson's adjustable pipe die containing four chasers
or toothed thread-cutting tools. These are set to cut the required
diameter by means of a small screw in each corner of the die, while they
are locked in their adjusted position by four screws on the face.
The tap is a tool employed to cut screw threads in internal surfaces, as
holes or bores. A set of taps for hand use usually consist of three: the
taper tap, Fig. 320; plug tap, Fig. 321; and bottoming tap, Fig. 322.
(In England these taps are termed respectively the taper, second, and
plug tap.) The taper tap is the first to be inserted, and (when the
hole to be threaded passes entirely through the work) rotated until it
passes through the work, thus cutting a thread parallel in diameter
through the full length of the hole. If, however, the hole does not pass
through the work, the taper tap leaves a taper-threaded hole containing
more or less of a fully developed thread according to the distance the
tap has entered.
[Illustration: Fig. 319.]
[Illustration: Fig. 320.]
[Illustration: Fig. 321.]
[Illustration: Fig. 322.]
To further complete the thread the plug tap is inserted, it being
parallel from four or five threads from the entering end of the tap to
the other end. If the work will admit it, this tap is also passed
through, which not only saves time in many cases, by avoiding the
necessity to wind the tap back, but preserves the cutting edge which
suffers abrasion from being wound back. To cut a full thread as near as
possible to the bottom of a hole the bottoming tap is used, but when the
circumstances will admit, it is best to drill the hole rather deeper
than is actually necessary, to avoid the trouble incident to tapping a
hole clear to the bottom.
On wrought iron and steel, which are fibrous and tough, the tap, when
used by hand, will not (if the hole be deeper than the diameter of the
tap) readily operate by a continuous rotary motion, but requires to be
rotated about half a revolution back occasionally, which gives
opportunity for the oil to penetrate to the cutting edges of the tap,
frees the tap and considerably facilitates the tapping operation,
especially if the hole be a deep one.
[Illustration: Fig. 323.]
When the tap is intended to pass entirely through the work with a
continuous rotary motion, as is the case, for example, in tapping nuts
in a tapping machine, it is made of similar form to the taper hand tap,
but longer, as shown in Fig. 323, the thread being full and parallel at
the shank end for a distance at least equal to the full diameter of the
tap measured across the tops of the thread.
If the thread of a tap be in diametral section a full circle, the sides
of the thread rub against the grooves cut by the teeth, producing a
friction which augments as the sharp edge of the teeth become dulled
from use, but the tap cuts a thread of great diametral accuracy.
To reduce this friction to a minimum as much as is consistent with
maintaining the standard size of the tapped hole, taps are sometimes
given clearance in the thread, that is to say, the back of each tooth
recedes from a true circle, as shown in Fig. 324, in which A A
represents a washer, and B A tap in the same, the back of the teeth
receding at C, D, E, from the true circle of the bore of A A, the tap
cutting when revolved in the direction of the arrow. The objection to
this is that when the tap is revolved backwards, as it must be to
extract it unless the hole passes clear through the work, the cuttings
lodge between the teeth and the thread in the work, rendering the
extraction of the tap difficult, unless, indeed, the clearance be small
enough in amount to clear the sides of the thread in the work
sufficiently to avoid friction without leaving room for the cuttings to
enter. If an excess of clearance be allowed upon taps that require to be
used by hand, the tap will thread the hole taper, the diameter being
largest at the top of the hole. This occurs because the tap is not so
well steadied by its thread, which fails to act as a guide, and it is
impossible to revolve the tap steadily by hand. Taps that are revolved
by machine tools may be given clearance because both the taps and the
work are detained in line, hence the tap cannot wobble.
[Illustration: Fig. 324.]
[Illustration: Fig. 325.]
In some cases clearance is given by filing or cutting off the tops of
the threads along the middle of the teeth, as shown in Fig. 325 at A, B,
C, which considerably reduces the friction. If clearance were given to a
tap after this manner but extended to the sides and to the bottom of the
thread, it would produce the best of results (for all taps that do not
pass entirely through the hole), reducing the friction and leaving no
room for the cuttings to jam in the threads when the tap is being backed
out. The threads of Sir Joseph Whitworth's taper hand taps are made
parallel, measured at the bottom of the thread, and parallel at the tops
of the thread for a distance equal to the diameter of the tap at the
shank end; thence, to the entering end of the tap, the tops of the
thread are turned off a straight taper, the amount of taper being
slightly more than twice the depth of the thread: hence, the thread is
just turned out at the entering end of the tap, and that end is the
exact proper size for the tapping hole.
This enables the tap to enter the tapping hole for a distance enveloping
one or perhaps two of the tap threads, leaving the extreme end of the
tap with the thread just turned out. In the practice of some tap makers
the diameter of the thread at the top is made the same as in the
Whitworth system, but there is more depth at the root of the thread and
near the entering end of the tap, hence the bottoms of the thread at
that end perform no cutting duty. This is done to enable the tap to take
hold of, and start a thread in, the work more readily, which it does for
the following reasons. In Fig. 326 is a piece of work with a tap A,
having a tapered thread, and a tap B, in which the taper is given by
turning off the thread. In the case of A the teeth points cut a groove
that is gradually widened and deepened as the tap enters, until a full
thread is finally produced. In the case of B the teeth cut at first a
wide groove, leaving a small projection, that is a part of the actual
finished thread, and the groove gets narrower as the tap enters; so that
in the one case no part of the thread is finished until the tap has
entered to its full diameter, while in the other the thread is finished
as it is produced. On entering, therefore, more cutting duty is
performed by B than by A, because a greater length of cutting edge is in
operation and more metal is being removed, and as a result B requires
more power to start it, so that in practice it is necessary to exert a
pressure upon it, tending to force it into the hole while rotating it.
The cutting duty on B decreases as the tap enters, because it gets less
width and area of groove to cut, while the cutting duty on A increases
as the tap enters, because it gets a greater width and area of groove to
cut. In the latter case the maximum of pressure falls on the tap when it
has entered the hole deepest, and hence can be operated steadiest,
which, independent of its entering easiest, is an advantage. When,
however, the bottom of a thread is taper (as must be the case to enable
it to cut as at A), the cutting edge of each tooth does not cut a groove
sufficiently large in diameter to permit the tooth itself to pass
through. In Fig. 327, for example, is shown a tap which is taper and has
a full thread from end to end (as is necessary for pipe tapping). Its
diameter increases as the thread proceeds from the end towards the line
A B. Now take the tooth O P, which stands lengthwise, in the plane C D.
Its cutting edge is at P, but the diameter of the tap at P is less than
it is at O, while O has to pass through the groove that P cuts. To
obviate this difficulty the tap is given clearance, as shown in Fig.
324, the amount being slightly more than the difference in the diameter
of the tap at O and at P in that figure. It follows, therefore, that a
tap having taper from end to end and a full thread also, as shown in the
lower tap in Fig. 328, is wrong in principle, and from the unsteady
manner in which it operates is undesirable, even though its thread be
given clearance.
[Illustration: Fig. 326.]
[Illustration: Fig. 327.]
In some cases the thread is made parallel at the tops and turned taper
for a distance of 1/3 or 1/2 the length of the tap, the root of the
thread at the taper part being deepened and the tops being given a
slight clearance. This answers very well for shallow holes, because the
taper tap cuts more thread on entering a given depth so that the second
tap can follow more easily, but the tap will not operate so steadily as
when the taper part is longer.
[Illustration: Fig. 328.]
It is on account of the tops of the teeth performing the main part of
the cutting that a tap taper may be sharpened by simply grinding the
teeth tops. In the Pratt and Whitney taps, the hand taper tap is made
parallel at the shank end for a distance equal in length to the diameter
of the tap.
The entering end of the taper tap is made straight or parallel for a
distance equal in length to one half the diameter of the tap, the
diameter at this end being the exact proper size of tapping hole. The
parallel part serves as a guide, causing the tap to enter and keep
axially true with the hole to be tapped. The plug and bottoming taps are
made parallel in the thread, the former being tapered slightly at and
for two or three threads from the entering, as shown in Fig. 328. The
threads are made parallel at the roots.
The Pratt and Whitney taper taps for use in machines are of the
following form:--
The entering end of the tap is equal in diameter to the diameter of the
tapping hole into which the tap will enter for a distance of two or
three threads. The thread at the shank end is parallel both at the top
and at the root for a distance equal, in length, to twice the diameter
of the tap. The top of the thread has a straight taper running from the
parallel part at the shank to the point or entering end, while the roots
of the thread are made along this taper twice the taper that there is at
the top of the thread, which is done to make the tap enter and take hold
of the nut more easily.
[Illustration: Fig. 329.]
A form of tap that cuts very freely on account of the absence of
friction on the sides of the thread is shown in Fig. 329. The thread is
cut in parallel steps, increasing in size towards the shank, the last
step (from D to E in the figure) being the full size. The end of the tap
at A being the proper size for the tapping hole, and the flutes not
being carried through A, insures that the tap shall not be used in holes
too small for the size of the tap, and thus is prevented a great deal of
tap breakage. The bottom of the thread of the first parallel step (from
A to B) is below the diameter of A, so as to relieve the sides of the
thread of friction and cause the tap to enter easily. The first tooth
of each step does all the cutting, thus acting as a turning tool, while
the step within the work holds the tooth to its cut, as shown in Fig.
330, in which N represents a nut and T the tap, both in section. The
step C holds the tap to its work, and it is obvious that, as the tooth B
enters, it will cut the thread to its own diameter, the rest of the
teeth on that step merely following frictionless until the front tooth
on the next step takes hold. Thus, to sharpen the tap equal to new, all
that is required is to grind away the front tooth on each step, and it
becomes practicable to sharpen the tap a dozen times without softening
it at all. As a sample of duty, it may be mentioned that, at the
Harris-Corliss Works, a tap of this class, 2-7/8 inches diameter, with a
4 pitch, and 10 inches long, will tap a hole 5 inches deep, passing the
tap continuously through without any backing motion, two men performing
the duty with a wrench 4 feet long over all, the work being of cast
iron.
[Illustration: Fig. 330.]
[Illustration: Fig. 331.]
[Illustration: Fig. 332.]
Another form of free cutting tap especially applicable to taps of large
diameter has been designed by Professor Sweet. Its principles may be
explained as follows:--
In the ordinary tap, with the taper four or five diameters in length,
there are far more cutting-edges than are necessary to do the work; and
if the taper is made shorter, the difficulty of too little room for
chips presents itself. The evil results arising from the extra cutting
edges are that, if all cut, then it is cutting the metal uselessly
fine--consuming power for nothing; or if some of the cutting edges fail
to cut, they burnish down the metal, not only wasting power, but making
it all the harder for the following cutters. One plan to avoid this is
to file away a portion of the cutting edges; but the method adopted in
the Cornell University tap is still better. Assume that it is desired to
make three following cutters, to remove the stock down to the dotted
line in Fig. 331. Instead of each cutter taking off a layer one-third
the thickness and the full width, the first cutter is cut away on each
side to about one-third its full width, so that it cuts out the centre
to its full depth, as shown in Fig. 331, the next cutter cutting out the
metal at A, and so on. This is accomplished by filing, or in any other
way cutting away the sides of one row of the teeth all the way up; next
cutting away the upper sides of the next row and the lower sides of the
third, leaving the fourth row (if it be a four-fluted tap) as it is left
by the lathe, to insure a uniform pitch and a smooth thread.
[Illustration: Fig. 333.]
Figs. 333, 334 and 335 represent an adjustable tap designed by C. R.
French, of Providence, R. I., to thread holes accurate in diameter.
The plug tap, Fig. 333, has at its end a taper screw, and the tap is
split up as far as the flutes extend, a second screw binds the two sides
of the tap together, hence by means of the two screws the size of the
tap may be regulated at will. In the third or bottoming tap, Fig. 334,
the split extends farther up the shank, and four adjusting screws are
used as shown, hence the parallelism of the tap is maintained.
In the machine tap, Fig. 335, there are six adjusting screws, two of
those acting to close the tap being at the extreme ends so as to
strengthen it as much as possible.
[Illustration: Fig. 334.]
[Illustration: Fig. 335.]
In determining the number, the width, the depth, and the form of flutes
for a tap, we have the following considerations. In a tap to be used in
a machine and to pass entirely through the work, as in the case of
tapping nuts, the flute need not be deep, because the taper part of the
tap being long the cutting teeth extend farther along the tap; hence,
each tooth takes a less amount of cut, producing less cuttings, and
therefore less flute is required to hold them. In taps of this class,
the thread being given clearance, the length of the teeth may be a
maximum, because they are relieved of friction; on the other hand,
however, the shallower and narrower the flute the stronger the tap, so
long as there is room for the cuttings so that they shall not become
wedged in the flutes. Taps for general use by hand are frequently used
to tap holes that do not pass entirely through the work; hence, the
taper tap must have a short length of taper so that the second tap may
be enabled to carry a full thread as near as possible to the bottom of
the hole without carrying so heavy a cut as to render it liable to
breakage, and the second or plug tap must in turn have so short a length
of its end tapered that it will not throw too much duty upon the
bottoming tap. Now, according as the length of the taper on the taper
tap is reduced, the duty of the teeth is increased, and more room is
necessary in the flute to receive the cuttings, and supposing the tap
to be rotated continuously to its duty the flute must possess space
enough to contain all the cuttings produced by the teeth, but on account
of the cuttings filling the flutes and preventing the oil fed to the tap
from flowing down the flute to the teeth it is found necessary in hand
taps (when they cannot pass through the work, or when the depth of the
hole is equal to more than about the tap diameter), to withdraw the tap
and remove the cuttings. On account of the tap not being accurately
guided in hand-tapping it produces a hole that is largest at its mouth,
and it is found undesirable on this account to give any clearance to
hand taps, because such clearance gives more liberty to the tap to
wobble in the hole and to enlarge its diameter at the mouth. It is
obvious also, that the less of the tap circumference removed to form the
flutes the longer the tap-teeth and the more steadily the tap may be
operated. On the other hand, however, the longer the teeth the greater
the amount of friction between them and the thread in the hole and the
more work there is involved in the tapping, because the tap must
occasionally be rotated back a little to ease its cut, which it is found
to do.
[Illustration: Fig. 336.]
[Illustration: Fig. 337.]
Fig. 336 represents a form of flute recommended by Brown and Sharp. The
teeth are short, thus avoiding friction, and the flutes are shallow,
which leaves the tap strong. The inclination of the cutting edges, as A
B (the cutting direction of rotation being denoted by the arrow), is
shown by the dotted lines, being in a direction to curve the chip or
cutting somewhat upward and not throw them down upon the bottom of the
flute. A more common form, and one that perhaps represents average
American practice, is shown in Fig. 337, the cutting edges forming a
radial line as denoted by the dotted line. The flute is deeper, giving
more room for the chips, which is an advantage when the tap is required
to cut a thread continuously without being moved back at all, but the
tap is weaker on account of the increased flute depth, the teeth are
longer and produce more friction, and the flutes are deeper than
necessary for a tap having a long taper or that requires to be removed
to clear out the cuttings. Fig. 338 shows the form of flute in the Pratt
and Whitney Company's hand taps, the cutting edges forming radial lines
and the bottoms of the flutes being more rounded than is usual. It may
here be remarked that if the flutes have comparatively sharp corners, as
at C in Fig. 339, the tap will be liable to crack in the hardening
process. The form of flute employed in the Whitworth tap is shown in
Fig. 340; here there being but three flutes the teeth are comparatively
long, and on this account there is increased friction. But, on the other
hand, such a tap produces, when used by hand, more accurate work, the
threaded hole being more parallel and of a diameter more nearly equal to
that of the tap, it being observed that even though a hand tap have no
clearance it will usually tap a hole somewhat larger than itself so that
it will unwind easily. If a hand tap is given clearance not only will it
cut a hole widest at the mouth, but it will cut a thread larger than
itself in an increased degree, and, furthermore, when the tap requires
to be wound back to extract it the fine cuttings will become locked in
the threads and the points of the tap teeth are liable to become broken
off. To ease the friction of long teeth, therefore, it is preferable to
do so either as in Fig. 325 at A, B, C, or as in Fig. 341. In Fig. 325
the tops of the teeth are shown filed away, leaving each end full, so
that the cuttings cannot get in, no matter in which direction the tap is
rotated; but the clearance is not so complete as in Fig. 341, in which
the teeth are supposed to be eased away within the area enclosed by
dotted lines, which gives clearance to the bottom as well as to the tops
and sides of the thread and leaves the ends of each tooth a full thread.
[Illustration: Fig. 338.]
[Illustration: Fig. 339.]
[Illustration: Fig. 340.]
[Illustration: Fig. 341.]
Concerning the number of flutes in taps, it is to be observed that the
duty the tap is to be put to, has much influence in this respect. In
hand tapping the object is to tap as parallel and straight as possible
with the least expenditure of power. Now, the greater the number of
flutes the less the tap is guided, because more of the circumferential
guiding surface is cut away. But on the other hand, the less the number
of flutes, and therefore the less the number of cutting edges, the more
power it takes to operate the tap on account of the greater amount of
friction between the tap and the walls of the hole. In hand tapping on
what may be termed frame work (as distinguished from such loose work as
nuts, &c.), the object is to tap the holes as parallel as possible with
the least expenditure of power while avoiding having to remove the tap
from the hole to clear it of the cuttings. Obviously the more flutes and
cutting edges there are the more room there is for the cuttings and the
less frequent the tap requires to be cleaned. If the tapping hole is
round and straight the tapping may be made true and parallel if due care
is taken, whatever the number of flutes, but less care will be required
in proportion as there are less flutes, while, as before noted, more
power and more frequent tap removals will be necessary. But if the hole
is not round, other considerations intervene.
[Illustration: Fig. 342.]
Thus in Fig. 342 we have a three-flute tap in a hole out of round at A,
and it is obvious that when a cutting edge meets the recess at A, all
three teeth will cease to cut; hence there will be no inducement for the
tap to move over toward A. But in the case of the four-flute tap in Fig.
343, when the teeth come to A there will be a strain tending to force
the teeth over toward the depression A. How much a given tap would
actually move over would, of course, depend upon the amount of
clearance; but whether the tap has clearance or not, the three-flute tap
will not move over, while with four flutes the tap would certainly do
so. Again, with an equal width of flute there is more of the
circumference tending to guide and steady the three-flute than the
four-flute tap. If the hole has a projection instead of a depression, as
at B, Figs. 344 and 345, then the advantage still remains with the
three-flute tap, because in the case of the three flutes, any lateral
movement of the tap will be resisted at the two points _c_ and D,
neither of which are directly opposite to the location of the projection
B; hence, if the projection caused the tap to move laterally, say,
1-100th inch, the effect at _c_ and D would be very small, whereas in
the four-flute, Fig. 345, the effect at E would be equal to the full
amount of lateral motion of the tap.
[Illustration: Fig. 343.]
[Illustration: Fig. 344.]
[Illustration: Fig. 345.]
In hand taps the position of the square at the head of the tap with
relation to the cutting-edges is of consequence; thus, in Fig. 346,
there being a cutting-edge A opposite to the handle, any undue pressure
on that end of the handle would cause A to cut too freely and the tap to
enlarge the hole; whereas in Fig. 347 this tendency would be greatly
removed, because the cutting-edges are not in line with the handle. In a
three-flute tap it makes but little difference what are the relative
positions of the square to the flutes, as will be seen in Fig. 348,
where one handle of the wrench comes in the most favorable and the other
in the most unfavorable position. Taps for use by hand and not intended
to pass through the work are sometimes made with the shank and the
square end which receive the wrench of enlarged diameter. This is done
to avoid the twisting of the shank which sometimes occurs when the tap
is employed in deep holes, giving it much strain, and also to avoid as
much as possible the wearing and twisting of the square which occurs,
because in the course of time the square holes in solid wrenches enlarge
from wear, and the larger the square the less the wear under a given
amount of strain.
[Illustration: Fig. 346.]
Brass finishers frequently form the heads of their taps as in Fig. 349,
using a wrench with a slot in it that is longer than the flat of the tap
head.
[Illustration: Fig. 347.]
The thickness of the flat head at A is made equal for all the taps
intended to be used with the same wrench. By this means one wrench may
be used for many different diameters of taps.
[Illustration: Fig. 348.]
For gas, steam pipe, and other connections made by means of screw
threads, and which require to be without leak when under pressure, the
tap shown in Fig. 350 is employed. It is made taper and full threaded
from end to end, so that the fittings may be entered easily into their
places and screwed home sufficiently to form a tight joint.
[Illustration: Fig. 349.]
[Illustration: Fig. 350.]
The standard degree of taper for steam-pipe taps is 3/4 inch per foot of
length, the taper being the same in the dies as on the taps. The
threading tools for the pipes or casings for petroleum oil wells are
given a taper of 3/8 inch per foot, because it was not found practicable
to tap such large fittings with a quick taper, because of the excessive
strain upon the threading tools. Ordinary pipe couplings are, however,
tapped straight and stretch to fit when screwed home on the pipe.
Oil-well pipe couplings are tapped taper from both ends, and there is
just enough difference in the taper on the pipe and that in the socket
to show a bearing mark at the end only when the pipe and socket are
tested with red marking.
PITCHES OF TAP THREADS IN USE IN THE UNITED STATES.
+-----------+---------+----------------+
| | | No. of Threads |
| Diameter. | Length. | to Inch. |
+-----------+---------+----------------+
| 1/4 | 2-3/4 | 16, 18 & 20 |
| 5/16 | 2-7/8 | 16 & 18 |
| 3/8 | 3-1/2 | 14 & 16 |
| 7/16 | 3-13/16 | 14 & 16 |
| 1/2 | 4-5/16 | 12, 13 & 14 |
| 9/16 | 4-3/4 | 12 & 14 |
| 5/8 | 5-1/8 | 10, 11 & 12 |
| 11/16 | 5-3/8 | 11 & 12 |
| 3/4 | 5-13/16 | 10, 11 & 12 |
| 13/16 | 6 | 10 |
| 7/8 | 6-1/8 | 9 & 10 |
| 15/16 | 6-3/8 | 9 |
| 1 | 6-13/16 | 8 |
| 1-1/8 | 7-1/4 | 7 & 8 |
| 1-1/4 | 8 | 7 & 8 |
+-----------+---------+----------------+
Fig. 351 represents the form of tap employed by blacksmiths for rough
work, and for the axles of wagon wheels. These taps are given a taper of
1/2 inch per foot of length, and are made with right and left-hand
threads, so that the direction of rotation on both sides of a wagon
wheel shall be in a direction to screw up the nuts and not to unscrew
the nut, as would be the case if both ends of the axle were provided
with right-hand threads.
[Illustration: Fig. 351.]
Taps that are used in a machine are sometimes so constructed that upon
having tapped the holes to the required depth, the pieces containing the
tap teeth recede from the walls of the hole, so that the tap may be
instantly withdrawn from the hole instead of requiring to be rotated
backwards. This is an advantage, not only on account of the time saved,
but also because the cutting edges of the teeth are saved from the
abrasion and its consequent wear which occur in rotating a tap
backwards.
[Illustration: Fig. 352.]
Figs. 352 and 353 represent a collapsing tap that is much used in
manufactories of pipe fittings.
[Illustration: Fig. 353.]
A is driven by the spindle of the machine, and drives B through the
medium of the pin H. In B are three chasers C, fitting into the dovetail
and taper grooves D. These chasers are provided with lugs fitting into
an annular groove E sunk in A, so that if the piece H rises, the chasers
will not rise with it, but will simply close together by reason of the
lifting or rising of the core B, with its taper dovetail grooves; or, on
the other hand, if the core B descends, the taper grooves in B force the
chasers outward, increasing their cutting diameter.
When the tap is cutting, it is driven as denoted by the arrow, and the
pin H is driven by the ends of the grooves, of which there are two, one
diametrically opposite the other, inclined in the same direction. But
when the tap has cut a thread to the required depth on the work, the
handles H may be pulled or pushed the working way, passing along the
grooves I, and causing B to lift within A, and allowing the chasers to
close away from the thread just cut, and the tap may be instantly
withdrawn, and handles H pushed back to expand the chasers, ready for
the next piece of work.
[Illustration: Fig. 354.]
Fig. 354 represents a collapsing tap used in Boston, Massachusetts, at
the Hancock Inspirator Works, in a monitor or turret lathe. It consists
of an outer shell A carrying three chasers B, pivoted to A at C, having
a small lug E at one end, and being coned at the inner end D. The inner
shell F is reduced along part of its length to receive the lug E of the
chaser, and permit the chasers to open out full at their cutting end. F
has a cone at the end G, fitting to the internal cone on the chasers at
D. At the other end of F is a washer H, against which abuts the spiral
spring shown, the other end of this spring abutting against a shoulder
provided in A. The washer H is bevelled on its outer or end face to
correspond with the bevel on a notch provided in lever I, as is shown.
Within the inner tube F is the stem J, into the end of which is fitted
the piece K, and on which is fixed the cone L. Piece K, and therefore L,
is prevented from rotating by a spline in K, into which spline the pin M
projects.
The operation is as follows. In the position in which the parts are
shown in the engraving, F is pushed forward so that its coned end G has
opened out the chaser to its fullest extent, which opening is governed
by contact of the lug E with the reduced diameter of F. Suppose that the
tap is operating in the work, then, when the foot N of K meets with a
resistance (as the end of the hole being tapped), J, and therefore L,
will be gradually pushed to the right, until, finally, the cone on L
will raise the end of lever I until the notch on I is clear of H, when
the spiral spring, acting against H, will force F to the right, and the
shoulder on F, at X, will lift the end E of the chaser, causing the
cutting end to collapse within A, the pivot C being its centre of
motion. The whole device may then be withdrawn from the work. To open
the chasers out again the rod J is forced, by hand, to the left, the
cone-piece L meeting the face of H and pushing it to the left until cone
G meets cone D, when the chasers open until the end E meets the body of
F, as in the cut. The rod J is then pulled to the right until L again
meets the curved end of lever I and all the parts assume the positions
shown in the cut. To regulate the depth of thread the tap shall cut, the
body A is provided with a thread to receive the nut O, by means of which
the collar P may be moved along A. This collar carries the pivots Q for
levers I, so that, by shifting O, the position of I is varied, hence the
point at which L will act upon the end of I and lift it to release H is
adjustable.
When used upon steel, wrought iron, cast iron, copper, or brass, a tap
should be freely supplied with oil, which preserves its cutting edge as
well as causes it to cut more freely, but for cutting the soft metals
such as tin, lead, &c., oil is unnecessary.
The diameters of tapping holes should be equal to the diameter of the
thread at the root, but in the case of cast iron there is much
difference of opinion and practice. On the one hand, it is claimed that
the size of the tapping hole should be such as to permit of a full
thread when it is tapped; on the other hand, it is claimed that
two-thirds or even one-half of a full thread is all that is necessary in
holes in cast iron, because such a thread is, it is claimed, equally as
strong as a full one, and much easier to tap. In cases where it is not
necessary for the thread to be steamtight, and where the depth of the
thread is greater by at least 1/8 inch than the diameter of the bolt or
stud, three-quarters of a full thread is all that is necessary, and can
be tapped with much less labor than would be the case if the hole were
small enough to admit of a full thread, partly because of the diminished
duty performed by the tap, and partly because the oil (which should
always be freely supplied to a tap) obtains so much more free access to
the cutting edges of the tap. If a long tap is employed to cut a
three-quarter full thread, it may be wound continuously down the hole,
without requiring to be turned backwards at every revolution or so of
the tap, to free it from the tap cuttings or shavings, as would be
necessary in case a full thread were being cut. The saving of time in
consequence of this advantage is equal to at least 50 per cent. in favor
of the three-quarter full thread.
As round bar iron is usually rolled about 1/32 inch larger than its
designated diameter, a practice has arisen to cut the threads upon the
rough iron just sufficiently to produce a full thread, leaving the
latter 1/32 inch above the proper diameter, hence taps 1/32 inch above
size are required to thread nuts to fit the bolts. This practice
should be discountenanced as destroying in a great measure the
interchangeability of bolts and nuts, because 1/32 inch is too small a
measurement to be detected by the eye, and a measurement or trial of the
bolt and nut becomes necessary.
A defect in taps which it has been found so far impracticable to
eliminate is the alteration of pitch which takes place during the
hardening process. The direction as well as the amount of this variation
is variable even with the most uniform grades of steel, and under the
most careful manipulation. Mr. John J. Grant, in reply to a
communication upon this subject, informs me that, using Jones and
Colver's (Sheffield) steel, which is very uniform in grade, he finds
that of one hundred taps, about 5 per cent. will increase in length, the
pitch of the thread becoming coarser; 15 per cent. will suffer no
appreciable alteration of pitch, and 80 per cent. will shrink in length,
the pitch becoming finer, and these last not alike. But it must be borne
in mind that with different steel the results will be different, and the
greater the variation in the grade of the steel the greater the
difference in the alteration of pitch due to hardening.
It is further to be observed that the expansion or contraction of the
steel is not constant throughout the same tap; thus the pitches of three
or four consecutive teeth may measure correct to pitch, while the next
three or four may be of too coarse or too fine a pitch.
There is no general rule, even using the same grade of steel, for the
direction in which the size of a tap may alter in hardening, as is
attested by the following answers made by Mr. J. J. Grant to the
respective questions:--
"Do the taps that shorten most in length increase the most in diameter?"
Answer.--"Not always; sometimes a tap that shortens by hardening becomes
also smaller in diameter, while sometimes a tap will increase in length,
and also in diameter from hardening."
"Do taps that remain of true pitch after hardening remain true, or
increase or diminish in diameter?"
Answer.--"They will generally be of larger diameter."
"Do small taps alter more in diameter from hardening than large ones?"
Answer.--"No; the proportion is about the same, and is about .002 per
inch of diameter."
"What increase in diameter do you allow for shrinkage in hardening of
hob taps for tapping solid dies?"
Answer.--"As follows:--
Diameter of Shrinkage
Hob Tap about
1/4 inch .003
1/2 " .003
3/4 " .005
1 " .008"
"Suppose a tap that had been hardened and tempered to a straw color
contained an error 1/1000 inch both in diameter and in pitch, was
softened again, would it when soft retain the errors, or in what way
would softening affect the tap?"
Answer.--"We have repeatedly tried annealing or softening taps that were
of long or short pitch caused by tempering, and invariably found them
about the same as before the annealing. The second tempering will
generally shorten them more than the first. Sometimes, however, a second
tempering will bring a long pitch nearer correct."
"Do you soften your taps after roughing them out in the lathe?"
Answer.--"Never, if we can possibly avoid it. Sometimes it is necessary
because of improper annealing at first. The more times steel is annealed
the worse the results obtained in making the tool, and the less durable
the tool."
The following are answers to similar questions addressed to the Morse
Twist Drill and Machine Co.:--
"The expansion of taps during hardening varies with the diameter. A
1-inch tap would expand in diameter from 1/1000 to 3/1000 inch."
"Taps above 1/2 inch diameter expand in diameter to stop the gauge every
time."
"The great majority of taps contract in pitch during the hardening, they
seldom expand in length."
"The shortening of the pitch and the expansion in diameter have not much
connection necessarily, though steel that did not alter in one direction
would be more likely to remain correct in the other."
"There does not seem to be any change in the diameter or pitch of taps
if measured after hardening (and before tempering) and again after
tempering them."
"Taps once out in length seem to get worse at every heating, whether to
anneal or to harden."
[Illustration: Fig. 355.]
It will now be obvious to the reader that the diameter of a tap, to give
a standard sized bolt a required tightness of fit, will, as a general
rule, require to vary according to the depth of hole to be tapped,
because the greater that depth the greater the error in the pitch.
Suppose a tap, for example, to get of finer pitch to the amount of .002
per inch of length, then a hole an inch deep and tapped with that tap
would err .002 in its depth, while a hole two inches deep would err
twice as much in its depth.
[Illustration: Fig. 356.]
Therefore a bolt that would be a hand fit (that is, screw in under hand
pressure) in the hole an inch deep would require more force, and
probably the use of a wrench, to wind it through the hole 2 inches deep;
hence in cases where a definite degree of fit is essential, the
reduction in diameter of the male screw or thread necessary to
compensate for the error in the tap pitch must vary according to the
depth of the hole, and the degree of error in the tap.
[Illustration: Fig. 357.]
It is obvious that the longer a tap is the greater the error induced by
hardening, and it often becomes a consideration how to tap a long hole,
and obtain a thread true to pitch. This may be accomplished as follows.
Several taps are made of slightly different diameters, the largest being
of the required finished size. Each tap is made taper for a distance of
two or three threads only, and is hardened at this tapered end, but left
soft for the remainder of its length. The smallest tap is used first,
and when it has tapped a certain distance, a larger one is inserted, and
by continuing this interchange of taps and slightly varying the length
of the taper, the work may be satisfactorily done.
To test the accuracy, or rather the uniformity, of a thread that has
been hardened, a sheet metal gauge, such as at G or at G´ (Fig. 355),
may be used, there being at _a_ and _b_ teeth to fit the threads. If the
edge of the gauge meets the tops of the threads, then their depth is
correct. If it is desired to test only the pitch, then the gauge may be
made as at G´, where, as is shown in the figure, the edge of the gauge
clears the tops of the threads, and in this way may be tried at various
points along the thread length.
[Illustration: Fig. 358.]
A method of truing hardened threads proposed by the author of this work
in 1877, and since employed by the Pratt and Whitney Company to true
their hardened steel plug-thread gauges, is as follows:--A soft steel
wheel about 3-1/2 inches in diameter, whose circumference is turned off
to the shape of the thread, is mounted upon the slide rest of a lathe,
and driven by a separate belt after the manner of driving emery wheels;
this wheel is charged with diamond dust, which is pressed into its
surface by a roller, hence it grinds the thread true.
The amount allowed for grinding is 3/1000 inch measured in the angles of
the thread, as was shown in Figs. 280 and 281.
In charging the wheel with diamond dust it is necessary to use a roller
shaped as in Fig. 356, so that the axis of the roller R and wheel W
shall be at a right angle, as denoted by the dotted lines. If the roller
is not made to the correct cone its action will be partly a rolling and
partly a sliding one, and it will strip the diamond dust from the wheel
rather than force it in, the reasons for this being shown in Figs. 57
and 58 upon the subject of bevel-wheels.
[Illustration: Fig. 359.]
Taps for lead and similar soft metal are sometimes made with three flat
sides instead of grooves. The tapping holes may in this case be made of
larger diameter than the diameter of the end of the tap thread, because
the metal in the hole will compress into the tap thread, and so form a
full thread. Taps for other metal have also been made of half-round
section. Fig. 357 represents a tap of oval cross section, having two
flutes, as shown, but it may be observed that neither half-round nor
oval taps possess any points of advantage over the ordinary forms of
three or four fluted taps, while the former are more troublesome and
costly to manufacture.
[Illustration: Fig. 360.]
When it is required to tap a hole very straight and true, it is
sometimes the practice to provide a parallel stem to the tap, as shown
in figure at C. This stem is made a neat working fit to the tapping
hole, so that the latter serves as a guide to the tap, causing it to
enter and to operate truly.
TAP WRENCH.--Wrenches for rotating a tap are divided into two principal
classes, single and double wrenches. The former has the hole which
receives the squared end of the tap in the middle of its length, as
shown in Fig. 358 at E, there being a handle on each side to turn it by.
[Illustration: Fig. 361.]
The single wrench has its hole at one end, as shown in Fig. 359 at D,
and is employed for tapping holes in locations where the double wrench
could not be got in.
[Illustration: Fig. 362.]
[Illustration: Fig. 363.]
In some cases double tap wrenches are made with two or three sizes of
square holes to serve as many different sizes of taps, but this is
objectionable, because unless the handles of the wrench extend equally
on each side of the tap, the overhanging weight on one side of the tap
exerts an influence to pull the tap over to one side and tap the hole
out of straight. For taps that have square heads the wrench should be a
close but an easy fit to the tap head, otherwise the square corners of
the tap become rounded. For the smaller sizes of taps, adjustable
wrenches, such as shown in Fig. 360, are sometimes employed. These
contain two dies; the upper one, which meets the threaded end of C,
being a sliding fit, and the joint faces being formed as shown at A, B.
By rotating the handle C its end leaves the upper die, which may be
opened out, leaving the square hole between the dies large enough to
admit the squared tap end. After the wrench is placed on the tap, C is
rotated so as to close the dies upon the tap.
[Illustration: Fig. 364.]
[Illustration: Fig. 365.]
When the location of the tapping hole leaves room for the wrench to
rotate a full circle, C is screwed up so that the dies firmly grip the
tap head, which preserves the tap head; but when the wrench can only be
rotated a part of a revolution, C is adjusted to leave the dies an easy
fit to the tap head, so as to enable the wrench to be removed from the
tap head with facility and again placed upon the tap head. C is operated
by a round lever or pin introduced in a hole in the collar, or the
collar may be squared to receive a wrench.
To insure that a tap shall tap a hole straight, the machinist, in the
case of hand tapping, applies a square to the work and the tap, as shown
in Fig. 361, in which W represents a piece of work, T a tap, and S S two
squares. If the tap is a taper one the square is sighted with the shank
of the tap, as shown in position 1, but if the thread of the tap is
parallel, the square may be applied to the thread of the tap, as in
position 2. If the tap leans over to one side, as in Fig. 362, it is
brought upright by exerting a pressure on the tap wrench handle B (on
the high side) in the direction of the arrow A, while the wrench is
rotated; but if the tap leans much to one side it is necessary to rotate
the tap back and forth, exerting the pressure on the forward stroke
only.
[Illustration: Fig. 366.]
[Illustration: Fig. 367.]
It is necessary to correct the errors before the tap has entered the
hole deeply, because the deeper the tap has entered the greater the
difficulty in making the correction. If the pressure on the tap wrench
be made excessive, it is very liable to cause the tap to break,
especially in the case of small taps, that is to say, those of 5/8 inch
or less in diameter. The square should be applied as soon as the tap has
entered the hole sufficiently to operate steadily, and should be applied
several times during the tapping operation.
When the tap does not pass through the hole it may be employed with a
guide which will keep it true, as shown in Fig. 363, in which W is a
piece of work, T the tap, and S a guide, the latter being bolted or
clamped to the work at B. In this case the shank of the tap is made
fully as large in diameter as the thread. In cases where a number of
equidistant holes require tapping, as in the case of cylinder ends, this
device saves a great deal of time and insures that the tapping be
performed true, the hole to receive the bolt B and that to receive the
tap being distant apart to the same amount as are the holes in the work.
In shops where small work is made to standard gauge, and on the
interchangeable system, devices are employed, by means of which a piece
that has been threaded will screw firmly home to its place, and come to
some definite position, as in the following examples. In Fig. 364 let it
be required that the stud A shall screw in the slide S; the arm A to
stand vertical when collar B is firmly home, and a device such as in
Fig. 365 may be employed. P is a plate on which is fixed a chuck C to
receive the slide S. In plate P is a groove G to hold the head H at a
right angle to the slideway in C, there being a projection beneath H and
beneath C to fit into G. The tap T is threaded through H, but not fluted
at the part that winds through H when the tapping is being done, so as
not to cause the thread in H to wear. H acts as a guide to the tap and
causes it to start the thread at the same point in the bore of each
piece S, and the stem will be so threaded that the screw starts at the
same point in the circumference of each piece.
[Illustration: Fig. 368.]
A second example of uniform tapping is shown in Figs. 366, 367, and 368.
The piece, Fig. 366, is to have its bore A tapped in line with the slot
C, and the thread is to start at a certain point in its bore. In Fig.
367 this piece is shown chucked on a plate D. F is a chuck having a lug
E fitting into the slot (C, Fig. 366) of the work. This adjusts the work
in one direction. The face D of the plate adjusts the vertical height of
the work, and the alignment of the hole to the axis of the tap is
secured in the construction of the chuck, as is shown in Fig. 369. A lug
K is at a right angle to the face B of the chuck and stands in a line
with lug E, as denoted by the dotted line _g_ _g_, and as lug K fits
into the slot G, Fig. 367, the work will adjust itself true when bolted
to the plate.
[Illustration: Fig. 369.]
Fig. 368 shows a method of tapping or hobbing four chasers (as for a
bolt cutter), so that if the chasers are marked 1, 2, 3 and 4, as shown,
any chaser of No. 1 will work with the others, although not tapped at
the same operation. C is a chuck with four dies (A, B, C, D) placed
between the chasers. By tightening the set-screws S, the dies and
chasers are locked ready for the tapping. N is a hub to receive a
guide-pin P, which is passed through to hold the chasers true while
being set in the chuck, and it is withdrawn before the tapping
commences; _d_ _e_ _f_ are simply to take hold of when inserting and
removing the dies. It is obvious that a chuck such as this used upon a
plate, as in Fig. 365, with the hob guided in the head H there shown,
would tap each successive set of chasers alike as a set, and
individually alike, provided, of course, that the hob guide or head H is
at each setting placed the same distance from the face of the chuck, a
condition that applies to all this class of work. In the case of work
like chasers, where the tap or hob does not have much bearing to guide
it in the work, a three-flute hob should be used for four chasers, or a
four-flute hob for three chasers, which is necessary so that the hob may
work steadily and tap all to the same diameter.
CHAPTER V.--FASTENING DEVICES.
Bolts are usually designated for size by their diameters measured at the
cylindrical stem or body, and by their lengths measured from the inner
side of the head to the end of the thread, so that if a nut be used, the
length of the bolt, less the thickness of the nut and washer (if the
latter be used), is the thickness of work the bolt will hold. If the
work is tapped, and no nut is used, the full length of the bolt stem is
taken as the length of the bolt.
A _black_ bolt is one left as forged. A finished bolt has its body, and
usually its head also, machine finished, but a finished bolt sometimes
has a black head, the body only being turned.
A square-headed bolt usually has a square nut, but if the nut is in
a situation difficult of access for the wrench, or where the head
of the bolt is entirely out of sight (as secluded beneath a flange) the
nut is often made hexagon. A machine-finished bolt usually has a
machine-finished and hexagon nut. Square nuts are usually left black.
[Illustration: Fig. 370.]
The heads of bolts are designated by their shapes, irrespective of
whether they are left black or finished. Fig. 370 represents the various
forms: _a_, square head; _b_, hexagon head; _c_, capstan head; _d_,
cheese head; _e_, snap head; _f_, oval head, or button head; _g_,
conical head; _h_, pan head; _i_, countersink head.
The square heads _a_ are usually left black, though in exceptional cases
they are finished. Hexagon heads are left black or finished as
circumstances may require; when a bolt head is to receive a wrench and
is to be finished, it is usually made hexagon. Heads _c_ and _d_ are
almost invariably finished when used on operative parts of machines, as
are also _e_ and F. Heads _g_ are usually left black, while _h_ and _i_
are finished if used on machine work, and left black when used as rivets
or on rough unfinished work.
The heads from _e_ to _i_ assume various degrees of curve or angle to
suit the requirements, but when the other end of the bolt is threaded to
receive a nut, some means is necessary to prevent them from rotating in
their holes when the nut is screwed up, thus preventing the nut from
screwing up sufficiently tight. This is accomplished in woodwork by
forging either a square under the head, as in Fig. 371, or by forging
under the head a tit or stop, such as shown in Figs. 372 and 373 at P.
Since, however, forging such stops on the bolt would prevent the heads
from being turned up in the lathe, they are for lathe-turned bolts put
in after the bolts have been finished in the lathe, a hole being
subsequently drilled beneath the head to receive the pin or stop, P,
Fig. 372, which may be tightly driven in. A small slot is cut in the
edge of the hole to receive the stop.
[Illustration: Fig. 371.]
[Illustration: Fig. 372.]
[Illustration: Fig. 373.]
Bolts are designated for kinds, as in Fig. 374, in which _k_ is a
machine bolt; _l_ a collar bolt, from having a collar on it; _m_ a
cotter bolt, from having a cotter or key passing through it to serve in
place of a nut; _n_ a carriage bolt, from having a square part under the
head to sink in the wood and prevent the bolt from turning with the nut;
and _o_ a countersink bolt for cases where the head of the bolt comes
flush.
[Illustration: Fig. 374.]
The simple designation "machine bolt" is understood to mean a black or
unfinished bolt having a square head and nut, and threaded, when the
length of the bolt will admit it, and still leave an unthreaded part
under the bolt head, for a length equal to about four times the diameter
of the bolt head. If the bolt is to have other than a square head it is
still called a machine bolt, but the shape of the head or nut is
specially designated as "hexagon head machine bolt," this naturally
implying that a hexagon nut also is required.
In addition to these general names for bolts, there are others applied
to special cases. Thus Fig. 375 represents a patch bolt or a bolt for
fastening patches (as plate C to plate D), its peculiarity being that it
has a square stem A for the wrench to screw it in by. When the piece the
patch bolt screws into is thin, as in the case of patches on steam
boilers, the pitch of the thread may, to avoid leakage, be finer than
the usual standard.
In countersink head bolts, such as the patch bolt in Fig. 375, the head
is very liable to come off unless the countersink in the work (as in C)
is quite fair with the tapped hole (as in D) because the thread of the
bolt is made a tight fit to the hole, and all the bending that may take
place is in the neck beneath the head, where fracture usually occurs.
These bolts are provided with a square head A to screw them in by, and
are turned in as at B to a diameter less than that at the bottom of the
thread, so that if screwed up until they twist off, they will break in
the neck at B.
[Illustration: Fig. 375.]
[Illustration: Fig. 376.]
Instead of the hole being countersunk, however, it may be cupped or
counterbored, as in Fig. 376, in which the names of the various forms of
the enlargement of holes are given. The difference between a faced and a
counterbored hole is that in a counterbored hole the head or collar of
the pin passes within the counterbore, the use of the counterbore being
in this case to cause the pin to stand firmly and straight. The
difference between a dished and a cupped is merely that cupped is deeper
than dished, and that between grooved and recessed is that a recess is a
wide groove.
Eye bolts are those having an eye in place of a head, as in Fig. 377,
being secured by a pin passing through the eye, or by a second bolt, as
in the figure. When the bolt requires to pivot, that part that is
within the eye may be made of larger diameter than the thread, so as to
form a shoulder against which the bolt may be screwed firmly home to
secure it without gripping the eye bolt.
[Illustration: Fig. 377.]
[Illustration: Fig. 378.]
Fig. 378 represents a foundation bolt for holding frames to the stone
block of a foundation. The bolt head is coned and jagged with chisel
cuts. It is let into a conical hole (widest at the bottom) in the stone
block, and melted lead is poured around it to fill the hole and secure
the bolt head.
[Illustration: Fig. 379.]
[Illustration: Fig. 380.]
Another method of securing a foundation bolt head within a stone block
is shown in Fig. 379; a similar coned hole is cut in the block, and
besides the bolt head B a block W is inserted, the faces of the block
and bolt being taper to fit to a taper key K, so that driving K locks
both the bolt and the block in the stone. When the bolt can pass
entirely through the foundation (as when the latter is brickwork) it is
formed as in Fig. 380, in which B is a bolt threaded to receive a nut at
the top. At the bottom it has a keyway for a key K, which abuts against
the plate P. To prevent the key from slackening and coming out, it has a
recess as shown in the figure at the sectional view of the bolt on the
right of the illustration, the recess fitting down into the end of the
keyway as shown.
[Illustration: Fig. 381.]
Another method is to give the bolt head the form at B in Fig. 381, and
to cast a plate with a rectangular slot through, and with two lugs A C.
The plate is bricked in and a hole large enough to pass the bolt head
through is left in the brickwork. The bolt head is passed down through
the brickwork in the position shown at the top, and when it has passed
through the slot in the plate it is given a quarter turn, and then
occupies the position shown in the lower view, the lugs A C preventing
it from turning when the nut is screwed home. The objection to this is
that the hole through the brickwork must be large enough to admit the
bolt head. Obviously the bolt may have a solid square head, and a square
shoulder fitting into a square hole in the plate, the whole being
bricked in.
[Illustration: Fig. 382.]
[Illustration: Fig. 383.]
Figs. 382 and 383 represent two forms of hook bolt for use in cases
where it is not desired to have bolt holes through both pieces of the
work. In Fig. 382 the head projects under the work and for some distance
beneath and beyond the washer, as is denoted by the dotted line, hence
it would suspend piece A from B or piece B from A. But in Fig. 383 the
nut pressure is not beneath the part where the hook D grips the work,
hence the nut would exert a pressure to pull piece B in the direction of
the arrow; hence if B were a fixed piece the bolt would suspend A from
it, but it could not suspend B from A.
In woodwork the pressure of the nut is apt to compress the wood, causing
the bolt head and nut to sink into the wood, and to obviate this, anchor
plates are used to increase the area receiving the pressure; thus in
Fig. 384 a plate is tapped to serve instead of a nut, and a similar
plate may of course be placed under the bolt head.
[Illustration: Fig. 384.]
The Franklin Institute or United States Standard for the dimensions of
bolt heads and nuts is as follows. In Fig. 385, D represents the
diameter of the bolt, J represents the short diameter or width across
flats of the bolt head or of the nut, being equal to one and a half
times the diameter of the bolt, plus 1/16 inch for finished heads or
nuts, and plus 1/8 inch for rough or unfinished heads or nuts. K
represents the depth or thickness of the head or nut, which in finished
heads or nuts equals the diameter of the bolt minus 1/16 inch, and in
rough heads equals one half the distance between the parallel sides of
the head, or in other words one half the width across the flats of the
head.
H represents the thickness or depth of the nut, which for finished nuts
is made equal to the diameter of the bolt less 1/16 inch, and therefore
the same thickness as the finished bolt head, while for rough or
unfinished nuts it is made equal to the diameter of the bolt or the same
as the rough bolt head. I represents the long diameter or diameter
across corners, which, however, is a dimension not used to work to, and
is inserted in the following tables merely for reference:--
[Illustration: Fig. 385.]
TABLE OF THE FRANKLIN INSTITUTE STANDARD DIMENSIONS FOR THE HEADS OF
BOLTS AND FOR THEIR NUTS, WHEN BOTH HEADS AND NUTS ARE OF HEXAGON FORM,
AND ARE POLISHED OR FINISHED.
+------------+-------------+-----------+---------------+-----------+
| Diameter | Diameter at | Number of | Diameter | Thickness |
| at top | bottom of | Threads | across Flats, | or |
| of Thread. | Thread. | per inch. | or short | Depth. |
| | | | diameter. | |
+------------+-------------+-----------+---------------+-----------+
| 1/4 | .185 | 20 | 7/16 | 3/16 |
| 5/16 | .240 | 18 | 17/32 | 1/4 |
| 3/8 | .294 | 16 | 5/8 | 5/16 |
| 7/16 | .345 | 14 | 23/32 | 3/8 |
| 1/2 | .400 | 13 | 13/16 | 7/16 |
| 9/16 | .454 | 12 | 29/32 | 1/2 |
| 5/8 | .507 | 11 | 1 | 9/16 |
| 3/4 | .620 | 10 | 1-3/16 | 11/16 |
| 7/8 | .731 | 9 | 1-3/8 | 13/16 |
| 1 | .837 | 8 | 1-9/16 | 15/16 |
| 1-1/8 | .940 | 7 | 1-3/4 | 1-1/16 |
| 1-1/4 | 1.065 | 7 | 1-15/16 | 1-3/16 |
| 1-3/8 | 1.160 | 6 | 2-1/8 | 1-5/16 |
| 1-1/2 | 1.284 | 6 | 2-5/16 | 1-7/16 |
| 1-5/8 | 1.389 | 5-1/2 | 2-1/2 | 1-9/16 |
| 1-3/4 | 1.491 | 5 | 2-11/16 | 1-11/16 |
| 1-7/8 | 1.616 | 5 | 2-7/8 | 1-13/16 |
| 2 | 1.712 | 4-1/2 | 3-1/16 | 1-15/16 |
| 2-1/4 | 1.962 | 4-1/2 | 3-7/16 | 2-3/16 |
| 2-1/2 | 2.176 | 4 | 3-13/16 | 2-7/16 |
| 2-3/4 | 2.426 | 4 | 4-3/16 | 2-11/16 |
| 3 | 2.629 | 3-1/2 | 4-9/16 | 2-15/16 |
| 3-1/4 | 2.879 | 3-1/2 | 4-15/16 | 3-3/16 |
| 3-1/2 | 3.100 | 3-1/4 | 5-5/16 | 3-7/16 |
| 3-3/4 | 3.377 | 3 | 5-11/16 | 3-13/16 |
| 4 | 3.567 | 3 | 6-1/16 | 3-15/16 |
| 4-1/4 | 3.798 | 2-7/8 | 6-7/16 | 4-3/16 |
| 4-1/2 | 4.028 | 2-7/8 | 6-13/16 | 4-7/16 |
| 4-3/4 | 4.256 | 2-5/8 | 7-3/16 | 4-11/16 |
| 5 | 4.480 | 2-1/2 | 7-9/16 | 4-15/16 |
| 5-1/4 | 4.730 | 2-1/2 | 7-15/16 | 5-3/16 |
| 5-1/2 | 4.953 | 2-3/8 | 8-5/16 | 5-7/16 |
| 5-3/4 | 5.203 | 2-3/8 | 8-11/16 | 5-11/16 |
| 6 | 5.423 | 2-1/4 | 9-1/16 | 5-15/16 |
+------------+-------------+-----------+---------------+-----------+
Note that square heads are supposed to be always unfinished, hence there
is no standard for their sizes if finished.
The Franklin Institute standard dimensions for hexagon and square bolt
heads and nuts when the same are left unfinished or rough, as forged,
are as follows:--
+----------+-------------+-------------+---------------+-----------+
| | Diameter | Diameter | Short | Thickness |
| Bolt | across | across | diameter, | or |
| Diameter | corners, or | corners or | or diameter | depth for |
| in | long | long | across flats | square or |
| Inches. | diameter of | diameter of | for square or | hexagon |
| | hexagon | square | hexagon heads | heads. |
| | heads. | heads. | and nuts. | |
+----------+-------------+-------------+---------------+-----------+
| | Inch. | Inch. | Inch. | Inch. |
| 1/4 | 37/64 | 7/10 | 1/2 | 1/4 |
| 5/16 | 11/16 | 10/12 | 19/32 | 19/64 |
| 3/8 | 51/64 | 63/64 | 11/16 | 11/32 |
| 7/16 | 9/10 | 1-7/64 | 25/32 | 25/64 |
| 1/2 | 1 | 1-15/64 | 7/8 | 7/16 |
| 9/16 | 1-1/8 | 1-23/64 | 31/32 | 31/64 |
| 5/8 | 1-7/32 | 1-1/2 | 1-1/16 | 17/32 |
| 3/4 | 1-7/16 | 1-49/64 | 1-1/4 | 5/8 |
| 7/8 | 1-21/32 | 2-1/32 | 1-7/16 | 23/32 |
| 1 | 1-7/8 | 2-19/64 | 1-5/8 | 13/16 |
| 1-1/8 | 2-2/32 | 2-9/16 | 1-13/16 | 29/32 |
| 1-1/4 | 2-5/16 | 2-53/64 | 2 | 1 |
| 1-3/8 | 2-17/32 | 3-3/32 | 2-3/16 | 1-3/32 |
| 1-1/2 | 2-3/4 | 3-23/64 | 2-3/8 | 1-3/16 |
| 1-5/8 | 2-31/32 | 3-5/8 | 2-9/16 | 1-9/32 |
| 1-3/4 | 3-3/16 | 3-57/64 | 2-3/4 | 1-3/8 |
| 1-7/8 | 3-13/32 | 4-5/32 | 2-15/16 | 1-15/32 |
| 2 | 3-5/8 | 4-27/64 | 3-1/8 | 1-9/16 |
| 2-1/4 | 4-1/16 | 4-61/64 | 3-1/2 | 1-3/4 |
| 2-1/2 | 4-1/2 | 5-31/64 | 3-7/8 | 1-15/16 |
| 2-3/4 | 4-29/32 | 6 | 4-1/4 | 2-1/8 |
| 3 | 5-3/8 | 6-17/32 | 4-5/8 | 2-5/16 |
| 3-1/4 | 5-13/16 | 7-1/16 | 5 | 2-1/2 |
| 3-1/2 | 6-7/64 | 7-39/64 | 5-3/8 | 2-11/16 |
| 3-3/4 | 6-21/32 | 8-1/8 | 5-3/4 | 2-7/8 |
| 4 | 7-3/32 | 8-41/64 | 6-1/8 | 3-1/16 |
| 4-1/4 | 7-9/16 | 9-3/16 | 6-1/2 | 3-1/4 |
| 4-1/2 | 7-31/32 | 9-3/4 | 6-7/8 | 3-7/16 |
| 4-3/4 | 8-13/32 | 10-1/4 | 7-1/4 | 3-5/8 |
| 5 | 8-27/32 | 10-49/64 | 7-5/8 | 3-13/16 |
| 5-1/4 | 9-9/32 | 11-23/64 | 8 | 4 |
| 5-1/2 | 9-23/32 | 11-7/8 | 8-3/8 | 4-3/16 |
| 5-3/4 | 10-5/32 | 12-3/8 | 8-3/4 | 4-3/8 |
| 6 | 10-19/32 | 12-15/16 | 9-1/8 | 4-9/16 |
+----------+-------------+-------------+---------------+-----------+
The depth or thickness of both the hexagon and square nuts when left
rough or unfinished is, according to the above standard, equal to the
diameter of the bolt.
The following are the sizes of finished bolts and nuts according to the
present Whitworth Standard. The exact sizes are given in decimals, and
the nearest approximate sizes in sixty-fourths of an inch:--
+-------------+------------------------+----------------------+
| Diameter of | Width of nuts across | Height of bolt |
| bolts. | flats. | heads. |
+-------------+----------+-------------+--------+-------------+
| 1/8 | .338 | 21/64 _f_ | .1093 | 7/64 |
| 3/16 | .448 | 29/64 _b_ | .1640 | 5/32 |
| 1/4 | .525 | 33/64 _f_ | .2187 | 7/32 |
| 5/16 | .6014 | 19/32 _f_ | .2734 | 17/64 |
| 3/8 | .7094 | 45/64 _f_ | .3281 | 21/64 |
| 7/16 | .8204 | 53/64 _b_ | .3828 | 3/8 _f_ |
| 1/2 | .9191 | 29/32 _b_ | .4375 | 7/16 |
| 9/16 | 1.011 | 1-1/64 _b_ | .4921 | 31/64 _f_ |
| 5/8 | 1.101 | 1-3/32 _f_ | .5468 | 35/64 |
| 11/16 | 1.2011 | 1-13/64 _b_ | .6015 | 19/32 _f_ |
| 3/4 | 1.3012 | 1-19/64 _f_ | .6562 | 21/32 |
| 13/16 | 1.39 | 1-25/64 _b_ | .7109 | 45/64 _f_ |
| 7/8 | 1.4788 | 1-31/64 _b_ | .7656 | 49/64 |
| 15/16 | 1.5745 | 1-37/64 _b_ | .8203 | 13/16 _f_ |
| 1 | 1.6701 | 1-43/64 _b_ | .875 | 7/8 |
| 1-1/8 | 1.8605 | 1-55/64 _f_ | .9843 | 63/64 |
| 1-1/4 | 2.0483 | 2-3/64 _f_ | 1.0937 | 1-3/32 |
| 1-3/8 | 2.2146 | 2-7/32 _b_ | 1.2031 | 1-13/64 |
| 1-1/2 | 2.4134 | 2-13/32 _f_ | 1.3125 | 1-5/16 |
| 1-5/8 | 2.5763 | 2-37/64 _b_ | 1.4128 | 1-27/64 |
| 1-3/4 | 2.7578 | 2-3/4 _f_ | 1.5312 | 1-17/32 |
| 1-7/8 | 3.0183 | 3-1/16 _f_ | 1.6406 | 1-41/64 |
| 2 | 3.1491 | 3-5/32 _b_ | 1.75 | 1-3/4 |
| 2-1/8 | 3.337 | 3-11/32 _b_ | 1.8523 | 1-55/64 |
| 2-1/4 | 3.546 | 3-35/64 _b_ | 1.9687 | 1-31/32 |
| 2-3/8 | 3.75 | 3-3/4 | 2.0781 | 2-5/64 |
| 2-1/2 | 3.894 | 3-57/64 _f_ | 2.1875 | 2-3/16 |
| 2-5/8 | 4.049 | 4-3/64 _f_ | 2.2968 | 2-19/64 |
| 2-3/4 | 4.181 | 4-3/16 _b_ | 2.4062 | 2-13/32 |
| 2-7/8 | 4.3456 | 4-11/32 _f_ | 2.5156 | 2-33/64 |
| 3 | 4.531 | 4-17/32 _b_ | 2.625 | 2-5/8 |
+-------------+----------+-------------+--------+-------------+
The thickness of the nuts is in every case the same as the diameter of
the bolts: _f_ = full, _b_ = bare.
When bolts screw directly into the work instead of passing through it
and receiving a nut, they come under the head of either tap bolts, set
screws, cap screws, or machine screws. A tap bolt is one in which the
full length of the stem or body is threaded, and differs from a set
screw, which is similarly threaded, in the respect that in a set screw
the head is square and its diameter is the same as the square bar of
steel or iron (as the case may be) from which the screw was made, while
in the tap bolt the head is larger in diameter than the bar it was made
from. Furthermore a tap bolt may have a hexagon head, which is usually
left unfinished unless ordered to be finished, as is also the case with
set screws.
Cap screws are made with heads either hexagon, square, or round, and
also with a square head and round collar, as in Fig. 386, the square
heads being of larger diameter than the iron from which they were made.
When the heads of cap screws are finished they are designated as "milled
heads."
[Illustration: Fig. 386.]
[Illustration: Fig. 387.]
A machine screw is a small screw, such as in Fig. 387, the diameter of
the body being made to the Birmingham wire gauge, the heads being formed
by upsetting the wire of which they are made. They have saw slots S for
a screw driver, the threads having special pitches, which are given
hereafter. The forms of the heads are as in Fig. 387, A being termed a
Fillister, B a countersink, and C a round head. The difference between a
Fillister head of a machine screw and the same form of head in a cap
screw is that the former is upset cold, and the latter is either forged
or cut out of the solid metal.
When the end of a screw abuts against the work to secure it, it is
termed a set screw. The ordinary form of set screw is shown in Fig. 389,
the head being square and either black or polished as may be required.
The ends of the set screws of commerce, that is to say, that are kept on
sale, are usually either pointed as at A, Fig. 388, slightly bevelled as
at B, or cupped as at D. If left flat or only slightly bevelled as at B,
they are liable, if of steel and not hardened, or if of iron and
case-hardened only, to bulge out as at C. This prevents them from
slacking back easily or prevents removal if necessary, and even though
of hardened steel they do not grip very firmly. On this account their
points are sometimes made conical, as at A. This form, however,
possesses a disadvantage when applied to a piece of work that requires
accurate adjustment for position, inasmuch as it makes a conical
indentation in the work, and unless the point be moved sufficiently to
clear this indentation the point will fall back into it; hence the
conical point is not desirable when the piece may require temporary
fixture to find the adjustment before being finally screwed home. For
these reasons the best form of set screw end is shown at D, the outside
of the end being chamfered off and the inside being cupped, as denoted
by the dotted lines. This form cuts a ring in the work, but will hold
sufficiently for purposes of adjustment without being screwed home
firmly.
In some cases the end of the set screw is tapped through the enveloping
piece (as a hub) and its end projects into a plain hole in the internal
piece of the work, and in this case the end of the thread is turned off
for a distance of two or three threads, as at A in Fig. 390. Similarly,
when the head of the screw is to act or bear upon the work, the thread
may be turned off as at B in the figure.
When a bolt has no head, but is intended to screw into the work at one
end, and receive a nut at the other, it is termed a stud or standing
bolt. The simplest form of standing bolt is that in which it is parallel
from end to end with a thread at each end, and an unthreaded part in the
middle, but since standing bolts or studs require to remain fixed in the
work, it is necessary to screw them tightly into their places, and
therefore firmly home. This induces the difficulty that some studs may
screw a trifle farther into the work than others, so that some of the
stud ends may project farther through the nuts than others, giving an
appearance that the studs have been made of different lengths. The
causes of this may be slight variations in the tapping of the holes and
the threading of the studs. If those that appear longest are taken out
and reduced to the lengths of the others, it will be found sometimes
that the stud on the second insertion will pass farther into the work
than at the first, and the stud will project less through the nut than
the others. To avoid this those protruding most may be worked backward
and forward with the wrench and thus induced to screw home to the
required distance, but it is better to provide to the stud a shoulder
against which it may screw firmly home; thus in Fig. 391 is a stud,
whose end A is to screw into the work, part B is to enter the hole in
the work (the thread in the hole being cut away at the mouth to receive
B). In this case the shoulder between B and C screwing firmly against
the face of the work, all the studs being made of equal length from this
shoulder to end E, then the thickness of the flange or work secured by
the nut being equal, the nuts will pass an equal distance on end D, and
E will project equally through all the nuts. The length of the plain
part C is always made slightly less than the thickness of the flange or
foot of the work to be bolted up, so that the nut shall not meet C
before gripping the flange surface.
There are, however, other considerations in determining the shape and
size of the parts A and C of studs.
Thus, suppose a stud to have been in place some time, the nut on end E
being screwed firmly home on the work, and perhaps somewhat corroded on
E. Then the wrench pressure applied to the nut will be in a direction to
unscrew the stud out of the work, and if there be less friction between
A and the thread in the work than there is between D and the thread in
the nut, the stud and not the nut will unscrew. It is for this purpose
that the end A requires firmly screwing into the work. But in the case
of much corrosion this is not always sufficient, and the thread A is
therefore sometimes made of a larger diameter than the thread at D. In
this case the question at once arises, What shall be the diameter of the
plain part C?
[Illustration: Fig. 388.]
[Illustration: Fig. 389.]
[Illustration: Fig. 390.]
[Illustration: Fig. 391.]
If it be left slightly larger than D, but the depth of the thread less
than A, then it may be held sufficiently firmly by the fit of the
threads (without the aid of screwing against a shoulder) to prevent
unscrewing when releasing the nut, and may be screwed within the work
until its end projects the required distance; thus all the studs may
project an equal distance, but there will be the disadvantage that when
the studs require removing and are corroded the plain part is apt to
twist off, leaving the end A plugging the hole. The plain part C may be
left of same diameter as A, both being larger than D; but in this case
the difficulty of having all the studs project equally when screwed
home, as previously mentioned, is induced; hence C may be larger than A,
and a shoulder left at B, as in the figure; this would afford excellent
facility for unscrewing the stud to remove it, as well as insuring equal
projection of E. The best method of all is, so far as quality goes, to
make the plain part C square, as in Fig. 392, which is an English
practice, the square affording a shoulder to screw up against and secure
an equal projection while serving to receive a wrench to put in or
remove the stud. In this case the holes in the flange or piece bolted up
being squared, the stud cannot in any case unscrew with the nut. The
objection to this squared stud is that the studs cannot be made from
round bar iron, and are therefore not so easily made, and that the
squaring of the holes in the flange or part of the work supported by the
stud is again extra work, and for these reasons studs with square
instead of cylindrical mid-sections have not found favor in the United
States.
[Illustration: Fig. 392.]
[Illustration: Fig. 393.]
An excellent method of preventing the stud from unscrewing with the nut
is to make the end A longer than the nut end, as in Fig. 393, so that
its threads will have more friction; and this has the further advantage
that in cast iron it serves also to make the strength of the thread
equal to that of the stud. As the faces of the nuts are apt when screwed
home to score or mark the face of the work, it adds to the neatness of
the appearance to use a washer W beneath the nut, which distributes the
pressure over a greater area of work surface.
In some practice the ends A of studs are threaded taper, which insures
that they shall fit tight and enables their more easy extraction.
[Illustration: Fig. 394.]
An excellent tool for inserting studs of this kind to the proper
distance is shown in Fig. 394. It consists of a square body _a_ threaded
to receive the stud whose end is shown at _c_. The upper end is threaded
to receive an adjusting screw _b_, which is screwed in so that its end
_d_ meets the end _c_ of the stud. It is obvious that _b_ may be so
adjusted that when _a_ is operated by a wrench applied to its body until
its end face meets the work and the stud is inserted to the proper
depth, all subsequent studs may be put into the same depth.
[Illustration: Fig. 395.]
When the work pivots upon a stem, as in Fig. 395, the bolt is termed a
standing pin, and as in such cases the stem requires to stand firm and
true it is usual to provide the pin with a collar, as shown in the
figure, and to secure the pivoted piece in place with a washer and a
taper pin because nuts are liable to loosen back of themselves.
Furthermore, a pin and washer admit of more speedy disconnection than a
nut does, and also give a more delicate adjustment for end fit.
In drilling the tapping holes for standing bolts, it is the practice
with some to drill the holes in cast iron of such a size that the tap
will cut three-quarters only of a full thread, the claim being that it
is as strong as a full thread. The difference in strength between a
three-quarter and a full thread in cast iron is no doubt practically
very small indeed, while the process of tapping is very much easier for
the three-quarter full thread, because the tap may, in that case, be
wound continuously forward without backing it at every quarter or half
revolution, as would otherwise be necessary, in order to give the oil
access to the cutting edges of the tap--and oil should always be used in
the process of tapping (even though on cast iron it causes the cuttings
to clog in the flutes of the tap, necessitating in many cases that the
tap be once or twice during the operation taken out, and the cuttings
removed) because the oil preserves the cutting edges of the tap teeth
from undue abrasion, and, therefore, from unnecessarily rapid dulling.
With a tap having ordinarily wide and deep flutes, and used upon a hole
but little deeper than the diameter of the tap, the cuttings due to
making a three-quarter full thread will not more than fill the flutes of
the tap by the time its duty is performed. We have also to consider that
with a three-quarter full thread it is much easier to extract the
standing bolt when it is necessary to do so, so that all things
considered it is permissible to have such a thread, providing the
tapping hole does not pass through into a cylinder or chamber requiring
to be kept steam-tight, for in that case the bolt would be almost sure
to leak. As a preventive against such leakage, the threads are sometimes
cut upon the standing bolts without having a terminal groove, and are
then screwed in as far as they will go; the termination of the thread
upon the standing bolt at the standing or short end being relied upon to
jam into and close up the thread in the hole. A great objection to this,
however, is the fact that the bolts are liable to screw into the holes
to unequal depths, so that the outer ends will not project an equal
distance through the nuts, and this has a bad appearance upon fine work.
It is better, then, in such a case, to tap the holes a full thread, the
extra trouble involved in the tapping being to some extent compensated
for in the fact that a smaller hole, which can be more quickly drilled,
is required for the full than for the three-quarter thread.
The depth of the tapping hole should be made if possible equal to one
and a half times the diameter of the tap, so that in case the hole
bottoms and the tap cannot pass through, the taper, and what is called
in England the second, and in the United States the plug tap, will
finish the thread deep enough without employing a third tap, for the
labor employed in drilling the hole deeper is less than that necessary
to the employment of a third tap. If the hole passes through the work,
its depth need not, except for cast-iron holes, be greater than 1/8 inch
more than the diameter of the bolt thread, which amount of excess is
desirable so that in case the nut corrodes, the nut being as thick as
the diameter of the tap, and therefore an inch less than the depth of
the hole at the standing end, will be more likely to leave the stud
standing than to carry it with it when being unscrewed.
[Illustration: Fig. 396.]
When it is desirable to provide that bolts may be quickly removed, the
flanges may be furnished with slots, as in Fig. 396, so that the bolts
may be passed in from the outside, and in this case it is simply
necessary to slacken back the nut only. It is preferable, however, in
this case to have the bolt square under the head, as in Fig. 397, so as
to prevent the bolt from turning when screwing up or unscrewing the nut.
The bolt is squared at A, which fits easily into the flange. The
flanges, however, should in this case be of ample depth or thickness to
prevent their breakage, twice the depth of the nut being a common
proportion.
[Illustration: Fig. 397.]
[Illustration: Fig. 398.]
In cases where it is inconvenient for the bolt head to pass through the
work a [T] groove is employed, as in Fig. 398. In this case the bolt
head may fit easily at A B to the sides A B of the groove, so that while
the bolt head will slide freely along the groove, the head, being
square, cannot turn in the slot when the nut is screwed home. This,
however, is more efficiently attained when there is a square part
beneath the bolt head, as in Fig. 399, the square A of the bolt fitting
easily to the slot B of the groove.
[Illustration: Fig. 399.]
[Illustration: Fig. 400.]
When it is undesirable that the slots run out to the edge of the work
they may terminate in a recess, as at A in Fig. 400, which affords
ingress of the bolt head to the slot; or the bolt head may be formed as
in Fig. 401, the width A B of the bolt head passing easily through the
top A B of the slot, and the bolt head after its insertion being turned
in the direction of the arrow, which it is enabled to do by reason of
the rounded corners C D. In this case, also, there may be a square under
the head to prevent the bolt head from locking in the slot, but the
corners of the square must also be rounded as in Fig. 402.
[Illustration: Fig. 401.]
[Illustration: Fig. 402.]
The underneath or gripping surface of a bolt head should be hollow, as
at A in Fig. 403, rather than rounding as at B, because, if rounding,
the bolt will rotate with the nut when the latter grips the work
surface. It should also be true with the axial line of the bolt so as to
bear fairly upon the work without bending. The same remarks apply to the
bedding surface of the nut, because to whatever amount the face is out
of true it will bend the threaded end of the bolt, and this may be
sufficient to cause the bolt to break.
[Illustration: Fig. 403.]
In Fig. 404, for example, is shown a bolt and nut, neither of which bed
fair, being open at A and B respectively, and it is obvious that the
strain will tend to bend or break the bolt across the respective dotted
lines C, D. In the case of the nut there is sufficient elasticity in the
thread to allow of the nut forcing itself to a bed on the work, the bolt
bending; but in the case of the bolt head the bending is very apt to
break off the bolt short in the neck under the head. In a tap bolt where
the wrench is applied to the bolt head, the rotation, under severe
strain, of the head will usually cause it to break off in all cases
where the bolt is rigidly held, so that it cannot cant over and allow
the head to bed fair.
[Illustration: Fig. 404.]
A plain tap bolt should be turned up along its body, because if out of
true the hole it passes through must be made large enough to suit the
eccentricity of the bolt, or else a portion of the wrench pressure will
be expended in rotating the bolt in the hole instead of being expended
solely in screwing the bolt farther into the work.
It is obvious therefore, that if a tap bolt be left black the hole it
passes through must be sufficiently large to make full allowance for the
want of truth in the bolt. For the same reasons the holes for tapped
bolts require to be tapped very true.
Black studs possess an advantage (over tap bolts) in this respect,
inasmuch as that if the holes are not tapped quite straight the error
may be to some extent remedied by screwing them fully home and then
bending them by hammer blows.
Nuts are varied in form to suit the nature of the work. For ordinary
work, as upon bolts, their shape is usually made to conform to the shape
of the bolt head, but when the nut is exposed to view and the bolt head
hidden, the bolt end and the nut are (for finished work) finished while
the bolt heads are left black.
[Illustration: Fig. 405.]
[Illustration: Fig. 406.]
The most common form of hexagon nut is shown in Fig. 405, the upper edge
being chamfered off at an angle of about 40°. In some cases the lower
edge is cut away at the corners, as in Fig. 405 at A, the object being
to prevent the corners of the nut from leaving a circle of bearing marks
upon the work, but this gives an appearance at the corners that the nut
does not bed fair. Another shape used by some for the end faces of deep
nuts, that is to say, those whose depth exceeds the diameter of the
bolt, is shown in Fig. 406. Nuts of extra depth are used when, from the
nut being often tightened and released, the thread wear is increased,
and the extra thread length is to diminish the wear.
To avoid the difficulty of having some of the bolt ends project farther
through some nuts than others on a given piece of work, as is liable to
occur where the flanges to be bolted together are not turned on all four
radial faces, the form of nut shown in Fig. 407 is sometimes employed,
the thread in the nut extending beyond the bolt end.
[Illustration: Fig. 407.]
[Illustration: Fig. 408.]
As an example of the application of this nut, suppose a cylinder cover
to be held by bolts, then the cylinder flange not being turned on its
back face is usually of unequal thickness; hence to have the bolt ends
project equally through the nuts, each bolt would require to be made of
a length to suit a particular hole, and this would demand that each hole
and bolt be marked so that they may be replaced when taken out, without
trying them in their places. Another application of this nut is to make
a joint where the threads may be apt to leak. In this case the mouth of
the hole is recessed and coned at the edge; the nut is chamfered off
with a similar cone, and a washer W, Fig. 408, is placed beneath the nut
to compress and conform to the coned recess; thus with the aid of a
cement of some kind, as red or white lead (usually red lead), a tight
joint may be made independent of the fit of the threads.
When the hole through which the bolt passes is considerably larger in
diameter than the bolt, the flange nut shown in Fig. 409 is employed,
the flange covering the hole. A detached washer may be used for the same
purpose, providing that its hole fit the bolt and it be of a sufficient
thickness to withstand the pressure and not bend or sink into the hole.
[Illustration: Fig. 409.]
[Illustration: Fig. 410.]
Circular nuts are employed where, on account of their rotating at high
speed, it is necessary that they be balanced as nearly as possible so as
not to generate unbalanced centrifugal force. Fig. 410 represents a nut
of this kind: two diametrically opposite flat sides, as A, affording a
hold for the wrench. Other forms of circular nuts are shown in Figs. 411
and 412. These are employed where the nuts are not subject to great
strain, and where lightness is an object.
[Illustration: Fig. 411.]
[Illustration: Fig. 412.]
That in Fig. 411 is pierced around its circumference with cylindrical
holes, as A, B, C, to receive a round lever or rod or a wrench, such as
shown in Fig. 459.
That shown in Fig. 412 has slots instead of holes in its circumference,
and the form of its wrench is shown in Fig. 461.
When nuts are employed upon bolts in which the strain of the duty is
longitudinal to the bolt, and especially if the direction of motion is
periodically reversed, and also when a bolt is subject to shocks or
vibrations, a single nut is liable to become loose upon the bolt, and a
second nut, termed a check nut, jamb nut, or safety nut, becomes
necessary, because it is found that if two nuts be employed, as in Fig.
413, and the second nut be screwed firmly home against the first, they
are much less liable to come loose on the bolt.
Considerable difference of practice exists in relation to the thickness
of the two nuts when a check nut is employed. The first or ordinary nut
is screwed home, and the second or check nut is then screwed home. If
the second nut is screwed home as firmly as the first, it is obvious
that the strain will fall mainly on the second. If it be screwed home
more firmly than the first, the latter may be theoretically considered
to be relieved entirely of the strain, while if it be screwed less
firmly home, the first will be relieved to a proportionate degree of the
strain. It is usual to screw the second home with the same force as
applied to the first, and it would, therefore, appear that the first
nut, being relieved of strain, need not be so thick as the first, but it
is to be considered that, practically, the first nut will always have
some contact with the bolt threads, because from the imperfections in
the threads of ordinary bolts the area and the force of contact is not
usually the same nor in the same direction in both nuts, unless both
nuts were tapped with the same tap and at about the same time.
When, for example, a tap is put into the tapping machine, it is at its
normal temperature, and of a diameter due to that temperature, but as
its work proceeds its temperature increases, notwithstanding that it may
be freely supplied with oil, because the oil cannot, over the limited
area of the tap, carry off all the heat generated by the cutting of a
tap rotated at the speeds usually employed in practice. As a result of
this increase of temperature, we have a corresponding increase in the
diameter of the tap, and a variation in the diameter of the threads in
the nuts. The variation in the nuts, however, is less than that in the
tap diameter, because as the heated tap passes through the nut it
imparts some of its heat to the nut, causing it also to expand, and
hence to contract in cooling after it has been tapped, and, therefore,
when cold, to be of a diameter nearer to that of the tap.
Furthermore, as the tap becomes heated it expands in length, and its
pitch increases, hence here is another influence tending to cause the
pitches of the nut threads to vary, because although the temperature of
the tap when in constant use reaches a limit beyond which, so long as
its speed of rotation is constant, it never proceeds; yet, when the tap
is taken from the machine to remove the tapped nuts which have collected
on its shank, and it is cooled in the oil to prevent it from becoming
heated any more than necessary, the pitch as well as the diameter of the
tap is reduced nearer to its normal standard.
[Illustration: Fig. 413.]
[Illustration: Fig. 414.]
So far, then, as theoretical correctness, either of pitch or diameter in
nut threads, is concerned, it could only be attained (supposing that the
errors induced by hardening the tap could be eliminated) by employing
the taps at a speed of rotation sufficiently slow to give the oil time
to carry off all the heat generated by the cutting process. But this
would require a speed so comparatively slow as not to be commercially
practicable, unless followed by all manufacturers. Practically, however,
it may be considered that if two nuts be tapped by a tap that has become
warmed by use, they will be of the same diameter and pitch, and should,
therefore, have an equal area and nature of contact with the bolt
thread, supposing that the bolt thread itself is of equal and uniform
pitch. But the dies which cut the thread upon the bolt also become
heated and expanded in pitch. But if the temperature of the dies be the
same as that of the tap, the pitches on both the bolt and in the nut
will correspond, though neither may be theoretically true to the
designated standard.
In some machines for nut tapping the tap is submerged in oil, and thus
the error due to variations of temperature is practically eliminated,
though even in this case the temperature of the oil will gradually
increase, but not sufficiently to be of practical moment.
Let it now be noted that from the hardening process the taps shrink in
length and become of finer pitch, while the dies expand and become of
coarser pitch, and that this alone precludes the possibility of having
the nut threads fit perfectly to those on the bolt. It becomes apparent,
then, that only by cutting the threads in the lathe, and with a
single-toothed lathe tool that can be ground to correct angle after
hardening, can a bolt and nut be theoretically or accurately threaded.
Under skilful operation, however, both in the manufacture of the
screw-cutting tools and in their operation, a degree of accuracy can be
obtained in tapped nuts and die-threaded bolts that is sufficient with a
single nut for ordinary uses, but in situations in which the direction
of pressure on the nut is periodically reversed, or in which it is
subject to shocks or vibrations, the check nut becomes necessary, as
before stated.
An excellent method of preventing a nut from slackening back of itself
is shown in the safety nut in Fig. 414; it consists of a second nut
having a finer thread than the first one, so that the motion of the
first would in unscrewing exceed that of the second, hence the locking
is effectually secured.
[Illustration: Fig. 415.]
Work may be very securely fastened together by the employment of what
are called differential screws, the principle of whose action may be
explained with reference to Fig. 415, which is extracted from
"Mechanics." It represents a piston head and piston rod secured together
by means of a differential screw nut. The nut contains an internal
thread to screw on the rod, and an external one to screw into the piston
head, but the internal thread and that on the rod differ from the
external one, and that in the head by a certain amount, as say one tenth
of the pitch. The nut itself is furnished with a hexagonal head, and
when screwed into place draws the two parts together with the same power
as a screw having a pitch equal to the difference between the two
pitches.
[Illustration: Fig. 416.]
When putting the parts together the nut is first screwed upon the rod B.
The outside threads are then entered into the thread in the piston C,
and by means of a suitable wrench the nut is screwed into the proper
depth. As shown in the engraving, the nut goes on to the rod a couple of
threads before it is entered in the piston. The tightening then takes
place precisely as though the nut had a solid bearing on the piston and
a fine thread on the rod, the pitch of which is equal to the difference
between the pitches of the two threads. Fig. 416 shows its application
to the securing of a pump plunger upon the end of a piston-rod. In this
case, as the rod does not pass through the nut, the latter is provided
with a cap, which covers the end of the rod entirely.
[Illustration: Fig. 417.]
The principle of the differential screw may be employed to effect very
fine adjustments in place of using a very fine thread, which would soon
wear out or wear loose. Thus in Fig. 417 is shown the differential foot
screws employed to level astronomical instruments. C D is a foot of the
instrument to be levelled. It is threaded to receive screw A, which is
in turn threaded to receive the screw B, whose foot rests in the recess
or cup in E F. Suppose the pitch of screw A is 30 per inch, and that of
B is 40, and we have as follows. If A and B are turned together the foot
C D is moved the amount due to the pitch of A. If B is turned within a
the foot is moved the amount due to the pitch of B. If A is turned the
friction of the foot of B will hold B stationary, and the motion of C D
will equal the difference between the pitches of the threads of A and B.
Thus one revolution of A forward causes it to descend through C D 1/30
inch (its pitch), tending to raise C D 1/30 inch. But while doing this
it has screwed down upon the thread of B 1/40 inch (the pitch of B) and
this tends to lower C D, hence C D is moved 1/120 inch, because
1/30-1/40 = 1/120.
To cause a single nut to lock itself and dispense with the second or
jamb nut, various expedients have been employed. Thus in Fig. 418 is
shown a nut split on one side; after being threaded the split is closed
by hammer blows, appearing as shown in the detached nut. Upon screwing
the nut upon the bolt the latter forces the split nut open again by
thread pressure, and this pressure locks the nut. Now there will be
considerable elasticity in the nut, so that if the thread compresses on
its bearing area, this elasticity will take up the wear or compression
and still cause the threads to bind. Sometimes a set screw is added to
the split, as in Fig. 419, in which case the split need not be closed
with the hammer.
Another method is to split the nut across the end as shown in Fig. 420,
tapping the nut with the split open, then closing the split by hammer
blows. Here as before the nut would pass easily upon the bolt until the
bolt reached the split, when the subsequent threads would bind. In yet
another design, shown in Fig. 421, four splits are made across the end,
while the face of the nut is hollowed, so that a flat place near each
corner meets the work surface. The pressure induced on these corners by
screwing the nut home is relied on in this case to spring the nut,
causing the thread at the split end to close upon and grip the bolt
thread.
Check nuts are sometimes employed to lock in position a screw that is
screwed into the work, thus screws that require to be operated to effect
an adjustment of length (as in the case of eccentric rods and eccentric
straps) are supplied with a check nut, the object being to firmly lock
the screw in its adjusted position.
The following are forms of nuts employed to effect end adjustments of
length, or to prevent end motion in spindles or shafts that rotate in
bearings.
Fig. 422 shows two cylindrical check nuts, the inner one forming a
flange for the bearing. The objection to this is that in screwing up the
check nut the adjustment of the first nut is liable to become altered in
screwing up the second one, notwithstanding that the first be held by a
lever or wrench while the second is screwed home.
Another method is to insert a threaded feather in the adjustment nut and
having at its back a set screw to hold the nut in its adjusted position,
as in Fig. 423. In this case the protruding head of the set screw is
objectionable. In place of the feather the thread of the spindle may be
turned off and a simple set screw employed, as in Fig. 424; here again,
however, the projecting set screw head is objectionable. The grip of an
adjustment nut may be increased by splitting it and using a pinching or
binding screw, as in Fig. 425, in which case the bore of the thread is
closed by the screw, and the nut may be countersunk to obviate the
objection of a projecting head. For adjusting the length of rods or
spindles a split nut with binding screws, such as shown in Fig. 426, is
an excellent and substantial device. The bore is threaded with a
right-hand thread at one end and a left-hand one at the other, so that
by rotating the nut the rod is lengthened or shortened according to the
direction of rod rotation. Obviously a clamp nut of this class, but
intended to take up lost motion or effect end adjustment, may be formed
as in Fig. 427, but the projecting ears or screw are objectionable.
[Illustration: Fig. 429.]
Where there is sufficient length to admit it an adjustment nut, such as
in Fig. 428, is a substantial arrangement. The nut A is threaded on the
spindle and has a taper threaded split nut to receive the nut B. Nut A
effects the end adjustment by screwing upon the spindle, and is
additionally locked thereon by screwing B up the taper split nut,
causing it to close upon and grip the spindle.
[Illustration: Fig. 430.]
Lost motion in square threads and nuts may be taken up by forming the
nut in two halves, A and B, in Fig. 429 (A being shown in section) and
securing them together by the screws C C. The lost motion is taken up by
letting the two halves together by filing away the joint face D of
either half, causing the thread in the nut to bear against one side only
of the thread of the screw. The same end may be accomplished in nuts for
[V]-shaped threads by forming the nut either in two halves, as shown in
Fig. 430, in which A is a cap secured by screws B, the joint face C
being filed away to take up the lost motion. Or the nut may be in one
piece with the joint C left open, the screws B crossing the nut upon the
screw by pressure. In this case the nut closes upon the circumference of
the thread, taking up the wear by closing upon both sides of the thread
instead of on one side only as in the case of the square thread.
[Illustration: Fig. 431.]
[Illustration: Fig. 432.]
[Illustration: Fig. 433.]
In cases where nuts are placed under rapid vibration or motion they are
sometimes detained in their places by pins or cotters. The simplest form
of pin used for this purpose is the split pin, shown in Fig. 431. It is
made from half round wire and is parallel, and does not, therefore,
possess the capability of being tightened when the nut has become
loosened from wear. As the wire from which these pins are made is not
usually a full half circle the pins should, if the best results are to
be obtained, be filed to fit the hole, and in doing this, care should be
taken to have the pin bear fully in the direction of the split which is
longitudinal to the bolt, as shown in Fig. 432, where the pin is shown
with its ends opened out as is required to prevent the pin from coming
out. If the pin bears in a direction across the bolt as at A D, in Fig.
433, it will soon become loose.
[Illustration: _VOL. I._ =END-ADJUSTMENT AND LOCKING DEVICES.= _PLATE
IV_.
Fig. 418.
Fig. 419.
Fig. 420.
Fig. 421.
Fig. 422.
Fig. 423.
Fig. 424.
Fig. 425.
Fig. 426.
Fig. 427.
Fig. 428.]
Pins of this class are sometimes passed through the nut itself as well
as through the bolt; but when this is the case, there is the objection
that the nut cannot be screwed up to take up any wear, because in that
case the hole in the nut would not come fair with that in the bolt, and
the pin could not be inserted. When, therefore, such a pin passes
through the nut, lost motion must be taken up by placing an additional
or a thicker washer behind the nut. The efficiency of this pin as a
locking device is much increased by passing it through the nut, because
its bearing, and, therefore, wearing area, is increased, and the pin is
prevented from bending after the manner shown in Fig. 434, as it is apt
to do under excessive wear, with the result that the end pressure of the
nut almost shears or severs the pin close to the perimeter of the bolt.
[Illustration: Fig. 434.]
[Illustration: Fig. 435.]
To enable the pin to take up the wear, it is a good plan to file on it a
flat place, which must be parallel to the sides of the pin-head and
placed against the nut-face. The hole in the bolt is in this case made
to fall slightly under the nut, as in Fig. 435, so that the flat place
is necessary to enable the pin to enter. By filing the flat place taper,
the lost motion that may ensue from wear may be taken up by simply
driving the pin in farther.
[Illustration: Fig. 436.]
[Illustration: Fig. 437.]
In place of this class of split pin, solid taper pins are sometimes
used, but these, if employed in situations where they are subject to jar
and vibration, are apt sometimes to come loose, especially if they be
given much taper, because in that case they do not wedge so tightly in
the hole. But if a taper pin be made too nearly parallel, it will drive
through too easily, and has less capability to take up the play due to
wear. An ordinary degree of taper is about 5/8 inch per foot of length,
but in long pins having ample bearing area, 1/2 inch per foot of length
is ample. To prevent taper pins from coming loose from vibration, they
are sometimes forged split at the small end, as in Fig. 436, and opened
out at that end after the manner shown in Fig. 432. This forms a very
secure locking device, and one easily applied. The split ends are closed
by hammer blows to remove the pin, and it is found that such pins may be
opened and closed many times without breaking, even though made of cast
steel. The heads and ends are rounded so as to prevent them from
swelling from the hammer blows necessary to drive them in and out. When
a taper pin is passed through a nut and bolt, it simply serves as a
locking device to secure the nut in position, and the lost motion due to
wear must be taken up by the application of a washer beneath the nut, as
already described. If, however, the taper pin be applied outside the
nut, it may be made to take up the wear, by filing on it a flat place,
and locating the hole in the bolt so that it will fall partly beneath
the nut, as shown in Fig. 435. In this case, the nut may be screwed up
to take up the wear, and the pin by being driven farther in will still
bear against the nut and prevent its slacking back.
Another and excellent locking device for bolts or nuts, is the cotter
shown in Fig. 437, which is sometimes forged solid and sometimes split,
as in the figure. By being made taper from A to B, it will take up the
wear if driven farther in. Its width gives it strength in the direction
in which it acts to lock, the overhanging head is to drive it out by,
and the bevelled corner C is to enable its easy insertion, because if
left sharp it would be liable to catch against the edge of the
cotter-way and burr up. If made split, its ends are opened out after it
is inserted, as shown at D. When closing the ends of either split
cotters or split pins to extract them it is better to close one side
first and bend it over a trifle too much, so that, when closing the
other side, by the time the pin is straightened the two ends will be
closed together, and extraction becomes easy.
[Illustration: Fig. 438.]
A very safe method in the case of a single nut or bolt head is to
provide a separate plate, as in Fig. 438. The plate P is provided with
three sides, corresponding to the sides of the hexagon, as shown, and in
the middle of these sides are cut the notches A B C, so that by giving
the nut N one-twelfth of a turn its corners D E would be held by the
notches B C, S being a small screw to hold P. It is obvious that a
simple set screw passed through the walls of the nut would grip the bolt
thread and serve to hold the nut, but this would damage the bolt thread,
and, furthermore, that thread would under jar or vibration compress and
let the set screw come loose.
A better plan than this is to provide a thick washer beneath the nut and
let a set screw pass through the washer and grip the bolt, fastening or
setting up the set screw after the nut is screwed home. This, however,
makes the washer a gripping piece and in no wise serves to lock the nut.
In addition to the washer a pin may project through the radial face of
the washer and into the work surface, which will prevent, in connection
with the set screw, both the bolt and the washer from turning.
When a bolt has no thread but is secured by a taper pin, set screw,
cotter, or device other than a nut, it is termed a pin. So, likewise, a
cylindrical piece serving as a pivot, or to hold two pieces together and
having no head, is termed a pin.
The usual method of securing a pin is by a set screw or by a taper pin
and a washer; and since the term pin applying to both may lead to
misunderstanding, the term bolt will here be applied to the large and
the term pin to the small or securing pin only.
The object of pins and washers is to secure an exact degree of fit and
permit of rapid connection or disconnection. An application of a taper
pin and washer to a double eye is shown in Fig. 439. It is obvious, in
this case, the pin E will drive home until it fills the hole through the
bolt, and hence always to the same spot, so that the parts may be taken
apart and put together again rapidly, while the fit is self-adjusting,
providing that the pin fills the hole, bears upon the groove in the
washer, and is driven home, so that by first letting the pin bind the
washer W slightly too tight, and then filing the radial faces of the
joint to a proper fit (which will ease the bearing of the pin on the
washer), an exact degree of fit and great accuracy may be obtained,
whereas when a nut is used it is difficult to bring the nut to the exact
same position when screwing it home. When the joints are to be thus
fitted, it is a good plan to drill the pin-hole (through the bolt) so
that its centre falls coincident with the face of the washer; to then
file out the grooves in the washer not quite deep enough. The pin may
then be filed to fit the hole through the bolt, but left slightly too
large, so that it shall not pass quite far enough through the bolt. The
joint faces may then be filed true, and when finished, the parts may be
put together, and the groove through the washer and hole through the
bolt may be simultaneously finished by reaming with a taper reamer. This
will leave the job a good fit, with a full bearing, without much
trouble, the final reaming letting the taper pin pass to its proper
distance through the bolt.
[Illustration: Fig. 439.]
[Illustration: Fig. 440.]
Taper pins are sometimes employed to secure in position a bolt that
rotates, or one that requires locking in position, in situations in
which there is no room for the bolt end to project and receive a nut or
washer. Examples of these kinds are shown in section in Figs. 440 and
441. In 441, B is a stud pin, to rotate in the bore of A. C is a semi
circular groove in B, and P a taper pin entering one-half in the groove
C and one-half in B, thus preventing B from moving endwise in A, while
at the same time permitting its free rotation. In this case it is best
to fit B to its place, a fit tight enough to hold it firmly while the
pin-hole is drilled and reamed through A and B simultaneously, then B
can be put in the lathe, and the groove cut in to coincide with the
half-hole or groove caused in the pin by the drilling, and after the
groove is turned the stud pin may be eased to the required degree of
working fit. The process for Fig. 440 is precisely the same, except that
no groove turning or easing of the pin will be necessary, because the
pin being locked in position may be left a tight fit. If, however, it is
considered desirable to give the taper pin in Fig. 440 a little draft,
so that any looseness (that may occur to the pin or stud) from wear may
be taken up, then after the taper pin-hole has been drilled and reamed,
the pin or stud (D in the figure) may be taken out, and its taper
pin-hole _in the arm E_ may be filed out all the way through on one
side, as denoted by the dotted half-circle. This will give draft to the
pin and allow it to drive farther through and grip the pin as it wears
smaller.
If a bolt and nut fit too tightly in their threads the nut may be wound
back and forth upon the bolt under free lubrication, which will ease the
fit by wearing away or compressing that part of the thread surface that
is in contact. If this should not suffice we may generally ease a nut
that fits so tight that it cannot be screwed upon the bolt with an
ordinary wrench, by screwing the nut on a thread or two, then rest it on
an iron block, and lightly hammer its sides; it will loosen its fit, and
if continued, the nut may be made to pass down the bolt comparatively
easily. Now, in this operation, it is not that the nut has been
stretched, but that the points of contact on the threads have become
compressed and imbedded; we have, in other words, caused the shape of
each thread to conform nearer to that of the other than it is
practicable to make them, because of reasons explained in the remarks on
screw threads, and on taps.
[Illustration: Fig. 441.]
To remove nuts or bolts that have become corroded in their places, we
may adopt the following methods:--
If the nuts are so corroded that they will not unscrew with an ordinary
wrench, we may, if the standing bolts and the wrench are strong enough
to stand it, place a piece of gas or other pipe on the end of the
wrench, so as to get a longer leverage; and, while applying the power to
the wrench, we may strike the end face of the nut a few sharp blows with
the hammer, interposing a set chisel, if the nut is a small one, so as
to be sure to strike the nut in the proper place, and not rivet the
screw end. If the joint is made with tap bolts we may strike the bolt
heads with the hammer direct, using as before a light hammer and sharp
blows, which will, in a majority of cases, start the thread, after which
the wrench alone will usually suffice to unscrew it. If, however, this
is not effective, we should take a thick washer, large enough in its
bore to pass over the nut, and heat it to a yellow heat and place it
over the nut, and the nut heating more rapidly than the stud or standing
bolt, will be proportionately expanded and loosened; and, furthermore,
the iron becomes stronger by being heated, providing the temperature
does not exceed about 400°. If standing bolts or studs are employed on
the joint, the heating is still advantageous, for the increase of
strength more than compensates for the expansion. In this case the
heating, however, may be performed more slowly, so that the hole may
also become heated, and the bolt, therefore, not made a tighter fit by
its excessive expansion. So also, in taking out the standing bolts or
studs, heating them will often enable one to extract them without
breaking them off in the hole, which would necessitate drilling out the
broken piece or part. If, however, this should become necessary, we may
drill a hole a little smaller than the diameter of the bottom of the
bolt thread, and then drive into the hole a taper square reamer, as
shown in Fig. 442, in which W represents the work, R the square reamer,
and S the drilled screw end, and then, with a wrench applied to the
reamer, unscrew the bolt thread. If this plan fails there is no
alternative, after drilling the hole, but to take a round-nosed cape or
cross-cut chisel and cut out the screw as nearly as possible, then pick
out the thread at the entrance of the hole, and insert a plug tap to cut
out the remaining bolt thread.
To take out a standing bolt, take two nuts and screw them on the bolt
end; then hold the outer one still with a wrench and unscrew the inner
one tightly against it. We may then remove the wrench from the outer or
top nut, and unscrew the bolt by a wrench applied to the bottom or inner
one. If the thread of a standing bolt has become damaged or burred, we
can easily correct the evil by screwing a solid die or die nut down it,
applying a little oil to preserve the cutting edge of the nut. If it is
found impossible to take off a corroded nut without twisting off the
standing bolt, it is the better plan to sacrifice the nut in order to
save the bolt; and we may first hold a hammer beneath the nut, and take
a cold chisel, and holding it so that the cutting edge stands parallel
with the chamfered edge of the nut, and slanting it at an angle obtuse
to the direction in which the nut in unscrewing would travel, strike it
a few sharp blows, using a light hand-hammer; and this will often start
it, especially if the nut is heated as before directed. The hammer held
beneath the nut should be a heavy one, and should be pressed firmly
against the square or hexagon side of the nut, the object being to
support it, and thus prevent the standing bolt from bending or breaking,
as it would otherwise be very apt to do. If this plan succeeds, the nut
may, for rough work, be used over again, the burr raised by the chisel
head being hammered down to close it as much as possible before filing
it off. By holding the chisel precisely as directed, the seating of the
nut acts to support it, and thus aids the heavy hammer in its duty. If
this procedure fails we may cut the nut off, and thus preserve the bolt.
[Illustration: Fig. 442.]
To do this, we must use a cross-cut or cape chisel, and cut a groove
from the end face to the seating of the nut--a narrow groove will do,
and two may be cut if necessary; light cuts should be taken, and the
chisel should be ground at a keen angle, so that it will keep to its cut
when held at an angle, as nearly parallel to the centre line of the
length of the bolt as possible, in which case the force of the blows
delivered upon the chisel head will be in a direction not so liable to
bend the bolt. The groove or grooves should be cut down nearly to the
tops of the bolt threads, and then a wrench will unscrew the nut or else
cause it to open if one, and break in halves, if two grooves were cut.
After the nuts are all taken off, we may take a hammer and two or three
wedges, or chisels (according to the size of the joint), and drive them
an equal distance into the joint, striking one chisel first, and the
diametrically opposite one next, and going over all the wedges to keep
an equal strain upon each. If the joint resists this method, we may take
a hammer and strike blows between the standing bolts on the outside
face, interposing a block of hard wood to prevent damage to the face,
and holding the wood so that the hammer strikes it endwise of the grain;
and this will, in most cases, loosen the material of which the joint is
made, and break the joint. If, however, the joint, after repeated
trials, still resists, we may employ the hammer without the
interposition of the wood, using a copper or lead hammer, if one is at
hand, so as not to cause damage to the face of the work. To facilitate
the entrance of the wedges, grooves should be cut in the joint of one
face, their widths being about an inch, and their depth 1/16 inch.
WASHERS.--Washers are placed upon bolts for the following purposes.
First, to provide a smooth seating for the nut in the case of rough
castings. Second, to prevent the nut corners from marking and marring
the surface of finished work. Thirdly, to give a neat finish, and in
some cases to increase the bearing area of the nut and provide an
elastic cushion to prevent the nut from loosening. Washers are usually
of wrought iron, except in the case of brass nuts, when the washers also
are of brass. The standard sizes adopted by the manufacturers in the
United States for wrought iron washers is given in the following
table:--
MANUFACTURERS' STANDARD LIST.
Adopted by "The Association of Bolt and Nut Manufacturers of the United
States," at their meeting in New York, December 11th, 1872.
+-----------+---------+-------------+---------+
| Diameter. | Size of | Thickness | Size of |
| | Hole. | Wire Gauge. | Bolt. |
+-----------+---------+-------------+---------+
| 1/2 | 1/4 | No. 18 | 3/16 |
| 5/8 | 5/16 | " 16 | 1/4 |
| 3/4 | 5/16 | " 16 | 1/4 |
| 7/8 | 3/8 | " 16 | 5/16 |
| 1 | 7/16 | " 14 | 3/8 |
+-----------+---------+-------------+---------+
| 1-1/4 | 1/2 | " 14 | 7/16 |
| 1-3/8 | 9/16 | " 12 | 1/2 |
| 1-1/2 | 5/8 | " 12 | 9/16 |
+-----------+---------+-------------+---------+
| 1-3/4 | 11/16 | " 10 | 5/8 |
| 2 | 13/16 | " 10 | 3/4 |
+-----------+---------+-------------+---------+
| 2-1/4 | 15/16 | " 9 | 7/8 |
| 2-1/2 | 1-1/16 | " 9 | 1 |
| 2-3/4 | 1-1/4 | " 9 | 1-1/8 |
| 3 | 1-3/8 | " 9 | 1-1/4 |
| 3-1/2 | 1-1/2 | " 9 | 1-3/8 |
+-----------+---------+-------------+---------+
[Illustration: Fig. 443.]
[Illustration: Fig. 444.]
The various forms of wrenches employed to screw nuts home or to remove
them are represented in the following figures. Fig. 443 represents what
is known as a solid wrench, the width between the jaws a being an easy
fit to the nuts across the flats. The opening between the jaws being at
an angle to the body enables the wrench to be employed in a corner which
would be too confined to receive a wrench in which the handle stood in a
line with the jaws, because in that common form of wrench the position
of the jaws relative to the handle would be the same whether the wrench
be turned over or not, whereas with the jaws at an angle as in the
figure, the wrench may be applied to the nut, rotating it a certain
distance until its handle meet an abutting piece, flange, or other
obstruction, and then turned over and the jaw embracing the same two
sides of the nut the handle will be out of the way and may again operate
the nut.
[Illustration: Fig. 445.]
In some cases each end of the wrench is provided with jaws, those at one
end standing at the same angle but being on the opposite side of the
wrench.
The proper angle of the jaws to the centre line of the jaws may be
determined as follows:--The most desirable angle is that which will
enable the wrench to operate the nut with the least amount of
wrench-motion, an object that is of great importance in cases where an
opening has to be provided to admit the wrench to the nut, it being
desirable to leave this opening as small as possible so as to impair the
solidity of the work as little as practicable. For a hexagon nut this
angle may be shown to be one of 15°, as in Fig. 444.
[Illustration: Fig. 446.]
[Illustration: Fig. 447.]
In Fig. 445, for example, the wrench is shown in the position in which
it will just engage the nut, and at the first movement it will move the
nut to the position shown in Fig. 446. The wrench is then turned upside
down and placed upon the nut as in Fig. 447, and moved to the position
shown in Fig. 448, thus moving the nut the sixth part of a revolution,
and bringing it to a position corresponding to that in Fig. 445, except
that it has moved the nut around to a distance equal to one of its
sides. Since the wrench has been moved twice to move the nut this
distance, and since there are six sides, it will take twelve movements
to give the nut a full revolution, and, there being 360° in the circle,
each movement will move the nut 30°, or one-twelfth of 360°, and
one-half of this must be the angle of the gripping faces of the jaws to
the body of the wrench. The width of the opening in the work to admit
the wrench in such a case as in Fig. 445 must be not less than 30°, plus
the width of the wrench handle, at the radius of the outer corner of the
opening.
[Illustration: Fig. 448.]
In the case of wrenches for square nuts it is similarly obvious that
when the nut makes one-eighth of a revolution its sides will stand in
the same position to receive the wrench that the nut started from, and
in one-eighth of a revolution there are 45°. As the wrench is applied
twice to the same side of the nut, its jaws must stand at one half this
angle (or 22-1/2°) to the handle.
[Illustration: Fig. 449.]
When a nut is in such a position that it can only be operated upon from
the direction of and in a line with the axis of the bolt, a box wrench
such as shown in Fig. 449, is employed, the cavity at B fitting over
the bolt head; but if there is no room to admit the cross handle, a hub
or boss is employed instead, and this hub is pierced with four radial
holes into which the point of a round lever may be inserted to turn the
wrench. Adjustable wrenches that may be opened and closed to suit the
varying sizes of nuts are represented in Figs. 450, 451, and 452. In
Fig. 450, A is the fixed jaw solid upon the square or rectangular bar E,
and passing through the wooden handle D. B is a sliding jaw embracing E,
and operated thereon by the screw C, whose head is serrated to afford a
good finger grip. Various modifications of this form of wrench are made;
thus, for example, in Fig. 451 A is the jaw, B a slotted shank, C the
handle, all made in one piece. D is the movable jaw having a sleeve
extension D´, and recesses which permit the jaw to slide on the shank
longitudinally, but which prevent it from turning. The movable jaw is
run to and from the nut or bolt head to be turned, by means of the screw
G.
[Illustration: Fig. 450.]
[Illustration: Fig. 451.]
In another class of adjustable wrench the jaws slide one within the
other; thus in Fig. 452, the fixed jaw of the wrench forms a part of the
handle, and is hollowed out and slotted to receive the stem of the loose
jaw, which plays therein, being guided by ribs in the slot, which take
into grooves in the stem of the loose jaw. A screw with a milled head
and a grooved neck serves to propel the loose jaw, being stopped from
moving longitudinally by a partly open fixed collar on the fixed jaw,
which admits the screw and engages the grooved neck of the same. The
threaded extremity of the screw engages a female screw in the loose jaw,
and while the same are engaged the screw cannot be released from the
embrace of the fixed collar, as it requires considerable lateral
movement to accomplish this.
[Illustration: Fig. 452.]
[Illustration: Fig. 453.]
Adjustable wrenches are not suited for heavy work because the jaws are
liable to spring open under heavy pressure and thus cause damage to the
edges of finished nuts, and indeed these wrenches are not suitable for
ordinary use on finely finished work unless the duty be light.
Furthermore, the jaws being of larger size than the jaws of solid
wrenches, will not pass so readily into corners, as may be seen from the
[S] wrench shown in Fig. 453. In the adjustable [S] wrench in Fig. 454,
each half is provided with a groove at one end and a tongue in the
other, so that when put together the tongues are detained in the
grooves. To open or close the wrench a right and left-hand screw is
tapped into the wrench as shown, the head being knurled or milled to
afford increased finger-grip.
[Illustration: Fig. 454.]
[Illustration: Fig. 455.]
In all wrenches the location of contact and of pressure on the nut is
mainly at the corners of the nut, and unless the wrench be a very close
fit, the nut corners become damaged. A common method of avoiding this is
to interpose between the wrench jaw and the nut a piece of soft metal,
as copper, sheet zinc, or even a piece of leather. The jaws of the
wrench are also formed to receive babbitt metal linings which may be
renewed as often as required. To save the trouble of adjusting an
accurately fitting wrench to the nut, Professor Sweet forms the jaws as
in Fig. 455, so that when moved in one direction the jaws will pass
around the nut without gripping it, but when moved in the opposite
direction the jaws will grip the nut but not damage the corners, while
to change the direction of a nut rotation it is simply necessary to turn
the wrench over.
[Illustration: Fig. 456.]
Fig. 456 represents a key wrench which is suitable for nuts of very
large size. The sliding jaw J is held by the key or wedge S, which is
operated by hammer blows. The projection at R is necessary to give
sufficient bearing to the sliding jaw.
[Illustration: Fig. 457.]
For use in confined places where but little handle-motion is obtainable,
the ratchet wrench is employed, consisting of a lever affording journal
bearing to a socket that fits the head of the bolt. The socket is
provided with a ratchet or toothed wheel in which a catch or pawl
engages. Fig. 457 represents the Lowell Wrench Company's ratchet wrench
in which a lag screw socket is shown affixed. The socket is removable so
that various sizes and shapes may be used with the same wrench. Each
socket takes two sizes of square and one of hexagon heads or nuts. So
long as the screw runs easily, it can be turned by the wooden handle
more conveniently and faster than by the fingers, and independently of
the ratchet motion. When this can no longer be done with ease, the
twelve-inch handle is brought into use to turn the screw home.
For carriage bolts used in woodwork that turn with the nut
notwithstanding the square under the head (as they are apt to do from
decay of the wood or from the bolt gradually working loose) the form of
wrench shown in Fig. 458 is exceedingly useful, it is driven into the
wood by hammer blows at A. The bevelled edges cause the jaws to close
upon the head in addition to the handle-pressure.
[Illustration: Fig. 458.]
For circular nuts such as was shown in Fig. 411, the pin wrench or
spanner wrench shown in Fig. 459 is employed, the pin P fitting into the
holes in the nut circumference. The pin P should be parallel and slope
very slightly in the direction of A, so that it may not meet and bruise
the mouths of the pin-holes, A, B, C. The pin must, of course, pass
easily into the pin-holes, and would, if vertical, therefore meet the
edge of the hole at the top, bruising it and causing the wrench to
spring or slip out, as would be the case if the pin stood in the
direction of B.
[Illustration: Fig. 459.]
[Illustration: Fig. 460.]
It is obvious that to reverse the motion of the nut it is necessary to
reverse the position of the wrench, because the handle end must, to
enable the wrench to grip the work, travel in advance of the pin end. To
avoid this necessity Professor Sweet forms the wrench as in Fig. 460, in
which case it can operate on the nut in either direction without being
reversed.
When a circular nut has its circumference provided with notches as was
shown in Fig. 412 the wrench is provided with a rectangular piece as
shown in Fig. 461. This piece should slope in the direction of a for the
reasons already explained with reference to the cylindrical pin in Fig.
459. It is obvious, however, that this wrench also may be made upon
Professor Sweet's plan, in which case the pin should be straight.
[Illustration: Fig. 461.]
KEYS AND KEYWAYS.--Keys and keyways are employed for two purposes--for
locking permanently in a fixed position, and for locking and adjusting
at the same time. Keys that simply permanently lock are usually simply
embedded in the work, while those that adjust the parts and secure them
in their adjusted position usually pass entirely through the work. The
first are termed sunk keys and keyways, the latter adjusting keys and
through keyways.
[Illustration: Fig. 462.]
The usual forms of sunk keyways are as follows:--Fig. 462 represents the
common sunk key, the head _h_ forming a gib for use in extracting the
key, which is done by driving a wedge between the head and the hub of
the work.
[Illustration: Fig. 463.]
The flat key, sunk key, and feather shown in Fig. 463, are alike of
rectangular form, their differences being in their respective
thicknesses, which is varied to meet the form of key way which receives
them. The flat key beds upon a flat place upon the shaft, the sunk key
beds in a recess provided in the shaft, and the feather is fastened
permanently in position in the shaft. The hollow key is employed in
places where the wheel or pulley may require moving occasionally on the
shaft, and it is undesirable that the latter have any flat place upon it
or recess cut in it. The flat key is used where it is necessary to
secure the wheel more firmly without weakening the shaft by cutting a
keyway in it. The sunk key is that most commonly used; it is employed in
all cases where the strain upon the parts is great. The feather is used
in cases where the keyway extends along the shaft beyond the pulley or
wheel, the feather being fast in the wheel, and its protruding part a
working fit in the shaft keyway. This permits the wheel to be moved
along the shaft while being driven through the medium of the feather
along the keyway or spline. The heads of the taper keys are sometimes
provided with a set screw as in Fig. 464, which may be screwed in to
assist in extracting the key.
[Illustration: Fig. 464.]
[Illustration: Fig. 465.]
Fig. 465 represents an application of keys to a square shaft that has
not been planed true. The wheel is hung upon the shaft and four
temporary gib-headed keys are inserted in the spaces _a_, _a_, _a_, _a_,
in Fig. 465. (It may be mentioned here that similar heads are generally
forged upon keys to facilitate their withdrawal while fitting them to
their seats, the heads being cut off after the key is finally driven
home.) These sustain the wheel while the permanent keys, eight in
number, as shown in the figure at _b_, _b_, _b_, _b_, _b_, _b_, _b_,
_b_, are fitted, the wheel being rotated and tested for truth from a
fixed point, the fitting of the keys being made subservient to making
the wheel run true.
The proportions of sunk keys are thus given by the Manchester (England)
rule. The key is square in cross section and its width or depth is
obtained by subtracting 1/2 from the diameter of the shaft and dividing
the sum thus obtained by 8, and then adding to the subtrahend 1/4.
Example.--A shaft is 6 inches in diameter, what should be the cross
section dimensions of its key diameter of shaft?
6 - 1/2 = 5-1/2, 5-1/2 ÷ 8 = .687, and .687 + .25 = 937/1000 inch.
In general practice, however, the width of a key is made slightly
greater than its depth, and one-half its depth should be sunk in the
shaft.
[Illustration: Fig. 466.]
[Illustration: Fig. 467.]
Taper keys are tapered on their surfaces A and B in Fig. 466, and are
usually given 1/8-inch taper per foot of length. There is a tendency
either in a key or a set screw to force the hub out of true in the
direction of the arrow. It therefore causes the hub bore to grip the
shaft, and this gives a driving duty more efficient than the friction of
the key itself. But the sides also of the key being a sliding fit they
perform driving duty in the same manner as a feather which fits on the
sides A, D in Fig. 467, but are clear either top or bottom. In the
figure the feather is supposed to be fast in the hub and therefore free
at C, but were it fast in the shaft it would be free on the top face.
[Illustration: Fig. 468.]
[Illustration: Fig. 469.]
Fig. 468 represents a shaft held by a single set screw, the strain being
in the direction of the arrow, hence the driving duty is performed by
the end of the set screw and the opposite half circumference of the bore
and shaft. On account, however, of the small area of surface of the set
screw point the metal of the shaft is apt, under heavy duty and when the
direction of shaft rotation is periodically reversed, to compress (as
will also the set screw point unless it is of steel and hardened),
permitting the grip to become partly released no matter how tightly the
set screw be screwed home. On this account a taper key will under a
given amount of strain upon the hub perform more driving duty, because
the increased area of contact prevents compression. Furthermore, the
taper key will not become loose even though it suffer an equal amount of
compression. Suppose, for example, that a key be driven lightly to a
fair seating, then all the rest of the distance to which the key is
driven home causes the hub to stretch as it were, and even though the
metal of the key were to compress, the elasticity thus induced would
take up the compression, preventing the key from coming loose. It is
obvious, then, that set screws are suitable for light duty only, and
keys for either heavy or light duty. It is advanced by some authorities
that keys are more apt to cause a wheel or pulley to run out of true
than a set screw, but such is not the case, because, as shown in Figs.
466 and 468, both of them tend to throw the wheel out of true in one
direction; but a key may be made with proper fitting to cause a wheel to
run true that would not run true if held by a set screw, as is explained
in the directions for fitting keys given in examples in vice work.
If two set screws be used they should both be in the same line (parallel
to the shaft axis) or else at a right angle one to the other as in Fig.
469, so that the shaft and bore may drive by frictional contact on the
side opposite to the screws. Theoretically the contact of their surface
will be at a point only, but on account of the elasticity of the metal
the contact will spread around the bore in the arc of a circle, the
length of the arc depending upon the closeness of fit between the pulley
bore and the shaft. If the bore is a close fit to the shaft it is by
reason of the elasticity of the metal relieved of contact pressure on
the side on which the set screw or key is to an amount depending upon
the closeness of the bore fit, but this will not in a bore or driving
fit to the shaft be sufficient to set the wheel out of true.
If two set screws are placed diametrally opposite they will drive by the
contact of their ends only, and not by reason of their inducing
frictional contact between the bore and the shaft.
A very true method of securing a hub to a shaft is to bore it larger
than the shaft and to a taper of one inch to the foot. A bushing is then
bored to fit the shaft and turned to the same taper as the hub is
turned, but left, say, 1/100 inch larger in diameter and 1/4 or 3/8
longer. The bush is then cut into three pieces and these pieces are
driven in the same as keys, but care must be taken to drive them equally
to keep the hub true.
[Illustration: Fig. 470.]
[Illustration: Fig. 471.]
Feathers are used under the following conditions:--When the wheel driven
by a shaft requires to slide along the shaft during its rotation, in
which case the feather is fast in the wheel and the shaft is provided
with a keyway or spline (as it is termed when the sliding action takes
place), of the necessary length, the sides of the feather being a close
but sliding fit in the spline while fixed fast in the wheel.
It is obvious that the feather might extend along the shaft to the
requisite distance and the spline or keyway be made in the wheel: but in
this case the work is greater, because the shaft would still require
grooving to receive the feather, and the feather instead of being the
simple width of the wheel would require to be the width of the wheel
longer than the traverse of the wheel on the shaft. Nor would this
method be any more durable, because the keyway's bearing length would be
equal to the width of the wheel only.
When a feather is used to enable the easy movement of a wheel from one
position to another a set screw may be used to fix the wheel in position
through the medium of the feather as is shown in Fig. 470.
Through keys and keyways are employed to lock two pieces, and sometimes
to enable the taking up of the wear of the parts. Fig. 471 represents an
example in which the key is used to lock a taper shaft end into a socket
by means of a key passing through both of them. When the keyway is
completely filled by the key as in the figure it is termed a solid key
and keyway, indicating that there is no draft to the keyway. Fig. 472
represents a key and keyway having draft. One edge, A C, of the key
binds against the socket edges only, and the other edge E binds against
the edge B of the enveloped piece or plug, so that by driving in the key
with A hammer the two parts are forced together. The space or distance
between the edge D and the key, and between edges E and F, is termed the
draft. The amount of this draft is made equal to the taper of the key,
hence, when the key is driven in so that its head comes level with the
socket or work surface, the draft will be all taken up and the key will
fill the keyway.
[Illustration: Fig. 472.]
Draft is given to ensure all the strain of the key forcing the parts
together, to enable the key to be driven in to take up any wear and to
adjust movable parts, as straps, journal boxes or brasses, &c. When the
bore of the socket and the end of the rod are parallel, the end of the
rod F, Fig. 473, should key firmly against the end E of the socket,
while the end D of the socket should be clear of the shoulder on the
rod; otherwise instead of the key merely compressing the metal at F it
will exert a force tending to burst the end F from G of the rod,
furthermore, the area of contact at the shoulder D being small the metal
would be apt to compress and the key would soon come loose.
In some cases two keys are employed passing through a sleeve, the
arrangement being termed a coupling, or a butt coupling.
[Illustration: Fig. 473.]
The usual proportions for this class of key, when the rod ends and
socket boxes are parallel, is width of key equals diameter of socket
bore, thickness of key equals one-fourth its width, with a taper
edgeways of about 1/4 inch in 10 inches of length.
[Illustration: Fig. 474.]
[Illustration: Fig. 475.]
As the keys in through keyways often require to be driven in very tight,
and as the parts keyed together often remain a long time without being
taken apart and in some situations become rusted together, it is often a
difficult matter to get them apart. First, it is difficult to drive it
out because the blows swell the end of the key so that it cannot pass
through the keyway, and secondly, driving the socket off the plug of the
two parts keyed together often damages the socket and may bend the rod
to which it is keyed. Furthermore, as the diameter of the socket is
usually not more than half as much again as the diameter of the plug,
misdirected blows are apt to fall upon the rod instead of upon the
socket end and damage it. Hence, a piece of copper, of lead, or a block
of wood should always be placed against the socket end to receive the
hammer blows. To force a plug out of a socket, we may use reverse keys.
These are pieces formed as shown in Fig. 474. A, A and B, B are edge and
face views respectively of two pieces of metal, formed as shown, which
are inserted in the keyway as shown in Fig. 475, in which A is the plug
or taper end of a rod and B the socket, C is one and D the other of the
reverse keys, while E is a taper key inserted between them, B driving E
through the keyway, A and B are forced apart. The action of the reverse
keys is simply to reverse the direction of the draft in the keyway so
that the pressure due to driving E through the keyway is brought to bear
upon the rod end in the part that was previously the draft side of the
keyway, and in like manner upon the keyway in the socket on the side
that previously served as draft.
Reverse keys are especially serviceable to take off cross heads, piston
heads, keyed crank-pins, and parts that are keyed very firmly together.
[Illustration: Fig. 476.]
[Illustration: Fig. 477.]
Hubs are sometimes fastened to their shafts by pins passing through both
the hub and the shaft. These pieces may be made parallel or taper, but
the latter obviously secures the most firmly. If the pin is located as
in Fig. 476, its resisting strength is that due to its cross sectional
area at A and B. But if the pin be located as in Fig. 477 it secures the
hub more firmly, because it draws the bore (on the side opposite to the
pin) against the shaft, causing a certain amount of friction, and,
furthermore, the area resisting the pressure of the hub is increased,
and that pressure is to a certain degree in a crushing as well as a
shearing direction.
[Illustration: Fig. 478.]
If unturned pins are used and the holes are rough or drilled but not
reamed, it is better that two sides of the pin should be eased off with
a file or on the emery wheel, so that all the locking pressure of the
pin shall fall where it is the most important that it should--that is,
where it performs locking duty. This is shown in Fig. 478, the hole
being round and the pin being very slightly oval (not, of course, so
much as shown in the drawing), so that it will bind at A B, and just
escape touching at C, D, so that all the pressure of contact is in the
direction to bind the hub to the shaft.
CHAPTER VI.--THE LATHE.
The lathe may be justly termed the most important of all metal-cutting
machine tools. Not only on account of the rapidity of its execution
which is due to its cutting continuously while many others cut
intermittently, but also because of the great variety of the duty it
will perform to advantage. In the general operations of the lathe,
drilling, boring, reaming, and other processes corresponding to those
performed by the drilling machine, are executed, while many operations
usually performed by the planing machine, or planer as it is sometimes
termed, may be so efficiently performed by the lathe that it sometimes
becomes a matter of consideration whether the lathe or the planer is the
best machine to use for the purpose.
The forms of cutting tools employed in the planer, drilling machine,
shaping machine, and boring machine, are all to be found among lathe
tools, while the work-holding devices employed on lathe work include,
substantially, very nearly all those employed on all other machines and,
in addition, a great many that are peculiar to itself. In former times,
and in England even at the present day, an efficient turner (as a lathe
operator is termed), or lathe hand, is deemed capable of skilfully
operating a planer, boring machine, screw-cutting machine, drilling
machine, or any of the ordinary machine tools, whereas those who have
learned to operate any or all of those machine tools would prove
altogether inefficient if put to operate a lathe.
[Illustration: Fig. 479.]
In almost all the mechanic arts the lathe in some form or other is to be
found, varying in weight from the jewellers' lathe of a few pounds to
the pulley or fly-wheel lathe of the engine builder, weighing many tons.
The lathe is the oldest of machine tools and exists in a greater variety
of forms than any other machine tool. Fig. 479 represents a lathe of
primitive construction actually in use at the present day, and
concerning which the "Engineering" of London (England), says, "At the
Vienna Exhibition there were exhibited wood, glasses, bottles, vases,
&c., made by the Hucules, the remnant of an old Asiatic nation which had
settled at the time of the general migration of nations in the remotest
parts of Galicia, in the dense forests of the Carpathian Mountains. The
lathe they are using has been employed by them from time immemorial.
They make the cones _b_, _b_ (of maple) serve as centres, one being
fixed and the other movable (longitudinally). They rough out the work
with a hatchet, making one end _a_ cylindrical, to receive the rope for
giving rotary motion. The cross-bar _d_ is fastened to the trees so as
to form a rest for the cutting tool, which consists of a chisel." C, of
course, is the treadle, the lathe or pole being a sapling.
In other forms of ancient lathes a wooden frame was made to receive the
work-centres, and one of these centres was carried in a block capable of
adjustment along the frame to suit different lengths of work. In place
of a sapling a pole or lath was employed, and from this lath is probably
derived the term lathe.
It is obvious, however, that with such a lathe no cutting operation can
be performed while the work is rotating backwards, and further, that
during the period of rest of the cutting tool it is liable to move and
not meet the cut properly when the direction of work rotation is
reversed and cutting recommences, hence the operation is crude in the
extreme, being merely mentioned as a curiosity.
The various forms in which the lathe appears in ordinary machine shop
manipulation may be classified as follows:--
The _foot lathe_, signifying that the lathe is driven by foot.
The _hand lathe_, denoting that the cutting tools must be held in the
hands, there being no tool-carrying or feeding device on the lathe.
The _single-geared lathe_, signifying that it has no gear-wheels to
reduce the speed of rotation of the live spindle from that of the cone.
The _back-geared lathe_, in which gear-wheels at the back of the
headstock are employed to reduce the speed of the lathe.
The _self-acting lathe_, or _engine lathe_, implying that there is a
slide rest actuated automatically to traverse the tool to its cut or
feed.
The _screw-cutting lathe_, which is provided with a _lead_ screw, by
means of which other screws may be cut.
The _screw-cutting lathe with independent feed_, which denotes that the
lathe has two feed motions, one for cutting threads and another for
ordinary tool feeding; and
The _chucking lathe_, which implies that the lathe has a face plate of
larger diameter than usual, and that the bed is somewhat short, so as to
adapt it mainly to work held by being chucked, that is to say, held by
other means than between the lathe centres.
There are other special applications of the lathe, as the boring lathe,
the grinding lathe, the lathe for irregular forms, &c., &c.
This classification, however, merely indicates the nature of the lathe
with reference to the individual feature indicated in the title; thus,
although a foot lathe is one run by foot, yet it may be a single or
double gear (back-geared) lathe, or a hand or self-acting lathe, with
lead screw and independent feed motion.
Again, a hand lathe may have a hand slide rest, and in that case it may
also be a back-geared lathe, and a back-geared lathe may have a hand
slide rest or a self-acting feed motion or motions.
Fig. 480 represents a simple form of foot lathe. The office of the
shears or bed is to support the headstock and tailstock or tailblock,
and to hold them so that the axes of their respective spindles shall be
in line in whatever position the tailstock may be placed along the bed.
The duty of the headstock is to carry the live spindle, which is driven
by the cone, the latter being connected by the belt to the wheel upon
the crank shaft driven by the crank hook and the treadle, which are
pivoted by eyes W to the rod X, the operation of the treadle motion
being obvious. The work is shown to be carried between the live centre,
which is fitted to the live spindle, and the dead centre fitting into
the tail spindle, and as it has an arm at the end, it is shown to be
driven by a pin fixed in the face plate, this being the simplest method
of holding and driving work. The lathe is shown provided with a hand
tool rest, and in this case the cutting tools are supported upon the top
of the tool rest N, whose height may be adjusted to bring the tool edge
to the required height on the work by operating the set screw S, which
secures the stem of N in the bore of the rest.
To maintain the axes of the live and dead spindles in line, they are
fitted to a slide or guideway on the shears, the headstock being fixed
in position, while the tailstock is adjustable along the shears to suit
the length of the work.
To lock the tailstock in its adjusted position along the shears, it has
a bolt projecting down through the plate C, which bolt receives the hand
nut D. To secure the hand rest in position at any point along the
shears, it sets upon a plate A and receives a bolt whose head fits into
a [T]-shaped groove, and which, after passing through the plate P
receives the nut N, by which the rest is secured to the shears.
To adjust the end fit of the live spindle a bracket K receives an
adjusting screw L, whose coned end has a seat in the end J of the live
spindle, M being a check nut to secure L in its adjusted position.
[Illustration: Fig. 480.]
The sizes of lathes are designated in three ways, as follows:--First by
the _swing_ of the lathe and the total length of the bed, the term
_swing_ meaning the largest diameter of work that the lathe is capable
of revolving or swinging. The second is by the _height of the centres_
(from the nearest corner of the bed) and the length of the shears. The
height of the centres is obviously equal to half the swing of the lathe,
hence, for example, a lathe of 28-inch swing is the same size as one of
14-inch centres. The third method is by the swing or height of centres
and by the greatest length of work that can be held between the lathe
centres, which is equal to the length of the bed less the lengths of the
head and tailstock together.
The effective size of a lathe, however, may be measured in yet another
way, because since the hand rest or slide rest, as the case may be,
rests upon the shears or bed, therefore the full diameter of work that
the lathe will swing on the face plate cannot be held between the
centres on account of the height of the body of the hand rest or slide
rest above the shears.
Fig. 481 shows a hand lathe by F. E. Reed, of Worcester, Massachusetts,
the mechanism of the head and tail stock being shown by dotted lines.
The live spindle is hollow, so that if the work is to be made from a
piece of rod and held in any of the forms of chucks to be hereafter
described, it may be passed through the spindle, which saves cutting the
rod into short lengths. The front bearing of the headstock has two
brasses or boxes, A and B, set together by a cap C.
The rear bearing has also a bearing box, the lower half D being threaded
to receive an adjustment screw F and check nut G to adjust the end fit
of the spindle in its bearings. In place of grooved steps for the belt
the cone has flat ones to receive a flat belt.
The tail spindle is shown, in Fig. 482, to be operated by a screw H,
having journal bearing at I, and threaded into a nut fast in the tail
spindle at J. To hold the tail spindle firmly the end of the tail stock
is split, and the hand screw K may be screwed up to close the split and
cause the bore at L to clasp the tail spindle at that end.
To lock the tail stock to the shears the bolt M receives the lever N at
one end and at the other passes through the plate or clamp O, and
receives the nut P, so that the tail stock is gripped to or released
from the shears by operating N in the necessary direction. The hand
rest, Fig. 483, has a wheel W in place of a nut, which dispenses with
the use of a wrench.
What are termed bench lathes are those having very short legs, so that
they may for convenience be mounted on a bench or fastened to a second
frame, as shown in Fig. 484.
It is obvious that when work is turned by hand tools, the parallelism of
the work depends upon the amount of metal cut off at every part of its
length, which to obtain work of straight outline, whether parallel or
taper, involves a great deal of testing and considerable skill, and to
obviate these disadvantages various methods of carrying and accurately
guiding tools are employed. The simplest of these methods is by means of
a slide rest, such as shown in Fig. 485.
The tool T is carried in the tool post P, being secured therein by the
set screw shown, which at the same time locks the tool post to the upper
slider. This upper slider fits closely to the cross slide, and has a
nut projecting down into the slot shown in the same, and enveloping the
cross feed screw, whose handle is shown at C, so that operating C
traverses the upper slider on the cross slide and regulates the depth to
which the tool enters the work, or in other words, the depth of cut.
[Illustration: Fig. 481.]
The cross slide is formed on the top of the lower slider, which has
beneath a nut for the feed screw, whose handle is shown at A, hence
rotating A will cause the lower slider to traverse along the lower slide
and carry the tool along the work to its cut. To maintain the fit of the
sliders to the slides a slip of metal is inserted, as at _e_ and at _c_,
and these are set up by screws as at _f_, _f_ and _b_, _b_.
[Illustration: Fig. 482.]
The lower or feed traverse slide is pivoted to its base B, so that it
may be swung horizontally upon the same, and is provided with means to
secure it in its adjusted position, which is necessary to enable it to
turn taper as well as parallel work. To set this lower slide to a given
degree of angle it may be marked with a line and the edge of base B may
be divided into degrees as shown at D.
[Illustration: Fig. 483.]
When a piece of work is rotated between the lathe centres its axis of
rotation may be represented by an imaginary straight line and the lower
slides must, to obtain parallel work, be set parallel to this straight
line, while for taper work the slide rest must be set at an angle to it.
Now, in the form of slide rest shown in figure the cross slide is
carried by the lower or feed traverse slide, hence setting the lower
slide out of parallel with the work axis sets the cross slide out of a
right angle to the work axis, with the result that when a taper piece of
work is turned that has a collar or flange on it, the face of that
collar or flange will be turned not at a right angle to the work axis as
it should be, but at a right angle to the surface of the cone. Thus in
Fig. 486 A represents the axis of a piece of work, and the slide nut
having been set parallel to the work axis, the face C will be at a right
angle to the surface B or axis A, but with the slide nut set at an angle
to turn the cone D, the cross slide will be at an angle to A, hence the
face E will be undercut as shown, and at a right angle to the surface D
instead of to A A. This may be obviated by letting the cross slide be
the lower one as in the English form of slide rest shown in Fig. 487, in
which the upper slide is pivoted at its centre to the cross slide and
may be swung at an angle thereto and secured in its adjusted position by
the bolt at F. The projection at the bottom of the lower slider fits
between the shears of the lathe and holds the lower slider parallel with
the line of lathe centres, which causes the slide rest to cut all faces
at a sight angle to the work axis whether the feed traverse slide be set
to turn parallel or taper. In either case, however, there is nothing to
serve as a guide to set the feed traverse slide parallel to the work
axis, and this must, therefore, be done as near as may be by the eye and
by taking a cut and testing its parallelism.
[Illustration: Fig. 484.]
[Illustration: Fig. 485.]
[Illustration: Fig. 486.]
The rest may be set approximately true by bringing the operator's eye
into such a position that the edge _a_ _a_, Fig. 488, of the slide rest
come into line with the edge _b_ _b_ of the lathe shears, because that
edge is parallel to the line of lathe centres, and therefore to the work
axis.
Slide rests which have a slide for traversing the tool along the work to
its cut are but little used in the United States, being confined to very
small lathes, and then (except in the case of watchmakers' lathes whose
forms of slide rest will be shown hereafter), mainly as an expedient to
save expense in the cost of the lathe, it being preferred to feed the
tool for the feed traverse (as the motion of the cutting tool along the
work is termed) by mechanism operated from the live spindle and to be
hereafter described. In England, however, slide rests are much used, a
specimen construction being shown in Fig. 489. The end face A of the
rest comes flush so that the tool shall be carried firmly when taking
facing cuts in which solidity in the rest is of most importance. The
tool is held by two clamps instead of by single tool posts, because the
slide rest is employed to take heavy cuts, and when this is the case
with boring tools whose cutting edges stand far out from the slide rest,
a single tool post will not hold the tool sufficiently firm.
[Illustration: Fig. 487.]
[Illustration: Fig. 488.]
The gib _e_, Fig. 485, is sometimes placed on the front side of the
slider, as in the figure, and at others on the back; when it is placed
in the front the strain of the cut causes it to be compressed against
the slide, and there is a strain placed upon the screws _f_ which lifts
them up, whereas if placed on the other side the screws are relieved of
strain, save such as is caused by the setting of the gib up.
[Illustration: Fig. 489.]
On the other hand, the screws are easier to get at for adjustment if
placed in front. When the screws _b_ of the upper gib _c_, Fig. 485, are
on the right-hand side, as in that figure, there is considerable strain
on the screws when a boring tool is used to stand far out, as for boring
deep holes. On the other hand, however, the screws can be readily got at
in this position, and may therefore be screwed up tightly to lock the
upper slider firmly to the cross slide, which will be a great advantage
in boring and also in facing operations. But the screws must not in this
case have simple saw slot heads, such as shown on a larger scale in
Fig. 490, but should have square heads to receive a wrench, and if these
four screws are used, the two end ones may be set to adjust the slicing
fit of the slider, while the two middle ones may be used to set the
slider form on its slide when either facing or boring. The corners of
the gibs as well as those of the slider and slide may with advantage be
rounded so that they may not become bruised or burred, and, furthermore,
the slider is strengthened, and hence less liable to spring under the
pressure of a heavy cut.
[Illustration: Fig. 490.]
A slide rest for turning spherical work is shown in Fig. 491. A is the
lower slide way on which is traversed the slide B, upon which is fitted
the piece C, pivoted by the bolt D; there is provided upon C a
half-circle rack, shown at E, and into this rack gears a worm-wheel
having journal bearing on B, and operated by the handle F. As F is
rotated C would rotate on D as a centre of motion, hence the tool point
would move in an arc of a circle whose radius would depend upon the
distance of the tool point from D as denoted by J, which should be
coincident with the line of centres of the lathe.
[Illustration: Fig. 491.]
The slide G is constructed in the ordinary manner, but the way on which
it slides should be short, so as not to come into contact with the work.
If the base slide way A be capable of being traversed along the lathe
shears S S by a separate motion, then the upper slide way and slide may
be omitted, G and C being in one piece. It is to be noted in a rest of
this kind, however, that the tool must be for the roughing cut set too
far from D to an amount equal to about the depth of cut allowed to
finish with, and for the finishing cut to the radius of the finished
sphere in order to obtain a true sphere, because if B be operated so
that D does not stand directly coincident with the line of lathe
centres, the centre of motion, or of the circle described by the tool
point, will not be coincident with the centre on which the work rotates,
hence the work though running true would not be a true sphere but an
oval. This oval would be longest in the direction parallel with the line
of centres whenever the pivot D was past the line of centres, and an
oval of largest diameter at the middle or largest diameter turned by the
tool whenever the pivot D was on the handle H side of the line of
centres. To steady C it may be provided with a circular dovetail, as
shown at the end I, provision being made (by set screw or otherwise) for
locking C in a fixed position when using the rest for other than
spherical work.
To construct such a rest for turning curves or hollows whose outline
required to be an arc of a circle, the pivot D would require to be
directly beneath the tool post, which must in this case occupy a fixed
position. The radius of the arc would here again be determined by the
distance of the tool point from the centre of rotation of the pivot, or,
what would be the same thing, from that of the tool post.
Next to the hand slide rest lathe comes the self-acting or engine lathe.
These are usually provided with a feed motion for traversing the slide
rest in the direction of the length of the bed, and sometimes with a
self-acting cross feed, that is to say, a feed motion that will traverse
the tool to or from the line of centres and at a right angle to the
same.
In an engine lathe the parallelism or truth of the work depends upon the
parallelism of the line of centres with the shears of the lathe, and
therefore upon the truth of the shears or bed, and its alignment with
the cone spindle and tail spindle, while the truth of the radial faces
on the turned work depends upon the tool rest moving on the cross slide
at a true right angle to the line of centres.
[Illustration: Fig. 492.]
Fig. 492 represents an 18-inch engine (or self-acting) lathe designed by
and containing the patented improvements of S. W. Putnam, of the Putnam
Tool Company, of Fitchburg, Massachusetts. The lathe has an elevating
slide rest self-acting feed traverse and self-acting cross feed, both
feeds being operative in either direction. It has also a feed rod for
the ordinary tool feeding and a lead screw for screw-cutting purposes.
Fig. 493 represents a cross-sectional view of the shears beneath the
headstock; A A are the shears or bed having the raised [V]s marked V´
and V on which the headstock and tailstock rest, and V´´ and V´´´ on
which the carriage slides. A and A´ are the shears connected at
intervals by cross girts or webs B to stiffen them. C C are the bolts to
secure the headstock to the shears. D is a bracket bolted to A´ and
affording at E journal bearing for the spindle that operates the
independent feed spindle. E is split at _f_ and a piece of soft wood or
similar compressible material is inserted in the split. The bolt F is
operated to close the split, and, therefore, to adjust the bore E to
properly fit the journal of the feed spindle, and as similar means are
provided in various parts of the lathe to adjust the fits of journals
and bearings the advantages of the system may here be pointed out.
First, then, the fit of the bearing may be adjusted by simply operating
the screw, and, therefore, without either disconnecting the parts or
performing any fitting operation, as by filing. Secondly, the presence
of the wood prevents the ingress of dust, &c., which would cause the
bearings and journals to abrade; and, thirdly, the compression of the
wood causes a resistance and pressure on the adjusting screw thread,
which pressure serves to lock it and prevent it from loosening back of
itself, as such screws are otherwise apt to do.
[Illustration: Fig. 493.]
As the pressure of the tool cut falls mainly on the front side of the
carriage, and as the weight of the carriage itself is greatest on that
side, the wear is greatest; this is counteracted by forming the front
[V], marked V´´´ in figure, at a less acute angle, which gives it more
wearing area and causes the rest to lower less under a given amount of
wear.
The rib A´´ which is introduced to strengthen the shears against
torsional strains, extends the full length of the shears.
[Illustration: Fig. 494.]
Fig. 494 is a sectional side elevation of the headstock; A A´ represents
the headstock carrying the bearing boxes B and B´, which are capable of
bore closure so as to be made to accurately fit the spindle S by the
construction of the front bearing B, being more clearly shown in Fig.
495; B is of composition brass, its external diameter being coned to fit
the taper hole in the head; it is split through longitudinally, and is
threaded at each end to receive the ring nuts C and C´. If C be loosened
from contact with the radial face of A, then C´ may be screwed up,
drawing B through the coned hole in A, and, therefore, causing its bore
to close upon S.
At the other end of S, Fig. 496, C´´ is a ring nut for drawing the
journal box B´ through _a´_ to adjust the bore of B´ to fit the journal
of S, space to admit the passage of B´ being provided at _e_. D is a box
nut serving to withdraw B´ or to secure it firmly in its adjusted
position, and also to carry the end adjusting step E. F is a check nut
to lock E in its adjusted position.
The method of preventing end motion to S is more clearly shown in Fig.
496, in which _h_ is a steel washer enveloping S, having contact with
the radial face of B´ and secured in its adjusted position by the check
nuts _g_, hence it prevents S from moving forward to the right. _f_ is a
disk of raw hide let into E; the latter is threaded in D and is squared
at the end within F to admit of the application of a wrench, hence E may
be screwed in until it causes contact between the face of _f_ and the
end of S, thus preventing its motion to the left. By this construction
the whole adjustment laterally of S is made with the short length from
_h_ to _f_, hence any difference of expansion (under varying
temperature) between the spindle and the head A A´, or between the boxes
and the spindle S, has no effect towards impairing the end fit of S in
its bearings.
The method of adjusting the bearings to the spindle is as follows:--C´´
and C´ are slackened back by means of a "spanner wrench" inserted in the
holes provided for that purpose. C and D are then screwed up,
withdrawing B and B´ respectively, and leaving the journal fit too easy.
C´ is then screwed up until B is closed upon the spindle sufficiently
that the belt being loose on the cone pulley, the latter moved by the
hand placed upon the smallest step of the cone can just detect that
there is contact between the bore of B and the spindle, then, while
still moving the cone, turn C´ back very slowly and a very little, the
object being to relieve the bore of B from pressure against S. C may
then be screwed up, firmly locking B in its adjusted position. C´´ may
then be operated to adjust B´ in a similar manner, and D screwed up to
lock it in its adjusted position. Before, however, screwing up D it is
better to remove F and release E from pressure against _f_, adjusting
the end pressure of E after D has been screwed home against A´.
To prevent B and B´ from rotating in the head when the ring nuts are
operated, each is provided with a pin, _q_, grooves _c_ and _c´_
permitting of the lateral movement of B and B´ for adjustment. The boxes
B, B´ admit of being rotated in their sockets in A and A´ so as to
assume different positions, the pins _q_ and _q´_ being removable from
one to another of a series of holes in the boxes B, B´ when it is
desired to partly rotate those boxes. The tops of the boxes are provided
with oil holes, and the oil ways shown at _r_, _s_ being the oil groove
through the head and _a_ simply a stopper to prevent the ingress of
dust, &c.
[Illustration: Fig. 495.]
The thread on S at Z, Fig. 494, is to receive and drive the face plates,
chucks, &c., which are bored and threaded to fit over Z. To cause the
radial faces of such face plates or chucks to run true, there is
provided the plain cylindrical part _l_, to which the bore in the hub of
the face plate or chuck is an accurate fit when the radial face of that
hub meets the radial face _m_.
Referring again to Fig. 494, G´ is the pinion to drive the back gear
while G receives motion from the back-gear pinion. The object of the
back gear is to reduce the speed of rotation of S and to enable it to
drive a heavier cut, which is accomplished as follows:--G´ is secured
within the end K of the cone and is free to rotate with the cone upon S;
at the other end the cone is secured to M, which is free to rotate upon
S so far as its bore is concerned. G is fixed upon S and hence rotates
at all times with it; but G may be locked to or released from M as
follows:--
[Illustration: Fig. 496.]
In G is a radial slot through which passes a bolt I provided with a cap
nut H, in M is an annular groove J. When I is lifted its head passes
into a recess in M, then H is screwed up and G is locked to M. This is
the position of I when the back gear is not in use, the motion of the
cone being communicated to S through I. But if H be loosened and I be
moved inwards towards S, the head of I passes into the annular groove J,
and the cone is free to rotate upon S while the latter and G remain
stationary unless the back gear is put into operation. In this latter
case the pinion G´ rotating with the cone drives the large gear of the
back gear and the small pinion of the latter drives G, whose speed of
rotation is reduced by reason of the relative proportions of the gear
wheels.
In this case it is obvious that since the pulley rotates upon the
spindle it requires lubrication, which is accomplished through the oil
hole tubes L.
The means of giving motion to the feed spindle and lead screw are as
follows:--N, Fig. 494, is a pinion fast upon S and operating the gear O,
which is fast upon the spindle P, having journal bearing in a stem in A´
and also at G´´. P drives the three-stepped cone R, which is connected
by belt to a similar cone fast upon the independent feed spindle. The
seat for the driving gear of the change wheels for the lead screw is on
P at V. To provide ample bearing surface for P in A´ the bush or sleeve
shown is employed, but this sleeve also serves to pivot the swing frame
W which carries the studs for the change wheels that go between the
wheel on V and that on the lead screw; _x_ _y_ are simply oil holes to
lubricate P in its bearings.
To provide a wider range of tool feed than that obtainable by the steps
on the feed cones, as R, they are provided at their ends with seats for
change wheels, the swing frame W carrying the intermediate wheels for
transmitting motion from V to a similar seat on the cone on the feed
spindle.
Fig. 497 represents the tailstock (or tailblock as it is sometimes
termed), shown in section. A represents the base which slides upon the
raised [V]s on the bed and carries the upper part B, in which slides the
tail spindle C, which is operated longitudinally by the tail screw D,
having journal bearing in E, and threaded through the nut F which is
fast in C. The hand wheel G is for rotating D, whose thread operating in
the nut F, causes C to slide within B in a direction determined by the
direction of rotation of G. To lock C in its adjusted position the
handled nut H is employed in connection with the bolt I, which is shown
in dotted lines; C is split as shown by the dotted lines at _f_; J is
the dead centre fitting accurately into a conical hole in C. When it is
required to remove J from C the wheel G is operated to withdraw C
entirely within B, and the end _d_ of D meets the end _e_ of J and
forces J from the coned hole in C.
The method of securing the tailstock to the shears or releasing it from
the same is as follows. A vertical prolongation of B affords at B´´ a
bearing surface for the nut-handle L and washer M. K is a bolt threaded
into L passing through M, B´´ and N, the latter of which it carries. N
spans the shears beneath the two [V]s on which the tailstock slides.
Moving or rather partly rotating the handle L in the necessary direction
lifts K and causes N to rise, and grip the shears beneath, while the
pressure of M on B´´ causes B to grip A and the latter to grip the
raised [V]s on the shears. If L be rotated in the opposite direction it
will cause N to fall, leaving A free to slide along the shears. To
prevent N from partly rotating when free, its ends are shaped to fit
loosely between the shears as shown at _n_.
To give to N sufficient rise and fall to enable it to grip or fall
entirely free from the shears with the small amount of rotary motion
which the handle-lever L is enabled from its position to have, the
following device is provided. M is a washer interposed between L and
B´´. This washer has upon it steps of different thickness as shown at M
and _m_, the two thicknesses being formed by an incline as shown. The
face of L has, as shown, similar steps; now as shown in the cut the step
_l_ on lever L meets the steps _m_ of the washer, the handle having
receded to the limit of its motion. The bolt K then has fallen to the
amount due to unscrewing the threaded or nut end of L, and also to the
amount of the difference of thickness at M and at _m_ of the washer, the
plate N being clear of the lathe-shears. But suppose the handle L be
pulled towards the operator, then the surface _l_ passing from a thin
section on to a thick one as M of the washer, will lift the bolt K,
causing N to meet the under surface of the shears, and then the motion
of L continuing the pressure of the thread will bind or lock N to the
bed.
[Illustration: Fig. 497.]
The surface A´ in Fig. 497 affords a shelf or table whereon tools, &c.,
may be placed instead of lying on the lathe bed, where they may cause or
receive damage.
Fig. 498 represents an end view of the tailstock viewed from the dead
centre end, the same letters of reference applying to like parts that
are shown in Fig. 497. The split at _f_ is here shown to be filled with
a piece of soft wood which prevents the ingress of dust, &c. At _d_ is a
cup or receptacle for oil, _e_ being a stopper, having attached to it a
wire pin flattened and of barb shape at the end, the object being to
cause the wire to withdraw from the cup a drop of oil to lubricate the
dead centre and centre in the work. The proximity of _e_ to the dead
centre makes this a great convenience, while the device uses much less
oil than would be used by an oil can.
[Illustration: Fig. 498.]
The method of setting over the upper part B to enable the turning of the
diameter of work conical or taper instead of parallel is shown in Fig.
498: P and P´ are square-headed screws threaded into the walls of A and
meeting at their ends the surface of B´. In A there is at _a_ a wide
groove or way, and on B there is at _b_ a projection fitting into the
way _a_ so as to guide B when it slides across A, as it will when P is
unscrewed in A and P´ is screwed into A. This operation is termed
setting over the tailstock, and its effect is as follows:--Suppose it be
required to turn a piece of work of smaller diameter at the end which
runs on the dead centre, then, by operating the screw P towards the
front of the lathe (or to the left as shown in the cut) and screwing P´
farther into A, the end of P´ will meet the surface of B´, causing B´ to
move over, and the centre of the dead centre J (which is the axis of
rotation of the work at that end) will be nearer to the point of the
cutting tool. Or suppose the work requires to be turned a taper having
its largest diameter at the end running on the dead centre, then P´
would be unscrewed and P screwed farther into A, carrying B farther
towards the back of the lathe.
The [V] grooves Q and Q´ fit upon the inner raised [V]s shown at V, V´
in Fig. 499.
[Illustration: Fig. 499.]
Fig. 499 is a side view of the slide rest for holding and traversing the
cutting tool. A represents the carriage resting upon the raised [V]s
marked V´´ and V´´´ and prevented from lifting by its own weight, and in
front also by the gib _a_ secured to A by the bolt _b_ and having
contact at _c_ with the shears. A carries at _d_ a pivot for the cross
slide B and at _e_ a ball pivot for the cross slide elevating screw C.
This screw is threaded through the end of B so that by operating it that
end of B may be raised or lowered to adjust the height of the cutting
tool point to suit the work. To steady B there is provided (in addition
to the pivots at _d_) on A two lugs _f_, between the vertical surfaces
of which B is a close working fit. The upper surface of B is provided
with a [V]-slide-way _g_, to which is fitted the tool rest D (the
construction being more clearly shown in Fig. 500).
[Illustration: Fig. 500.]
The means for traversing D along the slide _g_ on B is as follows:--
A nut _i_ is secured to D by the screw bolt _j_, and threaded through
the nut _i_ is the cross-feed screw E, which has journal bearing in the
piece _k_, which is screwed into the end face of B; there is a collar on
E which meets the inner end of _k_, and the handle F being secured by
nut to that end of E its radial face forms a shoulder at _m_ which with
the collar prevents any end motion of E, so that when F is rotated E
rotates and winds through the nut _i_ which moves D along B.
An end view of A, B, and D is shown in Fig. 500, in which the letters of
reference correspond to those in Fig. 499. B´ and B´´ are the
projections that pass into A and receive the pivoting screws _d_ and
_d_. To adjust the fit and take up any wear that may ensue on the slide
_g_, on B and on the corresponding surface on D, the piece _n_ is
provided, being set up by the adjusting screws O.
To adjust the fit and take up the wear at the pivots _d_ they are made
slightly taper, fitting into correspondingly taper holes in B.
The dotted circle T´, represents a pinion fast upon the cross-feed screw
(E, Fig. 499); the similar circles T and S´´ also represent pinions, the
three composing a part of the method of providing an automatic or
self-acting cross feed or cross traverse to D by rotating it through a
gear-wheel motion derived from the rotation of the independent feed
spindle, as is described with reference to Fig. 501.
_m_ in Fig. 500 represents a cavity or pocket to receive wool, cotton or
other elastic or fibrous material to be saturated with oil and thus
lubricate the raised [V]s while keeping dirt from passing between the
rest and the [V]s. The shape of these pockets is such as to enable them
to hold the cotton with a slight degree of pressure against the slides,
thus insuring contact between them.
The mechanical devices for giving to the carriage a self-acting traverse
in either direction along the bed, so as to feed the tool automatically
to its cut, and for giving to the tool rest (D, Fig. 499) traverse
motion so as to feed the tool to or from the line of centres along the
cross slide, are shown in Fig. 501, which presents two views of the feed
table or apron. The lower view supposes the feed table to be detached
from the carriage and turned around so as to present a side elevation of
the mechanism. The upper view is a plan of the same with two pinions (N
and N´), omitted. A represents the part of the lathe carriage shown at A
in Fig. 500. It has two bolts _p_ and _p´_, which secure the apron G,
Fig. 501, to A. At H is the independent feed spindle or feed rod
operated by belt from the cone pulley R, Fig. 494, or by a gear on stud
P at V. H is carried in bearings fixed to each end of the lathe shears
or bed, both of these bearings being seen in Fig. 492. H is also
provided with a bearing fixed on the feed apron as seen in Fig. 501, and
is splined as shown at _h_. At I is a bracket fast upon the apron G and
affording journal bearing to J, which is a bevel pinion having a hub
which has journal bearing in the bracket I. The fit of the bearing to
the journal is here again adjusted by a split in the bearing with a
screw passing through the split and threaded in the lower half (similar
to the construction of D in Fig. 493); J is bored to receive H, and is
driven by means of a feather projecting into the spline _h_. When
therefore, the carriage A is moved it carries with it the apron G, and
this carries the bracket I holding the bevel pinion J, which is in gear
with the bevel-wheel K, and therefore operates it when H has rotary
motion. At the back of K, and in one piece with it, is a pinion K´, both
being carried upon the stud L; pivoted upon this same stud is a plate
lever M, carrying two pinions N and N´ in gear together, but N only is
in gear with K´, hence K´ drives N and N drives N´. Now in the position
shown neither N or N´ is in gear with the gear-wheel O, but either of
them may be placed in gear with it by means of the following
construction:--
At the upper end of M there is provided a handle stud M´ passing through
the slot M´´ in G. Screwing up this stud locks M fast by binding it
against the surface of G. Suppose, then, M´ to be unscrewed, then if it
be moved to the right in the slot M´´, N will be brought into gear with
O and the motion will be transmitted in the direction of the arrows, and
screwing up N would retain the gear in that position. But suppose that
instead of moving M´ to the right it be moved to the left, then N´ will
be brought into gear with O and the direction of rotation of O will be
reversed.
[Illustration: Fig. 501.]
Thus, then, O may be made to remain stationary or to rotate in either
direction according to the position of M´ in the slot M´´, and this
position may be regulated at will.
The gear O contains in its radial face a conical recess, and upon the
same stud or pin (P) upon which O is pivoted, there is fixed the disk
P´, which is in one piece with the pinion P´´; the edge of P´ is coned
to fit the recess in the wheel O, so that if the stud P is operated to
force the disk P´ into the coned recess in O the motion of wheel O will
be communicated to disk P´, by reason of the friction between their two
coned surfaces. Or if P be operated to force the coned edge of the disk
out of contact with the coned bore or recess in gear O, then O will
rotate while P´ and P´´ will remain stationary. Suppose the coned
surfaces to be brought (by operating _x_) into contact and P´ to rotate
with O, then P´´ being in gear with wheel Q will cause it to rotate. Now
Q is fast to the pinion Q´, hence it will also rotate, and being in
contact with the rack which is fixed along the shears of the lathe and a
section of which is shown in the cut, the whole feed table or apron will
be made to traverse along the lathe shears.
The direction in which this traverse will take place depends upon the
adjusted position of M´ in M´´, or in other words upon whether N or N´
be the pinion placed in gear with O. As shown in the cut neither of them
is in gear, and motion from H would be communicated to N and N´ and
would there cease; but if M´ be raised in the slot M´´, N would drive O,
and supposing P´ to be held to O, the motion of all the gears would be
as denoted by the arrows, and the lathe carriage A would traverse along
the lathe bed in the direction of arrow Q´´. But if N´ be made to drive
O all the motions would be in the opposite directions. The self-acting
feed motion thus described is obviously employed to feed the cutting
tool, being too slow in its operation for use to simply move the
carriage from one part of the lathe bed to another; means for this
purpose or for feeding the carriage and cutting tool by hand are
provided as follows:--R is a pinion in gear with Q and fast upon the
stud R´, which is operated by the handle R´´. The motion of R´´ passes
from R to Q and Q´ which is in gear with the rack. But Q´ being in gear
with P´´ the latter also rotates, motion ceasing at this point because
the cone on P´ is not in contact with the coned recess in O. When,
however, P´ and O are in contact and in motion, that motion is
transmitted to R´´, which cannot then be operated by hand.
It is often necessary when operating the cross feed to lock the carriage
upon the lathe bed so that it shall not move and alter the depth of the
tool-cut on the radial face of the work. One method of doing this is to
throw off the belt that operates the feed spindle H, place N in gear
with O and P´ in contact with O, so that the transverse feed motion will
be in action, and then pull by hand the cone pulley driving H, thus
feeding the tool to its necessary depth of cut. The objection to this
method, however, is that when the operator is at the end of the lathe,
operating the feed cone by hand he cannot see the tool and can but
guess how deep a cut he has put on. To overcome this difficulty a brake
is provided to the pinion R as follows:--
The brake whose handle is shown at V has a hub V´ enveloping the hub
R´´´ which affords journal bearing to the stud R´. In the bore of this
hub V´ is an eccentric groove, and in R´´´ is a pin projecting into the
eccentric groove and meeting at its other end the surface of the stud
R´. When, therefore, V is swung in the required direction (to the left
as presented in the cut), the cam groove in V´ forces _r_ inwards,
gripping it and preventing it from moving, and hence the movement of R
which also locks Q and Q´.
It remains now to describe the method of giving rotary motion to the
cross-feed screw E (Fig. 499) so as to enable it to self-act in either
direction. S is a lever pivoted upon the hub of O and carrying at one
end the pinion S´´, while at the other end is a stud S´ passing through
a slot in G. The pinion S´´ is in gear with O and would therefore
receive rotary motion from it and communicate such motion to pinion T,
which in turn imparts rotary motion to T´. Now T´ is fast upon the
cross-feed screw as shown in Fig. 499 and the cross-feed screw E in that
figure would by reason of the nut _i_ in figure cause the tool rest D to
traverse along the cross-slide in a direction depending upon the
direction of motion of T´, which may be governed as follows:--
If S´ be moved to the left S´´ will be out of gear with T and the
cross-feed screw may be operated by the handle (F, Fig. 499). If S´ be
in the position shown in cut and M´´ also in the position there shown
(Fig. 501), operating the feed screw by its handle would cause its
pinion T´ to operate T, S´´, and O; hence S´ should always be placed to
disconnect S´´ from T when the cross-feed screw is to be operated by
hand, and S´ operated to connect them only when the self-acting cross
feed is to operate. In this way when the cross feed is operated by hand
T´ and T will be the only gears having motion. It has been shown that
the direction of motion of O is governed by the position of M´, or in
other words, is governed by which of the two pinions N or N´ operates,
and as O drives S´´ its motion, and therefore that of T´, is reversible
by operating M´.
The construction of S´ is as follows:--Within the apron as shown in the
side elevation it consists of what may be described as a crank, its pin
being at _t_; in the feed table is a slot through which the shaft of the
crank passes; _s_ is a handle for operating the crank. By rotating _s_
the end S´ of S is caused to swing, the crank journal moving in the slot
to accommodate the motion and permit S to swing on its centre.
The device for forcing the cone disk P´ into contact with or releasing
it from O is as follows:--The stud P is fast at the other end in P´ and
has a collar at _b_; the face of this collar forms one radial face, and
the nut W affords the other radial face, preventing end motion to _x_
without moving P endwise. If _x_ be rotated its thread at _x´_ causes it
to move laterally, carrying P with it, and P being fast to P´ also moves
it laterally. P´ is maintained from end motion by a groove at O´ in
which the end of a screw _a_ projects, _a_ screwing through W and into
the groove O´.
[Illustration: Fig. 502.]
The lead screw of a lathe is a screw for operating the lathe carriage
when it is desired to cut threads upon the work. It is carried parallel
to the lathe shears after the same manner as the independent feed
spindle, and is operated by the change wheels shown in Fig. 492 at the
end of the lathe. These wheels are termed change wheels on account of
their requiring to be changed for every varying pitch of thread to be
cut, so that their relative diameters, or, what is the same thing, their
relative number of teeth, shall be such as to give to the lead screw the
speed of rotation per lathe revolution necessary to cut upon the work a
thread or screw of the required pitch.
The construction of the bearings which carry the lead screw in the S. W.
Putnam's improved lathe is shown in Fig. 502, in which A represents the
bearing box for the headstock end of the lathe, having the foot A´ as a
base to bolt it to the lathe shears. L represents the lead screw, having
on one side of A the collar L´ and on the other the nut and washer N and
N´. The seat for the change wheel that operates the lead screw is at
L´´, the stop pin _l_ fitting into a recess in the change wheel so as to
form a driving pin to the lead screw. The washer N´ is provided with a
feather fitting into a recess into L so that it shall rotate with L and
shall prevent the nut N from loosening back as it would be otherwise apt
to do. End motion to L is therefore prevented by the radial faces of L´
and N´.
[Illustration: Fig. 503.]
At the other end of the lathe there are no collars on the lead screw,
hence when it expands or contracts, which it will do throughout its
whole length under variations of atmospheric temperature, it is free to
pass through the bearing and will not be deflected, bent, or under any
tension, as would be the case if there were collars at the ends of both
bearings. The amount of this variation under given temperatures depends
upon the difference in the coefficients of expansion for the metal of
which the lead screw and the lathe shears are composed, the shears being
of cast iron while lead screws are sometimes of wrought iron and
sometimes of steel.
The bearings at both ends are split, with soft wood placed in the split
and a screw to close the split and adjust the bearing bore to fit the
journal, in the manner already described with reference to other parts
of this lathe.
The construction of the swing frame for carrying the change wheels that
go between the driving stud V, Fig. 494, and that on the seat L´´, Fig.
502, are as follows:--
Fig. 503 represents the change wheel swing frame, an edge view of which
is partly shown at W in Fig. 494. S is a slot narrower at _a_ than at
_b_. Into this slot fit the studs for carrying the change wheels.
By enabling a feed traverse in either direction the lathe carriage may
be traversed back (for screw-cutting operations) without the aid of an
extra overhead pulley to reverse the direction of rotation of the lathe,
but in long screws it is an advantage to have such extra overhead pulley
and to so proportion it as to make the lathe rotate quicker backwards
than forward, so as to save time in running the carriage back.
The mechanical devices for transmitting motion from the lead screw to
the carriage are shown in Fig. 504, representing a view from the end and
one from the back of the lathe. B is a frame or casting bolted by the
bolt _b_ to the carriage A of the lathe. C is a disk having a handle C´
and having rotary motion from its centre. Instead of being pivoted at
its centre, however, it is guided in its rotary motion by fitting at _d_
_d_ into a cylindrical recess provided in B to receive it. C contains
two slots D and D´ running entirely through it. These slots are not
concentric but eccentric to the centre of motion of C. Through these
slots there pass two stud bolts E and E´ shown by dotted lines in Fig.
504, and these bolts perform two services: first by reason of the nuts F
and F´ they hold C to its place in B, and next they screw into and
operate the two halves G and G´ of a nut.
[Illustration: Fig. 504.]
Suppose, now, that the handle C´ be operated or moved towards arrow _e_,
then the dot at _f_ being the centre of its motion and the slots D and
D´ gradually receding from _f_ as their ends _g_ are approached they
will cause E to move vertically upward and E´ to move vertically
downward, a slot in B (which slot is denoted by the dotted lines _h_)
guiding them and permitting this vertical movement.
Since E and E´ carry the two halves of the nut which envelops the lead
screw L it is obvious that operating C´ will either close or release the
half nuts from L according to which direction it (C´) is moved in.
The screws H and H´ screw tightly into B, and the radial faces of their
heads are made to have a fair and full bearing against the underside of
the shears, so that they serve as back gibs to hold the carriage to the
shears and may be operated to adjust the fit or to lock the carriage to
the bed if occasion may require. This lathe is made with a simple tool
rest as shown in the engravings or with a compound slide rest. In some
sizes the rest is held to the carriage by a weight upon a principle to
be hereafter described. The bed is made (as is usual) of any length to
suit the purposes for which the lathe is to be used.
The next addition to the lathe as it appears in the United States is
that of a compound slide rest.
[Illustration: Fig. 505.]
Fig. 505 represents a 28-inch swing lathe by the Ames Manufacturing
Company, of Chicopee, Massachusetts. It is provided with the usual
self-acting feed motion and also with a compound slide rest. The swing
frame for the studs carrying the change wheels for screw cutting here
swings upon the end of the lead screw, the same spindle that carries the
driving cone for the independent feed rod which is in front of the
lathe, also carries the driving gear for the change wheels used for
screw cutting.
The construction of the compound rest is shown in Figs. 506 and 507. N
is the nut for the cross-feed screw (not shown in the cut) and is
carried in the slide A. A and the piece L above it are virtually in one,
since the latter is made separate for convenience of construction and
then secured to it firmly by screws. B is made separate from C also for
convenience of construction and fixed to it by screws; L is provided
with a conical circular recess into which the foot B of C fits. E is a
segment of a circle operated by the set screw F to either grip or
release B. The bolt D simply serves as a pivot for piece B C; at its
foot C is circular and is divided off into the degrees of a circle to
facilitate setting it to any designated angle.
If, then, F be unscrewed, C may be rotated and set to the required
angle, in which position screwing up F will lock it through the medium
of E. G is the feed nut for the upper slider H, which operates along a
slide way provided on C, the upper feed screw having journal bearing at
C´. I is the tool post, having a stepped washer J, by means of which the
height of the tool K may be regulated to suit the work.
[Illustration: Fig. 506.]
[Illustration: Fig. 507.]
Suppose, now, that it be required to turn a shaft having a parallel and
a taper part; then the carriage may be traversed to turn the parallel
part, and the compound slide C may be set to turn the taper part, while
the lower feed screw operating in N may be used to turn radial faces.
[Illustration: Fig. 508.]
The object of making A and L in two pieces is to enable the boring and
insertion of B, which is done as follows:--The front end of L as L´ is
planed out, leaving in it a groove equal in diameter and depth to the
diameter and depth of B, so that B may be inserted laterally along this
groove to its place in L. The segment E is then inserted and a piece is
then fitted in at L´ and held fast to A by screws. It is into this piece
that the set screw F is threaded.
Various forms of construction are designed for compound rests, but the
object in all is to provide an upper sliding piece carrying the tool
holder, such sliding piece being capable of being so set and firmly
fixed that it will feed the tool at an angle to the line of the lathe
centres.
Another and valuable feature of the compound rest is that it affords an
excellent method of putting on a very fine cut or of accurately setting
the depth of cut to turn to an exact diameter; this is accomplished by
setting the upper slide at a slight angle to the line of centres and
feeding the tool to the depth of cut by means of the screw operating the
upper slide. In this way the amount of feed screw handle motion is
increased in proportion to the amount to which the tool point moves
towards the line of lathe centres, hence a delicate adjustment of depth
of cut may be more easily made.
Suppose, for example, that a cut be started and that it is not quite
sufficiently deep, then, while the carriage traverse is still
proceeding, the compound rest may be operated to increase the cut depth,
or if it be started to have too deep a cut the compound rest may be
operated to withdraw the tool and lessen its depth of cut. Or it may be
used to feed the tool in sharp corners when the feed traverse is thrown
out, or to turn the tops of collars or flanges when the tailstock is
set over to turn a taper.
It is obvious, however, that comparatively short tapers only can be
conveniently turned by a compound slide rest; but most tapers, however,
are short.
To turn long tapers the tailstock of the lathe is set over as described
with reference to the Putnam lathe, but for boring deep holes the slide
rest must either be a compound one or a taper turning former or
attachment must be employed.
[Illustration: Fig. 509.]
When, however, the tailstock is set over, the centres in the work are
apt to wear out of true and move their location (the causes of which
will be hereafter explained).
In addition to this, however, the employment of a taper turning
attachment enables the boring of taper holes without the use of a
compound slide rest, thus increasing the capacity of the lathe not
having a simple or single rest.
In Fig. 508 is shown a back view of a Pratt and Whitney weighted lathe
having a Slate's taper turning attachment, the construction of which is
as follows:--Upon the back of the lathe shears are three brackets having
their upper surfaces parallel with and in the same plane as the surface
of the lathe shears. Pivoted to the middle bracket is a bar which has at
each end a projection or lug fitting into grooves provided in the end
brackets, these grooves being arcs of a circle whose centre is the axis
of the pivot in the middle bracket.
The end brackets are provided with handled nuts upon bolts, by which
means the bar may be fixed at any adjusted angle to the lathe shears.
Upon the upper surface of the bar is a groove or way in which slides a
sliding block or die, so that this die in traversing the groove will
move in a straight line but at an angle to the lathe bed corresponding
to the angle at which the bar may be adjusted. The slide rest upon being
connected by a bar or rod to the die or sliding block is therefore made
to travel at the same angle to the lathe bed or line of centres as that
to which the bar is set. The method of accomplishing this in the lathe,
shown in Fig. 508, is as follows:--
In Fig. 509 A is the bar pivoted at C upon the centre bracket B; E is
the sliding block pivoted to the nut bar F. This nut bar carries the
cross-feed nut, which in turn carries the feed screw and hence the tool
rest. When the nut bar is attached to the sliding block to turn a taper
it is free to move endways upon the lower part of the carriage in which
it slides, but when the taper attachment is not in use the bar is
fastened to the lower part of the carriage by a set screw.
The screw at D is provided to enable an accurate adjustment for the
angle of the bar A. G and H are screws simply serving to adjust the
diameter to which the tool will turn after the manner shown in Fig. 588,
G being for external and H for internal work.
When the lathe has a bed of sufficient length to require it, a slide is
provided to receive the brackets, which may be adjusted to any required
position along the slide, as shown in Fig. 510. This is a gibbed instead
of a weighted lathe, and the method of attaching the sliding block to
the lathe rest is as follows:--
A separate rod is pivoted to the sliding block. This rod carries at its
other end a small cross head which affords general bearing to the end of
the cross-feed screw, which has a collar on one side of the cross head
and a fixed washer on the other, to prevent any end motion of the said
screw.
[Illustration: Fig. 510.]
The cross-feed nut is attached to the traversing cross slide. The other
or handle end of the cross-feed screw has simple journal bearing in the
slide rest, but no radial faces to prevent end motion, so that one may
from the rod attached to the sliding-block traverse the cross-feed
slide, which will carry with it the feed screw. As a result, the line of
motion of the tool rest is governed by the sliding die, but the diameter
to which the tool will turn is determined by the feed screw in the usual
manner. When it is not required to use the taper attachment, the rod or
spindle is detached from the sliding die and is locked by a clamp, when
the rest may be operated in the usual manner.
Fig. 511 represents a compound duplex lathe of a design constructed by
Sir Joseph Whitworth, of Manchester, England. The two rests are here
operated on the same cross slide by means of a right and left-hand
cross-feed screw.
The tool for the back rest is here obviously turned upside down.
The lead screw is engaged at two places by the feed nut, which is in two
pieces attached to levers; while at a third point in its circumference
it is supported by a bracket, bolted to the lathe bed.
[Illustration: Fig. 511.]
Fig. 512 represents the New Haven Manufacturing Company's three tool
slide rest, for turning shafting. It is provided with a follower rest,
in front of which are two cutting tools for the roughing cuts, and
behind which is a third tool for the finishing cut. The follower rest
receives bushes, bored to the requisite diameter, to leave a finishing
cut. The first tool takes the preliminary roughing cut; the second tool
turns the shaft down to fit the bush or collar in the follower rest;
and, as stated, the last tool finishes the work.
Fig. 513 represents a 44-inch swing lathe, showing an extra and
detachable slide rest, bolted on one side of the carriage and intended
for turning work of too large a diameter to swing over the slide rest.
By means of this extra rest the cutting tool can be held close in the
rest, instead of requiring to stand out from the tool-post to a distance
equal to the width of the work. The ordinary tool post is placed in this
extra rest.
[Illustration: Fig. 512.]
When it is desired to bolt work on the lathe carriage and rotate the
cutting tools, as in the case of using boring bars, the cross slide is
sunk into instead of standing above the top surface of the carriage so
as to leave a flat surface to bolt the work to, and [T]-shaped slots are
provided in the carriage, to receive bolts for fastening the work to the
carriage, an example of this kind being shown in Fig. 514.
[Illustration: Fig. 513.]
Fig. 515 represents a self-acting slide or engine lathe by William
Sellers and Co., of Philadelphia. These lathes are made in various sizes
from 12 inches up to 48 inches swing on the same general design,
possessing the following features:--The beds or shears are made with
flat tops, the carriage being gibbed to the edges of the shears, these
edges being at a right angle to the top face of the bed. The dead centre
spindle is locked at each end of its bearing in the tailstock, thus
securing it firmly in line with the live spindle. The ordinary tool feed
is operated by a feed rod in front of the lathe, and this rod is
operated by a disc feed, which may be altered without stopping the lathe
so as to vary the rate of tool feed; and an index is provided whereby
the operator may at once set the discs to give the required rate of
feed. The lead screw for screw cutting is placed in a trough running
inside the lathe bed, so that it is nearer to the cutting tool than if
placed outside that bed, while it is entirely protected from the lathe
cuttings and from dirt or dust; and the feed-driving mechanism is so
arranged that both may be in gear with the live spindle, and either the
rod feed or screw-cutting feed may be put into action instantly, while
putting one into action throws the other out, and thus avoid the
breakage that occurs when both may be put into action at the same time.
The direction of the turning feed is determined by the motion of a lever
conveniently placed on the lathe carriage, and the feed may be stopped
or started in either direction instantly. The mechanism for putting the
cross feed in action is so constructed (in those lathes having a
self-acting cross feed) that the cross feed cannot be in action at the
same time as the turning feed or carriage traverse by rod feed.
Lathes of 12 and 16 inches swing are back-geared, affording six changes
of speed, and the lathe tool has a vertical adjustment on a single slide
rest. Lathes of 20 inches swing are back-geared with eight changes of
speed. Lathes of 25 inches and up to 48 inches swing inclusive are
triple-geared, affording fifteen changes of speed, having a uniformly
progressive variation at each change.
The construction of the live head or headstock for a 36-inch lathe is
shown in the sectional side view in Fig. 516, and in the top view in
Fig. 517, and it will be seen that there are five changes of speed on
the cone, five with the ordinary back-gear, and five additional ones
obtained by means of an extra pinion on the end of the back-gear
spindle, and gearing with the teeth on the circumference of the face
plate, the ordinary pinion of the back-gear moving on the back-gear
spindle so as to be out of the way and clear the large gear on the cone
spindle when the wheel of the extra back-gear pinion is in use, as shown
in Fig. 517.
[Illustration: Fig. 514.]
The front bearing of the live spindle is made of large diameter to give
rigidity, and the usual collar for the face plate to screw against is
thus dispensed with. End motion to the live spindle is prevented by a
collar of hardened steel, this collar being fast on the live spindle and
abutting on one side against the end face of the back bearing and on the
other against a hardened steel thrust collar.
[Illustration: Fig. 515.]
All these parts are enclosed in a tight cast-iron tail-block, which
serves as an oil well to insure constant and perfect lubrication. The
surfaces which confine the revolving collar back and front are so
adjusted as to allow perfect freedom of rotary motion to the spindle and
collar, but no perceptible end motion. The securing of the live spindle
endwise is thus confined to the thickness of the steel collar only, and
this is so enclosed in a large mass of cast iron as to insure uniformity
of temperature in all its parts, hence there is no liability for the
live spindle to stick or jam in its bearings, while the expansion of the
live spindle endways from this collar (if it expands more than the lathe
head) is allowed for in freedom of end motion through the front journal,
which is a little longer than the bearing it runs in. In turning work
held between the lathe centres the end thrust is taken against the
hardened steel collar on the live spindle, and the hardened steel collar
at the back of it, while in turning work chucked to the face plate the
spindle is held in place endways by the confinement of the steel collar
on the spindle between the steel collar behind it and the back end of
the back bearing. With this arrangement of the spindle the change from
turning between the lathe centres and turning chucked work requires no
thought or attention to be given to any adjustment of the live spindle
to accommodate it for the changed condition of end pressure between
turning between the centres and turning chucked work, as is the case in
ordinary lathes.
The double-geared lathes, as those of 12, 16 and 20 inches swing, are
provided with face plates that unscrew from the live spindle to afford
convenience for changing from one size of face plate to another, and all
such lathes have their front live spindle journal made of sufficiently
enlarged diameter above that of the screw, to afford a shoulder for the
face plate to abut against. The nose of the live spindle is not threaded
along its entire length, but a portion next to the shoulder is made
truly cylindrical but without any thread upon it, and to this unthreaded
part the face plate accurately fits so that it is held true thereby, and
the screw may fit somewhat loosely so that all the friction acts to hold
the face plate true and hard up against the trued face of the spindle
journal. Face plates fitted in this way may be taken off and replaced as
often as need be, with the assurance that they will be true when in
place unless the surfaces have been abused in their fitting parts.
[Illustration: Fig. 516.]
The construction of the tailstock or poppet-head, as it is sometimes
termed, is shown in Figs. 518, 519, and 520. To hold it in line with the
live spindle it is fitted between the inner edges of the bed, and it
will be seen that one of the bed flanges (that on the left of the
figure) is provided on its under side with a [V], and the clamp is
provided with a corresponding [V], so that in tightening up the bolt
that secures the tailstock to the bed the tailstock is drawn up to the
edge of the shears, and therefore truly in line with the live spindle,
while when this bolt is released the tailstock is quite free to be moved
to its required position in the length of the bed. As a result of this
form of design there is no wear between the clamp and the underneath
[V], and the tailstock need not fit tightly between the edges of the
bed, hence wear between these surfaces is also avoided, while the
tailstock is firmly clamped against one edge of the bed as soon as the
clamp is tightened up by the bolt on that side.
[Illustration: Fig. 517.]
Fig. 520 shows the method of locking the tailstock spindle and of
preventing its lateral motion in the bearing in the tailstock. At the
front or dead centre end of this bearing there is between the spindle a
sleeve enveloping the spindle, and coned at its outer end, fitting into
a corresponding cone in the bore of the tailstock. Its bore is a fit to
the dead spindle, and it is split through on the lower side. Its inner
end is threaded to a sleeve that is within the headstock, and whose end
is coned to fit a corresponding cone at the inner end of the bore of the
tailstock.
[Illustration: Fig. 518.]
To this second sleeve the line shown standing vertically on the left of
the hand wheel is attached, so that operating this handle revolves the
second sleeve and the two sleeves screw together, their coned ends
abutting in their correspondingly coned seats in the tailstock bore, and
thus causing the first-mentioned and split sleeve to close upon the dead
centre spindle and yet be locked to the tailstock.
[Illustration: Fig. 519.]
As the bore of the tailstock is exactly in line with the live spindle,
it follows that the dead spindle will be locked also in line with it.
Figs. 521 and 522 represent sectional views of the carriage and slide
rest of these lathes of a size over 16 inches swing. On the feed rod
there are two bevel pinions P, one on each side of the bevel-wheel A,
and by a clutch movement either of these wheels may be placed in gear
with bevel-wheel A.
The clutch motion is operated by a lever which, when swung over to the
right, causes the bevel pinion on the right to engage with the
bevel-wheel A, and the carriage feeds to the right, while with the lever
swung over to the left the carriage feeds to the left.
On the inclined shaft is a worm, or, as the makers term it, a spiral
pinion of several teeth which gears into a straight toothed spur
gear-wheel, giving a smooth and rolling tooth contact, and therefore
producing an even and uniform feed motion.
This spur gear is fast on a shaft C, which is capable of end motion and
is provided on each of its side faces with an annular toothed clutch. On
each side of this spur-wheel is a clutch, one of which connects with the
train of gears for the turning feed, and the other with the cross-feed
gear B.
[Illustration: Fig. 520.]
When the shaft (whose end is shown at C, and to which the spur gear
referred to is fast) is pulled endways outwards from the lathe bed, its
front annular clutch engages with the clutch that sets the cross-feed
gear B in motion, and B engages with a pinion which forms the nut of the
cross-feed screw.
When shaft C is moved endways inwards its other annular clutch engages
the clutch on that side of it, and the turning feed is put into
operation. The method of operating shaft C endways is as follows:--
In a horizontal bearing D is a shaft at whose end is a weighted lever L,
and on the end of this shaft is a crank pin shown engaging a sleeve E
which affords journal bearing to the outer end of shaft C, so that
operating the weighted lever L operates E, and therefore shaft C with
the spur gear receiving motion from the worm. A simple catch confines
lever L to either of its required limits of motion, and allows the free
motion of the operating lever to start or stop either the longitudinal
or the cross feed, either of which is started or stopped by this lever,
but no mistake can occur as to which feed is operated, because the catch
above mentioned requires to be shifted to permit the feed to be
operated.
The lower end of the bell crank F engages with the sleeve E, so that
when the shaft C is operated outwards the horizontal arm of bell crank F
is depressed and the spur pinion of the cross-feed nut is free to
revolve, being driven by the cross-feed motion. When the lever F is
moved towards the lathe bed (which occurs when the stop or catch is set
to allow the longitudinal feed to be used) the nut of the cross feed is
locked fast by the horizontal arm of the bell crank F. This device makes
the whole action from one direction of feed to another automatic, and
the attention of the workman is not needed for any complicated
adjustment of parts preparatory to a change from one feed to the other.
At H is a hand wheel for hand feeding, the pinion R meshing into the
rack that extends along the front of the lathe bed; back of the hand
wheel and at H´ a clamp is provided whereby the saddle or carriage may
be locked to the lathe bed when the cross feed is being used, thus
obviating the use of a separate clamp on the bed.
The top slide of the compound rest is long and its guideway is short,
the nut being in the stationary piece G, and it will be observed that by
this arrangement at no time does the bearing surfaces of the slides
become exposed to the action of chips or dirt.
[Illustration: Fig. 521.]
Fig. 523 is a sectional view of the carriage and slide rest as arranged
for 12 and 16-inch lathes when not provided with a self-acting cross
feed. In this case end motion to shaft C is given by lever H, which is
held in its adjusted position by the tongue T. In this lathe the
screw-cutting and the turning feed cannot be put into gear at the same
time.
[Illustration: Fig. 522.]
The tool nut is arranged to enable the tool to be adjusted for height
after it is fastened in the tool post by pivoting it to the cross slide,
a spring S forcing it upwards at its outer end, thus holding the tool
point down and in the direction in which the pressure of the cut forces
it, thus preventing the wear of the pivot from letting the tool move
when it first meets the cut. The nut N is operated to adjust the tool
height, and at the same time enables the depth of cut to be adjusted
very minutely. A trough catches the water, cuttings, &c., and thus
protects the slides and slideways from undue wear.
In all these lathes the feeding mechanism is so arranged that there are
no overhanging or suspended shaft pins or spindles, each of such parts
having a bearing at each end and not depending on the face surface of a
collar or pin, as is common in many lathes. Furthermore, in these
lathes the handle for the hand carriage feed moves to the right when the
carriage moves to the right; the cross-feed screw (and the upper screw
also in compound slide rests) has a left-hand thread, so that the nut
being fixed the slides move in the same direction as though the nut
moved as in ordinary lathes. The tailstock or poppet-head screw is a
right hand because the nut moves in this case. The object of employing
right-hand screws in some cases, and left-hand ones in others, is that
it comes most natural in operating a screw to move it from right to left
to unscrew, and from left to right to screw up a piece, this being the
action of a right-hand screw, left-hand screws being comparatively
rarely used in mechanism, save when to attain the object above referred
to.
[Illustration: Fig. 523.]
Fig. 524 represents the Niles Tool Works car axle lathe, forming an
example in which the work is driven from the middle of its length,
leaving both ends free to be operated upon simultaneously by separate
slide rests.
[Illustration: Fig. 524.]
The work being driven from its centre enables it to rotate upon two dead
centres, possessing the advantage that both being locked fast there is
no liberty for the work to move, as is the case when an ordinary lathe
having one live or running spindle is used, because in that case the
live spindle must be held less firmly and rigidly than a dead centre, so
as to avoid undue wear in the live spindle bearings; furthermore, the
liability of the workman to neglect to properly adjust the bearings to
take up the wear is avoided in the case of two dead centres, and no
error can occur because of either of the centres running out of true, as
may be the case with a rotating centre.
The cone pulley and back gear are here placed at the head of the lathe
driving a shaft which runs between the lathe shears and drives a pinion
which gears with the gear on the work driving head shown to stand on the
middle of the shears. This head is hollow so that the axle passes
through it. On the face of this gear is a Clement's equalizing driver
constructed upon the principle of that shown hereafter in Fig. 756.
The means for giving motion to the feed screw and for enabling a quick
change from the coarse roughing feed to a finer finishing feed to the
cutting tool without requiring to change the gears or alter their
positions, is shown in Fig. 525. _a_ and _b_ are two separate pinions
bored a working fit to the end of the driving shaft S, but pierced in
the bore with a recess and having four notches or featherways _h_. The
end of the driving shaft S is pierced or bored to receive the handled
pin _i_, and contains four slots to receive the four feathers _j_ which
are fast in _i_. In the position shown in the figure these feathers
engage with neither _a_ nor _b_, hence the driving shaft would remain
motionless, but it is obvious that if pin _i_ be pushed in the feathers
would engage _b_ and therefore drive it; or if _i_ were pulled outwards
the feathers would engage _a_ and drive it, because _a_ and _b_ are
separate pinions with a space or annular recess between them sufficient
in dimensions to receive the feathers. The difference in the rate of
feed is obviously obtained through the difference in diameters of the
pair of wheels _a_, _c_ and the pair _d_, _b_, the lathe giving to the
lead screw the slowest motion and, therefore, the finest feed.
The means for throwing the carriage in and out of feed gear with the
feed screw and of providing a hand feed for operating the tool in
corners or for quickly traversing the carriage, is shown in Fig. 526, in
which S represents the feed screw and B a bracket or casting bolted to
the carriage and carrying the hand wheel and feed mechanism shown in the
general cut figure.
[Illustration: Fig. 525.]
B provides a slide way denoted by the dotted lines at _b_, for the two
halves N and N´ of the feed nut. It also carries a pivot pin shown at
_p_ in the front elevation, which screws into B as denoted by _p´_ in
the end view; upon this pivot operates the piece D, having the handle
_d_. In D are two cam grooves _a_ _a_; two pins _n_, which are fast in
the two half-nuts N N´, pass through slots _c_ _c_ in B, and into the
cam grooves _a_ _a_ respectively.
[Illustration: Fig. 526.]
As shown in the cut the handle _d_ of D is at its lowest point, and the
half-nuts N´ and N are in gear upon the feed screw; but suppose _d_ be
raised, then the grooves _a_ _a_ would force their respective pins _n_
up the slots _c_, and these pins _n_ being each fast to a half of the
nut, the two half-nuts would be opened clear of the feed screw, and the
carriage would cease to be fed.
The hand-feed or guide-carriage traverse motion is accomplished as
follows:--B provides at _e_ journal bearing to a stud on which is the
hand wheel shown in the general cut; attached to this hand wheel is a
pinion operating a large gear (also seen in general cut) whose pitch
line is seen at _g_, in figure. The stud carrying _g_ has journal
bearing at _f_, and carries a pinion whose pitch circle is at _h_ and
which gears with the rack.
Fig. 527, which is taken from _The American Machinist_, represents an
English self-acting lathe capable of swinging work of 12 inches diameter
over the top of the lathe shears, which are provided with a removable
piece beneath the live centre, which when removed leaves a gap,
increasing the capacity of the lathe swing. The gears for reversing the
direction of feed screw motion are here placed at the end of the live
head or headstock, the screw being used for feeding as well as for screw
cutting.
Fig. 528 represents a pattern-maker's lathe, by the Putnam Tool Co., of
Fitchburg, Massachusetts. This lathe is provided with convenient means
of feeding the tool to its cut by mechanism instead of by hand, as is
usually done by pattern-makers, and this improvement saves considerable
time, because the necessity of frequently testing the straightness of
the work is avoided.
It is provided with an iron extension shears, the upper shears sliding
in [V]-ways provided in the lower one. The hand-wheel is connected with
a shaft and pinion, which works in a rack, and is used for the purpose
of changing the position of the upper bed, which is secured in its
adjusted position by means of the tie bolts and nuts, as shown on the
front of the lower shears. This enables the gap in the lower shears to
be left open to receive work of large diameter, and has the advantage
that the gap need be opened no more than is necessary to receive the
required length of work. The slide-rest is operated by a worm set at an
angle, so as to operate with a rolling rather than a sliding motion of
the teeth, and the handle for operating the worm-shaft is balanced. The
carriage is gibbed to the bed. The largest and smallest steps of the
cone pulley are of iron, the intermediate steps being of wood, and a
brake is provided to enable the lathe to be stopped quickly. This is an
excellent improvement, because much time is often lost in stopping the
lathe while running at a high velocity, or when work of large diameter
is being turned. The lathe will swing work of 50 inches within the gap,
and the upper shears will move sufficiently to take in 4 additional feet
between the centres.
In the general view of the lathe, Fig. 528, the slide-rest is shown
provided with a [T]-rest for hand tools, but as this sets in a clip or
split bore, it may readily be removed and replaced by a screw tool,
poppet for holding a gauge, or other necessary tool. To enable the
facing of work when the gap is used, the extra attachment shown in Figs.
529 and 530 is employed. It consists of an arm or bar A, bolted to the
upper shears S by a bolt B, and clamp C, in the usual manner, and is
provided with the usual slideway and feed-screw _f_ for operating the
lower slide T, which carries a hollow stem D; over D fits a hub K, upon
the upper slide E, which hub is split and has a bolt at F, by means of
which the upper slide may be clamped to its adjusted angle or position.
The upper slider H receives the tool-post, which is parallel and fits in
a split hub, so that when relieved it may be rapidly raised or lowered
to adjust the height of the tool.
The construction of the brake for the cone pulley is shown in Figs. 531
and 532, in which P represents the pulley rim, L the brake lever, S a
wooden shoe, and W a counter-weight. The lever is pivoted at G to a lug
R, provided on the live headstock, and the brake obviously operates on
the lowest part of the cone flange; hence the lever handle is depressed
to put the brake in action.
[Illustration: _VOL. I._ =EXAMPLES IN LATHE CONSTRUCTION.= _PLATE V._
Fig. 527.
Fig. 528.
Fig. 529.]
The construction of the front and back bearings for the live spindle is
the same as that shown in Figs. 495 and 496.
[Illustration: Fig. 530.]
Wood turners sometimes have their lathes so made that the headstock can
be turned end for end on the lathe shears, so that the face plate may
project beyond the bed, enabling it to turn work of large diameter. A
better method than this is to provide the projecting end of the lathe
with a screw to receive the face plate as shown in Fig. 533, which
represents a lathe constructed by Walker Brothers of Philadelphia. At
the end of the lathe is shown a hand rest upon a frame that can be moved
about the floor to accommodate the location, requiring to be turned upon
the work.
[Illustration: Fig. 531.]
For very large work, wood-workers sometimes improvise a facing lathe, as
shown in Fig. 534, in which A is a headstock bolted to the upright B; C
is the cone pulley, and E a face plate built up of wood, and fastened to
an iron face plate by bolts. The legs A, of the tripod hand rest, Fig.
535, are weighted by means of the weights B.
[Illustration: Fig. 532.]
In Fig. 536 is shown a chucking lathe, especially adapted for boring and
facing discs, wheels, &c. The live spindle is driven by a worm-wheel,
provided around the circumference of the face plate. The driving worm
(which runs in a cup of oil) is on a driving shaft, running across the
lathe and standing parallel with the face of the face plate. This shaft
is driven by a pulley as shown, changes of speed being effected by
having a cone pulley on the counter-shaft and one on the line of
shafting.
[Illustration: Fig. 533.]
This lathe is provided with two compound slide rests. One of which may
be used for boring, while the other is employed for facing purposes.
These rests are adjustable for location across the bed of the lathe by
means of bolts in slots, running entirely across the lathe bed.
These slide rests are given a self-acting motion by the following
arrangement of parts: at the back of the live spindle is an eccentric
rod, operating a connecting rod, which is attached at its lower end to
the arm of a shaft running beneath the bed, and parallel to the lathe
spindle. This shaft passes beyond the bed where it carries a bevel
gear-wheel, which meshes with a bevel gear-wheel upon a cross shaft.
This cross shaft carries three arms, one at each end and inside its
journal bearings in the bed, and one beneath and at a right angle to the
other two. These receive oscillating motion by reason of the eccentric
connecting rod, &c.
For each compound rest there are provided two handles as usual, and in
addition an [L] lever, one arm of the latter being provided with a
series of holes, while the other carries a weight.
[Illustration: Fig. 534.]
The [L] lever carries a pawl which operates a ratchet wheel, placed on
the handle end of the slide rest cross feed screw. If then a chain be
attached to one of the holes of the [L] lever, and to the oscillating
arm, the motion in one direction of the latter will be imparted to the
[L] lever (when the chain is pulled). On the return motion of the
oscillating arm, the chain hangs loose, and the weight on the [L] lever
causes that lever arm to fall, taking up the slack of the chain, the
feed taking place (when the pawl is made to engage with the ratchet
wheel) during the motion of the oscillating arm from right to left, or
while pulling the chain.
The rate of feed is varied by attaching the chain to different holes in
the [L] lever.
To operate the rests in a line parallel to the lathe spindle, a similar
[L] lever is attached by chain to the third oscillating arm, which is
placed on the cross shaft, mid-way of the bed, or between the two slide
rests. It is obvious then that with an [L] lever attachment on each feed
screw, both slides of each rest may be simultaneously operated, while
either one may be stopped either by detaching the chain or removing the
[L] lever.
For operating the rests by hand, the usual feed-screw handles are used.
Fig. 537 represents a 90-inch swing lathe by the Ames Manufacturing
Company of Chicopee, Massachusetts.
[Illustration: Fig. 535.]
The distinguishing feature of this lathe is that the tailstock spindle
is made square, to better enable it to bear the strain due to carrying
cutting tools in place of the dead centre; and by means of a pulley
instead of a simple hand wheel for operating the tail spindle, that
spindle may be operated from an overhead countershaft, and a tool may be
put in to cut key-ways in pulleys, wheels, &c., chucked on the face
plate (which of course remains stationary during the operation), thus
dispensing with the necessity of cutting out such key-ways by hammer,
chisel, and file, in wheel bores too large and heavy to be operated upon
in a slotting machine.
[Illustration: Fig. 538.]
On account of the weight of the tailstock it is fitted with rollers,
which may be operated to lift it from the bed when it is to be moved
along the lathe bed.
[Illustration: _VOL. I._ =CHUCKING LATHES.= _PLATE VI._
Fig. 536.
Fig. 537.]
Fig. 538 represents a 50-inch swing lathe by the New Haven
Manufacturing Company of New Haven, Connecticut. The compound rest is
here provided with automatic feed so that it may be set at an angle to
bore tapers with a uniform feed. The tailstock is provided with a
bracket, carrying a pinion in gear with the hand-feed rack, so as to
move the tailstock along the bed by means of the pinion. The feed screw
is splined to give an independent feed, and the swing frame is operated
by a worm as shown.
[Illustration: Fig. 539.]
GAP LATHE OR BREAK LATHE.
The gap lathe is one in which the bed is provided with a gap beneath the
face plate, so as to enable that plate or the chucks to swing work of
larger diameter, an example being given in Fig. 539.
[Illustration: Fig. 540.]
It is obvious, however, that the existence of the gap deprives the slide
rest of support on one side, when it is used close to the face plate.
This is obviated in some forms of gap lathes by fitting into the gap a
short piece of bed that may be taken out when the use of the gap is
required.
The gap lathe has not found favor in the United States, the same result
being more frequently obtained by means of the extension lathe, which
possesses the advantages of the gap lathe, while at the same time
enabling the width of the gap to be varied to suit the length of the
work. Fig. 540 represents an extension lathe by Edwin Harrington and
Son, of Philadelphia. There are two beds A and B, the former sliding
upon the latter when operated by the hand-wheel E, which is upon the end
of a screw that passes between the two beds, has journal bearing in the
upper bed, and engages a nut in the lower one, so that as the screw is
operated the wheel moves longitudinally with the upper bed. C is the
feed rod which communicates motion to the feeding screw D, which has
journal bearing on the upper bed and therefore travels with it when it
is moved or adjusted longitudinally. The cross slide has sufficient
length to enable the slide rest to face work of the full diameter that
will swing in the gap, and to support the slide rest when moved outwards
to the full limit, it is provided with a piece F, which slides at its
base upon the guideway or slide G.
Fig. 541 represents a double face plate lathe such as is used for
turning the wheels for locomotives. The circumference of both the face
plates are provided with spur teeth, so that both are driven by pinions,
which by being capable of moving endways into or out of gear, enable
either face plate to be used singly, if required, as for boring
purposes.
The slide rests are operated by ratchet arms for the self feed, these
arms being operated by an overhead shaft, with arms and chains.
[Illustration: Fig. 541.]
Fig. 542 represents a chucking lathe adapted more especially for boring
purposes. Thus the cone pulley is of small diameter and the parts are
light, so that the lathe is more handy than would be the case with a
heavier built lathe, while at the same time it is sufficiently rigid for
large work that is comparatively light.
[Illustration: Fig. 542.]
The compound rest is upon a pedestal that can be bolted in any required
position on the lower cross slide, and is made self-acting for the feed
traverse by the change wheels and feed screw, while the self-acting
cross feed is operated by a ratchet handle, actuated by a chain from an
overhead reciprocating lever; the latter being actuated from the crank
pin at A, which is adjustable in a slot in the crank disk B. A lathe of
this kind is very suitable for brass work of unusually large diameter,
because in such work the cuts and feeds are light, and the cutting speed
is quick, hence a heavy construction is not essential.
Figs. 543 and 544 represent a large lathe built by Thomas Shanks and
Co., of Johnstone, near Glasgow, Scotland; all the figures of this lathe
being from _The American Machinist_.
Fig. 543 shows the headstock and two of the slide rests, while Fig. 544
represents the remainder of the bed, the tailstock, and two of the slide
rests.
It will be seen from the figures that there are a compound rest and a
column or pillar rest both at the front and at the back of the lathe,
and that there is an additional rest on the front end of the tailstock
which may be used for facing the ends of the work.
Fig. 545 represents a section through, and a partial plan of the
headstock, and it will be seen that the live spindle is free from the
cone pulley and from the gearing, the chuck plate being driven from a
pinion engaging an internal gear at the back of the chuck plate. By this
construction the balancing of such work as crank shafts is facilitated,
because the chuck plate is not affected by the friction of the driving
gears, and may therefore be easily revolved to test the balance of the
work.
Fig. 546 represents a cross section through the bed, and through one of
the compound rests, and one of the pillar rests, the latter rests being
made thin so that they may pass between the cheeks of crank shafts, to
turn their faces and the crank journals.
Fig. 547 represents a view from the back end of the headstock, and Fig.
548 a view of the lathe from the tailstock end.
Figs. 549 and 550 represent a plan and a side view of the headstock and
the two slide rests nearest to it. The lathe being shown at work on the
crank shaft of the steamship service, which is shown in dotted lines,
and it will be seen that for turning the stem of the shaft all the rests
can be used at once, those at the back of the lathe having their
cutting tools turned upside down (as will be more clearly seen in the
cross-sectional view of the rests in Fig. 546).
[Illustration: Fig. 543.]
Figs. 551 and 552 represent a plan and a side view of the other half of
the lathe in operation upon the same crank shaft, which is again shown
in dotted lines.
[Illustration: Fig. 544.]
Referring now to the general construction of the lathe, the headstock or
live spindle has a front journal bearing 18 inches diameter and 24
inches long, and a back bearing 12 inches diameter and 15 inches long,
the bearings being parallel. The driving cone has five changes of speed
for a 6-inch belt, and is carried on an independent spindle. The cone is
turned inside as well as outside, so as to be in balance at high speeds.
[Illustration: Fig. 545.]
The face plate is 12 feet diameter, cast with internal gear at the back.
It is provided with [T]-slots and square holes for fixing work. It is
bolted to a large flange in one piece with the spindle, and fitted with
four steel expanding gripping jaws worked with screws and toothed
blocks. These are for doing chuck work, or for gripping work to be
driven, as the collars of propeller or crank shafts, or work of a
similar character. By the system of gearing adopted, when desired, the
face plate can be revolved almost free, which facilitates balancing for
turning crank shafts, as well as other operations. The thrust against
the live spindle is taken by an adjustable steel tail piece.
[Illustration: Fig. 546.]
[Illustration: Fig. 547.]
[Illustration: Fig. 548.]
[Illustration: Fig. 549.]
The beds are double, 10 feet in width over all, the sections being
joined together by massive ground plates and bolts. They are made with
square lips to resist the upward strain of cutting. The front bed is
fitted with two saddles, each carrying a compound slide rest having the
following movements: First, screw-cutting, by means of a leading screw,
situated inside the bed, with a sliding disengaging nut and reversing
motion for right or left-hand threads, or for instantaneously stopping
the longitudinal movement of the saddle. This is accomplished by a set
of clutch mitres placed inside the bed at headstock end, and actuated by
a lever in front: Second, a self-acting surfacing motion to slide rest
by means of a longitudinal shaft at the front of the bed, and clutch
mitres for reversing the saddle screw.
[Illustration: Fig. 550.]
Third, power motion for moving the saddles quickly to position along the
bed. This is done through the fast and loose pulleys at the headstock
end of lathe.
Fourth, hand rack motion to saddle. The back bed is fitted with two
saddles, each carrying a pillar rest, fitted for all movements in plain
turning like the front rests, and also with swiveling motion for corner
turning.
[Illustration: Fig. 551.]
The tailstock has a spindle 9 inches diameter. It is fitted in [V]s on
the bed, and held down by three [T]-head bolts on each side. The top
section is adjustable for turning tapers. It is moved along the ways by
engaging a nut with the main screw. An end-cutting rest is fitted to the
tailstock, which is adapted for operating on flanged couplings and
similar work.
There is a separate set of change wheels for each saddle, so arranged as
to cut standard pitches up to 3-inch pitch, and for self-acting feeds
down to 50 per inch. By this means, when both tools are in operation on
a piece of work, one tool may be used with coarse feed for roughing out,
while the other may be taking a fine or finishing cut either on the same
or a different part of the piece; or one tool may be cutting towards and
the other from the face plate, always maintaining the balance of a front
and back cut.
[Illustration: Fig. 552.]
Complete counter driving motion, consisting of wall brackets, shaft,
cone, and sets of fast and loose pulleys for quick reversing motion in
screw cutting, also belt bar shipping motion, and full set of
case-hardened wrenches are provided.
CHAPTER VII.--DETAILS IN LATHE CONSTRUCTION.
Although in each class of lathe the requirements may be practically the
same, yet there is a variety of different details of construction by
means of which these requirements may be met or filled, and it may be
profitable to enter somewhat into these requirements and the different
constructions generally employed to meet them.
[Illustration: Fig. 553.]
The cone spindle or live spindle of a lathe should be a close working
fit to its boxes or bearings, so that it will not lift under a heavy
cut, or lift and fall under a cut of varying pressure. This lifting and
falling may occur even though the work be true, and the cut therefore of
even depth all around the work, because of hard seams or spots in the
metal.
It is obvious that the bearings should form a guide, compelling the live
spindle to revolve in a true circle and in a fixed plane, the axis of
revolution being in line with the centre line of the tail spindle and
that means should be provided to maintain this alignment while
preserving the fit, or in other words taking up the wear. The spindle
journals must, to produce truly cylindrical work, be cylindrically true,
or otherwise the axis of its revolution will change as it revolves, and
this change will be communicated through the live centre to the work, or
through the chuck plate to the work, as the case may be.
The construction of the bearings should be such, that end motion to the
spindle is prevented in as short a length of the spindle as possible,
the thrust in either direction being resisted by the mechanism contained
in one bearing.
In Fig. 553 is a form of construction for the front bearing (as that
nearest to the live centre is called), in which end motion to the
spindle is prevented at the same time as the diametral fit is adjusted.
The spindle is provided with a cone at C and is threaded at T to receive
two nuts N which draw the spindle cone within the bearing. In this case
the journal at the back end may be made parallel, so that if the spindle
either expands or contracts more under variations of temperature than
the frame or head carrying the bearings or bearing boxes, it will not
bind endwise, nor will the fit be impaired save inasmuch as there may be
an inequality of expansion in the length of the front journal and its
box. In this case, however, the end pressure caused by holding the work
between the lathe centres acts to force the spindle into its bearing and
increase the tightness of its fit, hence it is not unusual to provide at
the back bearing additional means to resist the thrust of the dead
centre.
[Illustration: Fig. 554.]
Fig. 554, which is taken from "Mechanics," represents Wohlemberg's
patent lathe spindle, in which both journals are coned, fitting into
bushes which can be replaced by new ones when worn; the end thrust is
here taken by a steel screw, while the end fit is adjusted by means of a
ring nut which binds the face of the large cone gear against the inside
face of the front bearing and by the face of the gear that drives the
change gears. It may be pointed out, however, that in this construction
the spindle must be drawn within to adjust the fit of the front bearing,
which can only be done by adjusting the pinion that drives the change
gears, or by screwing up the nut that is inside the cone, and therefore
cannot be got at. The back bearing can be adjusted by means of the ring
nuts provided at each of its ends.
[Illustration: Fig. 555.]
Fig. 555 represents another design of cone bearing, in which the spindle
is threaded to receive the nuts A which draw it within the front bearing
and thus adjust the fit, and at the same time prevent end motion. The
back bearing is provided with a bush parallel outside, and furnished
with a nut at B to adjust the fit of the end bearing. To prevent the end
pressure of the dead centre from forcing the spindle cones too tightly
within their bearings a cross piece P is employed (being supported by
two studs provided in the head), and through P passes an adjusting screw
D, having nuts N and C, one on each side of P. Between the end of D and
of the lathe spindle a washer of leather or of raw hide is placed to
prevent the end faces from abrading. A similar device for taking up the
end thrust is often provided to lathes in which the journals are both
parallel, fitting in ordinary boxes, a top view of the device being
illustrated in Fig. 556, in which B is the back bearing box, S S two
studs supporting cross-piece P, and N and C are adjusting nuts. G is the
gear for driving the change wheels for screw cutting or for ordinary
feeding as the case may be. In this design the gear wheel G remains
fixed and the combinations of gears necessary to cut various pitches of
thread must be made on the lead screw and on the swing frame, which must
be long enough to permit the change gear stud to pass up to permit the
smallest change wheel to gear with wheel G, and which is provided with
two grooves E and F, Fig. 557, for two studs to carry two compounded
pairs of change wheels. This compounding in two places on the swing
frame enables gear G to be comparatively large, and thus saves the teeth
from rapid wear, while it facilitates the cutting of left-hand threads,
because it affords more convenience for putting in a gear to change the
direction of feed screw revolution.
[Illustration: Fig. 556.]
In many lathes of American design the journals are made parallel, and
the end play is taken up at the back bearing, an example being given in
Fig. 558, in which the back bearing boxes are made in two halves A and
B, the latter having a set screw (with check nut) threaded through it
and bearing against a washer that meets the end of the spindle.
[Illustration: Fig. 557.]
A simple method of preventing end motion is shown in Fig. 559, a bracket
B affording a support for a threaded adjusting screw, which is sometimes
made pointed and at others flat. When pointed it acts to support the
spindle, but on the other hand it also acts to prevent the journal from
bedding fairly in the boxes. In some cases of small lathes the back
bearing is dispensed with, and a similar pointed adjusting screw takes
its place, which answers very well for very small work.
Since the strain of the cut carried by the cutting tool falls mainly
upon the live centre end of the cone spindle, it is obvious that the
bearing at that end has a greater tendency to wear.
[Illustration: Fig. 558.]
In addition to this the weight of the cone itself is greatest at that
end, and furthermore the weight of the face plate or chuck, and of the
work, is carried mainly at that end. If, however, one journal and
bearing wears more than the other, the spindle is thrown out of line
with the lathe shears, and with the tail block spindle. The usual method
of obviating this as far as possible is to give that end a larger
journal-bearing area.
[Illustration: Fig. 559.]
The direction in which this wear will take place depends in a great
measure upon the kind of work done in the lathe; thus in a lathe running
slowly and doing heavy work carried by chucks, or on the face plate, the
wear would be downwards and towards the operator, the weight of the
chuck, &c., causing the downward, and the resistance or work-lifting
tendency of the cut causing the lateral wear. As a general rule the wear
will be least in a lateral direction towards the back of the lathe, but
the direction of wear is so variable that provision for its special
prevention or adjustment is not usually made. In the S. W. Putnam lathe,
provision is made that the bearing boxes may be rotated in the head, so
that when the lathe is used on a class of work that caused the live
spindle to wear the bearing boxes on one side more than on another, the
boxes may be periodically partly rotated in the head so that further
wear will correct the evil.
The coned hole to receive the live centre should run quite true, so that
the live centre will run true without requiring, when inserted, to be
placed in exactly the same position it occupied when being turned up at
its conical point. But when this hole does not run true a centre punch
dot is made on the end of the spindle, and another on the centre, so
that by placing the two dots to coincide at all times, the centre will
run true.
The taper given to lathe centres varies from 9/16 per foot to 1 inch per
foot. In the practice of Pratt and Whitney a taper of 9/16 per foot is
given to all lathes, the lengths of the tapers for different sizes of
lathes being as follows:
Length of Taper Socket
Swing of Lathe. for Live Centre.
13 inches 5 inches.
16 " 3-3/4 "
18 and 19 inches 7-11/16 "
" " with hollow spindle 5 inches long
and 1-1/16 diameter at the small end.
The less the amount of taper the more firmly the centre is held, but the
more difficult it becomes to remove the centre when necessary.
[Illustration: Fig. 560.]
The principal methods of removing live centres are shown in Fig. 560, in
which is shown at B a square part to receive a wrench, it being found
that if not less than about 1/2-inch taper per foot of length be given
to the live spindle socket, then revolving the centre with a wrench will
cause it to release itself, enabling it to be removed by hand. Another
method employed on small lathes is to drill a hole through the live
spindle to receive a taper pin P, the live centre end being shown at C.
Another and excellent plan for large lathes, is to thread the centre and
provide it with a nut M, which on being screwed against the end face of
the live spindle will release the centre. The objection to the use of
the pin P is that it is apt to become mislaid, and it is not advisable
to use a hammer about the parts of the lathe, especially in such an
awkward place as between the journal bearing and the cone, which is
where the pin hole requires to be located. The square section is,
therefore, the best method for small lathes, and the nut for large ones.
In cases where the live spindle is made hollow a bar may be passed
through from the rear end to remove the centre; this also enables rods
of iron to be passed through the spindle, leaving the end projecting
through the chuck for any length necessary for the work to be turned out
of its exposed end.
The dead centre may be extracted from the tail spindle by a pin and hole
as in Fig. 560, or, what is better, by contact with the end of the tail
screw as described when referring to the tail stock of the S. W. Putnam
lathe.
The cone pulley should be perfectly balanced, otherwise at high speeds
the lathe will shake or tremble from the unbalanced centrifugal motion,
and the tremors will be produced to some extent on the work. The steps
of the cone should be amply wide, so that it may have sufficient power,
without overstraining the belt, to drive the heaviest cut the lathe is
supposed to take without the aid of the back gear.
In some cases, as in spinning lathes, the order of the steps is
reversed, the smallest step of the cone being nearest to the live
centre, the object being to have the largest step on the left, and
therefore more out of the way.
The steps of the cone should be so proportioned that the belt will shift
from one to the other, and have the same degree of tension, while at the
same time they should give a uniform graduation or variation of speed
throughout, whether the lathe runs in single gear or with the back gear
in. This is not usually quite the case although the graduation is
sufficiently accurate for practical purposes. The variation in the
diameter of the steps of a lathe cone varies from an inch for lathes of
about 12-inch swing, up to 2 inches for lathes of about 30-inch swing,
and 3 inches for lathes of 5 or more feet of swing.
To enable the graduation of speed of the cone to be uniform throughout,
while the tension of the belt is maintained the same on whatever step
the cone may be, the graduation of the steps may be varied, and this
graduation may be so proportioned as to answer all practical purposes if
the overhead or countershaft cone and that on the lathe are alike.
The following on this subject is from the pen of Professor D. E. Klein,
of Yale College.
"The numbers given in the following tables are the differences between
the diameters of the adjacent steps on either cone pulley, and are
accurate within half a hundredth of an inch, which is a degree of
accuracy sufficient for practical purposes.
By simply omitting a step at each end of the cone, the two tables given
will be found equally well adapted for determining the diameters of
cones having four and three steps respectively.
The following are examples in the use of the tables. Suppose the centres
of a pair of pulley shafts to be 60 inches apart, and that the
difference of diameter between the adjacent steps is to be as near to
2-1/2 inches as can be, to obtain a uniformity of speed graduation and
belt tension, also that each cone is to have six steps, the smallest of
which is to be of five inches diameter.
To find the diameters for the remaining steps, we look in Table I.
(corresponding to cone pulleys with six steps), under 60 in. and
opposite 2-1/2 in. and obtain the differences,
2.37 2.43 2.50 2.57 2.63
Each of these differences is _subtracted_ from the _larger_ diameter of
the two adjacent steps to which it corresponds, thus:
17.50 = 1st step.
Difference of 1st and 2nd = 2.37
-----
15.13 = 2nd "
" 2nd " 3rd = 2.43
-----
12.70 = 3rd "
" 3rd " 4th = 2.50
-----
10.20 = 4th "
" 4th " 5th = 2.57
-----
7.63 = 5th "
" 5th " 6th = 2.63
-----
5.00 = 6th "
EXAMPLE 2. If we suppose the same conditions as in Example 1, with the
exception that each cone is to have four steps instead of six, the
largest diameter will, in this case, equal 12-1/2 in. and we may obtain
the remaining diameters by omitting the end differences of the above
example, and then subtracting the remaining differences as follows:
12.50 = 2nd step.
Difference of 2nd and 3rd = 2.43
-----
10.07 = 3rd "
" 3rd " 4th = 2.50
-----
7.57 = 4th "
" 4th " 5th = 2.57
-----
5.00 = 5th "
The 2nd, 3rd, 4th, and 5th steps of the table correspond respectively to
the 1st, 2nd, 3rd, and 4th steps of the cone, having but four steps. If
the smallest diameter had not been assumed equal to 5 in. we might have
dropped a step at each end of the six-step cone of the preceding
example, and employed the remaining four diameters, 15.13 in. 12.70 in.
10.20 in. and 7.63 in. for one four-step cone.
The present and the previous examples show that we can assume the size
of the smallest step anything that we please, and, other things being
equal, can make the required cones large or small.
I.--TABLE FOR FINDING CONE PULLEY DIAMETERS WHEN THE TWO PULLEYS ARE
CONNECTED BY AN OPEN BELT, AND ARE EXACTLY ALIKE.
The numbers given in table are the differences between the diameters of
the adjacent steps on either cone pulley, and can be employed when there
are either six or four steps on a cone. When there are six steps, the
largest is the first, and the smallest the sixth step of the table. When
there are four steps, the largest is the second, and the smallest the
fifth step of the table.
+-------------+-----------+------------------------------
| Average | Adjacent | DISTANCE BETWEEN THE CENTRES
| difference | steps, | OF CONE PULLEYS.
| between | whose +----+----+----+----+----+----+
| the | diffe- | | | | | | |
| adjacent | rence is | 10 | 20 | 30 | 40 | 50 | 60 |
| steps. | given in | i n c h e s. |
| | table. | | | | | | |
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|0.87|0.94|0.96|0.97|0.98|0.98|
| |2nd " 3rd|0.94|0.97|0.98|0.98|0.99|0.99|
| 1 inch |3rd " 4th|1.00|1.00|1.00|1.00|1.00|1.00|
| |4th " 5th|1.06|1.03|1.02|1.02|1.01|1.01|
| |5th " 6th|1.13|1.06|1.04|1.03|1.02|1.02|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.21|1.36|1.40|1.43|1.44|1.45|
| |2nd " 3rd|1.36|1.43|1.45|1.46|1.47|1.48|
| 1-1/2 inch |3rd " 4th|1.50|1.50|1.50|1.50|1.50|1.50|
| |4th " 5th|1.64|1.57|1.55|1.54|1.53|1.52|
| |5th " 6th|1.79|1.64|1.60|1.57|1.56|1.55|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.47|1.74|1.83|1.87|1.90|1.92|
| |2nd " 3rd|1.74|1.87|1.92|1.93|1.95|1.96|
| 2 inches |3rd " 4th|2.00|2.00|2.00|2.00|2.00|2.00|
| |4th " 5th|2.26|2.13|2.08|2.07|2.05|2.04|
| |5th " 6th|2.53|2.26|2.17|2.13|2.10|2.08|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.66|2.10|2.23|2.30|2.34|2.37|
| |2nd " 3rd|2.10|2.30|2.37|2.40|2.42|2.43|
|2-1/2 inches |3rd " 4th|2.50|2.50|2.50|2.50|2.50|2.50|
| |4th " 5th|2.90|2.70|2.63|2.60|2.58|2.57|
| |5th " 6th|3.34|2.90|2.77|2.70|2.66|2.63|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.76|2.42|2.62|2.71|2.77|2.81|
| |2nd " 3rd|2.42|2.71|2.81|2.86|2.88|2.90|
| 3 inches |3rd " 4th|3.00|3.00|3.00|3.00|3.00|3.00|
| |4th " 5th|3.58|3.29|3.19|3.14|3.12|3.10|
| |5th " 6th|4.24|3.58|3.38|3.29|3.23|3.19|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd| |3.95|3.31|3.49|3.59|3.66|
| |2nd " 3rd|2.94|3.49|3.66|3.75|3.80|3.83|
| 4 inches |3rd " 4th|4.00|4.00|4.00|4.00|4.00|4.00|
| |4th " 5th|5.06|4.51|4.34|4.25|4.20|4.17|
| |5th " 6th| |5.05|4.69|4.51|4.41|4.34|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd| |3.33|3.92|4.20|4.36|4.47|
| |2nd " 3rd|3.31|4.19|4.47|4.60|4.68|4.74|
| 5 inches |3rd " 4th|5.00|5.00|5.00|5.00|5.00|5.00|
| |4th " 5th|6.69|5.81|5.53|5.40|5.32|5.26|
| |5th " 6th| |6.67|6.09|5.80|5.64|5.53|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd| |3.52|4.42|4.83|5.08|5.23|
| |2nd " 3rd| |4.83|5.23|5.42|5.54|5.62|
| 6 inches |3rd " 4th| |6.00|6.00|6.00|6.00|6.00|
| |4th " 5th| |7.17|6.77|6.58|6.46|6.38|
| |5th " 6th| |8.48|7.58|7.17|6.92|6.77|
+-------------+-----------+----+----+----+----+----+----+
+-------------+-----------+-----------------------------+
| Average | Adjacent | DISTANCE BETWEEN THE CENTRES|
| difference | steps, | OF CONE PULLEYS. |
| between | whose +----+----+----+----+----+----+
| the | diffe- | | | | | | |
| adjacent | rence is | 70 | 80 | 90 | 100| 120| 240|
| steps. | given in | i n c h e s. |
| | table. | | | | | | |
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|0.98|0.98|0.99|0.99|0.99|1.00|
| |2nd " 3rd|0.99|0.99|0.99|0.99|1.00|1.00|
| 1 inch |3rd " 4th|1.00|1.00|1.00|1.00|1.00|1.00|
| |4th " 5th|1.01|1.01|1.01|1.01|1.00|1.00|
| |5th " 6th|1.02|1.02|1.01|1.01|1.01|1.00|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.46|1.46|1.47|1.47|1.48|1.49|
| |2nd " 3rd|1.48|1.48|1.49|1.49|1.49|1.49|
| 1-1/2 inch |3rd " 4th|1.50|1.50|1.50|1.50|1.50|1.50|
| |4th " 5th|1.52|1.52|1.51|1.51|1.51|1.51|
| |5th " 6th|1.54|1.54|1.53|1.53|1.52|1.51|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.93|1.93|1.94|1.95|1.96|1.98|
| |2nd " 3rd|1.96|1.97|1.97|1.97|1.98|1.99|
| 2 inches |3rd " 4th|2.00|2.00|2.00|2.00|2.00|2.00|
| |4th " 5th|2.04|2.03|2.03|2.03|2.02|2.01|
| |5th " 6th|2.07|2.07|2.06|2.05|2.04|2.02|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|2.39|2.40|2.41|2.42|2.43|2.47|
| |2nd " 3rd|2.44|2.45|2.46|2.46|2.47|2.49|
| 2-1/2 inches|3rd " 4th|2.50|2.50|2.50|2.50|2.50|2.50|
| |4th " 5th|2.56|2.55|2.54|2.54|2.53|2.51|
| |5th " 6th|2.61|2.60|2.59|2.58|2.57|2.53|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|2.84|2.86|2.87|2.88|2.90|2.95|
| |2nd " 3rd|2.92|2.93|2.94|2.94|2.95|2.98|
| 3 inches |3rd " 4th|3.00|3.00|3.00|3.00|3.00|3.00|
| |4th " 5th|3.08|3.07|3.06|2.06|3.05|3.02|
| |5th " 6th|3.16|3.14|3.13|3.12|3.10|3.05|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|3.71|3.75|3.78|3.80|3.83|3.91|
| |2nd " 3rd|3.85|3.87|3.88|3.89|3.91|3.96|
| 4 inches |3rd " 4th|4.00|4.00|4.00|4.00|4.00|4.00|
| |4th " 5th|4.15|4.13|4.12|4.11|4.09|4.04|
| |5th " 6th|4.29|4.25|4.22|4.20|4.17|4.09|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|4.55|4.60|4.64|4.68|4.74|4.87|
| |2nd " 3rd|4.77|4.80|4.82|4.84|4.86|4.93|
| 5 inches |3rd " 4th|5.00|5.00|5.00|5.00|5.00|5.00|
| |4th " 5th|5.23|5.20|5.18|5.16|5.14|5.07|
| |5th " 6th|5.45|5.40|5.36|5.32|5.26|5.13|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|5.34|5.42|5.49|5.55|5.62|5.80|
| |2nd " 3rd|5.67|5.71|5.75|5.77|5.81|5.90|
| 6 inches |3rd " 4th|6.00|6.00|6.00|6.00|6.00|6.00|
| |4th " 5th|6.33|6.29|6.25|6.23|6.19|6.10|
| |5th " 6th|6.66|6.58|6.51|6.45|6.38|6.20|
+-------------+-----------+----+----+----+----+----+----+
EXAMPLE 3. Let distance apart of the centres = 30 in. the average
difference between adjacent steps = 2 in. the diameter of the smallest
step = 4 in., and the number of steps on each of the cones = 5. The
largest step will then equal 12 in., and from Table II., under 30 in.
and opposite 2 in., we obtain the differences
1.87 1.96 2.04 2.13
and then subtracting as before we get the required diameters
12 in. 10.30 in. 8.17 in. 6.13 in. 4 in.
EXAMPLE 4. Let the conditions be as in the preceding example, the cone
pulley having, however, three steps instead of five, the largest
diameter will then equal 8 in.; and by dropping the end differences and
subtracting
8.00 = 2nd step.
Difference of 2nd and 3rd = 1.96
-----
6.04 = 3rd "
" 3rd " 4th = 2.04
-----
4.00 = 4th "
we get the diameters 8 in., 6.04, and 4 in., which correspond
respectively to 2nd, 3rd, and 4th steps of the table, and to the 1st,
2nd, and 3rd steps of the three-step cone.
EXAMPLE 5. Let the distance apart of the centres be 60 in., the average
difference between the adjacent steps be 2-1/8 in., the smallest step 7
in. and the number of steps = 5. The largest step will then be 7 in. +
(4 × 2-1/8) = 15-1/2 inches.
Now an inspection of Table II. will show that it contains no horizontal
lines corresponding to the average difference 2-1/8 inches, we cannot,
therefore, as heretofore, obtain the required differences directly, but
must interpolate as follows: since 2-1/8 inches is quarter way between 2
inches and 2-1/2 inches, the numbers corresponding to 2-1/8 inches (for
any given distance apart of the centres), will be quarter way between
the numbers of the table corresponding to 2 inches and 2-1/2 inches.
Thus, in Table II., we have under 60 inches,
and opposite 2-1/2 in.: 2.40 2.47 2.53 2.60
" 2 1.93 1.98 2.02 2.07
---- ---- ---- ----
.47 .49 .51 .53
Dividing these differences by 4, we get:
.12 .12 .13 .13
to which we add,
1.93 1.98 2.02 2.07
and get for the differences corresponding to 2-1/8 inches
2.05 2.10 2.15 2.20
and subtracting as before,
15.5 1st step.
difference of 1st and 2nd = 2.05
-----
13.45 = 2nd "
" 2nd " 3rd = 2.10
-----
11.35 = 3rd "
" 3rd " 4th = 2.15
-----
9.20 = 4th "
" 4th " 5th = 2.20
-----
7.00 = 5th "
Thus far, however, we have considered only the case where the two cone
pulleys were exactly alike. Now although this case occurs much more
frequently than the case in which the cone pulleys are unlike, it is
nevertheless true that unlike cone pulleys occur with sufficient
frequency to make it desirable that convenient means be established for
obtaining the diameters of their steps rapidly and accurately, and Table
III. was calculated by the writer for this purpose; its accuracy is more
than sufficient for the requirements of practice, the numbers in the
table being correct to within a unit of the fourth decimal place (_i.e._
within .0001). It should be noticed that the tabular quantities are not
the diameters of the steps, but these diameters divided by the distance
between the centres of the cone pulleys; in other words, the tabular
quantities are the effective diameters of the steps only when the
centres of the pulleys are a unit's distance apart. By thus expressing
the tabular quantities in terms of the distance apart of the axis, the
table becomes applicable to all cone pulleys whatever their distance
from each other, the effective diameters of the steps being obtained by
multiplying the proper tabular quantities by the distance between the
centres of the pulleys.
II.--TABLE FOR FINDING CONE PULLEY DIAMETERS WHEN THE TWO PULLEYS ARE
CONNECTED BY AN OPEN BELT, AND ARE EXACTLY ALIKE.
The numbers given in table are the differences between the diameters of
the adjacent steps on either cone pulley, and can be employed when there
are either five or three steps on a cone.
+-------------+-----------+-----------------------------+
| Average | Adjacent | DISTANCE BETWEEN THE CENTRES|
| difference | steps, | OF CONE PULLEYS. |
| between | whose +----+----+----+----+----+----+
| the | diffe- | | | | | | |
| adjacent | rence is | 10 | 20 | 30 | 40 | 50 | 60 |
| steps. | given in | i n c h e s. |
| | table. | | | | | | |
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|0.90|0.95|0.97|0.98|0.98|0.98|
| |2nd " 3rd|0.97|0.98|0.99|0.99|0.99|0.99|
| 1 inch |3rd " 4th|1.03|1.02|1.01|1.01|1.01|1.01|
| |4th " 5th|1.10|1.05|1.03|1.02|1.02|1.02|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.28|1.39|1.43|1.45|1.46|1.46|
| |2nd " 3rd|1.43|1.46|1.48|1.48|1.48|1.49|
| 1-1/2 inch |3rd " 4th|1.57|1.54|1.52|1.52|1.52|1.51|
| |4th " 5th|1.72|1.61|1.57|1.55|1.54|1.54|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.61|1.81|1.87|1.90|1.92|1.93|
| |2nd " 3rd|1.87|1.94|1.96|1.97|1.97|1.98|
| 2 inches |3rd " 4th|2.13|2.06|2.04|2.03|2.03|2.02|
| |4th " 5th|2.39|2.19|2.13|2.10|2.08|2.07|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.89|2.20|2.30|2.35|1.38|2.40|
| |2nd " 3rd|2.30|2.40|2.43|2.45|2.46|2.47|
| 2-1/2 inches|3rd " 4th|2.70|2.60|2.57|2.55|2.54|2.53|
| |4th " 5th|3.11|2.80|2.70|2.65|2.62|2.60|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|2.10|2.57|2.71|2.78|2.83|2.86|
| |2nd " 3rd|2.71|2.86|2.90|2.93|2.94|2.95|
| 3 inches |3rd " 4th|3.29|3.14|3.10|3.07|3.06|3.05|
| |4th " 5th|3.90|3.43|3.29|3.22|3.17|3.14|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd| |3.22|3.49|3.62|3.69|3.75|
| |2nd " 3rd|3.48|3.74|3.83|3.87|3.90|3.91|
| 4 inches |3rd " 4th|4.52|4.26|4.17|4.13|4.10|4.09|
| |4th " 5th| |4.78|4.51|4.38|4.31|4.25|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd| |3.77|4.20|4.40|4.52|4.60|
| |2nd " 3rd|4.19|4.60|4.73|4.80|4.84|4.87|
| 5 inches |3rd " 4th|5.81|5.40|5.27|5.20|5.16|5.13|
| |4th " 5th| |6.23|5.80|5.60|5.48|5.40|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd| |4.21|4.83|5.13|5.31|5.42|
| |2nd " 3rd|4.82|5.42|5.62|5.71|5.77|5.81|
| 6 inches |3rd " 4th|7.18|6.58|6.38|6.29|6.23|6.19|
| |4th " 5th| |7.79|7.17|6.87|6.69|6.58|
+-------------+-----------+----+----+----+----+----+----+
+-------------+-----------+-----------------------------+
| Average | Adjacent | DISTANCE BETWEEN THE CENTRES|
| difference | steps, | OF CONE PULLEYS. |
| between | whose +----+----+----+----+----+----+
| the | diffe- | | | | | | |
| adjacent | rence is | 70 | 80 | 90 | 100| 120| 240|
| steps. | given in | i n c h e s. |
| | table. | | | | | | |
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|0.99|0.99|0.99|0.99|0.99|1.00|
| |2nd " 3rd|0.99|1.00|1.00|1.00|1.00|1.00|
| 1 inch |3rd " 4th|1.01|1.00|1.00|1.00|1.00|1.00|
| |4th " 5th|1.01|1.01|1.01|1.01|1.01|1.00|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.47|1.47|1.48|1.48|1.48|1.49|
| |2nd " 3rd|1.49|1.49|1.49|1.49|1.49|1.49|
| 1-1/2 inch |3rd " 4th|1.51|1.51|1.51|1.51|1.51|1.51|
| |4th " 5th|1.53|1.53|1.52|1.52|1.52|1.51|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|1.94|1.95|1.96|1.96|1.97|1.98|
| |2nd " 3rd|1.98|1.98|1.99|1.99|1.99|1.99|
| 2 inches |3rd " 4th|2.02|2.02|2.01|2.01|2.01|2.01|
| |4th " 5th|2.06|2.05|2.04|2.04|2.03|2.02|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|2.41|2.42|2.43|2.44|2.45|2.47|
| |2nd " 3rd|2.47|2.47|2.48|2.48|2.48|2.49|
| 2-1/2 inches|3rd " 4th|2.53|2.53|2.52|2.52|2.52|2.51|
| |4th " 5th|2.59|2.58|2.57|2.56|2.55|2.53|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|2.87|2.89|2.90|2.91|2.93|2.96|
| |2nd " 3rd|2.96|2.96|2.97|2.97|2.98|2.99|
| 3 inches |3rd " 4th|3.04|3.04|3.03|3.03|3.02|3.01|
| |4th " 5th|3.13|3.11|3.10|3.09|3.07|3.04|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|3.78|3.81|3.83|3.84|3.87|3.94|
| |2nd " 3rd|3.92|3.94|3.94|3.95|3.96|3.98|
| 4 inches |3rd " 4th|4.08|4.06|4.06|4.05|4.04|4.02|
| |4th " 5th|4.22|4.19|4.17|4.16|4.13|4.06|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|4.66|4.71|4.73|4.76|4.80|4.90|
| |2nd " 3rd|4.89|4.90|4.91|4.92|4.93|4.96|
| 5 inches |3rd " 4th|5.11|5.10|5.09|5.08|5.07|5.04|
| |4th " 5th|5.34|5.29|5.27|5.24|5.20|5.10|
+-------------+-----------+----+----+----+----+----+----+
| |1st and 2nd|5.51|5.57|5.62|5.66|5.71|5.86|
| |2nd " 3rd|5.83|5.86|5.87|5.88|5.90|5.95|
| 6 inches |3rd " 4th|6.17|6.14|6.13|6.12|6.10|6.05|
| |4th " 5th|6.49|6.43|6.38|6.34|6.29|6.14|
+-------------+-----------+----+----+----+----+----+----+
Before describing and applying the table, we will call attention to the
term "effective" diameter. The effective radius--as is well
known--extends from the centre of the pulley to the centre of the belt;
the effective diameter, being twice this effective radius, must also
equal the actual diameter plus thickness of belt.
The table is so arranged that the diameter (divided by distance between
centres) of one step of a belted pair will always be found in the
extreme right-hand column; while its companion step will be found on the
same horizontal line, and in that vertical column of the table
corresponding to the length of belt employed. For example, if column 14
of the table corresponded to the length of belt employed, some of the
possible pairs of diameters would be as follows:
.7118 .5813 .42 .2164 .0474
.06 .24 .42 .60 .72
The upper row of this series of pairs being taken from column 14, and
the lower row from the extreme right-hand column, the numbers in each
pair being on the same horizontal line. If the distance between the
centers of the pulleys were 60 ins. the effective diameters of the steps
corresponding to the above pairs would be:
42.71 34.88 25.2 12.98 2.84 ins.
3.6 14.4 25.2 36.0 43.20
being obtained by multiplying the first series of pairs by 60; the
length of belt which would be equally tight on each of these pairs would
be 3.3195 × 60 ins. = 199.17 ins.
III.--TABLE FOR FINDING THE EFFECTIVE DIAMETERS OF THE STEPS OF CONE
PULLEYS, WHEN THE PULLEYS ARE CONNECTED BY AN OPEN BELT AND ARE UNLIKE.
Each vertical cone of the table corresponds to a given length of belt,
and the numbers in these columns are the required effective diameters of
the steps when the centres of the pulleys are a Unit's distance apart.
+--------------------------------------------------------------+------+
| LENGTH OF BELT WHEN THE CENTRES OF THE CONE PULLEYS ARE A | |
| UNIT'S DISTANCE APART. | |
+------+------+------+------+------+------+------+------+------+ |
|2.0942|2.1885|2.2827|2.3770|2.4712|2.5655|2.6597|2.7540|2.8482| |
+------+------+------+------+------+------+------+------+------+ [A] |
| =1= | =2= | =3= | =4= | =5= | =6= | =7= | =8= | =9= | |
+------+------+------+------+------+------+------+------+------+------+
| .0594| .1177| .1750| .2313| .2867| .3413| .3950| .4479| .5000| 0.00 |
| .03 | .0894| .1477| .2050| .2613| .3167| .3713| .4250| .4779| 0.03 |
| | .06 | .1194| .1777| .2350| .2913| .3467| .4013| .4550| 0.06 |
| | .0294| .09 | .1494| .2077| .2650| .3213| .3767| .4313| 0.09 |
| | | .0594| .12 | .1794| .2377| .2950| .3513| .4067| 0.12 |
| | | .0275| .0894| .15 | .2094| .2677| .3250| .3813| 0.15 |
| | | | .0575| .1194| .18 | .2394| .2977| .3550| 0.18 |
| | | | .0244| .0875| .1494| .21 | .2694| .3277| 0.21 |
| | | | | .0544| .1175| .1794| .24 | .2994| 0.24 |
| | | | | .0200| .0844| .1475| .2094| .27 | 0.27 |
| | | | | | .0500| .1144| .1775| .2394| 0.30 |
| | | | | | .0140| .0800| .1444| .2075| 0.33 |
| | | | | | | .0440| .1100| .1744| 0.36 |
| | | | | | | .0064| .0740| .1400| 0.39 |
| | | | | | | | .0364| .1040| 0.42 |
| | | | | | | | | .0664| 0.45 |
| | | | | | | | | .0271| 0.48 |
+------+------+------+------+------+------+------+------+------+------+
+--------------------------------------------------------------+------+
| LENGTH OF BELT WHEN THE CENTRES OF THE CONE PULLEYS ARE A | |
| UNIT'S DISTANCE APART. | |
+------+------+------+------+------+------+------+------+------+ |
|2.9425|3.0367|3.1310|3.2252|3.3195|3.4137|3.5080|3.6022|3.6965| |
|------+------+------+------+------+------+------+------+------+ [A] |
| =10= | =11= | =12= | =13= | =14= | =15= | =16= | =17= | =18= | |
+------+------+------+------+------+------+------+------+------+------+
| .5514| .6020| .6518| .7010| .7495| .7974| .8447| .8913| .9373| 0.00 |
| .5300| .5814| .6320| .6818| .7310| .7795| .8274| .8747| .9213| 0.03 |
| .5079| .5600| .6114| .6620| .7118| .7610| .8095| .8574| .9047| 0.06 |
| .4850| .5379| .5900| .6414| .6920| .7418| .7910| .8395| .8874| 0.09 |
| .4613| .5150| .5679| .6200| .6714| .7220| .7718| .8210| .8695| 0.12 |
| .4367| .4913| .5450| .5979| .6500| .7014| .7520| .8018| .8510| 0.15 |
| .4113| .4667| .5213| .5750| .6279| .6800| .7314| .7820| .8318| 0.18 |
| .3850| .4413| .4967| .5513| .6050| .6579| .7100| .7614| .8120| 0.21 |
| .3577| .4150| .4713| .5267| .5813| .6350| .6879| .7400| .7914| 0.24 |
| .3294| .3877| .4450| .5013| .5567| .6113| .6650| .7179| .7700| 0.27 |
| .30 | .3594| .4177| .4750| .5313| .5867| .6413| .6950| .7479| 0.30 |
| .2694| .33 | .3894| .4477| .5050| .5613| .6167| .6713| .7250| 0.33 |
| .2375| .2994| .36 | .4194| .4777| .5350| .5913| .6467| .7013| 0.36 |
| .2044| .2675| .3294| .39 | .4494| .5077| .5650| .6213| .6767| 0.39 |
| .1700| .2344| .2975| .3594| .42 | .4794| .5377| .5950| .6513| 0.42 |
| .1340| .2000| .2644| .3275| .3894| .45 | .5094| .5677| .6250| 0.45 |
| .0964| .1640| .2300| .2944| .3575| .4194| .48 | .5394| .5977| 0.48 |
| .0571| .1264| .1940| .2600| .3244| .3875| .4494| .51 | .5694| 0.51 |
| .0160| .0871| .1564| .2240| .2900| .3544| .4175| .4794| .54 | 0.54 |
| | .0460| .1171| .1864| .2540| .3200| .3844| .4475| .5094| 0.57 |
| | .0029| .0760| .1471| .2164| .2840| .3500| .4144| .4775| 0.60 |
| | | .0329| .1060| .1771| .2464| .3140| .3800| .4444| 0.63 |
| | | | .0629| .1360| .2071| .2764| .3440| .4100| 0.66 |
| | | | .0174| .0929| .1660| .2371| .3064| .3740| 0.69 |
| | | | | .0474| .1229| .1960| .2671| .3364| 0.72 |
| | | | | | .0774| .1529| .2260| .2971| 0.75 |
| | | | | | .0292| .1074| .1829| .2560| 0.78 |
| | | | | | | .0592| .1374| .2129| 0.81 |
| | | | | | | .0081| .0892| .1674| 0.84 |
| | | | | | | | .0381| .1192| 0.87 |
| | | | | | | | | .0681| 0.90 |
| | | | | | | | | .0138| 0.93 |
+------+------+------+------+------+------+------+------+------+------+
+--------------------------------------------------------------+------+
| LENGTH OF BELT WHEN THE CENTRES OF THE CONE PULLEYS ARE A | |
| UNIT'S DISTANCE APART. | |
+------+------+------+------+------+------+------+------+------+ |
|3.7907|3.8850|3.9792|4.0735|4.1677|4.2620|4.3562|4.4504|4.5447| |
|------+------+------+------+------+------+------+------+------+ [A] |
| =19= | =20= | =21= | =22= | =23= | =24= | =25= | =26= | =27= | |
+------+------+------+------+------+------+------+------+------+------+
| .9828|1.0277|1.0721|1.1159|1.1593|1.2021|1.2444|1.2861|1.3274| 0.00 |
| .9673|1.0128|1.0577|1.1021|1.1459|1.1893|1.2321|1.2744|1.3161| 0.03 |
| .9513| .9973|1.0428|1.0877|1.1321|1.1759|1.2193|1.2621|1.3044| 0.06 |
| .9347| .9813|1.0273|1.0728|1.1177|1.1621|1.2059|1.2493|1.2921| 0.09 |
| .9174| .9647|1.0113|1.0573|1.1028|1.1477|1.1921|1.2359|1.2793| 0.12 |
| .8995| .9474| .9947|1.0413|1.0873|1.1328|1.1777|1.2221|1.2659| 0.15 |
| .8810| .9295| .9774|1.0247|1.0713|1.1173|1.1628|1.2077|1.2521| 0.18 |
| .8618| .9110| .9595|1.0074|1.0547|1.1013|1.1473|1.1928|1.2377| 0.21 |
| .8420| .8918| .9410| .9895|1.0374|1.0847|1.1313|1.1773|1.2228| 0.24 |
| .8214| .8720| .9218| .9710|1.0195|1.0674|1.1147|1.1613|1.2073| 0.27 |
| .8000| .8514| .9020| .9518|1.0010|1.0495|1.0974|1.1447|1.1913| 0.30 |
| .7779| .8300| .8814| .9320| .9818|1.0310|1.0795|1.1274|1.1747| 0.33 |
| .7550| .8079| .8600| .9114| .9620|1.0118|1.0610|1.1095|1.1574| 0.36 |
| .7313| .7850| .8379| .8900| .9414| .9920|1.0418|1.0910|1.1395| 0.39 |
| .7067| .7613| .8150| .8679| .9200| .9714|1.0220|1.0718|1.1210| 0.42 |
| .6813| .7367| .7913| .8450| .8979| .9500|1.0014|1.0520|1.1018| 0.45 |
| .6550| .7113| .7667| .8213| .8750| .9279| .9800|1.0314|1.0820| 0.48 |
| .6277| .6850| .7413| .7967| .8513| .9050| .9579|1.0100|1.0614| 0.51 |
| .5994| .6577| .7150| .7713| .8267| .8813| .9350| .9879|1.0400| 0.54 |
| .57 | .6294| .6877| .7450| .8013| .8567| .9113| .9650|1.0179| 0.57 |
| .5394| .60 | .6594| .7177| .7750| .8313| .8867| .9413| .9950| 0.60 |
| .5075| .5694| .63 | .6894| .7477| .8050| .8613| .9167| .9713| 0.63 |
| .4744| .5375| .5994| .66 | .7194| .7777| .8350| .8913| .9467| 0.66 |
| .4400| .5044| .5675| .6294| .69 | .7494| .8077| .8650| .9213| 0.69 |
| .4040| .4700| .5344| .5975| .6594| .72 | .7794| .8377| .8950| 0.72 |
| .3664| .4340| .5000| .5644| .6275| .6894| .75 | .8094| .8677| 0.75 |
| .3271| .3964| .4640| .5300| .5944| .6575| .7194| .78 | .8394| 0.78 |
| .2860| .3571| .4264| .4940| .5600| .6244| .6875| .7494| .81 | 0.81 |
| .2429| .3160| .3871| .4564| .5240| .5900| .6544| .7175| .7794| 0.84 |
| .1974| .2729| .3460| .4171| .4864| .5540| .6200| .6844| .7475| 0.87 |
| .1492| .2274| .3029| .3760| .4471| .5164| .5840| .6500| .7144| 0.90 |
| .0981| .1792| .2574| .3329| .4060| .4771| .5464| .6140| .6800| 0.93 |
| .0438| .1281| .2092| .2874| .3629| .4360| .5071| .5764| .6440| 0.96 |
| | .0738| .1581| .2392| .3174| .3929| .4660| .5371| .6064| 0.99 |
| | .0157| .1038| .1881| .2692| .3474| .4229| .4960| .5671| 1.02 |
| | | .0457| .1338| .2181| .2992| .3774| .4529| .5260| 1.05 |
| | | | .0757| .1638| .2481| .3292| .4074| .4829| 1.08 |
| | | | .0131| .1057| .1938| .2781| .3592| .4374| 1.11 |
| | | | | .0431| .1357| .2238| .3081| .3892| 1.14 |
| | | | | | .0731| .1657| .2538| .3381| 1.17 |
| | | | | | .0050| .1031| .1957| .2838| 1.20 |
| | | | | | | .0350| .1331| .2257| 1.23 |
| | | | | | | | .0650| .1631| 1.26 |
| | | | | | | | | .0950| 1.29 |
| | | | | | | | | .0200| 1.32 |
+------+------+------+------+------+------+------+------+------+------+
+-----------------------------------------+------+
| LENGTH OF BELT WHEN THE CENTRES OF THE | |
|CONE PULLEYS ARE A UNIT'S DISTANCE APART.| |
+------+------+------+------+------+------+ |
|4.6389|4.7332|4.8274|4.9217|5.0159|5.1102| |
|------+------+------+------+------+------+ [A] |
| =28= | =29= | =30= | =31= | =32= | =33= | |
+------+------+------+------+------+------+------+
|1.3682|1.4085|1.4484|1.4877|1.5266|1.5650| 0.00 |
|1.3574|1.3982|1.4385|1.4784|1.5177|1.5566| 0.03 |
|1.3461|1.3874|1.4282|1.4685|1.5084|1.5477| 0.06 |
|1.3344|1.3761|1.4174|1.4582|1.4985|1.5384| 0.09 |
|1.3221|1.3644|1.4061|1.4474|1.4882|1.5285| 0.12 |
|1.3093|1.3521|1.3944|1.4361|1.4774|1.5182| 0.15 |
|1.2959|1.3393|1.3821|1.4244|1.4661|1.5074| 0.18 |
|1.2821|1.3259|1.3693|1.4121|1.4544|1.4961| 0.21 |
|1.2677|1.3121|1.3559|1.3993|1.4421|1.4844| 0.24 |
|1.2528|1.2977|1.3421|1.3859|1.4293|1.4721| 0.27 |
|1.2373|1.2828|1.3277|1.3721|1.4159|1.4593| 0.30 |
|1.2213|1.2673|1.3128|1.3577|1.4021|1.4459| 0.33 |
|1.2047|1.2513|1.2973|1.3428|1.3877|1.4321| 0.36 |
|1.1874|1.2347|1.2813|1.3273|1.3728|1.4177| 0.39 |
|1.1695|1.2174|1.2647|1.3113|1.3573|1.4028| 0.42 |
|1.1510|1.1995|1.2474|1.2947|1.3413|1.3873| 0.45 |
|1.1318|1.1810|1.2295|1.2774|1.3247|1.3713| 0.48 |
|1.1120|1.1618|1.2110|1.2595|1.3074|1.3547| 0.51 |
|1.0914|1.1420|1.1918|1.2410|1.2895|1.3374| 0.54 |
|1.0700|1.1214|1.1720|1.2218|1.2710|1.3195| 0.57 |
|1.0479|1.1000|1.1514|1.2020|1.2518|1.3010| 0.60 |
|1.0250|1.0779|1.1300|1.1814|1.2320|1.2818| 0.63 |
|1.0013|1.0550|1.1079|1.1600|1.2114|1.2620| 0.66 |
| .9767|1.0313|1.0850|1.1379|1.1900|1.2414| 0.69 |
| .9513|1.0067|1.0613|1.1150|1.1679|1.2200| 0.72 |
| .9250| .9813|1.0367|1.0913|1.1450|1.1979| 0.75 |
| .8977| .9550|1.0113|1.0667|1.1213|1.1750| 0.78 |
| .8694| .9277| .9850|1.0413|1.0967|1.1513| 0.81 |
| .84 | .8994| .9577|1.0150|1.0713|1.1267| 0.84 |
| .8094| .87 | .9294| .9877|1.0450|1.1013| 0.87 |
| .7775| .8394| .90 | .9594|1.0177|1.0750| 0.90 |
| .7444| .8075| .8694| .93 | .9894|1.0477| 0.93 |
| .7100| .7744| .8375| .8994| .96 |1.0194| 0.96 |
| .6740| .7400| .8044| .8675| .9294| .99 | 0.99 |
| .6364| .7040| .7700| .8344| .8975| .9594| 1.02 |
| .5971| .6664| .7340| .8000| .8644| .9275| 1.05 |
| .5560| .6271| .6964| .7640| .8300| .8944| 1.08 |
| .5129| .5860| .6571| .7264| .7940| .8600| 1.11 |
| .4674| .5429| .6160| .6871| .7564| .8240| 1.14 |
| .4192| .4974| .5729| .6460| .7171| .7864| 1.17 |
| .3681| .4492| .5274| .6029| .6760| .7471| 1.20 |
| .3138| .3981| .4792| .5574| .6329| .7060| 1.23 |
| .2557| .3438| .4281| .5092| .5874| .6629| 1.26 |
| .1931| .2857| .3738| .4581| .5392| .6174| 1.29 |
| .1250| .2231| .3157| .4038| .4881| .5692| 1.32 |
| .0500| .1550| .2531| .3457| .4338| .5181| 1.35 |
| | .0800| .1850| .2831| .3757| .4638| 1.38 |
| | | .1100| .2150| .3131| .4057| 1.41 |
| | | .0255| .1400| .2450| .3431| 1.44 |
| | | | .0555| .1700| .2750| 1.47 |
| | | | | .0855| .2000| 1.50 |
+------+------+------+------+------+------+------+
Legend: [A] = Assumed diameter of steps, divided by distance between the
centres of Cone Pulleys.
To get the actual diameters of these steps when thickness of belt = 7/32
= 0.22 in., we have simply to subtract 0.22 in. from the effective
diameters just given, thus:
42.49 34.66 24.98 12.76 2.62 in.
3.38 14.18 24.98 35.78 42.98
would be the series of pairs of actual diameters.
In solving problems relating to the diameters of cone pulleys by means
of the accompanying table, we must have, besides the distance between
centres, sufficient data to determine the column representing the length
of belt. The length of belt is seldom known because it is of small
practical importance to know its exact length; but it may be estimated
approximately, and then the determination of suitable diameters of the
steps becomes an extremely simple matter, as may be seen from what has
already preceded. When the length of the belt is not known, and has not
been assumed, we indirectly prescribe the length of belt by assuming the
effective diameters of the two steps of a belted pair; thus, in the
following Figure (561), the length of belt is prescribed when the
distance A B, and any one of the pairs of steps D_{1}_d__{1},
D_{2}_d__{2}, D_{3}_d__{3} and D_{4}_d__{4} are given. We will show in
the following examples how the length of belt and its corresponding
column of diameter may be found when a pair of steps (like
D_{1}_d__{1}), are given.
[Illustration: Fig. 561.]
EXAMPLE 1. Given the effective diameters
4.5 in. 9 in. 15 in. 21 in. on cone A,
-- -- 15 in. -- " B,
and the distance between centres equal to 50 inches.
Required the remaining diameters on cone B.
Since in this example the steps of the given pair are equal, we look for
15/50 = 0.30, in the extreme right-hand column of table; we will find it
in the 11th line from the top; now looking along this line for the
diameter of the other step, = 15/50 = 0.30, we will find it in column
10; consequently the numbers of this column may be taken as the
diameters of the steps which are the companions or partners of those in
the extreme right-hand column.
We can now easily determine the remaining members of the pairs to which
4.5 in., 9 in., and 21 in. steps respectively belong. To find the
partner of the 4.5 step, we find 4.5/50 = 0.09 in the right-hand column,
and look along the horizontal line on which 0.09 is placed till we come
to column 10, in which we will find the number 0.4850; 0.4850 × 50 in. =
24.25 in. will be the effective diameter of the companion to the 4.5 in.
step.
To find the partner to the 9 in. step, we proceed as before, looking for
9/50 = 0.18 in the right-hand column, and then along the horizontal line
of 0.18 to column 10, then will 0.4113 × 50 in. = 20.57 in. be the
required companion to the 9 in. step of cone A.
In like manner for the partner of the 21 in. step we get 0.1700 × 50 in.
= 8.5 in. The effective diameter therefore will be,
4.5 in. 9 in. 15 in. 21 in. on cone A,
24.25 20.57 15 in. 8.5 " B.
If the thickness of belt employed were 0.25 in. the _actual_ diameters
of steps would be,
4.25 8.75 14.75 20.75 on cone A,
24.00 20.32 14.75 8.25 " B,
and the length of belt would be 2.9425 × 50 = 147.125 in.
EXAMPLE 2. Given the effective diameters
6 in. 12 in. 18 in. 24 in. on cone A,
30 in. -- -- -- " B,
and the distance between centres = 40 in.
Required the unknown diameters on cone B.
We must, as before, first find the vertical column corresponding to the
length of belt which joins the pair of steps 6 in/30 in. We find the
number 6/40 = .15 in the right-hand column, and then look along its
horizontal line for its partner 30/40 = 0.75. Since we do not find any
number exactly equal to .7500, we must interpolate. For the benefit of
those not familiar with the method of interpolation we will give in
detail the method of finding intermediate columns of the table. On the
aforesaid horizontal line we find in column 16 a number 0.7520, larger
than the required 0.7500, and in column 15 a number 0.7014, smaller than
0.7500; evidently the intermediate column, containing the required
0.7500, must lie between columns 16 and 15. To find how far the required
column is from column 16, we subtract as follows:
0.7520 0.7520
0.7500 0.7014
------ ------
.0020 0.0506
then the fraction .0020/.00506 = 0.04 nearly will represent the position
of the required intermediate column; namely, that its distance from
column 16 is about 4/100 of the distance between the adjacent columns,
15 and 16.
To find other numbers in this intermediate column we have only to
multiply the difference between the adjacent numbers of columns 16 and
15 by 0.04, and subtract the product from the number in column 16. But
it is not necessary to find as many numbers of the intermediate columns
as are contained in either of the adjacent columns; it is only necessary
to find as many numbers as there are steps in each of the cone pulleys.
We will now illustrate what has preceded, by finding the partner to the
12 in. step of cone A. Find, as before, the horizontal line
corresponding to 12/40 = 0.30, then take the difference between the
numbers 0.6413 and 0.5867 of columns 16 and 15, and multiply this
difference, 0.0546, by 0.04; this product = 0.0022 subtracted from
0.6413, will give 0.6391, a number of the intermediate columns
corresponding to the length of belt of the present problem. Multiplying
by the distance between the axes = 40 in. we get 0.6391 × 40 = 25.56,
for the diameter of the step of cone B which is partner to the 12 in.
step of cone A.
To find the companion to the 18 in. step, we proceed in the same manner,
looking for the horizontal line 18/40 = 0.45, and interpolating as
follows:
0.5094 - (0.5094 - 0.4500) × 0.04 = 0.5070.
Consequently, 0.5070 × 40 in. = 20.28 in. will be the required partner
of the 18 in. step.
In like manner, for the 24 in. step, we have
0.3500 - (0.3500 - 0.2840) × 0.04 = 0.3474, and 0.3474 × 40 = 13.90.
The effective diameters are therefore
6 in. 12 in. 18 in. 24 in. on cone A.
30 25.56 20.28 13.9 " B.
The actual diameters, when thickness of belt = 0.20 in., are:
5.8 11.8 17.8 23.8 on cone A.
29.8 25.36 20.08 13.7 " B.
And the length of belt will be:
[3.5080 - (3.5080 - 3.4137) × 0.04] × 40 in. = 140.17 in.
EXAMPLE 3. Given the effective diameters:
12 in. 18 in. 24 in. 30 in. on cone A,
33 in. -- -- -- " B,
and the distance between the centres = 60 in.
Required the remaining diameters on cone B.
The horizontal corresponding to 12/60 = 0.20 lies 2/3rd way between the
horizontal line, corresponding to 0.18 and 0.21; the number 33/60 =
0.5500, corresponding to the companion of the 12 in. step, will
therefore lie 2/3rd way between the horizontal lines 0.18 and 0.21. We
have now to find two numbers on this 2/3rd line, of which one will be
less and the other greater than 0.5500. An inspection of the table will
show that these greater and less numbers must lie in columns 13 and 12.
The numbers on the 2/3rd line itself may now be found as follows:
In column 13, 0.5750 - 2/3(0.5750 - 0.5513) = 0.5592.
In column 12, 0.5213 - 2/3(0.5213 - 0.4967) = 0.5049.
0.5592 will be the number on the 2/3rd line, which is greater than
0.5500, and 0.5049 will be the one which is less than 0.5500. The
position of the intermediate column, corresponding to the length of belt
of the present example, may now be found, as before, briefly. It is:
0.5592 - 0.5500 = 0.0092
= 0.17.
0.5592 - 0.5049 = 0.0543
Consequently the required column lies nearest column 13, 17/100th way
between columns 13 and 12. To find any other number in the required
column, we have only to multiply the difference between two adjacent
numbers of columns 13 and 12 by 17/100, and subtract the product from
the number in column 13. For example, to find the diameter of the
partner to the 18 in. step of cone A, we find the numbers 0.4750 and
0.4177 of columns 13 and 12, which lie on the horizontal line
corresponding to 18/60 = 0.30; the difference, 0.0573, between the two
numbers is multiplied by 0.17, and the product, 0.0573 × 0.17 = 0.0097,
subtracted from 0.4750. This last difference will equal 0.4653, and will
be the number sought. If we now multiply by 60, we will get 27.92 in. as
the effective diameter of that step on cone B which is the partner to
the 18 in. step of cone A.
To find the companion of the 24 in. step, we proceed after the same
fashion; the horizontal line 24/60 = 0.40 lies 1/3rd way between 0.39
and 0.42; hence,
In column 13, 0.3900 - 1/3(0.3900 - 0.3594) = 0.3798;
In column 12, 0.3294 - 1/3(0.3294 - 0.2975) = 0.3188;
And 0.3798 - (0.3798 - 0.3188) × 0.17 = 0.3694.
The required effective diameter of the step, which is partner to the 24
in. step, will therefore be 0.3694 × 60 = 22.16 in.
In like manner we obtain partner for the 30 in. step, thus:
In column 13, 0.2944 - 2/3(0.2944 - 0.2600) = 0.2715.
In column 12, 0.2300 - 2/3(0.2300 - 0.1940) = 0.2060.
Also 0.2715 - (0.2715 - 0.2060) × 0.17 = 0.2604, and 0.2604 × 60 in. =
15.62 in. = diam. of step belonging to the same belted pair as the 30
in. step of cone A.
The effective diameters will be:
12 in. 18 in. 24 in. 30 in. on cone A,
33 27.92 22.16 15.62 " B,
and the actual diameters when belt is 0.22" thick:
11.78 17.78 23.78 29.78 in.
32.78 27.70 21.94 15.40
and the length of belt is found to be:
[3.2252 - (3.2252 - 3.1310) × 0.17] × 60 in. = 192.55 in.
In all the preceding problems it should be noticed that we arbitrarily
assumed _all_ the steps on one cone, and _one_ of the steps on the other
cone. It will be found that all of the practical problems relating to
cone-pulley diameters can finally be reduced to this form, and can
consequently be solved according to the methods just given.
For those who find difficulty in interpolating, the following procedure
will be found convenient: Estimate approximately the necessary length of
belt, then divide this length by the distance between the centres of the
cone pulleys; now find which one of the 33 lengths of belt (per unit's
distance apart of the centres) given in the table is most nearly equal
to the quotient just obtained, and then take the vertical column, at the
head of which it stands, for the companion to the right-hand column.
Those numbers of these companion columns which are on the same
horizontal line will be the companion steps of a belted pair. The table
is so large, that in the great majority of cases not only exact, but
otherwise satisfactory values can be obtained by this method, without
any interpolation whatever."
[Illustration: Fig. 562.]
The teeth of the back gear should be accurately cut so that there is no
lost motion between the teeth of one wheel, and the spaces of the other,
because on account of the work being of large diameter or of hard metal
(so as to require the slow speed), the strain of the cut is nearly
always heavy when the back gear is in use, and the strain on the teeth
is correspondingly great, causing a certain amount of spring or
deflection in the live spindle and back gear spindle. Suppose then, that
at certain parts of the work there is no cut, then when the tool again
meets the cut the work will meet the tool and stand still until the lost
motion in the gear teeth and the spring of the spindles is taken up,
when the cut will proceed with a jump that will leave a mark on the work
and very often break the tool. When the cut again leaves the tool a
second jump also leaving a mark on the work will be made. If the teeth
of the gears are cut at an angle to the axial line of the spindle, as is
sometimes the case, this jumping from the play between the teeth will be
magnified on account of a given amount of play, affording more back lash
in such gears.
The teeth of the wheels should always be of involute and not of
epicycloidal form, for the following reasons. The transmission of motion
by epicycloidal teeth is exactly uniform only when their pitch circles
exactly coincide, and this may not be the case in time because of wear
in the parts as in the live spindle journals and the bearings, and the
back gear spindle and its bearings, and _every variation of speed_ in
the cut, however slight it may be, produces a corresponding mark upon
the work. In involute teeth the motion transmitted will be smooth and
equal whether the pitch lines of the wheels coincide or not, hence the
wear of the journals and bearings does not impair their action.
The object of cutting the teeth at an angle is to have the point of
contact move or roll as it were from one end to the other of the teeth,
and thus preserve a more conterminous contact on the line of centres of
the two wheels, the supposition being that this would remove the marks
on the work produced by the tremor of the back gear. But such tremor is
due to errors in the form of the teeth, and also in the case of
epicycloidal teeth from the pitch lines of the teeth not exactly
coinciding when in gear.
The pitch of the teeth should be as fine as the requisite strength, with
the usual allowance of margin for wear and safety will allow, so as to
have as many teeth in continuous contact as possible.
Various methods of moving the back gear into and out of gear with the
cone spindle gears are employed. The object is to place the back gears
into gear to the exact proper depth to hold them securely in position,
and to enable the operator to operate the gears without passing to the
back of the lathe. Sometimes a sliding bearing box, such as shown in
Fig. 562, is employed; _a_ is the back gear spindle, _b_ its bearing
box, and _d_ a pin which when on the side shown holds _b_ in position,
when the back gear is in action. To throw it out of action _d_ is
removed, _b_ pushed back, and _d_ inserted in a hole on the right hand
of _b_; the objection is that there is no means of taking up the wear of
_b_, and it is necessary to pass to the back of the lathe to operate the
device.
[Illustration: Fig. 563.]
Another plan is to let the back gear move endwise and bush its bearing
holes with hardened steel bushes. This possesses the advantage that the
gear is sure, if made right, to keep so, but it has some decided
disadvantages: first, the pinion A, Fig. 563, must be enough larger than
the smallest cone-step B to give room between B and C for the belt, and
this necessitates that D also be larger than otherwise; secondly, the
gear-spindle F projects through the bearing at _f_, and this often comes
in the way of the bolt-heads used for chucking work to the face plate.
The method of securing the spindle from end motion is as follows: On the
back of the head is pivoted at _i_, a catch G, and on the gear shaft F
are two grooves. As shown in the sketch, G is in one of these grooves
while H is the other, but when the back gear is in, G would be in H.
[Illustration: Fig. 564.]
Sometimes a simple eccentric bush and pin is used as in Fig. 564, in
which _a_ is the spindle journal, _b_ a bush having bearing in the lathe
head, and _d_ a taper pin to secure _b_ in its adjusted position.
[Illustration: Fig. 565.]
In large heavy lathes having many changes of speed, there are various
other constructions, as will be seen upon the lathes themselves in the
various illustrations concerning the methods of throwing the back gear
in and out. The eccentric motion shown in Fig. 573 of the Putnam lathe,
is far preferable to any means in which the back-gear spindle moves
endways, because, as before stated, the end of the back-gear spindle
often comes in the way of the bolts used to fasten work to the large
face plate. This occurs mainly in chucked work of the largest diameter
within the capacity of the lathe.
[Illustration: Fig. 566.]
In many American lathes the construction of the gearing that conveys
motion from the live spindle is such that facility is afforded to throw
the change gears out of action when the lathe is running fast, as for
polishing purposes, so as to save the teeth from wear. Means are also
provided to reverse the direction of lead screw or feed screw
revolution. An example of a common construction of this kind is shown in
Fig. 565, in which the driving wheel A is on the inner side of the back
bearing as shown. It drives (when in gear) a pair of gears, one only of
which is seen in the figure at B, which drives C, and through R, D, I,
and S, the lead screw. A side view of the wheel A and the mechanism in
connection therewith is shown in Fig. 566, in which S represents the
live spindle and R is a spindle or shaft corresponding to R in Fig. 565.
L is a lever pivoted upon R and carrying two pinions B and E; pinion B
is of larger diameter than E, so that B gears with both C and E (C
corresponding to wheel C in Fig. 565), while E gears with B only.
[Illustration: Fig. 567.]
With the lever L in the position shown, neither B nor E engages with A,
hence they are at rest; but if lever L be raised as in Fig. 567, B will
gear with wheels A and C, and motion will be conveyed from A to C, wheel
E running as an idle wheel, thus C will revolve in the same direction as
the lathe spindle.
But if lever L be lowered as in fig. 568, then wheel E will gear with
and receive motion from A, which it will convey to B, and C will revolve
in the opposite direction to that in which the lathe spindle runs. To
secure lever L in position, a pin F passes through it and into holes as
I, J, provided in the lathe head. Lever L is sometimes placed inside the
head, and sometimes outside as in Fig. 569, and it will be obvious that
it may be used to cut left-hand threads without the use of an extra
intermediate change gear, which is necessary in the construction shown
in Fig. 570, in order to reverse the direction of lead screw revolution.
Sometimes the pin F is operated by a small spring lever attached
to L, so that the hand grasps the end of L and the spring lever
simultaneously, removing F from the hole in H, and therefore freeing L,
so as to permit its operation. By relaxing the pressure on the small
spring lever pin F finds its own way into the necessary hole in H, when
opposite to it, without requiring any hand manipulation.
In larger lathes the lever L is generally attached to its stud outside
the end bearing of the head H.
[Illustration: Fig. 568.]
It is preferable, however, that the device for changing the direction of
feed traverse be operative from the lathe carriage as in the Sellers
lathe, so that the operator need not leave it when it is necessary to
reverse the direction of traverse.
[Illustration: Fig. 569.]
The swing frame, when the driving gear D is outside of the back bearing
(as it is in Fig. 570), is swung from the axis of the lead screw as a
centre of motion, and has two slots for receiving studs for change
wheels. But when the driving gear is inside the back bearing as in Fig.
571, the swing frame may be suspended from the spindle (R, Fig. 565)
that passes through the lathe head, which may also carry the cone for
the independent feed as shown in Fig. 571, no matter on which side of
the lathe the lead screw and feed rod are. This affords the convenience
that when both lead screw and feed rod are in front of the lathe, the
feed may be changed from the screw cutting to the rod feed, or _vice
versâ_, by suitable mechanism in the apron, without requiring any change
to be made in the driving gears.
[Illustration: Fig. 570.]
In the lathe shown in Fig. 572, which is from the design of S. W.
Putnam, of the Putnam Tool Company of Fitchburg, Massachusetts, the cone
pinion for the back gear, and that for driving the feed motion, are of
the same diameter and pitch, so that the gear-wheel L in Fig. 573 may
(by means of a lever shown dotted in) be caused to engage with either of
them. When the latter is used in single gear it would obviously make no
difference which wheel drives L, but when the back gear is put in and L
is engaged with the cone pinion, its speed corresponds to that of the
cone, which being nine times faster than the live spindle, enables the
cutting of threads nine times as coarse as if the back gear was not in
use. This affords very great advantages for cutting worms and threads of
coarse pitches.
An excellent method of changing the direction of feed motion, and of
starting or stopping the same, is shown in Fig. 574, which represents
the design of the Ames Manufacturing Company's lathe.
[Illustration: Fig. 571.]
In the figure, A is the small step of the lathe cone, B the pinion to
drive the back gear, C a pinion to drive the feed gear, giving motion to
D, which drives E, the latter being fast to G and rotating freely upon
the shaft F, G drives H, which in turn drives I. The clutch J has a
featherway into which fits the feather _c_, on the shaft F, so that when
the clutch rotates it rotates J through the medium of _c_; K is a
circular fork in a groove in J, and operated by a lever operated by a
rod running along the front of the lathe bed. This rod is splined so
that a lever carried by the apron or feed-table, having a hub and
enveloping the rod, may by means of a feather filling into the spline
operate the rod by partly rotating it, and hence operate K. Suppose now
that this lever stands horizontal, then the clutch J would stand in the
position shown in the cut, and D, E, G, H, and I, would rotate, while F
would remain stationary. By lifting the lever, however, J would be moved
laterally on F (by means of K) and the lug _a_ on J would engage with
lug _b_ on G, and G would drive J, which through _c_ would drive F, on
which is placed a change gear at L, thus traversing the carriage
forward. To traverse it backward the lever would be lowered or depressed
below the horizontal level moving K, and therefore J, to the right, so
that lug _a_ would engage with lug _b_ on I, hence F would be driven by
I, whose motion is in an opposite direction to G, as is denoted by the
respective arrows.
[Illustration: Fig. 572.]
To throw all the feed motion out of gear, to run the lathe at its
quickest for polishing, &c., the operation is as follows.
[Illustration: Fig. 573.]
M is tubular and fast in N and affords journal bearing to wheel D.
Through M passes stud O, having a knob handle at P. At the end of the
hub of D is a cap fast in D, the latter being held endways between the
shoulder shown on O and the washer and nut T. If then P be pulled
outwards O will slide through M, and through the medium of T will cause
D to slide over M, in the direction of the arrow, and pass out of gear
from C, motion therefore ceasing at C.
Q is the swing frame for the studs to carry the change wheels, and R a
bolt for securing Q in its adjusted position. S is a journal and bearing
for H.
If it be considered sufficient the feed motion on small lathes (instead
of feeding in both directions on the lateral and cross feeds as in the
Putnam Lathe), may feed in the direction from the dead to the live
centre, and in one direction only on the cross slide.
[Illustration: Fig. 574.]
An example of a feed motion of this kind is shown in Figs. 575 and 576;
_f_ _f_ is the feed spindle splined and through the medium of a feather
driving the bevel pinion A having journal bearing in B. Pinion A drives
the bevel gear C, which is in one piece with pinion D. The latter drives
gear F, which drives pinion K, which is carried on a lever L, pivoted on
the stud which carries F, so that by operating L, pinion K is brought
into gear with pinion P, which is fast upon the cross-feed screw, and
therefore rotates it to effect the automatic cross feed.
[Illustration: Fig. 575.]
[Illustration: Fig. 576.]
As shown in the cut, the lever L is in such a position as to throw K out
of gear with P, and the cross feed screw is free to be operated by the
handle by hand. At M is a slot in L in which operates a cam or
eccentric, one end of which projects into L, while at the other end is
the round handle R, Fig. 575, which is rotated to raise or lower that
end of L so as to operate K. To operate the saddle or carriage the
motion is continued as follows:--at the centre of F is a pinion gear G
which operates a gear H, which is in one piece with the pinion I, and
the latter is in gear with the rack running along the lathe bed.
If the motion from A to I was continuous, the carriage feed or traverse
would be continuous, but means are provided whereby motion from F to I
may be discontinued, as follows:--A hand traverse or feed is provided.
J, Figs. 575 and 576, is carried by a stud having journal bearing in a
hub on X and receiving the handle Q; hence by operating Q, J is rotated,
operating the gear H, upon which is the pinion I, which is in gear with
the rack running along the lathe bed.
To lock the carriage in a fixed position, as is necessary when operating
the cross feed on large radial surfaces, the following device is
provided:--N is a stud fixed in a hub on X, and having a head which
overlaps the rim of H, as shown in figure. On the other side of that rim
is a washer Z on the same stud having a radial face also overlapping the
rim of H, but its back face is bevelled to a corresponding bevel on the
radial face on the hub of lever O (the hub of O being pivoted on the
same stud). When therefore O is depressed the two-bevel face of the hub
of O forces the washer Z against the face of the wheel H, whose radial
faces at the rim are therefore gripped between the face of the collar N
and that of the washer Z, hence H is locked fast. By raising the end of
lever O, Z is released and H is free to rotate.
Both the carriage feed and cross feed can only be traversed in one
direction so far as these gears and levers are concerned, but means are
provided on the lathe headstock for reversing the direction of motion of
the feed spindle _f_ so as to reverse the direction of the feeds. It
will be observed that so long as _f_ rotates, A, C, D, and F rotate, the
remaining motions only operating when S is screwed up.
In order to obtain a delicate tool motion from the handle Q it is
necessary to reduce the motion between J and I as much as possible, a
point in which a great many lathes as at present constructed are
deficient, because Q, although used to simply traverse the carriage
along the bed, in which case rapid motion of the latter is desirable, is
also used to feed the tool into corners when the lathe has no compound
rest to put on light cuts on radial faces, hence it should be capable of
giving a delicate tool motion.
[Illustration: Fig. 577.]
On account of the deficiency referred to it is often necessary to put on
a fine radial cut by putting the feed traverse in gear, and, throwing
the feed screw gear out of contact with the other change wheels, pull it
around by hand to put on the cut. In compound slide rests these remarks
do not apply, because the upper part of the rest may be used instead of
the handle Q.
Many small lathes are provided with a tool rest known as the _elevating
rest_, or weighted lathe.
An excellent example of an elevating rest for a weighted lathe is shown
in Figs. 577 and 578, which represent the construction in the Pratt and
Whitney lathe. A is the lathe shears upon which slides the carriage
provided with [V] slideways R for the sliding piece B, and provided at
the other end with the guides H. The cross slide S is pivoted upon B at
D, and fits at the other end between the guides H. At E is the elevating
screw which when operated raises or lowers that end of the elevating
rest to adjust the tool height. This also affords an excellent means of
making a minute adjustment for depth of tool cut. The tool rest F is
bolted to S.
[Illustration: Fig. 578.]
The weight W is suspended from S and, therefore, holds one end of S to
B, the lathe to C, and C to A; at the other end the weight holds S to C
(through the medium of the elevating screw E) and C to A. The cross feed
nut N is fast to S, the cross feed screw being operated by hand wheel G.
B is provided with the [V] slideways R, which slide upon corresponding
[V] slides R´ upon C; P is a lug cast upon C, and K is a screw threaded
in B. When the end of screw K abuts against P the motion of S, and,
therefore, of the cutting tool T, towards the work is arrested, hence
when the tool is adjusted to the proper depth of cut, K is operated to
abut firmly against P, and successive pieces may be turned to the same
diameter without requiring each piece to be measured for diameter. N is
the handle for opening and closing the nut for the feed screw Q, and Z
is the wheel for the hand feed traverse. The length of cross feed motion
is determined by the length of the cross [V] slides R´.
This class of rest possesses the advantage that no lost motion in the
slides occurs by reason of the wear, because the weight keeps the parts
in constant contact notwithstanding such wear; on the other hand,
however, the slide [V]s sustain the extra wear due to the weight W in
addition to the weight of the carriage. Lathes of this class are
intended for light work, and are less suited for boring than for plain
turning; they are, however, very convenient, and are preferred by many
to any other kind of lathe for short and light work.
[Illustration: Fig. 579.]
The tool rest being removable may be supplanted by other special forms
of rest. Thus Figs. 579 and 580 represent a special rest for carrying
two tools to cut pieces of work to the exact same length. Bolts D and E
are to secure the rest A to the elevating rest, and C C are the clamps
for the two tools B.
[Illustration: Fig. 580.]
Fig. 581 represents a cross sectional view of the Putnam Tool Company's
gibbed elevating rest, there being a gib on the underneath side of the
front shear. The elevating screw is pivoted by a ball joint. By
employing a gib instead of a weight, the bed may be provided with cross
girts or ribs joining the two sides of the shear, thus giving much
greater stiffness to it.
Figs. 582, 583, and 584 represent a lathe feed motion by William Munzer,
of New York. The object in this motion is to insure that no two feeds
can be put into operation simultaneously, because putting the feed in
motion in one direction throws it out of gear for either of the others.
Another object is to have the transmitting motion as direct as possible
so as to avoid the rotation of any wheels not actually necessary for the
transmission of the motion; and a third object is to enable the throwing
out of gear of all wheels (when no feed motion at all is required)
without leaving the apron.
The means employed to effect these objects are as follows:--
In Fig. 582 _f_ represents the independent feed spindle and S the
lead-screw: _f_ is splined to drive A, A´ and A´´, which is a sleeve in
one piece, and consists of a circular rack at A, a bevel pinion at A´,
and a second bevel pinion at A´´. This sleeve may be operated in either
direction along _f_ by rotating the pinion B. As shown in the cut A´ and
A´´ are both out of gear with the bevel-wheel C, but if B be rotated to
the right then A´ will be in gear with C, or if it be operated to the
left then A´´ will be in gear with C. Now the direction of rotation of C
will be governed by which pinion, A´ or A´´, drives it, and these are
the means by which the direction of the feed traverse and also of the
cross feed is determined.
If none of the feeds are required to operate, the sleeve occupies the
position shown in the cut, and the circular rack at A simply rotates
while B and all other parts remain at rest. On the same central pin as C
is the pinion D driving a spur gear E´´. On the same centre pin as E is
the gear F driving G, which is on the same central pin as C and D. The
gear H is fixed to and rotates with G and drives I; all these gears
serving to reduce the speed of motion when operating to feed the
carriage traverse in either direction.
A gear J is carried on the end of a lever K, being pivoted at L. In the
position shown J is out of gear with all gears, but it may be swung to
the right so as to engage with wheel I and wheel M, and convey the
motion of I to M. Upon the same spindle as M is the pinion N, engaging
with the rack O, which is fast on the lathe bed. This completes the
automatic feed traverse.
For a hand feed traverse, pinion P is employed to drive M, which is fast
to N. The cross feed is self-acted by moving lever K to the left,
causing it to engage with pinion Q as well as with T, Q being fast on
the cross feed screw. To lock J in either of its three positions there
is provided on lever K a spring locking pin R, shown clearly in Fig.
584, which represents an irregular section of the gearing viewed from
the headstock of the lathe. The pin R is pressed inward by the spiral
spring shown, and has a conical end fitting into holes provided in the
apron to receive it. There are three of these holes, shown in dotted
lines at _a_ _b_ _c_ in Fig. 582. When the pin is in _a_ the lever K,
and therefore wheel J, Fig. 582, is locked out of gear; when it is in
hole _b_ wheel J is locked in gear with I and M, and when it is in _c_
the wheel J is in gear with T and Q, and the cross feed is actuated.
[Illustration: Fig. 581.]
[Illustration: Fig. 582.]
A similar locking device is provided for the pinion B for actuating A;
thus in Fig. 582 B is the lever, the spring pin being at R´´; or
referring to Fig. 584, X is the lever fast at _x_ on the pin driving B,
and R´´ is the spring pin.
The nut for the lead screw is secured either in or out of gear with the
screw in the same manner, _x´_, Fig. 583, being the lever and R´ the
spring pin.
In screw cutting the cutting tool requires to be withdrawn from the
thread while the carriage traverses back, and it is somewhat difficult
to know just how far to move the tool in again in order to put on a
proper depth of cut. To facilitate this the device shown in Fig. 585
(which is taken from the "American Machinist,") is sometimes employed.
It consists of a ring C inserted between the cross slide D and the
handle hub B having journal bearing on and rotating with the latter.
When the first cut is put on, the mark on C is coincident with that on
D, and the ring is then, while the first cut is traversing, moved
(supposing the cross feed screw to have a right-hand thread) to the
left, as shown in the figure, to the amount the handle will be required
to move to the right to put on the next cut, and when the next cut is
put on the handle will be moved the distance it was moved to withdraw
the tool for the back traverse, and in addition enough to make the marks
coincide, then while the second cut is being taken the ring is again
moved to the left, as in the cut, to give the depth of cut for the next
traverse, and so on.
[Illustration: Fig. 583.]
If the cross feed screw has a left-hand thread, the mark on the ring
would require to be moved to the right instead of to the left of the
mark on D. It is obvious that this answers the same purpose, but is more
exact than the chalk mark before referred to, and, indeed, that chalk
mark could be used in the same way, leaving the chalk mark D and rubbing
out that on C while the cut is proceeding and making a new one for the
next cut.
[Illustration: Fig. 584.]
Another device for use on lathes specially designed for screw-cutting is
shown in Fig. 586, in which A represents the cross feed screw. It is
fast to the notched wheel B, and is operated by it in the usual way. C
is a short screw which provides journal bearing for the screw A by a
plain hole. It is screwed on the outside, and the plate in which it fits
acts as its nut. It is fast to the handle D, and is in fact operated by
it. The handle or lever is provided with a catch E, pivoted in the
enclosed box F, which also contains a means of detaining the catch in
the notches of the wheel, or of holding it free from the same when it is
placed clear. If, then, the lever D be moved back and forth the feed
screw A, and hence the slide rest, will be operated; while, if the catch
be placed in one of the notches on the wheel B, both the screws, A and
C, will act to operate the rests. When, therefore, the tool is set to
touch the diameter of the work, the catch E is lifted and the feed wheel
B rotated, putting on the cut until the catch E will fall into the next
notch in B, the lever D resting in the meantime on the stud G. When the
cut is carried along the work to the required distance the tool is
withdrawn by moving D over until it rests upon stud or stop H. While the
slide rest is traversing back E is lifted and B rotated so that E will
fall into the next notch, and when the tool starts forward again D is
moved over from H to G, as shown in the figure, and the tool cut is put
on.
[Illustration: Fig. 585.]
When the device is not required to be used E is thrown out, D rests on
E, and the feed is operated in the ordinary manner.
[Illustration: Fig. 586.]
A simple attachment for regulating on a slide rest the depth of tool cut
in screw cutting or for adjusting the cut to a requisite diameter when a
number of pieces are to be turned to diameter by a finishing cut, is
shown in Fig. 587, in which B represents the slide rest carriage, and E
the cross slide on which the slide rest A is traversed by means of the
cross feed screw _f_. A screw is screwed into the rest, as shown,
carrying the two circular milled edge nuts R P; the screw passes an easy
fit through the piece C, which is capable of being fixed in any position
along the slide E by means of the set screw S; the nut R is set in such
a position on the screw that it will abut against C when the tool is
clear of the work surface (for the back traverse) while P may be used in
two ways:--First it may be set so that when it comes against C the
thread is cut to the required depth, and thus act as stop to give the
thread depth without trying the gauge: or it may be used to answer the
same purpose and in the same way as the ring C in Fig. 585.
[Illustration: Fig. 587.]
The use of this device as a stop to gauge the thread depth is confined
to such lengths of work as enable the tool to cut several pieces without
requiring regrinding, because when the tool is removed to grind it, it
is impracticable to set it exactly the same distance out from the tool
post, hence the adjustment of P becomes destroyed. It is better,
therefore, in most cases where a number of threads of equal pitch and
diameter are to be cut, to rough them all out, cutting the threads a
little above the gauge diameter so as to leave a finishing cut to be
taken. In roughing out, however, the nut P may still be used to regulate
the depth.
For the finishing cut the tool may be ground and P adjusted to give the
requisite depth of cut, taking a single traverse over each thread to
finish it. This, of course, preserves the tool and enables it to finish
a larger number of threads without regrinding, and the consequent
readjustment of P.
It is obvious that the nut P may be employed in the same manner to turn
a number of plain pieces to an equal diameter.
[Illustration: Fig. 588.]
It is preferable in a device of this kind, however, to employ the two
adjusting nuts P and Q in Fig. 588, Q being a clamp nut that can be
closed by a screw so as to firmly grip the threaded stud. Q is adjusted
so that when P abuts against it the tool will cut to the correct
diameter when it is moved in as far as nuts P Q will permit. The use of
the second nut P is as follows:--Suppose a first cut has been taken and
P may be screwed up to just meet the face of clamp C. Then while the
carriage is traversing, P may be screwed back towards Q sufficiently to
put on the next cut, and so on, so that P is used to adjust the depths
of the roughing, and Q that of the finishing cut.
Sometimes a feed motion to a slide rest is improvised by what is known
as the _star feed_, the principle of action of which is as follows: Upon
the outer end of the feed screw of the boring bar or slide rest, as the
case may be, is fastened a piece of iron plate, which, from having the
form in which stars are usually represented, is called the star. If the
feed is for a slide rest a pin is fastened to the lathe face plate or
other revolving part, in such a position that during the portion of the
revolution in which it passes the star it will strike one of the star
wings, and move it around sufficiently to bring the next wing into
position to be struck by the pin during its succeeding revolution. When
the feed is applied to a revolving boring bar the construction is the
same, but in this case the pin is stationary and the star revolves with
the feed screw of the bar.
In Fig. 589 is shown a star feed applied to a slide rest. A is the slide
rest, upon the end of the feed screw of which the star, B, is fitted. C
is a pin attached to the face plate of the lathe, which, as it revolves,
strikes one of the star wings, causing it to partly rotate, and thus
move the feed screw. The amount of rotation of the feed screw will
depend upon the size of the star and how far the circle described by the
pin C intersects the circle described by the extreme points of the star
wings. Thus the circles denoted by D E show the path of the pin C; the
circle F H the path of the star points, and the distance from F to G the
amount which one intersects the other. It follows that at each
revolution of C an arm or wing of the star will be carried from the
point G to point F, which, in this case, is a sixth of a revolution. If
more feed is required, we may move the pin C, so that it may describe a
smaller circle than D E, and cause it to intersect F H to a greater
extent, in which case it will move the star through a greater portion of
its revolution, striking every other wing and doubling the amount of
feed.
It will be observed that the points F and G are both below the
horizontal level of the slide rest's feed screw, and therefore that the
sliding motion of the pin C upon the face of the star wings will be from
the centre towards the points. This is better, because the motion is
easier and involves less friction than would be the case if the pin
contact first approached and then receded from the centre, a remark
which applies equally to all forms of gearing, for a star feed is only a
form of gearing in which the star represents a tooth wheel, and the pin
a tooth in a wheel or a rack, according to whether its line of motion is
a circle or a straight line.
[Illustration: Fig. 589.]
It is obvious that in designing a star feed, the pitch of the feed screw
is of primary importance. Suppose, for example, that the pitch of a
slide rest feed screw is 4 to an inch, and we require to feed the tool
an inch to every 24 lathe revolutions; then the star must have 6 wings,
because each revolution of the screw will move the rest 1/6 in., while
each revolution of the pin C will move the star 1/6 of a revolution, and
4 × 6 = 24. To obtain a very coarse feed the star attachment would
require to have two multiplying cogs placed between it and the feed
screw, the smaller of the cogs being placed upon the feed screw.
In many lathes of European design, the feeds or some of them, are
actuated by ratchet handles, operated by an overhead shaft, having arms
which rock back and forth. Thus in Fig. 590 is a lathe on which there is
provided at A crank disc, carrying in a dovetail slot a pin P, for
rocking the overhead shaft from whose arms a chain is attached which may
be connected to the ratchet handle shown on the cross-feed screw, the
weight being for the purpose of carrying that handle down while the
chain pulls it up. To regulate the amount of feed the pin P is adjusted
in the slot in A, or the chain may be attached in different positions
along the length of the ratchet arm, the weight being provided with a
set screw so that it may be set in any required position along the
ratchet arm.
[Illustration: Fig. 590.]
TOOL-HOLDING DEVICES.--Perhaps no part of a lathe is found in American
practice with so many different forms of construction as the device for
holding the cutting tool. The requirements for a lathe to be used on
light work and where frequent changes in the position of the tool are
necessary, are quite different from those for a lathe intended to take
as heavy a cut as the lathe will properly drive, and wherein tools
having the cutting edge at times standing a long way out from the tool
post (as sometimes occurs in the use of boring tools). In the former
case a single holding screw will suffice, possessing the advantage that
the tool may be quickly inserted, adjusted for height and set to one
side or the other, with a range of motion which often permits of a tool
that has taken a parallel cut being moved in position to capacitate it
to take a facing one, which would not be the case were its capacity for
side adjustment limited.
In the case of the common American lathe having a self-acting feed and
no compound rest, the tool post is usually employed, the rest being
provided with a [T] slot such as shown in Fig. 577. This enables the
tool post to be moved from side to side of the tool rest, and swing
around in any required position. In connection with such tool posts
various contrivances are employed to enable the height of the cutting
edge of the tool to be readily adjusted. Thus in the Fig. 591, the tool
post is surrounded by a cupped washer W, and through the slot in the
tool post passes a gib G, which may be moved endways in the slot and
thus elevates or depresses the tool point.
The objection to this is that the tool is not lifted parallel, or in
other words is caused to stand out of its proper horizontal position
which alters the clearance of the tool, and by presenting the angles
forming the tool edge in an improper position, with relation to the
work, impair its cutting qualification, as will be shown hereafter when
treating of lathe cutting tools.
An improvement on this form has been pointed out by Professor John E.
Sweet, whose device is shown in Fig. 592. Here the washer or ring is
rounded and the bottom surface of the gib is hollowed, so that chips or
dirt will to a great extent fall off, and every time the tool post is
swung the gib acts to push off whatever dirt may lodge on the washer.
In the design shown in Fig. 593, the tool rests upon two washers W that
are tapered, and its height is adjusted by revolving one of these
washers, it being obvious that the limit of action to depress the tool
point is obtained when the two thin sides of the washers are placed
together, and on the same side of the tool post as the cutting edge of
the tool, while the limit of action to raise the tool point is obtained
when the washers have their thick sides together and nearest to the tool
point.
Here again the tool is thrown out of level, and to obviate this
difficulty the stepped washer shown in Fig. 594 may be used, the steps
on opposite sides of the washer being of an equal height. This enables
the tool to be raised or lowered without being set out of the horizontal
position; but it has the defect that the adjustment cannot be made any
finer than the height of the steps, and if the height is made to vary
but slightly, in order to refine, as it were, the adjustment, the range
of tool elevation or depression is correspondingly limited. Another form
of stepped washer is shown in Fig. 595, in which no two steps are of the
same height. This affords a wider range of adjustment, because the same
two steps will alter the height of the tool by simply turning the washer
one-half revolution. It has two defects, however; first, the least
amount of adjustment is that due to the difference in height of the
steps; and, second, when the tool is elevated it grips the washer at A,
so that the tool is not supported across the full width of face of the
washer, as it should be.
A defect common to all devices in which the tool is thrown out of level,
is that the binding screw does not bed fair upon the tool, and as a
result it is apt, if screwed home very firmly, as is necessary to hold
boring tools that stand far out from the tool post, to spread the screw
end as in Fig. 596, or to bend it.
A very convenient tool-adjusting device is shown in Fig. 597. It
consists of a threaded ring N receiving the threaded bush M, the tool
height being adjusted by screwing or unscrewing one within the other.
The objection to this is, that it occupies so much vertical height that
there is not always room to admit it, which occurs, for example, in
compound slide rests on small lathes.
On these rests, therefore, a single washer is more frequently used,
which answers very well when the tool post is in a slot, so that it can
be moved from side to side of the rest as occasion may require. When,
however, the position of the tool post is fixed it has the disadvantage
that the point P, Fig. 598, where the tool takes its leverage, is too
far removed, and the tool is therefore liable to bend or spring from the
pressure of the cut.
In Fig. 599 is an elevating device sometimes used on the compound rests
of large lathes. The top of the rest is provided with a hub H, threaded
externally to receive a ring nut R, around whose edge there are numerous
holes to receive a pin for operating the nut. The tool-post is situated
central in the hub. When the tool is loose the ring nut can be operated
by hand or the tool may be gripped lightly and the ring nut operated by
a pin. The level of the tool is here maintained; it is supported to
about the edge of the rest on account of the large diameter of the ring
nut, and a very delicate adjustment for height can be made, but such a
device is only suitable for large lathes on account of the depth of the
ring nut and hub.
[Illustration: Fig. 607.]
On small slide-rests the device shown in Fig. 600 is often found. It
consists of a holder H, in which is cut a seat for the tool, this seat
being inclined to give the piece of steel used as a tool a certain
constant degree of angle, and at the same time to permit of the tool
being moved endwise in the holder to set it for height; but, as the tool
requires to be pushed farther and farther through the holder to raise
it, it is not so well supported as is desirable when slight tools are
used, unless the holder is made long, so as to pass through the tool
post with the tool. Again, it does not support the tool sideways unless
the tool steel is dressed up and closely fits the groove in the holder.
In Fig. 601 W W are two inverted wedges which afford an accurate
adjustment, but the range is limited, because if the wedges have much
taper they are apt to move endways when the tool is fastened.
A convenient device for the compound rests of small lathes is shown in
Fig. 602. It consists of a holder pivoted upon a central post and
carrying two tool-binding screws, hence it can be revolved to set the
tool in any required position. A similar device is shown in Fig. 603, in
which the central post is slotted at A to receive the tool, and also
carries a plate C, held by the nut N, and provided with tool-holding
screws B and B´, which abut against the top of the rest, a top view of
the device being shown in Fig. 604. Plate C may thus be swung around to
set the tool in any required position on either side of the rest.
In Maudslay's slide rest, the tool clamp shown in Fig. 605 is employed.
Screws A are employed to grip the tool moderately firm, and a turn of
screws B (whose ends abut against the top of the slide rest) very firmly
secures the tool, since it moves the clamp C as a lever, whose fulcrum
is the screw A.
Figs. 606 and 607 represent the Whitworth tool clamp, the clamping
plates of which change about upon the four studs, and are supported at
their inner ends by a block equal in height to the height of the tool
steel.
Figs. 608, 609, 610, and 611 represent the "Lipe" tool post, so called
from the name of its inventor. The top of the cross slide is
cylindrical, and is bored to receive the tool post which has a
cylindrical stem. The cylindrical part of the tool post is split
vertically, and has two lips, the bolt D passing through one lip and
threading into the other, so that by operating bolt D the tool post may
be gripped very firmly or released, so that it may be revolved to bring
the tool into any required position after it is fastened in the tool
post, which is a great advantage because the tool is brought to a solid
seating in the post before its height is adjusted, and will not
therefore be altered in height by setting up the set screws as often
occurs in ordinary tool posts. From the shape of the tool post, the tool
may be gripped by one set screw only, when required for light duty, or
by two set screws for heavy duty or for boring, while in either case it
is supported clear to the edge of the rest.
[Illustration: Fig. 608.]
[Illustration: _VOL. I._ =TOOL-HOLDING AND ADJUSTING APPLIANCES.= _PLATE
VII._
Fig. 591.
Fig. 592.
Fig. 593.
Fig. 594.
Fig. 595.
Fig. 596.
Fig. 597.
Fig. 598.
Fig. 599.
Fig. 600.
Fig. 601.
Fig. 602.
Fig. 603.
Fig. 604.
Fig. 605.
Fig. 606.]
Fig. 608 shows the tool in position, held by a single screw, for work
requiring the tool to be close up to the work driver. In Fig. 609 a tool
is shown held as is required by work between centres, but both
set-screws are used. Fig. 610 shows a tool in position for boring, two
set-screws being used. Fig. 611 shows a tool being held for the same
purpose, but by a single screw, and it will be observed that the
advantage of the second set-screw is obtained without in any way
sacrificing the handiness of the post, when used with a single screw.
Whether one or two set-screws are used, the boring tool may be forged
from a single bar of octagon steel, which can be seated in a piece like
that shown at E in Fig. 610, which is grooved so as to receive and hold
the tool. As is well known, boring tools are the most troublesome both
to forge and to adjust in the lathe, and, as the result, a light tool is
often used because no other is at hand and it is costly to make a new
one. When, however, the tool can be forged from a plain piece of steel,
these objections are overcome, and a sufficient number of tools may be
had so that one can always be found suitable for any ordinary sized
hole, the object being to use as rigid a tool as can be got into the
hole bored. The feature of maintaining the tool level is of great
importance in boring work, because when the tool requires to be set out
of level to adjust its height, it will generally strike against the
mouth of the hole if the latter is of much depth. This annoyance is also
frequently met with in boring tools which are forged out of rectangular
steel, because the rounded stem is generally left taper. The largest end
of the taper is generally nearest the tool post. Hence the capacity to
use octagon steel and keep it level while adjusting its height, added to
the fact that the tool is supported clear to the edge of the tool rest,
and the tool post is so blocked as to virtually become a part of the
rest, constitute a very important advantage.
[Illustration: Fig. 609.]
[Illustration: Fig. 610.]
A common device on large lathes is shown in Fig. 612, the two clamps
being shown in position for outside turning, and being changed (so as to
stand at a right angle to the position they occupy in the figure) for
holding boring tools. The bolts are enveloped by spiral springs which
support the clamps.
Figs. 613 and 614 represent the tool holders employed in the Brown and
Sharpe small screw machines. In the front rest, Fig. 613, the piece R
receives two adjusting and tool-gripping screws S, upon which sits the
gib G, and upon this the tool is placed. The surface E at the top of the
tool post slot is curved so that it will bear upon the top of the tool
at a point only. The tool is here supported along the full length of the
gib, and there is no set-screw at the top of the tool post, which
enables a much more unobstructed view of the tool.
Fig. 614 is the tool post used at the back of the rest, the piece B
passing through the tool post slot. The tool rests upon the top of screw
E and upon the top of B at F, and is secured by set-screw S; its height
is therefore adjusted by means of screw E, which is threaded in B. The
set-screw S is not in this case objectionable, because it is at the back
of the rest, and therefore does not obstruct the view of the work, while
it is at the same time convenient to get at.
When the screw for traversing a lathe carriage is used for plain
feeding, it is termed the feed screw, but when it is used to cut threads
it is termed the lead screw.
A lead screw should be used for screw cutting only, so that it may be
preserved as much as possible from wear. As the greater portion of
threads cut in a lathe of a given size are short in comparison with the
length of the lathe, it follows that the part of the lead screw that is
in operation when the carriage or saddle is traversing over short work
is most worn, while the other end is least worn, hence it is not unusual
to so construct the screw and its bearings that it may be changed end
for end in the lathe, to equalize the wear. By turning a lead screw end
for end, therefore, to equalize the wear, the middle of the length of
the screw will become the least worn, and, therefore, the most true.
Hence it is better to use one end of the lead screw for general work,
and to reverse it and use the other end only for screws requiring to be
of very correct pitch.
[Illustration: Fig. 611.]
[Illustration: Fig. 612.]
[Illustration: Fig. 613.]
[Illustration: Fig. 614.]
To obviate the wear as much as possible the feed nut should embrace as
great a length of the screw as convenient, and should be of a material
that will suffer more from wear than the lead screw, or in other words
shall relieve the feed screw from wear as much as possible. The wear on
the nut being equal from end to end, the wearing away of one side of its
thread does not vary its pitch; hence the only consideration as to its
wearing qualification are the expense of its renewal and the length of
time that may occur between its being engaged with the lead screw and
giving motion to the lathe carriage, this time increasing in proportion
as the nut thread is worn. Under quick speeds or when the lathe is in
single gear, the rotation of the feed screw is so quick that not much
time is lost before the carriage feeds, but when the back gear is in
operation at the slowest speeds, the loss of time due to a nut much worn
is an item of importance.
In some lathes the feed screw is employed for screw cutting and for
operating an independent feed also. This is accomplished by cutting a
feather way or spline along it, so that a worm having journal bearing in
the apron of the rest carriage may envelop the lead screw and be driven
by it, through the medium of a feather fast into the worm gear. The
motion obtained from the worm gear is transferred through suitable
gearing to the rack pinion.
The spline is cut deeper than the thread, so as to prevent the latter as
far as possible from wear, by reason of the friction of the spline.
The lead screw if long should be supported, to prevent its sagging of
its own weight. In some cases the lead screw is supported in a trough
along its whole length, as is done in the Sellers lathe. In other cases,
bearings hanging from the [V]-slides, and movable along the bed, are
employed.
It is desirable that the feed screw and nut be as near the middle of the
carriage as possible, so that it shall pull the carriage at as short a
leverage as possible, thus avoiding the liability to tilt or twist the
carriage; but it is not practicable to place it midway between the lathe
shears, because in that case the cuttings, &c., from the work would fall
upon it, and cause excessive and rapid wear of the screw and nut.
In general the lead screw is located either in front, or at the back of
the lathe, and in considering the more desirable of the two locations,
we have as follows:
The feed nut should obviously remain axially true with the lead screw,
as by reason of the extra weight of the front of the carriage, both it
and the lathe shears wear most at the front, and the carriage,
therefore, falls to the amount of its own wear and the wear of the
shears. If the lead screw is used to feed with (as it should not be),
the nut wears coincidently with the carriage and the shears, and the
screw alignment is not impaired; but with an independent feed, only a
small portion of the carriage traversing is done with the lead screw,
hence the carriage lowers from the wear due to the independent feeding,
and when the lead screw comes to be used its nut is not in true
alignment with it. It is obviously preferable, then, to place the lead
screw at the back, where the carriage and shears wear the least.
Furthermore, this relieves the carriage front from the weight of the
nut, &c., tending to equalize the back and front wear, while removing
the nut-operating device from the front to the back of the shears, and
thus reducing the number of handles in front, and thus avoid
complication in small lathes.
LATHE LEAD SCREWS.--Lead screws have their pitches in terms of the inch
throughout all parts of the world; or, in other words, the lead screws
of all lathes contain so many full threads per inch of length.
Lead screws are usually provided with square threads of the usual form,
or with threads whose sides have about fifteen degrees of angle, so that
the two halves of the feed nut may be let together to take up the wear.
It is obvious that in a [V]-thread or in a thread whose sides are at an
angle, the feeding strain tends to force the two halves of the feed nut
apart, and therefore places a strain on the feed-nut operating mechanism
that does not exist in the case of a square thread. Furthermore it can
be shown that with a [V]-thread the opportunities to lock the carriage
on a wrong place, after traversing it back by hand in screw cutting, are
increased, thus augmenting the liability to cut intermediate and
improper threads.
[Illustration: Fig. 615.]
In Fig. 615, for example, we have a pitch of lead screw of three threads
per inch, and the gears arranged to cut six threads per inch on the
work. As the bottom wheel has twice as many teeth as the top one, it is
clear that, while the top one makes one, the bottom one will make half
revolution, and the lead screw will make half a turn for every turn the
work makes. Now, suppose the tool point to stand opposite to space A,
and the nut (supposing it to have but one thread only, which is all that
is required for our purpose), stand opposite to space D. Suppose,
further, that the lathe makes one revolution, and space B on the work
will have moved to occupy the position occupied by space A, or, rather,
there will still be a place at A fully in front of the tool, as should
be the case, but the lead screw will have made half revolution, the top
_e_ of the thread coming opposite to the feed nut, as in the position of
tool and nut shown in the figure at T and N; hence the nut would not
engage, without moving the lathe carriage sideways, and thus throwing
the tool to one side of the thread in the work. When, however, the work
had made another revolution, both the feed screw and the work would
again come into position for the tool and nut to engage properly, and it
follows that in this case the tool will always fall into proper position
for the nut to be locked.
It is obvious, however, that had the lead screw thread been a square
one, and the nut thread to accurately fit to the lead screw thread, so
as to completely fill it, then the nut could not engage with the lead
screw until the lathe had made a complete revolution, at which time the
work will have made two full or complete revolutions, and the tool
would, therefore, fall into proper position to follow in the groove or
part of a thread cut at the first tool traverse.
[Illustration: Fig. 616.]
In Fig. 616, we have the same lead screw geared to cut five or an odd
number of threads per inch. The tool and the nut are shown in position
to properly engage, but suppose, the nut being disengaged, that the work
makes one revolution, and during this period the lead screw will have
made 3/5ths of a revolution, hence the nut will not be in position to
engage properly, because, although space B will have travelled forward
so as to occupy the position of space A in the figure (that is, there
will be a space fairly in front of the tool point), yet the nut will not
engage properly, because the nut point will not be opposite to the
bottom of the lead screw thread. When the work has made its second
revolution, and space C moves to the position occupied by A, the lead
screw will have made 6/5 or 1-1/5 revolutions, and the nut cannot engage
properly; when the lathe has made its third revolution, the lead screw
will have made 1-4/5 revolutions and the nut will still fall to one side
of the thread space, and will not lock properly. The work having made
its fourth turn, the lead screw will have made 2-2/5 turns, and the nut
will not be in position to lock fairly. The work having made its fifth
turn, however, the lead screw will have made three turns, and the
threads will fall into the same position that they occupy in the figure,
and both tool and feed nut will fall into their proper positions in
their respective threads. It does not follow, however, that, the lead
screw having a [V]-shaped thread, the nut cannot be forced to engage but
once in every five turns of the lead screw, because, were this the case,
it would be impossible to lock the nut in an improper position.
[Illustration: Fig. 617.]
Suppose, for example, that we have in Fig. 617, the same piece of work
and lead screw as in Fig. 616, and that a first groove, A, has been cut
with the tool in the position shown, and the nut engaged in the position
marked 1. Now, suppose the nut be disengaged and the work allowed to
make one revolution, then the lead screw will, during this revolution,
revolve 3/5 of a revolution, and the position of the nut point with
relation to the lead screw will be as at position 2. If, then, the nut
was forced into the lead screw thread, it would, acting on the wedge
principle, move the carriage to the right sufficiently to permit the nut
to engage fully in thread G, and the tool would then cut a second groove
on thread B. If the nut then be withdrawn from thread G, and the work
allowed to make another revolution, the nut will stand in a precisely
similar position with relation to the lead screw thread as it did in
position 2, and by forcing it down into thread H the carriage would be
again forced to the right, causing a third thread, C, to be cut. By
repeating the operation of withdrawing the nut, letting the work make
another revolution and then engaging the nut again, it will seat in
thread K, and a fourth thread D will be cut. On again repeating the
operation, however, the nut will come into position 5, and, on being
drawn home into thread, or, rather, into space L, the tool will fall
into groove A again. Thus there will be four threads, each having a
pitch equal to that of the lead screw. The second (B) of these four will
fall to the left of thread A to an amount or distance equal to 2/5 of
the pitch of the lead screw, because, in forcing the nut from position 2
down into the lead screw, the slide rest, and therefore the tool, will
be moved to the right 2/5 of the pitch of the lead screw. The third
thread C will fall to the left of thread B also to an amount equal to
2/5 of the pitch of the lead screw, because, in forcing the thread to
seat itself into thread H from position 3, the slide rest was again
moved (to that amount) to the right. The fourth thread D will fall to
the left of thread C to the same amount and for the same reason.
But in this case, as before, if the lead screw had a square thread and
the nut threads completely filled the spaces between the lead screw
threads, then the nut could not engage at the 2nd, 3rd, or 4th work
revolution, hence the false threads B, C, and D, could not have been
cut, even though the feed nut was disengaged and the lathe carriage was
traversed back by hand.
Now, suppose that two threads on the work measure less than the amount
the lead screw advances during the time that the work makes a
revolution, and if the lead screw has a [V]-shaped thread, the case is
altered. We have, for example, in Fig. 618, a pitch of lead screw of 3
to cut 12 and 13 threads respectively. In the case of the 13 threads it
will be seen that, supposing there to have been a first cut taken on the
work, and the feed nut to be disengaged while the work makes a
revolution, then the lead screw will revolve 3/13 revolution and the
point A on the lead screw will have moved up to point B, and the nut
point remaining at N, seating it in the thread, would cause it to engage
with the same thread that it did before, and no second thread would be
cut. If the nut be then released, the work allowed to make another
revolution and the nut again closed, the operation would be the same as
before, and no error would be induced, and so on. Suppose, further, that
after the nut was disengaged the lathe was permitted to make two
revolutions, and the lead screw would make 6/13, or less than half a
turn, and closing it would still cause it to pass back into the same
thread on the lead screw and produce correct work. But if after the nut
was released the work made three turns, the lead screw would make 9/13
of a turn, and the nut would fall on the right-hand side of the lead
screw thread, and in closing would move the lathe carriage to the right,
causing the tool to cut a second thread. Now, the same operation that
occurred with the first thread would during the next three trials occur
with the second thread, and at the next or seventh trial a third thread
would be cut, which would be again operated upon during the next
succeeding three trials. At the eleventh trial a fourth thread would be
cut, but on the next three trials the tool would again fall into the
groove first cut and the work proceed correctly. In the case of the 12
threads, the thread cut at the first and second trials would be correct.
At the third trial the nut would seat itself in the groove C of the lead
screw, causing the carriage to move to the right to a distance equal to
twice the pitch of thread being cut, but the tool would still fall into
the same groove in the work, as it also would on the fourth. At the
fifth trial the process would be repeated, and so on, so that no second
thread would be cut.
[Illustration: Fig. 618.]
It may now be noted that if we draw the lead screw and the thread to be
cut as in the figure, and draw the dotted lines shown, then those that
meet the bottom of the thread on the lead screw, and also meet the
groove cut on the work, at the first trial, represent the cases in which
the nut will fall naturally into its proper position for the tool to
fall into the correct groove, while whenever the nut is being forced
home it seats in a groove in the lead screw, the bottom of which groove
meets a line drawn from the first thread cut; the results obtained will
be made correct by reason of the movement given to the slide nut when
artificially seating the nut. This is shown to be the case in Fig. 619,
which represents a lead screw having an even number of threads per inch,
and from which it appears that in cutting 12 threads (an even number
also) the nut cannot be engaged wrong, whereas in the case of 13 threads
it can be engaged right three times in 13 trials, and 10 times wrong,
the latter causing the tool to cut three wrong threads.
[Illustration: Fig. 619.]
To prevent end motion of a lead screw it should have collars on both
sides of one bearing, and not one at each bearing. By this means the
screw will be permitted to expand and contract under variations of
atmospheric temperature, without binding against the bearing faces.
When a lead screw is long it requires to be supported, otherwise, either
its weight will be supported or lifted by the feed nut in gear, or if
that nut does not lift the screw, the thread cut will be finer than that
due to the pitch of the lead screw, by reason of its deflection or sag.
A lead screw should preferably be as near as possible to the middle of
the lathe shears, and as close to the surface as possible, so as to
bring it as nearly in line with the strain on the tool as possible, but
on account of the cuttings, which falling upon the screw would cause it
to wear rapidly, it is usual to locate it on one side, so as to protect
it from the cuttings. It is better to locate it on the front side of the
lathe rather than on the back, because the strain of the cut falls
mainly on the front side (especially in work of large diameter when this
strain is usually greatest) and it is desirable to pull the carriage as
near in a line with the resistance of the cut as possible, because the
farther off the feed nut from the cutting tool point, the greater the
tendency to twist the carriage on the shears.
To preserve the nut from wear, it should be made as long as convenient,
as, say, five or six times the diameter of the lead screw; it is usually
made, however, three or four diameters.
It is obvious that the pitch of the thread should be as accurate as
possible, but it has not as yet been found practicable to produce a
screw so accurate that it would not show an error, if sufficient of its
length be tested, as, say, several feet.
If the error in a screw be equal, and in the same direction at all parts
of its length, various devices may be employed to correct it. Thus Fig.
620 represents a device employed by the Pratt and Whitney Co.
It was first ascertained by testing the lathe that its lead screw was
too short by 7/100ths of a revolution in a length of 2 feet, the pitch
of its thread being 6 to an inch. Now in 2 feet of the screw there would
be 144 threads, and since 7/100ths (the part of a revolution the thread
was too short) × 1/6 (the pitch of the thread) = 7/600ths (which was
called 1/85th), the error amounted to 1/85th inch in 144 turns of the
screw. The construction of the device employed to correct this error is
as follows: In Fig. 620, A represents the bearing of the feed screw of
the lathe, and B _b_ a sleeve, a sliding fit upon A, prevented from
revolving by the pin _h_, while still having liberty to move endways. C
represents a casing affording journal bearing to B _b_, having a fixed
gear-wheel at its end C´, and an external thread upon a hub at that end.
D is the flange of C to fasten the device to the shears of the latter,
being held by screws. E represents an arm fast upon the collar of the
feed screw, and carrying the pinion F, the latter being in gear with the
pinion C´, and also with G, which is a pinion containing two internal
threads, one fitting to B at _b_, and the other fitting to C at _c_, the
former having a pitch of 27 threads to an inch, the latter a pitch of 25
to an inch.
[Illustration: Fig. 620.]
The operation is as follows:--The ordinary change wheels are connected
to the feed screw, or lead screw, as it is sometimes termed, at J in the
usual manner. The arm E being fast to the feed screw will revolve with
it, and cause the pinion F to revolve around the stationary gear-wheel
C´. F also gears with G. Now, F is of 12 diametrical pitch and contains
26 teeth, C´ is of 12 diametrical pitch and contains 37 teeth, and G is
of 12 diametrical pitch and contains 36 teeth. It follows that the
pinion F, while moving around the fixed gear C´, will revolve the pinion
G (which acts as a nut), to an amount depending upon the difference in
the number of its teeth and those of fixed gear C´ (in this case as 36
is to 37), and upon the difference in the pitches of the two threads, so
that at each revolution G will move the feed screw ahead of the speed
imparted by the change gears, the end of the sleeve B abutting against
the collar of the feed screw to move it forward.
In this case there are 36 turns of the feed screw A for one turn of the
nut pinion G, the thread on sleeve B being 27, and that on the hub of C
being 25 to the inch; hence, 36 turns of the feed screw gives an end
motion to the sleeve B of 1/25 minus 1/27 = 2/675, and 1/36 of that =
1/12150 of an inch = the amount of sliding motion of the sleeve _b_, for
each revolution of the lathe feed screw. By varying the proportions
between the number of teeth in C´ and G and the pitches of the two
threads in a proper and suitable ratio, the device enables the cutting
of a true thread from any untrue one in which the variation is regular.
It is usual to fasten to the side of the lathe head stock a brass plate,
giving a table of threads, and the wheels that will cut them, and
obviously such tables vary according to the pitch of the lead screw, but
a universal table may be constructed, such as the following table
(prepared by the author) that will serve for any lathe.
At the top of the table is the number of teeth in wheels, advancing by
four from 12 to 80 teeth, but it may be carried as much beyond 80 as
desired. On the left hand of the table is a column of the same wheels.
At the bottom of the scale are pitches of lead screw from 3 up to 20
threads per inch. Over each lead screw pitch are thread pitches, thus on
lead screw pitch 4 we have 20, 19, 18, and so on.
The use of the table is as follows:--
Find the pitch of the lead screw, and at the head of that column is the
number of teeth for the lathe stud or mandril. Then find in that column
the number of threads to be cut, and on the same line, but at the left
hand, will be found the number of teeth for the lead screw.
NUMBERS OF TEETH FOR WHEEL TO GO ON LATHE SPINDLE, LATHE STUD, OR
MANDRIL.
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
Lead |12|16|20|24|28|32|36| 40| 44| 48| 52| 56| 60| 64| 68| 72| 76| 80
Screw.| | *| | | | | | | | | | | | | | | |
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
12 | 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
16 | 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
20 | 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
24 | 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
28 | 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
32 | 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
36 | 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
40 |10|10|10|10|10|10|10| 10| 10| 10| 10| 10| 10| 10| 10| 10| 10| 10
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
44 |11|11|11|11|11|11|11| 11| 11| 11| 11| 11| 11| 11| 11| 11| 11| 11
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
48 |12|12|12|12|12|12|12| 12| 12| 12| 12| 12| 12| 12| 12| 12| 12| 12
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
*52 |13|13|13|13|13|13|13| 13| 13| 13| 13| 13| 13| 13| 13| 13| 13| 13
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
56 |14|14|14|14|14|14|14| 14| 14| 14| 14| 14| 14| 14| 14| 14| 14| 14
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
60 |15|15|15|15|15|15|15| 15| 15| 15| 15| 15| 15| 15| 15| 15| 15| 15
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
64 |16|16|16|16|16|16|16| 16| 16| 16| 16| 16| 16| 16| 16| 16| 16| 16
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
68 |17|17|17|17|17|17|17| 17| 17| 17| 17| 17| 17| 17| 17| 17| 17| 17
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
72 |18|18|18|18|18|18|18| 18| 18| 18| 18| 18| 18| 18| 18| 18| 18| 18
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
76 |19|19|19|19|19|19|19| 19| 19| 19| 19| 19| 19| 19| 19| 19| 19| 19
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
80 |20|20|20|20|20|20|20| 20| 20| 20| 20| 20| 20| 20| 20| 20| 20| 20
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
Lead | | | | | | | | | | | | | | | | | |
Screw |3.|4.|5.|6.|7.|8.|9.|10.|11.|12.|13.|14.|15.|16.|17.|18.|19.|20.
Pitch | | | | | | | | | | | | | | | | | |
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
EXAMPLE.--The lead screw has a pitch of 4, and I require to cut 13
threads per inch. At the head of the column is 16, and on a line with
the 13 of the column, but on the left is 52, each number being marked by
a * hence the 16 and 52 are the wheels; if we have not those wheels,
multiply both by 2 and 32, and 104 will answer.
If the pitch of the lead screw is 2 threads per inch, the wheels must
advance by 6 teeth, as indicated below:--
NUMBERS OF TEETH FOR WHEEL TO GO ON LATHE STUD, LATHE SPINDLE OR
MANDRIL.
+-----+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| |Lead |12|18|24|30|36|42|48|54|60|66|72|78|84|90|96|
| |Screw. | | | | | | | | | | | | | | | |
|NUM- +--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
|BER | 12 | 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2|
|OF | 18 | 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3|
|TEETH| 24 | 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4|
|FOR | 30 | 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5|
|WHEEL| 36 | 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6|
|TO | 42 | 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7|
|GO | 48 | 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8|
|ON | 54 | 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9|
|LEAD | 60 |10|10|10|10|10|10|10|10|10|10|10|10|10|10|10|
|SCREW+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| |Pitch of| | | | | | | | | | | | | | | |
| |Lead | 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|
| |Screw. | | | | | | | | | | | | | | | |
+-----+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
This table may be used for compound lathes by simply dividing the pitch
of the lead screw by the ratio of the compounded pair of wheels. For
example, for the wheels to cut 8 threads per inch, the pitch of lead
screw being 4 and the compounded gears 2 to 1, as the ratio of the
compounded pair is 2 to 1, we divide the pitch of lead screw by 2, which
gives us 2, and we thus find the wheels in the column of pitch of lead
screw 2, getting 12 and 48 as the required wheels, the 12 going on top
of the lathe because it is at the top of the table, and the 48 on the
lead screw because it is at the left-hand end of the table, and the lead
screw gear is at the left-hand end of the lathe.
The table may be made for half threads as well as whole ones by simply
advancing the left-hand column by two teeth, instead of by four, thus:--
+------+--------------------------------------------------------------+
|Teeth | Teeth for Wheel on Stud. |
| for |------+------+------+------+------+------+------+------+------+
|Wheel | | | | | | | | | |
| on | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 |
| Lead | | | | | | | | | |
|Screw.| | | | | | | | | |
+------+------+------+------+------+------+------+------+------+------+
| 12 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
+------+------+------+------+------+------+------+------+------+------+
| 14 | 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 16 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
+------+------+------+------+------+------+------+------+------+------+
| 18 | 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 20 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
+------+------+------+------+------+------+------+------+------+------+
| 22 | 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 24 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |
+------+------+------+------+------+------+------+------+------+------+
| 26 | 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 28 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |
+------+------+------+------+------+------+------+------+------+------+
| 30 | 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 32 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |
+------+------+------+------+------+------+------+------+------+------+
| 34 | 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 36 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 |
+------+------+------+------+------+------+------+------+------+------+
| 38 | 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 40 |10 |10 |10 |10 |10 |10 |10 |10 |10 |
+------+------+------+------+------+------+------+------+------+------+
| 42 |10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|
+------+------+------+------+------+------+------+------+------+------+
|Pitch | | | | | | | | | |
| of | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10 |11 |
| Lead | | | | | | | | | |
|Screw.| | | | | | | | | |
+------+------+------+------+------+------+------+------+------+------+
For quarter threads we advance the left-hand column by one tooth, or for
thirds of threads by three teeth, and so on.
If we require to find what wheels to provide for a lathe, we take the
pitch of the lead screw for the numerator, and the pitch required for
the denominator, and multiply them first by 2, then by 3, then by 4, and
so on, continuing until the numerator or denominator is as large as it
can be to give the required proportion of teeth, and not exceed the
greatest number that the largest wheel can contain.
For example: A lathe has single gear, and its lead screw pitch is 8 per
inch, what wheels will cut 18, 17, 16, 15, 14, or 13 threads per inch?
Wheels.
Pitch of lead screw 8 16 24 32
-- × 2 = -- -- --
Pitch required 18 36 54 72
Pitch of lead screw 8 16 24 32
-- " -- -- --
Pitch required 17 34 51 68
Pitch of lead screw 8 16 24 32
-- " -- -- --
Pitch required 16 32 48 64
Pitch of lead screw 8 16 24 32
-- " -- -- --
Pitch required 15 30 45 60
Pitch of lead screw 8 16 24 32
-- " -- -- --
Pitch required 14 28 42 56
Pitch of lead screw 8 16 24 32 40
-- " -- -- -- --
Pitch required 13 26 39 52 65
If we suppose that the greatest number of teeth permissible in one wheel
is not to exceed 100, then in this table we have all the combinations of
wheels that can be used to cut the given pitches; and having made out
such a table, comprising all the pitches to be cut, we may select
therefrom the least number of wheels that will cut those pitches. The
whole table being made out it will be found, of course, that the
numerators of the fractions are the same in each case; that is, in this
case, 16, 18, 24, 32, and so on as far as we choose to carry the
multiplication of the numerator. We shall also find that the
denominators diminish in a regular order: thus taking the fractions
whose numerators are in each case 16, we find their denominators are, as
we pass down the column, 36, 34, 32, 30, 28, and 26, respectively, thus
decreasing by 2, which is the number we multiplied the left-hand column
by to obtain them. Similarly in the fractions whose numerators are 24,
the denominators diminish by 3, being respectively 54, 51, 48, 45, 42,
and 39; hence the construction of such a table is a very simple matter
so far as whole numbered threads are concerned, as no multiplication is
necessary save for the first line representing the finest pitch to be
cut.
For fractional threads, however, instead of using the pitch of the lead
screw for the numerator, we must reduce it to terms of the fraction it
is required to cut. For example, for 5-1/2 threads we proceed as
follows. The pitch of the lead screw is 8, and in 8 there are 16 halves,
hence we use 16 instead of 8, and as in the 5-1/2 there are 11 halves we
use the fraction 16/11 and multiply it first by 2, then by 3, and then
by 4, and so on, obtaining as follows: 16/11, 32/22, 48/33, 64/44,
obtaining as before three sets of wheels either of which will cut the
required pitch. In selecting from such a table the wheels to cut any
required number of pitches, the set must, in order to cut a thread of
the same pitch as the lead screw, contain two wheels having the same
number of teeth.
Now, suppose that the pitch of the lead screw was 6 instead of 8 threads
per inch, and the table will be as follows:--
6 12 18 24
-- -- -- --
18 36 54 72
6 12 18 24
-- -- -- --
17 34 51 68
6 12 18 24
-- -- -- --
16 32 48 64
6 12 18 24
-- -- -- --
15 30 45 60
6 12 18 24
-- -- -- --
14 28 42 56
6 12 18 24
-- -- -- --
13 26 39 52
Here, again, we find that in the first vertical column the denominators
decrease by two for each thread less per inch, in the second column they
decrease by three, and in the third by four; this decrease equalling the
number the first fraction was multiplied by.
But suppose the lead screw pitch is an odd one, as, say, 3 threads per
inch, and we construct the table as before, thus--
Pitch of lead screw 3 6 9 12 15
-- -- -- -- --
Pitch to be cut 18 32 54 72 90
Now it is useless to multiply by 2 or by 3, because they give a less
number of teeth than the smallest wheel should have, hence the first
multiplier should be 4, giving the following table:--
3 12 15 18
-- -- -- ---
18 72 90 108
3 12 15 18
-- -- -- ---
17 68 85 102
3 12 15 18
-- -- -- --
16 64 80 96
3 12 15 18
-- -- -- --
15 60 75 90
By continuing the table for other pitches we shall find that in the
first vertical column the denominators diminish by 4, the second column
by 5, and the third by 6; and it is seen that by diminishing the pitch
of the lead screw, we have rendered necessary one of two things, which
is, that either larger wheels containing more teeth must be used, or the
change gears must be compounded.
Assuming that the pitch of the lead screw was 5 per inch, the table
would be as follows:--
5 15 20 25
-- × 3 = -- -- --
18 54 72 90
5 15 20 25
-- " -- -- --
17 51 68 85
5 15 20 25
-- " -- -- --
16 48 64 80
The wheels in the first column here decrease by 3, the second by 4, and
the third by 5.
In nearly all lathes the advance or decrease is by 4 or by 6. In
determining this rate of advance or decrease, there are several
elements, among which are the following. Suppose the lathe to be geared
without compounding, then the distance between the lathe spindle and the
lead screw will determine what shall be the diameters of the largest and
of the smallest wheel in the set, it being understood that the smallest
wheel must not contain less than 12 teeth. Assume that in a given case
the distance is 10 inches, and it is obvious that the pitch of the teeth
at once commands consideration, because the finer the pitch the smaller
the wheel that will contain 12 teeth, and the larger the wheel on the
lead screw may be made. Of course the pitch must be coarse enough to
give the required tooth strength.
Let it be supposed that the arc pitch is 3/4-inch, then the pitch
circumference of a 12-toothed wheel would be 9 inches and its radius
1.432 in.; this subtracted from the 10 leaves 8.568 in. as the radius,
or 17.136 in. as the largest diameter of wheel that can be used on the
lead screw, supposing there to be no intermediate gears. Now a wheel of
this diameter would be capable of containing more than 75 teeth, but
less than 76. But from the foregoing tables it will be seen that it
should contain a number of teeth divisible either by 4 or by 6 without
leaving a remainder, and what that number should be is easily determined
by means of a table constructed as before explained. Thus from the
tables it would be found that 72 teeth would be best for a lead screw
having a pitch of either 8, 6, 5, or 3 threads per inch, and the
screw-cutting capacity of the lathe would (unless compounded) be
confined to such pitches as may be cut with wheels containing between 12
and 72 teeth both inclusive.
But assume that an arc pitch of 3/8-inch be used for the wheel teeth,
and we have as follows: A wheel of this pitch and containing 12 teeth
will have a radius of 7-16/1000 inches, leaving 9.284 in. as the radius
of the largest wheel, assuming it to gear direct with the 12-tooth
pinion. With this radius it would contain 155 teeth and a fraction of a
tooth; we must, therefore, take some less number, and from what has been
said, it will be obvious that this lesser number should be one divisible
by either 4 or 6. If made divisible by 6, the number will be 150,
because that is the highest number less than 155 that is divisible by 6
without leaving a remainder. But if made divisible by 4, it may contain
152 teeth, because that number is divisible by 4 without leaving a
remainder. With 150 teeth the latter could cut a thread 12-1/2 times as
fine as the lead screw, because the largest wheel contains 12-1/2 times
as many teeth as the smallest one; or it would cut a thread 12-1/2 times
as coarse as the lead screw, if the largest wheel be placed on the
mandril and the smallest on the lead screw. With 152 teeth the lathe
would be able to cut a thread 12-84/100 times as fine or as coarse as
the lead screw. Unless, however, the lathe be required to cut fractional
pitches, it is unnecessary that the largest wheel have more teeth than
divisible, without leaving a remainder, by the number of teeth in the
smallest wheel, which being 12 we have 144 as the number of teeth for
the largest wheel. In the United States standard pitches of thread,
however, there are several pitches in fractions of an inch, hence it is
desirable to have wheels that will cut these pitches.
LATHE SHEARS OR BEDS.--The forms of the shears and beds may be
classified as follows.
The term shear is generally applied when the lathe is provided with
legs, while the term bed is used when there are no legs; it may be
noted, however, that by some workmen the two terms of _shear_ and _bed_
are used indiscriminately.
The forms of shears in use on common lathes are, in the United States,
the raised [V], the flat shear and the shear, with the edge at an angle
of 90° or with parallel edges. In England and on the continent of
Europe, the flat shear is almost exclusively employed.
Referring to the raised [V] it possesses an important advantage in that,
first, the slide rest does not get loosely guided from the wear; and
second, the wear is in the direction that least affects the diameter of
the work.
[Illustration: Fig. 621.]
In Fig. 621, for example, is a section of a lathe shear, with a slide
rest shown in place, and it will be observed that the wear of the [V]
upon the lathe bed, and of the [V]-groove in the slide rest, will cause
the rest to fall in the direction of arrow A, and that a given amount of
motion in that direction will have less effect in altering the diameter
than it would in any other direction. This is shown on the right hand of
the figure as follows: Suppose the cutting point of the tool is at _a_,
and the work will be of the diameter shown by the full circle in the
figure. If we suppose the tool point to drop down to _f_, the work would
be turned to the diameter denoted by dotted arc _g_, while if the tool
were moved outwards from _a_ to _c_ the work would be turned to the
diameter _e_. Now since _f_ and _c_ are equidistant from the point _a_,
therefore the difference in the diameters of _e_ and _g_ represents the
difference of effect between the wear letting the rest merely fall, or
moving it outwards, and it follows that, as already stated, the diameter
of the work is less affected by a given amount of wear, when this wear
is in the direction of A, than when it is in the direction of B. When
the carriage is held down by a weight as is shown in Figs. 577 and 578,
there is therefore no lost motion or play in the carriage, which
therefore moves steadily upon the shears, unless the pressure of the cut
is sufficient in amount, and also in a direction to lift the carriage
(as it is in the case of boring with boring tools); but to enable the
carriage to remain firm upon the shears under all conditions, it is
necessary to provide means to hold it down upon the [V]s, which is done
by means of gibs G, G, which are secured to the carriage, and fit
against the bottom of the bed flange as shown.
Now since lathes are generally used much more frequently on short than
on long work, therefore the carriage traverses one part of the shears
more than another, and the [V]s wear more at the part most traversed,
and it follows that if gibs G are set to slide properly at some parts
they will not be properly set at another or other parts of the length of
the shears; hence the carriage will in some parts have liberty to move
from the bed, there being nothing but the weight of the carriage, &c.,
to hold it down to the [V]s. Now, the wear in the direction of A acts
directly to cause this inequality of gib fit, whereas that in the
direction of B does so to a less extent, as will appear hereafter.
Meantime it may be noted that when the carriage is held down by a
suspended weight the shears cannot be provided with cross girts, and are
therefore less rigid and more subject to torsion under the strain of the
cut; furthermore the amount of the weight must be sufficient to hold the
carriage down under the maximum of cut, and this weight acts
continuously to wear the [V]s, whether the carriage is under cutting
duty or not, but the advantage of keeping the carriage firmly down upon
the [V]s is sufficiently great to cause many to prefer the weighted
carriage for light work driven between the lathe centres.
[Illustration: Fig. 622.]
Fig. 622 represents the flat shear, the edges being at an angle and the
fit of the carriage to the shears being adjusted by the gibs at _a_ _a_,
which are set up by bolts _c_ _c_ and _d_ _d_. In this case there is a
large amount of wearing surface at _b_ _b_, to prevent the fall of the
carriage _c_, but the amount of end motion (in the direction of B, Fig.
621), permitted to the carriage by reason of the wear of the gibs and
shear edges, is greater than the amount of the wear because of the edges
being at an angle. It is true that the amount of fall of the carriage on
the raised [V] is also (on account of the angle of the [V]) greater than
the actual amount of the wear, but the effect upon the work diameter is
in this case much greater, as will be readily understood from what has
already been said. The wearing surface of the raised [V] may obviously
be increased by providing broader [V]s, or two [V]s instead of having
four. This would tend to keep the lathe in line, because the wear due to
moving the tailblock would act upon those parts of the shear length that
are less acted upon by the carriage, and since the front journal and
bearing of the live spindle wear the most, the alignment of the lathe
centres would be more nearly preserved.
[Illustration: Fig. 623.]
Fig. 623 represents another form of parallel edged shears in which the
fit of the carriage to the shears is effected at the front end only, the
other or back edge being clear of contact with the carriage, but
provided with a gib to prevent the carriage from lifting. This allows
for any difference in expansion and contraction between the carriage and
the shears, while maintaining the fit of the carriage to the bed.
[Illustration: Fig. 624.]
A modification of this form (both these forms being taken from
"Mechanics") is shown in Fig. 624, in which the underneath side of the
front edge is beveled so that but one row of screws is required to
effect the adjustment.
[Illustration: Fig. 625.]
Fig. 625 represents a form of bed in which the fit adjustment is also
made at the front end only of the bed, and there is a flange or slip at
_a_, which receives the thrust outwards of the carriage; and a similar
design, but with a bevelled edge, is shown in Fig. 626.
[Illustration: Fig. 626.]
[Illustration: Fig. 627.]
In Fig. 627 is shown a lathe shear with parallel edges, the fit being
adjusted by a single gib D, set up by set-screws S. In this case the
carriage will fall or move endwise, to an amount equal to whatever the
amount of the wear may be, and no more, but it may be observed that in
all the forms that admit of wear endways (that is to say in the
direction of B in Fig. 621), the straightness of the shears is impaired
in proportion as its edges are more worn at one part than at another.
[Illustration: Fig. 628.]
A compromise between the flat and the raised [V]-shear is shown in Fig.
628, there being a [V]-guide on one side only, as at J. When the
carriage is moved by mechanism on the front side of the lathe, and close
to the [V], this plan may be used, but if the feed screw or other
mechanism for traversing the carriage is within the two shears, the
carriage should be guided at each end, or if the operating mechanism is
at the back of the lathe, the carriage should be guided at the back end,
if not at both ends.
In flat shear lathes the tailstock is fitted between the inside edges of
the two shears, and the alignment of the tailstock depends upon
maintaining a proper fit notwithstanding the wear that will naturally
take place in time. The inside edges of the shears are sometimes
tapered; this taper makes it much easier to obtain a correct fit of the
tailstock to the shears, but at the same time more hard to move the
tailstock along the bed. To remedy this difficulty, rollers are
sometimes mounted upon eccentrics having journal bearing in the
tailstock, so that by operating these eccentrics one half a turn, the
rollers will be brought down upon the upper face of the shears, lifting
the tailstock and enabling it to be easily moved along the bed to its
required position.
In many of the watchmakers' lathes the outer edges are beveled off as in
Fig. 629, the bearing surfaces being on the faces _b_ as well as on the
edges _a_. As a result, edges _a_ are relieved of weight, and therefore
to some extent of wear also, and whatever wear faces _b_ have helps the
fit at _a_ _a_.
In the Barnes lathe, as in several other forms in which the lathe is
made (as, for example, in screw-making lathes) the form of bed in Fig.
630 is employed. The tailblock may rest on the surfaces A, A´, B, C, D,
and E, or as in the Barnes lathe the tailstock may fit to angles A B,
but not to E D, while the carriage fits to B E, and C D, but not to A,
the intention being to equalize the wear as much as possible.
[Illustration: Fig. 629.]
The shears of lathes require to be as rigid as possible, because the
pressure of the cut, as well as the weight of the carriage, slide rest,
and tailstock, and of the work, tends to bend and twist them.
[Illustration: Fig. 630.]
The pressure of the dead centre against the end of the work considered
individually, is in a direction to bend the lathe shears upward, but the
weight of the work itself acts in an opposite direction.
The strain due to the cut falls in a direction variable with the shape
of the cutting tool, but mainly in a direction towards the operator,
and, therefore, tending to twist the shears. To resist these strains,
lathe shears are usually given the [I] form shown in the cuts.
[Illustration: Fig. 631.]
[Illustration: Fig. 632.]
Figs. 631 and 632 represent the ribbing in the Putnam Tool Company's
lathe; a middle rib running the entire length, which greatly stiffens
it.
The legs supporting lathe shears are, in lathes of ordinary length,
placed at each end of the bed, so that the weight of the two heads, that
of the work, and that of the carriage and slide rest, as well as the
downward pressure of the cut, act combined to cause it to deflect or
bend. It is necessary, therefore, in long beds to provide intermediate
resting or supporting points to prevent this deflection.
[Illustration: Fig. 633.]
Professor Sweet has pointed out that a lathe shears will be more truly
supported on three than on four resting points, if the foundation on
which the legs rest do not remain permanently level, and in lathes
designed by him has given the right-hand end of the shears a single
supporting point, as shown at _a_ in Fig. 633.
[Illustration: Fig. 634.]
J. Richards in an article in "Engineering," has pointed out also that,
when the lathe legs rest upon a floor that is liable from moving loads
upon it to move its level, it is preferable that the legs be shaped as
in Fig. 634, being narrowest at the foot, whereas when upon a permanent
foundation, in which the foundation is intended to impart rigidity to
the legs, they should be broader at the base, as in Fig. 635.
[Illustration: Fig. 635.]
The rack on a lathe bed should be a cut one, and not simply a cast one,
because when a cutting tool is running up to a corner as against a
radial face, the self-acting motion must be stopped and the tool fed
into the corner by hand. As a very delicate tool movement is required to
cut the corner out just square, it should be capable of easy and steady
movement, but in the case of cast racks, the rest will, from defects in
the rack teeth, move in little jumps, especially if the pitch of the
teeth be coarse. On the other hand it is difficult to cast fine pitches
of teeth perfectly, hence the racks as well as the gear teeth should be
cut gear and of fine pitch.
The tailblock of a lathe should be capable of easy motion for adjustment
along the shears, or bed of the lathe, and readily fixable in its
adjusted position. The design should be such as to hold the axial line
of its spindle true with the axial line of the live spindle. If the
lathe bed has raised [V]s there are usually provided two special [V]s
for the tailblock to slide on, the slide rest carriage sliding on two
separate ones. In this case the truth of the axial line of the tail
spindle depends upon the truth of the [V]s.
If the lathe bed is provided with ways having a flat surface, as was
shown in Fig. 622, the surfaces of the edges and of the projection are
apt in time to wear, permitting an amount of play which gives room for
the tailblock to move out of line. To obviate this, various methods are
resorted to, an example being given in the Sellers lathe, Fig. 518.
In wood turners' lathes, where tools are often used in place of the dead
centre, and in which a good deal of boring is done by such use of the
tail spindle, it is not unusual to provide a device for the rapid motion
of that spindle. Such a device is shown in Fig. 636; it consists of an
arm A to receive the end C of the lever B, C being pivoted to A. The
spindle is provided with an eye at E, the wheel W is removed and a pin
passed through D and E, so that by operating the handle the spindle can
be traversed in and out without any rotary motion of the screw.
When the tailblock of a lathe fits between the edges of the shears,
instead of upon raised [V]s, it is sometimes the practice to give them
a slight taper fitting accurately a corresponding taper on the edges of
the shears. This enables the obtenance of a very good fit between the
surfaces, giving an increased area of contact, because the surfaces can
be filed on their bearing marks to fit them together; but this taper is
apt to cause the tailstock to fit so tightly between the shears as to
render it difficult to move it along them, and in any event the friction
is apt to cause the fit to be destroyed from the wear. An excellent
method of obviating these difficulties is by the employment of rollers,
such as shown at R in Figs. 637 and 638, which represent the tailstock
of the Putnam Tool Company's lathe. In some cases such rollers are
carried on eccentric shafts so that they may be operated to lift the
tailstock from the bed when moving it.
[Illustration: Fig. 636.]
[Illustration: Fig. 637.]
[Illustration: Fig. 638.]
[Illustration: Fig. 639.]
A very ready method of securing or releasing a small tailstock to a
lathe shears is shown applied to a wood turner's hand rest in Fig. 639,
in which A A represents the lathe shears, B the hand rest, C the
fastening bolt, D a piece hinged at each end and having through its
centre a hole to receive the fastening bolt, and a counter-sink or
recess to receive the nut and prevent it unscrewing. E represents a
hinged plate, and F a lever, having a cam at its pivoted end. A slot for
the fastening bolt to pass through is provided in the plate E. In this
arrangement a very moderate amount of force applied to bring up the cam
lever will cause the plate D to be pressed down, carrying with it the
nut, and binding the tailstock or the tool rest, as the case may be,
with sufficient force for a small lathe.
When a piece of work is driven between the lathe centres, the weight of
the work tends to deflect or bend down the tail spindle. The pressure of
the cut has also to be resisted by the tail spindle, but this pressure
is variable in direction, according to the shape of the tool and the
direction of the feed; usually it is laterally towards the operator and
upwards. In any event, however, the spindle requires locking in its
adjusted position, so as to keep it steady. The pressure on the conical
point of the dead centre is in a direction to cause the tail screw to
unwind, unless it be a left-hand thread, as is sometimes the case.
If the spindle and the bore in which it operates have worn, the
resulting looseness affords facility for the spindle to move in the bore
as the pressure of the cut varies, especially when the spindle is far
out from the tailstock.
Now, in locking the tail spindle to obviate these difficulties, it is
desirable that the locking device shall hold that spindle axially true
with the live spindle of the lathe, notwithstanding any wear that may
have taken place. The spindle is released from the pressure of the
locking device whenever it is adjusted to the work, whether the cut be
proceeding or not. Hence, the wear takes place on the bottom of the
spindle and of the hole, wear only ensuing on the top of the spindle and
bore when the spindle is operated under a slight locking pressure, while
the cut is proceeding in order to take up the looseness that may have
arisen from wear in the work centres.
In all cases the feed of the cut should be stopped while the centre is
adjusted, so as to relieve the spindle and bore from undue wear; but
most workmen pay little heed to this; hence the wear ensues, being, as
already stated, mainly at the bottom. It is obvious, then, that, if the
spindle is to be locked to the side of the bore on which it slides, it
will be held most truly in line if it be locked to that side which has
suffered least from wear, and this has been shown to be at the top.
[Illustration: Fig. 640.]
[Illustration: Fig. 641.]
The methods usually employed to effect this locking are as follows:--In
Fig. 640, S is the tail spindle, B part of the tailblock in section, R a
ring-bolt, and H a handled nut. Screwing up the nut H causes R to clamp
S to the upper part of the bore of B; while releasing H leaves S free to
slide. There are three objections to this plan. The ring R tends to
spring or bend S. The weight of R tends to produce wear upon the top of
the spindle, and the spindle is not gripped so near to its dead centre
end as it might be. If S is a close fit in B the pressure of R could not
spring or bend S; but, so soon as wear has taken place, S becomes simply
suspended at R, having the pressure of R, and the weight of the work
tending to bend it. Another locking device is shown in Fig. 641. It
consists of a shoe placed beneath S, and a wedge-bolt beneath it,
operated by the handled nut C. Here the pressure is again in a direction
to lift S, as denoted by the arrow; but when the wedge W is released the
shoe falls away from S, hence the locking device produces no wear upon
S. This device may be placed nearer to the end of B, since the wedge may
pass through the front leg of the tailstock instead of to the right of
it, as in Fig. 640. But S is still suspended from the point of contact
of the shoe, and the weight of the work still bends it as much as its
play in B will permit.
[Illustration: Fig. 642.]
Another clamping device is shown in Fig. 642. In this the cylindrical
part B of the tailblock is split on one side, and is provided with two
lugs. A handled screw passes through the upper lug, and is threaded into
the lower one, so that by operating the handle C, the bore may be
closed, so as to grip S, or opened to relieve it. This possesses the
advantages: First, that it will cause S to be gripped most firmly at the
end of B, and give a longer length of bearing of B upon S; and,
secondly, that it will grip S top and bottom, and, therefore, prevent
its springing from the weight of the work. But, on the other hand, B
will close mainly on the side of the split, as denoted by the dotted
half-circle, and therefore tend to throw S somewhat in the direction of
the arrow, which it will do to an amount answerable to the amount of
looseness of S in B. In the Pratt and Whitney lathes this device is
somewhat modified, as is shown in Fig. 643. A stud E screws into the
lower lug D, having a collar at E let into the upper lug, with a square
extending above the upper lug so that the stud may be screwed into D,
exerting sufficient pressure to close the bore of B to a neat working
fit to the spindle. The handled nut, when screwed up, causes B to grip
the spindle firmly; but when released, leaves the spindle a neat working
fit and not loose to the amount of the play; hence, the locking device
may be released, and the centre adjusted to take up the wear in the work
centres while the cut is proceeding, without any movement of the spindle
in B, because there is no play between the spindle and B.
[Illustration: Fig. 643.]
[Illustration: Fig. 644.]
In the design shown in Fig. 644, the end B of the tailblock is threaded
and is provided with a handled cap nut A A. In the end of the tailblock
where the spindle emerges, is provided a cone, and into this cone fits a
wedge-shaped ring, as shown. This ring is split quite through on one
side, while there are two other slots nearly but not quite splitting the
wedge-ring. When the handle C is pulled towards the operator it screws A
up on the end B, and forces the wedge-ring up in the conical bore in B.
From the split the ring closes upon the spindle S, and grips it. Now, as
the ring is weakened by slots in two places besides the split, it closes
more nearly cylindrically true than if it had only a split, there being
three points where the ring can spring when closing upon S; and from the
cone being axially true with the live spindle of the lathe, S is held
axially true, notwithstanding any wear of the spindle, because the
locking device, being at the extreme end of B, is as near to the dead
centre as it is possible to get it; and, furthermore, when C is operated
for the release, the wedge-ring opens clear of S, so that S does not
touch it when moved laterally. The wear of the bore of B has, therefore,
no effect to throw S out of line, nor has the gripping device any
tendency to bend or spring S, while the latter is held as close to the
work as possible; hence the weight of the work has less influence in
bending it. The pitch of the thread and the degree of cone are so
proportioned that less than one-quarter rotation of A will suffice to
grip or release S, the handle C being so placed on A as to be about
vertical when the split ring binds S; hence C is always in a convenient
position for the hand to grasp.
[Illustration: Fig. 645.]
In this case, however, the spindle being locked at the extreme end of
the hole, there is more liability of the other end moving from the
pressure of the cut, or from the weight of the work; hence it would seem
desirable that a tail spindle should be locked in _two_ places; one at
the dead centre end of the hole, and the other as near the actuating
wheel, or handle, as possible, and also that each device should either
hold it central to the original bore, notwithstanding the wear, an end
that is attained in the Sellers lathes already described.
Slide rests for self-acting or engine lathes are divided into seven
kinds, termed respectively as follows: simple, or single, elevating,
weighted, gibbed, compound, duplex, and duplex compound. A simple, or
single, slide rest contains a carriage and one cross slide, as in Fig.
621. An elevating slide rest is one capable of elevation at one end to
adjust the cutting tool height, as in Fig. 499. A weighted slide rest is
one held to the shears by a weight, as in Fig. 577. A gibbed slide rest
is held to the shears by gibs, as in Fig. 621. A compound slide rest has
above the cross slide, a second slide carrying the tool holder, this
second slide pivoting to stand at any required angle, as in Fig. 505. A
duplex slide rest has two rests on the same cross slide, and in a
compound duplex both these two rests are compound, as in Fig. 511. The
rest shown on the Putnam lathe in Figs. 492 and 499, is thus an
elevating gibbed single rest.
TESTING A LATHE.--To test a lathe to find if its live and dead spindles
are axially in line one with the other and with the guides on the lathe
bed, the following methods may be employed in addition to those referred
to under the heading of Erecting.
To test if the live spindle is true with the bed or shear guides, a
piece such as in Fig. 645 may be turned up between the lathe centres,
the end A fitting into the live spindle in place of the live centre, and
the collars B C being turned to an equal diameter, and the end face D
squared off true. The end A must then be placed in the lathe in place of
the live centre, the dead centre being removed from contact with the
work; with the lathe at rest a tool point may be set to just touch
collar C, and if when the carriage is moved to feed the tool past
collar B, the tool draws a line along it of equal depth to that it drew
along C, the live head is true; the dead centre may then be moved up to
engage the work end D, and the lathe must be revolved so that (the tool
not having been moved at all by the cross-feed screw) the tool may be
traversed back to draw another line along C, and if all three lines are
of equal depth the lathe is true. The tool should be fine pointed and
set so as to mark as fine a line as possible.
[Illustration: Any View.
Fig. 646.]
[Illustration: Side View.
Fig. 647.]
[Illustration: Side View.
Fig. 648.]
[Illustration: Top View.
Fig. 649.]
Another method is to turn up two discs, such as in Fig. 646, their stems
A and B fitting in place of the live and dead centres. One of these
discs is put in the place of the live, and the other in that of the dead
centre, and if then the lathe tailstock be set up so that the face of B
meets that of A, their coincidence will denote the truth of the live and
dead spindles. The faces of the discs may be recessed to save work and
to meet at their edges only, but their diameters must be equal. If the
discs come one higher than the other, as in Fig. 647, the centres are of
unequal height. If the faces meet at the top and are open at the bottom,
as in Fig. 648, it shows that the back bearing of the live spindle is
too high, or that the tail spindle is too low at the dead centre end. If
the discs, when viewed from above, come as in Fig. 649, it is proof that
either the live spindle or the tail spindle does not stand true with the
lathe shears. If the disc faces come so nearly fair that it is difficult
to see if they are in contact all around, four pieces of thin paper may
be placed equidistant between them, and the grip upon them tested by
pulling.
If the tailstock has been set over to turn taper and it is required to
set it back to turn parallel again, place a long rod (that has been
accurately centred and centre-drilled) between the lathe centres, and
turn up one end for a distance of an inch or two.
Then turn it end for end in the lathe and let it run a few moments so
that the work centre, running on the dead centre of the lathe, may wear
to a proper bed or fit to the lathe centre, and then turn up a similar
length at the dead centre end, taking two cuts, the last a fine
finishing cut taken with a sharp tool, and feeding the finishing cut
from left to right, so that it will be clear of the work end when the
cut is finished. Without moving the cross-feed screw of the lathe after
the finishing cut is set, take the bar out of the lathe and wind the
slide rest carriage, so that the turning tool will stand close to the
live centre. Place the bar of iron again in the lathe, with the turned
end next to the live centre, and move the lathe carriage, so that the
tool is on the turned end of the bar.
Rotate the bar by hand, and if the tool just touches the work without
taking a cut the line of centres is parallel with the ways. If there is
space between the tool point and the turned end of the bar, the
tailstock requires setting over towards the back of the lathe, while if
the tool takes a cut the tailstock requires to be set over towards the
operator. If a bar is at hand that is known to be true, a pointed tool
may be adjusted to just make a mark on the end of the bar when the slide
rest is traversed. On the bar being reversed, the tool should leave,
when traversed along the bar, a similar mark on the bar.
To test the workmanship of the back head or tailstock, place the
forefinger on the spindle close to the hub whence it emerges, and
observe how much the hand wheel can be moved without moving the spindle;
this will show how much, if any, lost motion there is between the screw
and the nut in the spindle. Next wind the back spindle about three
quarters of its length out of the tailstock, take hold of the dead
centre and pull it back and forth laterally, when an imperfect fit
between the spindle and the hole in which it slides will be shown by the
lateral motion of the dead centre. Wind the dead centre in again, and
tighten and loosen the spindle clamp, and see if doing so moves the
spindle in the socket.
To examine the slide rest, move the screw handles back and forth to find
how much they may be moved without giving motion to the slides; this
will determine the amount of lost motion between the collars of the
screws and between the screws themselves and the nuts in which they
operate. To try the fit of the slide rest slides, in the stationary
sliding ways or [V]s, remove the feed screws and move the slide so that
only about one-half inch is in contact with the [V]s, then move the
slide back and forth laterally to see if there is any play. Move the
slide to the other end of the [V]s, and make a similar test, adjusting
the slide to take up any play at either end. Then clean the bearing
surfaces and move the slide back and forth on the [V]s, and the marks
will show the fit, while the power required to move the slide will show
the parallelism of the [V]s.
If the lathe carriage have a rack feed, operate it slowly by hand, to
ascertain if it can be fed slowly and regularly by hand, which is of
great importance. Then put the automatic feed in gear, and operate the
feed gear back and forth, to determine how much it can be moved without
moving the slide rest. To test the fit of the feed screw to the feed
nut, put the latter in gear and operate the rack motion back and forth.
To determine whether the cross slide is at a right angle with the ways
or shears, take a fine cut over a radial face, such, for example, as the
largest face plate, and test the finished plate with a straight edge. If
the face plate runs true and shows true with a straight edge, so that it
is unnecessary to take a cut over it, grind a piece of steel a little
rounding on its end, and fasten it in the tool post or clamp, with the
rounded end next to the face plate. Let the rounded end be about 1/4 in.
away from the face plate, and then put the feed motion into gear, and,
with the steel near the periphery of the face plate, let the carriage
feed up until the rounded steel end will just grip a piece of thin paper
against the face plate tight enough to cause a slight strain in pulling
the paper out, then wind the tool in towards the lathe centre and try
the friction of the paper there; if equal, the cross slide is true.
To find the amount of lost motion in the screw feed gear, adjust it
ready to feed the saddle, and pull the lathe belt so as to revolve the
cone spindle backward, until the slide rest saddle begins to move, then
mark a fine line on the lathe bed making the line coincident with the
end of the lathe saddle or carriage. Then revolve the cone spindle
forward, and note how much the cone spindle rotates before the saddle
begins to traverse.
If the lathe has an independent feed motion it may be tested in the same
manner as above.
In large lathes this is of great consideration, because the work
revolves very slowly, and if there is much lost motion in the feed gear,
it may take considerable time after the feed is put in gear before the
carriage begins to travel. Suppose, for example, a 14-foot pulley is
being turned, and that the tool cuts at 15 feet per minute, it will take
nearly three minutes for the work to make a revolution.
CHAPTER VIII.--SPECIAL FORMS OF THE LATHE.
The lathe is made in many special or limited forms, to suit particular
purposes, the object being to increase its efficiency for those
purposes, which necessarily diminishes its capacity for general work.
In addition to this, however, there are machine tools whose construction
varies considerably from the ordinary form of lathe, which nevertheless
belong to the same family, and must, therefore, be classified with it,
because they operate upon what is essentially lathe work. Thus boring
and turning mills are essentially what may be termed horizontal lathes.
Figs. 650 to 655 inclusive, represent the American Watch Tool Company's
special lathes for watch-makers, which occupy a prominent position in
Europe, as well as in the United States.
In lathes of this class, refinement of fit, alignment, truth, and
durability of parts are of the first importance, because of the
smallness of the work they perform, and the accuracy to which that work
must be made. Furthermore, such lathes must be constructed to hold and
release the work as rapidly as possible, because in such small work the
time occupied by the tools in cutting is less, while that occupied in
the insertion and removal of it is greater in comparison than in larger
jobs; it often takes longer to insert and remove the work than to
perform it.
These facts apply with equal force to all such parts as require the
removal to or from the lathe-bed, or frequent adjustment upon the same.
Thus the devices for holding and releasing the tool post or hand rest
and tailblock are each so constructed that they may be set without the
use of detached wrenches.
Fig. 650 represents a general view of the lathe, while Fig. 651
represents a sectional view of the headstock. The live spindle consists
of two parts, an outer sleeve A A, having journal bearing in the head,
and an inner hollow spindle B B, threaded at its front end _e_, to
receive the chucks. The main spindle at the front end works in a journal
box _c_, that is cylindrical to fit the headstock, but double coned
within to afford journal bearing to the spindle A. The inner step of
this double cone is relied upon mainly to adjust the diametral fit of
the bearing, while the outer step is relied upon mainly to adjust the
end fit of the spindle; but it is obvious in both cases there is an
action securing simultaneously the diametral and the end fit. In the
back bearing there are two cones. The outer one _r_ is cylindrical
outside where it fits into the head, and coned in its bore to receive
the second cone _s_, which rotates with spindle A. The nut F is threaded
upon A, so that by operating F, A is drawn within _c_, and S is
simultaneously moved within _r_, so that both bearings are
simultaneously adjusted. D D are _dust_ rings, being ring-caps which
cover the ends of the bearings and the oil holes so as to prevent the
ingress of dust.
The inner spindle B has a bearing in A at the back end to steady it, and
a bearing at end _e_, and is provided with the hand wheel H, by which it
may be rotated to attach the chucks which screw into its mouth at _e_.
To rotate or drive the chucks there is in A a feather at _g_, the chucks
having a groove to receive this feather and screwing into B at E, when B
is rotated.
The mouth of A is coned, as shown at _h_, and the chucks are provided
with a corresponding male cone, as shown at _h_ in Figs. 652 and 653, so
that the chucks are supported and guided by the cone, and are therefore
as close to the work as possible while having a bearing at _g_. But the
cone on the chucks being split, (as is shown in Fig. 652), rotating B
while holding A stationary (which may be done by means of the band
pulley P), causes the chucks to move endwise in A, and if the motion is
in the direction to draw the chuck within A, the cone _h_ causes the
chuck to close upon and grip the work. Thus in Fig. 652 is shown a step
chuck. The thread at J enters the end _e_ of B, in Fig. 651, which
screws upon it. Cone _h_ fits mouth _h_ in Fig. 651, and _l_ represents
the splits in the chuck, which enable it to close when the cone _h_ is
drawn within the mouth _h_ of spindle A.
The chuck is employed to hold cylindrical plates or discs, such as
wheels and barrels, and the various steps are to suit the varying
diameters of these parts in different sizes of watches.
Fig. 653 represents a wire chuck, having the cone at _h_, and the three
splits at _l_, as before, the cone-mouth _h_ closing the chuck as the
latter is drawn within the spindle A.
In both the chucks thus far described, the construction has been
arranged to close the splits and thus grip the circumferences of
cylindrical bodies, but in Fig. 654 is shown the arrangement for
enabling the chuck to expand and grip the bores of hollow work, such as
rings, &c.
The outer spindle A corresponds to the outer spindle A in Fig. 651, and
the inner one to spindle B in that figure. The chuck is here made in two
separate parts, a sleeve V fitting in and driven by A, and a plug X
fitting into a cone in the mouth of V, and screwing into the end of
drawing spindle B. But while V is driven by and prevented from rotating
within A by means of the feather at _g_, so likewise X is prevented from
rotating within V by means of a feather _h_ fast in X and fitting into a
groove or featherway in V. It follows then that when B is rotated X may
be traversed endways in V, to open or close the steps Y according to the
direction of rotation of B.
It will now be apparent that in the case of chucks requiring to grip
external diameters, the gripping jaws of the chucks will, when out of
the lathe, be at their largest diameter, the splits _l_ being open to
their fullest, and that when by the action of the cones, they are closed
to grip the work, such closure must be effected against a slight spring
or resistance of the jaws, and this it is that enables and causes the
chuck to open out of itself, when the enveloping cone permits it to do
so.
But in the case of the opening or expanding chuck, the reverse is the
case, and the chuck is at its smallest diameter (the splits _l_ being at
their closest) when the chuck is removed from the lathe, as is obviously
necessary. In reality the action is the same in both cases, for the
chuck moves to grip the work under a slight resistance, and this it is
that enables it to readily release the work when moved in the necessary
endwise direction.
The band pulley P is fast upon A, and is provided with an index of 60
holes on its face G, and which are adjusted for any especial work by a
pin Q, so that a piece of work may have marked on it either 60, 30, 20,
15, 12, 10, 6, 5, 4, 3, or 2 equidistant lines of division, each of
those numbers being divisors of 60. In marking such lines of division
upon the work a sharp point may be used, supported by the face of the
hand rest as a guide; or a sharp-pointed tool may be placed in the slide
rest to cut a deeper line upon the work. The index plates used for
cutting wheels and pinions may be placed on the rear end of A, the pawl
being secured to the work-bench. The wheel H is for rotating spindle B
to screw the chucks on or off the same.
[Illustration: _VOL. I._ =WATCHMAKER'S LATHE.= _PLATE VIII._
Fig. 650.
Fig. 651.
Fig. 652.
Fig. 653.
Fig. 654.]
[Illustration: _VOL. I._ =DETAILS OF WATCHMAKER'S LATHE.= _PLATE IX._
Fig. 655.
Fig. 656.
Fig. 657.
Fig. 658.
Fig. 659.
Fig. 660.
Fig. 661.
Fig. 662.]
Fig. 655 represents an end view from the tailstock end of the lathe; A´
is the bed having the angles _a_ _a_ to align the heads and rests. The
means of holding or releasing the tailstock, on the lathe-bed, is the
same as that for holding the headstock, the construction being as
follows: _b_ is the shoulder of a bolt through which passes the shaft
_c_, with a lever _d_ to operate it. This shaft is eccentric where it
passes through the bolt, so that by using the lever aforesaid the bolt
secures or releases the head according to the direction in which it is
moved. A very small amount of motion is needed for this. The standard
for the hand rest is split, and a screw is used to tighten it in an
obvious manner, the screw being operated by the handle _e´_. An end view
of the rest, showing the device for securing the foot _h_ to the bed, is
shown in Fig. 656, _f_ is a shoe spanning the bed and fitting to the bed
angles _a_. Through _f_ passes the bolt _g_, its head passing into the
[T]-shaped groove _h_; N´ is a hand wheel for operating bolt _g_. At S
is a spiral spring, which by exerting an end pressure on washer _w_ and
nut N´, pulls _g_ and the head _h_ down upon _f_, and therefore _f_ down
upon the bed, whether the rest be locked to the bed or not; hence when
N´ is released to remove or adjust the rest, neither dust nor fine
cuttings can pass either between the rest and shoe or the shoe and the
lathe-bed, and the abrasion that would otherwise occur is thus avoided.
Two qualities of these lathes are made: in the better quality all the
working parts are hardened and afterwards ground true. In the other the
parts are also ground true, but the parts (which in either case are of
steel) are left soft for the sake of reducing the cost. In all, the
parts are made to gauge and template, so that a new head, tailstock, or
any other part in whole or in detail may be obtained from the factory,
either to make additions to the lathe or to replace worn parts.
Two styles of slide rest are made with these lathes: in the first, shown
in Fig. 657, the swivel for setting the top slide at an angle for taper
turning is at the base of the top slide, hence the lower slide turns all
radial faces at a right angle to the line of lathe centres. In the
second, Fig. 658, there is a third slide added at the top, so that the
bottom slide turns radial faces to a right angle with the line of lathe
centres, the next slide turns the taper and the top slide may be used to
turn a radial face at a right angle to the surface of the taper, and not
at a right angle to the axis of the work. Both these rests are provided
with tool post clamps, to hold tools made of round wire, such clamps
being shown in position in figure 657.
Fig. 659 represents an additional tailstock for this lathe, the tail
spindle lying in open bearings so that it can be laid in, which enables
the rapid employment of several spindles holding tools for performing
different duties, as drilling, counter-boring, chamfering, &c.
Fig. 660 represents a filing fixture to be attached to the bed in the
same manner as the slide rest. It consists of a base supporting a link,
carrying two hardened steel rolls, upon which the file may rest, the
rolls rotating by friction during the file strokes, and serving to keep
the file flat and fair upon the work.
Fig. 661 represents a fixture for wheel and pinion cutting; it is
attached to the slide rest. When the cutter spindle is vertical the belt
runs directly to it from the overhead counter shaft, but when it is
horizontal the belt passes over idler pulleys, held above the lathe. The
cutter spindle is carried on a frame, pivoted to the sliding piece on
the vertical slide, so that it may be swivelled to set in either the
vertical or horizontal position.
Fig. 662 represents a jewelers' rest for this lathe. It fits on the bed
in the place of the tailstock, and is used for cutting out the seats for
jewels, in plates, or settings. It is especially constructed so as to
receive the jewel at the top and bore the seating to the proper
diameter, without requiring any measurements or fitting by trial, and
the manner in which this is accomplished is as follows:--
[Illustration: Fig. 663.]
[Illustration: Fig. 664.]
[Illustration: Fig. 665.]
Fig. 663 is a side elevation, Fig. 664 an end elevation, and Fig. 665 a
plan view of this rest, and similar letters of reference indicate like
parts in each of the three figures. A is the base, held to the lathe bed
by the bolt B, whose operation is the same as that already described for
the head and tailstocks.
In one piece with A is the arm C, carrying at its head three gauge
tongues or pieces D E F, which are adjustable by means of the screws _d_
_e_ _f_, which move the gauge tongues horizontally. Through a suitable
guide I is a standard or head; pivoted to A at J J, and carrying at its
top three gauge tongues K L M.
Midway between pivots J J and the ends of the gauge tongues, is the
centre or tool carrying spindle O. If a piece of work, as a jewel, be
placed between the tongues F and M, Fig. 664 [swinging M, and with it I
(which is pivoted at J), laterally], then the point of the centre N will
be thrown out of line with the lathe live spindle half the diameter of
the jewel, because from J to the centre N, of O, is exactly one half of
the vertical distance from J to the jewel. If then a tool be placed in
the dead centre and its cutting edge is in line with the axis of spindle
O, it will bore a hole that will just fit the jewel. Hence placing the
jewel between the two tongues sets the diameter to which the tool will
bore and determines that it shall equal the diameter of the jewel.
The object of having three pair of gauge tongues is to enable the
obtaining of three degrees of fit; thus with a piece placed between D K
the hole may be bored to fit the piece easily, with it placed between E
L the fit may be made barely movable, while with it placed between F M
the fit may be too tight to be a movable one save by pressure or
driving, each degree of fit being adjusted by means of the screws _e_
_f_ _g_.
The tool is fed by moving spindle O by hand, the screw P being adjusted
so that its end abuts against stop Q, when the hole is bored to the
requisite depth; R is simply a guide for the piece S, which being
attached to O, prevents it from rotating.
In watch manufactories special chucks and appliances are necessary to
meet their particular requirements. There is found to exist, for
example, in different rods of wire of the same nominal diameter, a
slight variation in the actual diameter, and it is obvious that with the
smaller diameters of wire the split chucks will pass farther within the
mouth _h_ of A, Fig. 651, because the splits of the chucks will close to
a greater extent, and the cones on the chucks therefore become reduced
in diameter.
If then it be required to turn a number of pieces of work to an exact
end measurement, or a number of flanges or wheels to equal thicknesses,
without adjusting the depth of cut for each it becomes necessary to
insure that the successive pieces of work shall enter the chucks to an
equal distance, notwithstanding any slight variation in the work
diameter at the place or part where it is gripped by the chuck.
To accomplish this end what is termed a sliding-spindle head is
employed. In this the _outer spindle_ has the end motion necessary to
open and close the chuck, the chuck having no end motion.
[Illustration: Fig. 666.]
The construction of this sliding-spindle head is shown in Fig. 666, in
which a wire chuck is shown in position in the spindles; L is the live
spindle passing through parallel bearings, so that it may have end
motion when the nut M is operated. The inner spindle N to which the
chucks are screwed is prevented from having end motion by means of the
collar _p_ and nut _q_ at the rear bearing. When nut M is rotated and N
is held stationary by means of the pulley P, L slides endways, and the
chuck opens or closes according to the direction in which the nut moves
the spindle L.
To regulate the exact distance to which the work shall be placed within
the chuck, a piece of wire rod may be placed within the hollow spindle N
being detained in its adjusted position by the set screw S.
The construction whereby the nut is permitted to revolve with spindle L,
and be operated by hand to move spindle L when the lathe is at rest, is
as follows.
The cylindrical rim _t_ of the nut is provided with a series of notches
arranged around its circumference. R is a lever whose hub envelops nut
M, but has journal bearing on V. R receives the pin S, which rests upon
a spiral spring T. When, therefore, S is pushed down it depresses the
spring T and its end W enters some one of the notches in the rim _t_,
and operates the nut after the manner of a ratchet. But so soon as the
end pressure on R is released, the spiral spring lifts it and M is free
to revolve with L as before. The inner spindle is driven by means of the
feather G.
Pulley P has two steps Y for the belt, and a friction step _z_, around
which passes a friction band operated by the operator's foot to stop the
lathe quickly. This performs two functions, as follows. The thread of M
is a left-hand one so that the inertia of the nut will not, when the
lathe is started, operate to screw the nut back, and release the chuck
jaws from the work, by moving spindle L endwise. Per contra, however, in
stopping the lathe suddenly by means of the brake, there is a tendency
of nut M to stop less quickly than spindle L, and this operates to
unscrew nut N and release the work. To assist this R is sometimes in
lathes for watch manufactories provided with a hand wheel whose weight
is made sufficient for the purpose.
[Illustration: Fig. 667.]
[Illustration: Fig. 668.]
Figs. 667 and 668 represent a pump centre head for watch manufactories,
being a device for so chucking a piece of work that a hole may be
chucked true and enlarged or otherwise operated upon, with the assurance
that the work will be chucked true with the hole. Suppose two discs be
secured together at their edges, their centres being a certain distance
apart, as, for example, a top and bottom plate of a watch movement, and
that the holes of one plate require to be transferred to the other, then
by means of this head they may be transferred with the assurance that
they shall be axially in line one with the other, and at a right angle
to the faces of the plates, as is necessary in setting jewels in a watch
movement.
In holes of such small diameters as are used in watch work, it is
manifestly very difficult to set them true by the ordinary methods of
chucking and it is tedious to test if they are true, and it is to
obviate these difficulties that the pump centre head is designed. Its
operation is as follows.
There are in this case three spindles A, B, and C, in Fig. 667; A
corresponds to spindle A in Fig. 651, driving the chuck D which screws
on A as shown; B simply holds the work against the face _d_ of D, and C
holds the work true by means of the centre _e_, which enters the hole or
centre in the work and is withdrawn when the work is secured by spindle
B.
The chuck D is open on two sides as shown at E E in Fig. 668, which is
an end face view of the chuck, and through these openings the work is
admitted to the chuck. The rod or spindle C is then pushed, by hand,
endwise, its centre _e_ entering the hole or centre in the work (so as
to hold the same axially true) and forcing the work against the inside
faces _d_, spindle B is then operated, the face _p_ forcing the work
against face _d_, and between these two faces _d_ _p_ the work is held
and driven by friction. The spindle C and its centre _e_ is then
withdrawn by hand, leaving the hole in the work free to be operated
upon.
The journal bearings for spindle A are constructed as described for A in
Fig. 666; spindle B is operated endways within A as follows. A is
threaded at G to receive the hub H of wheel I, at the end of B is a
collar which is held to and prevented from end motion within the hub H:
hence when wheel I is rotated and A is held stationary (by means of the
band pulley), H traverses on G and carries B with it. Operating I in one
direction, therefore moves _p_ against the work, while operating it in
the other direction releases face _p_ from contact with the work.
It is obviously of the first importance that the spindle C be held and
maintained axially true, notwithstanding any wear, and that it be a
close fit within B so as to remain in any position when the lathe is
running, and thus obviate requiring to remove it. To maintain this
closeness of fit the following construction is designed. Between spindle
A and spindle B, at the chuck end of the two, is a steel bush which can
be replaced by a new one when any appreciable wear has taken place.
Between B and C are two inverted conical steel bushes, which can also be
replaced by new ones, to take up any wear that may have taken place.
[Illustration: Fig. 669.]
Fig. 669 represents an improved hand lathe by the Brown and Sharpe
Manufacturing Company, of Providence, R. I. It is specially designed for
the rapid production of such cylindrical work as may be held in a chuck,
or cut from a rod of metal passing through the live spindle, which is
hollow, so that the rod may pass through it. Short pieces may be driven
by the chuck or between the centres of a face plate (shown on the floor
at _e_) screwing on in the ordinary manner. When, however, this face
plate is removed a nut _d_ screws on in its stead, to protect the thread
on the live spindle.
The chuck for driving work in the absence of face plate _e_ (as when the
rod from which the work is to be made is passed through the live
spindle) may be actuated to grip or release the work without stopping
the lathe. The pieces _j_ _j_ are to support the hand tool shown in
Figs. 1313 and 1314, in connection with hand turning, the tool stock or
handle being shown at _k_ on the floor. The lever for securing the
tailstock to or releasing it from the shears is shown at _t_. The tail
spindle is operated by a lever pivoted at _g_ so that it may be operated
quickly and easily, while the force with which the tail spindle is fed
may be more sensitively felt than would be the case with the ordinary
wheel and screw, this being a great advantage in small work. The tail
spindle is also provided with a collar _r_, that may be set at any
desired location on the spindle to act as a stop, determining how far
the tail spindle can be fed forward, thus enabling it to drill holes,
&c., of a uniform depth, in successive pieces of work.
The live spindle is of steel and will receive rods up to 1/2 inch in
diameter. Its journals are hardened and ground cylindrically true after
the hardening. It runs in bearings which are split and are coned
externally, fitting into correspondingly coned holes in the headstock.
These bearings are provided with a nut by means of which they may be
drawn through the headstock to take up such wear in the journal and
bearing fit, as may from time to time occur.
[Illustration: Fig. 670.]
It is obvious that the lathe may be removed from the lower legs and
frame and bolted to a bench, forming in that case a bench lathe.
Fig. 670 represents a special lathe or screw slotting machine, as it is
termed, for cutting the slots in the heads of machine or other screws.
The live spindle drives a cutter or saw _e_, beneath which is the device
for holding the screws to be slotted, this device also being shown
detached and upon the floor.
The screw-holding end of the lever _a_ acts similarly to a pair of
pliers, one jaw of which is provided on handle _a_, while the other is
upon the piece to which _a_ is pivoted. The screw to be slotted is
placed between the jaws of _a_ beneath _e_; handle _a_ is then moved to
the left, gripping the screw stem; by depressing _a_, the screw head is
brought up to the cutter _e_ and the slot is cut to a depth depending
upon the amount to which _a_ is depressed, which is regulated by a screw
at _b_; hence after _b_ is properly adjusted, all screw heads will be
slotted to the same depth.
The frame carrying the piece to which _a_ is pivoted may be raised or
lowered to suit screws having different thicknesses of head by means of
a screw, whose hand nut is shown at _d_.
The frame for the head of the machine is hollow, and is divided into
compartments as shown, in which are placed the bushings used in
connection with the screw-gripping device, to capacitate it for
different diameters of screws, and also for the wrenches, cutters, &c.
[Illustration: Fig. 671.]
[Illustration: Fig. 672.]
[Illustration: Fig. 673.]
Figs. 671, 672, and 673, represent a lathe having a special feed motion
designed and patented by Mr. Horace Lord, of Hartford, Connecticut. Its
object is to give to a cutting tool a uniform rate of cutting speed
(when used upon either flat or spherical surfaces), by causing the
rotations of the work to be retarded as the cutting tool traverses from
the centre to the perimeter of the work, or to increase as the tool
traverses from a larger to a smaller diameter. If work of small diameter
be turned at too slow a rate of cutting speed, it is difficult to obtain
a true and smooth surface; hence, as the tool approaches the centre, it
is necessary to increase the speed of rotation. As lathes are at present
constructed, it is necessary to pass the belt from one step to another
of the driving cone, to increase the speed. In this two disadvantages
are met with. First, that the increase of speed occurs suddenly and does
not meet the requirements with uniformity. Second, that the strain upon
the cutting tool varies with the alteration of cutting speed. As a
result, the spring of the parts of the lathe, as well as of the cutting
tool, varies, so that the cut shows plainly where the sudden increase or
decrease (as the case may be) of cutting speed has occurred. The
greatest attainable degree of trueness is secured when the cutting speed
and the strain due to the cut are maintained constant, notwithstanding
variations of the diameter.
This, Mr. Lord accomplishes by the following mechanism: Instead of
driving the lathe from an ordinary countershaft, he introduces a pair of
cones which will vary the speed of the lathe as shown in Fig. 672 as
applied to ball turning. L is a belt cone upon the counter-shaft driven
from the line shaft. L drives H, which may be termed the lathe
countershaft, and from the stepped cone K the belt is connected to the
lathe in the usual manner. P is a shipper bar to move the belt N upon
and along the belt cones, and thus vary the speed. R is a vertical shaft
extending up at the end of the lathe and carrying a segment. This
segment is connected to the belt shipper bar P by two cords, one passing
from _r_^{1} around half the segment to _r_^{2}, and the other passing
from _r_^{3} to _r_^{4}, so that if the segment be rotated, say to the
right, it and the bar will move as denoted by the dotted lines, or if
moved in an opposite direction, the bar motion will correspond and move
the belt N along the cones respectively left or right.
At the back of the lathe is a horizontal shaft S, similar to an ordinary
feed spindle, and connected to the segment shaft by a pair of bevel
gears S^{2}. Between the two ears _e_ _e_, at the rear of the lathe
carriage, is a pinion _t_, which drives the splined shaft S, which works
in a rack T´. The tool rest is pivoted directly beneath the ball, to be
turned after the usual manner of spherical slide rests, and carries a
gear _a_^{2}, which, as the rest turns, rotates a gear _a_^{3}. Upon the
face of the latter is a pin _a_^{4} working in a slot _a_^{5} at the end
of the rack T´; hence as the tool rest feeds, motion is transmitted from
_a_^{2} through _a_^{3}, _a_^{4}, _a_, T´, T, and _s_ _s_^{2} to R,
which operates the belt shipper P. As it is the rate of tool feed that
governs the speed of these motions, the effect is not influenced by
irregularity in feeding; hence the speed of the work will be equalized
with the tool feed under all conditions. The direction of motion of all
the parts will correspond to that of the tool feed from which their
motion is directed, and therefore the work speed will augment or
diminish automatically to meet the requirements.
[Illustration: Fig. 674.]
Fig. 673 illustrates the action of the mechanism when used for surfaces,
like a lathe face plate. In this case the two gears and the rack T´
simply traverse with the cross-feed slider, and the mechanism is
actuated as before. In Fig. 674 a different method of actuating the belt
shipper is illustrated. A pulley is attached to the intermediate stud of
the change gears, being connected by belt to the shipper, which is
threaded as shown at _d_, the belt guiding forks, as _p_^{2}, being
carried on a nut actuated by the screw _d_.
CUTTING-OFF MACHINE.--The cutting-off machine is employed to cut up into
the requisite lengths pieces of iron from the bar. As the cutting is
done by a tool, the end of the work is left true and square and a great
saving of time is effected over the process of heating and cutting off
the pieces in the blacksmith's forge, in which case the pieces must be
cut off too long and the ends left rough.
[Illustration: Fig. 675.]
Fig. 675 represents Hyde's cutting-off machine, which consists of a
hollow live spindle through which the bar of iron is passed and gripped
by the chucks C C. At G is a gauge rod whose distance from the tool rest
R determines the length of the work. F is a feed cone driven by a
corresponding cone on the live spindle and driving the worm W, which
actuates the self-acting tool feed, which is provided with an automatic
motion, which throws the feed out of action when the work is cut off
from the bar. The stand S is movable and is employed to support the ends
of long or heavy bars.
To finish work smooth and more true than can be done with steel cutting
tools in a lathe, what are known as grinding lathes are employed. These
lathes are not intended to remove a mass of metal, but simply to reduce
the surfaces to cylindrical truth, to true outline and to standard
diameter, hence the work is usually first turned up in the common lathe
to the required form and very nearly to the required diameter, and then
passed to the grinding lathe to be finished. The grinding lathe affords
the best means we have of producing true and smooth cylindrical parallel
work, and in the case of hardened work the only means. In place of steel
cutting tools an emery wheel, revolved at high speed from an
independent drum or wide pulley, is employed, the direction of rotation
of the emery wheel being opposite to that of the work.
[Illustration: Fig. 676.]
Fig. 676 represents Pratt and Whitney's weighted grinding lathe. The
headstock and tailstock are attached to the bed in the usual manner, the
frame carrying the emery wheel is bolted to the slide rest as shown, the
rest traversing by a feed spindle motion. The carriage traverse is
self-acting and has three changes of feed, by means of the feed cones
shown.
To enable the lathe to grind taper work (whether internal or external)
the lathe is fitted with the Slate taper attachment shown in Figs. 508
and 509.
It is obvious that in a lathe of this kind, there must be an extra
overhead shaft, driving a drum of a length equal to the full traverse of
the lathe carriage, or of the plate carrying the head and tailstocks,
and the arrangement of this drum with its belt connection to the pulley
on the emery wheel arbor, is sufficiently shown in figure. To protect
the ways of the bed from the abrasion that would be caused by the emery
and water falling upon them, guards are attached to the carriage
extending for some distance over the raised [V]s.
[Illustration: Fig. 677.]
It is essential that the work revolve in a direction opposite to that of
the emery wheel, for the following reasons. In Fig. 677 let A represent
a reamer and B a segment of an emery wheel. Now suppose A and B to
revolve in the direction that would exist if one drove the other from
frictional contact of the circumferential surfaces, then the pressure of
the cut would cause the reamer A to spring vertically and a wedging
action between the reamer and wheel would take place, the reamer
vibrating back and forth under varying degrees of this wedging; as a
result the surface of A would show waves and would be neither round nor
smooth.
[Illustration: Fig. 678.]
In the absence of a proper grinding lathe, an ordinary lathe is
sometimes improvised for grinding purposes, by attaching to the slide
rest a simple frame and emery wheel arbor with pulley attached as in
Fig. 678, in which A is the emery wheel, C the pulley for driving the
arbor, and B the frame, D being a lug for a bolt hole to hold the frame
to the lathe rest.
In some cases the work may remain stationary and the emery wheel only
rotate. Thus, suppose it was required to grind the necessary clearance
to relieve the cutting edge C of the reamer, then A could be rotated
until C stood in the required position with relation to B, and the
revolving emery wheel may either be traversed along, or the work may
traverse past the wheel, according to the design of the grinding lathe,
but in either case A remains stationary during each cut traverse; after
each successive traverse A may be rotated sufficiently to give a cut for
the next traverse.
Fig. 679 represents Brown and Sharpe's universal grinding lathe.
[Illustration: Fig. 679.]
This lathe is constructed to accomplish the following ends. First, to
have the lathe centres axially true with the work when grinding tapers,
so that the lathe centres shall not wear and gradually throw the work
out of true from the causes explained in the remarks on turning tapers
in a lathe of ordinary construction.
Second, to have the headstock B capable of lateral swing, so as to
enable the grinding of taper holes.
The manner in which these results are accomplished is as follows:
The headstock B and the tailstock are attached to the bed or table A,
which is pivoted at its centre to a table beneath it, this latter table
being denoted by C. This permits table A to swing laterally upon C and
stand at any required angle. To enable a delicate adjustment of this
angle, a screw _a_ having journal bearing in a lug on C is threaded
through a piece carried in projection on the end of A.
The table C traverses back and forth past the emery wheel, after the
manner of an ordinary iron planing machine, the mechanical parts
effecting this motion being placed within the bed upon which C slides.
The carriage supporting the emery frame and table D remains stationary
in its adjusted position, while C (carrying A with it) traverses back
and forth.
Now, if A be adjusted so that the line of centres is parallel with the
line of motion of C, then the work will be ground parallel, but if _a_
be operated to move A upon its pivoted centre and draw the tailstock end
of A towards the operator, then the work will be ground of larger
diameter at the tailblock end. Conversely, by operating screw _a_ in the
opposite direction, it will be of smaller diameter at that end.
But whatever the degree of angle of A to C, the line of centres of the
head and tailstocks will be axially true with the axial line of the
work, hence the work centres are not liable to wear off true, as is the
case when the tailstock only sets over (as will be fully explained in
the remarks on taper turning).
To grind conical holes the headstock B is pivoted at its centre upon a
piece held by bolts to the table A, so that it is capable of being swung
laterally to the degree requisite for the required amount of taper in
the work bore, and of being locked in that adjusted position, the work
being held in a chuck screwed upon the spindle in the usual manner. The
pulley _d_ being removed to enable the grinding of cones, chamfers, or
tapers of too great an angle to permit of A setting over to the required
degree. The line of cross-feed motion of the emery wheel may be set to
the required angle as follows.
The frame carrying the emery wheel arbor is fixed to a table D, which is
capable of being operated (in a direction across the table A) upon a
carriage beneath A. This carriage, or saddle (as it may perhaps be more
properly termed), is pivoted so as to allow of its movement and
adjustment in a horizontal plane, and since D operates in the slide of
the carriage, its line of motion in approaching or receding from the
line of centres will be that to which the saddle is set. This enables
the grinding of such short cones as the circumferences of bevelled
cutters, chamfers, &c., at whatever angle the saddle may be set,
however, D may be operated from the feed screw disc and handle _f_.
The lever handle at the left hand is for operating or rather traversing
C by hand; _b_ is a pan to catch the grit and water, the water being led
to the back of machine into a pail; _c_ is a back rest to steady the
work when it is slight and liable to deflection.
The slot and stops shown upon the edge of C are to regulate the points
of termination of the traverse (in the respective directions) of C. A
guard is placed over the emery wheel to arrest and collect the water
cuttings, &c., which would otherwise fly about.
A large amount of work which has usually been filed in a lathe, can be
much more expeditiously and accurately finished by grinding in this
machine.
Work to be ground may obviously be held in the same chucks or
work-holding appliances as would be required to hold it to turn it with
cutting tools, or where a quantity of similar work is to be done special
chucks may be made.
[Illustration: Fig. 680.]
Fig. 680 (from _The American Machinist_) shows a special chuck for
grinding the faces of thin discs, such as very thin milling cutters,
which could not be held true by their bores alone. The object of the
device is to hold the cutter by its bore and then draw it back against
the face of the chuck, which, therefore, sets it true on the faces. The
construction of the chuck is as follows. The hub screws upon the lathe
like an ordinary face plate, and has a slot running diametrically
through it. Upon its circumference is a knurled or milled nut C, which
is threaded internally to receive the threaded wings of the bush B. A
collar behind C holds it in place upon the hub. To admit piece B the
front of the chuck is bored out, and after B is inserted and its
threaded wings are engaged in the ring nut C a collar is fitted over it
and into the counter-bore to prevent B from having end motion unless C
is revolved. D is a split bushing that fits into B, its stem fitting the
bore of the disc, or cutter to be ground: the enlarged end of D is
countersunk to receive the head of the screw E, whose stem passes
through D and threads at its end into B, so that when E is screwed up
its head expands D and causes it to grip the bore of the disc or cutter
to be ground. After E is screwed up the ring nut C is revolved, drawing
B within the chuck and therefore bringing the inside face of the disc or
cutter against the face of the chuck or face plate, and truing it upon
the bushing D. All that is necessary therefore in using the chuck is to
employ a bushing of the necessary diameter for the bore of the cutter,
insert it in B, then screw up the screw E and then revolve the ring nut
C until the work is brought to bear evenly and fair against the face of
the chuck, and to insure this it is best not to screw E very tightly up
until after the ring nut C has been operated and brought the work up
fair against the chuck face.
[Illustration: Fig. 681.]
Fig. 681 represents the J. Morton Poole calender roll grinding lathe,
which has attained pre-eminence both in Europe and the United States
from the great accuracy and fine finish of the work it produces.
In all other machine tools, surfaces are made true either by guiding the
tool to the work or the work to the tool, and, in either case,
guide-ways and slides are employed to determine the line of motion of
the tool or the work, as the case may be. These guideways and slides are
usually carried by a framing really independent of the work, so that the
cutting depends entirely upon the truth or straightness of the
guideways, and is not determined by the truth, straightness, or
parallelism of the work itself. As a result, the surface produced
depends for its truth upon the truth of the tool-guiding ways. In the
Poole lathe, however, while guideways are necessarily employed to guide
the emery wheels in as straight a line as is possible, by means of such
guides, the roll itself is employed as a corrective agent to eliminate
whatever errors may exist in the guide. The rolls come to this machine
turned (in the lathe Fig. 730), and with their journals ground true (on
dead centres).
Fig. 681 represents a perspective view of the machine, as a whole. It
consists of a driving head, answering to the headstock of an ordinary
lathe. B B are bearings in which the rolls are revolved to be ground. C
is a carriage answering to the carriage of an ordinary lathe, but seated
in sunken [V]-guideways, corresponding to those on an ordinary iron
planing machine. Referring to Fig. 682, F is a swing-frame suspended by
four links at G, H, I, J, which are upon shafts having at their ends
knife edges resting in small [V]-grooves on the surface of standards S,
which are fixed to carriage C. The frame F being thus suspended and
being in no way fixed to C, it may be swung back and forth crosswise of
the latter, the links at G, H, I, J, swinging as pendulums. At the top
of F are two slide rests A A, one on each end, carrying emery or
corundum wheels W, and the roll R, which rests in the bearings B,
rotates between these emery wheels. The carriage C is fed along the bed
as an ordinary lathe carriage, and the emery wheels are revolved from an
overhead countershaft. Now, it will be found that from this form of
construction the surface of the roll, when ground true, serves as a
guide to determine the line of motion of the emery wheels, and that the
emery wheels may be compared to a pair of grinding calipers that will
operate on such part of the roll length as may be of larger diameter
than the distance apart of the perimeters of the emery wheels, and
escape such parts in the roll length as may be of less diameter than the
width apart of those perimeters; hence parallelism in the roll is
inevitable, because it is governed solely by the width apart of the
wheel perimeters, which remain the same, while the wheels traverse the
roll, except in so far as it may be affected by wear of emery-wheel
diameters in one traverse along the roll.
[Illustration: Fig. 682.]
Supposing now that we have a roll R (Fig. 683), placed in position and
slowly revolved, and that the carriage C is fed along by feed screw E,
then the line of motion of the emery wheels will be parallel to the axis
of the roll, provided, of course, that the bearings B (Figs. 681 and
687) are set parallel to the [V]-guideways in the bed, and that these
guideways are straight and parallel. But the line of travel of the emery
wheels is not guided by the [V]s except in so far as concerns their
height from those [V]s, because the swing-frame is quite free to swing
either to the right or to the left, as the case may be. Its natural
tendency is, from its weight, to swing into its lowest position, and
this it will obviously do unless some pressure is put on it in a
direction tending to swing it. Suppose, then, that instead of the roll
running true, it runs eccentrically, or out of true, as it is termed, as
shown in Fig. 683, when the high side meets the left-hand wheel it will
push against it, causing the carriage C to swing to the left and to
slightly raise. The pressure thus induced between the emery wheel and
the roll causes the roll surface to be ground, and the grinding will
continue until the roll has permitted the swing-frame to swing back to
its lowest and normal position. When the high side of the roll meets the
right-hand emery wheel it will bear against it, causing the swing-frame
to move to the right, and the pressure between the wheel and the roll
will again cause the high side of the latter to be reduced by grinding.
This action will continue so long as the roll runs out of true, but when
it runs true both emery wheels will operate, grinding it to a diameter
equal to the distance between the emery-wheel perimeters, which are, of
course, adjusted by the slide rests A A. If the roll is out of true in
the same direction and to the same amount throughout its length, the
emery wheel will act on an equal area (for equal lengths of roll)
throughout the roll length; but the roll may be out in one direction at
one part and in another at some other part of the length; still the
emery wheel will only act on the high side, no matter where that high
side may be or how often it may change in location as the carriage and
wheels traverse along the roll. Now, the roll does not run true until
its circumference is equidistant at every point of its surface from the
axis on which the roll revolves, and obviously when it does run true its
circumference is parallel to the axis of revolution of the roll, because
this axis is the line which determines whether the roll runs true or
not, and therefore the swing-frame is actually guided by the axis of
revolution of the roll, and will therefore move parallel to it.
[Illustration: Fig. 683.]
It is obvious that if by any means the swinging of frame F is slightly
resisted, as by a plate between it and C, with a spring to set up the
plate against F, then the emery wheels will be capacitated to take a
deeper cut than if the frame swing freely, this plan being adopted until
such time as the roll is ground true, when both wheels will act
continuously and simultaneously, and F may swing freely.
A screw may be used to set up the spring and plate when they are
required to act.
Suppose now that the roll was not set exactly level with the
[V]-guideways of the bed, there being a slight error in the adjustment
of the roll journals in the bearings on B, and the emery-wheels would
vary in height with relation to the height of the roll axis, and
theoretically they would grind the roll of larger diameter at one end
than at the other.
[Illustration: Fig. 684.]
This, however, is a theoretical, rather than a practical point, as may
be perceived from Fig. 684, in which R is a part of a section of a roll,
and W a part of a section of a wheel. Now, assuming that the [V]-ways
were as much as even a sixteenth out of true, so far as height is
concerned, all the influence of the variation in height is shown by the
second line of emery-wheel perimeter, shown in the figure, the two arcs
being drawn from centres, one of which is 1/16th inch higher than the
other. It is plain, then, that with the ordinary errors found in such
[V]-guideways, which will not be found to exceed 1/30th of an inch, no
practical effect will be produced upon the roll. Again, if one [V] is
not in line with the other, no practical effect is produced, because if
the carriage C were inclined at an angle, though the plane of rotation
of the emery-wheel would be varied, its face would yet be parallel to
the roll axis. If the [V]s were to vary in their widths apart (the
angles of the [V]s being 45° apart), all the effect it would have would
be to raise or lower the carriage C to one-half the amount the [V]s were
in error. It will be thus perceived that correctness of the roll both
for parallelism and cylindricity is obtained independent of absolute
truth in the [V]-guides.
Referring now to some of the details of construction of the lathe, the
slide rest A, Fig. 683, is bored to receive sockets D D, Fig. 685, and
is provided with caps, so that the sockets may be firmly gripped and
held axially true one with the other. The socket-bores are taper, to
receive the taper ends of the arbor _x_, and are provided with oil
pockets at each end. There is a driving pulley on each side of the
emery-wheel, and equal belt-speed is obtained as follows: Two belt
driving drums M N are employed, and each belt passes over both, as in
Figs. 683 and 685, and down around the pulleys P. The diameter of the
drum N is less than the diameter of the drum M by twice the thickness of
the belt, thus equalizing inside and outside belt diameters, since they
both pass over the pulley of the emery-arbor. The piece T is a guard to
catch the water from the emery-wheels, and is hinged at the back so that
the top is a lid that may be swung back out of the way when necessary.
[Illustration: Fig. 685.]
[Illustration: Fig. 686.]
The method of securing the emery-wheels is shown in Fig. 686. Two
flanges Z (made in halves) are let into the wheel, and clamp the wheel
by means of the screws shown. The bore of these flanges Z is larger than
the diameter of pulleys P, so that the emery-wheels may be changed on
the arbor without removing the pulley. Fig. 687 represents an end view
of the bearings B for the roll to revolve in, being provided with three
pieces, the two side ones of which are adjustable by the set-screws, so
as to facilitate setting the roll parallel with the bed of the lathe.
The height is adjusted by means of screws K, K, which may also be used
in grinding a roll of large diameter at the middle of its length, by
occasionally raising the roll as the carriage C proceeds along the roll
(the principle of this action is hereafter explained with reference to
turning tapers on ordinary lathe work). When the wheels have traversed
half the length of the roll, the screws K are operated to lower it
again, it being found that the effect of a slight operating of the
screws K is so small that the workman's judgment may be relied upon to
use them to give to a roll with practical accuracy any required degree
of enlarged diameter at the middle of its length with sufficient
accuracy for all practical purposes.
[Illustration: Fig. 687.]
There are, however, other advantages of this system, which may be noted
as follows. When a single emery-wheel is used there is evidently twice
the amount of wear to take a given amount of metal off (per traverse)
that there is when two wheels are used, and furthermore the reduction of
every wheel diameter per traverse is evidently twice as great with one
wheel as it is with two. From some experiments made by Messrs. Morton
Poole, it was found that using a pair of 10-inch emery-wheels it would
take 40,000 wheel traverses along an average sized calender roll, to
reduce its diameter an inch, hence the amount of error due to the
reduction of the emery-wheel diameters, per traverse, may be stated as
1/40000 of an inch per traverse, for the two wheels.
[Illustration: Fig. 688.]
Now referring to Fig. 688, let R represent a roll and W W the two
emery-wheels.
Suppose the wheels being at the end of a traverse, the roll is 1/40000
inch larger at that end on account of the wear of the emery-wheels, then
each wheel will have worn 1/40000 inch diameter or 1/80000 inch radius,
hence the increase of roll diameter is equal to the wear of wheel
diameter.
[Illustration: Fig. 689.]
Now, suppose that one wheel be used as in Fig. 689, and its reduction of
_diameter_ will be equal to that of the two wheels added together, or
1/20000 inch, this would be 1/40000 in the radius of the wheel,
producing a difference of 1/20000 difference in the diameter of the
wheel.
There is another advantage, however, in that a finer cut can be easier
put on in the Poole system, because if a feed be put on of 1/100th inch,
the roll is only reduced 1/100th inch in diameter, but if the same
amount of feed be put on with a single wheel, it will reduce the roll
1/50th inch, hence for a given amount of feed or movement of emery-wheel
towards the roll axis, the amount of cut taken is only half as much as
it would be if a single wheel is used. This enables a minimum of feed to
be put on the wheel, wear being obviously reduced in proportion as the
feed is lighter and the duty therefore diminished.
The method of driving the roll is as follows: Shaft _t_, Fig. 681, runs
in bearings in the head, and spindle _r r´_ passes through, and is
driven by shaft _t_. A driving pulley is fitted on the spindle at end
_r´_, at the other end is a driving chuck _p_ for driving the roll
through the medium of a _wabbler_, whose construction will be shown
presently. Spindle _r_ may be adjusted endwise in _t_, so that it may be
adjusted to suit different lengths of rolls without moving the bearing
blocks B.
The wabbler is driven by _p_ and receives the end of the roll to be
ground, as shown in Fig. 690, the end of the roll being a taper square
and fitting very loosely in a square taper hole in the end of the
wabbler; similarly _p_ may have a taper square hole loosely fitting the
squared end of the wabbler. The looseness of fit enables the wabbler to
drive the roll without putting any strain on it tending to lift or twist
it in its bearings in block B, and obviates the necessity for the axis
of the rolls to be dead in line with the axis of _r r´_. Various lengths
of wabblers may be used to suit the lengths of roll and avoid moving
blocks B, and it is obvious also that if the ends of the roll are round
instead of square, two set-screws may be used to hold the roll end being
set diametrically opposite, and if set screws are used in _p_ to drive
the wabbler they should be two in number, set diametrically opposite,
and at a right angle to the two in the wabbler, so that it may act as a
universal joint.
[Illustration: Fig. 690.]
The method of automatically traversing the carriage C is as follows:
Referring to Fig. 681, two gears _a_, _b_ are fast upon shaft _t_, gear
_a_ drives _c_ which is on the same shaft as _e_, gear _b_ drives _d_
which drives a gear not seen in the cut, but which we will term _x_, it
being on the same shaft as _c_ and _e_. Now if _e_ is driven through the
medium of _a_ _c_, it runs in one direction, while if it is driven
through the medium of _b_ _d_ _x_, it revolves _e_ in the opposite
direction, and since _e_ drives _g_ and _g_ is on the end of the feed
screw (E, Fig. 682) the direction of motion of carriage C is determined
by which of the wheels _a_ or _b_ drives _e_. At _h_ is a stand
affording journal bearing to a shaft _n_, whose end engages a clutch
upon the shaft of wheels _c_, _x_ and _e_. On the outer end of shaft _n_
is ball lever _l´´_, whose lower end is attached to a rod _k_, upon
which are stops _l l´_ adjustable along rod _k_ by means of set-screws.
At _m_ is a bracket embracing rod _k_.
Now suppose carriage C to traverse to the left, and _m_ will meet _l_
moving rod _k_ to the left, the ball _i_ will move up to a vertical
position and then fall over to the right, causing the clutch to
disengage from gear _c_ and engage with the unseen gear _x_, reversing
the motion of _e_ and of _g_, and therefore of carriage C, which moves
to the right until _m_ meets _l´_ and pushes it to the right, causing
_i_ to move back to the position it occupies in the engraving, the
clutch engaging _c_, which is then the driving wheel for _e_.
SCREW MACHINE.--The screw machine is a special form of lathe in which
the work is cut direct from the bar, without the intervention of forging
operations, and it follows therefore that the bar must be large enough
in diameter to suit the largest diameter of the work, the steps or
sections of smaller diameter being turned down from the full size of the
bar. The advantages of the screw machine are, that the work requires no
centring since it is held in a chuck, that forging operations are
dispensed with, that any number of pieces may be made of uniform
dimensions without any measuring operations save those necessary when
adjusting the tool for the first piece, and that it does not require
skilled labor to operate the machine after the tools are once set.
The capacity of the screw machine is, therefore, many times greater than
that of a lathe, while the diameters and lengths of the various parts of
the work will be more uniform than can be done by caliper measurements,
being in this case varied by the wear of the cutting edges of the tools
only, which eliminates the errors liable to independent caliper
measurement. Hollow work, as nuts and washers, may be equally operated
on being driven by a mandril held in the chuck.
Fig. 691 represents Brown and Sharpe's Number 1 screw machine, which is
designed for the rapid production of small work.
Three separate tool-holding devices may be employed: first, cutting
tools may be placed in the holes shown to pierce (horizontally) the
circular head F; second, tools may be fixed in the tool posts shown in
the double slide rest, which has two slides (one in the front and one at
the back of the line of centres); and third, tools may be placed in what
may be termed the screw-cutting slide-rest J.
F is a head pierced horizontally with seven holes, and is capable of
rotation upon L; when certain mechanism is operated L slides on D and
the mechanism of these three parts is arranged to operate as follows.
The lever arms K traverse L in D. When K is operated from right to left,
L advances towards the live spindle until arrested at some particular
point by a suitable stop motion, this stop motion being capable of
adjustment so as to allow F to approach the live spindle a distance
suitable for the work in hand.
When, however, K is operated from left to right L moves back, and when
it has traversed a certain distance, the head F rotates 1/7 of a
rotation, and becomes again locked so far as rotation is concerned. Now
the relation between the seven holes in F is such that when F has
rotated its 1/7 rotation, one of the seven holes is in line with the
live spindle. Suppose then seven cutting tools to be secured in the
holes in F, then K may be operated from right to left, traversing L and
F forward, and one of the cutting tools will operate upon the work until
L meets the stop; K may then be moved from left to right, L and F will
traverse back, then F will rotate 1/7 rotation and L and F may be
traversed by K, and a second tool will operate upon the work, and so on.
The diameter of the work is determined by the distance of the cutting
edge of the tool from the line of centres, when such tool is in line
with the work, or, in other words, is in position to operate upon the
work. The end measurements of the work are secured by placing the
cutting edges of the tools the requisite distance out from F, when L is
moved forward as far as the stop motion will permit. But it is evident
that the length of cut taken along the work, would under these simple
conditions vary with the distance of the end of the work from the face
of the chuck driving it, but this is obviated as follows:--
The live spindle is made hollow so that the rod of metal, of which the
work is to be made, may pass through that spindle. A chuck on the
spindle holds the work or releases it in the usual manner. Suppose then
the chuck to be open and the bar free to be moved, then there is placed
in the hole in F, that is in line with the work, a stop instead of a
cutting tool. The end of the work may then, for the first piece turned,
be squared up by a tool placed in the slide rest and then released from
the chuck and pushed through the live spindle until it abuts against the
stop so adjusted and affixed in the hole in F; K may then be operated to
act on the work. The first tool may reduce the work to its largest
required diameter, the second turn down a plain shoulder, the third may
be a die cutting a thread a certain distance up the work, the fourth may
be a tool turning a plain part at the beginning of the thread, the fifth
may round off the end of the work, and the sixth may be a drill to
pierce a hole a certain distance up the end of the work.
[Illustration: _VOL. I._ =EXAMPLES OF SCREW MACHINES.= _PLATE X._
Fig. 691.
Fig. 692.]
Now suppose the work to require its edge at the other end to be
chamfered, then there may be placed in the slide rest tool posts a tool
to sever the work from the bar out of which it has been made, while the
other may be used to chamfer the required edge, or to round it if needs
be to any required form.
Work held in the chuck but not formed from a rod may be, of course,
operated upon in a similar manner.
In the case, however, of work of large diameter requiring to be
threaded, the threading tool may be held and operated differently and
more rigidly as follows. I is a lever carrying under its bend and over
the projecting end of the live spindle, a segment of a nut whose thread
must equal in pitch the pitch of thread to be given to the work. A
collar or ring, oftentimes called the leader, having a thread of the
same pitch, is then secured upon the live spindle, so as to rotate with
it, and have no end motion; when therefore I is depressed, the nut will
come into work with the collar or ring, and I will be traversed at a
speed proportioned to the pitch of the threads on the collar and nut.
Now I is attached to a shaft having journal bearing (and capable of end
motion) at the back of the lathe head, and on this bar is attached the
slide rest J, in which the turning or threading tool may be placed. The
shaft above referred to having end motion, may be operated (when the nut
in the lever I is lifted clear of the collar) laterally by means of the
lever I; hence to traverse J to the right, or for the back traverse, I
is raised and pulled to the right, I is then lowered, the nut engages
with the collar, and the tool is traversed to the cut. The cut is
adjusted for diameter by the slide rest, which is provided with an
adjustable stop to determine the depth to which the tool shall enter the
work.
It is obvious that this part of the machine, may be employed for
ordinary turning operations, if the collar be of suitable pitch for the
feed.
[Illustration: Fig. 693.]
Figs. 692 and 693 represent A screw machine for general work.
A is a chuck with hardened steel [V]-shaped jaws. It is fast on the
hollow arbor of the machine. B is a steadying chuck on the rear end of
the arbor. The arbor has a two and one-sixteenth hole through it and its
journals are very large and stiff. It is of steel, and runs in gun-metal
boxes. The cone pulley and back gear is of the full proportion and power
of an eighteen-inch lathe. C is an ordinary lathe carriage fitted to
slide on the bed, and be operated by hand-wheel D and a rack pinion as
usual. Across this carriage slides a tool rest E operated by screw as
usual, and having two tool posts, one to the front and one to the rear
of the work. This tool rest, instead of sliding directly in the carriage
as is the case with lathes, slides on an intermediate slide which fits
and slides in the carriage. This intermediate slide is moved in and out,
a short distance only, by means of cam lever G. An apron on the front
end of this slide carries the lead screw nut H. When the cam lever is
raised it brings the slide outward about half an inch, and the tool rest
E comes out with it and at the same time the nut leaves the lead screw.
The inward movement of the slide is always to the same point, thus
engaging the lead screw and resetting the tool. In cutting threads with
a tool in the front tool post the tool is set by moving the tool rest as
usual, and at the end of the cut the cam lever serves to quickly
withdraw the tool and lead screw nut so that the carriage can be run
back. The tool rest is then advanced slightly and the new cut taken. By
this means threads are cut without any false motions, and the threads
may be cut close up to a shoulder.
I is the lead screw. This screw does not extend, as is usual, to the
head of the machine. It is short and is socketed into a shaft which runs
to the head of the machine and is driven by gearing as usual. The lead
screw is thus a plain shaft with a short, removable, threaded end. The
gearing is never changed. Different lead screws are used for different
threads, thus permitting threads to be cut without running back. The
lead screws are changed in an instant by removing knob J. The lead screw
nut H is a sectional nut, double ended, so that each nut will do for two
pitches, by turning end for end in the apron. L is an adjustable stop
which determines the position of the carriage in cutting off, facing,
&c. K is an arm pivoted to the rear of the carriage and carrying three
open dies like a bolt cutter head. At M is a block sliding or capable of
being fed along the bed. N is a gauge screw attached to this block and
provided with two nuts. The stop lever shown in the cut turns up to
straddle this screw, and the position of the nuts determines how far
each way the block may slide. O is the turret fitted to turn on the
block. It has six holes in its rim to receive sundry tools. It can be
turned to bring any of these tools into action, and is secured by the
lock lever P.
[Illustration: Fig. 694.]
The turret slide is moved quickly by hand, by means of the capstan
levers U, which, by an in-and-out motion, also serve to lock the turret
at any point. The turret slide is fed, in heavy work, by the crank-wheel
R on its tail screw. This tail screw carries, inside the crank-wheel,
two gears S, which are driven at different speeds by a back shaft behind
the machine. These two gears are loose on the tail screw, and a clutch
operated by lever T locks either one to the screw. Both the carriage and
turret are provided with oil pots not shown in the cuts.
[Illustration: Fig. 695.]
A top view of the turret is shown in Fig. 694, a set of tools being
shown in place.
The end gauge which is shown removed from the chuck in Fig. 695, is
composed of a hollow shank A fitting the hole in the turret, and a gauge
rod B fitting the bore of the shank. The shank A may be set farther in
or out of the turret, and the rod B may be set farther in or out of the
shank, the two combined being so set that when the turret is clear back
against its stop the end of the rod B will gauge the proper distance
that the bar iron requires to project outwards from the chuck of the
machine. The centre shown in Fig. 696 corresponds to an ordinary lathe
centre, and is only used when chasing long work in steel.
[Illustration: Fig. 696.]
The turner shown removed from the chuck in Fig. 697, consists of a
hollow shank A, fitting the turret and having at its front end a
hardened bushing B secured to A by a set screw. It has also a heavy
mortised bolt C in the front lug of the shank; an end-cutting tool D
shaped like a carpenter's mortising chisel, and clamped by the mortised
bolt; a collar screw E to hold the tool endwise; and a pair of
set-screws F to swivel the tool and its bolt. Bushing B is to suit the
work in hand. The tool D is a piece of square steel hardened throughout.
It is held by its bolt with just the proper clearance on its face. It
cuts with its end without any springing, and will on this account stand
a very keen angle of cutting edge. There is hardly any limit to its
cutting power. It will cut an inch bar away at one trip with a coarse
feed. It does not do smooth work, and is, therefore, used only to remove
the bulk of the metal, leaving the sizer to follow.
[Illustration: Fig. 697.]
[Illustration: Fig. 698.]
The sizer Fig. 698, consists of a hollow shank A fitting the turret and
carrying in its front end a hardened bushing B and a flat cutting tool
C. The sizer follows the turner and takes a light finishing cut with oil
or water, giving size and finish with a coarse feed, and having only a
light and clean duty it maintains its size.
[Illustration: Fig. 699.]
The die holder shown in Figs. 699 and 700, is arranged to automatically
stop cutting when the thread is cut far enough along the work. It will
cut a full thread cleanly up against a solid shoulder. It consists of a
hollow shank A fitting the turret; a sleeve B fitted to revolve and
slide on the front end of the shank C; a groove E bored inside the
sleeve; a pin D on the shank fitting freely in the groove E; a keyway F
at one point in the groove and leading out each way from it; and a
thread die G held in the front end of the sleeve. When the turret is
run forward, the thread die takes hold of the bolt to be cut, but it
revolves idly instead of standing still to cut, until the pin D comes
opposite the keyway F when, the turret still being moved forward, the
pin enters the back of the keyway. The sleeve now stands still, the die
cuts the thread and pulls the turret along by the friction of the pin in
the keyway. Finally the turret comes against its front stop and can move
forward no farther. Consequently the sleeve is drawn forward on its
shank C, and the instant the pin D reaches the groove E the die and
sleeve commence to revolve with the work and cease cutting. The machine
is then run backward, and the turret moved back a trifle. This causes
the pin to catch in the front end of the keyway and the sleeve is again
locked. The die then unscrews, and, in doing so, pushes the turret back.
A tap holder may be inserted in place of the die, and plug taps may be
run to an exact depth without danger.
[Illustration: Fig. 700.]
[Illustration: Fig. 701.]
Drills and other boring tools are held in suitable sockets, which fit
into the turret.
[Illustration: Fig. 702.]
The following are the operations necessary to produce in this machine an
hexagon-headed bolt.
First operation: The bar is inserted through the open chuck.
Second operation: Turret being clear back against its stop and revolved
to bring present the end gauge, the bar is set against the end gauge,
and the chuck is tightened. This chucks the bar and leaves the proper
length projecting from the chuck.
Third operation: Front tool in the carriage, a bevelled side tool cones
the end of the bar so turret tools will start nicely.
Fourth operation: Turret being revolved to present the turner, the bar
is reduced, at one heavy cut, to near the proper size, the turret stop
determining the length of the reduced portion.
Fifth operation: Turret being revolved to present the sizer, the body of
the bolt is brought to exact size by a light, quick, sliding cut.
Sixth operation: Open die arm being brought down, the bolt is threaded;
the left carriage stop indicating the length of the threaded part.
Seventh operation: Turret being revolved to present the die holder, the
solid die is run over the bolt, bringing it to exact size with a light
cut, and cutting _full thread to the exact point desired_.
Eighth operation: Front tool in the carriage chamfers off the end
thread.
Ninth operation: Back tool of carriage, a parting tool, cuts off the
bolt; the left carriage stop determining the proper length of head.
Tenth operation: Bolt being reversed in chuck, the top of the head is
water cut finished by a front tool in the carriage. This operation is
deferred till all the bolts of the lot are ready for it.
Fig. 703 represents a general view of a screw machine designed by Jerome
B. Secor, of Bridgeport, Connecticut. The details of the machine are
shown in Figs. 704, 705, 706, 707, 708, 709, 710, and 711.[13] The live
spindle is of steel and is hollow, and its journals are ground. The
boxes are lined with babbitt, so that no other metal touches the
spindle, and may, by a special device, be re-babbitted and bored exactly
parallel with the planing of the bed.
[13] From _Mechanics_.
A steel collar J, Fig. 704, between the front end of the forward box and
the spindles, receives the thrust due to the cut, and a nut on the
spindle acts against the cone to adjust it forward on a feather K in the
spindle to take up end wear. The wire or rod from which the work is to
be made is passed through the spindle and collar on the stand, and is
held by a thumb-screw in the collar, which is influenced by the weight
and cords, so that when the wire is released in the chuck the weight
pulls the collar and wire forward, forcing the wire out through the
front end of the chuck until it comes against the stop in the turret,
which gauges the length needed to make the piece required. From time to
time, as the rod is used up, the thumb-screw in the sliding collar is
loosened, and the collar is shoved back on the rod as far as it will go,
and the set-screw is again tightened.
[Illustration: Fig. 703.]
[Illustration: Fig. 704.]
Fig. 704 shows in section the front bearing and the automatic chuck. M
is a hollow spindle within which is the hollow spindle H, through which
the rod or wire to make the work passes. It is prevented from end motion
by the cone hub on one side and the collar J on the other side of the
bearing, while H may be operated endwise within M by means of the
hand-lever shown on the left-hand of the headstock in the general view.
The core A of the chuck screws upon M, and is threaded to receive the
adjustment nut B, which receives and holds the adjustment wedges C at
their ends by the talon shown. The shell D is secured to H by the screws
I, which pass through slots in A, and therefore move endwise when H is
operated by its hand-lever. Now the mouth of D, against which the
adjustment wedges C rest, is coned 2-1/2°, as marked; hence the end
motion of D to the left causes C, and therefore F, to approach the axis
of the chuck and grip the rod or wire, while its motion to the right
causes C, and therefore F, to recede from the chuck axis and to release
the wire. Since B is screwed upon A, and C is guided at the end by B,
and since also F is detained endwise in A, the motions of C and of F are
at a right angle to the chuck axis. Hence in gripping the rod or wire
there is no tendency to move it endways, as there is where the gripping
jaws have, as in many machines, a certain amount of end motion while
closing. When this end motion exists, tightening the jaws upon the work
draws it away from the stop in the turret and impairs the adjustment for
length of work. The gripping jaws are closely guided in slots in D and
in A, and three sets of these jaws are necessary to cover a range of
work from the full diameter of the bore of H down to zero. The capacity
of each of these sets of jaws, however, may be varied as follows: The
adjustment ring B is threaded upon A, and may be operated along A to
move C endwise by means of the tangent screw E, whose threads engage
with teeth parallel to the axis of B, and running across its width all
around its circumference, hence rotating E, rotates B, causing it to
move along A, and carry C beneath F. By this method of adjustment F need
be given only enough motion to and from the chuck axis to grip and
release the work, and the reduction of motion between the hand-lever
operating H and the motion of F is so great, that with a very moderate
force at the lever the wire may be held so that its projecting end may
be twisted off without slipping the wire within the jaws or impairing
the jaw grip.
[Illustration: Fig. 705.]
Fig. 705 is a sectional and end view of the core A of the chuck, and
Fig. 706 a sectional and end view of the shell D.
[Illustration: Fig. 706.]
Fig. 707 represents a sectional side view and an end view of the cross
slide, or cutting-off slide, which carries two tool posts, and therefore
two cutting tools, one of which is at the back of the rest. In place of
a feed screw and nut, or of a hand lever and link, it is provided with a
segment of a gear-wheel P operating in a rack R, which avoids the
tendency to twist the cross slides in its guides which exists when a
hand lever and link is used.
[Illustration: Fig. 707.]
The cross slide is adjusted to fit in its guideway by a jaw S^{1}, Fig.
707, which is firmly screwed to and recessed into R. To take up the
wear, the face of S^{1} is simply reduced. This possesses a valuable
advantage, because it is rigid and solid, does not admit of improper
adjustment, nor can the adjustment become impaired at the hands of the
operator.
To adjust the position of the cross slide upon the shears a screw passes
between the shears and is threaded into the stud Q. This screw is
operated by a hand wheel shown in the general view, Fig. 703, beneath
the rear bearing of the headstock.
A special and excellent feature of the machine is the stop device for
the motion of the cross slide which is shown in Fig. 707.
The screw S has one collar C, solid on it, and the screwed end is tapped
into the sliding sleeve T, which is held from turning by the stud A.
Between the solid collar C and the loose collar B there is a short,
stiff spiral spring, as shown; by means of the fast and loose collars,
the spring and the screwed thimble D, a strong friction is had on the
collar B, which is ample to keep the screw from turning while in use as
a stop, although it permits the screw to turn easily enough when a
wrench is applied to the square end. Precisely the same device is used
at the other end of the slide to stop it in the opposite direction.
[Illustration: Fig. 708.]
Details of the mechanism of the turret and turret slide are shown in
Figs. 708, 709, and 710. Fig. 708 is an end sectional view of the turret
slide, which is traversed on its base by a segment D of a gear operating
in a rack R (in the same manner as the cutting-off slide), the segment
being connected by stud N to handle M. O represents the body of the
slide, which is grooved at the sides to receive the gibs X, which secure
it to the base P on which it slides. P is clamped to its adjusted
position on the shears or bed by means of the gib, shown in dotted
lines, which is pulled laterally forward by the screw S, which is tapped
into the stem of the gib. The method of rotating the slide and of
locking it in position is shown in Fig. 709, which is a top view of the
turret head, and Fig. 710, which shows O removed from P and turned
upside down. Pivoted to segment D is a rod E having at K a pin that as
motion proceeds falls into S and rotates T, which is fast to the bottom
of the turret. Upon the handle M being moved backward the segment begins
its motion forward, as indicated by the arrow in Fig. 710, thereby
moving the slide backward upon the gibs by the working of its cogs into
the rack R, Fig. 708, which is attached to the base P. When the segment
D has accomplished about one-half its motion the pin H, which is on the
upper side of the segment D, comes in contact with the projection or lug
on the side of the cam F, as shown by the arrow head in Fig. 710,
bringing the opposite side of the cam against the pin G, Fig. 709,
thereby moving it backward, compressing the spring U, and drawing the
bolt L from its seat in the disc V. This operation is completed before
the motion of the segment brings the pin K in contact with the
ratchet-wheel T. The segment D in continuing its motion after the pin K
is brought into the notch S, begins the revolution of the turret on its
axis. As will be seen by the inspection of Fig. 710, the pin H works
upon a much longer radius than the projection upon the cam with which it
comes in contact, and therefore, after a given part of its motion is
complete, gets beyond the reach of the cam, thereby releasing its hold
and allowing the bolt L, Fig. 709, to be forced against the disc V by
the expansion of the spring U, which occurs soon after the turret has
commenced its revolution by the contact of pin K with the wheel T. The
completion of the movement of the handle M (and the segment D) completes
the revolution of the turret one-sixth of its circumference, thereby
allowing the bolt L, by the further expansion of the spring U, to be
forced into its next opening or seat in the disc V. The forward motion
of the handle M brings the turret forward to its position at the work
and restores the parts to their former positions, as shown in the
illustrations.
[Illustration: Fig. 709.]
[Illustration: Fig. 710.]
The stop motion for the forward motion of M, and that therefore
determines the length of turret traverse forward, and hence the distance
each tool shall carry its cut along the work, is shown in Fig. 711. The
end of the screw A abuts against the stop B in the usual manner; it is,
however, threaded through the eye of a bolt C, as well as through the
end of the turret slide, so that it may be locked by simply operating
the nut D. Thus the use of a wrench is obviated, and the adjustment is
more readily effected.
[Illustration: Fig. 711.]
Figs. 712 and 713 represent a screw machine by the Pratt and Whitney
Company, of Hartford, Connecticut, and having Parkhurst's patent wire or
rod feed for moving the work through the hollow spindle and into
position to be operated upon by the tools. The reference letters
correspond in both figures.
At A is the front and at B the back bearing, affording journal bearing
to a hollow spindle C, which carries the shell D of the work-gripping
chuck, the clutch ring H and a collar I, in which is pivoted, at J, the
clutch levers G. This collar is threaded upon C and is locked in
position by a ring lock nut J´. The clutch arm K slides upon a rod X,
and has a feather projecting into a spline in X. The core E of the
work-gripping chuck is fast upon the inner spindle F, which revolves
with the outer one C. The left-hand end of F abuts against the short
arms of the clutch levers G, and it is obvious that when K is operated
back and forth upon X, it moves the clutch H endways upon C, and the
cone upon H operates the levers G, causing them to move the inner
spindle F endways and the inner cone E of the chuck to open or close.
Suppose, for example, that K (and hence H) is moved to the right, and
the long ends of G will be released and may close moving their short
ends away from the end of F, and therefore releasing E from its grip
upon the work. In moving K to the right the sleeve L is also moved to
the right, and its serrations at L´ being engaged with the tongue P, the
sleeve M is pulled forward. Now the bar or rod of which the work is made
is held at one end by the chuck, it is supported by the bushing Z in the
end of spindle C, and in the bushing S in the arm of sleeve M, while it
has fast upon it a collar T. When therefore M is pulled forward or to
the right, its arm meets T and pulls the rod or bar for the work through
the chuck E.
[Illustration: Fig. 712.]
[Illustration: Fig. 713.]
On the other hand when K and therefore H, L, and M, are moved to the
left, levers G are opened at their long ends by the cone of H. The short
ends of G push the inner spindle F to the right, E passes through D, and
being split, closes upon the work and grips it, the parts occupying the
positions shown in the figure. The same motion of K passes L through the
sleeve M (the teeth at N raise the catch P, allowing L´ to pass through
M) so that at the next movement of K to the right, M will be pulled a
second step forward, again passing the work through the chuck. Q is
merely a pin wherewith to lift P and enable M to be moved back, when
putting in a new rod for the work; K is operated by a link from U to V,
the handle for moving this link being shown at W in the general view.
To prevent the sleeve M from moving back with L it is provided with a
shoe O, pressed by the spring R against X, thus producing a friction
between M and X that holds M while L slides through it. R´ is to
regulate the tension of the spring at R. _y_ is merely a sleeve to
protect the clutch mechanism from dust, &c.
Box tools for screw machines are used for a great variety of special
work. They are simply boxes or heads carrying tools and a work-steadying
rest.
Fig. 714 represents a box tool for a screw machine. The cylindrical stem
fits into the turret holes and contains a steadying piece or rest G to
support the work and keep it to its cut. In the box tool shown in the
figure, there are four cutting tools set in to the depth of cut by the
screws A, B, C, and D respectively, and a fifth for rounding off the end
of the work is shown at E.
[Illustration: Fig. 714.]
Fig. 715 represents a top view, Fig. 715_a_ a front view, and Fig.
715_b_ an end view, of a box tool for shaping the handles for the wheels
of the feeding mechanism of machines. The work is first turned true and
to its required diameter, and the rest is set to just bear against the
work to steady it and hold it against the pressure of the cut. The
cutter is cylindrical with a gap cut in it at G, so as to give a cutting
edge. By grinding the face of this gap the tool is sharpened without
altering its shape, as is explained with reference to circular or disc
tools for lathe work. The cutter is provided with a stem by which it is
held in the slide, through the medium of the clamp. The slide is
operated by an eccentric on the spindle or rod R, which is operated by
the handle H. The stop obviously arrests the motion of the slide when it
meets the box B, and this determines the diameter of the work, which is
represented by W in the end view figure.
[Illustration: Fig. 715.]
[Illustration: Fig. 715_a_.]
[Illustration: Fig. 715_b_.]
Fig. 716 represents the die holder and die for the Pratt and Whitney
Co.'s screw machine. The die is cut through on four sides, and is
enveloped by a split ring having a screw through its two lugs, so that
by operating the screw the die may be closed to take up the wear and
adjust it for diameter. It is secured in a collar by the set-screw
shown, and this collar is clutch shaped on its back face, engaging a
similar clutch face on the shoulder of the arbor, the object of this
arrangement being as follows. Suppose it is required to cut a thread a
certain distance, as say, 3/4 inch, along a stud, and that the depth of
the clutch is 1/4 inch. Suppose that when the turret is fed forward
sufficiently the thread is cut half an inch along the work at the moment
that the turret meets its stop and comes to rest, then the die will
continue to feed forward one-quarter of an inch, moving along the body
or stem of the holder until its clutch face disengages, when the die
will revolve with the work.
[Illustration: Fig. 716.]
[Illustration: Fig. 717.]
Fig. 717 represents a cutting-off tool and holder for a screw machine.
The tool fits into a dovetail groove in the split end of the holder, and
is ground taper in thickness to give the necessary clearance on the
sides. It is held by the screw shown, which closes the split and grips
the dovetail; obviously the top face only is ground to resharpen it.
[Illustration: Fig. 718.]
Fig. 718 represents a special lathe for wood work designed and
constructed by Charles W. Wilder, of Fitchburg, Massachusetts. It is
intended to produce small articles in large quantities, cutting them to
duplicate form and size without any further measurements than those
necessary to set the tools in their proper respective positions. It is
employed mainly for such work as druggists' boxes, tool handles,
straight spokes for toy vehicles, piano pins, balls, rings, and similar
work.
Its movements are such that the tools are guided by stops determining
the length and the diameter of the work so as to make it exactly
uniform, while the form of the cutting tools determines the form of the
work, which must therefore be uniform.
The lathe may be described as one having a carriage rest spanning the
bed of the lathe, which rest holds the work axially true with the lathe
centres without the aid of the dead centre, while it at the same time
trues the end of the work and leaves it free to be operated upon by
other tools, which, after once being set and adjusted, shape any number
of pieces of work to exact and uniform diameter and shape.
[Illustration: Fig. 719.]
The manner in which this is accomplished is as follows: Fig. 718 is a
general external view of the lathe; Fig. 719 is an end elevation view of
the rest from the cone spindle end, and Fig. 720 is an end view of the
rest viewed from the tailstock end of the lathe. A is a ring fastened in
the rest R by the set-screw B. The mouth C of the ring which first meets
the work is coned, or beveled, as shown, and an opening on one side of
the ring admits a cutting tool T. Now the work is placed one end in the
cone driving chuck on the lathe spindle, and the other end in the cone
or mouth C, Fig. 719, being kept up to the driving chuck by the end
pressure of C. As the work rotates, the tool T cuts it to the diameter D
of the ring bore, the carriage or rest R traversing along the lathe bed
as fast as tool cuts; hence the bore D serves as a guide to hold the
work and make it run true, this bore being axially true with the lathe
centres. The cone surface of C thus operates the same as the sole of an
ordinary carpenter's plane, the tool T cutting more or less rapidly
according as its cutting edge is set to project more or less in advance
of the surface of the cone or recess C. This admits of the tool cutting
at a rate of feed that may best suit the diameter of the work and the
nature of the wood. The tool T, is operated laterally to increase or
diminish the rate of feed by the screw E, which also serves as a pivot,
so that by operating the thumb-screw F, the tool point may be adjusted
for distance from the centre of the bore D, or in other words the
diameter to which the tool T will turn the work is adjusted by the
thumb-screw F. G is the head of the pivot screw that the swing tool
holder H works upon, and this swing motion carries the forming tool or
cutter X, which shapes the work to the required form. I is a shaft upon
which a lever, carrying the tool holder J, works, the latter carrying
the severing tool K, which severs the finished work from the stick of
wood from which the work is made.
The tool holders H and J are connected by means of the arms L and M to
the stud O, fast in wheel P, operated by a knee lever Q, which is
pivoted at S to _u_, which is fast to one of the gibs that hold the
carriage to the lathe [V]s. The knee lever Q is connected to the wheel P
by a raw-hide strap, or belt V, so that the operator, by pressing his
knee upon the end of the lever Q, causes the wheel P, to partly rotate,
carrying O with it (O being fast in P), and gives a forward radial
motion to tool holder H and cutter X, causing the latter to enter the
work until such time as the stud O and the screw stud W are in line,
horizontally with the centre of the wheel P, after which tool holder H
will move back, while the severing tool K (which has a continuous upward
or vertical movement) is cutting off the finished work, which has been
formed to shape, and reduced to the required diameter by the forward
movement of the tool or cutter X. The object of the backward or retiring
motion of H is to relieve the shaping tool X from contact with the work,
while K cuts it off, or otherwise the work might meet X when cut off,
and receive damage from contact with it. The stud W, connecting tool
holder H with the wheel P, is threaded with a right and left-hand screw,
by operating which the tool X may be operated to reduce the work to any
required diameter.
The rest or carriage R traverses along the lathe shears or bed Z,
carrying with it all the levers and tools, so far described.
[Illustration: Fig. 720.]
The tailstock, or back head, carries a tool holder in the rear of the
spindle, in which fits also a drill bit or other cutting tool. The
method of traversing and operating the carriage R and the back head is
as follows:
At the back of the bed or shears is a table, shown at T, in Fig. 718.
Upon this table is a stand to which is pivoted the end of a lever, as is
shown at 1 in figure. This lever has a joint at 2, and is connected to
the tailstock spindle at a joint marked 3. It is obvious that by
operating the lever laterally, joint 2 will double, and the tail spindle
will be moved along the bed. If the tail spindle is not locked it will
simply feed through the tailstock and the tool in the spindle will
operate, but if it is locked (by the ordinary screw shown), then the
handle will slide the whole tailstock and the tool in the holder at the
back of the tail spindle may operate.
[Illustration: Fig. 721.]
At 4 is an adjusting screw, which, by coming into contact with the
carriage R causes it also to traverse, which it will do until it meets
against a screw on the other side, marked 5, in Fig. 718, which,
standing farther out than the chuck prevents the cutting tool from
meeting the chuck.
The movement of the carriage continues until the stop-gauge 6 meets the
end of the work, hence the length of the work is from the cutting-off
tool to the face of stop 6. The adjustment for the length of the work is
made by means of screw 4, which will slide the carriage R, as soon as it
meets it, independent of what distance the stop 6 may be from the work
end. The tailstock carries two tool holders, similar to those on an
ordinary lathe. When the cutting tools are used to cut completely over
the end of the work, as in ball turning or a round ended handle, the
stop 6 is not used, the tool which rounds the end acting as a stop of
itself.
When bits are used they are held in the tail spindle and are made of a
proper length to give the required depth of hole, or sometimes the face
of the bit-holder may be used as a stop.
When the tools, cutters, and belts are all properly adjusted in position
to cut to the required respective diameters or lengths the operator has
simply to place a stick of wood in the lathe and operate the respective
handles or levers in their proper consecutive order, and the work will
be finished and cut off, the operation being repeated until the stick is
used up, when a new one may be inserted, and so on.
LATHES FOR IRREGULAR FORMS.--In lathes for irregular forms (which are
chiefly applied to wood and very rarely to metal turning), the work is
performed by rotary cutting tools carried in a rapidly rotating head.
The work itself is rotated slowly, and the carriage or frame carrying
the cutting tools is caused to follow the outline of the pattern or
_former_ at every point in its circumference as well as in its length.
The principle of action by means of which these ends are attained is
represented in Fig. 721, in which S represents a slide which carries the
sliding head, affording journal bearing to the rotating head H, driven
by the belt E, and carrying the cutters, and also the wheel W. F
represents the pattern or former, and B a piece of wood requiring to be
turned to the same form as that of F. Suppose then that F be slowly
rotated by A and C, receiving rotary motion from A (through the medium
of D), then the rotations of C will equal those of F, because the
diameter of A is equal to that of C. The diameter of the circle
described by the cutters at H is also equal to the diameter of W, hence
the motion of the extremities of the cutters is precisely the same as
that of the circumference of W, and as W receives its motion from F it
is obvious that the cutters will reduce G to the same form and size as
F, and if the head be traversed in the same direction as the axis of F,
then the diameter and form of B will be made to correspond to that of F
at every corresponding point throughout its length. Contact between W
and F is maintained by means of a weight or spring, the rotation of F
being sufficiently slow to insure its being continuous, while the
necessary rapidity of cutting speed for the tools is attained by
rotating H at the required speed of rotation.
This class of lathe is termed the "Blanchard" lathe from the name of the
inventor, or "Lathe for irregular forms," from the chief characteristic
of the work, but is sometimes designated from the special article it is
intended to turn, as "The Shoe-last lathe," "Axe-handle lathe," "Spoke
lathe," &c., &c.
[Illustration: Fig. 722.]
Let Fig. 722 represent a lathe of this kind provided with a frame A
affording journal bearing to the shaft of the drum B, which is driven by
the pulleys C. Let E represent a pulley receiving motion from B by the
belt D. The cutting tools are carried by the head F which is rotated by
pulley E. Let the carriage or frame carrying the shaft of E carry a dull
pointed tracer, with continuous contact with the _former_ H by means of
a weight or spring, the carriage being so connected to the way N on
which it traverses that it is capable of rocking motion, and if H be
rotated the carriage will, by reason of the tracing point, have a motion
(at a right angle to the axis of H) that will be governed by the shape
of H; hence since G rotates equally with H, the form of the blank work G
will be similar to that of H, but modified by reason of the tracing
point being at a greater distance than F from the centre of rocking
motion.
All that is necessary to render this motion positive throughout the
lengths of G and H is to connect them together by gears of equal
diameter, and traverse the carriage along N for the full length of the
pieces. But the effect will be precisely the same if the frame carrying
G and H be pivoted below, capable of a rocking motion, and H be kept
against the tracing point by means of a spring or weight, in which case
the carriage may travel in a straight line upon N and without any
rocking motion. This would permit of the carriage operating in a slide
way on N enabling it to traverse more steadily.
To maintain continuous contact between the tracing point and the
_former_ H, the rotations of H are slow, the necessary rapidity of tool
cutting action being obtained by means of the rapid rotation of the head
and cutters F.
Since motion from the line shaft to the machine is communicated at C it
is obvious that the gears or devices for giving motion to H and G may be
conveniently derived from the shaft carrying C and B, for which purpose
it extends beyond the frame at one end as shown. Lathes of this kind are
made in various forms, but the principles of action in all are based
upon the principles above described.
[Illustration: Fig. 723.]
BACK KNIFE GAUGE LATHE.--This lathe, Fig. 723, has a carriage similar to
that described with reference to Fig. 718, and carries similar tools
upon the tailstock. It is further provided, however, with a self-acting
feed traverse to the carriage, and by means of a rope and a weight, with
a rapid carriage feed back or from left to right on the bed, and also
with a knife at the back. This knife stands, as seen in the engraving,
at an angle, and is carried (by means of an arm at each end) on a
pivoted shaft that can be revolved by the vertical handle shown. The
purpose of this knife is first to shape the work and then to steady and
polish the wood or work. Obviously when the knife is brought over upon
the work its cutting edge meets it at an angle and cuts it to size and
to shape; the surface behind the cutting edge having no clearance rubs
against the work, thus steadying it while polishing it at the same time.
These lathes are used for turning the parts of chairs, balusters, and
other parts of household furniture, the beads or other curves or members
being produced on the work by suitably shaped knives, which obviously
cut the work to equal shape and length as well as diameter, and it is
from this qualification that the term "gauge" is applied to it.
Fig. 724 represents the Niles Tool Works special pulley turning lathe,
in which motion from the cone spindle to the live spindle is conveyed by
means of a worm on the cone spindle and a worm-wheel on the live
spindle. Two compound slide rests are provided, the tool on the rear one
being turned upside down as shown. These rests may be operated singly or
simultaneously, and by hand or by a self-acting motion provided as
follows:--A screw running parallel to the cone spindle is driven by
suitable gearing from the cone spindle. At each end of this screw it
gears into a worm-wheel having journal bearing on the end of the slide
rest feed screw as shown. By a small hand wheel on the end of the slide
rest feed screw the worm-wheel may be caused to impart motion to the
feed screw by friction causing the slide rest to feed. But releasing
this hand wheel or circular nut releases its grip upon the feed screw,
and permits of its being operated by the handle provided at the other
end. The rail carrying the slide rest is adjustable in and out to suit
varying diameters of pulleys, being secured in its adjusted position by
the bolts shown.
The cut is put on by means of the upper part of the compound rest. To
turn a crowning pulley the rails carrying the slide rests are set at an
angle, the graduations shown on the edge of the ways to which they are
bolted being to determine the degree of angle. When the pulley surface
of the pulley is to be "straight" both tools may commence to operate on
one edge of the pulley surface, the advance tool taking a roughing and
the follower tool a finishing cut; but for crowning pulleys the tools
may start from opposite edges of the pulley, the cuts meeting at the
middle of the face; hence the angles at which the respective rails are
set will be in opposite directions.
The pulleys to be turned are placed upon mandrels and driven by two arms
engaging opposite arms of the pulley. To drive both arms with an equal
pressure, as is necessary to produce work cylindrically true, an
equalizing driver on Clements' principle (which is explained in Fig.
756, and its accompanying remarks) is employed.
For driving the pulleys to polish them after they are turned the cone
spindle is hollow at the rear end and receives a mandrel. The high speed
at which the cone spindle runs renders this possible, which would not be
the case if wheels and pinions, instead of worm-gear, were employed to
communicate motion from the cone to the live spindle. A wheel shown in
position for polishing is exhibited in the cut, the pivoted arm in front
affording a rest for the polishing stick or lever.
BORING AND TURNING MILLS.--The boring and turning mill patented in
England by Bodmer in 1839, has developed into its present improved form
in the United States, being but little known in other countries. It
possesses great advantages over the lathe for some kinds of turning and
boring, as wheels, pulleys, &c.
The principal advantages of its form of construction are:--
[Illustration: Fig. 724.]
[Illustration: Fig. 725.]
1st. That its work table is supported by the bed at its perimeter as
well as at its centre, whereas in a lathe the weight of the chuck plate
as well as that of the work overhangs a journal of comparatively small
diameter, and is therefore more subject to spring or deflection and
vibration.
2nd. It will carry two slide rests more readily adjustable to an angle,
and more readily operated simultaneously, than a lathe slide rest.
3rd. It is much more easy to chuck work on a boring mill table than on a
lathe, because on the former the work is more readily placed upon the
table, and rests upon the table, so that in wedging up or setting any
part of the circumference of the work to the work table, there is no
liability to move the work beneath the other holding plates; whereas in
a lathe the work standing vertical is apt when moving or setting one
part to become unset at other points, and furthermore requires to be
held and steadied while first being gripped by the chucking dogs,
plates, or other holding devices.
Figs. 725, 726, 727, 728, and 729 represent the design of the Niles Tool
Works (of Hamilton, Ohio), boring and turning mill. In this design
provision is made to raise the table so that it takes its bearing at the
centre spindle only when used upon small work where a quick speed of
rotation is necessary, or it may be lowered so as to take its
circumferential bearing for large heavy work where slower speeds and
greater pressure are to be sustained.
The bearing surfaces are, in either case, protected from dust, &c., and
provided with ample means of lubrication. Each tool bar is so balanced
that the strain due to the balancing weights is in a line parallel to
the bar axis in whatever position and at whatever angle to the work
table the bar may be set. This prevents the friction that is induced
between the bar and its bearings when the balancing strain is at an
angle to the bar axis, and consequently pulls the bar to one side of or
in a line to twist the bar. The bar is therefore more easily operated,
and the feed gear is therefore correspondingly relieved of strain and
wear.
The general construction of the machine is shown in Fig. 725. It
consists of a base or bed, affording journal bearing and support to a
horizontal work table, rotated by devices carried upon the bed. To each
side of the bed are attached uprights or standards, forming a rigid
support to a cross slide or rail for the two sliding heads carrying the
tool bars.
The various motions of the machine are as follows: There are 16 speeds
of work table, 8 with the single, and the same with the back gear. The
cross slide is capable of being raised or lowered, to suit the height of
the work, by an automatic motion. Both tool rests are capable of hand or
automatic feed motion at various rates of speed, in a line parallel to
the surface of the work table. Both are also capable of automatic or
hand feed motion, either vertically or at any required angle to the work
table, and have a quick return motion for raising them, while each may
be firmly locked while taking radial or surfacing cuts, thus preventing
spring or vibration to the tool bar. In addition to this, however, there
is provided, when required, a tailstock, carrying a dead centre after
the manner of a lathe, so that the work may be steadied from above as
well as by the work table. In Figs. 726 and 727 are shown the devices
for raising the work table and those for actuating the feed screws and
the feed rod; thus operating the sliding heads horizontally and the tool
bars vertically. A is the base or bed supporting the work carrying table
B´, and affording its spindle journal bearing at D´. A step within and
at the foot of D´ rests upon the wedge F´ so that when the wedge is
caused to pass within D´ it lifts the step, which in turn lifts the
table spindle, and hence the table, sufficiently to relieve its contact
with the outer diameter of the bed. F´ is operated as follows: The lever
G´ is pivoted at E´ and carries at its upper end a nut H´, operated by a
screw on the end of the bolt I´; hence rotating I´, operates wedge F´.
For operating the automatic feed motions, _f_ is a disc upon a shaft
that is rotated by suitable gears beneath the work table; _g_ is a disc
composed of two plates, having a leather disc between them, the
perimeter of the disc having sufficient frictional contact with _f_ to
cause _g_ to rotate when _f_ does so: _g_ drives the vertical spindle
_i_, which has a worm at J´ driving a worm-wheel which rotates the gears
upon the feed spindles V, F, W, in the figures; _f_ rotates in a
continuous direction, but the spindle _i_ is caused to rotate in either
direction, according to whether it has contact with the top or bottom of
the face of _f_, it being obvious that the motion of _f_ above its
centre is in the opposite direction to that below its centre of
rotation. The means of raising and lowering _g_ to effect this reversal
of rotative direction is as follows: It is carried on a sleeve _g´_
which is provided with a rack operated by a pinion that is rotated by
means of hand wheel _h_; hence, operating _h_ raises or lowers _g´_, and
therefore _g_; _h´_ is a hand wheel for locking the pinion, and hence
detaining the rack (and therefore _g_) in its adjusted position. This
design is an excellent example of advanced American practice for
obtaining a variable rate of feed motion in either direction, it being
obvious that _g_, being driven by the radial face of _f_, its speed of
rotation will be greater according as it is nearer to the perimeter of
_f_ and less as it approaches the centre of _f_, at which point the
rotary motion of _g_ would cease. Here, then, we have a simple device,
by means of which the direction and rate of feed may be governed at will
with the mechanism under continuous motion, and conveniently situated
for the operator, without his requiring to move from the position he
naturally occupies when working the machine.
[Illustration: Fig. 726.]
The means of raising or lowering the height of the rail R on the side
standards Z are as follows: K is a pulley driven by belt from the
countershaft and operating pinion _l_, which operates pinion _n_,
driving _m_. O is a gear on the shaft driving the pinions _p_, _p_,
which operate the gears _q_, _q_, on the vertical screws which engage
with nuts attached to R; _m_ and _n_ are carried on a bell-crank _r_
pivoted on the shaft of pulley K. Pinion _n_ is always in gear with
pinion _l_, and pinion _m_ is always in gear with pinion _n_ (and not
with pinion _l_). With the bell-crank in one position, motion passes
from _l_ to _n_ and to O; but with it in the other position, motion
passes from _l_ to _n_, thence to _m_, and from it to O. The motion of
_m_, therefore, is always in a direction opposite to that of _n_; hence
O, and gears _p_ and _q_, may be operated in either direction by
regulating which of the two gears _n_, _m_ shall drive O, and this is
accomplished as follows: The bell-crank _r_ is connected by an arm to
rod _s_, and the latter is connected by a strap to an eccentric _t_,
operated by the handle shown. When this handle stands horizontally, both
_m_ and _n_ are disengaged from pinion O; but if the handle be raised,
rod _s_ is raised, and _m_ is brought into gear with O. If, however, it
be lowered from the horizontal position, _n_ is brought into gear with
O, and _m_ becomes an idle wheel.
[Illustration: Fig. 727.]
There are two feed screws--one for operating each boring bar-head, and a
spindle for operating the vertical feeds of the bars in the sliding
heads. Fig. 728 shows the arrangement for engaging and disengaging the
feed nuts of these heads. A is the slide that traverses the rail. It
carries a nut made in two halves, N and N´, which are carried in a guide
or slide-way, and which open from or close upon the screw F when the
handle O is operated in the necessary direction. Each half of the nut is
provided with a pin projecting into eccentric slots _x_ in the face of a
pivoted plate (shown dotted in), to which the handle O is attached. W, W
represent bearings for the vertical feed spindle W in Fig. 726. _a_ is
the annular groove for the bolts _b_ in Fig. 729.
[Illustration: _VOL. I._ =ROLL-TURNING LATHE.= _PLATE XI._
Fig. 730.
Fig. 731.]
For a quick hand traverse for the head the ratchet, P is provided,
operating a pinion _s_, which engages with a rack T, running along the
underneath side of the cross-rail R. To adjust the fit of A to the rail
the gibs _y_ and _y´_ and the wedge _x_ are employed.
[Illustration: Fig. 728.]
Fig. 729 represents the automatic feed motion within the head for
operating the tool bars vertically. R is the cross rail on which slides
A carrying B, and permitting it to swivel at any angle by means of bolts
_b_, whose heads pass within an annular groove, _a_ in A. In B is
carried the boring bar G, having the rack shown. P is a pinion to
operate the rack. W is the feed-rod driving the worm H, which drives the
worm-wheel I. This worm-wheel is provided with a coned recess, into
which the friction plate C fits, so that when the two are forced
together rotary motion from I is communicated to C, and thence to C´
(which is a sleeve upon C), where it drives pinion P by means of pin P´.
_i_ rotates upon and is supported by the stud J, which is threaded into
C^{2} (the latter being also a continuation of C); hence when hand-wheel
K is operated in one direction, C^{2} acting as a nut causes J to clamp
I to C, and the tool bar to therefore feed. Conversely, when K is
operated in the opposite direction, I is released from C, and may,
therefore, rotate while C remains at rest. For feeding the tool bar G by
hand, or for moving it rapidly, the hand-wheel M is provided, being fast
to the sleeve at its section C^{2}, and, therefore, capable of rotating
pinion P. D affords journal bearing to C at its section C´. The chain
from the weights which counterbalance the bars G pass over sheaves which
are fixed to the piece B in which the bar slides, so that they occupy
the same position with relation to the axis of the bar at whatever angle
the latter may be set, and thus the counterbalancing weight is delivered
upon the bar in a line parallel to its axis. As an example of the
efficiency of the machine, it may be mentioned that at the Buckeye
Engine Co.'s Works, at Salem, Ohio, a pulley 12 feet in diameter,
weighing 8860 pounds, and having a 27-inch face, was bored and turned on
one of these machines in 17 hours, taking three cuts across the face,
turning the edge of the rim facing off the hub and recessing the bore in
the middle of its length for a distance of several inches, the bore
being in all 18 inches deep. The machine is made in different sizes, and
with some slight variations in each, but the main features of the
design, as clearly shown in our engravings, are common to all sizes.
Fig. 730 represents a lathe for turning chilled rolls such as are used
for paper calendering machines, and is constructed by the J. Morton
Poole Company of Wilmington, Delaware.
In the figure a roll is shown in position in the lathe. The journals of
the rolls are first turned in a separate lathe, and form the guide by
which the body of the roll is turned in the lathe shown in the figure.
The lathe consists of a bed plate P, at one end of which is mounted the
driving head. Upon this bed plate are also mounted three standards or
vertical frames, to the two end ones of which are pivoted the binder
arms shown. These frames hold the bushes at L and N, in which the
journals of the roll revolve. They also carry the bar G, secured to the
arm W of the frame by clamps _a_, _a_, _a_. Upon the bar G are two slide
rests, consisting of a tool rest E, a tool clamp A, and a feed yoke B,
which is screwed up by a wrench applied to the nuts as shown on the
right-hand tool rest in the figure. The binder arm is adjusted to hold
the bushings L N (which are varied to suit the size of the roll journal)
a fair working fit upon the roll journals, the bolts S holding the
binder arms firmly against the enormous pressure due to the cut. It is
obvious that the frames W may be adjusted anywhere along the bed plate P
to suit the length of roll to be turned, and that the slide rests may be
moved to any required position along the bar G. Further details of the
construction are as follows. Fig. 731 is an end, and Fig. 732 is a top
view of the tool rest; A is the tool clamp securing the tool to the rest
E, R representing a section of the roll, B is the feed yoke, which to
put on a cut is screwed inwards by operating the nuts D. The pins C are
fast in B, and their ends abut against the tool, which is fed in under
the full pressure of the clamp A. The tool is shown at F in figure, and
also at F in Fig. 733, which is a view of the rest with the clamp A
removed. The form of tool employed is shown in Fig. 734, its length
varying from five to six inches. As the tool feeds in and does not
traverse along the roll it is obvious that it cuts along its entire
length, the cuttings coming off like a bundle of fine ragged needles.
[Illustration: Fig. 729.]
When the tool has been fed in cutting the roll to the required diameter
the rest is moved along the bar G, a distance equal to the length of the
tool, and the operation is repeated until the full length of the roll
has been turned. It is obvious that to feed the tool in parallel, both
nuts D of the tool rest are operated. The tool is held as close in to
the rest as the depth of cut to be taken will permit, and is used at a
cutting speed varying from about 2-1/3 feet to 5 feet per minute
according to the hardness of the roll. The tool has four cutting edges,
and each cutting edge will carry in at least one cut, and may sometimes
be used for a second one. The tools are used dry and the amount of
clearance is just sufficient to clear the roll and no more.
The rolls are driven by a socket bolted to the lathe face plate, and
containing a square hole, in which fits loosely the square end of the
roll. The object of this arrangement is to permit the roll to be guided
entirely by the bearings in which it rotates, uninfluenced by the
guiding effect that accompanies the use of centres in the ordinary
method of turning.
[Illustration: Fig. 732.]
Fig. 735 represents a lathe designed and constructed by the American
Tool and Machine Company, of Boston, Mass. This class of lathe is
strictly of American origin, and has become the most important tool in
the brass finishing shop.
[Illustration: Fig. 733.]
In its design the following advantages are obtained:--
1st. The front of the lathe is entirely unobstructed by the ordinary
lathe carriage and slide rest, hence the work may be more easily chucked
and examined, while in the case of work requiring to be ground together,
while one part is in the chuck, the trouble of moving the slide rest out
of the way is entirely obviated.
2nd. In place of the single cutting tool carried in a slide rest and of
the tailstock of the ordinary lathe, there is provided, what is known as
a turret, or turret rest, carrying 6 tools, each of which can be
successively brought into action upon the work by the simple motion of a
lever or handle.
[Illustration: Fig. 734.]
3rd. The rest for traversing single pointed screw cutting tools or
chasers (for internal threads) is at the back of the lathe where it is
out of the way.
4th. In place of the usual change wheels required to operate the lead
screw, the chasing bar is operated by a single threaded collar or hob,
which is more easy of application and removal.
5th. The slide rest carrying the screw cutting tool is capable of such
adjustment, that the tool will thread successive pieces of duplicate
work to an exactly equal diameter, so as to obviate the necessity of
either measuring or trying the work after the tool has been accurately
set for the first piece.
6th. When the threading tool has traversed to the end of its cut it may
be lifted from the same and pulled back by hand, ready to take a second
cut, thus avoiding the loss of time involved in traversing it back by a
lead screw or its equivalent.
7th. Each of the tools in the turret may be set so as to operate to an
equal depth and diameter upon successive pieces of work.
[Illustration: Fig. 735.]
In the particular lathe shown in our example, there is another and
special advantage as follows:--
In lathes operating upon small work and upon the softer metals, as
composition, brass, &c., the time occupied in traversing the cutting
tool is comparatively short, and from the comparative softness of the
metal the speed of lathe rotation is quick, and the tool motions must be
correspondingly quick. In addition to this the work being so much more
quickly performed, changes and readjustments of the parts are
necessarily more frequent, hence the rests traverse the bed more rapidly
as well as more frequently and the wear of the [V]s on the lathe, and
the corresponding [V]-grooves in the tool rest, slide rest, or turret,
is increased; as a result, tools carried in the tailstock or the turret,
as the case may be, which tools should for a great many purposes stand
axially true with the live spindle, stand below it, and hence instead of
boring a hole equal to their own diameter, bore one of larger diameter.
In the case of tools, however, which, as in the case of drills,
endeavour to find their own centre in the work, this action takes place
to some extent as the tool enters the work, and as a result the hole is
made a taper, whose largest diameter is at the mouth. This induces
another evil in that it dulls the advance edge of the drill flute, and
wears away the clearance which is of such vital importance to the free
action of the drill.
The manner in which these advantages are obtained is as follows:--
In place of the ordinary tailstock a back head is provided which has a
cross slide operating after the manner of the ordinary slide rest; this
carries an upper slide, thus forming a compound slide rest. On the top
of this rest is carried a rotating head or turret head, serving the same
purpose as the head shown in Fig. 694, and carrying a series of tool
holders. These tool holders may be operated by the feed screw of the
compound rest, or may be operated by the hand lever shown standing
horizontally. In addition to the ordinary back gear for reducing the
live spindle speed there is provided on the live spindle a second small
pinion, driving at the back of the lathe head a shaft, on the left-hand
end of which is a seat for collars or hobs, operating a bar running
along the back of the lathe, and forming what is termed the screw
apparatus, whose operation is as follows:--
This bar carries the slide rest shown, a handle or lever for partly
rotating the slide rest, spanning the bed of the lathe. When this handle
is lifted, the bar at the back of the lathe rotates in its journals. On
this bar is an arm which carries a segment of a circle, containing a
thread corresponding in pitch to the thread on the collar or hob. When
the lever is raised the segment moves away from the hob, and the bar may
be moved laterally by hand, but when the lever is lowered the arm falls,
and the segment comes into contact with the hob thread, which therefore
feeds the bar; all that is necessary for thread cutting is, therefore,
to place on the lathe a hob having the required pitch for the thread to
be cut, and place in the slide rest a chaser or single-pointed threading
tool, and set the tool to the work by means of the slide rest,
depressing the lever to cause the tool to feed forward, and elevating it
to move the bar back by a lateral hand pressure. To put on successive
cuts the slide rest is operated, the lever always being lowered till it
meets the surface of the lathe bed. To cause the slide rest to cut
successive threads to the same diameter, a suitable stop motion is
provided to the slide rest, and when the rest has been operated as far
as the stop will permit it, the thread is cut to the required depth and
diameter.
A stop motion is also provided to the lateral motion of the turret, so
that the tools being set to enter the work to their respectively
required distances, all pieces will be turned to equal depths or
lengths.
To enable the centres of the tool holders to maintain true alignment
with the live spindle, notwithstanding the wear of the lathe bed and
back head, the bed is made in two parts. One of them carries the
headstock, and on the vertical face of this part is a slide in which the
end of the second part fits, so that by means of adjusting screws the
second part may be elevated to effect the true alignment when necessary.
Fig. 736 represents a square arbor brass-finisher's lathe. The object of
the square arbor or tail spindle is to enable it to carry cutting tools
in place of the dead centre. A cross slide is provided to the tailstock,
and upon this slide the head of the tailstock is pivoted so as to bore
taper holes; the tailstock thus virtually becomes a compound slide rest.
This lathe is provided at the back of the bed with a bar carrying a
slide rest, operated in the same way and for the same purpose as that
described with reference to Fig. 735. Both these lathes are furnished
with separate compound slide rests, and with a hand rest.
[Illustration: Fig. 736.]
When work of considerable weight requires to be bored with holes of
moderate diameter, it is more convenient that it remain fixed upon a
table, and that the boring tools rotate, and a machine constructed by
the Ames Manufacturing Company for this purpose is shown in Fig. 737; a
standard occupies the position of the ordinary tailstock. It carries an
horizontal table, or angle plate, on which the work may be chucked. This
table is capable of a vertical and a cross shear movement, so that when
the work is chucked upon it, holes whose axes are parallel, but situated
in different locations upon the same surface, may be drilled or bored by
so moving the table as to bring each successive hole into line with the
live spindle. The feed motions are as follows:--
[Illustration: Fig. 737.]
At the back of the smallest step on the cone and fast on the cone
spindle is a gear-wheel gearing into a pinion, which drives the lower
shaft shown behind the back bearing, and on this shaft are two pinions.
One drives the upper feed cone, shown at the back of the back bearing,
which cone connects by belt to the feed cone below, which operates a
traverse feed for the work table; the other drives the tool holding
spindle which passes through the cone spindle. This tool holding or
driving spindle is threaded at its back end, passing through a nut which
causes it to self-feed from left to right, or in other words, towards
the work table. To throw this feed out of operation the pinion on the
end of the lower or feed driving spindle is moved laterally out of gear
with the pinion driving it.
To provide a quick hand-feed traverse the shaft or spindle, shown with a
hand-wheel, is provided, being connected to the tool driving spindle by
gearing.
When employed to operate a boring bar, a bearing to support the bar at
the tail or footstock end may be bolted to the table, such bearing
carrying a bushing which may be changed to suit the diameter of the
boring bar.
[Illustration: Fig. 738.]
Fig. 738 represents a cylinder boring lathe. D is the driving cone, on
whose shaft is the worm W, driving the worm-wheel G, which is fast upon
the boring bar _g_, having journal bearing in the standards H and H´,
the latter of which must be moved out of the way to get the work over
the bar. _h_ is a head provided with slots to carry the cutting tools;
_h_ is a close sliding fit to the bar _g_, and is traversed along _g_ as
follows:--_g_ is hollow and there passes through it a feed screw, which
operates a nut on _h_, which nut passes through a longitudinal opening
in the bar _g_. At the end of this feed screw is the gear-wheel D. Now
fast upon the end of _g_, and therefore rotating with it, is the gear A,
driving gear B, which is fast on the same sleeve as C, which it
therefore drives; C drives D. The diameter of A is less than that of B,
while that of C is less than that of D; hence the rotation of D is
slower than that of A, and the difference in the relative velocities of
D and A causes the feed screw to rotate upon its axis and feed the head
_h_ along the bar. If C be placed out of gear with D, the feed screw
(and hence the head H) may be operated by the handle E.
[Illustration: Fig. 739.]
There are several objections to this form of machine, as will be seen
when comparison is made with Fig. 739, which represents a special
cylinder boring lathe, designed and constructed by William Sellers and
Co., of Philadelphia, Pennsylvania. The boring bar is here supported in
two heads, and is hollow, the feed screw for traversing the head
carrying the boring cutters being within the bar. The feed is effected
through the medium of the train of gearing shown at the end. The two
face plates shown which drive the boring bar, also carry two slide rests
which are used to face off the ends of cylinders while the boring bar is
in operation, these slide rests being operated by a star feed, acting on
the principle described with reference to Fig. 589. The boring bar in
this case being driven from each side of the work the torsion due to the
strain of the cut is divided between the two halves of the bar; or in
other words, when a boring bar is driven from one end the strain due to
the cut falls upon that part of the bar that lies between the
boring-head and the point at which the bar is driven; but when the bar
is driven from each end then the strain is divided between the two ends,
causing a bar of a given strength to operate more steadily and take a
heavier cut for roughing, and a smoother one for finishing. A greater
advantage, however, is that it gives to the bar a rigidity, enabling it
to carry a cutter having a long cutting edge without chattering, thus
allowing a very coarse finishing feed, which will finish a bore with
less wear to the tool edge (and therefore more parallel) because for a
given amount of work the cutting-edge is under duty for a less period of
time, the cutting speed remaining the same, or even slower than would be
desirable for a fine feed. The driving-cone, which is shown to be below
the boring-bar, is so situated to accomplish two objects, which are to
operate the two face plates by a shaft having two pinions (within the
bed) gearing with the circumferential teeth on the face plates, and to
operate at the same time the table (shown on the bed between the
face-plates) to which the cylinder is bolted.
In a boring machine it is of the utmost consequence that the bar shall
be as free from vibration as possible, while lost motion, or looseness
from wear, is especially to be avoided. By carrying the bar in two
bearings, as it were, the wear is greatly reduced.
The duty of facing the cylinder ends is sometimes done by facing cutters
carried in the head. Such cutters, however, must have a cutting edge
equal to the breadth of the surface faced by them, because the cutter
cannot be fed radially to its cut. Furthermore, the cut is carried by
the bar at a considerable leverage, and as a result it is very difficult
indeed to make the radial faces true or even nearly true, the cutter
dipping into the softer parts of the iron or into spongy places if there
are any. In any event springing away from its cut, resisting it until
forced to cut, and then cutting deeper than should be, so that on a
finished surface it is often apparent to the eye where the cutter began
and left off. When, however, the radial faces are operated upon by a
slide rest, as in the Sellers machine, the tool is more firmly held, and
may be fed radially to the cut, producing true faces, and saving a great
deal of time in making the cylinder cover joints, as well as in the
boring and facing operations.
Fig. 740 represents a double boring and facing lathe by G. A. Gray,
Junior, of Cincinnati, Ohio. Two driving heads are provided, each having
a main spindle, but holding the boring bar after the manner of an
ordinary lathe, and within each spindle is another capable of
longitudinal traverse. The main spindle is provided with a head
corresponding to a slide rest and carrying a cutting tool for facing
purposes, the feed being obtained by means of a _star-feed_. The work is
bolted to the carriage and fed to the cut for boring purposes. It is
provided with an automatic feed and also with hand feed. When facing is
to be done the carriage may be firmly locked to the lathe shears.
In boring and facing a steam pump centre, or other similar piece, the
casting is fastened to the carriage in a special fixture. The carriage
is then moved so that the work will come nearly in contact with tool in
the fast head, the loose head is moved up to the work, and both the
carriage and loose head are clamped.
[Illustration: Fig. 740.]
Both ends of the casting may be operated upon at the same time or
separately, as occasion requires, the object being, however, to work
upon as many places at one time as the nature of the work will permit;
this being the main point in the economical performance of work. It is
evident also that if the machine is true, and the piece is finished at
one setting, the work will be true.
[Illustration: Fig. 741.]
In the detail engravings, Fig. 741 represents boring, tapping, and
facing steam pump centres, in which operations the carriage is locked.
[Illustration: Fig. 742.]
[Illustration: Fig. 743.]
Fig. 742 illustrates the manner of boring and facing cylinders and
similar pieces, the loose head stock being used as a tailstock and the
fast headstock as the driver. The facing is done either before or after
the boring, all the work obviously being done at one chucking.
Fig. 743 shows a longitudinal cross section of the headstocks showing
the main and the internal spindles.
Fig. 744 represents a lathe constructed by the Defiance Machine Works
for turning the hubs for carriage and wagon wheels.
[Illustration: Fig. 744.]
The blank from which the hub is turned is driven by a mandrel having a
square stem fitting in the live or driving-spindle, this mandrel being
supported at the other end by the ordinary dead centre operated by the
upper hand-wheel. The bed is provided (between the driving-spindle and
tailstock) with the usual raised [V]s on which rests a carriage carrying
a cross slide. This cross slide carries, at the back of the lathe, a
head or stock containing the roughing-knives, and at the front a table
carrying the finishing-knives, hence, by operating the large hand-wheel
(which gives transverse motion to the cross slide) in one direction the
roughing-knives are brought into operation, while by operating it in the
opposite direction the finishing-knives are brought into operation (the
roughing-knives receding). By suitable stops, the motion of the roughing
and finishing-knives respectively are arrested when those knives have
cut the blanks to the desired diameter, the finishing-knives shaping the
work correctly by reason of their form of outline. Upon the same cross
slide are the equalizing-knives, one on each side of the front table.
These knives operate simultaneously with the finishing-knives, cutting
the hubs to uniform length. Thus the hubs are cut to exact uniformity of
diameter, shape and length, by simply operating the large hand-wheel
first in one direction and then in the other.
If it be required to cup the hubs, as in the case of standard wagon
hubs, suitable cutters carried in a bar (having sliding motion in a
guide way on the tailstock) are caused to do such cupping, the
cupper-bar being operated by the left-hand lever.
The live, or driving, spindle is started and stopped by a tight and
loose pulley, the belt being passed from one to the other by means of
the lever on the right, which simultaneously operates a brake attached
to the belt stopper, operating upon the tight pulley. By this means the
lathe can be started and stopped more quickly than would be the case
with a cone pulley, whose extra weight and inertia would take time to
overcome.
CHAPTER IX.--DRIVING WORK IN THE LATHE.
The devices employed to drive work that is suspended between the lathe
centres are shown in the following illustrations.
They are termed lathe dogs, drivers, or carriers. It is to be observed,
however, that since the term dog is also applied to a device for holding
work to the lathe face plate, as well as to the jaws of chucks, either
the term driver or the English term carrier is preferable to the term
dog.
[Illustration: Fig. 745.]
[Illustration: Fig. 746.]
Fig. 745 represents a lathe dog, driver, or carrier D, in position to
drive a piece of work in the lathe. It is obvious that the work is
secured within the carrier or driver by means of the set-screw shown.
The tail of the driver here shown is bent around to pass within the slot
provided in the face plate, a plan which is convenient, but is
objectionable, because in this manner of driving the work two improper
strains are induced, both of which act to spring or bend the work. The
first of these strains is caused by the carrier being driven at a
leverage to the work, as shown at A in the figure, which causes the live
centre to act as a fulcrum, from which the work may be bent by the
strain caused by the cut.
[Illustration: Fig. 747.]
The second strain is caused by driving the carrier from one side or end
only, and is shown in Fig. 746, where the dog receives the face-plate
pressure at the point A, and the cut or resistance being on the opposite
side of the work, the leverage of the driving point causes a tendency to
lift the work in the direction of the arrow C. The direction of this
latter strain, however, varies as the work revolves. For example, in
Fig. 747 the dog is shown in position at another point in its
revolution, and the point A, where the power is applied to the carrier,
is here on the same side as the tool cut; hence there is less tendency
to spring the work. It becomes obvious then, that work driven in this
manner will be liable to be oval, or out of round, as it is commonly
termed.
[Illustration: Fig. 748.]
The methods of overcoming these two sources of error are as follows:
Instead of the end of the dog being bent around to pass within the slot
in the face plate, as in Fig. 745, the leverage A in that figure may be
avoided by the means shown in Fig. 748, in which a driver having
straight ends is used, and a pin P is fastened to the face plate to
drive the carrier. But this does not remove the tendency (shown in Fig.
746) acting to spring the work from the pressure of the cut; hence, to
obviate this latter tendency, two driving-pins P P, in Fig. 749, are
sometimes used with the idea of driving the work from both sides, and
thus equalizing the strain. But this is effective only when each pin is
in working contact with the dog. This condition is difficult to secure
for several reasons. First, suppose the two ends of the carrier to be of
equal thickness, and the driving-pins to be of equal diameter, while the
work receiving hole of the carrier is quite central to these two ends,
then the work also must be true, in order to cause the pins to act
equally on the ends of the carrier. Hence, this method is only
applicable, even if all the above conditions be fulfilled, to the
finishing cuts, and these would have to be taken on work that had been
sprung in the roughing cuts, so that it would be difficult to obtain
accurate results. A nearer approach to correctness is therefore sought
by various means. Thus, Fig. 750 represents a face plate provided with
an annular [T]-groove, having a cut at H to admit two nuts into which
the pins P are screwed. These pins may be tightened lightly, so that
they will slip under the pressure of the roughing cut, and thus come to
an equal bearing upon the carrier or work, as in case of the arms of a
pulley where a carrier is not used. When the pins have adjusted
themselves to have as near as may be an equal driving bearing, they may
be tightened up. By this means the pins are compelled to act at an equal
leverage upon the carrier or work, but there is no assurance of an equal
degree of pressure of the pins P.
Another method is shown in Fig. 751, in which a clamp in two parts is
employed, the driving-pins P fitting into two holes equidistant from the
lathe centre, while loosening one bolt, J or K, and tightening the other
is resorted to, to equalize the driving contact on the two arms, but in
this case again there is no certainty that the two pins will drive
equally, and there is danger of drawing the work somewhat out of true.
Another form is shown in Fig. 752, the idea being to equalize the
pressure of the driving pins, by means of the four screws, but here
again, there is no means of knowing whether the driving pressure is
equalized.
[Illustration: Fig. 749.]
The best form of driver is shown in Fig. 753, which represents a
Clement's driver. The driving-plate F has four slots; two of them, A and
B, pass entirely through this plate to admit bolts C D, which have a
shoulder, so that they may be secured firmly to the lathe face plate,
but which are an easy fit in the plate F, so as to permit it to move
upon the lathe face plate. The other two are [T]-shaped slots to receive
nuts, into which the pins P P are to be screwed. The bolts C D drive F,
and the pins P drive the work, the freedom of the plate E to move upon
the lathe face plate permitting this strain-equalizing action of the
driving-plate and driving-pins.
[Illustration: Fig. 750.]
[Illustration: Fig. 751.]
[Illustration: Fig. 752.]
Sometimes, as in cutting screws, the work requires to be revolved
backwards, without having any lost motion between the arm and carrier,
or in other words, the carrier must revolve backwards as soon as the
face plate does. To accomplish this, a common plan is to tie the driver
or carrier to the driving-pin, but a better plan is to employ a bent
tailed dog and secure its end in the face-plate slot. A convenient form
of face plate for this purpose is shown in Fig. 754, A, B, C, and D,
being slots, and E a set-screw for binding the dog as shown in Fig. 755.
[Illustration: Fig. 753.]
For special lathes in which the work is of uniform diameter, the driving
pins P, Fig. 753, may be replaced by solid jaws, thus in Fig. 756 is a
Clement driver, such as is used on axle lathes, C C being driving lugs
in place of the pins P in figure.
To prevent the ends of the set-screw or screws of the driver from
damaging the surface of finished work, the form of driver shown in Fig.
757 has been patented in England. It consists of a disc arched to
receive a lever C, which is pivoted in the disc at D. A set-screw
provided in the disc binds one end of the lever to the work, and as the
pressure to drive the work is applied at the other end of the same
lever, it serves to assist (to some extent) the set-screw in binding the
lever to the work. The work is held between a [V] in the disc and one on
the lever, the object being to provide a large area of contact, and thus
prevent the damage to finished work which screw ends are apt to cause.
[Illustration: Fig. 754.]
The same end may be obtained for ordinary drivers by using a copper or
brass ring, such as shown in Fig. 758, which may be opened or closed,
within certain limits, to suit the diameter of the work, being placed on
the end of the work, and within the dog, to receive the pressure of the
set-screws.
[Illustration: Fig. 755.]
One such ring will serve for several diameters of work, springing open
when forced, under hand pressure, upon the work, or closing upon the
work as the pressure of the dog set-screw is received. It is obvious
that the split of the ring should be placed diametrally opposite to the
dog set-screw.
[Illustration: Fig. 756.]
In very small lathes the driver is sometimes driven by the device shown
in Fig. 759, which consists of a small chuck, screwed on the live
spindle, and containing the live centre and a driving arm B, which
passes through the chuck, and is set to any required distance out, by
the set-screw C. The objection to this is, first, that either the live
centre must be very short, or the arm B must be very long; and, second,
if the chuck wears out of true, it carries the live centre also out of
true; hence this class of driver is but little used, even in foot
lathes.
[Illustration: Fig. 757.]
[Illustration: Fig. 758.]
In small drivers of this kind it is sometimes the practice to cut away
rather more than one quarter of the thread on each side of the live
spindle as shown in Fig. 760 at A, and to then cut away one quarter of
the thread on each side of the bore of the driver as at B in the figure.
This enables the driver to be passed upon the spindle and screwed home
with one quarter of a turn, thus saving time in putting on and taking
off the driver.
Fig. 761 illustrates a work driver very convenient for turning bolts. It
consists of a piece of iron or plate P bolted to the lathe face plate F,
and having jaws so as to fit to the sides of the bolt B and drive it.
This not only saves the time that would otherwise be required to put on
a driver or carrier but leaves the underneath face of the bolt clear to
be faced up by the turning tool, an example of its use being shown in
connection with the knife tool or facing tool.
[Illustration: Fig. 759.]
[Illustration: Fig. 760.]
Fig. 762 represents a driver of this kind having a sliding jaw so that
it may be set for different sizes of bolt heads. When the driving end of
the work is threaded an ordinary dog or driver cannot be used because
its screw would damage the thread on the work. A common method of
overcoming this difficulty is to place over the ring a split ring of
copper, or to place on it two nuts, putting a common dog on the end nut.
It is better, however, to use a driver, threaded part of the way
through, as in figure 762 (from _The American Machinist_) and to screw
it upon the work.
[Illustration: Fig. 761.]
Fig. 763 represents a very useful form of work driver designed by Mr.
William A. Lorenz. It consists of two jaws A, A held together by two
screws, and threaded to receive two driving screws D, E in the figure,
which enable it to be used to hold work to the live centre as is
necessary when using the steady rest, as is shown in the figure, in
which B represents the work and C the jaws of the steady rest. It is
obvious that the dog may be thus employed to chuck work independently of
the steady rest, because the live centre may be removed, and the face of
the work held against the face of the chuck, the short screws H being
used instead of the long ones D, E.
[Illustration: Fig. 762.]
If the carrier is used to simply drive the work without clamping it to
the live centre or face plate, one or both of the screw pins J, K may be
used in place of bolts D, E, the carrier being balanced when both are
used.
[Illustration: Fig. 763.]
[Illustration: Fig. 764.]
Fig. 764 represents a driver, carrier, or dog threaded in its bore to
drive threaded work, which the screw of the ordinary dog would obviously
damage.
[Illustration: Fig. 765.]
[Illustration: Fig. 766.]
[Illustration: Fig. 767.]
Fig. 765 represents an excellent driver for cored work such as the piece
W. Its hub A is screwed on the live spindle in place of the face plate,
and carries the rods B, B´, both of which are adjustable in the distance
they stand out from A, so that B may be set to suit the work, and B´ set
out sufficiently to balance B and D. The driving arm D is adjustable
along B, and by being bent to the form shown is more out of the way, and
obviates the necessity of using a dog on many kinds of work. The other
end of the work is shown supported by a cone centre C, whose
construction is shown in Figs. 766 and 767. Its object is to avoid the
wear that occurs at the mouth of the hole in cored work, when it is run
on the dead centre, and to avoid the necessity of plugging the hole to
provide a temporary centre. In the figures, A represents a stem (fitting
into the tailstock spindle S, in place of the ordinary dead centre),
having a collar B and carrying the cone C. The work is supported upon C,
which revolves upon the stem of A. At E is a raw-hide washer, intended
to prevent the abrasion which would occur on the faces of B and C. The
pin F prevents C from coming off D, one half of its cross section being
in C, and the other half in a semicircular groove running around D. An
oil groove is provided through the collar B, and passes along the stem
D. This is an exceedingly handy device for cored work, and may also be
used to sustain work against the lathe face plate, while chucking the
work true by its bore.
[Illustration: Fig. 768.]
The work drivers employed by wood turners, for work held between the
lathe centres, are as follows:--
Fig. 768 represents two views of a fork centre to be placed in the cone
spindle of the lathe, and serve as a live centre, while also driving the
work; C is a sharp conical point, which should run true, because it
serves to centre the work; D, E are two wings which enter the wood to
drive it. This device answers well for work that can be finished without
taking it in and out of the lathe, it being difficult to place the work
in the lathe so as to run true after removal therefrom; in case,
however, that this should become necessary, the work should be replaced
so that each wing falls into its original impression. For heavy work
this device is unsuitable, hence the two plates shown in Fig. 769 are
employed, being termed centre plates. They are composed of iron and are
held to the work by screws passing through the respective holes shown at
the corners of the plates. The plate having the round centre hole is for
the dead centre end of the work, while that having the rectangular slot
is for the live centre end of the work. The rectangular slot is made a
close fit to the wings of the fork centre shown in figure. Figs. 770 and
771 represent a spur centre designed to hold pieces of soft wood, that
may be liable to split from the pressure of the centres. The spurs are
made parallel on their outer surfaces, while the inner ones are at an
angle, so as to close the wood around the central point, and not spread
the wood outwards. The plate for the dead centre is formed on the same
principle as is shown in figure 769.
[Illustration: Fig. 769.]
[Illustration: Fig. 770.]
Another form of chuck centre or driving centre for wood work is shown in
Fig. 772, being especially useful when the work cannot be supported by
the lathe dead centre. The body A screws on to the thread on the live
spindle of the lathe, while the work screws on the pointed screw B,
which will hold disc-shaped pieces of moderate diameter, as about 4 or 5
inches, leaving its face to be operated on as may be desired. To prevent
B from splitting the work, or when hard wood is to be turned, a small
hole may be bored up the work to permit B to enter sufficiently easily.
[Illustration: Fig. 771.]
[Illustration: Fig. 772.]
When a piece of work to be turned between the lathe centres is of such a
form that there is no place to receive centres, provision must be made
to supply the deficiency.
[Illustration: Fig. 773.]
In Fig. 773, for example, a temporary centre B is fitted into the socket
to receive the centre.
In small work that has been drilled or bored, a short mandrel is used
instead of the piece B.
[Illustration: Fig. 774.]
If a half-round piece is to be turned it should be forged with a small
projecting piece to receive the lathe centre, as in Fig. 774.
[Illustration: Fig. 775.]
When the end of the work is flat and not in line with the axial line of
the main body of the work, a piece of metal to contain the centre may be
held to the work by a driving clamp, as in Fig. 775, in which A
represents the end of the work and B a temporary piece containing the
centre C. In this case it is best to make the centre C after the piece B
is clamped to the work.
[Illustration: Fig. 776.]
To provide a temporary centre for a piece having a taper hole, a taper
plug is used, as shown in Fig. 776, W representing the work and P the
plug, which must be an accurate fit to the taper of the hole, and must
not reach to the bottom of the hole.
MANDRELS OR ARBORS.--Work (of about 6 inches and less in diameter) that
is bored is driven by the aid of the mandrel or arbor, which is held
between the lathe centres, as in Fig. 777, in which W represents a
washer and M the mandrel, driven into the washer bore so as to drive it
by friction. At A is a flat place to receive the set-screw of the driver
or lathe dog, and at B a flat place upon which the diameter of the
mandrel is marked. The mandrel diameter is made slightly larger at D
than at C, so as to accommodate any slight variation in the diameter of
holes bored by standard reamers, which gradually reduce in diameter by
wear; thus if a reamer be made 1-1/1000 inch diameter, with a limit of
wear of 1/1000 inch, then the mandrel may be made 1 inch at C and
1-1/1000 inch at D. It is well to taper the end of the mandrel from C to
E about 1/2000 inch, so that it may enter the work easily before being
driven in. Instead, however, of driving mandrels into work, it is better
to force them in under a press. If driving be resorted to a lead hammer,
or for very light mandrels a raw-hide mallet, may be used.
[Illustration: Fig. 777.]
[Illustration: Fig. 778.]
In the absence of a lead hammer, a driver, such as in Fig. 778, is a
good substitute, consisting of a socket containing babbitt or some other
soft metal at B (the mandrel being represented by M). If copper be used
instead of babbitt a hole may be drilled through it, as denoted by the
dotted lines.
[Illustration: Fig. 779.]
[Illustration: Fig. 780.]
The centres of mandrels should either have an extra countersink, as at A
in Fig. 779, or else the cut should be recessed as at B, Fig. 780.
Mandrels are best made of steel hardened and ground up after hardening.
If the bore of the work is coned, and of too great a cone to permit the
mandrel to be driven, and drive the work by friction, the cone mandrel
shown in Fig. 781 may be used. M is the mandrel in one piece with the
collar C. The work W is held between two cones A, A, which slide a close
fit upon the mandrel, and grip the work by screwing up the nut N, there
being a thread upon the mandrel, as at S, to receive the nut. It is
obvious, however, that work having a parallel bore may also be held by
the cone mandrel, as shown in Fig. 782.
[Illustration: Fig. 781.]
[Illustration: Fig. 782.]
To obviate the necessity of having the large number of mandrels that
would be necessary so as to have on hand a mandrel of any size that
might happen to be required, mandrels with provision for expanding or
contracting the diameter of the parts used to hold the work are made.
[Illustration: Fig. 783.]
Thus in Fig. 783 is shown Le Count's expanding mandrel, in which G H is
the body of the mandrel, turned parallel along a certain distance, to
fit the bore of the sleeve A, which is a close-sliding fit on this
parallel part of E.
From the end H of the mandrel there extends towards the end G four
dovetail grooves, which receive four keys B. The heads of these four
keys are enclosed and fit into an annular groove provided in the head C
of the sleeve A, so that moving the sleeve A along the mandrel causes
the four keys to slide simultaneously in their respective grooves.
Now these grooves, while concentric at any one point in their transverse
section to the axis of the mandrel, are taper to that axis, so that
sliding the sleeve A along the parallel part of the mandrel increases or
decreases (according to the direction in which A is moved) the diameter
of the keys.
If the sleeve be moved towards the end G, the keys while sliding in
their taper grooves recede from the axis of the mandrel, while if moved
towards H they approach the axis of the mandrel, or what is the same
thing, if the sleeve be held stationary and the body of the mandrel be
moved, the keys open or close in diameter in the same manner; hence all
that is necessary is to insert the mandrel in the bore of the work, and
drive the end G, when the keys will expand radially and grip the work
bore.
The keys, it will be observed, are stepped on their diametral or
work-gripping surfaces, which is done to increase the capacity of the
tool, since each step will expand to the amount equal to the whole
movement of the keys in their grooves or slots.
Mandrels or arbors are sometimes made adjustable for diameter by forcing
a split cone upon a coned plug, examples being given in the following
figures, which are extracted from _Mechanics_. In Fig. 784, A is a cone
having the driving head extending on both sides of the centre so as to
balance it. Over its coned body fits the shell B, which is split, as
shown in Fig. 785, the splits C, D being at a right angle to splits E,
F.
It is obvious that the range of adjustment for such a shell is small,
but several diameters of shell may be fitted to one cone, the thickness
being increased to augment the diameter. The diameter of the shell
should be made to enter the work without driving, the tightening being
effected by screwing the nut up to force the shell up the cone.
[Illustration: Fig. 784.]
[Illustration: Fig. 785.]
[Illustration: Fig. 786.]
[Illustration: Fig. 787.]
[Illustration: Fig. 788.]
[Illustration: Fig. 789.]
[Illustration: Fig. 790.]
Figs. 786, 787, 788, and 789 represent an expanding mandrel designed by
Mr. Hugh Thomas, of New York City. The body B of the mandrel is
provided with a taper section _g_, and either three or four gripping
pieces _a_, _a_, _a_, _a_, let through mortises or slots in a sleeve C,
which fits the body of the mandrel at each end.
This sleeve when forced up the mandrel by the nut D, carries the
gripping pieces along the cone at _g_, and causes them to expand
outwards and grip the bore of the work, which is shown in the end view
in Fig. 788 to be a ring or washer W.
The advantage of this form is that the cone at _g_ can be easily turned
or ground to keep it true, and the gripping pieces _a_ may be fastened
in their mortises by means of the screws shown at _h_ in the end view,
and thus kept true. It is obvious that for long work there may be
gripping pieces at each end of the mandrel, as in Fig. 789, and the work
will be held true whether its bore be parallel, stepped, or taper, a
valuable feature not usually found in expanding mandrels.
[Illustration: Fig. 791.]
When a mandrel is used upon work having its bore threaded the mandrel
also must be threaded, and must abut against a radial face, as at _a_,
in Fig. 790, because otherwise the pressure of the cut would hold the
work still while the mandrel revolved, thus causing the work to traverse
along the mandrel. If the thread of the mandrel be made so tight a fit
that it will drive the work by friction it will require considerable
force to remove the work from the mandrel, so much so, in fact, that
finished pieces would be much damaged in the operation. It is better
therefore to have the work such a fit that it can be just screwed home
against the radial face of the mandrel under heavy hand pressure (if the
work be not too heavy for this, in which case a clamp may be employed).
Small work, as nuts, &c., are turned on a mandrel of this kind, which
has a stem, and fits into the cone or live spindle in the same manner as
the live centre, which will drive work up to about 1 inch in diameter
without fear of slipping. Threaded mandrels that are in frequent use
soon become a loose fit to the work by reason of the thread wear, with
the result that if the face of the work is not true with the thread, it
meets the mandrel shoulder, as in Fig. 791, and as the nut cants over,
one side as T in the figure, is turned too thick. When the nut is
reversed on the mandrel, the turned face will screw up fair against the
mandrel shoulder, and the faces of the nut, though true one with the
other, are not square with the axis of the thread, and will not
therefore bed fair when placed in position upon the work.
[Illustration: Fig. 792.]
To obviate this difficulty we have Boardman's device, which is shown in
Fig. 792. It consists of a threaded mandrel provided with a ring, with
two rounded projections A, A and B, B, on each radial face, those on one
side being at a right angle to those on the other. This ring adapts
itself to the irregular surface of the nut and by equally distributing
the pressure on each side of the nut destroys the tendency to cant over,
hence the nut may be turned true, notwithstanding any irregularity of
its radial faces, and independently of its fitting the arbor or mandrel
thread tightly.
[Illustration: Fig. 793.]
Another form of mandrel for the same purpose is shown in Fig. 793, the
mandrel being turned spherical, instead of having a square shoulder, and
the washer W being cupped to fit, so that the washer will cant over and
conform to the nut surface.
[Illustration: Fig. 794.]
The mandrel thread may be caused to fill the nut thread better if it be
provided with three or more splits A, B, C, Fig. 794, a hole D being
drilled up the centre of the mandrel, the thread may then be turned
somewhat large, the splits permitting the thread to close from the nut
thread pressure.
[Illustration: Fig. 795.]
When a mandrel is fitted to the sockets for the lathe centre, it should
have a thread and nut, as shown in Fig. 795, so as to enable its
extraction from the socket without striking it, as has been described
with reference to lathe centres.
[Illustration: Fig. 796.]
[Illustration: Fig. 797.]
Mandrels may be employed to turn work, requiring its outside diameter to
be eccentric to the bore, by the following means:--In Fig. 796, let the
centre C represent the centre of the mandrel, and D a centre provided in
each end of the mandrel, distant from C to one half the amount the work
is required to be eccentric. The mandrel must be placed with the centres
D receiving the lathe centres. In this operation great care must be
taken that a radial line drawn on each end of the mandrel, and passing
through the centre of the centres D, shall exactly meet and coincide
with the line L drawn parallel to the axis of the mandrel. If this be
not the case the work will be less eccentric at one end than at the
other. As it is a somewhat difficult matter to test this and ascertain
if the mandrel has become out of true from use, it is an excellent plan
to turn such a mandrel down at each end, as shown in Fig. 797, and draw
on it the lines L, L, which correspond to the line L L in Fig. 796. If
then a steel point be put in the lathe rest and fed in to the work, so
that revolving the latter just causes the tool point to touch the lines
L at each end, or if the tool point makes long lines as at _a_, _a_, the
two lines L, L, should intersect the lines _a_, _a_ at the centre of
their respective lengths. The lines L L should be marked as fine as
possible, but deep enough to remain permanently, so that the truth of
the eccentricity of the mandrel may be tested at any time. An equivalent
device is employed in turning the journals of crank shafts, as is shown
in Figs. 798 and 799, in which D, D are two pieces fitted on the ends of
the crank shaft, being equal in thickness to the crank throw, as shown
at A, B in the figure, so that when D, D lie in the same plane as the
crank cheeks (as when all will lie level on a plate, as in the figure)
the centres C will be in line with the journal in the crank throw.
Pieces D are broadened at one end to counterbalance the weight of the
crank, which will produce more true work than counterbalancing by means
of weights bolted to the face plate of the lathe, as is sometimes done,
causing the crank throw to be turned oval instead of round. In the case
of a double crank, however, the centre pieces cannot be widened to
counterbalance, because what would counterbalance when the centres A in
Fig. 799 were used, would throw the crank more out of balance when
centres B were used for the throw B. In this case, therefore, the centre
pieces are provided with seats for the bars E, E, which may be bolted on
to carry the counterbalancing weights, the bars being changed on the
centre pieces when the centres are changed. The bars, for example, are
shown in their position when the centres A are being used to turn up the
journal A, the necessary amount of weight for counterbalancing being
bolted on them with a set-screw through the weight.
[Illustration: Fig. 798.]
[Illustration: Fig. 799.]
The centres are steel plugs screwed tightly into the pieces D, and are
hardened after being properly centre-drilled and countersunk.
[Illustration: Fig. 800.]
To enable the pieces D to be easily put on and taken off, it is a good
plan to make the bore a tight fit to the shaft and then cut it away as
at E, as shown in Fig. 801, using set-screws to hold it.
[Illustration: Fig. 801.]
Great care is necessary in putting in the work centres, since they must,
if the crank throws are to be at a right angle one to the other, as for
steam engines, be true to the dotted lines in figure, these dotted lines
passing through the centre of the axle and being at a right angle one to
the other. If the thickness of the centre pieces are greater than the
crank throws they may be adjusted as in Fig. 800, in which B, B´
represent the centre pieces, and C the crank, while S is a
straight-edge; the edge surfaces of B, B being made true planes parallel
to each other on each arm, and parallel to the axial line of the bore
fitting the end of the crank axle.
The straight-edge is pressed at one end, as at F, firmly to an edge face
of B, the other end being aslant so as not to cover the edge of the
piece B´ at the opposite end of the crank (as shown at G, Fig. 801).
While being so pressed the other end must be swung over the end arm of
B´ at the opposite end of the crank, when the edge of the straight-edge
should just meet and have slight contact with the surface of the edge
of B´. This test should be applied to all four edges of B, and in two
positions on each, as at G, H--I, J, and for great exactitude may be
applied from each end of the crank. It is to be observed, however, that
the tests made on the edges standing vertical, as at I, J, will be the
most correct, because the straightness of the straight-edge is when
applied in those positions not affected by deflection of the
straight-edge from its own weight.
In shops where such a job as this is a constantly recurring one
attachments are added to a press of some kind, so that the axle and the
pieces B may be guided automatically and forced to their proper places,
without requiring to be tested afterwards.
[Illustration: Fig. 802.]
When the work is sufficiently long or slender to cause it to sag and
bend from its own weight, or bend from the pressure of the cut, it is
supported by means of special guides or rests. Fig. 802 represents a
steady rest of the ordinary pattern; its construction being as
follows:--F is a base fitting to the [V]s of the lathe shears at F, and
capable of being fastened thereto by the bolt C, nut N, and clamp A. F´
is the top half of the frame, being pivoted at P to F, the bolt P´
forming the pivot for both halves (F and F´), of the frame, which may be
secured together by the nut of P´. On the other side of the frame the
bolt is pivoted at _b_ to F. This bolt passes through an open slot in
F´, so that its nut being loose, it may swing out of the way as denoted
by the arrow _e_, and the top half frame _f´_ may be swung over in the
direction of arrow _g_, the centre of motion or pivot being on the bolt
P´. With F´ out of the way the work may be placed within the frame, the
nut of B and also that of P´ may be tightened up so as to lock the two
halves of the frame firmly together.
On this frame and forming a part of it are the three ways, G G´ G´´,
which contain cavities or slide ways to which are fitted and in which
may slide the respective jaws J, and to operate these jaws are the
respective square-headed screws S, which are threaded through the tops
of the respective ways G, G´, and G´´. The screws are operated until the
ends of the jaws J have contact with the work W, and hold it axially
true with the line of centres of the lathe, or otherwise, as the nature
of the work may require. When adjusted the jaws are locked to the frame
by means of the bolts D, which are squared to fit in the rectangular
openings, shown at _h_ in the respective jaws, so as to prevent the
bolts from rotating when their locking nuts _d_ are screwed home.
As an example of the use of this device as a steadying rest, suppose a
long shaft to require turning from end to end and to be so slight as to
require steadying, then a short piece of the shaft situated somewhat
nearer the live centre than the middle of the length of the work is
turned upon the work, so that this place shall be round and true to
receive the jaws, or plates _p_, and revolve smoothly in them. The jaws
are then adjusted to fit the turned part a close sliding fit, but not a
tight fit, as that would cause the jaws to score the work. To prevent
this even under a light pressure of contact, oil should be occasionally
supplied. This steadies the work at its middle, preventing it from
springing or trembling when under the pressure of the cut.
By placing the steady rest to one side of the middle of the work length,
at least one half of that length may be turned before reversing the work
in the lathe centres. After reversing the work end for end in the lathe
centres, the jaws, or plates _p_, are adjusted to the turned part, and
the turning may be completed.
In adjusting the plates _p_ to the work, great care is necessary or they
will spring the work out of its normal line of straightness, and cause
it to be out of parallel, or to run out of true in the middle of its
length, as explained in the remarks referring to the cat head shown in
Fig. 809.
The plates _p_ should be gripped to the frame by the nuts with
sufficient force to permit them to be moved by the set-screw S under a
slight pressure, which will help their proper adjustment. They should
also be adjusted to just touch the work, without springing it, the two
lower ones being set up to the work first, so that their contact shall
serve to relieve the work of its spring or deflection, due to its own
weight. This is especially necessary in long slender spindles, in which
the deflection may occur to a sensible degree.
If the work does not require turning on its full length, the steady rest
may be applied but a short distance from the length of the part to be
turned, so as to hold the work more steadily against the pressure of the
cuts.
Steady rests are often used to support the end of work without the aid
of the dead centre, but it is not altogether suitable for this class of
work, because it has no provision to prevent the work from moving
endways and becoming loose on the dead centre. A provision of this kind
is sometimes made by tying the work driver to the face plate or to the
pins driving the work driver or dog, or bolts and plates holding the
work driver towards the lathe face plate; but these are all
objectionable in that unless the pressure thus exerted be equal, it
tends to spring or bend the work.
Another method of preventing this is to drive the work by means of a
universal chuck; but this again is objectionable, because the jaws of
these chucks do not keep dead true under the wear, and indeed if made to
run concentrically true (in cases where the chuck has provision for that
purpose) the gripping surfaces of the chuck jaws have more wear at the
outer than at the inner ends, hence those surfaces become in time
tapering. Again the jaws wear in time so easy a fit in their radial
slots that they spring under pressure, and the wear not being equal, the
amount of spring is not equal, so that it is impracticable to do dead
true work chucked in this way.
The reasons that the chuck jaws do not wear equal in the radial slots
may be various, as the more frequent presence of grit in one than in the
other, less perfect lubrication, inequalities in the fit, less perfect
cleaning, and so on, so that it is not often that the wear is precisely
equal. In addition to these considerations there are others rendering
the use of the steady rest in some cases objectionable; suppose, for
example, a piece of cylindrical work, say 6 feet long, to have in one
end a hole of 2 inches diameter, which requires to be very true (as, for
example, the cone spindle for a lathe). Now let the face plate end be
driven as it may, it will be a difficult matter to set the steady rest
so as to hold the other end of the work in perfect line, so that its
axial line shall be dead true with the line of lathe centres, because
the work will run true though its axial line does not stand true in the
lathe.
Here it may be added that it will not materially aid the holding of the
work true at the live centre end, by placing it on the live centre and
then tightening the universal chuck jaws on it, because the pressure of
those jaws will spring it away to some extent from the live centres.
This will occur even though the work be placed between the two lathe
centres, and held firmly by screwing up the dead centre tight upon the
work, before tightening the chuck jaws upon the work, because so soon as
the pressure of the dead centre is removed, the work will to some extent
relieve its contact with the live one.
If the jaws of the chuck are not hardened, they may be trued up to suit
a job of this kind as follows:--A ring (of such a size that when gripped
in the outer steps of the chuck jaws, the inner steps will be open to an
amount about equal to the diameter of the work at the live centre end)
may be fastened in the chuck, and the inner ends of the jaws may be
turned up with a turning tool, in which case the jaws will be made true
while under pressure, and while in the locations upon the chuck in which
they will stand when gripping the work, under which conditions they
ought to hold the work fairly upon the live centre. But even in this
case the weight of the work will aid to spring it, and relieve it from
contact with the live centre.
[Illustration: Fig. 803.]
Now let us suppose that the piece of work is taper on its external
diameter at each end, even truing of the chuck jaws will be of no avail,
nor will the steady rest be of avail, if the taper be largest at the
dead centre end. Another form of steady rest designed to overcome these
objectionable features is shown in Fig. 803. In this case the stand that
is bolted to the lathe bed is bored to receive a ring. This ring is made
with its middle section of enlarged diameter, as denoted by the dotted
circle C. Into the wide part of the stand fits a ring F, its external
diameter fitting into C. The ring carries the jaws, hence the ring is
passed over the work, and is then inserted into the stand, while the
work is placed between the lathe centres.
The ring revolves with the work and has journal bearing in the stand,
the enlarged diameter C preventing end motion. There is nothing here to
take up the lost motion that would in time ensue from the wear of the
radial faces of the ring, hence it is better to use the cone-plate shown
in Fig. 805.
[Illustration: Fig. 804.]
When, however, the work will admit of being sufficiently reduced in
diameter, it may be turned down, leaving a face F in Fig. 804, that may
bear against the radial faces of the jaws of the steady rest; or a
collar may be set upon the work as in Fig. 804 at C. But these are
merely makeshifts involving extra labor and not producing the best of
results, because the radial face is difficult to keep properly
lubricated, and the work is apt to become loose on the live centre.
[Illustration: Fig. 805.]
For these reasons the cone plate shown in Fig. 805 is employed; A is a
standard fitting the shears or bed of the lathe and carrying the
circular plate C by means of the stud B, which is fitted so as to just
clamp the plate C firmly to the frame A when the nut of B is screwed
firmly home with a wrench.
The plate C contains a number of conical holes, 1, 2, 3, &c., (as shown
in section at D) of various diameters to suit varying diameters of work.
The frame is fitted to the lathe bed so that the centre stud B stands
sufficiently out of the line of lathe centres to bring the centres of
the conical holes true with the line of lathe centres. The centres of
the conical holes are all concentric to B. Around the outer diameter of
the cone plate are arranged taper holes G, so situated with reference to
the coned holes that when the pin, shown at G in the sectional view,
will pass through the plate and into the frame A as shown, one of the
coned holes will stand axially true with the line of lathe centres.
Hence it is simply necessary to place one end of the work in the live
centre, with a work driver attached in the usual manner; to select a
coned hole of suitable size; to move the frame A along the lathe bed
until it supports the overhanging end of the work in a suitably sized
coned hole without allowing the work any end motion, and to then fasten
the frame A to the lathe bed, and the work will be ready to operate on.
The advantages of this device are that the pin shown at G in the
sectional view holds the conical hole true, and thus saves all need of
adjustment and liability to error, nor will the work be sprung out of
true, furthermore the tool feed may traverse back and forth, without
pulling the work off the live centre. With this device a coarse pitch
left-hand internal thread may be cut as easily as if it were an external
thread and the work was held between the lathe centres, heavy cuts being
taken which would scarcely be practicable in the ordinary form of steady
rest.
The pins B and G and the coned holes should be of cast steel hardened,
so as to avoid wear as much as possible. The plate may be made of cast
iron with hardened steel bushes to fit the coned holes.
It is obvious that the radial face of the work at the cone plate end, as
well as the circumference, must be trued up, so that the work end may
have equal contact around the bore of the coned rings.
[Illustration: Fig. 806.]
[Illustration: Fig. 807.]
Figs. 806 and 807 represent a class of work that it would be very
difficult to chuck and operate on without the aid of a cone plate. The
former requires to have a left-hand thread cut in its bore A, and the
latter a similar thread in end A. A universal chuck cannot be used to
drive the work, because in the former case it would damage its thin
edge, and in the latter the jaws would force the work out of the chuck;
a steady rest cannot be used on the former on account of its being
taper, while if used on the latter there would be nothing to prevent the
work from moving endwise, unless a collar be improvised on the stem,
which on account of the reduced diameter of the stem would require to
be made in two halves. It can, however, be driven on the live centre by
a driver or dog, and supported at the other end by the cone plate
without any trouble, and with an assurance of true work.
[Illustration: Fig. 808.]
Fig. 808 represents a form of steady rest designed by Wm. MacFaul, of
the Freeland Tool Works, for taper work. The frame affords journal
bearing to a ring A, having four projections B, to which are a close but
easy sliding fit, the steadying jaws C. These are held to the work or
cue blank W by the spiral springs shown in the projections or sockets B,
which act against the ends of C. It will be observed that the work being
square could not move in any direction without moving sideways the two
of the steadying jaws C which stand at a right angle to that direction.
But the jaws C fit the bore of the sockets, and cannot, therefore, move
sideways; hence it is evident that the work is firmly supported,
although the steadying jaws are capable of expanding or contracting to
follow the taper of the blank cue or other piece of work. This enables
the steady rest to lead the cutting tool instead of following it, so
that the work is steadied on both sides of the tool. Obviously, the
stand may be fastened to the leading side of the lathe carriage or
fitted upon the cross-slide, as may be most convenient.
[Illustration: Fig. 809.]
To steady work that is unturned and of so great a length that it springs
too much to permit of its being turned true, the sleeve or cat head
shown in Fig. 809 is employed; it may contain three or four screws C, to
true it upon the work. The body B is turned true.
The set-screws are so adjusted upon the work, that the outside runs
quite true from end to end. The jaws of the steady rest are then set to
just touch the circumference of the sleeve, care being taken that their
pressure does not spring the axial line of the work out of its normal
straight line. If the shaft is to be turned from end to end, the cat
head should be placed sufficiently to one side of the centre of the
length of the work and nearer the live centre, that the lathe tool may
turn up the work for a distance of at least half its length, or slightly
more than half. One half of the work being turned, the shaft is reversed
end for end in the lathe, when the cat head may be moved to envelop the
turned part, and again set true, or the jaws of the steady rest may be
set direct upon the work; in this latter case, however, the friction
between the jaws and the work will be apt to leave rings or marks upon
the latter.
If the cat head is not set to run quite true upon the work, the latter
will not run true when the steady rest is removed, and if the jaws of
the steady rest spring the axial line of the work out of its normal
straightness, the work will be turned either larger or smaller in
diameter in the middle of its length, according to the direction in
which the work is sprung.
Suppose, for example, that the work is sprung laterally towards the tool
point, then the work will be turned smaller in the middle, or if the
work were sprung laterally in the opposite direction, it would be turned
larger in the middle than at the ends. If the work is sprung vertically
so as to approach or recede from the lathe bed, the amount of the error
will be less than if it were sprung laterally, and the nature of the
error will depend upon the height of the cutting tool with relation to
the work. If, for example, the point is above the centre of the work,
and the latter is sprung towards the lathe bed, the work will turn of
largest diameter in the middle of its length; or with the tool point
placed at the centre of the work, the same result will follow, whether
the work be sprung up or down; but if the work be sprung up or away from
the lathe bed, and the tool point be placed above the centre, the
diameter of the work will be turned smaller than that at the ends.
[Illustration: Fig. 810.]
When the work is to be turned from end to end or for a considerable
distance, a follower rest such as shown in Fig. 810 should be employed,
being similar to the steady rest shown in Fig. 802, except that it is
open in front, and being fastened to the slide rest carriage, of course
travels with the tool; hence the plates P may be either directly in
front of the tool or following it, but if the work W has been turned
true and parallel, the plates P may be in front of the tool, or rather
may lead it.
[Illustration: Fig. 811.]
[Illustration: Fig. 812.]
The follower rest should always be set to the work when as near as
practicable to the dead centre, in which case it will be easier to set
it without springing the work.
For work of small diameter for which the plates P would be too large,
and therefore in the way, the plate P, Fig. 811, may be used, being
bolted to the follower rest. For work of larger diameter the device
shown in Fig. 812 is sometimes used. It consists of a plate P with a
cap C, and bolts for holding the bearings B, B. These bearings are bored
slightly larger in diameter than the finished diameter of the work.
The advantage of the use of this device is that bearings of the
requisite bore having been selected they may be inserted and adjusted a
proper fit to the work before P is fastened to the follower rest, thus
avoiding the liability of being either too tight or too loose as may
happen when the plates cannot be moved or rotated to test the fit.
Another and great advantage is that if after the adjustment of the
bearings B, B to the work, the plate P is carefully bolted to the
follower rest, the liability of springing the work is eliminated, hence
truer work will be produced.
[Illustration: Fig. 813.]
A representative of another class of follower rest is shown in Fig. 813,
the hub H is accurately bored to receive collars or rings of various
diameters of bore to suit the work. The bore of H may be made to stand
axially true with the lathe centres, and thus avoid the trouble of
setting, by employing the steady pin S, which, being a close fit in the
follower rest and in the lathe carriage will bring the rest to its
proper distance from the lathe centres, where it may be secured by the
bolt B, which may screw into the metal of the carriage or operate to
lift a wedge or guide slip so as to grip the [V]-slide of the carriage
and take up any lost motion between the slide in the rest and that in
the lathe carriage.
[Illustration: Fig. 814.]
Fig. 814 shows a follower rest in position on the cross slide of a
lathe.
CHUCKS AND CHUCKING.
There is a large class of small work that could be held between the
lathe centres, but that can be more conveniently held in chucks. Chucks
are devices for holding work to the live spindle, and may be divided
into classes as follows:
1st. Those in which the work is secured by a simple set-screw.
2nd. Drill chucks, which are applied mainly to drive drills, but which
may also be used to drive very small work to be operated upon by cutting
tools, the mechanism causing the jaws to move simultaneously to grip or
release the work.
3rd. Independent chucks, in which the jaws are operated separately.
4th. Universal chucks, which are larger than drill chucks, and in which
the jaws operate simultaneously.
5th. Combination chucks, in which the jaws may be operated either
separately or simultaneously as may be required.
[Illustration: Fig. 815.]
Referring to the first, Fig. 815 represents a simple form of set-screw
chuck, the stem S fitting into the live centre hole, and the outer end
being pierced to receive a drill shank, and the iron from which a piece
of work may require to be turned, which is secured in the chuck by the
set-screw B. In the case of drill or other cutting tools, however, it is
better that they be provided with a flat place A, to receive the
set-screw pressure, and enable it to hold them more securely. The
objections to this class of chuck are threefold: First, each chuck is
suitable for one diameter of work only; secondly the screw head B is in
the way; and thirdly, the set-screw pressure is in a direction to set
the work out of true, which it will do unless the work is a tight fit to
the bore of the chuck. In this case, however, it is troublesome to
insert and remove the drill, unless the bore of the socket is relieved
on the half circumference nearest to the set-screw, as shown at C in the
end view, in which case the efficiency of the chuck is greatly enhanced.
[Illustration: Fig. 816.]
Referring to the second class they are made to contain either two or
three jaws.
[Illustration: Fig. 817.]
When two jaws are employed they are made to slide in one slideway, and
are operated therein by a right and left-handed screw, causing them to
simultaneously advance or recede from the chuck axis. Fig. 816
represents a chuck of this class, the jaws fitting one into the other to
maintain each other in line, and prevent their tilting over from the
pressure.
In scroll chucks the mechanism for operating the jaws is constructed
upon two general principles. The first may be understood from Fig. 817,
in which the body of the chuck is provided upon its end face with a
scroll C, with which the ends of the jaws A engage. These jaws fit into
radial slots in the shell E, which is capable of rotation upon B and is
held thereto by the cap D; hence rotating E carries around the jaws A,
and the thread C causes them to approach or recede from the chuck axis,
according to their direction of rotation.
[Illustration: Fig. 818.]
The second general principle upon which small drill chucks are
constructed may be understood from Fig. 818, in which C may be taken to
represent the end of a lathe spindle or a stem fitting into the live
centre hole in the same. At the other end it is to receive the shell D
which screws upon it. D is coned at the outer end of its bore, and the
jaws E are made to fit the cone, and it is obvious that if D be rotated
to screw farther upon C, the coned bore of D will act to force the jaws
E nearer to the chuck axis and cause them to close upon and grip the
work. To operate D it is knurled or milled at G, or it may have pin
spanner holes as at H. In this class of chuck it is essential that the
direction of rotation of D to close the jaws must be opposite to that in
which the drill rotates, otherwise the resistance of the work against
the jaws would cause D to rotate upon C, and the work to become released
from the jaw grip. Furthermore, as the larger the work the more severe
the duty in driving it, it is usually provided by the construction of
such chucks that the jaws shall be opened to their maximum when at their
nearest approach to the body (as C) of the chuck, and shall close as
they move outward or away from the same. This principle of moving the
jaws radially by means of a cone sliding upon a cone is applied in
numerous ways, thus sometimes the jaws are provided with wings that
slide upon a cone or in slide ways that are at an angle to the chuck
axis.
[Illustration: Fig. 819.]
[Illustration: Fig. 820.]
[Illustration: Fig. 821.]
Figs. 819, 820, and 821 represent Gage's patent chuck, in which the
gripping surfaces of the jaws are serrated to increase the grip, and to
further secure the same object the jaws move at an angle instead of in a
radial line, so that the body of the jaws is more directly in the line
of strain, and therefore resists it better. The serrations are
left-handed, so that the tendency is to force the drill forward and
toward the cut, supposing them to act as a nut and screw upon the drill
shank. The jaws are supported by the central cylindrical piece that
contains them out to the extreme end, and have in addition a lug which
slides in radial grooves. Fig. 819 is a side elevation, with a piece of
the shell removed to show the jaw and its slide way, and an end view
showing the arrangement of the jaws. Fig. 820 is a sectional side
elevation, and Fig. 821, two views of the jaws removed from the chuck; A
represents the jaws with the lug E to slide in the radial slots provided
in B. The wings A´ of the jaws slide in the ways in B, the ways passing
through the opening F in Fig. 821; C is the cone for causing the jaws to
open and close radially. The driving piece H has A left-hand thread
operating in B. It also has a collar abutting over one side against the
end of B, and secured on the other by the cap I, which threads into the
shell G. A pin in C secures it to the cap I, so that if rotated both
move together. On the other hand, if H be rotated and G is held
stationary, the thread on H operates on B as a nut, causing it to slide,
carrying the jaws with it, and the jaws are simultaneously opened or
closed according to the direction of rotation of H. Fig. 819 shows the
jaws screwed partly out, and therefore partially closed, while in Fig.
820 the jaws are shown within the chuck, and therefore opened to their
fullest extent.
[Illustration: Fig. 822.]
Figs. 822 and 823 represent a chuck employed by the Hancock Inspirator
Co., of Boston, for very true work. This chuck will not get out of true
by wear, and holds brass work against a good lathe-cut without indenting
it.
Fig. 822 shows the chuck complete. Fig. 823 is a mid-section of chuck
complete. Fig. 824 is a side and an end of the work-gripping piece. The
chuck is composed of three pieces, A, B and C. Piece A screws upon the
lathe spindle and is bored to receive C; piece B screws upon A and
receives the outer end of C, which is provided with a double cone D E,
and is split nearly its full length at three places, one of which is
shown at F, so that when B is screwed upon A the two cones upon A, B
compress C, and cause the diameter of its bore to decrease and grip the
work. The splits F are made long, so that C shall not close at its outer
end only, but on both sides of the cones, and thus grip the work
parallel.
There are several advantages in this form of construction; thus the
parallel bore of A, in which C fits, is not subject to strain or wear,
and therefore remains true and holds C true. Furthermore, B has no
tendency to wear out of true, because it fits upon A at the part G, as
well as at its threaded end, while the cone E of C also acts to keep it
true. As B is screwed up with a wrench fitting its hexagon exterior, the
work can be held against any amount of cut that the lathe will drive.
[Illustration: Fig. 823.]
It is obvious that the capacity of the chuck, so far as taking in range
of different diameters, is quite limited, but the excellence of its
execution far more than compensates for this when work is to be turned
out true and correct to standard gauge.
To increase the range of capacity of the chuck, the split piece only
needs to be changed. Before hardening the split piece the jaws should be
sprung well apart, so that they will spring open when released by
unscrewing the outside shell to release the work and insert another
piece.
[Illustration: Fig. 824.]
In proportion as the diameter of the work is increased it requires to be
more firmly held, and the chucks are made with jaws moved by screws
operated by wrench power. These chucks are made with two, three, or four
jaws, and the bite of the jaw is shaped to suit the nature of the work,
the gripping area being reduced for very small work, and serrated
parallel to the chuck axis so as to form gripping teeth for firmly
gripping rough work, as shown in some of the following examples:--
[Illustration: Fig. 825.]
[Illustration: Fig. 826.]
Figs. 825 and 826 represent the Horton two-jawed chucks with false or
slip jaws, which are removable so that jaws of various shapes in the
bore may be fitted to the same chuck, thus enabling the jaws to be
varied to suit the shape of the work to be held. The jaws are secured in
place by the pins shown.
[Illustration: Fig. 827.]
Fig. 827 shows a two-jawed solid jaw chuck, the bite of the jaws being
made hollow, so as not to mark the surface of the work, while they will
hold it very firmly.
In Fig. 828 is shown what is termed a box-body two-jawed chuck, which is
mainly used by brass turners. The object of this form of body is to
permit the flanges, &c., of castings escaping the face of the chuck.
Fig. 829 also represents a two-jawed chuck, the body being cylindrical,
and having a [V]-groove at A to receive the work. The screws C, D may
act independently of each other, or a continuous screw may be used,
having, as in the figure, a left-hand thread at C, and a right-hand one
at D, so that the jaws move simultaneously when the screw is operated.
The difference between these two methods being as follows:--
When one screw is used the jaws will hold the work so that the centre of
rotation will be midway between the points of contact of the jaws of the
chuck and the work, hence work cannot be set eccentrically, unless
pieces of iron are inserted between it and one of the jaws. When two
screws are used the jaws may be operated separately, and one jaw may be
set to such distance from the centre of rotation as the necessities of
the work may require; but in this case more adjustment is required to
set either square or cylindrical work to rotate on its axis than when
the jaws operate simultaneously as with a right and left-hand screw. It
is obvious that the axial line of the screw or screws must stand
parallel with the plane of the face F. It will be observed that the back
of each jaw is cut away at B: this serves two purposes, first it permits
of a piece of work having a small flange, head or projection being held
in the [V]s of the jaws; and secondly, it equalizes the wear on the jaws
of the chuck, because in jaw chucks generally there is more wear at the
outer than at the inner end of the jaws, because work shorter than the
length of the jaws, or requiring to be held as far out from the jaws as
possible, does not have contact at the back end of the work holding jaw
faces, hence the jaws are apt to wear, in course of time, taper. By
cutting away the jaws at the back, the tendency to unequal wear is
greatly reduced, hence this plan is adopted to a more or less degree in
the dogs or jaws of all chucks, being in many cases merely a small
recess from 1/16 to 1/8 inch deep only.
[Illustration: Fig. 828.]
When the jaws have a [V]-groove as in the cut, the face F of the chuck
does not form a guide in setting the work, the truth of the [V]-grooves
being solely relied upon for that purpose.
[Illustration: Fig. 829.]
[Illustration: Fig. 830.]
The form of two-jawed chuck shown in Fig. 830 is intended for square or
rectangular work, and is mainly used by wood workers. It may be operated
by a right and left-hand screw, but is generally preferred with
independent screws. The face F of the chuck may be employed to serve as
a guide in setting the work as shown in the cut, in which W represents a
piece of work held between the jaws A, A, and resting against the face
F, which therefore serves as a guide against which to set the work to
insure that its axial line shall stand parallel with the face F, or in
other words at a right angle to the line of centres of the lathe.
[Illustration: Fig. 831.]
In Fig. 831 is an example of a machinist's two-jawed chuck. The jaws are
operated simultaneously by a right and left-hand screw. The jaws are
provided with slides to receive the two separate pieces shown in figure,
which may be made to suit the form of special work. The two screws shown
on each side of the chuck face are to support a piece of work that is
too large to be otherwise held firmly by the chuck. These screws may be
operated by screw-driver wrench, to enable the face of the work to rest
on them, and therefore be supported parallel or true with the chuck
face. The jaws may be turned end for end in their slide ways as shown in
Fig. 833, to enable them to grip work of small diameter, the separate
pieces shown in Fig. 832, being placed on the jaws for such small pieces
as drills, &c.
[Illustration: Fig. 832.]
In the larger sizes, lathe chucks are provided with either three or
four jaws, which are caused to operate either independently or
simultaneously, and in some cases the construction is such that the same
chuck may be used as an independent or as a universal one at will, in
which case they are termed combination chucks. Concerning the number of
jaws it may be observed that a three-jawed chuck will hold the work with
an equal pressure on all three jaws, whether it be cylindrical or not,
but in a four-jawed chuck the jaws will not have an equal grip upon the
work, unless the same be either cylindrically true or square, hence it
is obvious that a three-jawed chuck is less liable to wear out of true,
and is also preferable for holding unturned cylindrical work, while it
is equal to a four-jawed one for true, but unsuitable for square work.
[Illustration: Fig. 833.]
[Illustration: Fig. 834.]
Fig. 834 represents the construction of the Horton chuck. Upon the
screws that operate the jaws are placed pinions that gear into a
circular rack, so that by operating one jaw with a wrench the rack is
revolved and the remaining jaws are operated simultaneously. The chuck
being constructed in two halves, the rack may be removed and the jaws
operated separately, or independently as it is termed.
[Illustration: Fig. 835.]
Fig. 835 represents one of the jaws with its operating screw and pinion
removed from the chuck. The gripping surfaces of the steps in the jaws
are serrated to increase their grip upon the work, and the nuts A, A,
against which the works rests, are ground true with the face of the
chuck. The corner between the faces A and the bite or gripping surfaces
of the jaws are recessed so that the work cannot bind in them, but will
bed fairly against the faces A, A, which serve to set the work against
and hold it true instead of the face of the chuck.
[Illustration: Fig. 836.]
Fig. 836 represents a Horton chuck for work up to four inches diameter.
[Illustration: Fig. 837.]
Fig. 837 represents a similar chuck for all sizes between 4 and 15
inches, the designated sizes of the chuck being 6, 9, and 12 inches,
these diameters being the largest the chucks will take in.
[Illustration: Fig. 838.]
Fig. 838 represents a Horton chuck with outside bites for opening out to
grip the bores of rings or other hollow work.
The term scroll chuck is applied to universal chucks in which the jaws
are operated throughout their full range by means of a scroll thread
such as was shown in Fig. 817. The objection to this form is that the
threads on the jaws cannot be made to have a full bearing in the scroll
thread.
[Illustration: Fig. 839.]
In Fig. 839, for example, let A A and B B represent grooves between the
scroll threads, and if the thread on the jaws be made to the curve and
width of A A, it would not pass in that of B B, and _vice-versâ_, and it
would take but five revolutions of the thread to pass a nut thread from
A to B. To overcome this difficulty the jaw threads are not made correct
to either curvature but so formed as to fit at points C, D, E, when in
the groove A and at points F, G, H, when in groove B. This obviously
reduces their bearing area and therefore their durability. To avoid this
defect the jaws of many universal chucks are operated by screws in the
same way as independent jaw chucks, but provision is made whereby the
operation of any one of the jaw screws will simultaneously operate all
the others, so that all the jaws are moved by the operation of one
screw.
Thus in the following figures is shown the Sweetland chuck.
[Illustration: Fig. 840.]
Fig. 840 represents the chuck partly cut away to show the mechanism,
which consists of a pinion on each jaw screw, and a circular rack
beneath. The rack is shown in gear with a pinion at O, and out of gear
with a pinion at C, which is effected as follows:--
The rack is stepped, being thicker at its outer diameter, and the thin
part forms a recess and the shoulder between the thick and thin part
forms a bevel or cone. Between this circular rack and the face of the
plate at the back of the chuck is placed, beneath each jaw, a cam block
bevelled to correspond with the bevelled edge of the recess in the ring.
The cam block stem passes through radial slots in the face of the chuck,
so that it can be moved to and from the centre of the chuck. When it is
moved in, its cam head passes into the recess in the ring rack, which
then falls out of gear with the jaw screw pinion; but when it is moved
outward the cam head slides (on account of the bevelled edges) under the
ring rack and puts it in gear with the jaw screw pinion. Thus, to change
the chuck from an independent one to a universal one all that is
necessary is to push out the bolt heads on the cam block stems, the said
heads being outside the chuck. The washers beneath these heads are
dished to give them elasticity and enable them to steady the cams
without undue friction.
[Illustration: Fig. 841.]
To enable the setting of the jaws true for using the chuck as a
universal one, after it has been used as an independent one, a ring is
marked on the face, and to this ring the edges of all the jaws must be
set before operating the cams radially to put the rack ring in gear. In
Fig. 841 a three-jawed chuck on this principle is shown acting as an
independent one to hold an eccentric. On account of the spring of the
parts, which occurs when the strain is transmitted from one part to
another, it is desirable when using the chuck as a universal one to
first operate one screw to grip the work and then pass to the others and
operate them so that they may receive the pressure direct from the screw
head and not entirely through the medium of the rack, and there will be
found enough movement of the screws when thus operated to effect the
object of relieving the rack to some extent from strain.
[Illustration: Fig. 842.]
[Illustration: Fig. 843.]
[Illustration: Fig. 844.]
Figs. 842, 843, 844, and 845 represent Cushman's patent combination
chuck, in which each jaw may be operated independently by means of its
screw thread, or a circular rack may be made to engage with the
respective pinions, as shown in Fig. 844, in which case operating any
one of the screws operates simultaneously all the jaws. The method of
engaging and disengaging is shown in Fig. 845. C represents the circular
rack and D a circular ring beneath it. This ring is threaded on its
circumference, screwing into the body of the chuck, so that revolving it
in one direction moves the circular rack forward and into mesh with the
pinions, while revolving it backward causes the rack to recede from the
pinions. To operate this ring the lug shown near the top of the chuck in
figure is simply pushed in the required direction, while to lock the
ring when out of gear with the pinions the spring catch shown on the
left of that figure is moved radially. When the rack is in gear, the
chuck is a universal one, all the jaws moving simultaneously and
equally, whether they be set in such position in their slots as may be
necessary to grip an oval or round piece of work; when the rack is out
of gear the jaws may be moved by their respective screws so as to run
true as for round work, or to hold the work to any degree of
eccentricity required.
[Illustration: Fig. 845.]
The jaws may be reversed in their slots and operated simultaneously as a
universal chuck, or independently as a simple jaw chuck.
It is obvious that the truth of the jaws for concentricity may be
adjusted within the degree of accuracy due to the number of teeth in one
pinion divided into the pitch of the jaw operating screw, because each
screw may be revolved separately to bring each successive tooth into
mesh until the greatest obtainable jaw truth is secured.
[Illustration: Fig. 846.]
Fig. 846 represents a front, and Fig. 847 a sectional view, of the
Westcott combination chuck. F is the main body of the chuck screwing on
to the lathe spindle. F carries the annular ring D, which has a thread
on its face, as shown. D is kept in place by the ring E, which screws in
an annular recess provided in the back of the chuck. C is a box fitting
in the radial slots of the chuck. The back of the box C meshes into the
radial thread on D, hence, when D is revolved, the boxes C move radially
in the slots. Now the boxes C afford journal bearing to, and carry the
worm or screws B as well as the chuck jaws A, hence revolving D operates
the jaws simultaneously and concentrically as in a scroll or universal
chuck. By means of the screws B, the jaws may be operated individually
(the boxes C and ring D remaining stationary) as in an independent jaw
chuck.
[Illustration: Fig. 847.]
Suppose, now, the jaws to have been used independently, and that they
require to be set to work simultaneously and concentric to the centre of
the chuck, then the screws B may be operated until the jaws at their
outer edge are even with the circumference of the chuck (or, if the jaws
are nearer the centre of the chuck, they may be set true with a
pointer), and the ring D may be operated. In like manner, if a number of
pieces of work are eccentric, the screws B may be used to chuck the work
to the required eccentricity, and when the next piece is to be chucked
the ring D may be operated, and the chuck will be used as a universal
one, although the shape of the work be irregular, all that is necessary
being to place the same part of the work to the same jaw on each
occasion.
[Illustration: Fig. 848.]
The faces of the jaws of jaw chucks when they are true with the face of
the chuck (or what is the same thing, run true, and are at a right angle
to the axial line of the lathe centres), form guides wherefrom to set
the work true, but this will only be the case when they remain true,
notwithstanding the pressure of the jaws upon the work. Their truth,
however, is often impaired by their wear in the chuck slots which gives
them play and permits them to cant over. Thus in Fig. 848 is shown a
chuck gripping a piece of work W, and it is obvious that to whatever
extent the jaws may spring, or have lost motion in the ways or slots in
the chucks, the jaws will move in the direction of the dotted lines A A,
the face of the jaw then standing in the direction of dotted lines B B,
instead of being parallel to the chuck face. If the spring or wear of
the mechanism were equal for each jaw, the work would be held true,
notwithstanding that the jaws be out of line, but such is not found to
be the case, and as a result the work cannot be set quite true.
[Illustration: Fig. 849.]
When the jaws are applied within the work, as in Fig. 849 (representing
the jaws of the chuck within the bore of a ring or piece of work W), the
jaws spring in the opposite direction as denoted by dotted lines C, C,
and when the jaws are locked to the work the latter moves in the
direction of D and away from the chuck face. It will be observed that
there is no true surface to put the face of the work against in either
case.
[Illustration: Fig. 850.]
This is remedied in independent dog chucks by the construction shown in
Fig. 850, in which each jaw has a square A, fitting in the grooves of
the chuck, and a nut and washer at B secure the jaw to the face of the
chuck so that the lost motion due to wear of the parts may be taken up.
[Illustration: Fig. 851.]
[Illustration: Fig. 852.]
The Judson patent chuck is designed to overcome this difficulty, and is
constructed as shown in Figs. 851 and 852, the former being a face view
and the latter a sectional edge view of the chuck.
The jaws A of the chuck are hollow, and the nut instead of being solid
in the jaw is a separate piece, having two wings, the outer of which
bears upon a pin in the jaw, while the inner bears upon an inclined
surface as plainly shown in the cut, so that the pressure of the screw
is distributed equally upon the pin and the inclined surface. The nut B
being below the centre of the pin and inclined surface causes the
pressure to throw the jaw fair against the face of the chuck, hence the
faces of the jaws will serve (equally as well as the surface of the
chuck) as a guide to set the work against.
From the short length of gripping surface on the jaws of jaw chucks,
they are incapable of holding work of any greater length than, say,
about 6 inches, without the aid of the dead centre at the other end of
the work; but if the dead centre be used in this way the work will be
out of true, unless the jaws of the chuck be quite true, which is not
always the case, especially after the chuck has been much in use.
Furthermore, it is at times a difficult if not even an impracticable job
to set work quite true in this way.
For special work made in quantities the form of the chuck may be varied
to conform to the special requirements of the work. The variety of
chucks that may thus be formed is obviously as infinite as the
variations in form of the work. Thus threaded work may be screwed into
threaded chucks, or cylindrical work may be driven into bored blocks
forming chucks, or a ring may be chucked and then used as a mandrel to
drive the work by friction.
[Illustration: Fig. 853.]
An excellent example of special chuck is shown in Fig. 853, representing
a chuck for holding piston rings. It resembles a face plate screwing on
the live spindle at B, and having 8 radial dogs or jaws A, let into the
face D, and secured thereto, when adjusted by the bolts and nuts E. A
mandrel is fast in the centre of the chuck carrying the cone C, upon
which rest the cone surfaces on the ends of the dogs A, so that screwing
up C, by means of the nut shown, throws the dogs A outwards, causing
them to grip the inside of the piston ring as shown in the face view of
the chuck.
[Illustration: Fig. 854.]
In Fig. 854 is shown Swazey's expanding chuck. B is the body of the
chuck driven on an arbor A. The hub of B is turned taper to receive a
disc C, which is split partly through in three places, and wholly
through at Z. By means of the nut and washer D E, the disc is forced up
the taper hub and caused to expand in diameter and grip the bore of the
work, or ring R, the face of B serving to set the face of the ring
against to hold it true sideways.
The chucks employed by wood workers for driving work without, the aid of
the back or dead centre of the lathe are as follows:--On account of the
fast speed at which the wood-workers' lathe revolves, it would be
undesirable to have their chucks of iron, because of the time it would
take the lathe to start them to full speed, and also to stop them after
shifting the belt from the driving to the loose pulley of the
countershaft, and further because of the damage the tool edges would
receive if they accidentally came into contact with the face of the
chuck. For these reasons wood workers' chucks are usually built up upon
small iron face plates.
[Illustration: Fig. 855.]
Fig. 855 represents a cement chuck, consisting of a disc of hard wood A,
screwed firmly to the face plate B; at C is a round steel point located
at the axis of the chuck.
This chuck is employed to drive very thin work by the adhesion between
the surface of the work and that of the chuck. The surface of the chuck
is coated with a mixture of 8 parts of resin to one part of beeswax run
into sticks. The chuck is waxed or cemented by rotating it at high
velocity while holding the sticks against it. The whole surface of the
chuck being thus coated, the centre of the work is forced on the steel
point C, and the lathe is kept running until the surface of the work
nearly touches that of the chuck, when the belt is passed to the loose
pulley overhead and the work forced against the chuck surface until it
stops or else revolves the work against the hand pressure, the friction
between the surfaces having melted the wax or cement, and cemented the
work to the chuck. This leaves the face and the circumference of the
work free to be operated upon. The work is removed from the chuck by the
gradual insertion between the two of a long thin-bladed knife.
For work of large diameter, however, a mere disc of wood will not
answer, it being too weak across the grain: and here it may be remarked
that the work often supports the chuck, and therefore we should always,
in fixing, make the grain of the work cross that of the chuck, because
the centrifugal force due to the high velocity is so great that both the
chuck and the work have before now been rent asunder by reason of the
non-observance of this apparently small matter. When it is considered
that the chuck has not sufficient strength across the grain, battens
should be screwed on at the back; but a chuck so strengthened will
require truing frequently on account of the strains to which its fibres
will be subjected from the unequal expansion or contraction of its
component parts. Fig. 856 shows the back of a chuck strengthened by the
battens A, A, A.
[Illustration: Fig. 856.]
[Illustration: Fig. 857.]
Another and superior method of making a chuck suitable for work of about
the same diameter is shown in Fig. 857. Its construction enables it to
better resist outward strains in every direction, while the strains to
which it must necessarily be subject, from variations of temperature and
humidity, are less than in the former. It will also be found that it can
be trued with greater facility, especially on the diameter, as the
turning tool will not be exposed to the end grain of the wood.
The crossed bars at the back of the chuck are half checked, as shown at
A, so that both pieces may extend clear across the chuck and not
terminate at the centre. They are fastened together at the centre by
glue, and also with screws. Upon these bars as a frame, the four pieces
composing the body or face of the chuck are fastened by both glue and
screws. These pieces need not extend clear to the centre, but may leave
an open square as shown, because the centre of a large chuck rarely
requires to be used.
[Illustration: Fig. 858.]
For very large chucks a cross of this kind would not afford sufficient
strength, hence, the form shown in Fig. 858 is employed. The arms are
bolted to an iron face plate, as shown, their number increasing with the
diameter of the chuck. To keep the chuck true, the arms should have a
level and fair bed upon the face plate, the segments composing the rim
being fairly bedded to the arms and well jointed at the ends. They
should be both glued and screwed, care being taken that the points of
the screws do not meet the face of the chuck, in which case they would
damage the turning tools used to true the chuck.
As wooden chucks are liable to warp and become out of true it is
requisite to test them on each occasion before use, and true them if
necessary. The work is fastened to these chucks by means of screws whose
heads are sunk beneath the work surface a sufficient depth so that there
is no danger of their coming into contact with the turning tools. In
other cases the work is glued to the chuck, a piece of paper being
interposed between the work and the chuck, which, by being damped, will
enable the more ready removal of the work from the chuck.
[Illustration: Fig. 859.]
Another form of chuck used by wood workers is shown in Fig. 859. It
consists of a disc of wood A; screwed to the face plate and carrying
the two pieces B, B. The pieces C, C are wedges which slide endways to
grip the work. This chuck is especially handy for small work of
rectangular form.
From the shape of some work, it cannot be chucked in jaw chucks of any
description, and this is especially the case with work of large
diameter, hence, large lathes, as, say those that will swing more than
three feet, are not usually provided with universal chucks, although
sometimes provided with independent jaw-chucks. So likewise in small
lathes there are many forms of work that cannot be chucked in jaw
chucks, and yet other forms that can be more conveniently held or
chucked on face or chuck plates, &c.
If, for example, the surface of the chuck requires to be used in setting
the work, the jaws will often be in the way of the tools or instruments
employed to set the work. Again, there may be projections on the work
which will require the body of the work to be held too far from the face
of the chuck to enable its jaws to grip the work.
To meet the requirements of these classes of work chucking devices,
which may be classified as follows, are employed:--
1st. Chucking by bolting work to the face plate or chuck plate with
bolts and plates.
2nd. Chucking between dogs movable about the face chuck plate, and
holding the work from that plate.
3rd. Chucking with the aid of the angle plate, or with the angle plate
employed in conjunction with the chuck plate.
[Illustration: Fig. 860.]
The chuck plate is simply a face as large in diameter as the lathe will
swing, and is sometimes termed the large face plate. Chuck plates for
smaller lathes, as 30 inches swing, or less, are sometimes provided with
numerous round or square holes to receive the bolts which hold the work,
but usually with slots and holes as in Fig. 860. The larger sizes of
chuck plates are similarly formed, but are sometimes provided with short
slots that meet the circumference of the plate as in Fig. 861, which
represents a chuck plate of the Whitworth pattern. The face of the chuck
plate must be maintained true in order that true work may be produced,
and it is necessary when putting it upon the lathe to carefully clean
its threads and those of the live spindle, as, on account of its large
diameter, a very little dirt between it and the live spindle will throw
it considerably out of truth at the circumference.
[Illustration: Fig. 861.]
It is better if there be any error in a chuck plate or face plate that
it be hollow rather than rounding when tested with a straightedge,
because in that case a given amount of error in the plate will produce
less error in the work.
[Illustration: Fig. 862.]
[Illustration: Fig. 863.]
[Illustration: Fig. 864.]
In Fig. 862, for example, A represents a chuck plate hollow across the
face, and B a link requiring to be bored through its double eye C, the
centre line of the lathe being line E E, and the centre line of the hole
in the hub D of the link being denoted by F, and as E and F are not
parallel one to the other it is obvious that the holes will not be
parallel. Suppose, now, that the chuck face was rounding, and the centre
line of D would stand at G G, and the holes in C and D would be out of
true in the opposite direction. In this case the error would be equal,
but suppose we have a ring or disc such as B in Fig. 863 to chuck by
bolts and plates C, D and it will be chucked true, notwithstanding that
the face of the plate is hollow. But were the face of the plate rounding
the disc may be chucked as in Fig. 864, the face F of the work not being
held at a right angle to the line of centres E as it is in Fig. 863. The
truth of the chucking in Fig. 864 depends upon whether the clamps C were
screwed up with equal force upon the work. A hollow chuck plate will
lose this advantage in proportion as the work covers more of one side of
the chuck plate than it does of the other, but in any event it will
chuck more true than a rounding one. Suppose we have, for example, a
ring chucked eccentrically as in Figs. 865 and 866, the chuck being as
much hollow in the one case as it is rounding in the other, and that
shown in Fig. 866 will stand out of true to an amount greater than the
chuck is in an equal amount of its radius. While that shown in Fig. 865
would be nearer true than the chuck is in an equal length of its radius,
both amounts being in proportion to the length of the line A to that of
line B.
[Illustration: Fig. 865.]
[Illustration: Fig. 866.]
If the chuck plate is known to be either rounding or hollow, pieces of
paper of sufficient thickness to remedy the error may be placed at C and
D respectively. It is better, however, to true up the faces of plates so
that the surface of the work bolted against it will be true and stand at
a right angle to the line of lathe centres.
In truing up a face plate, the bearings of the live spindle should be
adjusted so that there is no play on them, and the screw or other device
used to prevent end motion to the live spindle should be properly
adjusted.
A bar or rod of iron should also be placed between the lathe centres to
further steady the live spindle, and the square holes or radial slots
should have the edges rounded or bevelled off, as shown in Fig. 867, so
that when the tool point strikes the sides A of the holes or slots it
will leave its cut gradually and not with a sudden jerk or jump, while,
when it again takes its cut on the side B, it will also meet it
gradually and will not meet the sand or hard skin on the face of the
casting, which would rapidly dull the tool.
[Illustration: Fig. 867.]
In facing or truing up a chuck plate, the feed nut should be put in gear
with the feed screw or feed spindle, and the cut should be put on by
revolving the feed spindle or feed screw. This will take up any lost
motion in the feeding mechanism, after which the carriage may, if there
are devices for the purpose, be locked to the lathe bed so as to prevent
its moving.
It is better that the thread of the chuck be not too tight a fit upon
that on the lathe spindle, the radial face of the chuck hub and of the
cone spindle collar being relied upon to set the chuck true, because it
is somewhat difficult to produce threads so true as to hold the faces
true.
To preserve the threads both upon the chuck bore and the lathe spindle
from undue wear, the chuck when taken off the lathe should be stood on
edge so that falling dust may not accumulate in the thread. Before
putting the chuck upon the lathe spindle the threads of both and the
radial faces of the chuck hub and cone spindle collar should be
carefully cleaned, because the presence of any dirt or dust on those
faces will throw the face of the chuck plate out of true to an amount
that may be of importance at and near the chuck's circumference.
[Illustration: Fig. 868.]
[Illustration: Fig. 869.]
As an example of simple chucking on a face plate, or chuck plate, let it
be required to bore, cut a thread in the bore, and recess the piece of
work shown in Fig. 868, the radial faces being already true planes not
requiring to be turned.
[Illustration: Fig. 870.]
This could be held as shown in Fig. 869, in which C is the chuck plate,
W the work, S a strap plate, and B, B are bolts and nuts, a face view of
the work already chucked being shown in Fig. 870. The surface of the
work being bolted direct against the face of the chuck plate will be
held true to that face, and all that is necessary is to set it true
concentrically. While performing this setting, the work should not be
bolted too firmly, but just firm enough to permit of its being moved on
the chuck plate by light blows, the final tightening of the clamps being
effected after the work is set true. The bolts should be tightened upon
the work equally, otherwise one end of the plate will grip the work
firmly, while the other being comparatively slack, the work will be apt
to move under the pressure of a heavy cut.
A form of strap not unusually employed for work chucked in this manner
is shown in Fig. 871, its advantage being that it is capable of more
adjustment about the chuck plate, because the slots afford a greater
range for the bolts to come even with the holes in the chuck plate.
If the work be light, it may be held to the face plate while the holding
or clamping plates are applied as shown in Fig. 872, in which F is the
face plate or chuck plate, W the work, P a plate of iron, D a rod, and C
the back lathe centre. The latter is forced out by the hand wheel of the
tailstock with sufficient force to hold the work by friction while the
bolts and plates are applied. It is obvious, however, that if the work
has no hole in its centre, the plate P may be dispensed with, and that
if a strap plate, such as shown in Fig. 871, be employed, it must first
be hung on the tail spindle so that it may be passed over the rod D to
the work. Strap plates are suitable for work not exceeding about 6
inches in diameter. For larger work, bolts and plates are used, as
shown, for example, in Fig. 873, which represents a piece of work W held
to the chuck plate by plates P and bolts B, there being at E E packing
pieces or pieces of iron to support those ends of the clamps or clamping
plates P. It is necessary that these packing pieces E be of such a
height as to cause the plates P to stand parallel to the face of the
chuck for the following reasons:--
[Illustration: Fig. 871.]
[Illustration: Fig. 872.]
[Illustration: Fig. 873.]
Suppose that in Fig. 874, W is a piece of work clamped to the chuck
plate, and that packing piece E is too high, and packing piece E´ is too
low, as shown, both pieces throwing the plates P out of level, then in
setting the hole in the work to run true it will be found difficult to
move it in the direction of the arrow, because moving it in that
direction acts to force it farther under plate P´, and therefore, to
tighten its nut. In the case of plate P, the packing piece E will be
gripped by the plate more firmly than the work is, which will be held
too loosely, receiving so little of the plate pressure as to be liable
to move under the pressure of the tool cut. It is better, however, that
the packing piece be slightly above, rather than below the level of the
work surface. The position of the plates with relation to the work
should be such as to drive rather than to pull it, which is accomplished
in narrow work by placing them as in Fig. 873.
[Illustration: Fig. 874.]
The position of the bolts should be as close as possible or convenient
to the work, because in that case a larger proportion of its pressure
falls upon the work than upon the packing piece. For the same reason,
the packing piece should be placed at the end of the plates. This
explains one reason why it is preferable that the packing piece be
slightly above rather than below the level of the work surface, because,
the bolt being nearer to the work than to the packing piece, will offset
in its increased pressure on the work the tendency of the packing piece
to take the most bolt pressure on account of standing the highest.
If a packing piece of the necessary height be not at hand, two or more
pieces may be used, one being placed upon the other. Another plan is to
bend the end of the clamping plate around, as in Fig. 875, in which case
a less number of packing pieces will be required, or, in case the part
bent around is of the right length or height, packing pieces may be
dispensed with altogether. This is desirable because it is somewhat
difficult to hold simultaneously the plate in its proper position and
the packing pieces in place while the nut is screwed up, there being too
many operations for the operator's two hands. To facilitate this
handling, the nuts upon the bolts should not be a tight fit, because, in
that case, the bolt will turn around in the bolt holes or slot of the
chuck, requiring a wrench to hold the head of the bolt while the nut is
screwed up, which, with holding the plate, would be more than one
operator could perform. If the holes in the chuck plate are square, as
they should be, the bolt may be made square under the head, as in Fig.
876 at A, which will prevent it from turning in the hole. This, however,
necessitates that the head of the bolt be placed at the back of the
chuck, the nut end of the bolt being on the work side, which is
permissible providing that the bolt is not too long, for in that case
the end of the bolt projecting beyond the nut would prevent the slide
rest from traversing close up to the work, which would necessitate that
the cutting tools stand farther out from the slide rest, which is always
undesirable. Bolts that are not square under the head should, therefore,
be placed with the head in the work side of the chuck plate, because it
is of little consequence if the bolt ends project beyond the nuts at the
back of the chuck plate.
[Illustration: Fig. 875.]
[Illustration: Fig. 876.]
The heads of the bolts should be of larger diameter than the nuts,
because the increased area under the head will tend to prevent the bolt
from turning when the nut is screwed up.
[Illustration: Fig. 877.]
It sometimes happens that a projection on the work prevents the surface
that should go against the surface of the chuck plate from meeting the
latter. In this case, what are known as parallel pieces are employed.
These are pieces of metal, such as shown in Fig. 877, the thickness A
varying from the width B so as to be suitable for work requiring to
stand at different distances from the chuck plate surface, it being
always desirable to have the work held as near as possible to the chuck
plate so that it may not overhang the live spindle bearings any more
than necessary.
[Illustration: Fig. 878.]
An example of chucking with bolts and plates and with parallel pieces is
given in Fig. 878, in which the work has projections _a_, _a_ and _b_,
_b_, which prevent it going against the face of the chuck; E, E are the
parallel pieces which, being of equal thickness, hold the inside face of
the work parallel to the chuck face.
[Illustration: Fig. 879.]
Another example of the employment of parallel pieces is shown in Fig.
879, which represents a connecting rod strap with its brasses in place,
and chucked to be bored. B is a small block of iron inserted so that the
key may bind the brasses in the strap and P P is one parallel piece, the
other being hidden beneath the key and gib. The object in this case is
to chuck the brasses true with the face A of the strap, the plates S
being placed directly above or over the parallel pieces. This is a point
requiring the strictest attention, for otherwise the pressure of the
clamping plates will bend both the work and the chuck plate.
[Illustration: Fig. 880.]
In Fig. 880, for example, the parallel pieces being placed at _p_, _p_,
and the clamping plates at P, P, the pressure of the latter will bend
the work as denoted by the dotted lines, and the chuck plate in the
opposite direction, and in this case the work being weaker than the
chuck plate will bend the most.
As a result the face of the work will not be true when released from the
pressure of the bolts and nuts holding it. Parallel pieces should
therefore always be placed directly beneath the clamping plates,
especially in the case of light work, because if they be but an inch
away the work will be bent, or spring as it is termed, from the holding
plate pressure. In very large work the want of truth thus induced would
be practically discernible, even though the work be quite thick, as,
say, three inches, if the parallel pieces were as much as, say, 6 inches
from the holding plates.
[Illustration: Fig. 881.]
Fig. 881 shows an example of chucking by means of parallel strips in
conjunction with parallel pieces. B, B are a pair of brasses clamped by
the strips S, S, which are bolted together by the bolts A, A; P, P are
the parallel pieces.
The strips being thus held parallel to the surface of the chuck plate,
all that is necessary is to set the flanges of the work fair against the
surface of the strips and true with the dotted circle, and the brass
bore will be bored at a true right angle to the inside face of the
flange. If the inside face of the brasses was true, the parallel pieces
might be omitted, but this is rarely the case.
An excellent example of bolt and plate chucking is given in a heavy ring
of, say, three feet diameter, and 5 or 6 inches cross section, requiring
to be turned quite true, and of equal thickness all over. This job may
be chucked in three different ways; for example, in Fig. 882, A, B, C, D
are four-chucking dogs, so holding the work that its two radial faces
and outside diameter may be turned. This being done, four more dogs may
be placed to grip the diameter of the work, and the inside ones may then
be removed and the bore turned out. In this way the work would not be
unchucked until finished. There is danger, however, that the dogs
applied outside may spring the work out of true, in which case it would
require setting by a pointer in the slide rest.
Another plan would be to hold the work by dogs applied on the outside,
and turn the bore and both of the faces. To these fasten four plates on
the chuck plate, and turn their ends to the size of the bore and place
the work on them, as in Fig. 883, in which A, B, C, D are the four
plates, and are clamping plates. This plan is often employed, but it is
not a desirable one in heavy work, because the weight of the work is
quite apt to move the plates during its setting. A better plan than
either of these is to first turn off one face and then turn the work
around in the lathe and hold it as in Fig. 884. The bore may then be
turned, and all that part of the face not covered by the plates. Four
holding plates must then be applied with the bolts within the bore, and
when screwed firmly down the outside plates may be removed, leaving the
work free to have the remainder of its face and its circumference turned
up. In this way the work may be turned more true than by either of the
two previously described methods, because it has no opportunity to move
or become out of true.
[Illustration: Fig. 882.]
Cylindrical work to be chucked with its axis parallel to the face plate
is chucked by wood workers as shown in Fig. 885, in which B, B are two
blocks screwed to the chuck C, and having [V]s in to receive the work as
shown; the work is held to the blocks B, by means of the straps S, S,
which are held to B, B by screws. An example of a different class of
chucking by bolts and clamps may be given in the engine crank. A common
method of chucking such a crank is to level the surface of the crank in
a planing machine, and to hold that surface to the chuck-plate by bolts
and plates, while boring both the holes, merely reversing the crank end
for end for the second chucking.
This method has several inherent defects, especially in the case of
large cranks. First, it is a difficult matter to maintain large chuck
plates quite true, and as a result by this method of chucking any want
of truth in the surface of the chuck will be doubled in the want of
parallelism in the bores of the crank.
[Illustration: Fig. 883.]
Suppose, for example, that the chuck surface is either slightly hollow
or rounding as tested with a straight-edge placed across its face, then
the axial line of the hole bored in the crank will not be at a true
right angle with the planed surface of the crank. When the crank is
turned end for end on the chuck-plate and again bolted with its plain
surface against the surface of the chuck, the second hole bored will
again not stand at a true right angle to the planed surface, and
furthermore the error in one hole will be in a directly opposite
direction to that of the other hole, so that the error in the crank will
be double the amount that it is on the chuck surface. To this it may be
answered that if such an error is known to exist it may be corrected by
placing a piece of paper of the requisite thickness at the necessary end
of the crank for both chuckings. But this necessitates testing the chuck
on each occasion of using it, and the selection of a sheet of paper of
the exact proper thickness, which is labor thrown away so long as an
equally easy and more true way of chucking can be found. Furthermore
there is a second and more important element than want of truth in the
chuck to be found, which is that of the alteration of form which occurs
in the crank (as each part of its surface is cut away) as explained in
the remarks with which the subject of chucking is prefaced.
[Illustration: Fig. 884.]
First, the planed surface of the crank will alter in truth so soon as
the crank is released from the pressure of the holding devices on the
planer or planing machine; second, that surface will again alter in form
and truth from the removal of the metal around the surface of the hole
first bored; and third, the planed surface will be _to some extent_
sprung from the pressure of the plates holding the crank to the chuck
plate, hence the following method is far preferable.
[Illustration: Fig. 885.]
If it is intended to plane the back surface of the crank let that be
done first as before, and let it be held to the face-plate by bolts and
plates as before, while the hole and its radial face at the large end of
the crank are turned and finished. In doing this, however, first rough
out the radial face, and then rough out the hole, so that if the work
alters in form a fine finishing cut on both the radial face and the bore
will correct the evil. Then release the crank from the pressure of the
holding plates; and it is obvious that however the planed surface may
have altered in truth from removing the surface metal, the radial face
just turned will be true with the bore turned at the same chucking. Now
to chuck the crank to bore the second hole, turn it end for end as in
Fig. 886, and bolt the face already turned to the chuck plate (as at A
in the figure) with one or more bolts and strap plates. To steady the
other end of the crank, and prevent it from moving under the pressure of
the cut, take two bolts and plates B, and place a washer between them
and the chuck surface as shown at C, then bolt the plates to the chuck
plate, so adjusting them that their ends just have contact with the
crank when it is set true. In setting it true it may be moved by
striking the outer ends of the plates.
[Illustration: Fig. 886.]
In this method of chucking, we have the following advantages:--
1st. If the chuck plate is not true we may place a piece of paper
beneath the crank surface A, to correct the error as in the former
method, or if this is neglected, the second hole bored will be out of
true to an amount answerable to the want of truth in the chuck, and not
to twice as much as in the former method.
2nd. Any alteration of form that may take place during the first
chucking does not affect the truth of the second chucking as in the
other case.
3rd. The crank being suspended during the second chucking, any
alteration of form that may accompany the boring of the second hole will
be corrected by the finishing cut, hence the crank will be bored with
its two holes as axially true as they can be produced in the lathe.
It now remains to explain the uses of the pieces W in Fig. 886, simply
weights termed counterbalances bolted to the chuck plate to balance it
against the overhanging weight of the crank on one side of the chuck
plate. If these weights are omitted the holes in the work will be bored
oval, because the centrifugal force generated by the revolution of the
work will take up any lost motion there may be between the cone spindle
journal and its bearings, or if there be no such lost motion the
centrifugal force will in many cases be sufficient to spring the cone
spindle.
In selecting these weights it is well to have them as nearly as possible
heavy enough to counterbalance the work when placed at the same distance
from the lathe centre as the outer end of the work. The proper
adjustment of the weight is ascertained by revolving the lathe and
letting it slowly come to rest, when, if the outer end, or overhanging
end as it termed, of the work comes to rest at the bottom of the circle
of revolution on two or three successive trials the weight of the
counterbalance must be increased by the addition of another weight, or
the weight may be moved farther from the lathe centre.
To enable a piece of work, such as a crank for example, to have two or
more holes bored at one chucking, a class of chuck such as shown in Fig.
887 is sometimes employed. S is a slide in one piece with the hub that
screws on the live spindle and standing at a true right angle with the
axial line of the cone spindle and made as long as will swing over the
lathe bed. It contains a dovetail groove (as shown in the edge view)
into which a bar _t_, running across the back of the face plate P,
passes. To cause the bar _t_ to accurately fit the dovetail,
notwithstanding any wear of the surfaces, a slip G is introduced, being
set up to _t_ by set-screws passing through that side of the dovetailed
piece. The work, as the crank C, is bolted to the face plate, and the
set-screws on G are eased so that the plate can be moved to set the work
true; when true, the set-screws are tightened, and the first hole may be
bored. To bore the second hole all that is necessary is to slacken the
set-screws on G, move the plate, which will slide in the dovetail
groove, and set the work; when the set-screws are again set up tight,
the boring may again be proceeded with. In this way both holes may be
bored without unclamping the work. The whole truth of the job, _before
being unclamped from the chuck plate_, depends in this case upon the
dovetail groove being at a true right angle to the axial line of the
lathe cone spindle, it being of no consequence whether the face plate
stands true or not. But suppose the removal of the metal to have
released strains in the casting or forging, then the clamping plates
will have prevented the crank from quite assuming its normal shape after
the release of those strains, and the crank, when finished, though true
while clamped, will change its form the instant the clamping plates are
removed, and the holes bored will in all probability not have their
axial lines true one with the other. Another objection is that throwing
the chuck plate out of balance on the lathe spindle as well as the crank
induces the evils due to the centrifugal motion. This may be offset by
increased counterbalancing, of course, but the counterbalancing becomes
cumbersome, and is not so easy a matter. For these reasons, chucks of
this class are not desirable unless it may be for comparatively small
and light work. It is obvious that the dovetail groove may be provided
with a screw, and the back of the plate with a nut, so as to move the
plate along the groove by revolving the screw. This will assist in
adjusting or setting the work, but it will increase the amount of weight
requiring to be counterbalanced.
[Illustration: Fig. 887.]
When a number of pieces are to be bored with their holes of equal
diameters and of the same distance apart, the chucking should be
performed as in Figs. 888 and 889; one and the same end of each link
should be bored and faced, the links being held by the stem, placed on
parallel pieces with plates. A pin such as shown in Fig. 889 should then
be provided, its diameter across A being a close sliding fit into the
bores of the links; while the length of A should be slightly less than
the length of the hole in the link, the part D should be made to
accurately fit the hole bored by any suitably sized reamer; a washer B
should be provided, and each end should be threaded to receive nuts.
There should then be provided in the chuck plate a hole whose distance
from the centre of the chuck must exactly equal the distance apart the
holes in the links are required to be, and into whose bore the end D of
the pin shown in Fig. 889 must drive easily. The pin should be locked in
this hole by a nut as shown in Fig. 889. The bored ends of the links may
then be placed on the pin and fastened by a nut as in Fig. 888, which
will regulate the distance apart of the holes.
[Illustration: Fig. 888.]
[Illustration: Fig. 889.]
It is obvious that the pin may be passed through one of the radial slots
in the chuck, and set the required distance from the centre, but in this
case the pin would be liable to become moved in its position in the
slot.
Side plates to prevent the link from moving should of course be applied
as at D, D in the figure.
The whole process of the second chucking will thus consist of fastening
the links on the pin, and setting the free end to the circle made to
mark its location. This is done as shown in Fig. 890, which represents
the free end of a link, D is the circle marked to set the link by, and P
a pointed tool held firmly in the slide rest tool post. The link is
obviously set true when the dotted circle on its end face runs true, the
pointer merely serving to test the dotted circle.
[Illustration: Fig. 890.]
When, however, one or two links only require to be turned it will not
pay to make the pins shown in Fig. 888, especially if the holes of the
different links vary in diameter, hence the work must be set by lines.
In the promiscuous practice of the general workshop, where it may and
often does happen that two pieces of work are rarely of the same shape
and size, lines whereby to set the work are an absolute necessity, not
only to set the work by in chucking it, but also to denote the quantity
of metal requiring to be taken off one face in order to bring its
distance correct with relation to other faces. An example of this kind
is given in Fig. 891, which represents a lever to be bored and faced at
the two ends, the radial faces standing at different distances from the
centre of the lever stem as denoted by the lines (defined by centre
punch dots) E, F, G, H, I, J, K, L. It will be noted that at H, I, F,
and E there is but little metal to be taken off, while there is ample at
L. Suppose then that the face L were the first one turned, and it was
only just trued up, then when F or H were turned there would be no metal
to turn, for they may be too near the plane of L already.
[Illustration: Fig. 891.]
The necessity for these lines now being shown, we may proceed to show
how they should be located and their services in setting the work. The
line A is called the centre line, it passing through the centre of the
thickness of the link body on both edges of the link. From it all the
other lines, as J, F, L, G, E, K, and H, I, are marked.
The first question that arises in the chucking is, which of the holes B,
C, or D, shall be bored first. Now the faces K and L are those that
project farthest from the centre line A, hence if the hole at that end
be bored and the faces K, L, be turned first, we may bolt those faces
against the chuck plate, and thus insure that all three holes shall
stand axially true one with the other. If the holes B or C were bored
first, L projecting beyond J and F (which are the faces of holes B, C)
would prevent the radial face first turned from serving as a guide in
the subsequent chuckings, unless a parallel piece were placed between
the face and the chuck. In this case, however, there is not only the
extra trouble of using the parallel piece, but there would obviously be
more liability of error, as from the parallel piece not being dead true
and the amount of the error multiplying in the length of the lever, and
so on.
The hole D is the one, therefore, to be bored first, the chucking
proceeding as follows:--Two parallel pieces of sufficient thickness to
keep L clear of the chuck plate should be placed one on each side of the
hub E, and bolts and plates placed directly over them. The work must be
set so that the line A on each side of the link stands exactly parallel
with the face of the chuck, the parallelism being tried at each end of
the line, because any error that may be made in setting the work by the
full length of the line will have a less effect upon the work than the
same amount of error in a shorter length of line. For this reason the
centre line should always be marked as long as possible and used to set
by, unless there is a longer line running parallel to it and marked on
both sides of the link, as would be the case if the dotted line at J
and that at L were equidistant from A, in which event they may
preferably be used.
The work is set true to the lines by a scribing block, or surface gauge,
but as that instrument is more used in setting work with chuck dogs its
application will be shown in connection with chucking by dogs; hence to
proceed: To set the work true to the line A it may be necessary to place
a thickness of paper, a piece of sheet tin, or the equivalent, beneath
one of the parallel pieces to bring A parallel with the chuck plate
surface. This being done, however, and the circle D being set to run
true, the hole may be bored and the radial face L turned off so as to
just split the dotted line at L, and this radial face may be used
instead of the line A for all subsequent chuckings, so as to avoid the
errors that might occur in referring to the line, and from the
alterations that might occur in the form of the work from removing the
surface metal.
[Illustration: Fig. 892.]
Fig. 892 represents a view of the end L as held for the second chucking.
C is a section of the chuck plate, and O O represents the line of
centres of the lathe, and it is obvious that the radial face of the
lever end (which is here represented by L) being used for all but the
first chucking, the holes will all stand axially true one with the
other, no matter how many chuckings and holes there may be, hence it
becomes obvious that the face that will meet the chuck plate is the one
that should be turned at the first chucking. It is of no consequence in
the case of a single lever whether the pin fits the hole in the end of
L, Fig. 892, or not, because the dotted circles at B, C, D in Fig. 891
form the guides whereby to set the holes for distance apart, and any
bolt may be used to clamp the work.
It is usual in an example of this kind to turn the stem of the lever to
its proper thickness for a short distance from the hubs, so as to have
the stem true with the bores, and form a guide whereby to set the lever
in the planer or shaper when cutting down the lever stem to size. The
rules of chucking and the balance weighting described with reference to
chucking a crank, of course also apply to this example.
It will now be observed that in all cases in which work is chucked by
bolts and plates, the whole of the faces cannot be turned at one
chucking unless the shape of the work is such that it will permit the
plates and the bolts to pass or be below the level of the work surface.
It will further be noticed that if one face of the work is held against
the chuck surface it cannot be turned at the same chucking that the
other face is turned at. Now it may be very desirable that a part or the
whole of the back face as well as the front one be turned at the same
chucking as that at which the hole is bored, so as to have the hole and
those two faces true without incurring the errors that might arise from
a second chucking. Again, the diameter of the work may be equal to that
of the chuck so as to preclude the possibility of using bolts and plates
outside of the circumference, and though there be cavities or slots
running through the work through which the bolts might be passed, yet
the presence of the plates would prevent the face from being turned.
[Illustration: Fig. 893.]
To meet these and many other requirements that might be named, chucking
by the aid of chucking dogs is resorted to, one of these dogs being
shown in Fig. 893. B represents a section of the chuck plate with a
piece broken out to show the stem A of the dog, which is squared to
prevent its revolving when the nut D, which holds the dog to the chuck
plate, is tightened, the holes of the chuck, of course, being square
also; E is the set-screw which holds the work, its end at E being turned
down below the thread, and the head squared to receive a wrench.
[Illustration: Fig. 894.]
Fig. 894 represents an example of chucking by dogs, it being required to
face the work off to the dotted line F F. Three of the four dogs used
are shown at D, D, D. To set the work the scribing block shown in the
figure is employed, the point of the needle being set to the line at any
one spot, and the scribing block or surface gauge carried around the
work rested with its base against the chuck plate and the needle point
tried for coincidence with the line at various points in the work's
circumference. The work is not at first held too firmly by the dogs, so
that light blows will suffice to so move the work that the surface gauge
needle point applied as shown and at any point around the work will
coincide with the line. It will here be observed that using the dogs
obviates the necessity for parallel pieces, when the work has
projections at the back face as shown in the cut.
[Illustration: Fig. 895.]
Fig. 895 represents another example in chucking by dogs. It is required
to surface the whole of the surfaces shown, to bore the hole C and to
face a face similar to A, but on the other side or chuck side of the
work. Then the work is placed so that its outer face will project beyond
the extreme surface of the dogs, and the whole of the operations can be
performed at one chucking. It will be observed that in this case the
surface of the chuck plate does not automatically serve to guide the
work in the chucking, because there is no contact between the two, but
the chuck surface can be used as a guide whereby to chuck the work as
has just been shown. Or suppose the work to require to be set as true as
can be to its exposed face, then the work end of the surface gauge is
applied as shown in Fig. 896 at E.
[Illustration: Fig. 896.]
[Illustration: Fig. 897.]
[Illustration: Fig. 898.]
The surface gauge may indeed be dispensed with if the work is
sufficiently light that the lathe can be swung around by pulling the
chuck plate with the hand, and the work merely requires to be set to run
true on its exposed radial face. A pointer held in the slide rest, and
applied as in Fig. 890, will denote the setting of the work, which must
be tapped until the pointer touches it equally on four equidistant
points of the surface; but if it is essential to take as little as
possible off the face while truing it up, the tool point should be held
stationary, while the work should be so set that the four most distant
points (in that circle on the work which is equivalent in radius to the
radius to which the tool point stands from the chuck centre) are
equidistant as measured by a rule from the tool point. The philosophy of
this will be understood from a reference to Fig. 894 and the remarks
thereon, this being a parallel case, but applied to a radial face
instead of to a circumference.
Now suppose we have the piece of work shown in Fig. 897, which requires
to have its surfaces A and B parallel and at a right angle to C and D,
the end faces E and F parallel to each other, and at a right angle to
both A, B, C, and D, the hole at G is to be axially true with the
surfaces A, B, C, and D, as well as with the pin at I, and the hole at H
at a dead right angle to that at G.
We may put a plug in G and turn up the surfaces E and F, and turn the
pin I; this, however, would leave the hole G unbored, whereas it should
be bored when the surface E is turned; again, after these surfaces are
turned they are of no advantage as guides in the subsequent chuckings.
We may grip the surfaces E and F in a jaw chuck to turn the surfaces A,
B, C and D, but depending upon the face jaws of the dogs to set the work
surface true by; but this would not be apt to produce true work on
account of the spring of the jaws, as explained in the remarks upon jaw
chucks; furthermore, the work, supposing it to be a foot long, could not
be held in a dog chuck sufficiently firmly to enable the turning of the
end face E or the pin I, and this brings us to that most excellent
adjunct to a general chucking lathe, the angle plate shown in Fig. 898.
It is simply a plate of the form shown in the figure, having two flat
and true surfaces, one at a right angle to the other; one of these
surfaces bolts to the chuck plate, while the other is to fasten the work
on. The slots shown are to pass the bolts through to fasten the angle
plate to the chuck plate, and the work surface of the plate contains
similar slots and holes to receive the bolts used to fasten the work.
[Illustration: Fig. 899.]
Suppose, then, we fasten the piece of work to the angle plate as shown
in Fig. 899, and face off the surface C, and bore the hole H, the work
being set true with its surface, or to a line, by the aid of a surface
gauge, as may be required. We then turn surface C down to meet the
surface of the angle plate, fasten it to the same with bolts and plates
and setting it as before, and on turning its surface A we shall have the
two surfaces A and C at a right angle to one another. We then turn the
surface A down upon the angle plate and bolt it again as before. But we
have now to set it so that the surface C shall be quite parallel with
the surface of the chuck plate. This we may do by placing one or more
parallel strips behind it, as at S S, in the plan view, Fig. 900,
setting the work so that it binds the parallel strips tight against the
chuck plate along their full lengths; or we may measure the distance of
C from the chuck plate surface with a pair of inside calipers; or we may
turn the bent end of a surface-gauge needle outwards and gauge the work
as shown in the plan view, trying the work all along. On turning the
surface D, Fig. 897, we shall have three of the surfaces done at right
angles and with C and D parallel.
[Illustration: Fig. 900.]
It is obvious that the surface D may be turned down on the angle plate
and bolted as before, the surface A being set parallel to the chuck
plate surface as before, and all four of these surfaces will be finished
true as required. Next come the two end surfaces and the pin I. For F
and the pin I we chuck the work on the angle plate, as shown in the plan
view, Fig. 901, P, P representing the clamping-plates. The angle plate
will here again serve to hold the work true one way, and all we have to
do to set it true the other way is to fasten a pointer in the tool post
and bring it up to just touch the corners of the work at the outer end,
as at K. Now run the carriage up so as to bring the pointer to position
L, and when the work is so set that all four corners just touch the
pointer, tried in their two positions, _without touching the cross-feed
screw_, the work is true, and the end surface E and hole G may be
turned; E will then be at a true right angle to the four faces, A, B, C,
D, while G will be axially true with them.
[Illustration: Fig. 901.]
We may, instead of using the pointer at K and L, or in addition to so
using it, apply a square against the chuck plate and bring the blade
against the work, as shown at R.
We have now to turn the pin I and end face, and to do this we simply
reverse the work, end for end, and bolt it as before. But we may now
employ the trued surface E as an aid in setting by causing it to abut
against the chuck plate surface, and, as an aid to finding that it abuts
fair, we may put two strips of the same piece of paper behind it, one on
each side of the square, and, after the work is bolted, see that both
are held firm; but it is necessary to test with the pointer as before,
as well as with the square.
It is obvious that the angle plate requires counterbalancing, which is
done by means of the weight W. (Fig. 900).
An excellent example of angle plate chucking is furnished in a pipe bend
requiring both flanges to be turned up. The method of chucking is shown
in Figs. 902 and 903, the flanges being simply bolted to the angle
plate. The work may be set true to the body of the bend close to the
neck of the flange or by the circumference of the flange. The face of
the flange will be held true one way by the face on the angle plate, but
must be set true the other way. The truest flange should be the one
first bolted to the angle plate.
[Illustration: Fig. 902.]
[Illustration: Fig. 903.]
[Illustration: Fig. 904.]
A common but good example of angle plate chucking is shown in Fig. 904,
which represents a cross head requiring to have its two holes bored one
at a right angle to the other, the jaws faced inside and outside, and
the hub or boss turned.
[Illustration: Fig. 905.]
It would be proper to mark the cross-head out by lines, giving dotted
circles to set the work by, and dotted lines to give the thickness of
the jaws. In thus marking out two centre lines A A and B B in Fig. 905
would be used to locate the centres of the holes; and the thickness of
the jaws would be marked from the line B B. In marking these lines the
cross head should be rested upon a table or plate as in Fig. 905, and
the line A A should be made with the jaws of the cross head lying flat
on the table, that is without the interposition of any packing or paper
between them and the plate, so that the edges of the jaws on that side
will be true with the line A A, and will therefore serve to apply a
square against when chucking to bore the hole through the jaws. If the
jaw edges are not sufficiently true to permit of their lying on the
table, they should be made so by filing a flat place on them, so that
when a square is applied to them as in Fig. 906, the edges C, C will be
parallel with the axis A A of the holes in the chucks or jaws. The first
chucking should be as in Fig. 907, the cross head being bolted to an
angle plate set true by the circle on the end face of its hub D, and a
square being applied to the centre line A, as in Fig. 908, and to the
dotted lines on the jaws as shown in Fig. 909. A balance weight W, Fig.
907, is necessary to counterbalance the weight of the angle plate.
[Illustration: Fig. 906.]
The second chucking to bore the cheeks and face them inside and out to
the required thickness would be as in Fig. 910, a single plate and two
bolts being used to hold the cross head to the angle plate. To set the
cross head true in one direction, the outer circle shown marked upon the
face of the cheek is used.
It remains to so set the face of the cheeks that the hole through them
shall be central with that already bored through the hub D and all that
is necessary to accomplish this is to set the edge true as shown in the
top view in Fig. 911, in which S is a square rested against the face of
the chuck and applied to the edges of the cheeks, these edges being
those that were rested on the plate when marking the line A A in Fig.
905, or that were filed square if it was found necessary as already
mentioned.
[Illustration: Fig. 912.]
The inside faces of the cheeks are turned to the dotted lines shown in
Fig. 909, and the outside faces being turned each to the proper
thickness measured from the outside ones, the job will be complete and
true in every direction.
[Illustration: _VOL. I._ =EXAMPLES IN ANGLE-PLATE CHUCKING.= _PLATE XII._
Fig. 907.
Fig. 908.
Fig. 909.
Fig. 910.
Fig. 911.]
An excellent example of angle plate chucking is shown in Fig. 912--the
actual dimension of the piece, measuring, say, 24 inches in length. It
is required to have the cylindrical stems A, B turned parallel to each
other, of equal diameters, equidistant from the central hole C, and true
with the hub D. A large piece of work of this kind would be marked off
with lines defined by centre-punch dots, as shown. The ends of A, B, D
would require dotted circles to set them by. Now, in all work of this
kind it is advisable to turn that surface first that will afford the
greatest length of finished surface, to serve as a guide for the
subsequent chucking, which in this case is the hub D, and the face on
that side as denoted by the dotted line which has to be cut to that
line. The method of chucking would, for this purpose, be as in Fig. 913.
[Illustration: Fig. 913.]
[Illustration: Fig. 914.]
[Illustration: Fig. 915.]
The second chucking would be as in Fig. 914 to bore the hole at C,
while, at the same time, the surface from F to G may be turned. Either
inside calipers or a surface gauge may be employed to set E E parallel
to the chuck plate surface. It is supposed that the location C is
defined by a dotted circle, by which the work may be set for
concentricity, as should be the case. At the next chucking it will
simply be necessary to move the work on the angle plate to the position
shown in Fig. 915, setting the circle on the end of A to run true, and
the surface E parallel to the chuck surface as before. The third
chucking is made by simply moving the work on the angle plate again, and
setting as in the last instance.
CHAPTER X.--CUTTING TOOLS FOR LATHES.
The cutting tools for lathes are composed of a fine grain of cast steel
termed "tool-steel," and are made hard, to enable them to cut, by
heating them to a red heat and dipping them in water, and subsequently
reheating them to temper them or lower their degree of hardness, which
is necessary for weak tools.
These cutting tools may be divided into two principal classes, viz.,
slide rest tools, or those held in the slide rest, and hand tools, which
are held by hand.
The latter, however, have lost most of their former importance in the
practice of the machine shop, by reason of the employment of self-acting
lathes.
The proper shape for lathe slide rest tools depends upon--
1st. The kind of metal to be cut.
2nd. Upon the amount of metal to be cut off.
3rd. Upon the purpose of the cut, as whether to rough out or to finish
the surface.
4th. Upon the degree of hardness of the metal to be cut.
5th. Upon the distance the tool edge is required to stand out from the
tool clamp, or part that supports it.
Lathe tools are designated either from the nature of their duty, or from
some characteristic peculiar to the tool itself.
The term "diamond point" is given because the face of the tool is
diamond shaped; but in England and in some practice in the United States
the same tool is termed a front tool, because it is employed on the
front of external work.
A side tool is one intended for use on the side faces of the work, as
the side of a collar or the face of a face plate. An outside tool is one
for use on external surfaces, and an inside one for internal, as the
walls or bores of holes, &c.
A spring tool is formed to spring or yield to excessive pressure rather
than dig or jump into the work.
A boring tool is one used for boring purposes.
[Illustration: Fig. 916.]
[Illustration: Fig. 917.]
The principal forms of cutting tools for lathes are the diamond points
or front tools, the side tools (right and left), and the cutting off or
parting tool. The cutting edges of lathe tools are formed by grinding
the upper surface, as _a_ in Fig. 916, and the bottom or side faces as
_b_, so that the cutting edges _c_ and _d_ shall be brought to a clean
and sharp edge, the figure representing a common form of front tool. The
manner in which this tool is used to cut is shown in Fig. 917, in which
the work is supposed to be revolved between the lathe centres in the
manner already described with reference to driving work in the lathe.
The tool is firmly held in the tool post or tool clamp, as the case may
be, and is fed into the work by the cross-feed screw taking a cut to
reduce the work diameter and make it cylindrically true; the depth to
which the tool enters the work is the depth of the cut. The tool is
traversed, or fed, or moved parallel to the work axis, and the motion in
that is termed the feed, or feed traverse.
[Illustration: Fig. 918.]
The cutting action of the tool depends upon the angles one to the other
of faces B, D (Fig. 918), and the position in which they are presented
to the work, and in discussing these elements the face D will be termed
the top face, and its inclination or angle above an horizontal line, or
in the direction of the arrow in Fig. 918, will be termed the rake, this
angle being considered with relation to the top A A, or what is the same
thing, the bottom E E of the tool steel. The angle of the bottom face B
to the line C is the bottom rake, or more properly, the clearance.
[Illustration: Fig. 919.]
In the form of diamond point or front tool, shown in Fig. 916, there is
an unnecessary amount of surface to grind at _b_, hence the form shown
in Fig. 919 is also employed on light work, while it is in its main
features also employed on large work, hence it will be here employed in
preference to that shown in Fig. 916, the cutting action of the two
being precisely alike so long as the angles of the faces are equal in
the two tools.
The strength of the cutting edge is determined by the angles of the rake
and clearance, but in this combination the clearance has the greater
strength value. On the other hand the keenness of the tool though
dependent in some degree upon the amount of clearance, is much more
dependent upon the angle of the top face.
It follows therefore that for copper, tin, lead, and other metals that
may be comparatively easily severed, a tool may be given a maximum of
top rake, and it is found in practice that top rake can be employed to
advantage upon steel, wrought iron, and cast iron, but the amount must
be decreased in proportion as the nature of either of those metals is
hard.
For the combinations of copper and tin which are generally termed brass
or composition, either no top rake or negative top rake is employed
according to the conditions.
[Illustration: Fig. 920.]
It may be pointed out, however, that in a given tool the cutting
qualification is governed to a great extent by the position in which the
tool is presented to the work, thus in Fig. 920, let C represent a piece
of work and B, B, B, B, four tools having their top and bottom faces
ground at the same angle to each other. In position 1, the top face of
the tool is at an acute angle below the radial line A, hence the tool
possesses top rake, the amount being about suitable for hard steel or
hard cast iron.
In position 2 the top face is at an acute angle above the radial line A,
hence the tool has negative top rake, the amount being about suitable
for brass work under some conditions.
In position 3 the top face has no rake of any kind, and the tool is
suitable (in this respect) for ordinary brass work.
In position 4 the tool possesses an amount of top rake about suitable
for ordinary wrought-iron work.
If the tool was presented to brass work in positions 1 or 4 it would rip
or tear the metal instead of cutting it, while if the tool was presented
to iron or steel (of an ordinary degree of hardness) in positions 2 or
3, it would force rather than cut the metal.
Furthermore it will be readily perceived that though each tool may have
its faces, whose junction forms the cutting edge, at the same angles,
yet the strength of the cutting edge is varied by the position in which
the tool is presented to the work, thus the edge in position 2, will be
weaker than that in position 4.
We have now to consider another point bearing upon the proper
presentment of top rake and the presentment of the tool to the work. It
is obvious that the strain of the cut falls upon the top face of the
tool, and therefore the direction in which this strain is exerted is the
direction in which the tool will endeavour to move if the strain is
sufficient to bend the tool and cause motion.
[Illustration: Fig. 921.]
In Fig. 921 let W represent the work having a cut C being taken off by
the tool T; let E represent the slide rest, and F the extreme point at
which the tool is supported; then the pressure placed by C on the top
face of the tool will be at a right angle to the plane of that top face,
or in the direction of the arrow B; to whatever amount therefore the
tool sprung under the cut pressure (its motion being in an arc of a
circle, of which F is the centre) it would enter the work deeper, and as
a result, the rough work not being cylindrically true, the tool will dip
farthest beyond its proper line of work where the cut is deepest, and
therefore will not cut the work cylindrically true; as this, however,
naturally leads to a variation in the direction of the top rake, and as
the cutting action of the point of such a tool differs from that of the
side edge, which also leads to a variation in the direction of the top
rake, it becomes necessary to consider just what the cutting action is
both at the point and on the side of the tool.
Suppose, then, that the tool carries so fine a cut that it cuts at the
point only, and the pressure will be as denoted by the arrow B in Fig.
921.
[Illustration: Fig. 922.]
If the tool be given no traverse, but be merely moved in towards the
centre of the work, the cut will move outward and in a line with the
body of the tool, the cutting coming off as shown in Fig. 922.
So soon, however, as the tool is fed to its feed traverse the form of
the cutting alters to the special form shown in Fig. 917, and moves to
one side of the tool, as well as outwards from the work.
[Illustration: Fig. 923.]
Fig. 923 is a top view of a tool and piece of work, and the arrow A
denotes the direction of the resistance of the work to the cut, being at
a right angle to plane of the cutting edge.
Now the duty of the side edge is simply to remove metal, while that of
the point is to finish the surface, and it is obvious that for finishing
purposes the most important part of the tool edge is the point, and this
it is that requires to be kept sharp, hence the angle or rake should be
in the direction of the point. But when the object is to remove metal
and prepare the work for the finishing cut the duty falls heavily on the
side edge of the tool, and the angle of the top face and the direction
of its rake may be varied with a view to increase the efficiency of the
side edge, and at the same time to diminish the amount of power
necessary to pull the tool along to its feed traverse. This may be
accomplished by altering the top rake from front to side rake, which is
done in varying degrees according to the nature of the work.
[Illustration: Fig. 924.]
In Fig. 924 the angle of the top face in the direction of A is the
front, and that in the direction of B is the side rake.
In small work where the cuts are not great, and where but one roughing
cut is taken, it is an object to have the roughing cut leave the work
with as smooth a surface as possible, and the amount of side rake may be
small as in Fig. 924. For heavy deep cuts, however, a maximum of side
rake may be used.
[Illustration: Fig. 925.]
Thus in Fig. 925 is an engraving of a tool used for roughing in the
Morgan Iron Works, its top rake being all side rake.
When a tool has side rake, its cutting capacity is obviously increased
on one side only, hence it should be fed to cut on that side only. It is
for this reason that no side rake is given to tools for very small and
short work, because it is then more convenient to traverse the tool to
cut in either direction at will.
In long and large work, however, where the motion of the slide rest is
slow, tools having right and left-hand side rake are used. The tools in
Figs. 924 and 925 are right-hand tools, their direction of feed travel
being to the left.
[Illustration: Fig. 926.]
In Fig. 926 is a left-hand tool, its direction of feed traverse being
from left to right; hence edge G is the cutting one, edge F being dulled
by the side angle B.
[Illustration: Fig. 927.]
It is obvious that various combinations of side rake and front rake may
be given to produce the same degree of keenness to the tool. For
example, a tool may have its keenness from side rake alone, or it may
have the same degree of keenness by using less side rake and some front
rake. The principles governing the selections of these combinations are
as follows:--
Suppose that in addition to say 20 degrees of side rake a tool is given
a certain amount of front rake as denoted in Fig. 927 by E E, and
suppose that the tool is moved in to its cut by the cross feed screw.
During this motion and until the tool point meets the work surface the
contact between the cross feed screw and feed nut will be on the sides
of the threads facing the line of lathe centres, and all the play
between those threads will be on their other sides, but so soon as the
tool meets the cut it will jump forward and into the work to the amount
that the play between the threads will allow it, and this is very apt to
cause the tool to break. Furthermore the point of the tool is apt from
its extreme keenness to become dulled quickly.
[Illustration: Fig. 928.]
The amount of side rake may, however, be considerably increased if the
heel D, Fig. 928, be made higher than the point A in that figure, the
plane of the middle being denoted by the arrow at A; a view of the other
side of this tool is shown in Fig. 929, the plane of the cutting edge
being denoted by the dotted line.
[Illustration: Fig. 929.]
A tool thus formed will require a slight cross feed screw pressure to
force it to its cut, thus causing the cross feed nut to have contact
with the sides of the thread in contact when winding the tool into its
cut, hence the tendency to jump into the depth of cut is eliminated, and
regulating the depth of the cut is much more easily accomplished.
In proportion as a tool is given side rake, it is more easily traversed
to its cut, as will be perceived from the following:--
[Illustration: Fig. 930.]
[Illustration: Fig. 931.]
Fig. 930 represents a section of a tool T, whose feed traverse is in the
direction of A. Now all the force that is expended in bending the
cutting C out of the straight line, or in other words the pressure on
the top face of the tool, acts to a great extent to force the tool to
the left, and therefore traverse it to its feed. The more side rake a
tool has the nearer the thickness of its cutting will accord to the
thickness of the feed traverse. For example, if a tool having a side
rake of say 35 degrees of angle feeds forward 1/32 inch per work
revolution, the thickness of the cutting will but slightly exceed 1/32
inch, but if no top rake at all be given, as shown in Fig. 931, then the
cutting will come off nearly straight, will be considerably thicker than
1/32 inch, and will be ragged and broken up, and it follows that the
thickening and the bending of the cutting has required an expenditure of
the driving power of the lathe, diminishing the depth of cut the lathe
will be capable of driving. With such a tool the pressure of the cut
will fall downwards as denoted by the arrow B.
[Illustration: Fig. 932.]
In the practice of many tool makers in the Eastern States the tool is
ground to a point A, Fig. 932, that is, ground sharp and merely rounded
off with an oil-stone. This may serve when the lathe has an exceedingly
fine feed, and the strain being in that case very slight the tool point
may be made to stand well above the level of the body of the steel, as
in the figure, and thus save forging; but this is a slow method of
procedure, and produces no better work than a tool which is rounded at
the point, and therefore capable of producing smoother work with a much
coarser feed.
The diameter of the curls of the cutting, shaving, or chip produced by a
turning and also the direction in which it moves after leaving the tool,
depends upon the amount of the top rake and the direction in which it is
provided. The greater the amount of rake, whether it be front or side
rake, the larger the coils of the cutting, and, therefore, the less the
amount of power expended in bending it. Furthermore, it may be remarked
that the thickness of the cutting is always greater than is due to the
amount of feed traverse, and it requires power to produce this
thickening of the cutting. The larger the coils of the cutting the
nearer the thickness accords with the rate of feed.
[Illustration: Fig. 933.]
In these considerations we have referred to the angle of the top face
only, but if we consider the angle of the two faces one to the other we
shall see that they form a wedge, and that all cutting tools are simply
wedges which enter the material the more easily in proportion as the
angles are more acute, providing always that they are presented to the
work in the most desirable position, as was explained with reference to
Fig. 920.
[Illustration: Fig. 934.]
We may now consider the degree of a bottom rake or clearance desirable
for a tool, and this it can be shown depends entirely upon the
conditions of work, diameter, and rate of tool traverse, and cannot,
therefore, be made a constant degree of angle. This is shown in Fig.
934, in which a tool T is represented in three positions, marked
respectively 1, 2, and 3. Line A A is at a right angle to the axis of
the work W, and the side of the tool is given in each case 5° of angle
from this line A A. In position 1 the tool has 3° of clearance from the
side of the cut; in position 2 it has 2° clearance, but in position 3 it
would require to have 2° more clearance given to it to enable the
cutting-edge to meet the side of the cut, without even then having the
clearance necessary to enable it to cut. This occurs because the side of
the cut is not at a right angle to the work axis, but at an angle the
degree of which depends upon the rate of feed.
[Illustration: Fig. 935.]
Thus in Fig. 935 the three tools have the same amount of clearance, and
if they are supposed to be facing off the work they will maintain that
clearance under all conditions of work, diameter, and rate of feed, but
if they were traversed along instead of across the work the angle of the
tool (both on the top and bottom face) to the cut will become changed,
and will continue to change with every change of work diameter, so that
the same tool stands at a different angle at each successive cut taken
off the work, even though the lathe were used at or possessed but one
rate of feed. But lathe tools are used at widely varying rates of feed,
and we may therefore take an example in which a tool is at work taking a
cut of the same diameter and depth at different rates of feed.
[Illustration: Fig. 936.]
This is shown in Fig. 936, tool 1 taking the coarsest, and 2 the finest
feed, and it is seen that the finer the rate of feed the more clearance
the tool has with a given degree of side clearance (for all the three
tools have 7° of side angle). The only way to obtain an equal degree of
clearance from the cut, therefore, clearly lies in giving to a tool a
different angle for every variation, either in work diameter or in rate
of feed traverse, and to show how much this will affect the shape of the
tool, we have Fig. 937, in which the same rate of feed is used for all
three cuts, and the tool is given in each position 5° of clearance from
the cut. In position 1 the tool side stands at 8-1/2° of angle from line
A, which is at a right angle to the work axis. In position 2 it stands
at 10-1/2°, and in position 3 at 15° of angle from line A, a variation
of 6-1/2°. Referring now to the top face of the tool, the variations
occur to the same extent and from the same causes. It is in a fine
degree of perception of these points that constitutes the skill of
expert workmen in grinding their lathe tools, varying the angle of the
tool at every grinding to suit the varying requirements.
[Illustration: Fig. 937.]
It has been shown that for freedom of cutting and ease of driving a
given cut, the direction of top rake as well as its degree needs to be a
maximum that the nature of the material and its degree of hardness will
admit; but this is not the only consideration, because in a finishing
cut the surface requires to be left as smooth and clean cut as possible,
and it remains to consider how this may best be accomplished. Now let it
again be considered that it is that part of the cutting edge that lies
at a right angle to the axial line of the work that removes the metal,
while it is that part that lies parallel to the work axis (or in other
words parallel to the finished work surface) that performs the finishing
cutting duty.
[Illustration: Fig. 938.]
Now, in proportion as the length of the cutting edge is disposed
parallel to the work axis, the tool has a tendency to spring (under an
increase of cut) into the work, and also to dip into soft places or
seams in the work, and the amount of its front rake must be decreased,
because such rake causes a pressure pulling the tool deeper into its
cut, as was explained with reference to Fig. 921. Round-nosed front
tools, therefore, such as in Fig. 938, cannot be given so much front
rake as ordinary ones, such as in the preceding figures.
[Illustration: Fig. 939.]
Round-nosed tools are used to cut out round corners, and the roughing
tools are given a less curvature than that to be formed on the work,
thus in Fig. 939 is an ordinary form of small round nose shown operating
in what is termed a hollow corner, the directions of tool feed being
marked by arrows. The tool may be fed by the feed traverse, and the tool
gradually withdrawn, thus forming the work to the required curve.
The amount of cut a lathe will drive, the degree of hardness which the
tool may be given, the length of time the tool will last without
grinding, the speed at which the work may run, and the cleanness and
truth of the cut, depend almost entirely upon the perfect adaptability
of the tool to the conditions under which it is to be used. Upon the
same kind of work, and using the same kind of tools, some workmen will
give a tool from 20° to 30° more angle than others.
[Illustration: Fig. 940.]
It is a difficult matter to determine at just what point the utmost duty
is being obtained from cutting tools, because the conditions of use are
so variable; but one good general guide is the speed at which the tool
cuts, and another is the appearance of the cuttings or chips.
[Illustration: Fig. 941.]
Both these guides, however, can only be applied to metal not unusually
hard, and to tools rigidly held, and having their cutting edges
sufficiently close to the tool point or clamp that the tool itself will
not bend and spring from the pressure of the cut. The cutting speed for
chilled cast-iron rolls, such, for example, as calender rolls, is but
about 7 feet per minute, and the angles one to the other of the tool
faces is about 75 degrees, the top face being horizontally level, and
standing level with the axis of the roll.
When a tool has front rake only, the form of its cutting will depend
upon the depth of its cut. With a very fine cut the cutting will come
off after the manner shown in Fig. 940, while as the depth of the cut is
increased, the cutting becomes a coil such as shown in Fig. 941. These
coils lie closer together in proportion as the top face of the tool is
given less rake, as is necessary for steel and other hard metal. Thus
Fig. 940 represents a cutting from steel, the tool having front rake
only, while Fig. 941 represents a cutting from a steel crank pin, the
tool having side rake. The following observations apply generally to the
cuttings.
[Illustration: Fig. 942.]
The cleaner the surface of a cutting, and the less ragged its edges are,
the keener the tool has cut; thus, in Fig. 941, the raggedness shows
that the tool was slightly dulled, although not sufficiently so to
warrant the regrinding of the tool. Such a cutting, however, taken off
wrought iron would show a tool too much dulled, or else possessing too
little top rake to cut to the best advantage. In wrought iron, the tool
having a keener top face, the cuttings will coil larger, and the
direction in which they coil and move as they leave the tool will depend
upon the shape of the tool and its height to the work.
[Illustration: Fig. 943.]
[Illustration: Fig. 944.]
In Fig. 942, for example, is a tool having front and side angle in about
an equal degree, and its cutting is shown in Fig. 943, the side angle
causing it to move to the right, and the front angle causing it to move
towards the tool post.
The tool in Fig. 944 has side rake mainly, and the point is slightly
depressed, hence its cutting would leave the work moving horizontally
and towards the right hand.
[Illustration: Fig. 945.]
[Illustration: Fig. 946.]
In Fig. 945 the point of the tool is made considerably lower than the
point B, and as a result the cutting would rise somewhat vertically as
in Fig. 946. Indeed the heel B may be raised so as to cause the cutting
to move but little to the right, but rise up almost vertically, being
thrown over towards the work, and in extreme cases the cutting will rub
against the surface of the work and the friction will prevent the
cutting from moving to the right, hence it will roll up forming a ball,
the direction of the rotation occasionally changing.
Whatever irregularities may appear in the coil of the cuttings will, if
the tool is not dulled from use, arise from irregularities in the work
and not from any cause attributable to the tool.
The strength of a cutting forms to a great extent a guide as to the
quality of the tool, since the stronger the cutting the less it has
become disintegrated, and therefore less power has been expended in
removing it from the work.
The cutting speed for wrought iron should be sufficiently great that
water being allowed to fall upon the work in a quick succession of drops
as, say, three per second, the cuttings will leave the work so hot as to
be almost unbearable in the hands, if the cut is a heavy one, as, say,
reducing the work diameter 1/2 inch at a cut.
If wrought-iron cuttings break off in short pieces it may occur from
black seams in the work, but if they break off short and show no
tendency to coil, the tool has too little rake. If the tool gets dull
too quickly and the cutting speed is not excessive, then the tool has
too much clearance. If the tool edge breaks there is too much rake
(providing of course that the tool has not been burnt in the forging or
hardening), a fine feed will generally produce longer and closer coiled
cuttings (that is of smaller diameter) than a coarse feed, especially
if the work be turned dry or without the application of water.
[Illustration: Fig. 947.]
Aside from these general considerations which apply to all tools, there
are peculiar characteristics of particular metals; thus, for example,
cast iron will admit of the tool having a greater width of cutting edge
in a line with the finished surface of the metal than either steel,
wrought iron, copper or brass, which renders it possible to use a
finishing tool of the form shown in Fig. 947, whose breadth of cutting
edge A, lying parallel with the line of feed traverse, may always exceed
that for other metals, and may in the case of cast iron be increased
according to the rigidity of the work, especially when held close in to
the tool post.
[Illustration: Fig. 948.]
The corners B C may for roughing the work be rounded so as to be more
durable, but for finishing cuts they should be bevelled as shown,
because by this means face A can more easily be left straight than would
be the case with a rounded corner. In the absence of the bevels there
would be a sharp corner that would soon become dull. For finishing
purposes the corners need not be so much bevelled as in figure, but may
be very slightly relieved at the corners A and B, in Fig. 948, the width
of the flat nose being slightly greater than the amount of feed per
lathe revolution. Such tools produce the quickest and best work without
chattering when the conditions are such that the work and the tool are
held sufficiently rigid, and in that case may be used for the harder and
tougher metals, as wrought iron and steel.
We have now to consider the height of the tool with relation to the
work, which is a very important point.
[Illustration: Fig. 949.]
In Fig. 949, for example, let E be the washer or ring under the tool,
and F therefore the fulcrum from which the tool will bend. Let the
horizontal dotted line a represent the centre of the work, and it is
plain that to whatever amount the tool may spring under the pressure of
the cut, its motion from this spring will be in the direction of the
dotted arc H, causing the tool to dip deeper into the work in proportion
as the tool point is set above the work centre line A. Now the amount of
tool spring will even under the most rigid conditions vary in a heavy
cut with every variation in the depth of cut or in the hardness of the
metal. Furthermore, as the cutting edge of the tool becomes dulled from
use, its spring will increase, because the pressure required to force it
to its cut becomes greater, and as a result when the conditions are such
that a perceptible amount of tool spring or deflection occurs, the work
will not be turned cylindrically true. Obviously the work under these
conditions will be most true when the tool point is set level with the
line A, passing through the work axis.
[Illustration: Fig. 950.]
There are two advantages, however, in setting the tool above the work
centre: first it severs the metal easier; and second, it enables the
employment of more bottom rake without increasing the bottom clearance.
[Illustration: Fig. 951.]
Thus in Figs. 950 and 951 the diameters of the work W and the top rake
of the respective tools are equal, but the tool that is set above the
centre, Fig. 950, has more bottom rake but no more clearance, which
occurs from the manner in which the cutting edge is presented to the
work; the dotted lines represent the line of severance for each, and it
is obvious that in Fig. 950, being of the shortest length for the depth
of the cut will require least power to drive, because it is, as
presented to the work, the sharpest wedge, as will be perceived by
referring to Fig. 952, in which the tool shown in Fig. 950 is simply
placed below the work centre, all other conditions as angle, &c., being
equal.
From these considerations it appears that while for roughing cuts it is
advantageous to set the tool above the centre, it is better where great
cylindrical truth is required to set it at the centre for finishing cut.
[Illustration: Fig. 952.]
It may also be observed that if the lathe bed be worn it will usually be
most worn at the live centre end, where it is most used, and a tool set
above the centre will gradually fall as the cut proceeds towards the
live centre, entering the work farther, and therefore reducing its
diameter. This can be offset by setting the tailstock over, but in this
case the wear of the work centres is increased, and the work will be
more liable to gradually run out of true, as explained with reference to
turning taper work. Sir Joseph Whitworth recommends that the tool edge
be placed at the "centre" of the work, while at the same time on a line
with the middle of the body of the steel. To accomplish this result it
is necessary that the form of the tool be such as shown in Fig. 953, in
which W represents a piece of work, R the slide rest, A the fulcrum of
the tool support, the dotted line the centre of the work, and the arrow
the direction in which the tool point would move from its deflection or
spring. Now take the conditions shown in Fig. 954, and it will be
perceived at once that the least tool deflection will have an
appreciable effect in causing the tool point to advance into the work in
the direction denoted by the arrow. This would impair the cylindrical
truth of the work, because metals are not homogeneous but contain in
forged metals seams and harder and softer places, and in cast metals
different degrees of density, that part laying at the bottom of the
mould being densest (and therefore hardest) by reason of having
supported the weight of the metal above it when cooling in the mould.
[Illustration: Fig. 953.]
This brings us to another consideration, inasmuch as supposing the tool
edge to be set level with the work centre (as in Figs. 951 and 953), the
arc of deflection of the tool point will vary in its direction with
relation to the work according to the vertical distance of the top of
the tool rest (R in Figs. 953 and 954) from the horizontal centre of the
work.
Thus the vertical distance between the point A in Fig. 953 and the work
centre is less than that between A and the horizontal work centre in
Fig. 954, as may be measured by prolonging the dotted lines in both
figures until they pass over A, and then measuring the respective
vertical distances between A and those dotted lines. It is to be noted
that this distance is governed by the vertical distance of the top of
the tool rest R from the work centre, but where this distance is
required or desired to be reduced a strip of metal may be placed beneath
the tool and between it and the slide rest.
[Illustration: Fig. 954.]
It will now be obvious that to produce work as nearly cylindrical as
possible, the tool edge should stand as near to the slide rest as the
circumstances will permit, which will hold the tool more firmly and
prevent, as far as possible, its deflection or spring from the cut
pressure. Both in roughing out and in finishing, this is of great
importance, influencing in many cases the depth of cut the tool will
carry as well as the cylindrical truth of the work.
We may now present some others of the ordinary forms of tools used in
the slide rests on external or outside work, bearing in mind, however,
that these are merely the principal forms, and that the conditions of
practice require frequent changes in their forms, to suit the conditions
of access to the work, &c.
Fig. 955 represents a diamond point tool much used by eastern tool
makers. The sides are ground flat and the point is merely oil-stoned to
take off the sharp corner. This tool is used with very fine feeds as,
say, 180 work revolutions to an inch of tool traverse, taking very fine
cuts, and in sharpening it the top face only is ground; hence as the
height of the tool varies greatly before it is worn out, the tool
elevating device must have a great range of action.
[Illustration: Fig. 955.]
In Fig. 956 is shown a side tool for use on wrought iron; it is bent
around so that its cutting edge A may be in advance of the side of the
steel, and thus permit the cutting edge to pass up into a corner. When
it is bent to the left as in the figure, it is termed a right-hand side
tool, and per contra when bent to the right it is a left-hand tool. The
edge A must form an acute angle to edge B, so that when in a corner the
point only will cut, or when the edge A meets a radial face, as in Fig.
957, the cutting edge B will be clear of the work as shown.
[Illustration: Fig. 956.]
If the angle of A to B is such that both those edges cut at once, the
pressure due to such a broad cutting surface would cause the tool to
spring or dip into the work, breaking off the tool point and perhaps
forcing the work from between the lathe centres.
This tool may be fed from right to left on parallel work, or inwards and
outwards on radial faces, but it produces the truest work when fed
inwards on radial faces, and to the left on parallel work, while it cuts
the smoothest in both cases when fed in the opposite direction.
[Illustration: Fig. 957.]
It is a very desirable tool on small work, since it may be used on both
the stem of the work, and on the radial face, which saves the trouble of
having to put in a front tool to turn the stem, and a separate tool for
the radial face.
In cutting down a radial face with this tool, it is best (especially if
much metal is to be cut off), if the face of the metal is hard, to carry
the cut from the circumference to the centre, as shown in the plan view
in Fig. 958, in which _a_ is the cutting edge of the tool, B a collar
on a piece of work, _c_ the depth of the cut, and D a hard skin surface.
Thus the point of the tool cuts beneath the hard surface, which breaks
away without requiring to be actually cut.
[Illustration: Fig. 958.]
[Illustration: Fig. 959.]
Fig. 959 represents a cutting off or parting tool for wrought iron, its
feed being directly into the metal, as denoted by the arrow. This tool
should be set exactly level with the work centre when it is desired to
completely sever the work. When, however, it is used to merely cut a
groove, it may be set slightly above the centre.
[Illustration: Fig. 960.]
[Illustration: Fig. 961.]
When the tool is very narrow at _c_, Fig. 960, or long as in Fig. 961,
it may be strengthened by being deepened, the bottom B projecting below
the level of the tool steel, which will prevent undue spring and the
chattering to which this tool is liable.
[Illustration: Fig. 962.]
[Illustration: Fig. 963.]
To enable the sides of the tool to clear the groove it cuts, the width
at _c_ should slightly exceed that at D, and the thickness along the top
_a_ should slightly exceed that at the bottom B.
When the tool is used to cut a wide groove as, say, 3/8-inch wide, in a
small lathe, it is necessary to carry down two cuts, making the tool
about 1/4 inch wide at _c_, which is a convenient size, affording
sufficient strength for ordinary uses.
[Illustration: Fig. 964.]
[Illustration: Fig. 965.]
When used on wrought iron the top face may, with advantage, be given top
rake as in Fig. 962, which on account of causing the tool to cut easier,
will reduce the spring of the work W in the direction of arrow A. For
brass work, however, the top should be ground in an opposite direction,
as in Figs. 963 and 964, which will enable it to cut smoother and with
less liability to rip into the metal, especially if the tool requires to
be held far out from the tool post. To capacitate the tool to cut a
groove close up to a shoulder, it should be forged to the shape shown in
Fig. 965. As it is very subject to spring, it should not, unless the
conditions are such as to give rigidity to both the work and the tool,
be set above the work centres.
[Illustration: Fig. 966.]
When a grooving or parting tool is to be used close up to the lathe dog,
its cutting end may be bent at an angle, as in Fig. 966, so that it may
be adjusted on the lathe rest, so that the work driver will not strike
against the slide rest.
[Illustration: Fig. 967.]
In Figs. 967, 968, and 969, are represented the facing tool, side tool,
or knife tool, as it is promiscuously termed, which is sometimes made
thicker at the bottom as in Fig. 969. It is mainly used for squaring up
side faces, as upon the ends of work or the sides of heads or collars. A
is the cutting edge which may be ground so as to cut at and near the
end, for large work in which it is necessary to feed the tool in with
the cross slide, or to cut along its full length for small work in which
the longitudinal feed is used. To facilitate the grinding, the bottom
may be cut away, as at B in Fig. 968.
[Illustration: Fig. 968.]
[Illustration: Fig. 969.]
In some practice the bottom B, Fig. 969, of the tool, is made thicker
than the top A, which is, however, unnecessary, unless for heavy cuts,
for which the tool would be otherwise unsuitable on account of weakness.
For all ordinary facing purposes, it should be made of equal thickness,
which will reduce the area to be ground in sharpening the tool.
[Illustration: Fig. 970.]
[Illustration: Fig. 971.]
On small work the edge A A should be ground straight, and set at a right
angle to the work, so that it may face off the whole surface at once,
but for work of large diameter it should be ground and set as in Figs.
970 and 971, so that it will cut deepest at the end E, enabling it to
carry a finishing cut from the circumference to the centre, by feeding
it with the cross-feed screw.
[Illustration: Fig. 972.]
The cutting edge should be level with the centre of the work, the angle
of the top face D being about 35 degrees in the direction of the arrow C
for wrought iron, and level if used for brass. When this tool is to be
used for a face close to the work driver it should be bent at an angle
as in Fig. 972, so as to enable the driver to clear the slide rest, and
when used for countersunk head bolts, it may be bent at an angle as in
Fig. 973, so that when it is once set to give the head the correct
degree of taper, it will turn successive heads to the correct taper
without requiring each head to be fitted to its place.
[Illustration: Fig. 973.]
In Fig. 974 is shown the spring tool which is employed to finish
smoothly round corners or sweeps, which it will do to better advantage
than any other slide rest tool, because it is capable of carrying a
larger amount of cutting edge in simultaneous operation. This property
is due to the shape of the tool, the bend or curve serving as a spring
to enable the tool to bend rather than dig into the work.
[Illustration: Fig. 974.]
This form of tool is sometimes objected to on the ground that it does
not turn true, but this is not the case if the tool is properly formed
and placed at the correct height with relation to the work. In the first
place the top face should, even on wrought iron, have but very little
top rake, and indeed none at all if held far out from the tool post,
while for brass, negative top rake may be employed to advantage. The
height of the cutting edge B should be level with the top of the tool
steel as denoted by the dotted line in the figure, and in no case should
it stand above that level. The cutting edge should be placed about
level with the horizontal centre of the work, but in no case above it.
It is from this error that the tool is frequently condemned, because if
placed above, the broad cutting edge causes the tool to spring slightly
and dig into the metal, whereas when placed at the middle of the height
of the work the spring will not have that effect, as already explained
when referring to front tools. Furthermore, the spring of the tool (from
inequalities in the texture or from seams in the metal) will be in a
line so nearly coincident with the work surface that the latter will be
practically true, and from the smoothness and the evenness of the curve
this tool will produce a much better work than any other tool, unless
indeed the curve be of a very small radius, as, say, about 1/4 inch
only, in which case a hand tool such as shown in Fig. 1292 may be
employed; spring tools are intended to finish only, and not to rough out
the work.
[Illustration: Fig. 975.]
The curves, as B in Fig. 974 for a round corner and C for a bead, should
be carefully and smoothly finished to the required curve and the top
face only ground to sharpen the tool, so as to maintain the curve as
nearly as possible; but if the curve is a very large one, the tool will
require to be a part of the curve only, and must be operated by the
slide rest around the curve.
For finishing the curves or round corners in cast-iron work the spring
tool is especially advantageous, as it will produce a polished clean
surface of exquisite finish if used with water, and the cutting speed is
exceedingly slow, as about 7 feet per minute.
LATHE SLIDE REST TOOLS FOR BRASS WORK.
Nearly all the tools used in the slide rest upon iron work may be
employed upon brass work, but the top faces should not have rake, that
is to say, they should have their top faces lying in the same plane as
the bottom plane of the tool steel which rests on the slide rest. For if
the top face is too keen it rips rather than cuts the brass, giving it a
patchy, mottled appearance.
[Illustration: Fig. 976.]
Fig. 975 represents a front tool for brass, which is used for carrying
cuts along outside work or for facing purposes, corresponding, so far as
its use is concerned, to the diamond point or front tool for iron. The
top face of this tool must in no case be given rake of any kind, as that
would cause it to tear rather than to cut the metal, and also to
chatter. The point A should be slightly rounded and the width at B and
depth at C must be regulated to suit the depth of cut taken, the rule
being that slightness in either of these directions causes the tool to
chatter. When held far out from the tool post or under other conditions
in which the tool cannot be rigidly held, the top face should be ground
away towards the end, thus depressing the point A, after the manner
shown with reference to the cutting-off tool for brass in Fig. 963. The
manner in which the cuttings come off brass work when a front tool is
used, depends upon the hardness of the brass and the speed at which the
tool cuts.
[Illustration: Fig. 977.]
[Illustration: Fig. 978.]
In the harder kinds of brass, such as that termed gun metal,
composition, or bell metal, the cuttings will fly off the tool in short
angular grains, such as indicated in Fig. 976, travelling a yard or two
after leaving the tool if a fairly quick cutting speed is used. But if
the cutting speed is too slow the cuttings will come off slowly and fly
but a few inches. In the softer kinds of brass, such as yellow brass,
the cuttings are longer and inclined to form short curls, which will, if
cut at a high speed, fly a few inches only after leaving the tool.
In Fig. 977 is shown a right-hand side tool for brass work. It is used
to carry cuts along short work, and to carry facing cuts at the same
time, thus avoiding the necessity to move the position of the tool to
enable it to carry a facing cut, as would be necessary if a front tool
for brass were used. It is peculiarly adapted, therefore, for brass
bolts, or other short work having a head or collar to be faced
especially; hence, it may be traversed to its cut in either direction
without requiring to be moved in the tool post. It may also be used to
advantage for boring purposes. It will be found that this tool will cut
smoother and will be less liable to chatter if its top face is ground
slightly down towards the point and if it be not forged too slight
either in depth or across B. Its clearance on the side is given by
forging it to the diamond shape shown in the sectional view. To make the
tool a left-handed one it must be bent to the right, the clearance being
in any case on the inside of the curve.
[Illustration: Fig. 979.]
The forms of single-pointed slide rest tools employed to cut [V]-threads
in the lathe are shown in Fig. 978, which represents a tool for
external, and Fig. 979, which represents one for an internal [V]-thread,
the latter being a tool ground to accurate shape and secured in a holder
by the set screw S.
It is obvious that a Whitworth thread might be cut with a single-pointed
tool such as shown in Fig. 980, the corner at B being rounded to cut the
rounded tops of the thread. It is more usual, however, to employ a
chaser set in the tool point in the same manner as a single-pointed
tool, or in a holder fixed in the tool post. When a single-pointed tool
is employed to cut a thread, the angles of its sides are not the same as
the angle of the thread it produces, which occurs because the tool must
have clearance to enable it to cut. In Fig. 981, for example, is a
single-pointed tool without any clearance, and, as a result, it cannot
enter the work to cut it. In Fig. 982 the tool is shown with clearance,
and, as a result, the angle of the cutting edge is not the same angle as
the sides of the tool are, because the top face is not at a right angle
to the sides of the tool. It is obvious that the angle of the sides of
the tool must be taken along the dotted line in Fig. 982.
[Illustration: Fig. 980.]
It follows then that a tool whose sides are at a given angle will cut a
different angle of thread for every variation in the amount of
clearance. But whatever the amount of clearance may be, the tool will
produce correct results providing that the gauge to which the tool is
ground is held level, as in Fig. 983 at A, and not at an angle as at B.
The tool, however, must be set at the correct height with relation to
the work, and its top surface must point to the work axis to produce
correct results.
[Illustration: Fig. 981.]
[Illustration: Fig. 982.]
Suppose, for example, that in Fig. 984 A is a piece of work, its
horizontal centre being represented by the dotted line C, and its centre
of revolution being at C. Now suppose D is a screw-cutting tool cutting
a depth of thread denoted by E. G is another lathe tool having teeth of
the same form and angle as D, but lifted above the horizontal centre of
the work. The depth of thread cut by G is denoted by F, which is
shallower, though it will be seen that the point of G has entered the
work to the same depth or distance (of the tool point) as D has. It is
obvious, however, that for any fixed height, a tool suitable to cut any
required depth or angle can be made, but it would be difficult to gauge
when the tool stood at its proper height.
[Illustration: Fig. 983.]
To facilitate setting the height of the tool, a gauge such as shown in
Fig. 985 may be used, the height of the line A from the base equalling
the height or distance between the top surface of the cross slides and
the axial line of the lathe centres. If the lathe, however, have an
elevating slide rest, the rest must be set level before applying the
gauge. Or in place of using the gauge, the tool stool or tool holder, as
the case may be, may be made of such height that when level in the tool
post its top face points to the axis of the lathe centre, the tool being
sharpened on the angles and not ground on the top face.
[Illustration: Fig. 984.]
[Illustration: Fig. 985.]
But in the case of a tool holder, or of a chaser holder, the tool may be
ground on the top face, and adjusted for height by any suitable means,
the top of the holder serving as a guide to set the tool by.
[Illustration: Fig. 986.]
The line of the cutting edge of the tool must, to obtain correct
results, be presented to the work in the same manner as it was presented
to the gauge to which its angles were ground, so that if the tool were
in position in the tool post, and the gauge were applied, it would point
to the axis of the lathe centre, for if this is not the case the thread
cut will not be of correct angle or depth. Thus, in Figs. 986 and 987
the tool T would cut threads too shallow, although placed at the correct
height, because the cutting edges are at an angle to the radial lines C
C.
[Illustration: Fig. 987.]
It becomes obvious, then, that it is improper to set the height of a
screw-cutting tool by means of any tool elevating or setting-device that
throws it out of the horizontal position. To enable the correct setting
of threading tools, and to avoid having to grind the angles correct to
gauge every time the tool requires sharpening, various kinds of tool
holders have been designed by means of which the tool may be ground on
the top face, and set at correct height and in the proper plane.
[Illustration: Fig. 988.]
[Illustration: Fig. 989.]
To facilitate grinding the tools to a correct angle, the gauge shown in
Fig. 988 is employed, the various notches being for the pitches of
thread for which they are respectively marked, but, the edge of the
gauge being circular, does not afford much guide to the eye in grinding
the angles equal from the sides of the body of the tool; hence the form
of gauge shown in Fig. 989 is preferable, because the tool can be so
ground that the edge of the gauge stands parallel with the side of the
tool steel, so that the tool will, when in correct position, point
straight to the work axis. To insure correctness in setting the tool, it
may then be set with a square S in Fig. 990, held firmly with its back
against the side of the tool, which may be adjusted in the tool post
until the blade B comes fair with the work.
[Illustration: Fig. 990.]
Another method of setting the tool is with a gauge as in Fig. 991, which
sets it true with the angle independent of whether the angle is true
with the side of the tool or not. In Fig. 992 is a form of gauge that
will serve to grind the tool by to correct angle, and also to set it in
the lathe by the angles, independent of the side of the tool.
The same gauge may be used for setting internal threading tools by first
facing the work quite true and then applying the gauge as in Fig. 993.
[Illustration: Fig. 991.]
[Illustration: Fig. 992.]
[Illustration: Fig. 993.]
By reason of the comparatively sharp points of thread-cutting tools,
they are more readily dulled than the rounder pointed ordinary lathe
tool, and by reason of their cutting edges extending along a greater
length of the work, and therefore causing it to spring or bend more from
the strain of the cut, they cannot be employed to take such heavy cuts
as ordinary tools. Hence, in all thread cutting, it is necessary to turn
the work down to the finished diameter before using the threading tool,
so that the thread will be finished when it is cut to the proper depth.
To test that depth on a piece of work having a United States standard,
or a sharp [V]-thread, a gauge such as shown in Fig. 994 may be used,
consisting of a piece of sheet steel about 1/50 inch thick, having a
single tooth formed correct for the space of the thread, so that the
edge of the gauge will meet the tops of the thread when the space is cut
to admit the tooth on the gauge; the most accurate method of producing
such a gauge having been described in the remarks upon screw threads.
[Illustration: Fig. 994.]
If the tool is known to be ground to the correct angle and is set
properly, the gauge for depth may be dispensed with by turning the body
of the work to correct diameter, and also turning a small part, as a in
Fig. 995, down to the correct diameter for the bottom of the thread, so
that when the tool point meets A the thread will be cut to correct
depth.
[Illustration: Fig. 995.]
Figs. 996 and 997 represent a method of cutting a round top and bottom,
or any other form of thread, by means of a single-pointed circular
cutting tool, which is mounted on a holder. On the circumference of the
cutter is cut a single thread, and a piece is cut out at E to form a
cutting edge. To cut a right-hand thread on the work, a left-hand one
must be cut on the cutter, so as to make its thread slant in the proper
direction. The tool is sharpened by grinding the top face, and moved on
the holding pin to set it to the proper height or in position to enable
it to cut. A top view of the tool and holder is shown in figure 997.
[Illustration: Fig. 996.]
It is obvious that two gaps may be cut in the wheel or cutter so as to
provide two cutting edges, one of which may be used for roughing, and
the other for finishing cuts.
[Illustration: Fig. 997.]
In roughing out coarse threads, a single-pointed tool, formed as in Fig.
998, and set considerably above the centre as shown, may be used to
great advantage. It will carry a heavy cut and throw off a cutting but
very little curved; hence but little power is absorbed in bending the
cutting. To preserve the cutting edge, the point of the tool should be
slightly rounded. Such a tool, however, requires to be rigidly held, and
requires experience to use it to the best advantage.
[Illustration: Fig. 998.]
An English tool holder for a single-pointed tool for cutting coarse
pitch threads, such as square threads, is shown in Fig. 999. The stem of
the holder is cylindrical, and is held between two clamping pieces,
while the short piece of steel used as a tool (which is thinnest at the
bottom, so as to provide for the clearance without grinding it) is
clamped in a swiveled post, so that it may be set at the angle sideways
required for the particular pitch of thread to be cut, as is shown in
the end view.
[Illustration: Fig. 999.]
[Illustration: Fig. 1000.]
[Illustration: Fig. 1001.]
The difficulty of adjusting the height of threading tools that are
ground on their top faces to sharpen them is obviated in a very
satisfactory manner by the tool holder patented by the Pratt and Whitney
Company, and represented in Figs. 1000 and 1001. A is the body of the
holder, C is the tool clamp, and B the set screw for C; D is a pin fast
in A and projecting into C to adjust it square upon A. The threading
tool G has a groove H, into which the projection E fits, so that the
tool is held accurately in position. F is the screw which adjusts the
height of the tool, being threaded into A and partly into G, as is shown
at I. The holder once being set in correct position, the threading tool
may be removed for grinding, and reset with accuracy. The face K of the
holder is made at 30° to the front or leading face of the holder, so
that the stem or body of the holder will be at an angle and out of the
way of the work driver.
[Illustration: Fig. 1002.]
If a chaser instead of a single-pointed tool be used to cut a thread,
the thread requires to be gauged for its full diameter only, because
both the angles of the thread sides and the thread depth are determined
by the chaser itself. Chasers are also preferable to a single-pointed
tool when the work does not require to be cut to an exact diameter, nor
to have a fully developed thread clear up to a shoulder; but when such
is the case a single-pointed tool is preferable, because if the leading
tooth should happen to run against the shoulder the whole of the teeth
dig into the work, and more damage is done to it than with a
single-pointed tool. When the thread does not run up to a shoulder, or
in cases where the thread may be permitted to run gradually out, and,
again, where the thread is upon a part of enlarged diameter, a chaser
may have its efficiency increased in two ways, the first of which is
shown in Fig. 1002. When the chaser is set and formed as at A in the
figure, the leading tooth takes all the cut, and the following tooth
will only cut as it is permitted to do so from the wear of the leading
bolt. This causes the tooth to wear, but the teeth may be caused to each
take a proportion of the cut by chamfering them as at B in the figure,
which will relieve the front tooth of a great part of its duty and let
the following teeth perform duty, and thus preserve the sharpness of the
cutting edges. We are limited in the degree of chamfer that may be given
to the teeth, first, because as the cutting edge is broader and the
strain of the cut is greater it causes the tool to spring or bend more
under the cut pressure; and secondly, because if the tool be given many
teeth in order to lengthen the chamfer, then the pitch is altered to a
greater extent by reason of the expansion which accompanies the
hardening of the chaser.
[Illustration: Fig. 1003.]
[Illustration: Fig. 1004.]
A chaser thus chamfered may be set square in the tool post by placing a
scale against the work as at S in Fig. 1003, and setting the bottoms of
the chaser teeth fair with the outer edge of the scale as in the figure.
The second method of increasing the efficiency of a chaser is to grind
the top face at an angle as from A to B in Fig. 1004, and set it so that
the last tooth B is at or a little above the work axis D. This causes
the last tooth B to stand sufficiently nearer the work axis than the
other teeth to enable it to take a light scraping cut, producing a
smooth cut, because the duty on the last tooth being light it preserves
its cutting edge, and therefore its form.
Chasers are often in shops, doing general work, formed in one piece in
the same way as an ordinary tool, but it is preferable to use short
chasers and secure them in holders.
[Illustration: Fig. 1005.]
Figs. 1005 and 1006 show a convenient form of holder, the chaser A being
accurately fitted into a recess in the holder D, so that it may be set
square in the holder without requiring to be adjusted to come fair with
the thread grooves after having been ground to resharpen it. The short
chasers are held by the clamp B, which has at C a projection fitting
into a recess in the holder to cause the clamp to adjust itself fairly.
In setting a chaser to correct position in a tool post the points of the
teeth may be set to the surface of the work as in Fig. 1007, or if the
thread is partly produced and the lathe has a compound slide rest, the
tool may be set to the tops of the thread as in Fig. 1008, and then
brought into position to meet the thread grooves by operating the slide
rest.
[Illustration: Fig. 1006.]
[Illustration: Fig. 1007.]
[Illustration: Fig. 1008.]
It is obvious that the height and position of a chaser require to be as
accurately set as a single-pointed tool, but it is more difficult to set
it because it can only be sharpened by grinding the top face, and this
alters the height at each grinding.
Thus, suppose that when new its teeth are of correct height, when the
bottom face I, Fig. 1009, lies upon the rest R, the face H being in line
with the centre B B of the work, then as face H is ground the tool must
be lifted to adjust its height. On account, however, of the curve of the
teeth it is very difficult to find when the chaser is in the exact
proper position, which in an ordinary chaser will be when it has just
sufficient clearance to enable it to cut, as is explained with reference
to cutting up chasers and using them by hand.
[Illustration: Fig. 1009.]
To obviate these difficulties, an excellent form of chaser holder is
shown in Figs. 1010 and 1011. Its top face C being made of such a height
that when the holder rests on the surface of the slide rest and is in
the tool box, C will stand horizontally level with the horizontal centre
of the work, as denoted by the horizontal line D E; then the tool proper
may have long teeth as denoted by A, and the surface of the teeth may
always be brought up level with the top surface of the tool holder as
tested with a straight-edge. This is a ready and accurate mode of
adjustment. A top view of the tool holder is shown in Fig. 1011, in
which A is the tool holder, B the threading tool, with a clamp to hold
B, and a screw to tighten the clamp.
[Illustration: Fig. 1010.]
It may now be pointed out that a common sharp [V]-chaser may be used to
cut a United States standard thread by simply grinding off the necessary
flats at the points of the teeth, because when the chaser has entered
the work to the proper depth it will leave the necessary flat places at
the top of the thread, as is shown in Fig. 1012.
In cutting internal, inside, or female threads (these terms being
synonymous) the diameter of the bore or hole requires to be made of the
diameter of the male thread _at the root_.
[Illustration: Fig. 1011.]
Since, however, it is impracticable to measure male threads at the root,
it becomes a problem as to the proper size of hole to bore for any given
diameter and pitch of thread. This, however, may be done by the
following rules:--
To find the diameter at the roots or bottom of the thread of United
States standard threads:
Rule.--Diameter - (1.299 ÷ pitch) = diameter at root.
Example.--What is the diameter at the root of a United States standard
thread measuring an inch in diameter at the top of the thread and having
an 8 pitch?
Here 1.299 ÷ 8 = .162375.
/ 1.000000 \
Then 1 - .162375 | .162375 | = .8376.
| -------- |
\ .837635 /
For the sharp [V]-thread the following rule is employed:
Rule.--Diameter - (1.73205 ÷ pitch) = diameter at root.
Example.--What is the diameter at the root of a sharp [V]-thread of 8
pitch, and measuring 1 inch diameter at the top of the thread?
Here 1.73205 ÷ 8 = .21650.
/ 1.0000 \
Then 1 - .2165 | .2165 | = .7835.
| ------ |
\ .7835 /
For cutting square threads the class of tool shown in Fig. 1013 is
employed, being made wider at the cutting point C than at B or at D, so
that the cutting may be done by the edge C, and the sides _a_ may clear,
which is necessary to reduce the length of cutting edge and prevent an
undue pressure of cut from springing the work.
[Illustration: Fig. 1012.]
The sides of the tool from _a_ to B must be inclined to the body of the
tool steel, as shown in Fig. 1014, the degree of the inclination
depending upon the pitch of thread to be cut. It may be determined,
however, by the means shown in Fig. 1015.
[Illustration: Fig. 1013.]
[Illustration: Fig. 1014.]
[Illustration: Fig. 1015.]
Draw the line A, and at a right angle to it line B, whose length must
equal the circumference of the thread to be cut and measured at its
root. On the line A set off from B the pitch of thread to be cut as at
C, then draw the diagonal D, which will represent the angle of the
bottom of the thread to the work axis, and the angle of the tool sides
must be sufficiently greater to give the necessary clearance. The width
of the point C of the tool should be made sufficiently less than the
width of the thread groove to permit of the sides of the thread being
pinched (after the thread is cut to depth) with a tool such as was shown
in Fig. 968.
[Illustration: Fig. 1016.]
For coarser pitches the thread is cut as shown in Fig. 1016. The tool
is made one-half the width of the thread groove, and a groove, _a_, _a_,
_a_, is cut on the work. The tool is then moved laterally and a second
cut as at B B is taken, this second cut being shown in the engraving to
have progressed as far as C only for clearness of illustration. When the
thread has in this manner been cut to its proper depth, the side tools
are introduced to finish the sides of the thread. If the thread is a
shallow one each side may be finished at one cut by a side tool ground
and set very true; but in the case of a deep one the tool may be made to
cut at and wear its end only, and after taking a cut, the tool fed in
and another cut taken, and so on until, having begun at the top of the
thread, the tool operated or fed, after each traverse, by the cross
feed, finally reaches the bottom of the thread. If a very fine or small
amount of cut is taken, both sides of the thread may in this way be
finished together, the tool being made to the exact proper width.
[Illustration: Fig. 1017.]
[Illustration: Fig. 1018.]
When used on wrought iron the tool is sometimes given top rake, which
greatly facilitates the operation, as the tool will then take a heavier
as well as a cleaner cut.
[Illustration: Fig. 1019.]
After the first thread cut is taken along the work, it is usual to
remove it from the lathe and drill, at the point where it is desired
that the thread shall terminate, a hole equal in diameter to the width
of the thread groove, and in depth to the depth of the thread. This
affords relief to the cutting tool at the end of the cut, enables the
thread to end abruptly, and leaves a neat finish.
[Illustration: Fig. 1020.]
On account of the broad cutting edge on a screw-cutting tool, the lathe
is always run at a slower speed than it would be on the same diameter of
work using an ordinary turning tool. After the tool is set to just clear
the diameter of the work it is moved (for a right-hand thread) past the
end of the work at the dead centre, and a cut is put on by operating the
cross-feed screw. The feed nut is then engaged with the feed screw and
the tool takes its cut as far along the work as the thread is to be,
when the tool is rapidly withdrawn from the work and the lathe carriage
traversed back again, ready to take another cut. If, however, the thread
to be cut runs close up to a shoulder, head, or collar, the lathe may be
run slower as the tool approaches that shoulder by operating the belt
shipper and moving the overhead belt partly off the tight pulley and on
to the loose one, or the lathe may be stopped when the tool is near the
shoulder and the belt pulled by hand.
An excellent method of finishing square threads after having cut them in
the lathe to very nearly the finished dimensions is with an adjustable
die in a suitable stock, such as in Figs. 1017 and 1018, in which S is a
stock having handle H, and containing a die D, secured by a cap C,
pivoted at P. To adjust the size of the die, two screws, _a_ and _b_,
are used, _a_ passing through the top half of the die and threading into
the half below the split, while _b_ threads into the lower half and
abuts against the face of the split in the die, so that, by adjusting
these two screws, the wear may be taken up and the size maintained
standard. This device is used to take a very light finishing cut only,
and is found to answer very well, because it obviates the necessity of
fine measurement in finishing the thread. The die D is seated in a
recess at the top and at the bottom so as to prevent it moving sideways
and coming out.
LATHE TOOL HOLDERS FOR OUTSIDE TOOLS.--When a lathe cutting tool is made
from a rectangular bar of steel it requires to be forged to bring it to
the required shape at the cutting end, and to avoid this labor, and at
the same time attain some other advantages which will be referred to
presently, various forms of tool holders are employed.
These holders fasten in the tool post, or tool clamp, and carry short
tools, which, from their shapes and the manner in which they are
presented to the work, require no forging, and maintain their shapes
while requiring a minimum of grinding.
Fig. 1019 represents a side view of Woodbridge's tool holder at work in
the lathe, and Fig. 1020 is a view of the same set at an angle to the
tool rest. Fig. 1021 is an end view of the tool and holder removed from
the lathe.
The tool seat A is at an angle of about 4 degrees to the base of holder
(a greater degree being shown in the cut for clearness of illustration),
so that the side J of the tool will stand at an angle and have clearance
without requiring such clearance to be produced by grinding. The seat B
of the cap C upon the tool is curved, so that the cap will bind the
middle of the tool and escape the edges, besides binding the tool fair
upon its seat A. The top face is formed at the angle necessary for free
and clean cutting, and the tools are, when the cutting edge is provided
at one end only, hardened for half their length.
The holder, and therefore the tool, may obviously be swung at any chosen
angle of the work or to suit the requirements.
[Illustration: Fig. 1021.]
[Illustration: Fig. 1022.]
[Illustration: Fig. 1023.]
Fig. 1022 shows a right and left-hand diamond-point tool in position in
the holder with the cap removed, the cutting edge being at G, the angle
of the top face being from F to E. The tool, it will be observed from
the dotted line, is supported close up to its cutting corner.
[Illustration: Fig. 1024.]
Fig. 1023 shows a right and left-hand side tool in position, the dotted
line showing that it is supported as close to the cutting edge D as the
nature of facing work will permit. When left-hand tools are used the
holder is turned end for end, so as to support the tools in the same
manner as for right-hand ones, and for this purpose it is that the
holder is beveled off at each end.
By grinding both ends of one tool, however, to the necessary shape and
angle, one tool may be made to serve for both right and left, the tool
holder being simply reversed end for end in the tool post. There are,
however, furnished with each holder a right and left-hand diamond point
and a right and left-hand side tool, each being hardened for half its
full length.
It is obvious, however, that there is no front rake to the tool, and
that it therefore derives its keenness from the amount of side rake,
which may be regulated to suit the conditions.
When tool holders of this class are employed, the end face only of the
tool requires grinding to resharpen the cutting edges; hence the area of
metal requiring to be ground is much less than that on forged tools, and
therefore the grinding occupies less time; and if the workman grinds the
tools, he is enabled to run more lathes and not keep them idle so long
while grinding the tool. Or if the tools are kept ground in stock (about
200 of the tools or cutters serving to run 24 lathes a week) the workman
has but to slip in a new tool as the old one becomes dull, no adjustment
for height being necessary as in the forged tool.
When the tool requires to be set to an exact position, as in the case of
screw cutting, it is desirable that the tool holder be so constructed
that the tool may be removed therefrom and replaced without disturbing
the position of the tool holder in the tool post or tool clamp; and
means must therefore be provided for securing the tool to the holder
independently of the tool post or clamp screw. Fig. 1024 represents a
tool holder possessing these features: H is the holder provided with a
clamp C, secured by a screw B, T representing the tool, which is in this
case a chaser, having teeth down the full length of its front face; K is
a key or feather fast in the holder H, and fitting into a groove
provided in the side of the tool. The vertical angle of this feather
obviously determines the angle of clearance at which the tool shall
stand to the work.
The Pratt and Whitney Company, who are the manufacturers of this holder,
make this angle of clearance 15 degrees. The height of the tool in the
holder is adjusted by the screw S, which has journal bearing in the
holder, and threads to the end edge of the tool.
Now it is obvious that the holder H, once being set to its proper
position in the tool post, the tool T may be removed from and replaced
in the exact same position, both in the holder and with reference to the
work.
In Fig. 1025, for example, is a top view of the holder with a
single-pointed threading tool T in place. W represents a piece of work
supposed to be in the lathe, and G a tool-setting gauge; and it is
obvious that, if the holder is not moved, the tool T may be removed,
ground up, and replaced with the assurance that it will stand in the
exact same position as before, producing the exact same effect upon the
work, providing that the height is maintained equal, and the tool is not
altered in shape by the grinding. To maintain the height equal, all that
is necessary is to have the upper face (H, Fig. 1024) of the holder
horizontally level and in line with the line of centres of the lathe,
and to set the top face of the tool level with that of the holder. In
sharpening the tool the top face only is ground; hence the angles are
not altered.
Fig. 1026 represents the holder with a tool in position to true up a
lathe centre, the angle of the tool holder to the line of centres being
the same as in Fig. 1025; and Fig. 1027 represents various forms of
tools for curves. All these serve to illustrate the advantages of such a
tool holder.
[Illustration: Fig. 1025.]
If, for example, a piece of work requires the use of two or more such
tools, and the holder is once set, the tools may be removed and
interchanged with a certainty that each one put into place will stand at
the exact angle and position required, not only with relation to the
work, but also in relation to the other tools that have preceded it.
Each hollow or round will not only be correct in its sweep, but will
also stand correct in relation to the other sweeps and curves, no matter
how often the tools may be changed. Inasmuch as the tool is ground at
the top only for the purpose of resharpening, it maintains a correct
shape until worn out.
[Illustration: Fig. 1026.]
The pin shown at _f_ in Fig. 1024 is fast in the holder, and fits
loosely in clamp C to prevent it from swinging around on B when B is
loosened.
When the tool requires to preserve its exact shape it may also be made
circular with the required form for the cutting edge formed round the
perimeter. Thus Figs. 1028 and 1029, which are extracted from _The
American Machinist_, represent tool holders with circular cutting tools.
[Illustration: Fig. 1027.]
The holder A fits the lathe tool post, carrying the cutting tool B,
which is bolted to the holder and has at F a piece cut out to form the
cutting edge.
To facilitate the grinding, holes are drilled at intervals through B. A
plan view of this tool and holder is shown at C, the shape of the
cutting edge being shown at D. The cutting edge is shown in the side
view to be level with the centre of the tool holder height, but it may
be raised to the level of the top of the tool steel by raising the hole
to receive the bolt that fastens the cutter, as is shown at E; or the
cutter may be mounted on top of the holder as shown at H, having a stem
passing down through the holder, and capable of being secured by the
taper pin I. A plan view of this arrangement is shown at J.
[Illustration: Fig. 1028.]
[Illustration: Fig. 1029.]
[Illustration: Fig. 1030.]
[Illustration: Fig. 1031.]
Another form of circular cutter is shown in Fig. 1030. It consists of a
disk or cutter secured to a holder fitted to the tool post, the cutter
edge being formed by a gap in the disk, as shown in the figure, which
represents a cutter for a simple bead or round corner. The front end of
the holder has a face A, whose height is level with the line of lathe
centre when the holder is set level in the tool post. Hence the top face
of the cutting edge may be known to be set level with the line of
centres when it is fair with the face A of the holder. The bottom
clearance is given by the circular shape of the cutter, while side
clearance may be given by inclining the face B of the holder (against
which the face of the cutter is bolted) to the necessary angle from a
vertical line. The face C is ground up to resharpen the cutting edge,
and may be reground until the circumference of the wheel is used up.
Figs. 1031, 1032, 1033, and 1034 represent lathe tool holders by Messrs.
Bental Brothers, of Fullbridge Works, Maldon, England. The holder
consists of a bar A, having at the front end a hub H, containing a bush
in two halves, through which the tool T passes; this tool consisting of
a piece of [V]-shaped steel. A set screw on top of the hub clamps the
two half-bushes together, and these, as their faces do not meet, grip
the tool.
[Illustration: Fig. 1032.]
[Illustration: Fig. 1033.]
[Illustration: Fig. 1034.]
The advantage possessed by this form of holder is that the top face of
the tool may be given any desired degree of side rake or angle required
by the nature of the work by simply revolving the bushes in the hub of
the holder. Thus, in Fig. 1034 the top face of the tool stands level, as
would be required for brass work; in Fig. 1032 the tool is canted over,
giving its top face angle a rake in the direction necessary when cutting
wrought iron and feeding toward the dead centre; and in Fig. 1033 the
tool is in position for carrying a cut on wrought iron, the feed being
toward the live centre of the lathe. This capacity to govern the angle
of the top face of the tool is a great advantage, and one not possessed
by ordinary tool holders, especially since it does not sensibly alter
the height of the tool point with relation to the work. Again, the
[V]-shape of the tool steel causes the bushes to grip and support the
tool sideways, and, by reducing the area of tool surface requiring to be
ground, facilitates the tool grinding to that extent. Altogether, this
is an exceedingly handy device. It is obvious, however, that it cannot
be moved from side to side of the tool rest unless a right and left-hand
tool holder be used; that is to say, there must be two holders having
the hub on the opposite side of the body A.
[Illustration: Fig. 1035.]
[Illustration: Fig. 1036.]
Figs. 1035, 1036, 1037, and 1038 represent tool holders in which the
tools consist of short pieces of steel held end-wise and at a given
angle, so that the amount of clearance is constant. The holders Figs.
1035 and 1036 are split, and the tool is secured by the screw shown.
Fig. 1037 represents a tool holder in which the tool is held by a clamp,
whose stem passes through the body of the holder so as to bring the
fastening nut out at the end, where it is more convenient to get at than
are the screw heads in Figs. 1035 and 1036. It is obvious, however, that
such a holder is weak and unsuitable for any tools save those used for
very light duty indeed, while all this class of holders is open to the
objection that the side of the holder prevents the tool from passing up
into a corner, hence the cut cannot be carried up to a shoulder on the
work. This may, however, be accomplished by bending the end of the
holder round; but in this case two holders, a right and a left, will be
necessary.
Fig. 1038 represents a form of tool holder of this kind in which the
tool may be set for height by a set screw beneath it.
[Illustration: Fig. 1037.]
Fig. 1039 represents a tool holder and work-steadying device combined.
The holder is held in the lathe tool rest in the usual manner, and
affords slideway to a slide operated by the handle shown at the
right-hand end.
[Illustration: Fig. 1038.]
The tool is carried at the other end of this slide, there being shown in
the figure a cutting-off tool in position. At the end of the holder is a
hub and three adjusting screws whose ends steady the work, and which are
locked in their adjusted position by the chuck nuts shown.
[Illustration: Fig. 1039.]
THE POWER REQUIRED TO DRIVE CUTTING TOOLS.--From experiments made by Dr.
Hartig, he concluded that by multiplying the weight of the metal
cuttings removed per hour by certain decimal figures (or constants) the
horse-power required to cut off that quantity of metal might be
obtained. These decimal constants are as follows:
Lbs. of metal cut off per hour, cast iron × .0314 = horse-power required
to drive the lathe.
" " " wrought iron × .0327 = "
" " " steel × .4470 = "
FOR PLANING TOOLS.
Lbs. of steel cut off per hour × .1120 = horse-power required to drive planer.
" wrought iron " × .0520 = " "
" gun metal " × .0127 = " "
CHAPTER XI.--DRILLING AND BORING IN THE LATHE.
For drilling in the lathe, the twist drill is employed not only on
account of its capacity to drill true, straight, and smooth holes, but
also because its flutes afford free egress to the cuttings and obviate
the necessity of frequently withdrawing the drill to clear the hole of
the cuttings.
In the smaller sizes of twist drill, the stem or shank is made parallel,
as in Fig. 1040, while in the larger sizes it is made taper, as in Fig.
1041, for reasons which will appear hereafter.
[Illustration: Fig. 1040.]
The taper shanks of twist drills are given a standard degree of taper of
5/8 inch per foot of length, which is termed the Morse taper. A former
standard, termed the American standard, is still used to a limited
extent, its degree of taper being 9/16 inch per foot.
[Illustration: Fig. 1041.]
Parallel shanked twist drills are driven by chucks, while taper, shanked
ones, are driven by sockets, such as in Fig. 1042, from C to D, fitting
into the lathe centre hole, while the bore at the other end is the Morse
standard taper, to receive the drills E E, which have a projection such
as shown at A, which by fitting into a slot that meets the end of the
taper holes in the socket, lock the drill and prevent its revolving in
the socket, while affording a means of forcing the drill out by
inserting a key K, as shown in the figure.[14]
[14] See also Shanks and Sockets for Drills used in the Drilling
Machine.
[Illustration: Fig. 1042.]
Each socket takes a certain number of different sized drills, the shanks
of the smaller drills being in some cases longer than the drill body.
Number 1 socket receives drills from 1/8 to 19/32 inch inclusive.
" 2 " " 5/8 " 29/32 " "
" 3 " " 15/16 " 1-1/4 " "
" 4 " " 1-9/32 " 2 " "
" 5 " " 2-1/32 " 2-1/2 " "
These sockets are manufactured ready to receive the drills, but are left
unturned at the shank end so that they may be fitted to the particular
lathe or machine in which they are to be used, no standard size or
degree of taper having as yet been adopted.
A twist drill possesses three cutting edges marked A, B, C respectively
in Fig. 1043, and of these C is the least effective, because it cannot
be made as keen as is desirable for rapid and clean cutting, and
therefore necessitates that the drill be given an unusually fine rate of
feed as compared with other cutting tools.
The _land_ of the drill--or, in other words, the circumference between
the flutes--is backed off to give clearance, as is shown in Fig. 1044, a
true circle being marked with a dotted line, and the drill being of full
diameter from A to B only. The object of this clearance is to prevent
the drill from seizing or grinding against the walls of the hole, as it
would otherwise be apt to do when the outer corner wore off, as is
likely to be the case.
[Illustration: Fig. 1043.]
[Illustration: Fig. 1044.]
Twist drills having three and more flutes have been devised and made,
but the increased cost and the weakness induced by the extra flutes have
been found to more than counterbalance the gain due to an increase in
the number of cutting edges, Further, the increase in the number of
flutes renders the grinding of the drill a more delicate and complicated
operation.
The keenness and durability of the cutting edge of a twist drill are
governed by the amount of clearance given by the grinding to the cutting
edge, by the angle of one cutting edge to the other, and by the degree
of twist of the flute. Beginning with the angle of the front face, we
shall find that it varies at every point in the diameter of the drill,
being greatest at the outer corner and least at the centre of the drill,
whatever degree of spirality the groove or flute may possess. In Fig.
1045, for example, we may consider the angle at the corner C and at the
point F in the length of the cutting edge. The angle or front rake of
the corner C is obviously that of the outer edge of the spiral C D,
while that of the point F is denoted by the line F _f_, more nearly
parallel to the drill axis, and it is seen that the front rake increases
in proportion as the corner C is approached, and diminishes as the drill
centre or point is approached.
[Illustration: Fig. 1045.]
[Illustration: Fig. 1046.]
[Illustration: Fig. 1047.]
It follows, then, that if the angle of the bottom face of the drill be
the same from the centre to the corner of the drill, and we consider the
cutting edge simply as a wedge and independent of its angle presentation
to the work, we find that it has a varying degree of acuteness at every
point in its length. This may be seen from Fig. 1046, in which the end
face is ground at a constant angle from end to end to the centre line of
the drill, and it is seen that the angle A represents the wedge at point
C and the angle B the wedge at the point F in the length of the cutting
edge, and it follows that the wedge becomes less acute as the centre of
the drill is approached from the point C. If, then, we give to the end
face a degree of clearance best suited for the corner C, it will be an
improper one for the cutting edge near the drill point; or if we adopt
an angle suitable for the point, it will be an improper one for the
corner C.
This corner performs the most cutting duty, because its path of
revolution is the longest, or rather of the greatest circumference, and
it operates at the highest rate of cutting speed for the same reason,
hence it naturally wears and gets dull the quickest.
As this wear proceeds the circumferential surface near this corner
grinds against the walls of the hole, causing the drill to heat and
finally to cease cutting altogether.
For these reasons it is desirable that the angle of the end face, or the
angle of clearance, be made that most suitable to obtain endurance at
this corner. It may be pointed out, however, that the angle of one
cutting edge to the other, or, what is the same thing, its angle to the
centre line of the drill, influences the keenness of this corner. In
Fig. 1045, for example, each edge is at an angle of 60° to the drill
axis, this being the angle given to drills by the manufacturers as most
suitable for general use. In Fig. 1047, the angle is 45°, and it will be
clearly seen that the corner C is much less acute; an angle of 45° is
suitable for brass work or for any work in which the holes have been
cored out and the drill is to be used to enlarge them.
[Illustration: Fig. 1048.]
Referring again to the angle of clearance of the end faces, it can be
shown that in the usual manner of grinding twist drills the conditions
compel the amount of clearance to be made suitable for the point of the
drill, and therefore unsuitable for the corner C, giving to it too much
clearance in order to obtain sufficient clearance for the remainder of
the cutting edge. Suppose, for example, that we have in Fig. 1048 a
spiral representing the path of corner C during one revolution, the rate
of feed being shown magnified by the distance P, and the spiral will
represent the inclination of that part of the bottom of the hole that is
cut by corner C, and the angle of the end face of the drill to the drill
axis will be angle R. The actual clearance will be represented by the
angle between the end face S of the drill and the spiral beneath it, as
denoted by T. But if we take the path of the point F, Fig. 1045, during
the same revolution, which is represented by the spiral in Fig. 1049, we
find that, in order to clear the end of the hole, it must have more
angle to the centre line of the drill, as is clearly shown, in order to
have the clearance necessary to enable the point F to cut, because of
the increased spiral. It follows that, if the same degree of clearance
is given throughout the full length of the cutting edge, it must be made
suitable for the point of the drill, and will therefore be excessive for
the corner C.
This fault is inseparable from the method of grinding drills in ordinary
drill-grinding machines, which is shown in Fig. 1050, the line A A
representing the axis of the motion given to the drill in these
machines. It is obvious that the line A A being parallel to the face of
the emery-wheel, the angle of clearance is made equal throughout the
whole length of the cutting edge. This is, perhaps, made more clear in
Fig. 1051, in which we have supposed the drill to take a full revolution
upon the axis A A, and as a result it would be ground to the cylinder
represented by the dotted lines. We may, however, place the axis on
which the drill is moved to grind it at an angle to the emery-wheel
face, as at B, Fig. 1052, and by this means we shall obtain two
important results: (1) The angle of B may be made such that the
clearance will be the same to the actual surface it cuts at every point
in the length of the cutting edge, making every point in that length
equally keen and equally strong, the clearance being such as it is
determined is the most desirable. (2) The clearance may be made to
increase as the heels of each end face are approached from the cutting
edge. This is an advantage, inasmuch as it affords freer access to the
oil or other lubricating or cooling material. If we were to prolong the
point of the drill sufficiently, and give it a complete revolution on
the axis B, we should grind it to a cone, as shown by the dotted lines
in Fig. 1052.
[Illustration: Fig. 1049.]
[Illustration: Fig. 1050.]
[Illustration: Fig. 1051.]
[Illustration: Fig. 1052.]
[Illustration: Fig. 1053. Top View.]
[Illustration: Fig. 1054. Sectional View.]
In Fig. 1053 we have a top, and in Fig. 1054 a sectional, view of a
conical recess cut by a drill, with a cylinder R lying in the same. P
represents in both views the outer arc or circle which would be
described by the outer corner, Fig. 1045, of the drill, and Q the path
or arc described or moved through by the point at F, Fig. 1045, of the
drill. At V and W are sectional views of the cylinder R, showing that
the clearance is greater at V than at W. The cylinder obviously
represents the end of a drill as usually ground. In Figs. 1055 and 1056
we have two views of a cone lying in a recess cut by a drill, the arcs
and circles P and Q corresponding to those shown in Fig. 1055, and it is
seen that in this case the amount of clearance between V and P and
between W and Q are equal, V representing a cross-section of the cone at
its largest end, and W a cross-section at the point where the cone
meets the circle Q. It follows, therefore, that drills ground upon this
principle may be given an equal degree of clearance throughout the full
length of each cutting edge, or may have the clearance increase or
diminished towards the point at will, according to the angle of the line
B in Fig. 1052.
In order that the greatest possible amount of duty may be obtained from
a twist drill, it is essential that it be ground perfectly true, so that
the point of the drill shall be central to the drill and in line with
the axis on which it revolves. The cutting edges must be of exactly
equal length and at an equal degree of angle from the drill axis. To
obtain truth in these respects it is necessary to grind the drill in a
grinding machine, as the eye will not form a sufficiently accurate guide
if a maximum of duty is to be obtained. The cutting speeds and rates of
feed recommended by the Morse Twist Drill and Machine Company are given
in the following table.
[Illustration: Fig. 1055. Top View.]
[Illustration: Fig. 1056. Sectional View.]
The following table shows the revolutions per minute for drills from
1/16 in. to 2 in. diameter, as usually applied:--
+----------+------+------+------++----------+------+------+------+
| Diameter |Speed |Speed |Speed || Diameter |Speed | Speed|Speed |
|of Drills.| for | for | for ||of Drills.| for | for | for |
| |Steel.|Iron. |Brass.|| |Steel.| Iron.|Brass.|
+----------+------+------+------++----------+------+------+------+
| inch. | | | || inch. | | | |
| 1/16 | 940 | 1280 | 1560 || 1-1/16 | 54 | 75 | 95 |
| 1/8 | 460 | 660 | 785 || 1-1/8 | 52 | 70 | 90 |
| 3/16 | 310 | 420 | 540 || 1-3/16 | 49 | 66 | 85 |
| 1/4 | 230 | 320 | 400 || 1-1/4 | 46 | 62 | 80 |
| 5/16 | 190 | 260 | 320 || 1-5/16 | 44 | 60 | 75 |
| 3/8 | 150 | 220 | 260 || 1-3/8 | 42 | 58 | 72 |
| 7/16 | 130 | 185 | 230 || 1-7/16 | 40 | 56 | 69 |
| 1/2 | 115 | 160 | 200 || 1-1/2 | 39 | 54 | 66 |
| 9/16 | 100 | 140 | 180 || 1-9/16 | 37 | 51 | 63 |
| 5/8 | 95 | 130 | 160 || 1-5/8 | 36 | 49 | 60 |
| 11/16 | 85 | 115 | 145 || 1-11/16 | 34 | 47 | 58 |
| 3/4 | 75 | 105 | 130 || 1-3/4 | 33 | 45 | 56 |
| 13/16 | 70 | 100 | 120 || 1-13/16 | 32 | 43 | 54 |
| 7/8 | 65 | 90 | 115 || 1-7/8 | 31 | 41 | 52 |
| 15/16 | 62 | 85 | 110 || 1-15/16 | 30 | 40 | 51 |
| 1 | 58 | 80 | 100 || 2 | 29 | 39 | 49 |
+----------+------+------+------++----------+------+------+------+
To drill one inch in soft cast iron will usually require: For 1/4 in.
drill, 125 revolutions; for 1/2 in. drill, 120 revolutions; for 3/4 in.
drill, 100 revolutions; for 1 in. drill, 95 revolutions.
The rates of feed for twist drills are thus given by the same Company:--
Diameter of Revolutions per inch
drill. depth of hole.
1/16 inch 125
1/4 " "
3/8 " 120 to 140
1/2 " " "
3/4 " 1 inch feed per minute
1 " " " " "
1-1/2 " " " " "
Taking an inch drill as an example, we find from this table that the
rate of feed is for iron 1/100th inch per drill revolution, and as the
drill has two cutting edges it is obvious that the rate of feed for each
edge is 1/200th inch per revolution. But it can be shown that this will
only be the case when the drill is ground perfectly true; or, in other
words, when the drill is so ground that each edge will take a separate
cut, or so that one edge only will cut, and that in either case the rate
of feed will be diminished one-half.
In Fig. 1057, for example, is shown a twist drill in which one cutting
edge (_e_) is ground longer than the other, and the effect this would
produce is as follows. First, suppose the drill to be fed automatically,
the rate of feed being 1/100th inch, and the whole of this feed would
fall on cutting edge _e_, and, being double what it should be, would in
the first place cause the corner _c_ to dull very rapidly, and in the
second place be liable to cause the drill to break when _c_ became dull.
[Illustration: Fig. 1057.]
[Illustration: Fig. 1058.]
In the second place the drill would make a hole of larger diameter than
itself, because the point of the drill will naturally be forced by the
feed to be the axis or centre of cutting edge revolution, which would
therefore be on the line _b_ _b_. This would cause the diameter of hole
drilled to be determined by the radius of the cutting edge _e_ rather
than by the diameter of the drill. Again, the side of the drill in line
with corner _c_ would bind against the side of the hole, tending to
grind away the clearance at the corner _c_, which, it has been shown, it
is of the utmost importance to keep sharp. But assuming 1/200th inch to
be the proper feed for each cutting edge, and the most it can carry
without involving excessive grinding, then the duty of the drill can
only be one-half what it would be were both cutting edges in action.
In Fig. 1058 is shown a twist drill in which one cutting edge is ground
longer than the other, and the two cutting edges are not at the same
angle to the axis _a_ _a_ of the drill.
Here we find that the axis of drill rotation will be on the line _b_
from the point of the drill as before, but both cutting edges will
perform some duty. Thus edge _e_ will drill a hole which the outer end
of _f_ will enlarge as shown. Thus the diameter of hole drilled will be
determined by the radius of corner _c_, from the axis of drill
revolution, and will still be larger than the drill. A drill thus ground
would drill a more true and round hole than one ground as in Fig. 1057,
because as both cutting edges perform duty the drill would be steadied.
[Illustration: Fig. 1059.]
The rate of feed, however, would require to be governed by that length
of cutting edge on _f_ that acts to enlarge the hole made by _e_, and
therefore would be but one-half what would be practicable if the drill
were ground true. Furthermore, the corner _c_ would rapidly dull because
of its performing an undue amount of duty, or in other words, because it
performs double duty, since it is not assisted by the other corner as it
should be. In both these examples the drill if rigidly held would be
sprung or bent to the amount denoted by the distance between the line
_a_ _a_, representing the true axis of the drill, and line _b_ _b_,
representing the line on which the drill point being ground and
one-sided compels the drill to revolve; hence one side of the drill
would continuously rub against the walls of the hole the drill produced,
acting, as before observed, to grind away the clearance that was shown
in figure and also to dull corner _c_.
Fig. 1059 shows a case in which the point of the drill is central to the
drill axis _d_ _d_, but the two cutting edges are not at the same angle.
As a result all the duty falls on one cutting edge, and the hole drilled
will still be larger in diameter than the drill is, because there is a
tendency for the cutting edge _e_ to push or crowd the drill over to the
opposite side of the hole.
It will be obvious from these considerations that the more correctly the
drill is ground, the longer it will last without regrinding, the greater
its amount of feed may be to take an equal depth of cut, and the nearer
the diameter of the hole drilled to that of the drill--the most correct
results being obtained when the drill will closely fit into the hole it
has drilled and will not fall through of its own gravity, a result it is
somewhat difficult to attain.
Professor John E. Sweet advocates grinding twist drills as in Fig. 1060
(which is from _The American Machinist_), the object being to have a
keener cutting edge at the extreme point of the drill.
In a paper on cutting tools read before the British Institution of
Mechanical Engineers the following examples of the efficiency of the
twist drill are given--
Referring to a 1/2 inch twist drill, it is said:
"The time occupied from the starting of each hole in a hammered
scrap-iron bar till the drill pierced through it varied from 1 minute 20
seconds to 1-1/2 minutes. The holes drilled were perfectly straight. The
speed at which the drill was cutting was nearly 20 feet per minute in
its periphery, and the feed was 100 revolutions per inch of depth
drilled. The drill was lubricated with soap and water, and went clean
through the 2-3/4 inches without being withdrawn, and after it had
drilled each hole it felt quite cool to the hand, its temperature being
about 75°. It is found that 120 to 130 such holes can be drilled before
it is advisable to resharpen the twist drill. This ought to be done
immediately the drill exhibits the slightest sign of distress. If
carefully examined after this number of holes has been drilled, the
prominent cutting parts of the lips which have removed the metal will be
found very slightly blunted or rounded to the extent of about 1/100th
inch, and on this length being carefully ground by the machine off the
end of the twist drill, the lips are brought up to perfectly sharp
cutting edges again.
"The same sized holes, 1/2 inch diameter and 2-3/4 inches deep, have
been drilled through the same hammered scrap-iron at the extraordinary
speed of 2-3/4 inches deep in 1 minute and 5 seconds, the number of
revolutions per inch being 75. An average number of 70 holes can be
drilled in this case before the drill requires resharpening. The writer
considers this test to be rather too severe, and prefers the former
speed.
"In London, upward of 3000 holes were drilled 5/8 inch diameter and 3/8
inch deep through steel bars by one drill without regrinding it. The
cutting speed was in this instance too great for cutting steel, being
from 18 to 20 feet per minute, and the result is extraordinary. Many
thousands of holes were drilled 1/8 inch diameter, through cast iron
7/16ths inch deep with straight-shank twist drills gripped by an
eccentric chuck in the end of the spindle of a quick-speed drilling
machine. The time occupied for each hole was from 9 to 10 seconds only.
Again, 1/4-inch holes have been drilled through wrought copper 1-3/8
inches thick at the speed of one hole in 10 seconds. With special twist
drills, made for piercing hard Bessemer steel, rail holes, 13/16ths inch
deep and 29/32nds inch diameter, have been drilled at the rate of one
hole in 1 minute and 20 seconds in an ordinary drilling machine. Had the
machine been stiffer and more powerful, better results could have been
obtained. A similar twist drill, 29/32nds inch in diameter, drilled a
hard steel rail 13/16ths inch deep in 1 minute, and another in 1 minute
10 seconds. Another drill, 5/8 inch diameter, drilled 3/4 inch deep in
38 seconds, the cutting speed being 22 feet per minute. This speed of
cutting rather distressed the drill; a speed of 16 feet per minute would
have been better. The steel rail was specially selected as being one of
the hardest of the lot."
[Illustration: Fig. 1060.]
Drills ground by hand may be tested for angle by a protractor, as in
Fig. 1061, and for equal length of cutting edge by resting them upon a
flat surface, as B in Fig. 1062, and applying a scale as at S in the
figure. In the case of very small drills, it is difficult to apply
either the protractor or the scale, as well as to determine the amount
of clearance on the end face. This latter, however, may be known from
the appearance of the cutting edge at the point A in Fig. 1063, for if
the line A is at a right angle to E, there is no clearance, and as
clearance is given this line inclines as shown at B in the figure, the
inclination increasing with increased clearance, as is shown at C. When
this part of the edge inclines in the opposite direction, as at D in the
figure, the curved edges _e_ _f_ stand the highest, and the drill cannot
cut. The circumferential surface of a drill should never be ground, nor
should the front face or straight side of the flute be ground unless
under unusual conditions, such as when it is essential, as in drilling
very thin sheet metal, to somewhat flatten the corner (C in Fig. 1062),
in order to reduce its tendency to run forward, in which case care must
be taken not to grind the front face sufficiently to reduce the full
diameter. In Fig. 1064, for example, that part of the circumference
lying between A and B being left of full circle, the faces of the flutes
might be ground away as denoted by the dotted lines C D without
affecting the drill diameter.
[Illustration: Fig. 1061.]
[Illustration: Fig. 1062.]
[Illustration: Fig. 1063.]
[Illustration: Fig. 1064.]
[Illustration: Fig. 1065.]
[Illustration: Fig. 1066.]
Fig. 1065 represents the Farmer lathe drill, in which the flutes are
straight and not spiral, by which means the tendency to run forward when
emerging through the work is obviated.
[Illustration: Fig. 1067.]
When a twist drill is to be used for wood and is driven by a machine it
is termed a bit, and is provided with a conical point to steady it, and
two wings or spurs, as in Fig. 1066, which sever the fibres of the wood
in advance of their meeting the main cutting edges and thus produce a
smooth hole. The sharp conical point is used in place of the conical
screw of the ordinary wood auger to avoid the necessity of revolving the
drill or bit backwards to release the screw in cases in which the hole
is not bored entirely through the work.
[Illustration: Fig. 1068.]
When the drill revolves and the work is to be held in the hands a rest
or table whereon to rest the work and hold it fair is shown in Fig.
1067, the taper shank fitting in the dead centre hole and the tailstock
spindle being fed up by hand to feed the drill to its cut. The face A A
of the chuck is at a right angle to the shank, and a coned recess is
provided at the centre, as denoted by the dotted lines, to permit the
drill point to pass through the work without cutting the chuck.
[Illustration: Fig. 1069.]
For larger work a table, such as shown in Fig. 1068, is used, the cavity
C permitting the drilling tool to pass through the work, there being a
hole H provided for that purpose. The stem S fits in place of the dead
centre. For cylindrical work the rest or chuck shown in Figs. 1069 and
1070 may be employed. It consists of a piece fitted to the tail spindle
in place of the dead centre, its end being provided with [V]-grooves.
These grooves are made true with the line of centres of the lathe, so
that when the work is laid in them it will be held true. It is obvious
that one groove would be sufficient, but two are more convenient--one
for large work and one for small work--so that the side of the shaft to
be drilled shall not pass within the fork, but will protrude, so that
the progress of the work can be clearly seen. In Fig. 1070 an end view
of this chuck is shown. It may be observed, however, that when starting
the drill care must be taken to have it start true, or the drill may
bend, and thus throw the work out of the true. For this reason the
drills should be as short as possible when their diameters are small.
For square work this class of work table or chuck may be formed so as to
envelop the work and prevent its revolving, thus relieving the fingers
of that duty, and it may be so formed as to carry the work back or off
the drill when the latter is retired after the drilling is performed.
[Illustration: Fig. 1070.]
Another and quite convenient method of holding work to be drilled by a
revolving drill in the lathe is shown in Fig. 1071. It consists of
simply a bracket, _a_ _b_, fitted to the tool-box of the slide rest,
carrying a spindle with one end screwed to receive any face plates or
chucks that fit the lathe live spindle. The bracket is kept in position
by two pins in the under side of it, fitting into holes in the bottom
piece of tool-box. If it be required to drill a straight row of holes,
the spindle is fixed by the set-screws in its bracket, and the work is
bolted to the face plate at the proper level, and traversed across
opposite the drill in the lathe mandrel, by the cross screw of the slide
rest, while it is fed up to the drill by the upper screw or the rack and
pinion.
For circular rows of holes the centre line of the spindle is adjusted
parallel with and at a proper distance from that of the mandrel. For
holes in the edge of the work, the whole top of slide rest is turned
round till the spindle is at right angles with the mandrel.
[Illustration: Fig. 1071.]
Work merely requiring to be held fast for drilling is bolted on one side
of the face plate, and can then be adjusted exactly to the drill by the
combined motions of the cross screw and the face plate on its centre.
Small round work, while drilled in the end, can be held in a scroll
chuck screwed on the spindle the same as a face plate.
The convenience of this device consists in this, that the work turned on
the chuck may be drilled without moving it from the chuck, which may be
so set as to cause the drilled holes to be at any required angle to the
work surface, which is quite difficult of accomplishment by other
ordinary means.
On account of the readiness with which a flat drill may be made to suit
an odd size or employed to recess work with a flat or other required
shape of recess, flat drills are not uncommonly used upon lathe work,
and in this case they may be driven in the drill chucks already shown. A
very convenient form of drill chuck for small drills is shown in Fig.
1072. It consists of a cylindrical chuck fitting from A to B into the
coned hole in the live spindle so as to be driven thereby. At the
protruding end C there is drilled a hole of the diameter of the wire
forming the drill. At the end of this hole there is filed a slot D
extending to the centre of the chuck. The end of the drill is filed half
round and slightly taper, as shown in Fig. 1073 at D, so that the
half-round end of the drill will pass into the slot of the chuck,
therefore forming a driving piece which effectually prevents the drill
from slipping, as is apt to occur with cylindrical stem or shank drills.
If one size of wire be used for all drills, and the drill size be
determined by the forging, the drill will run true, being held quite
firmly, and may be very readily inserted in or removed from the chuck.
[Illustration: Fig. 1072.]
But the flat drill possesses several disadvantages: thus, referring to
figure, it must be enough smaller at A than at B to permit the cuttings
to find egress, and this taper causes the diameter of the drill to be
reduced at each drill grinding. The end B may, it is true, be made
parallel for a short distance, but in this case the cuttings will be apt
to clog in the hole unless the drill be frequently removed from deep
holes to clear the cuttings. For these reasons the fluted drill or the
twist drill is preferable, especially as their diameters are maintained
without forging. For deep holes, as, say, those having a depth equal to
more than twice the diameter, the flat drill, if of small diameter, as,
say, an inch or less, is unsuitable because of the frequency with which
it must be removed from the hole to clear it of cuttings.
[Illustration: Fig. 1073.]
For fluted or twist drills the lathe may run quicker than for a flat
drill, which is again an advantage. It sometimes becomes convenient in
the exigencies which occur in the work of a general machine shop to hold
a drill in a dog or clamp and feed it into the work with the lathe dead
centre. In this case the drill should be held very firmly against the
dead centre, or otherwise the drill may, when emerging through the back
of the hole, feed itself forward, slipping off the dead centre, and
causing the drill to catch and break, or moving the work in the chuck,
to avoid which the drill should have a deep and well countersunk centre.
[Illustration: Fig. 1074.]
A very effective drill for holes that are above two inches in diameter
and require enlarging is shown in Fig. 1074. It consists of a piece of
flat steel A, with the pieces of wood B fastened on the flat faces, the
wood serving to steady the drill and prevent it from running to one side
in the work. This drill is sometimes used to finish holes to standard
size, in which case the hole to be bored or drilled should be trued out
a close fit to the drill for a distance equal to about the diameter of
the drill, and the face at the entrance of the hole should be true up.
This is necessary to enable the drill to start true, which is
indispensable to the proper operation of the drill.
This drill is made by being turned up in the lathe, and should have at
the stock end a deep and somewhat large centre, so that when in use it
may not be liable to slip off the dead centre of the lathe. The drill is
held at the stock end by being placed in the lathe dead centre and is
steadied, close to the entrance of the hole in the work, by means of a
hook which at one end embraces the drill, as shown in Fig. 1075, in
which A represents the hook and B the drill.
[Illustration: Fig. 1075.]
This drill will bore a parallel hole, but if the same be a long or a
deep one it is apt to bore gradually out of true unless the bore of the
hole is first trued from end to end with a boring tool before using the
drill. It is often employed to enlarge a hole so as to admit a stout
boring tool, and to remove the hard surface skin from which the boring
tool is apt to spring away.
[Illustration: Fig. 1076.]
[Illustration: Fig. 1077.]
HALF-ROUND BIT OR POD AUGER.--For drilling or enlarging holes of great
depth (in which case it is difficult to drill straight holes with
ordinary drills), the half-round bit--Figs. 1076 and 1077--is an
excellent tool. Its diameter D is made that of the required hole, the
cutting being done at the end only from A to B, from B to C being ground
at a slight angle to permit the edge from A to B to enter the cut. When
a half-round bit is to be used on iron or steel, and not upon brass, it
may be made to cut more freely by giving the front face rake as at E F,
Fig. 1078.
[Illustration: Fig. 1078.]
[Illustration: Fig. 1079.]
To enable a bit of this kind to be adjusted to take up the wear, it may
be formed as in Fig. 1079, in which a quarter of the circumference is
cut away at _a_, and a cutter _c_ is bolted in position projecting into
a recess at _b_ to secure the cutter in addition to the bolts. Pieces of
paper may be inserted at _b_ to set out the cutter.
An excellent form of boring bar and cutter is shown in Figs. 1080 and
1081.
Fig. 1082 shows a side view of the cutter removed from the bar; Fig.
1081 an end, and Fig. 1080 a side view of the bar and cutter. The cutter
is turned at A and B to fit the bore of the bar. The cutting edge C
extends to the centre of the bar, while that at D does not quite reach
the centre. These edges are in a line as shown in the end view. On
account of the thickness of the cutter not equaling the diameter of the
bore through the bar there is room for a stream of water to be forced
through the bar, thus keeping it cool and forcing out the cuttings which
pass through the passages G and H in the bar. The cutter drives lightly
into the bar. By reason of one cutting edge not extending clear to the
centre of the cutter there is formed a slight projection at the centre
of the hole bored which serves as a guide to keep the cutter true,
causing it to bore the hole very true.
[Illustration: Fig. 1080.]
For finishing the walls of holes more true, smooth, and straight, and of
more uniform diameter than it is found possible to produce them with a
drill, the reamer, or rymer, is employed. It consists of a hardened
piece of steel having flutes, at the top of which are the cutting edges,
the general form of solid reamer for lathe work being shown in Fig.
1083. The reamer is fed end-ways into the work at a cutting speed of
about 15 to 18 feet per minute.
[Illustration: Fig. 1081.]
[Illustration: Fig. 1082.]
The main considerations in determining the form of a reamer are as
follows:--
1. The number of its cutting edges.
2. The spacing of the teeth.
3. The angles of the faces forming the cutting edges.
4. Its maintenance to standard diameter.
[Illustration: Fig. 1083.]
As to the first, it is obvious that the greater the number of cutting
edges the more lines of contact there are to steady it on the walls of
the hole; but in any case there should be more than three teeth, for if
three teeth are used, and one of them is either relieved of its cut or
takes an excess of cut by reason of imperfections in the roundness of
the hole, the other two are similarly affected and the hole is thus made
out of round.
An even number of teeth will not work so steadily as an odd one, for the
following reasons.
In Fig. 1084 is represented a reamer having 6 teeth and each of these
teeth has a tooth opposite to it; hence, if the hole is out of round two
teeth only will operate to enlarge its smallest diameter. In Fig. 1085
is a reamer having 7 teeth, and it will be seen that if any one tooth
cuts there will be two teeth on the opposite side of the reamer that
must also cut; hence, there are three lines of contact to steady the
reamer instead of two only as in the case of the 6 teeth. An even number
of teeth, however, may be made to operate more steadily by spacing the
teeth irregularly, and thus causing three teeth to operate if the hole
is out of round. Thus, in Fig. 1086 the teeth are spaced irregularly,
and it will be seen that as no two teeth are exactly opposite, if a
tooth on one side takes a cut there must be two on the opposite side
that will also cut. The objection to irregular spacing is that the
diameter of the reamer cannot be measured by calipers. Another method of
obtaining steadiness, however, is to make the flutes and the cutting
edges spiral instead of parallel to the axis, but in this case the
spiral must be left-handed, as in Fig. 1087, or else the cutting edges
acting on the principle of a screw thread will force the reamer forward,
causing it to feed too rapidly to its cut. If, however, a reamer have
considerable degree of taper, it may be given right-hand flutes, which
will assist in feeding it.
[Illustration: Fig. 1084.]
[Illustration: Fig. 1085.]
[Illustration: Fig. 1086.]
[Illustration: Fig. 1087.]
Referring to the second, the spacing of the teeth must be determined to
a great extent by the size of the reamer, and the facility afforded by
that size to grind the cutting edges to sharpen them.
[Illustration: Fig. 1088.]
The method employed to grind a reamer is shown in Fig. 1088, in which is
shown a rapidly-revolving emery-wheel, above the reamer, and also a
gauge against which the front face of each tooth is held while its top
or circumferential face is being sharpened. The reamer is held true to
its axis and is pushed end-ways beneath the revolving emery-wheel. In
order that the wheel may leave the right-hand or cutting edge the
highest (as it must be to enable it to cut), the axis of the emery-wheel
must be on the left hand of that of the reamer, and the spacing of the
teeth must be such that the periphery of the emery-wheel will escape
tooth B, for otherwise it would grind away its cutting edge. It is
obvious, however, that the less the diameter of the emery-wheel the
closer the teeth may be spaced; but there is an objection to this,
inasmuch as that the top of the tooth is naturally ground to the
curvature of the wheel, as is shown in Fig. 1089, in which two
different-sized emery-wheels are represented operating on the same
diameter of reamer. The cutting edge of A has the most clearance, and is
therefore the weakest and least durable; hence it is desirable to employ
as large a wheel as the spacing of the teeth will allow, there being at
least four teeth, and preferably six, on small reamers, and their number
increasing with the diameter of the reamer.
[Illustration: Fig. 1089.]
It would appear that this defect might be remedied by placing the
emery-wheel parallel to the teeth as in Fig. 1090; but if this were
done, the wear of the emery-wheel would cause the formation of a
shoulder at S in the figure, which would round off the cutting edge of
the tooth. This, however, might be overcome by giving the emery-wheel
enough end motion to cause it to cross and recross the width of the top
facet; or the reamer R may be presented to the wheel W at an angle to
the plane of wheel rotation, as in Fig. 1091, which would leave a
straight instead of a curved facet, and, therefore, a stronger and more
durable cutting edge.
[Illustration: Fig. 1090.]
[Illustration: Fig. 1091.]
Another method of accomplishing the same object would be to mount the
emery-wheel as in Fig. 1092, using its side face, which might be
recessed on the side, leaving an annular ring of sufficient diameter to
pass clear across the tooth, and thus prevent a shoulder from forming on
the side face of the wheel.
Yet another method is to use an emery-wheel bevelled on its edge, and
mount it as in Fig. 1093, in which case it would be preferable to make
the bevel face narrow enough that all parts would cross the facet of the
tooth.
[Illustration: Fig. 1092.]
[Illustration: Fig. 1093.]
Referring to the third, viz., the angles of the faces forming the
cutting edges, it is found that the front faces, as A and B in Fig.
1094, should be a radial line, for if given rake as at C, the tooth will
spring off the fulcrum at point E in the direction of D, and cause the
reamer to cut a hole of larger diameter than itself, an action that is
found to occur to some extent even where the front face is a radial
line. As this spring augments with any increase of cut-pressure, it is
obvious that if a number of holes are to be reamed to the same diameter
it is essential that the reamer take the same depth of cut in each, so
that the tooth spring may be equal in each case. This may be
accomplished to a great extent by using two reamers, one for equalizing
the diameters of the holes, and the other for the final finishing. The
clearance at the top of the teeth is obviously governed by the position
of the reamer with relation to the wheel, and the diameter of the wheel,
being less in proportion as the reamer is placed farther beneath the
wheel, and the wheel diameter is increased. In some forms of reamer the
teeth are formed by circular flutes, such as at H in Fig. 1094, and but
three flutes are used. This leaves the teeth so strong and broad at the
base that the teeth are not so liable to spring; but, on the other hand,
the clearance is much more difficult to produce and to grind in the
resharpening.
[Illustration: Fig. 1094.]
[Illustration: Fig. 1095.]
[Illustration: Fig. 1096.]
As to the maintenance of the reamer to standard diameter, it is a matter
of great importance, for the following reasons: The great advantage of
the standard reamer is to enable holes to be made and pieces to be
turned to fit in them without requiring any particular piece to be
fitted to some particular hole, and in order to accomplish this it is
necessary that all the holes and all the pieces be exactly alike in
diameter. But the cutting edges of the reamer begin to wear--and the
reamer diameter, therefore, to reduce--from the very first hole that it
reams, and it is only a question of time when the holes will become too
small for the turned pieces to enter or fit properly. In all pieces that
are made a sliding or a working fit, as it is termed when one piece
moves upon the other, there must be allowed a certain latitude of wear
before the one piece must be renewed.
One course is to make the reamer when new enough larger than the proper
size to bore the holes as much larger as this limit of wear, and to
restore it to size when it has worn down so that the holes fit too
tightly to the pieces that fit them. But this plan has the great
disadvantage that the pieces generally require to have other cutting
operations performed on them after the reaming, and to hold them for
these operations it is necessary to insert in them tightly-fitting
plugs, or arbors, as they are termed. If, therefore, the holes are not
of equal diameter the arbor must be fitted to the holes, whereas the
arbor should be to standard diameter to save the necessity of fitting,
which would be almost as costly as fitting each turned piece to its own
hole. It follows, therefore, that the holes and arbors should both be
made to a certain standard, and the only way to do this is to so
construct the reamer that it may be readily adjusted to size by moving
its teeth.
It is obvious that a reamer must, to produce parallel holes, be held
axially true with the holes, or else be given liberty to adjust itself
true. Fig. 1095 shows a method of accomplishing this object. The reamer
is made to have a slight freedom or play in the sleeve, being 1/32 inch
smaller, and the hole for the pin is also made large so that the reamer
may adjust itself for alignment.
For short holes the shell reamer shown in Fig. 1096 may be employed. Its
bore is coned so that it will have sufficient friction upon its driving
arbor to prevent its coming off; when it is to be withdrawn from the
work it is provided with two slots into which fit corresponding lugs on
the driving arbor. Fig. 1097 shows the Morse Twist Drill and Machine
Company's arbor.
[Illustration: Fig. 1097.]
[Illustration: Fig. 1098.]
The rose reamer, or rose bit, has its cutting edges on the end only, as
shown in Fig. 1098, the grooves being to supply lubricating material (as
oil or water) only, and, as a result, will bore a more parallel hole
than the ordinary reamer in cases in which the reamer has liberty to
move sideways, from looseness in the mechanism driving it. Furthermore,
when the work is composed of two parts, the outer one, through which the
reamer must pass before it meets the inner one, guides the reamer
without becoming enlarged by reason of the reamer having cutting edges,
which is especially advantageous when the inner hole requires to be made
true with the outer one, or in cases where a piece has two holes with a
space between them, and one hole requires to be made true with the
other, and both require to be made to the same diameter as the reamer.
Fig. 1099 represents the Morse Twist Drill Company's shell rose reamer
for short holes, corresponding in principle to the solid rose reamer,
but fitting to an arbor for the same purposes as the shell reamer.
Instead of having upon a reamer a flat tooth top to provide clearance,
very accurate and smooth work may be produced by letting the back of the
tooth, as A in Fig. 1100, proceed in a straight line to B, leaving the
reamer, when soft, too large, so that after hardening it may be ground
by an emery-wheel to size; and the clearance may be given by simply
oilstoning the top of each tooth lengthwise, the oilstone marks barely
effacing the emery marks at the cutting edge and removing slightly more
as the back of the tooth is approached from the cutting edge. This
produces cutting edges that are very easily fed to the cut, which must
obviously, however, be a light one, as should always be the case for
finishing, so that the wear of the teeth may be a minimum, and the
reamer may therefore maintain its standard diameter as long as possible.
[Illustration: Fig. 1099.]
[Illustration: Fig. 1100.]
When a solid reamer has worn below its required diameter, the same may
be restored by upsetting the teeth with a set chisel, by driving it
against the front face; and in determining the proper diameter for a
reamer for work to be made to gauge under the interchangeable system the
following considerations occur.
Obviously the diameter of a reamer reduces as it wears; hence there must
be determined a limit to which the reamer may wear before being restored
to its original diameter. Suppose that this limit be determined as
1/1000 inch, then as the reamer wears less in diameter the bolts to fit
the holes it reams must also be made less as the reamer wear proceeds,
or otherwise they will not enter the reamed holes. But it is to be
observed that while the reamer wears smaller, the standard gauges to
which the pins or bolts are turned wear larger, and the wear is here
again in a direction to prevent the work from fitting together. It is
better then to make the reamer when new too large to the amount that has
been determined upon as the limit of wear, so that when the work begins
to go together too tight, the reamer requires resharpening and
restoring.
[Illustration: Fig. 1101.]
A still better plan, however, is to use reamers adjustable for diameter,
so that the wear may be taken up, and also the reamer sharpened, without
being softened, which always deteriorates the quality of the steel.
Reamers that are too small to be made adjustable for size by a
combination of parts may be constructed as in Fig. 1101, in which the
reamer is drilled and threaded, and countersunk at the end to receive a
taper-headed screw S, which may be screwed in to expand the reamer,
which contains three longitudinal splits to allow it to open. To cause S
to become locked in its adjusted position a plug screw P is inserted for
the end of S to abut against. It is obvious that in this form the reamer
is expanded most at the end.
Fig. 1102 represents a single-tooth adjustable reamer, in which the body
A is ground to the standard diameter, and the wear of the cutter C is
taken up by placing paper beneath the cutter. In this case the reamer
cannot, by reason of the wear of the cutting edge, ream too small,
because the body A forms a gauge of the smallest diameter to which the
reamer will cut. The cutter may, however, be set up to the limit allowed
for wear of cutting edge, which for work to fit should not be more than
1/5000 inch.
[Illustration: Fig. 1102.]
An adjustable reamer designed and used by the author for holes not less
than 1-1/2 inches in diameter, is shown in Fig. 1103, in which A
represents the body of the reamer containing dovetail grooves tapered in
depth with the least depth at the entering end. The grooves receive
cutters B, having gib heads. C is a ring or washer interposed between
the gib heads of the cutter and the face or shoulder of A, the cutters
being locked against that face by a nut and a washer E. By varying the
thickness of C, the cutters are locked in a different position in the
length of the grooves, whose taper depth therefore causes the cutters to
vary in diameter. Suppose, for example, that with a given thickness of
washer C, the cutters are adjusted in diameter so as to produce a hole a
tight working fit to a plug turned to a 2-inch standard gauge: a
slightly thinner washer may be used, setting the cutters so as to bore a
hole an easy working fit to the plug; or a slightly thicker washer may
be employed so as to produce a hole a driving fit to the same plug.
Three or more washers may thus be used for every standard size, their
thickness varying to suit the nature of the fit required.
[Illustration: Fig. 1103.]
It will be noted that it is mentioned that three _or more_ washers may
be used, and this occurs because a diameter of fit that would be a
driving fit for a hole of one length would be too tight for a driving
fit of a much longer hole, the friction of course increasing with the
length of hole, because of the increase of bearing area.
For large sizes, a reamer of this description is an excellent tool,
because if it be required to guide the reamer by means of a plain
cylindrical shank, a washer, or sleeve, having a bore to fit the shank
at the termination of the thread, may be used, but such a reamer is not
suitable for small diameters, because of the reduction of shank
necessary to provide for the nut and thread.
Reamers for roughing out taper holes may be made with steps, as in Fig.
1104, which is taken from _The American Machinist_, there being a
cutting edge where each step meets a flute. Such a reamer may be used to
enlarge parallel holes, or to rough out taper ones, and the flutes (if
not to be used for brass work) may be spiral, as in the figure. The end
step being guided by the hole serves as a guide to the first cutting
edge; the second step serves as a guide for the cutting edge that
follows it, and so on.
[Illustration: Fig. 1104.]
[Illustration: Fig. 1105.]
The steps are best turned a trifle larger, say 1/1000 inch larger, at
the cutting end. Half-round taper reamers, such as shown in Fig. 1105,
are used for finishing holes. The flat face is cut down, leaving rather
more than a half circle; the clearance being filed or ground on the
cutting side so as to enable the reamer to cut, and extending from the
cutting edge to nearly half-way to the bottom of the reamer.
For holes, however, that are large enough to admit a tool of sufficient
strength, the single-pointed boring tool produces the most true work.
Brass finishers use square taper reamers, which produce upon brass more
true work than the half-round reamer.
[Illustration: Fig. 1106.]
[Illustration: Fig. 1107.]
For reaming the bores of rifles, a square reamer, such as shown in Fig.
1106, is employed; the edges A B are the cutting ones, the edges C D
being rounded off; E is a piece of wood, beneath which slips of paper
are placed to restore the size as the wear proceeds. The entering end of
the reamer is slightly tapered. On account of the extreme length of this
reamer in proportion to its diameter, it is fed to its cut by being
pulled instead of pushed as is usually the case, the pull placing the
rod of the reamer under tension and thus stiffening it; the line of pull
is of course true with the axis of the rifle bore. The reamer is
revolved at high speed and freely supplied with oil.
[Illustration: Fig. 1108.]
By means of the slips of paper successive cuts and minute increases of
diameter may be taken with the same reamer.
Fig. 1107 represents a class of rose bit employed to reduce pins to a
uniform diameter, and face off the shoulder under the head, or it may be
used to cut a recess round a pin, or to cut a recess and leave a pin.
For making a recess round a hole, or, in other words, for cutting a
flat-bottom countersink, a facing countersink, Fig. 1108, may be used,
its cutting edges being at A, B, C, &c. The clearance is given at the
ends of the teeth only, being shown from B to D. The pin P steadies the
tool, and is made a working fit to the hole in the work. Or if too
small, a ferrule may be placed upon it, thus increasing the capacity of
the tool. When a tool of this kind is to be used on iron, steel, or
copper, and not upon brass, the front face of the teeth may be given
rake by cutting the grooves at an angle, as in Fig. 1109.
BORING TOOLS FOR LATHE WORK.--The principal object in forming a boring
tool to be held in a slide rest is to have the body of the tool as large
as can be conveniently got into the size of the hole to be bored; hence
the cutting edge should not stand above the level of the top of the
steel. By this means the tool will be as stiff as possible, and less
liable to spring away from its cut, as boring tools are apt to do,
especially when the cut or hole is a long one.
It is so difficult a matter to bore a long hole parallel with a long
boring tool that cutters of various forms are usually preferred, and
these will be described hereafter.
[Illustration: Fig. 1109.]
[Illustration: Fig. 1110.]
The boring tool is, upon cast iron and brass, exceedingly liable to
chatter, but this may always be avoided by making the angles forming the
cutting edge less acute: thus, in Fig. 1110 are three boring tools, A,
B, C, operating in a piece of work D. Now the lateral pressure of a cut
is exerted upon the tool at a right angle to the length of the cutting
edge; hence (in addition to the vertical pressure) the lateral pressure
of the tool A will be in the direction of the dotted line and arrow A,
that on B in the direction of dotted line and arrow B, and that on C in
the direction of dotted line and arrow C; hence the pressure of the cut
would tend to force A towards the centre of the hole and off or away
from its cut, B back from its cut, and C deeper into its cut. Now as the
cut proceeds, the tool edge dulls, hence it would appear that a
compromise between C and B would be the most desirable, as giving to the
tool enough of the tendency to deepen its cut to compensate for the
tendency to spring away from its cut, as the cutting edge dulls (which
it does from the moment the cut begins). This is quite practicable in
tools to be used on wrought iron, as shown in Fig. 1111, which
represents the most desirable form.
In this form the part of the cutting edge performing duty under a deep
cut will be mainly in front of the tool, but in light cuts the cutting
edge would be farther back, where it is more nearly parallel to the line
of the work bore, and will hence cut smoother.
[Illustration: Fig. 1111.]
[Illustration: Fig. 1112.]
Where a boring tool is intended for light cuts only on wrought iron it
may have all, or nearly all, its rake at the top, as shown in Fig. 1112,
from _a_ to B representing the cut, and C the tool.
Under ordinary conditions that in the form of tool shown in Fig.
1113[15] is best for brass work, the face A being horizontal or slightly
depressed towards the point. Boring tools require very little bottom
rake, and the cutting points should be as rounded as they can be made
without chattering. On wrought iron the top rake may be as much as is
consistent with strength, and water should be freely applied to the cut.
For cast iron the best form of tool is that shown in Fig. 1114, the edge
A being parallel with the bore of the hole, and the feed being a coarse
one, taking a very light cut when finishing.
[15] From "The Complete Practical Machinist."
[Illustration: Fig. 1113.]
[Illustration: Fig. 1114.]
In cases, however, where the tool point requires to cut up to a sharp
corner, the form of tool shown in Fig. 1115 (which represents a top and
end view) may be used. Its end face C is at an obtuse angle to the
length of the tool, so that on passing up a bore and meeting a radial
face the point only will meet that face. This angle, however, gives to
the tool a keenness that will cause chattering on brass work unless the
top face be bevelled to the tool body, as is A to B in the figure.
[Illustration: Fig. 1115.]
It frequently happens in boring cast iron that the skin or the surface
of the metal is very hard, rapidly dulling the tool and forcing it away
from its cut, unless the cut is deep enough to allow the point of the
tool to cut beneath it, as shown in Fig. 1116, in which the hardness is
supposed to extend from the bore to the dotted line.
In this case a tool formed as at C is employed, the point cutting in
advance of the rest of the tool, and entering the soft metal beneath the
hard metal; the hard metal will then break away in lumps or pieces,
without requiring to be absolutely cut into chips or turnings, because
of being undercut, as shown at B.
The cross slider or tool rest of a lathe should be adjusted to closely
fit the cross slide of the lathe if true and parallel work is to be
bored, because any lost motion that may exist in the slide is multiplied
by the length the tool stands out from the tool post. Thus the centre of
motion of the rest if it has play, as at B, Fig. 1117, and the direction
of motion at the tool point, will be an arc of a circle of which B is
the centre, the bend of the tool from the pressure of the cut will have
its point of least motion or fulcrum at A; hence, both tend to cause the
tool point to dip and spring unequally under the varying cut pressure
that may arise from hard or soft places in the metal, and from
inequalities in the cut depth.
[Illustration: Fig. 1116.]
The pressure of the cut increases as the tool point loses its sharpness,
and this makes sufficient difference for the amount of tool spring in
light boring tools or in long holes to cause the tool to bore a larger
hole at the beginning than it does at the end of its feed traverse; or,
in other words, to bore a taper hole, whose largest end is that at which
the cut was started. If, therefore, the cut is traversed from the front
to the back of the hole the latter will be of the smallest diameter at
the back, and conversely if the cut proceeds from the back to the front
of the hole the front will be of smallest diameter. The amount of the
taper so caused (or in other words the error from parallelism) will
obviously increase with the length of the hole.
To obviate this taper, the slide of the rest should for the finishing
cut be set up firmly, and the tool after being sharpened should take a
finishing cut through the hole, and then let traverse back, which can be
done providing that care be taken not to bore the hole too large.
[Illustration: Fig. 1117.]
A boring tool will take a smoother cut and chatter less if the final cut
be from the back to the front of the hole, and for the following
reasons: When the tool is fed in, the strain or pressure of the cut is
in a direction to partly compress and partly bend the steel which is
being pushed to its cut, but when it is fed in the opposite direction it
is pulled to its cut and the strain is in a direction to stretch the
steel, and this the tool is more capable of resisting, hence it does not
so readily vibrate to cause chattering.
In consequence, however, of the liability of a boring tool to spring
away from its cut, it is far preferable to finish holes with standard
cutters, reamers, or bits, in which case the boring tool may be
employed to rough out and true up the hole, leaving a _fine_ cut for the
finishing cutter or bit, so as to wear its cutting edge as little as
possible. To further attain this latter object, the cutter or bit should
be used at a slow cutting speed and with a coarse feed.
[Illustration: Fig. 1118.]
[Illustration: Fig. 1119.]
If cutters or bits are not at hand, tool holders are desirable, and the
forms of these depend upon the nature, or rather the diameter, of the
hole to be bored. In all cases, however, the best results will be
obtained when the diameter of the tool holder is as near that of the
hole to be bored as will give it clearance. This occurs on account of
the rigidity of the holder being greater than that of the tool.
[Illustration: Fig. 1120.]
[Illustration: Fig. 1121.]
For large work tool holders are desirable, in that the tools, being
short, are easier to forge, to handle, and to grind.
For example, a tool holder of a cross section of two inches square may
contain a tool whose cross section is 1 by 3/4 inch, in which case it is
necessary to forge, grind, &c., the small tool only, whereas in the
absence of the holder the tool would require to be of a cross section
equal to that of the holder to obtain an equal degree of rigidity.
A boring tool holder suitable for holes of from 2 to 4 or 5 inches is
shown in Fig. 1118, in which A represents a round bar shaped at the end
B to fit into the tool post of the slide rest, and having a groove
across the diameter of the end C D to receive a short tool. The slot and
tool may be either square or [V]-shaped, the tool being locked by a
wedge. It is obvious that instead of shaping the end B as shown, the bar
may be held (if the slide-rest head is provided with a clamp instead of
a tool post) by two diametrically opposite flat faces.
For holes of a greater diameter a holder such as shown in Fig. 1119
should be used, the body being a square bar, and the tool being held in
the box A A by two set screws B. For holes of small diameter, as, say,
less than 1-1/2 inches, a tool holder is especially desirable, because
when a boring tool is forged out of a piece of tool steel, its length is
determined, and in order to have tools suitable for various depths of
hole a number of tools of varying lengths are requisite. Suppose, for
example, that a piece of steel be forged into a boring tool suitable for
a hole of an inch diameter, and 4 inches deep, then the steel must be
forged round for a distance of at least 4 inches from the cutting end,
and if such a tool were applied to a hole, say, two inches deep, the
cutting edge would stand out from the tool post at least two inches more
than is necessary, which would cause the employment of a tool weaker
than necessary for the work. To enable the use of one tool for various
depths of work, and yet hold it in each case as close to the tool post
as the work depth admits, tool-clamping devices, such as in Fig. 1120
(which are extracted from _The American Machinist_), are employed. 1 and
2 are pieces of steel fitting in the tool post and clamping the tool,
which for very small holes is made of octagon or round forged steel. The
tool may be passed to any required distance through the clamp, so as to
project only to the amount necessary for the particular depth of hole
requiring to be bored. These clamping pieces 1 and 2 should bed upon the
tool fairly along their full length; or, what is better, they may bed
the firmest at their extremities, which will insure that the tool is
gripped firmly as near to the cutting edge as possible.
In place of a steel tool, a tool holder turned cylindrically true and
parallel may be used to carry a short boring tool, as shown in Fig.
1121, in which A is the tool secured by the set-screw B into the holder
C. The latter may be provided with a line running true longitudinally,
and may have a fine groove similar to a thread, and having a pitch
measuring some part of an inch, as 1/8, 1/4, 1/2 inch, &c., so that the
distance the tool projects from the holder may be known without
measuring the same. But when a tool and holder of this description are
used, the tool cannot be employed unless the hole passes entirely
through the work, which occurs because of the presence of the set-screw
B.
It is obvious that for a tool-holding bar such as this, a clamping
device such as shown in Fig. 1120 is requisite, and that the position of
the clamping device may be adjusted to suit the work by setting it more
or less through the tool post.
The manner in which the deflection of a boring tool will affect the bore
of the work depends upon the height of the boring tool in the work. If
the tool is above the horizontal centre of the work, as in Fig. 1122,
the spring vertically will cause it to leave the cut, and bore the hole
to a corresponding amount smaller; and since the tool gets duller as the
wear proceeds, it will spring more at the latter end of each tool
traverse, leaving the end of the hole last cut of smallest diameter.
If, on the other hand, the tool be below the horizontal centre, as in
Fig. 1123, the vertical spring will be in a direction to increase the
amount of the cut, and thus offset the tapering effect of the increased
tool spring due to the wear of the tool. Furthermore, the shaving will
be easier bent if the tool be below than if above the horizontal centre,
because the metal will be less supported by the metal behind it. It is
always desirable therefore to have the cutting edge of a boring tool
used on small work below rather than above the horizontal centre of the
work. On large work, however, as say, having a bore of 6 inches and
over, the curve of the bore in the length of the circumference affected
by the cut or bending of the cut is so small, that the height of the
tool is of less consequence.
[Illustration: Fig. 1122.]
To enable the use of a stout-bodied boring tool, while keeping its
cutting edge below the centre, the top face of the tool may be
depressed, as shown in Fig. 1123.
[Illustration: Fig. 1123.]
An excellent attachment for boring parallel holes is shown in Figs. 1124
and 1125, in which there is fixed to the cross slide A the bracket B,
which is bored to receive a number of bushes C, whose bores are made to
suit varying diameters of boring-bars or reamers D. The hub of the
bracket is split on one side to enable it to be closed (by the bolt _e_)
upon the bush C and grip it firmly, the bush also being split at _f_.
The bracket B is provided with a taper pin G, which brings it in
position upon the slide so that the bushes C are true with the line of
lathe centres. It is also provided with the screws H, which lock it
firmly to the cross slide and prevent any spring or movement from play
or looseness.
When the bracket is adjusted and the bar fastened up (by screw _e_), the
lathe-carriage feeds the boring tool to the cut in the usual manner. Now
suppose that, as shown in our illustrations, a pulley P requires to be
bored, and the boring tool or reamer may be set to have its cutting end
stand out just as far as the length of the hub requires, and no farther,
so that the bar will be held and supported as close to the pulley hub as
is possible from the nature of the job. There need not be a separate
bush for every size of reamer, because the bodies of several size bars
may fit to one size of bush, especially if the set of reamers for every
size of bush be made with its smallest size equal to the bore of the
bush; because in that case the whole of the set may be adjusted to bore
any required depth of hole by sliding the reamer through the bush to the
required distance. If there are a number of lathes in a shop, each lathe
may have its own bracket B, all these brackets being bored to receive
the same bushes, and therefore the same boring-bars or reamers.
[Illustration: Fig. 1124.]
[Illustration: Fig. 1125.]
A bracket or stand of this kind may obviously be used to carry a bar,
having a head such as is shown in Fig. 1126, each dovetail groove
carrying a cutting tool, and for wrought iron or steel work these
grooves may be at an angle to the bar axis, as in the figure, to give
each cutter front rake, and increase its keenness.
[Illustration: Fig. 1126.]
BORING BARS FOR LATHE WORK.--Boring bars for lathe work are of two
kinds, those in which the cutters are held in a fixed position in the
length of the bar, and those in which the cutters are held in a head
which traverses along the work. The former are the least desirable,
because they require to be more than twice the length of the work, which
must be on one side of the cutter at the commencement of the cut, and on
the other at the termination of the same. But to traverse the head
carrying the tools along the bar necessitates a feed screw either within
the bar or outside of it. If within, the metal removed to give it place
weakens the bar, while in small holes there is no room for it; hence
solid bars with fixed cutting tools are used for small holes, and tools
held in a traversing head for those sufficiently large to give room for
a head without weakening the bar too much. A boring bar is best driven
from both ends.
[Illustration: Fig. 1127.]
"The boring bar is one of the most important tools to be found in a
machine shop, because the work it has to perform requires to be very
accurately done; and since it is a somewhat expensive tool to make, and
occupies a large amount of shop room, it is necessary to make one size
of boring bar answer for as many sizes of hole as possible, which end
can only be attained by making it thoroughly stiff and rigid. To this
end a large amount of bearing and close fitting, using cast iron as the
material, are necessary, because cast iron does not spring or deflect so
easily as wrought iron; but the centres into which the lathe centres fit
are, if of cast iron, very liable to cut and shift their position, thus
throwing the bar out of true. It is, therefore, always preferable to
bore and tap the ends of such bars, and to screw in a wrought-iron or
steel plug, taking care to screw it in very tightly, so that it shall
not at any time become loose. The centres should be well drilled and of
a comparatively large size, so as to have surface enough to suffer
little from wear, and to well sustain the weight of the bar. The end
surface surrounding the centres should be turned off quite true to keep
the latter from wearing away from the high side, as they would do were
one side higher than the other."[16]
[16] From "The Complete Practical Machinist."
[Illustration: Fig. 1128.]
The common form of the smaller sizes of boring bar is that shown in Fig.
1127. A A being the bar, D D the lathe centres, B the cutter passing
through a slot or keyway in the bar, and C a key tapered (as is also the
back edge of the cutter) to wedge or fasten the cutter to the bar. It is
obvious that, if the cutter is turned up in the bar, and is of the exact
size of the hole to be bored, it will require to stand true in the bar,
and will therefore be able to cut on both ends, in which case the work
may be fed up to it twice as fast as though only one edge were
performing duty. To facilitate setting the cutter quite true, a flat and
slightly taper surface should be filed on the bar at each end of the
keyway, and the cutter should have a recess filed in it, as shown in
Fig. 1128, the recess being shown at A, and the edges B B forming the
diameter of the cutters. The backing off is shown at C, from which it
will be observed that the cutting duty is performed by the edge C, and
not along the edge B, further than is shown by the backing off. The
recess must be made taper, and to fit closely to the flat places filed
on the bar. Such a cutter, if required to be adjustable, must not be
provided with the recess A, but must be left plain, so that it may be
made to extend out on one side of the bar to cut any requisite size of
bore; it is far preferable, however, to employ the recess and have a
sufficient number of cutters to suit any size of hole, since, as already
stated (there being in that case two cutting edges performing duty), the
work may be fed up twice as fast as in the former case, in which only
one cutting edge operates.
Messrs. Wm. Sellers and Co. form the cutters for their celebrated car
wheel boring bar machine as in Fig. 1129, the bottom or plain edge
performing the cutting. By this means the recess to fit the bar is not
reduced in depth from sharpening the tool. The tool is sharpened by
grinding the ends of the lower face as shown by the unshaded parts, and
the cutter is said to work better after the cutting part has begun to be
oblique from grinding.
[Illustration: Fig. 1129.]
The cutter is hardened at the ends and left soft in the middle, so that
the standard size of the cutter may be restored when necessary, by
pening and stretching the soft metal in the middle. These cutters will
bore from 50 to 250 car wheels, without appreciable reduction of size.
The description of bar shown in Fig. 1127 may be provided with several
slots or keyways in its length, to facilitate facing off the ends of
work which requires it. Since the work is fed to the cutter, it is
obvious that the bar must be at least twice the length of the work,
because the work is all on one side of the cutter at the commencement,
and all on the other side at the conclusion of the boring operation. The
excessive length of bar, thus rendered necessary, is the principal
objection to this form of boring bar, because of its liability to
spring. There should always be a keyway, slot, or cutter way, near to
the centre of the length of the bar, so as to enable it to bore a hole
as long as possible in proportion to the length of the boring bar, and a
keyway or cutter way at each end of the bar, for use in facing off the
end faces of the work.
If a boring bar is to be used only for work that does not require facing
at the ends, the cutter, slot, or keyway should be placed in such
position in the length of the bar as will best suit the work (keeping in
mind the desirability of having the bar as short as possible), and the
bar should be tapering from the middle towards each end, as shown in
Fig. 1130. This will make the bar stronger in proportion to its weight,
and better able to resist the pressure of the cut and the tendency to
deflect. The parallel part at A is to receive the driving clamp, but
sometimes a lug cast on at that end is used instead of a clamp.
For bores too large to be bored by the bar alone, a tool-carrying head
is provided, being sometimes fixed upon the bar by means of a locking
key, and at others fed along the bar by a feed screw provided on the
bar.
[Illustration: Fig. 1130.]
When the head is fixed on the bar the latter must be twice as long as
the bore of the work, as the work is on one side of the head at the
beginning, and on the other at the end of a cut; hence it follows that
the sliding or feeding head is preferable, being the shortest, and
therefore the most rigid, unless the bar slides through bearings at each
end of the head.
Fig. 1131 represents a bar with a fixed head in operation in a cylinder,
and having three cutting tools, and it will be observed that if tool A
meets a low spot and loses its cut, the pressure on tools B and C, both
being on the opposite side of the head, would cause the bar to spring
over towards A, producing a hole or bore out of round, and it follows
that four tools are preferable.
Fig. 1132 is a side view of a bar with four cutters, and Fig. 1133 an
end view of the same shown within a cylinder, and it will be seen that
should one of the cutters lose its cut, the two at right angles to it
will steady the bar.
[Illustration: Fig. 1131.]
[Illustration: Fig. 1132.]
When the cutters require to stand far out from the head, the bar will
work more steadily if the cutters, instead of standing radially in the
head, are placed as in Fig. 1134, so that they will be pulled rather
than pushed to their cut.
[Illustration: Fig. 1133.]
[Illustration: Fig. 1134.]
An excellent form of boring bar fixed head, employed by Messrs. Wm.
Sellers and Co. on their horizontal cylinder boring machine, is shown in
Fig. 1135. The boring head is split at A, so that by means of the bolt B
it may be gripped firmly to the bar D, or readily loosened and slid
along it. The head is provided with cutters C (of which there are four
in the latest design of bar), fitting into the radial slots E. These
cutters are secured to the head by the clamps and nuts at G.
Fig. 1136 represents a boring bar, with a sliding head fed by a feed
screw running along the bar, and having at its end a pinion that meshes
upon a gear or pinion upon the dead centre of the lathe.
[Illustration: Fig. 1135.]
The tools employed for the roughing cuts of boring bars should, for
wrought iron, cast iron, steel, or copper, have a little front rake, the
cutting corner being at A in Fig. 1137.
If the cutters are to be used for one diameter of bore only, they will
work more steadily if but little or no clearance is given them on the
end B, Fig. 1138, but it is obvious that if they are to be used on
different diameters of bores they must have clearance on these ends. The
same tool may be used both for roughing and finishing cuts.
[Illustration: Fig. 1136.]
The lip or top rake must, in case the bar should tremble during the
finishing cut, be ground off, leaving the face level; and if, from the
bar being too slight for its duty, it should still either chatter or
jar, it will pay best to reduce the revolutions per minute of the bar,
keeping the feed as coarse as possible, which will give the best results
in a given time. In cases where, from the excessive length and smallness
of the bar, it is difficult to prevent it from springing, the cutters
must be made as in Fig. 1139, having no lip, and but a small amount of
cutting surface; and the corner A should be bevelled off as shown. Under
these conditions, the tool is the least likely to chatter or spring into
the cut.
The shape of the cutting corner of a cutter depends entirely upon the
position of its clearance or rake. If the edge forming the diameter has
no clearance upon it, the cutting being performed by the end edges, the
cutter may be left with a square, slightly rounded, or bevelled corner;
but if the cutter have clearance on its outside or diametrical edge, as
shown on the cutters in Fig. 1137, the cutting corner should be bevelled
or rounded off, otherwise it will jar in taking a roughing cut, and
chatter in taking a moderate cut. The principle is that bevelling off
the front edge of the cutter, as shown in Fig. 1139, tends greatly to
counteract a disposition to either jarring or chattering, especially as
applied to brass work.
[Illustration: Fig. 1137.]
The only other precaution which can be taken to prevent, in exceptional
cases, the spring of a boring bar is to provide a bearing at each end of
the work, as, for instance, by bolting to the end of the work four iron
plates, the ends being hollowed to fit the bar, and being so adjusted as
to barely touch it; so that, while the bar will not be sprung by the
plates, yet, if it tends to spring out of true, it will be prevented
from doing so by contact with the hollow ends of the plates, which
latter should have a wide bearing, and be kept well lubricated.
[Illustration: Fig. 1138.]
It sometimes happens that, from play in the journals of the machine, or
from other causes, a boring bar will jar or chatter at the commencement
of a bore, and will gradually cease to do so as the cut proceeds and the
cutter gets a broader bearing upon the work. Especially is this liable
to occur in using cutters having no clearance on the diametrical edge;
because, so soon as such a cutter has entered the bore for a short
distance, the diametrical edge (fitting closely to the bore) acts as a
guide to steady the cutter. If, however, the cutter has such clearance,
the only perceptible reason is that the chattering ceases as soon as the
cutting edge of the tool or cutter has lost its fibrous edges. The
natural remedy for this would appear to be to apply the oil-stone; this,
however, will either have no effect or make matters worse. It is,
indeed, a far better plan to take the tool (after grinding) and rub the
cutting edge into a piece of soft wood, and to apply oil to the tool
during its first two or three cutting revolutions. The application of
oil will often remedy a slight existing chattering of a boring bar, but
it is an expedient to be avoided, if possible, since the diameter or
bore cut with oil will vary from that cut dry, the latter being a trifle
the larger.
The considerations, therefore, which determine the shape of a cutter to
be employed are as follows: Cutters for use on a certain and unvarying
size of bore should have no clearance on the diametrical edges, the
cutting being performed by the end edge only. Cutters intended to be
adjusted to suit bores of varying diameter should have clearance on the
end and on the diametrical edges. For use on brass work the cutting
corner should be rounded off, and there should be no lip given to the
cutting edge. For wrought iron the cutter should be lipped, and oil or
soapy water should be supplied to it during the operation. A slight lip
should be given to cutters for use on cast iron, unless, from slightness
in the bar or other cause, there is a tendency to jarring, in which case
no lip or front rake should be given.
[Illustration: Fig. 1139.]
"In boring work chucked and revolved in the lathe, such, for instance,
as axle boxes for locomotives, the bar shown in Fig. 1140 is an
excellent tool. A represents a cutter head, which slides along, at a
close working fit, upon the bar D D, and is provided with the cutters B,
B, B, which are fastened into slots provided in the head A by the keys
shown. The bar D D has a thread cut upon part of its length, the
remainder being plain, to fit the sliding head. One end is squared to
receive a wrench, which resting against the bed of the lathe, prevents
the bar from revolving upon the lathe centres F, F, by which the bar is
held in the lathe. G, G, G are plain washers, provided to make up the
distance between the thread and plain part of the bar in cases where the
sliding head A requires considerable lateral movement, there being more
or less washers employed according to the distance along which the
sliding head is required to move. The edges of these washers are
chamfered off to prevent them from burring easily. To feed the cutters,
the nut H is screwed up with a wrench.
"The cutter head A is provided in its bore with two feathers, which
slide in grooves provided in the bar D D, thus preventing the head from
revolving upon the bar. It is obvious that this bar will, in consequence
of its rigidity, take out a much heavier cut than would be possible with
any boring tool, and furthermore that, there being four cutters, they
can be fed up four times as fast as would be possible with a single tool
or cutter. Care must, however, be exercised to so set the cutters that
they will all project true radially, so that the depth of cut taken by
each will be equal, or practically so; otherwise the feeding cannot
progress any faster than if one cutter only were employed."[17]
[17] From Rose's "Complete Practical Machinist."
[Illustration: Fig. 1140.]
For use on bores of a standard size, the cutters may be made with a
projecting feather, fitting into a groove provided in the head to
receive it, as shown in Fig. 1141, which shows the boring bar and head,
the nuts and washers being removed. A, A represent cutters, B the bar, C
the sliding head, and D, D keys which fasten the cutters in the head.
The cutters should be fitted to their places, and each marked to its
place; so that, if the keyways should vary a little in their radius from
their centre of the bar, they will nevertheless be true when in use, if
always placed in the slot in which they were turned up when made. By
fitting in several sets of cutters and turning them up to standard
sizes, correctness in the size of bore may be at all times insured, and
the feeding may be performed very fast indeed.
For boring cannon the form of bar shown in Fig. 1142 is employed. The
cannon is attached to the carriage or saddle of the lathe and fed to the
boring bar. The working end only of the bar is shown in the figure, the
shank stem or body of the bar being reduced in diameter to afford easy
access to the cuttings. The cutters occupy the positions indicated by
the letters A, A, A, being carefully adjusted as to distance from the
axis of the bar by packing them at the back with very thin paper. As may
be observed they are arranged in two sets of three each, of which the
first set performs almost the whole of the work, the second being
chiefly added as a safeguard against error in the size of the bore on
account of wear of the cutting edges, which takes place to a small but
an appreciable extent in the course of even a single boring. Following
the cutters is a series of six guide-bars (B B B), arranged spirally,
which are made exactly to fit the bore. Provided that the length of
these is sufficient, and their fit perfect, it is evident that the
cutters cannot advance except in a straight line. The spiral arrangement
of the cutters is employed to steady the bar and to give it front rake.
[Illustration: Fig. 1141.]
[Illustration: Fig. 1142.]
[Illustration: Fig. 1143.]
[Illustration: Fig. 1144.]
BORING TAPERS WITH A BORING BAR OR ATTACHMENT.--In cases where the
degree of taper is very great a live centre may be bolted to a chuck
plate, as in Fig. 1143, by which means any degree of taper may be bored.
Instead of a star feed, a gear feed may be provided by fastening one
gear, as A, on the dead centre, and another, as B, on the feed-screw.
The cutting tool must stand on the side of the sliding-head--that is,
farthest from the line of lathe centres.
[Illustration: Fig. 1145.]
[Illustration: Fig. 1146.]
Small holes may readily be bored taper with a bar set over as in Fig.
1144, the work being carried by a chuck. The head H carries the cutting
tool, having a feather which projects into the spline S to prevent the
head from rotating on the bar. To prevent the bar from rotating, it is
squared on the end F to receive a wrench. The head is fed by the nut N,
which is screwed upon the bar. W, W, W, W are merely washers used to
bring the nut N at the end of the thread when the head is near the mouth
of the work, their number, therefore, depending upon the depth of the
work. A bar of this kind is more rigid than a tool held in the tool
post.
Instead of setting the dead centre of the lathe over, the bar may be set
over, as in Fig. 1145, in which the boring tool is carried in the
sliding head at T, and is fed by a screw having a star feed on its end.
At B is a block sliding in the end of the bar and capable of movement
along the same, to adjust the degree of taper by means of the screw
shown in the end view, Fig. 1146. N is a nut to secure B in its adjusted
position.
In this case the work must be bolted to the lathe carriage, and the tool
feeds to the cut, and the largest end of the hole bored will be at the
live spindle end of the lathe.
But we may turn the bar around, as in Fig. 1147, driving the work in a
chuck, and holding the dead centre end of the bar stationary, feeding
the sliding head to the cut by the feed screw F.
To increase the steadiness of the sliding head it may with advantage,
be made long, as in Fig. 1148, in which S is a long sleeve fitting to
the bar B at the head end H, and recessed as denoted by the dotted
lines. The short cutting tool C may be fastened to H by a set-screw in
the end of H, or by a wedge, as may be most desirable. The bar may
obviously set over to bore tapers as in the cut, and the sliding head
may be prevented from turning by a driver resting on the top of the tool
rest, and pushed by a tool secured to the tool post, the self-acting
carriage feed being put in operation.
[Illustration: Fig. 1147.]
[Illustration: Fig. 1148.]
It is obvious that when a boring bar is set over to bore a taper, the
lathe centres do not bed fair in the work centres, hence the latter are
subject to excessive wear and liable to wear to one side more than to
another, thus throwing the bar out of true and altering the taper it
will bore. This, however, may be prevented by fitting to the bar at each
end a ball-and-socket centre, such as shown in section in Fig. 1149. A
spherical recess is cut in the bar, a spherical piece is fitted to this
recess and secured therein by a cap as shown, the device having been
designed by Mr. George B. Foote.
[Illustration: Fig. 1149.]
BORING DOUBLE TAPERS.--To prevent end play in journal bearings where it
is essential to do so, the form of journal shown in Fig. 1150 is
sometimes employed, hence the journal bearing requires to be bored to
fit.
[Illustration: Fig. 1150.]
[Illustration: Fig. 1151.]
Fig. 1151 represents a bearing box for such a journal, the brasses A, B
having flanges fitting outside the box as shown. The ordinary method of
doing such a job would be to chuck the box on the face plate of the
lathe, setting it true by the circle (marked for the purpose of setting)
upon the face of the brasses, and by placing a scribing point tool in
the lathe tool post and revolving the box, making the circle run true to
the point, which would set the box one way, and then setting the flanges
of the box parallel with the face plate of the lathe to set the box true
the other way; to then bore the box half way through from one side and
then turn it round upon the face plate, reset it and bore the other
half; thus the taper of the slide rest would not require altering. This
plan, however, is a tedious and troublesome one, because, as the flanges
protrude, parallel pieces have to be placed between them and the lathe
face plate to keep them from touching; and as the face of the casting
may not be parallel with the slide ways, and will not be unless it has
been planed parallel, pieces of packing, of paper or tin, as the case
may be, must be placed to true the ways with the face plate, and the
setting becomes tedious and difficult. But the two tapers may be bored
at one chucking, as shown in Fig. 1152, in which A represents the lathe
chuck, and B is a sectional view of the bearing chucked thereon, C, C
being the parallel pieces. Now it will be observed that the plane of the
cone on the front end and on one side stands parallel with the plane of
the cone on the back end at an exactly opposite diameter, as shown by
the dotted lines D and E. If then the top slide of the lathe rest be set
parallel with those lines, we may bore the front end by feeding the tool
from the front of the bore to the middle as marked from F to G, and
then, by turning the turning tool upside down, we may traverse or feed
it along the line from H to J, and bore out the back half of the double
cone without either shifting the set of the lathe rest or chucking the
box after it is once set.
[Illustration: Fig. 1152.]
In considering the most desirable speed and feed for the cutting tools
of lathes, it may be remarked that the speeds for boring tools are
always less than those for tools used on external diameters, and that
when the tool rotates and the work is stationary, the cutting speed is a
minimum, rarely exceeding 18 feet per minute, while the feed, especially
upon cast iron, is a maximum.
The number of machines or lathes attended by one man may render it
desirable to use a less cutting speed and feed then is attainable, so as
to give the attendant time to attend to more than one, or a greater
number of lathes. In the following remarks outside work and a man to one
lathe is referred to.
The most desirable cutting speeds for lathe tools varies with the
rigidity with which the tool is held, the rigidity of the work, the
purpose of the cut, as whether to remove metal or to produce finish and
parallelism, the hardness of the metal and stoutness of the tool, the
kind of metal to be cut, and the length the tool may be required to
carry the cut without being reground. The more rigid the tool and the
work the coarser the feed may be, and the more true and smooth the work
requires to be the finer the feed. In a roughing cut the object is to
remove the surplus metal as quickly as possible, and prepare the work
for the finishing cut, hence there is no objection to removing the tool
to regrind it, providing time is saved. Suppose, for example, that at a
given speed and feed the tool will carry a cut 12 inches along the work
in 20 minutes, and that the tool would then require regrinding, which
would occupy four minutes, then the duty obtained will be 12 inches
turned in 24 minutes; suppose, however, that by reducing the speed of
rotation, say, one-half, the tool would carry a cut 24 inches before
requiring to be reground, then the rate of tool traverse remaining the
same per lathe revolution, it would take twice as long (in actual
cutting time) to turn a foot in length of the work. If we take the
comparison upon two feet of work length, we shall have for the fast
speed 24 inches turned in 40 minutes of actual cutting time, and 10
minutes for twice grinding the tool, or 24 inches in 50 minutes; for the
slow speed of rotation we shall have 24 inches turned in 80 minutes.
In this case therefore, it would pay to run the lathe so fast that the
tool would require to be ground after every foot of traverse. But in the
case of the finishing cut, it is essential that the tool carry the cut
its full length without regrinding, because of the difficulty of
resetting the tool to cut to the exact diameter. It does not follow from
this that finishing cuts in all cases require to be taken at a slower
rate of cutting speed, because, as a rule, the opposite is the case,
because of the lightness of the cut; but in cases where the work is
long, the rate of cutting speed for the finishing cut should be
sufficiently slow to enable the tool to take a cut the whole work length
without grinding, if this can be done without an undue loss of time,
which is a matter in which the workman must exercise his judgment,
according to the circumstances. In tools designed for special purposes,
and especially upon cast iron the work being rigid the tool may be
carried so rigidly that very coarse feeds may be used to great
advantage, because the time that the cutting edge is under cutting duty
is diminished, and the cutting speed may be reduced and still obtain a
maximum of duty; but the surfaces produced are not, strictly speaking,
smooth ones, although they may be made to correct diameter measured at
the tops of the tool marks, or as far as that goes at the bottom of the
tool marks also, if it be practicable.
In the following table of cutting feeds and speeds, it is assumed that
the metals are of the ordinary degree of hardness, that the conditions
are such that neither the tool nor the work is unduly subject to spring
or deflection, and that the tool is required to carry a cut of at least
12 inches without being reground; but it may be observed that the 12
inches is considered continuous, because on account of the tool having
time to cool, it would carry more than the equivalent in shorter cuts,
thus if the work was 2 inches long and the tool had time to cool while
one piece of work was taken out and another put in the lathe, it would
probably turn up a dozen such pieces without suffering more in sharpness
than it would in carrying a continuous cut of 12 inches long. The rates
of feed here given are for work held between the lathe centres in the
usual manner.
CUTTING SPEEDS AND FEEDS.
FOR WROUGHT IRON.
+---------+--------+-----------+-------------+-----------+------------+
| Work |Roughing| Roughing |Feed as lathe| Finishing | Finishing |
|diameter.| cuts. | cuts. | revolutions |cuts. Lathe| cuts. Lathe|
| Inches. |Feet per| Lathe | per inch of |revolutions| revolutions|
| | minute.|revolutions| tool travel.|per minute.| per inch |
| | |per minute.| | |tool travel.|
|---------+--------+-----------+-------------+-----------+------------|
| 1/2 | 40 | 305 | 30 | 305 | 60 |
| 1 | 35 | 133 | 30 | 133 | 60 |
| 1-1/2 | 30 | 76 | 30 | 76 | 60 |
| 2 | 28 | 53 | 25 | 53 | 60 |
| 2-1/2 | 28 | 42 | 25 | 42 | 50 |
| 3 | 28 | 35 | 25 | 35 | 50 |
| 3-1/2 | 26 | 28 | 25 | 30 | 50 |
| 4 | 26 | 24 | 20 | 26 | 50 |
| 5 | 25 | 18 | 20 | 21 | 50 |
| 6 | 25 | 15 | 20 | 16 | 50 |
| CAST IRON. |
| 1 | 45 | 163 | 30 | 163 | 40 |
| 1-1/2 | 45 | 135 | 25 | 135 | 30 |
| 2 | 40 | 76 | 25 | 76 | 25 |
| 2-1/2 | 40 | 61 | 20 | 61 | 20 |
| 3 | 35 | 44 | 20 | 50 | 16 |
| 3-1/2 | 35 | 38 | 18 | 43 | 16 |
| 4 | 35 | 33 | 18 | 38 | 16 |
| 4-1/2 | 30 | 25 | 16 | 28 | 14 |
| 5 | 30 | 22 | 16 | 26 | 14 |
| 5-1/2 | 30 | 20 | 14 | 24 | 12 |
| 6 | 30 | 19 | 14 | 22 | 12 |
| BRASS. |
| 1/2 | 120 | 910 | 25 | 910 | 40 |
| 3/4 | 110 | 556 | 25 | 556 | 40 |
| 1 | 100 | 382 | 25 | 382 | 40 |
| 1-1/4 | 90 | 275 | 25 | 275 | 40 |
| 1-1/2 | 80 | 203 | 25 | 203 | 40 |
| 1-3/4 | 80 | 174 | 25 | 174 | 40 |
| 2 | 75 | 143 | 25 | 143 | 40 |
| 2-1/2 | 75 | 114 | 25 | 114 | 40 |
| 3 | 70 | 89 | 25 | 89 | 40 |
| 3-1/2 | 70 | 76 | 25 | 76 | 40 |
| 4 | 70 | 66 | 25 | 66 | 40 |
| 4-1/2 | 65 | 55 | 25 | 55 | 40 |
| 5 | 65 | 50 | 25 | 50 | 40 |
| 5-1/2 | 65 | 45 | 25 | 45 | 40 |
| 6 | 65 | 41 | 25 | 41 | 40 |
| TOOL STEEL. |
| 3/8 | 24 | 245 | 60 | 245 | 60 |
| 1/2 | 24 | 184 | 60 | 184 | 60 |
| 5/8 | 24 | 147 | 50 | 147 | 60 |
| 3/4 | 24 | 122 | 40 | 122 | 60 |
| 7/8 | 20 | 87 | 30 | 87 | 60 |
| 1 | 20 | 76 | 30 | 76 | 60 |
| 1-1/4 | 20 | 61 | 25 | 61 | 50 |
| 1-1/2 | 18 | 45 | 25 | 45 | 50 |
| 2 | 18 | 34 | 25 | 34 | 50 |
| 2-1/2 | 18 | 27 | 25 | 27 | 50 |
| 3 | 18 | 22 | 25 | 22 | 40 |
| 3-1/2 | 18 | 19 | 25 | 19 | 40 |
| 4 | 18 | 17 | 25 | 17 | 40 |
| 4-1/2 | 18 | 15 | 25 | 15 | 40 |
+---------+--------+-----------+-------------+-----------+------------+
These cutting speeds and feeds are not given as the very highest that
can be attained under average conditions, but those that can be readily
obtained, and that are to be found used by skilful workmen. It will be
observed that the speeds are higher as the work is smaller, which is
practicable not only on account of the less amount of work surface in a
given length as the diameter decreases, but also because with an equal
depth of cut the tool endures less strain in small work, because there
is less power required to bend the cutting, as has been already
explained.
When it is required to remove metal it is better to take it off at a
single cut, even though this may render it necessary to reduce the
cutting speed to enable the tool to stand an increase of feed better
than excessive speed. Suppose, for example, that a pulley requires 1/4
inch taken off its face, whose circumference is 5 feet and width 8
inches. Now the tool will carry across a cut reducing the diameter 1/8
inch, at a cutting speed of 40 feet per minute, or 10 lathe revolutions
per minute; but if the speed be reduced to about 35 feet per minute, the
tool would be able to stand the full depth of cut required, that is, 1/8
inch deep, reducing the diameter of the pulley 1/4 inch. Now with the
fast speed two cuts would be required, while with the slow one a single
cut would serve; the difference is therefore two to one in favor of the
deep cut, so far as depth of cut is concerned.
The loss of time due to the reduced rotative speed of work would of
course be in proportion to that reduction, or in the ratio of 35 to 50.
It is apparent then that the tool should, for roughing cuts, be set to
take off all the surplus metal at one cut, whenever the lathe has power
enough to drive the cut, and that the cutting speed should be as fast as
the depth of cut will allow.
Concerning the rate of feed, it is advisable in all cases, both for
roughing and finishing cuts, to let it be as coarse as the conditions
will permit, the rates given in the table being in close approximation
of those employed in the practice of expert lathe hands.
It is to be observed, however, that under equal conditions, so far as
the lathe and the work is concerned, it is not unusual to find as much
difference as 30 per cent. in the rate of cutting speed or lathe
rotation, and on small work 50 per cent. in the rate of tool traverse
employed by different workmen, and here it is that the difference is
between an indifferent and a very expert workman.
An English authority (Mr. Wilson Hartnell), who made some observations
(in different workshops and with different workmen) on this subject,
stated that taking the square feet of work surface _tooled_ over in a
given time, he had often found as much as from 100 to 200 per cent.
difference, and that he had found the rate of _tooling_ small fly-wheels
vary from 2 to 8 square feet per hour without any sufficient reason. The
author has himself observed a difference of as much as 20 feet of work
rotation per minute on work of 18 and less inches in diameter, and as
much as 50 per cent. in the rate of tool traverse per lathe revolution.
It is only by keeping the speed rotation at the greatest consistent with
the depth of cut, and by exercising a fine discretion in regulating the
rotations of feed and cutting speed, that a maximum of duty can under
any given conditions be obtained.
It has hitherto been assumed that the workman's attention is confined to
running one lathe, but cases are found in practice where the lathes,
having automatic feed and stop motions, one man can attend to several
lathes, and in this case the feeds and speeds may be considerably
reduced, so as to give the operator time to attend to a greater number
of lathes. As an example, in the use of automatic lathes, several of
which are run by one man, the following details of the practice in the
Pratt and Whitney Company's tap and die department are given.
[Illustration: Fig. 1153.]
Lathe Number 1.--Lathe turning tool steel 3/8 inch in diameter and 1-1/4
long, reducing the diameter of the work 1/8 inch. Revolutions of work
per minute 125. Feed one inch of tool travel to 200 lathe revolutions.
Lathe Number 2.--Turning tool steel 2 inches long and 1/2 inch diameter,
reducing diameter 1/8 inch. Revolutions of work 100 per minute. Feed 200
lathe revolutions per inch of tool travel.
Lathe Number 3.--Turning tool steel 4 inches long and 7/8 inch in
diameter, reducing the diameter 1/8 inch. Revolutions of work 40 per
minute. Feed 200 lathe revolutions per inch of tool travel.
Lathe Number 4.--Turning tool steel 6 to 8 inches long and 1-3/16
diameter, reducing work 1/8 inch in diameter. Revolutions of work 35 per
minute. Feed 200 lathe revolutions per inch of tool travel.
Lathe Number 5.--Turning tool steel 8 to 10 inches long, and 2 inches in
diameter, reducing diameter 1/8 inch. Lathe revolutions 30 per minute.
Feed 200 lathe revolutions per inch of tool travel.
Lathe Number 6.--Turning tool steel 5 inches long and 3-1/2 inches
diameter, reducing diameter 3/16. Lathe revolutions 19 per minute. Feed
200 lathe revolutions per inch of tool travel.
The power required to drive the work under a given depth of cut varies
greatly with the following elements:--
1st. The diameter of the work, all other conditions being equal.
2nd. The degree of hardness of the metal, all other conditions being
equal.
3rd. Upon the shape of the cutting tool; and--
4th. Upon the quality of the steel composing the cutting tool, and the
degree of its hardness.
That the diameter of the work is an important element in small work may
be shown as follows:--
[Illustration: Fig. 1154.]
[Illustration: Fig. 1155.]
In Fig. 1153 let W represent a piece of work having a cut taken off it,
and the line of detachment of the metal from the body of the work will
be represented by the part of the dotted line passing through the depth
of the cut (denoted by C). Let Fig. 1154 represent a similar tool with
the same depth of cut on a piece of work of larger diameter, and it will
be observed that the dotted line of severance is much longer, involving
the expenditure of more power.
In boring these effects are magnified: thus in Fig. 1155 let W represent
a washer to be bored with the tool T, and let the same depth of cut be
taken by the tool, the diameter of the work being simply increased. It
is manifest that the cutting would require to be bent considerably more
in the case of the small diameter of work than in that of the large, and
would thus require more power for an equal depth of cut.
Again, from a reference to Figs. 950 and 952, it will be observed that
the height of the tool will make a difference in the power required to
drive a given depth of cut, the shaving being bent more when the tool is
above the centre in the case of boring tools, and below the centre in
the case of outside tools. But when the diameter of the work exceeds
about 6 inches, it has little effect in the respects here enumerated.
The following, however, are the general rules applicable when
considering the power required for the cutting of metal with lathe or
planer tools. The harder the metal, the more power required to cut off a
given weight of metal. The deeper the cut the less power required to cut
off a given weight of metal. The quicker the feed the less power
required to cut off a given weight of metal. The smaller the diameter of
outside work, and the larger the diameter of inside or bored work, the
less power required.
Copper requires less power than brass; yellow, and other brass
containing zinc, less than brass containing a greater proportion of tin.
Brass containing lead requires less power than that not containing it.
Cast iron requires more power than brass, but less than wrought iron;
steel requires more power than wrought iron.
CHAPTER XII.--EXAMPLES IN LATHE WORK.
TECHNICAL TERMS USED WITH REFERENCE TO LATHE WORK.--Work held between
the lathe centres is said to run true, when a fixed point set to touch
its perimeter will have an equal degree of contact all around the
circumference, and at any part of the length of the same when the work
is cylindrical and is rotated. When such a fixed point has contact at
one part more than at another of the work circumference, it is said to
run "out of true," "out of truth," or not to run true.
Radial or side faces (as they are sometimes called) also run true when a
fixed point has equal contact (at all parts of the revolution) with the
work surface.
Work that is held in chucks is said to be set true when it is adjusted
in the intended position.
To true up is to take off the work a cut of sufficient depth to cause a
fixed point to touch the work surface equally at each point in the
revolution.
To clean work up is to take off it a cut sufficiently deep to cause it
to run true, and at the same time removes the rough surface or scale
from the metal.
Roughing out work is taking off a cut which reduces it to nearly the
finishing size, leaving sufficient metal to take a finishing cut, and
reduce it to the proper size.
_Facing_ a piece of work is taking a cut off its radial face.
When a radial face or surface is convex, it is said to be _rounding_ or
_round_, and when it is concave it is said to be _hollow_.
When a radial face is at a right angle to a cylindrical parallel
surface, it is said to be _square_; but in taper work, it is said to be
_square_ when it is at a right angle to the axis of the taper.
_Outside work_ includes all operations performed on a piece of work
except those executed within the bores of holes or recesses, which is
termed inside or internal work.
_Jarring_ or _chattering_ is the term applied to a condition in which
the tool does not cut the work smooth, but leaves a succession of
elevations and depressions on it, these forming sometimes a regular
pattern on the work. In this case the projections only will have contact
with the measuring tools, or with the enveloped or enveloping work
surface, when the two pieces are put together.
Jarring or chattering more commonly occurs in the bores of holes or upon
radial surfaces, than upon plain cylindrical surfaces, unless the latter
be very long and slender. It occurs more also upon brass than upon iron
work, and more upon cast than upon wrought iron or steel. It is caused
mainly by vibrations of either the work or the tool.
It is induced by weakness (or want of support) in the work, by weakness
in the tool, or by its being improperly formed for the duty. Thus, if a
tool have too broad a cutting surface it will jar; if it be held out far
from the tool post it may jar; if it have too keen a top face for the
conditions it will jar.
Jarring may almost always be remedied on brass work by reducing the
keenness of the top face, giving it if necessary negative rake, as shown
in Fig. 964. On iron or steel work it may be avoided by using as stiff a
cutting tool as possible, holding its cutting edge as close to the tool
post as convenient, and reducing the length of cutting edge to a
minimum.
It may be prevented sometimes by simply placing the finger or a weight
upon the tool, or by applying oil to the work, but if this be done it
should be supplied continuously throughout the cut, as a tool will cut
to a different depth when dry from what it will when lubricated.
In using hand tools such as scrapers, too thin a tool may cause jarring,
which may be obviated by keeping the tool rest as close to the work as
possible, and placing a piece of leather between the work and the rest.
EXAMPLES IN LATHE WORK.--The simplest class of lathe work is that cut
from rods or short lengths of rod metal, which may be turned by being
held in a small chuck, or between the lathe centres.
Such work is usually of small diameter and short length, and is
therefore difficult to get at if turned between the lathe centres,
because the dog that drives it, the lathe face plate, and the dead
centre are in the way; such work may be more conveniently driven by a
small chuck.
It is usually made of round wire or rod, cut into lengths to suit the
conditions; thus if the lathe have a hollow spindle, the rod lengths may
be so long as to pass entirely through the spindle, otherwise the
lengths may be passed through the chuck, and as far as possible into the
live spindle centre hole.
In any event it is desirable to let the rod project so far out from the
chuck as to enable its being finished and cut off, without removal from
or moving it in the chuck, because such chucks are apt in course of time
to wear, so that the jaws do not grip the work quite concentric to the
line of centres; hence, if the work be moved in the chuck after having
been turned, it is apt to run out of true.
Sometimes, however, the existence of a collar on the work prevents it
from being trued for fit at both ends without being cut off from the
rod, in which case, if it requires correction after being cut off, it
must be rechucked, and it may be necessary at this rechucking to grip it
in several successive positions (partly rotating it in the chuck at each
trial) before it will run true.
Sometimes the length of work that may advantageously be driven by such a
chuck is so great as to render the use of the dead centre to support one
end necessary, in which case the rod should be removed from the chuck
before each piece is turned, so as to centre drill the dead centre end.
There is one special advantage in driving small work in a chuck of this
kind, inasmuch as the work can be tried for fit without removing it from
the lathe, while in some cases operations can be performed on it which
would otherwise require its removal to the vice; suppose, for example, a
thread of very small diameter and pitch requires to be cut on the work
end, then a pair of dies or a screw plate may be placed on it, and the
lathe pulled round by the belt; after the dies have commenced to start
the thread, they may be released and allowed to rotate with the lathe,
which will show if they are starting the thread true upon the work.
In cases also where the end of the work requires fitting to a seat, or
where it requires turning to a conical point, there is the advantage
that the work can be tried to the seat, or turned to the point without
taking from the lathe, or without any subsequent operations, whereas in
the case of a conical point, the existence of a work centre would
necessitate turning the cone some distance from the end, and cutting off
the work centre.
As the size of the work increases, the form of the chuck is varied to
make it more powerful and strong to resist the strains, but when the
size of the chuck becomes so large that it is as much in the way as the
face place would be, it is better to turn the work between the lathe
centres.
For work to be turned between the lathe centres, it is essential that
those centres run true, and be axially in line, and that both centres be
turned to the same degree of angle or cone, which is usually for small
lathes an angle of 60°, and for lathes of about 30 inches swing and over
an angle of about 70°. Both centres should be of an equal angle, for the
following reasons.
It is obvious that the work centres wear to fit the dead centre, because
of the friction between the two. Now in order to turn a piece of work
from end to end, it is necessary to reverse it in the lathe, because at
the first turning one end is covered by the carrier or driver driving
it. At the first turning one work centre only will have worn to fit the
lathe centre; hence when at the second, the other work centre wears to
fit the dead centre and in the process of such wearing moves (as it
always does to some degree) its location, the part first turned will no
longer run true. To obviate this difficulty it is proper at the first
turning to cut the work down to nearly the finished size, and then
reverse it in the lathe and turn up the other end. At this second
turning the work will have had both work centres worn to fit the dead
centre, hence if it be of the same angle as the live centre, the work
will properly bed to both centres, otherwise it will plainly not bed
well to the live centre, and in consequence will be apt to run in some
degree out of true at the live centre end.
The lathe centres should, for parallel work, stand axially true one with
the other, and this can only be the case when the live centre runs true.
If the live centre does not run true the following difficulties are met
with.
[Illustration: Fig. 1156.]
If one end only of the work requires to be turned and it can be
completely finished without moving the work driver, the work will be
true (assuming the live spindle to run true in its bearings and to fit
the same). It will also run true if the work be taken from the lathe and
replaced without moving the driver or carrier, providing that the driver
be so placed as to receive the driving pressure at the same end as it
did when the work was driven; and it is therefore desirable, on this
account alone, to always so place the work in the lathe that the driver
is driven by its tail end, and not from the screw or screw head. But if
the work be turned end for end it will not run true, because the work
centre at the unturned end of the work will not be true or central to
the turned part of the work.
It is obvious then that lathe centres should run true. But this will not
be the case unless the holes into which they fit in the lathe are
axially true one with the other and with the lathe spindles. If these
holes are true, and the centres are turned true and properly cleaned
before insertion, the centres may be put into their places without any
adjustment of position. Otherwise, however, a centre punch mark is made
on the radial or end face of the live spindle, and another is made on
the live centre, so that both for turning up and for subsequent use the
centre will run true when these centre punch marks are exactly opposite
to each other.
The best way to true lathe centres is with an emery-wheel. In some
lathes there are special fixtures for emery grinding, while in others an
attachment to go in the tool post is used. Fig. 1156 shows such an
attachment.
In the figure A is a frame to be fastened in the slide rest tool post at
the stem A´. It affords journal bearing to the hand wheel B, to the
shaft of which is attached the gear-wheel C, which drives a pinion D, on
a shaft carrying the emery-wheel E, the operation being obviously to
rotate wheel B, and drive the emery-wheel E, through the medium of the
multiplying gear-wheels C, D.
The emery-wheel is fed to its depth of cut on the lathe centre P, by the
cross feed screw of the lathe, and is traversed by pulling or pushing
the knob F, the construction of this part of the device being as
follows: G and H are two bushes, a sliding fit in the arms of frame A,
but having on top flat places I and J, against which touch the ends of
the two set-screws _k_, _l_, to prevent them from rotating. The
emery-wheel and gear pinion D are fast together, and a pin passes
through and holds G and H together. Hence the knob F pushes or pulls, as
the case may be, the bushes through the bearings G, H, in the frame A,
the pinion and emery-wheel traversing with them. Hence pinion D is
traversed to and fro by hand, and it is to admit of this traverse that
it requires its great length. The stem A is at such an angle that, if it
be placed true with the line of cross feed, the lathe centre will be
ground to the proper angle.
Fig. 1157 represents a centre grinding attachment by Trump Brothers, of
Wilmington, Delaware. In this device the emery-wheel is driven by belt
power as follows. A driving wheel A is bolted to the lathe face plate,
and a stand carries at its top the over-head belt pulleys, and at its
base the emery-wheel and spindle. This stand at C sets over the tool
post, and is secured by a bar passing through C and through the tool
post, whose set-screw therefore holds the stand in position. On the end
of the emery-wheel spindle is a feed lever, by means of which the
emery-wheel may be fed along the lathe centre. Cup piece B is for
enabling wheel A to be readily set true on the lathe face plate, one end
of B fitting the hub of A, while the other receives the dead centre
which is screwed up so that B will hold A in place, while it is bolted
to the lathe face plate, and at the same time will hold it true.
In the absence of a centre grinding attachment, lathe centres may be
turned true with a cutting tool, and finished with water applied to the
tool so as to leave a bright and true surface. They should not, for the
finest of work, be finished by filing, even though the file be a dead
smooth one, because the file marks cause undue wear both to the lathe
centres and the work centres.
The dead centres should be hardened to a straw color, and the live
centre to a blue; the former so as to have sufficient strength to resist
the strain, and enough hardness to resist abrasion, and the latter to
enable it to be trued up without softening it.
[Illustration: Fig. 1157.]
When, after turning them up, the centres are put into their places, the
tailstock may be moved up the bed so that the dead centre projects but
very little from the tailstock, and is yet close to the live centre, and
the lathe should be run at its fastest speed to enable the eye to
perceive if the live centre runs true, and whether the dead centre is in
line with the live one, and the process repeated so that both centres
may be tested.
A more correct test, however, may be made with the centre indicator.
[Illustration: Fig. 1158.]
CENTRE INDICATORS.--On account of the difficulty of ascertaining when a
centre runs quite true, or when a very small hole or fine cone as a
centre punch mark runs true when chucked in a lathe, the centre
indicator is used to make such tests, its object being to magnify any
error, and locate its direction. Fig. 1158, from _The American
Machinist_, represents a simple form of this tool, designed by Mr. G. B.
Foote, for testing lathe centres. A is a piece of iron about 8 inches
long to fit the lathe tool post, B is a leather disk secured to A by a
plate C, and serving to act as a holding fulcrum to the indicator
needle, which has freedom of movement on account of the elasticity of
the leather washer, and on account of the hole shown to pass through A.
It is obvious that if the countersunk end of the needle does not run
true, the pointed end will magnify the error by as many times as the
distance from the needle point to the leather washer is greater than
that from the leather washer to the countersunk end of the needle. It is
necessary to make several tests with the indicator, rotating the lathe
centre a quarter turn in its socket for each test, so as to prove that
the centre runs true in any position in the lathe spindle. If it does
not run true the error should be corrected, or the centre and the lathe
spindle end may be marked by a centre punch done to show in what
position the centre must stand to run true.
[Illustration: Fig. 1159.]
The tension of the leather washer serves to keep the countersunk against
the lathe centre without a very minute end adjustment. Or the same end
may be attained by the means shown in Fig. 1159, which is a design
communicated by Mr. C. E. Simonds to _The American Machinist_. The
holder is cupped on one side to receive a ball as shown, and has a
countersink on the other to permit a free vibration of the needle. The
ball is fitted to slide easily upon the needle, and between the ball and
a fixed collar is a spiral spring that keeps the ball in contact with
its seat in the holder.
[Illustration: Fig. 1160.]
One end of the needle is pointed for very small holes or conical
recesses, while the other is countersunk for pointed work, as lathe
centres. The countersink of the needle may be made less acute than the
lathe centre, so that the contact will be at the very point of the lathe
centre, the needle not being centre-drilled. The end of the needle that
is placed against the work should be as near to the ball or fulcrum as
convenient, so as to multiply the errors of work truth as much as
possible.
In some forms of centre indicators the ball is pivoted, so that the
needle only needs to be removed to reverse it end for end, or for
adjusting its distance, it being made a close sliding fit through the
ball. Thus, in Fig. 1160 the ball E is held in a bearing cut half in the
holder A, and half in cap B, which is screwed to A by screws C D.
Or the ball may be held in a universal joint, and thus work more
frictionless. Thus, in Fig. 1161 it is held by the conical points of two
screws diametrically opposite in a ring which is held by the conical
points of two screws threading through an outer ring, these latter
screws being at a right angle to those in the inner ring. The outer ring
is held to the holder by the conical points of two screws, all the
conical points seating in conical recesses.
[Illustration: Fig. 1161.]
It is obvious that the contact of the point of the needle and the work
may be more delicately made when there is some elasticity provided, as
is the case with the spiral spring in Fig. 1159.
Indicators of this class may be used to test the truth of cylindrical
work: thus, in Fig. 1162 is an application to a piece of work between
the lathe centres, there being fitted to one end of the needle a fork
_a_ that may be removed at pleasure.
[Illustration: Fig. 1162.]
One of the difficulties in turning up a lathe centre to run true arises
from the difference in cutting speed at the point and at the full
diameter of the cone, the speed necessary to produce true smooth work at
the point being too fast for the full diameter. This may be remedied on
centres for small work, as, say, three inches and less in diameter, by
cutting away the back part of the cone, leaving but a short part to be
turned up to true the centre.
To permit the cutting off or squaring tool to pass close up to the
centre, and thus prevent leaving a burr or projection on the work end,
the centre may be thus relieved at the back and have a small parallel
relief, as in Fig. 1164 at A, the coned point being left as large as
possible, but still small enough to pass within the countersink.
In centres for large and heavy work it is not unusual to provide some
kind of an oil way to afford means of lubrication, and an excellent
method of accomplishing this object is to drill a hole A, Fig. 1163, to
the axis of the centre and let it pass thence to the point as denoted by
the dotted line; there may also be a small groove at B in the figure to
distribute the oil along the centre, but grooves of this kind make the
returning of the centre more difficult and are apt to cause the work
centres to enlarge more from wear, especially in turning tapers with the
tailstock set over the lathe centre, these being out of line with the
work centre.
To enable a broad tool such as a chaser to meet work of smaller diameter
than the lathe centre, the latter is cut away on one side as in Fig.
1164. It is obvious also that the flat place being turned uppermost,
will facilitate the use of the file on work of smaller diameter than the
lathe centre, and that placed in the position shown in the cut, it will
permit a squaring tool to pass clear down to the centre and avoid
leaving the projecting burr which is left when the tool cannot pass
clear down the face to the edge of the countersink of the work centre.
[Illustration: Fig. 1163.]
[Illustration: Fig. 1164.]
The method to be employed for centring work depends upon its diameter,
and upon whether its ends are square or not. When the pieces are cut
from a rod or bar in a cutting-off machine, the ends are square, and
they may be utilized to set the work by in centring it. Thus, in Fig.
1165 is a top, and in Fig. 1166 is an end view of a simple device, or
lathe attachment for centre drilling. S is a stand bolted to the lathe
shears and carrying two pins P, which act as guides to the cup chuck or
work guide G; between the heads of pins P and the hubs of G are spiral
springs, forcing it forward, but permitting it to advance over the drill
chuck; the work W is fed forward to the drill. At the dead centre end
the work is supported by a female cone centre D in the tail spindle T.
The work rests in mouths of G and D, and as the pieces are cut from the
rod they are sufficiently straight, and being cut off in a cutting-off
machine the ends are presumably square; hence the coned chucks will hold
them sufficiently true with the ends, and the alignment of the centre
drilled holes will not be impaired by any subsequent straightening
processes; for it is to be observed, that if work is centre-drilled and
straightened afterwards, the straightening throws the centre holes out
of line one with the other, and the work will be more liable to
gradually run out of true as its centres wear.
[Illustration: Fig. 1165.]
Thus, in Fig. 1167, let W represent a bent piece of work centre-drilled,
and the axis of the holes will be in line as denoted by the dotted line,
but after the piece is straightened the holes will lie in the planes
denoted by the dotted line in Fig. 1168, and there will be a tendency
for the work centres to move over towards the sides C D as the wear
proceeds.
[Illustration: Fig. 1166.]
In Fig. 1169 is shown a centre-drilling machine, which consists of a
live spindle carrying the centre-drilling tool, and capable of end
motion for the drill feed. The work is held in a universal chuck, and if
long is supported by a stay as shown in the figure. The axis of the work
being in line with that of the chuck, the work requires no setting.
[Illustration: Fig. 1167.]
In this case the centre hole will be drilled true with that part of the
work that is held in the chuck, and the alignment of the centre hole
will depend upon the length of the rod being supported with its axis in
line with the live spindle. If the work is not straightened after
drilling, the results produced are sufficiently correct for the
requirements; but it follows from what has been said, that work which
requires to be straightened and tried for straightness in the lathe
should be centred temporarily and not centre-drilled until after the
straightening has been done.
[Illustration: Fig. 1168.]
In Fig. 1170 is shown a combined centre-drill and countersink not
unfrequently used in centring machines. The objection to it is, that the
cutting edges of the drill get dull quicker than those of the
countersink, and in regrinding them the drill gets shorter. Of course
the drill may be made longer than necessary so as to admit of successive
grindings, but this entails drilling the centre holes deeper than
necessary, until such time as the drill has worn to its proper length.
To overcome this difficulty the countersink may be pierced to receive a
drill as in Fig. 1171, the drill being secured by a set-screw S.
[Illustration: Fig. 1169.]
Among the devices for centring work by hand, or of pricking the centre
preparatory for centre-drilling, are the following:--
[Illustration: Fig. 1170.]
[Illustration: Fig. 1171.]
In Fig. 1172 is a centre-marking square. A B C D represents the back and
E the blade of the square. Suppose then that the dotted circle F
represents the end of a piece of work, and we apply the square as shown
in the cut and mark a line on the end of the work, and then moving the
square a quarter turn around the work, draw another line, the point of
contact of these two lines (as at G in the cut) will be the centre of
the work, or if the work is of large diameter as denoted by the circle H
H, by a similar process we obtain the centre E. In this case, however,
the ends A B of the square back must be of equal lengths, so that the
end faces at A B will form a right angle to the edge of the blade, and
this enables the use of the square for ordinary purposes as well as for
marking centres.
[Illustration: Fig. 1172.]
The point _a_ of the centre punch shown in Fig. 1173 is then placed at
the intersection of the two lines thus marked, and a hammer blow
produces the required indentation. The centre punch must be held upright
or it will move laterally while entering the metal. The part _b_ of the
centre punch is tapered so as to obstruct the vision as little as
possible, while it is made hexagon or octagon at the upper end to afford
a better grip. By increasing the diameter at C, the tool is stiffened
and is much less liable to fly out of the fingers when the hammer blow
does not fall quite fair.
[Illustration: Fig. 1173.]
In Fig. 1174 is shown a device for guiding the centre punch true with
the axis of the work, so as to avoid the necessity of finding the same
by lines for the centres. It consists of a guide piece B and a parallel
cylindrical centre punch A, C representing a piece of work. B is pierced
above with a parallel hole fitting and guiding the centre punch, and
has a conical hole at the lower end to rest on the work, so that if the
device be held upright and pressed down upon the end of the work, and
the top of the centre punch is struck with the hammer, the indentation
made will be central to the points of contact of the end of the work
with the coned hole of B. If then the end of the work has no projecting
burrs the centring will be centred true.
[Illustration: Fig. 1174.]
[Illustration: Fig. 1175.]
In the absence of these devices, lines denoting the location for the
conical recess or centre may be made, when either of the following
methods may be pursued.
[Illustration: Fig. 1176.]
[Illustration: Fig. 1177.]
[Illustration: Fig. 1178.]
In Fig. 1175 is shown what is known as a pair of hermaphrodite calipers,
which consists of two legs pivoted at the upper end; the bent leg is
placed against the perimeter of the work, as shown, and held steadily,
while with the point a line is marked on the work. This operation is
performed from four equidistant (or thereabouts) points on the work,
which will appear as shown in Fig. 1176, providing the radius to which
the point was set be equal to the radius of the work. The point at which
the lines meet is in this case the location for the centre. If, however,
the radius to which the points are set is less than the radius of the
work, the lines will appear as in Fig. 1177, in which case the location
is in the centre of the inscribed square, as denoted by the dot; or if
the radius be set too great the lines will appear as in Fig. 1178, and
the location for the centre will again be as denoted by the dot.
[Illustration: Fig. 1179.]
Another and very old method of marking these lines is to place the work
on a pair of parallel pieces and draw the lines across it, as shown in
Fig. 1179, in which W represents the work, P, P the parallel pieces of
equal thickness, S a stand (termed a scribing block) carrying a needle
N, which is held by a thumb screw and bolt at B. The point of the needle
is adjusted for the centre of the work, a line is drawn, the work is
then rotated, another line drawn, and so on, until the four lines are
drawn as in Fig. 1180, when the work may be turned end for end if light,
or if heavy the scribing block may be moved to the other end of the
work.
[Illustration: Fig. 1180.]
The centre locations are here made true with the part of the work that
rests on the parallel pieces, and this is in some cases an essential
element in the centring.
Thus, in Fig. 1181, it is required to centre a piece true with the
journals A B, and it is obvious that those journals may be rested on
parallel pieces P, P, and the centres marked by the scribing block on
the faces E, F in the manner before described.
[Illustration: Fig. 1181.]
If there is a spot in the length of a long piece of work where the metal
is scant and out of round, so that it is necessary to centre the work
true by that part, the surface gauge and parallel pieces may be used
with advantage, but for ordinary centring it is a slow process. When a
piece of work is not cylindrical, and it is doubtful if it will clean
up, the centring requires care, for it must not always be assumed, that
if two diametrically opposite points meet the turning tool at an equal
depth of cut, the piece is centred so as to true up to the largest
possible diameter.
[Illustration: Fig. 1182.]
This is pointed out in Fig. 1182, which is extracted from an article by
Professor Sweet. "In a piece of the irregular form A, the points _a_ and
_b_ might be even and still be no indication of the best location for
the centre, and in the piece B it is evident that if _c_ and _d_ were
even, nothing like the largest cylinder could be got from it. In the
case of shape A, the two points _e_ and _f_ should be equidistant from
the centre, and in the case of shape B, the three points _g_, _h_, _i_
should be equidistant from the centre."
The depth of the centre drill holes should be such as to leave them in
the work after it is cut off to its proper length, and will, therefore,
be deeper as the amount to be cut off is greater.
The diameter of the centre drill is larger as the size of the work
increases, and may be stated as about 3/64 for work of about 1/2 inch,
increasing up to 1/8 inch for work of about an inch, and up to three
inches in diameter; for work of a foot or over the centre drill may be
3/16 inch in diameter.
[Illustration: Fig. 1183.]
The centre drilling and countersinking may, when the work is cut to
length, be performed at one operation, but when it requires to be cut to
length in the lathe, that should be done before the countersinking. A
very simple chuck for centre drilling is shown in Fig. 1183, with a
twist drill (which is an excellent tool for centre-drilling). If the
work is held in the hand and fed to the drill by the lathe dead centre,
the weight of the work will cause the hole to be out of straight with
the work axis, unless the grip is occasionally relaxed, and the work
made to rotate a half or a quarter turn as the drilling proceeds.
After the work is centre-drilled and cut off to length, it must be
finally countersunk, so as to provide ample bearing area for the lathe
centres.
[Illustration: Fig. 1184.]
The countersinking should be true to the centre hole; and it is
sometimes made to exactly fit the lathe centres, and in other cases it
is made more acute than the lathe centre, so that the oil may pass up
the countersink, while it is bedding itself to the lathe centres.
If the countersinking is done before the end of the work is squared, it
will not be true with the centre-drilled hole.
In order that the countersinking may wear true with the centre-drilled
hole, it may be made of a more obtuse angle (as, say, one degree) than
the lathe centre, as in Fig. 1184, so that the hole may form a guide to
cause the lathe centre to wear the countersinking true to the hole, and
thus correct any error that may exist.
[Illustration: Fig. 1185.]
If the countersink is made more acute than the lathe centre, as shown in
Fig. 1185, the wear of its mouth will act as a guide, causing the centre
to be true with the countersinking; and when the bearing area extends to
the centre-drilled hole, there will be introduced, if that hole does not
run true, an element tending to cause the work to run out of true again,
because the countersinking will have more bearing area on one side than
on the other.
It is to be observed, however, that if the difference between the
countersink angle and that of the lathe centre be not more than about
one degree, the work centre will bed itself fully to the lathe centre
very rapidly, and usually before the first cut is carried over the work,
unless the work centres have been made to have unduly large
countersinks.
[Illustration: Fig. 1186.]
Fig. 1186 represents a half-round countersink, in which the cutting edge
is produced by cutting away the coned point slightly below the dotted
axial line. This secures two advantages: first, it gives the cutting
edge clearance without requiring the grinding or filing such clearance;
and, secondly, the cone being the same angle as the lathe centres,
filing away more than half of it causes it to give the lathe centre at
first a bearing at the small end of the countersink, as in Fig. 1184,
and this secures the advantage mentioned with reference to that figure.
It is obvious that such a reamer, however, does not produce strictly a
cone countersink, as is shown in Fig. 1187, where the cutting away of
the cone is carried to excess simply to explain the principle, and the
cone becomes an hyperbolic curve.
The small amount, however, that it is necessary to carry the face below
the line of centres, practically serves to make the cone somewhat less
acute, and is not therefore undesirable.
[Illustration: Fig. 1187.]
Another method of forming the half-round countersink is shown in Fig.
1188, in which the cone is of the same angle as the lathe centres; the
back A is ground away to avoid its contact with the work and give
clearance, while clearance to the cutting edge is obtained by filing or
grinding a flat surface B at the necessary angle to the upper face of
the cone. In this case it is assumed that the centre-drilling and
countersinking are true one with the other. Yet another form of
countersink is shown in Fig. 1189, consisting of a cone having three or
four teeth. It may be provided with a tit, which will serve as a guide
to keep the countersink true with the hole, and this tit may be made a
trifle larger in diameter than the hole, and given teeth like a reamer,
so as to ream the hole out while the countersinking is proceeding.
[Illustration: Fig. 1188.]
[Illustration: Fig. 1189.]
Unless one side of a half-round reamer is filed away so as to give the
cutting edge alone contact with the bore of the hole, an improper strain
is produced both upon the work and the countersink.
In Fig. 1190, for example, is shown, enlarged for clearness of
illustration, a hole, and a half-round countersink in section, and it is
evident that if the countersink is set central to the hole, it will have
contact at A and at B, and A cannot enter the metal to cut without
springing towards C.
[Illustration: Fig. 1190.]
[Illustration: Fig. 1191.]
But when the lathe has made rather more than one-half a revolution, the
forcible contact at B will be relieved, and either the work or the
countersink will move back towards D. This may be remedied by setting
the countersink to one side, as in Fig. 1191, or by cutting it away on
one side, as in Fig. 1192, when the half-round reamer will, if the work
be rigidly held while being countersunk, act as a cutting tool. But it
is more troublesome to hold the work rigidly while countersinking it
than it is to simply hold it in the hands, and for these reasons the
square centre is an excellent tool to produce true countersinking.
[Illustration: Fig. 1192.]
[Illustration: Fig. 1193.]
[Illustration: Fig. 1194.]
Fig. 1193 represents a square centre, the conical end being provided
with four flat sides, two of which appear at A B, or it may have three
flat sides which will give it keener cutting edges, and will serve
equally well to keep it true with the drilled hole. But it is
questionable whether it is not an advantage not to have the cutting
edges so keen as is given by the three flat faces, because the less keen
the cutting edges are, the more true the countersinking will be with the
hole, the extra pressure required to feed the square centre tending to
cause it to remain true with the hole notwithstanding any unequal
density of the metal on different sides of the hole. An objection to the
square centre is that it involves more labor in the grinding to
resharpen it, and is not so easy to grind true, but for fine work this
is more than compensated for in the better quality of its work.
[Illustration: Fig. 1195.]
[Illustration: Fig. 1196.]
This labor, however, may be lessened in two ways: first, the faces may
be fluted, as in Fig. 1194, at A and at B, or its diameter may be turned
down, as in Fig. 1195. In using the square centre it is placed in the
position of the live centre and revolved at high speed, all the cutting
edges operating simultaneously; the work is fed up by the dead centre
and held in the hand.
To prevent the weight of the work from causing the countersinking being
out of true with the hole, the work should be occasionally allowed (by
relaxing the grip upon it) to make part of a revolution, as explained
with reference to centre-drilling without a work guide. Another and
simple form of square centre for countersinking is shown in Fig. 1196.
It consists of a piece of square steel set into a stock or holder.
[Illustration: Fig. 1197.]
Work that is to be hardened and whose centres are, therefore, liable to
warp in the hardening, may be countersunk as in Fig. 1197, there being
three indentations in the countersink as shown. This insures that there
shall be three points of contact, and the work will run steadily and
true. Furthermore, the indentations form passages for the oil,
facilitating the lubrication and preventing wear both to the work and to
the lathe centres.
[Illustration: Fig. 1198.]
These indentations are produced after the countersinking by the punch,
shown in Fig. 1198. Except when tapers are turned by setting the lathe
centres out of line with the lathe shears (as in setting the tailstock
over), all the wear falls on the dead centre end of the work, as there
is no motion of the work centre on the live centre, hence the work
centres will not have worn to a full bearing until the work has been
reversed end for end in the lathe.
[Illustration: Fig. 1199.]
[Illustration: Fig. 1200.]
If it be attempted to countersink a piece of work whose end face is not
square, the countersinking will not be true with the centre hole, and
furthermore the causes producing this want of truth will continue to
operate to throw the work out of true while it is being turned. Thus, in
Fig. 1199, _a_ represents a piece of work and B the dead centre; if the
side C is higher than side D of the work end, the increased bearing area
at C will cause the most wear to occur at D, and the countersink in the
work will move over towards D, and it follows that the face of a rough
piece of work should be faced before being countersunk. Professor Sweet
designed the centre-drilling device shown in Fig. 1200, which consists
of a stock fitting the holes for the lathe centres, and carrying what
may be called a turret head, in which are the centre drills, facing
tools, and countersinks. The turret has 6 holes corresponding to the
number of tools it carries, and each tool is held in position by a pin,
upon a spring, which projects into the necessary hole, the construction
being obvious. The facing tool is placed next to the drill and is
followed by a countersink, in whatever direction the turret is rotated
to bring the next tool into operation. The work should, on account of
the power necessary for the facing, be driven in a chuck.
[Illustration: Fig. 1201.]
A similar tool, which may, however, be used for other work besides
centring and countersinking, is shown in Fig. 1201. It consists of a
stem fitting into the hole of the tail spindle, and carrying a base
having a pin D, on which fits a cap having holes _b_, and set-screws C
for fastening drills, countersinks, or cutting tools. The cap is pierced
with six taper holes, and a pin projects through the base into these
holes to lock the cap in position, this pin being operated by the spring
lever shown.
[Illustration: Fig. 1202.]
Work that has already been turned, but has had its centres cut off, may
be recentred as follows. One end may be held and driven by a chuck,
while the other end is held in a steady rest such as was shown in Fig.
802, and the centre may then be formed in the free end by a half-round
reamer, such as shown in Fig. 1190, placed in the position of the dead
centre, or the square centre may be used in place of the dead centre,
being so placed that one of its faces stands vertically, and therefore
that two of its edges will operate to cut. The location for the work
centre should be centre punched as accurately as possible, and the work
is then placed in the lathe with a driver on it, as for turning it up; a
crotch, such as shown in Fig. 1202, is then fastened in the lathe tool
post, and fed up by the cross-feed screw until it causes the work to run
true, and the square centre should then be fed slowly up and into the
work, with a liberal supply of oil. If the work runs out of true, the
crotch should be fed in again, but care must be taken not to feed it too
far. So long as the square centre is altering the position of the centre
in the work, it will be found that the feed-wheel of the tailstock will
feed by jumps and starts; and after the feeding feels to proceed evenly,
the crotch may be withdrawn and the work tried for being true. The
crotch, as well as the square centre, should be oiled to prevent its
damaging the work surface. It is obvious that in order to prevent the
lathe dead centre point from seating at the point or bottom of the work
centre, the square centre should be two or three degrees more acute in
angle than the lathe dead centre. If the work is tried for truth while
running on the square centre, the latter is apt to enlarge the work
centre, while the work will not run steadily, hence it is better (and
necessary where truth is a requisite) to try the work with the dead
centre in place of the square one.
In thus using a square centre to true work, great care should be taken
not to cut the work centres too large, and this may be avoided by making
the temporary centre-punch centres small, and feeding the crotch rapidly
up to the work, until the latter runs true, while the square centre is
fed up only sufficiently to just hold the work steady.
[Illustration: Fig. 1203.]
To test the truth of a piece of rough work, it may, if sufficiently
light, be placed between the lathe centres with a light contact, and
rotated by drawing the hand across it, a piece of chalk being held in
the right hand sufficiently near to just touch the work, and if the
chalk mark extends all round the work, the latter is as true as can be
tested by so crude a test, and a more correct test may be made by a tool
held in the tool rest. If the test made at various positions in the
length of the work shows the work to be bent enough to require
straightening, such straightening may be done by a straightening lever.
In shops where large quantities of shafting are produced, there are
special straightening tools or devices: thus, Figs. 1203 and 1204
represent two views of a straightening machine. The shaft to be
straightened is rotated by the friction caused by its own weight as it
lies between rollers, which saves the trouble of placing the shaft upon
centres. Furthermore, the belt that is the prime mover of the gears
driving these rollers is driven from the line shaft itself without the
aid of any belt pulley. The tension of this driving belt is so adjusted
that it will just drive the heaviest shaft the machine will straighten;
but if the operator grasps the shaft in his hand, the driving mechanism
will stop and the belt will slip, the shaft remaining stationary until
the operator sets it in motion again with his hand, when the belt ceases
to slip and the mechanism again acts to drive the shaft.
Fig. 1203 represents the mechanism for driving the shaft S, to be
straightened, which lies upon and between two rollers, R, R´. Upon the
shafts of these rollers are the gear-wheels A and B, which are in gear
with wheel C, the latter being driven by gear-wheel D. Motion to D is
derived from a pair of gears, the pinion of which is driven by the belt
from the line shaft. H is a head carrying all these gears (and the
rollers) except D. There are two of these heads, one at each end of the
machine, the two wheels D being connected by a rod running between the
shears, but the motion is communicated at one end only of this rod, the
shaft is driven between four rollers, of which two, R R´, are shown in
the engraving.
[Illustration: Fig. 1204.]
[Illustration: Fig. 1205.]
In Fig. 1204 the straightening device is shown. A frame consisting of
two parts, F, F´, is gibbed to the edge of the shears at G and H. The
upper part of this frame carries a square-threaded screw I, and is
capable of sliding across the shears upon the part F´. It rests upon the
shears through the medium of four small rollers (which are encased), two
of which are at J, K, and two are similarly situated at the back of the
frame F´. The motion of F across the machine is provided so that the
upper part F may be pushed back out of the way, to permit the shaft
being easily put on and taken off the friction rollers R R´. The motion
along the shears is provided to enable the straightening device to be
moved to the required spot along the shaft S´. The shaft S is laid on
two pieces N, P, and a similar piece _r_ is placed above to receive the
pressure of the screw I, which is operated by a hand lever to perform
the straightening. The pieces N, P rest upon two square taper blocks V,
which are provided with circular knobs at their outer ends to enable
them to be held and pushed in or pulled out so as to cause N, P to meet
the shaft before I is operated. This is necessary to accommodate the
different diameters of shaft S. The operator simply marks the rotating
shaft with chalk in the usual manner to show where it is out of true,
and then straightens wherever it is found necessary.
Fig. 1205 represents a similar device for straightening rods or shafts
while they are in the lathe. A is a frame or box which is fitted to rest
on the [V]s of the lathe shears, the straightening frame resting on the
box. Instead, however, of simply adjusting the height of the pieces P to
suit different diameters of the shaft, the whole frame is adjusted by
means of the wedge W, which is inserted between the frame F and the
upper surface of the box A. At H is a hole to admit the operator's hand
to move A along the lathe shears.
[Illustration: Fig. 1206.]
A method of straightening wire or small rods that are too rigid to be
straightened by hand, and on which it is inadvisable to use hammer
blows, is shown in Fig. 1206. It consists of a head revolved in a
suitable machine, and having a hole passing endways through it. In the
middle is a slot and through the body pass the pins A, being so located
that their perimeters just press the rod or wire when it is straight,
and in line with the axis of the bore through the head, each successive
pin A touching an opposite side of the wire or rod. It is obvious that
these pins in revolving force out any crooks or bent places in the wire
or rod, and that as the work may be pulled somewhat rapidly through the
head or frame, the operation is a rapid one.
When pieces of lathe work are to be made from rod or bar iron, they
should be cut off to the proper length in a cutting-off machine, such as
described in special forms of the lathe, and for the reasons set forth
in describing that machine.
An excellent tool, however, for cutting up rods of not more than 1/2
inch in diameter, is Elliott's cutting-off tool shown in Fig. 1207. It
consists of a jaw carrying steadying pieces for the rod to be cut up,
these pieces being adjusted to fit the rod by the screw and nut shown.
On the same jaw is pivoted a tool-holder, carrying a cutting-off tool,
which is fed to its cut by the upper handle being pressed towards the
lower one.
An adjustable stop or gauge is attached, by means of a small rod, to the
swinging arm which carries the cutting tool, and can be removed when its
use is not desirable.
[Illustration: Fig. 1207.]
The operation of this tool is as follows:--The rod to be cut up is held
in the lathe chuck, projecting beyond any desired distance, and arranged
to revolve at the same speed as for turning. The tool is placed upon the
rod, and the movable jaw of the rest adjusted to a bearing. If several
pieces are to be cut to a length, the gauge is adjusted, the tool moved
along the rod till the gauge-stop comes in contact with the end, the
handles pressed together, which moves the cutting tool up to the work in
such a way that it will come exactly to the centre, thus cutting the
piece entirely off, no adjustment of the tool ever being necessary to
provide for its cutting to the centre, except keeping the cutting edge
(which is not in this respect changed by grinding) at a distance
specified in the directions from the part in which it is clamped. As the
tool is moved up to cut, by the same operation the gauge is moved back
out of contact with the end. When the pressure on the handles is
removed, a spring returns the cutting tool to its original position, and
also brings the gauge in position for determining the length of the next
piece to be cut. The operation is repeated by simply moving the tool
along the rod, the cutting up being done with great rapidity and
accuracy. It will be noticed that all the appliances for cutting,
gauging, &c., being a part of the tool itself, if the rod runs out of
truth--in other words, wabbles--it will have no effect on the cutting,
the rod to be cut forming the gauge for all the operations required;
also that comparatively no time is lost in adjustment between the
several pieces to be cut from a rod.
The cutting tool is a piece of steel of the proper thickness, cleared on
the sides by concave grinding. It is held in place by a clamp and two
small screws, and requires grinding on the end only.
When the work is centred, it should, for reasons already explained, have
its end faces trued up.
In doing this, however, it is desirable in some cases to cut off the
work to its exact finished length. This possesses the advantage, that
when the work is finished, the work centres will be left intact, and the
work may be put into the lathe at any time, and it will run true to the
original centres. But this is not always the best plan; suppose, for
example, that there are a number of collars or flanges on the work, then
it is better to leave a little extra length to the work when truing up
the ends, so that if any of the collars are scant of metal, or if it be
desirable to turn off more on one side of a collar than on another, as
may be necessary to turn out a faulty place in the material, the end
measurements on the work may be conformed to accommodate this
requirement, and not confined to an exact measurement from the end of
the work.
Again, in the case of work having a taper part to be fitted, it is very
difficult to obtain the exact proper fit and entrance of taper to an
exact distance, hence it is best to leave the work a little too long,
with its collars too thick, and to then fit the taper properly and
adjust all other end measurements to suit the taper after it is fitted.
Before any one part of a piece of work turned between the lathe centres
is finished to diameter, all the parts to be turned should be roughed
out, and for the following reasons, which apply with additional force to
work chucked instead of being turned between the lathe centres.
It is found, that all iron work changes its form if the surface metal be
removed from it. Thus, though the lathe centres be true, and a piece of
work be turned for half its length in the lathe, after it has been
turned end for end in the lathe to turn the other half of its length,
the part already turned will run out of true after the second half is
turned up. This occurs from the tension and unequal internal strains
which exist in the metal from its being forged or rolled at a constantly
diminishing temperature, and from the fact that the surface of the metal
receives the greatest amount of compression during the forging.
In castings it is caused by the unequal and internal strains set up by
the unequal cooling of the casting in the mould, because of one part
being thicker than another.
When the whole of the work surfaces have been cut down to nearly the
finished size, this alteration will have taken place, and the finishing
may be proceeded with, leaving the work as true as possible. In chucked
work, or the most of it rather, it is impracticable (from being too
troublesome) to rough out all over before finishing; hence at each
chucking all the work to be done at that chucking is finished.
The roughing cuts on a piece of work should always be taken with as
coarse a feed as possible, because the object is to remove the mass of
the metal to be cut away rather than to produce a finish, and this may
be most quickly done by a deep cut and coarse feed. Theoretically also
the finishing should be done with a coarse feed, since the coarser the
feed, the less the length of time the cutting edge is in action. But the
length of cutting edge in action, with a given tool and under a given
depth of cut, increases as that edge is made longer to carry the coarse
feed, and the long cutting edge produces a strain that tends to spring
or bend the work, and that causes the tool to dip into seams or soft
spots, or into spongy or other places, where the cutting strain is
reduced, and also to spring away from hard spots or seams, where the
cutting strain is increased. The most desirable rate of feed, therefore,
is that which is as coarse as can be used without springing either the
work or the tool, and this will depend upon the rigidity of the work of
the lathe, and of the cutting tool. Short or slight work may be turned
very true by a light cut fine feed and quick cutting speed, but the
speed must obviously be slower in proportion as the length of the work
increases, because the finishing cut should be taken without taking the
tool out to resharpen it, since it is very difficult to set the tool to
the exact proper depth a second time.
Since the cutting edge will, at any given rate of cutting speed, retain
its keenness better for a given surface of work in proportion as the
time it is under duty is diminished, it follows, therefore, that the
coarser the feed the better (so long as both the work and the tool are
sufficiently rigid to withstand the rate of feed without springing).
Under conditions of rigidity that are sufficiently favorable a tool,
such as in Fig. 948, may be used on wrought or cast iron, at a feed of
1/2 or even 3/4 inch of traverse per lathe revolution, producing true
and smooth work, providing that the tool be given a very slight degree
of clearance, that its cutting edge is ground quite straight, that it is
set parallel to the line of feed, or what is the same thing, to the work
axis, and that the length of cutting edge is greater than the amount of
tool traverse per lathe revolution, as is shown in the figure, the
amount of tool traverse per lathe revolution obviously being from A to
B. It may also be observed that the leading corner of the tool may with
advantage be very slightly rounded as shown, so that there shall be no
pointed corner to dull rapidly.
In proportion as the work is light and the pressure of the cut may
spring it, the feed must be lessened, so that on very slender work a
feed of 100 lathe revolutions per inch of tool travel may be used. On
cast-iron work the feeds may be coarser than for wrought-iron, the other
conditions being equal, because cast iron cuts easier and therefore
springs the work less for a given depth of cut. But since cast iron is
apt to break out, exposing the pores of the metal, and thus leaving
small holes plainly visible on the work surface, the finishing cut
should be of very small depth, indeed a mere scrape; and if the surface
is to be polished, a fine feed and a quick speed will leave a cleaner
cut surface, and one that will require the least polishing operations to
produce a clean and spotless surface. Brass work also is best finished
with a fine feed and a quick speed.
It is obvious that the top face of the tool should be given more rake
for wrought iron than for cast iron or steel, and that in the case of
the very fine feeds, the form of tool shown in figure is the best for
finishing these metals.
In turning a number of pieces requiring to be of the same diameter, it
is to be borne in mind that a great part of the time is consumed in
accurately setting the tool for the finishing cut, and that if one piece
is finished at a time, this operation will require to be done separately
for each piece.
It is more expeditious, therefore, to rough all the pieces out, leaving
enough metal for a fine finishing cut to be taken, and then finish these
pieces without moving the tool; which may be done, after the tool is
once set, by letting the tool stand still at the end of the first
finishing cut, and taking the work out of the lathe. The carriage is
then traversed back to the dead centre, and another piece of work is put
in, and it is obvious that as the cross-feed screw is not operated after
the tool is once set, the work will all be turned to the same diameter
without any further measuring than that necessary for the first piece.
If the tool is traversed back to the dead centre before the lathe is
stopped or before the work is removed from the lathe, one of two results
is liable to follow. If the lathe is left running, the tool will
probably cut a spiral groove on the work, during its back traverse; or
if the lathe be stopped, the tool point will mark a line along the work,
and the contact of the tool point with the work will dull the cutting
edge of the tool. The reason of this is as follows: When the slide rest
and carriage are traversing in one direction, the resistance between the
tool and the cut causes all the play in the carriage and rest, and all
the spring or deflection of those parts, to be in an opposite direction.
Now if the play and spring were precisely equal for both directions, the
tool should cut to an equal diameter with the carriage traversed in
either direction, but the carriage in feeding is fed by the feed nut or
friction feed device, while when being traversed back the traversing
handle is used; thus the power is applied to the carriage in the two
cases at two different points, hence the spring of the parts, whether
from lost motion, or play from wear, or from deflection, is variable.
Again, even with the tool fed both to its cut and on the back traverse
with the hand feed handle, the play is, from the altered direction of
resistance of the cut, reversed in direction, and the depth of cut is
therefore altered.
Thus, in Fig. 1208, let S S represent the cross slide on the carriage
and R R the cross slide of the tool rest shown in section, and suppose
the tool to be traversing towards the live centre, then to whatever
amount there may be play or spring between the slide and the slide way,
the slide will from the pressure of the cut twist over, bearing against
the slide way at A and B, and being clear of it at G and H. On reversing
the direction of traverse of the rest, so as to feed the tool towards
the dead centre, the exactly opposite condition will set in, that is,
the pressure of the cut will force the slides in the opposite direction,
or in other words, the contact will be as in Fig. 1209, at C, D, and the
play at E, F. During the change of location of bearing between the
slides and the way, there will have been a certain amount of tool motion
altering the distance of the tool point from the line of centres, and
therefore the diameter to which it will cut. The angle at which the body
of the tool stands will influence the effect: thus, if when traversing
towards the live centre the tool stands at an angle pointing towards the
live centre, it would recede and cause the tool to clear the cut, if
removed on the back traverse without being moved to or from the line of
centres. Conversely, if the body of the tool was at an angle, so that it
pointed towards the dead centre, and a cut was taken towards the live
centre, and the tool was traversed back without being moved in or out,
it would take another cut while being moved back.
The conditions, however, are so uncertain, that it is always advisable
to be on the safe side, and either wind the tool out from its cut before
winding the rest and carriage back (thus destroying its set for
diameter), or else to stop the lathe and remove the work before
traversing the carriage back as already directed. If the latter plan is
followed the trouble of setting the tool is avoided and much time is
saved, while greater accuracy of work diameter is obtained. It is
obvious that this plan may be adopted for roughing cuts in cases where
two cuts only are to be taken, so as to leave finishing cuts of equal
depths; or if three cuts are to be taken, it may advantageously be
followed for the second and last cuts, the depth of the first cut being
of less importance in this case.
The following rules apply to all tools and metals:
[Illustration: Fig. 1208.]
[Illustration: Fig. 1209.]
When the pressure between the tool and the work is sufficient, from the
proportions of the work, to cause the work to spring or bend, the length
of acting cutting edge on the tool should be reduced.
As the diameter and rigidity of the work increases, the length of tool
cutting edge may increase. The cutting edge of the tool should be kept
as close as the work will conveniently admit to the slide rest tool
post, 1/4 _inch even_ of this distance being _important_.
The slide rest tool should always be resharpened to take the finishing
cut, with which, for wrought iron or steel, soapy water with soda in it
should be used, the soda serving to prevent the dripping water from
rusting the parts of the lathe.
Cast iron will cut with an exquisite polish if finished at a _very slow_
rate of cutting speed, and turned with a spring tool, such as was shown
in Fig. 974, and water is used. But being a slow process it is not usual
to finish it in this manner, though for round corners, curves, &c., this
method is highly advantageous.
For cast iron the tool should be as keen as the hardness of the metal of
the work will permit. If an insufficiently keen tool, or too deep a cut,
or too coarse a feed be taken, the metal will break out instead of
cutting clean, and numerous fine holes will be perceived over the whole
surface, impairing that dead flatness which is necessary to an even and
fine polish.
To remove these specks or holes in cylindrical work, the file may be
used, but for radial faces hand-scrapers, such as shown in Fig. 1295,
are used, the work rotating in either case at high speed. Such scrapers
are oilstoned and held with the handle end above the horizontal level.
The _rest_ should be so conformed to suit the shape of the work, that
the scraper will be supported close to the work, which will prevent
chattering, and a piece of leather should (as a further preventive of
chattering) be placed beneath the scraper. A very good method of using a
scraper is to adjust it to the work, and holding it still on the rest,
traverse the slide rest to move the scraper to its cut.
After the scraping, three methods of polishing radial faces are commonly
employed; the first is to use emery paper only, and the second is by the
use first of grain, emery, and oil, and the subsequent use of emery
paper or cloth, and the third is by the use of emery wheels and crocus
cloth.
If the work is finished by emery paper only, and it requires much
application of the same to efface the scraper marks, the evil will be
induced that the emery cuts out the metal most where it is most porous,
so that the finished surface is composed of minute hills and hollows,
and the polish, though bright and free from marks, will not have that
dead flat smooth appearance necessary to a really fine polish and
finish; indeed, the finish is in this case to some extent sacrificed to
obtain the polish.
It is for this reason that stoning the work (as hereafter described) is
resorted to, and that grain emery and lead is employed, which is done as
follows:--
For a flat radial face, a flat piece of lead, say 3/8 inch thick, and of
a size to suit the work, may be pivoted to the end of a piece of wood of
convenient length and used with grain emery and oil, the work rotating
quickly. To afford a fulcrum for the piece of wood, a lever or rest of
some kind, as either a hand rest or a piece fastened in the tool post,
is used.
The rest should be placed a short distance from the work surface and the
lever held partly vertical until the lead meets the work surface, when
depressing the lever end will force the lead against the work. The lever
end must be quickly moved laterally, so that the lead will approach and
then recede from the work centre; this is necessary for two reasons.
First, to prevent the emery from cutting rings in the work surface, and
secondly, to prevent the formation of grooves behind any hollow spots or
specks the work may contain. The reason of the formation of these
grooves is that the emery lodges in them and works out from the contact
of the lead, so that if on working out they move always in the same line
they cut grooves.
When a lathe is provided with belt motion to run both ways, it is an
excellent plan to apply the lead with the lathe running forward and then
with it running backward.
When by this means the scraper marks are removed, the next object is to
let the marks left by the lead be as fine and smooth as possible, for
which purpose flour emery should be used; but towards the last no emery,
but oil only, should be applied, the lead being kept in constant lateral
motion, first quickly and then slowly, so that the marks on the work
cross and recross it at different angles.
For round or hollow corners the lead need not be pivoted to the stick,
but should be spherical at the end, the marks being made to cross by
partly rotating the lever first in one direction and then in the other.
Sometimes the end of the lever is used without the addition of lead, but
this does not produce so flat a surface, as it cuts out hollows in the
pores of the metal.
For polishing to be done entirely in the lathe, emery paper and crocus
may follow the lead, being used dry and kept also in constant lateral
motion. Each successive grade of emery paper must entirely remove all
marks existing on the work at the time of its (the paper's) first
application, and, furthermore, each successive grade should be continued
until it is well worn, because of two pieces of emery paper of the same
grade that most worn will cut the smoothest and polish the best. For the
final polishing a piece of the finest emery paper should be prepared in
the manner hereafter described for polishing plain cylindrical surfaces.
The radial faces of wrought iron must be finished as smoothly and true
as possible, because being harder than cast iron the emery acts less
rapidly upon it. For radial faces on brass the surfaces should be
finished as smooth as possible with the slide rest tool, which should be
round nosed, with the round flattened somewhat where the tool cuts, and
the tool should not, under any condition, have any rake on its top face,
while the feed should be fine as, say, 32 revolutions per inch of tool
travel. Under skillful manipulation scraping may then be dispensed with,
although it may be used to a slight extent without impairing the truth.
Very small radial surfaces of brass may best be finished by the scraper
and polished with emery paper, while large ones may be finished with dry
emery paper.
Round corners on brass work should be finished with a spring tool, such
as shown in Fig. 974, but having negative top rake; but if the corners
are of small radius a well oilstoned hand-scraper is best.
To enable the smooth and true turning of all radial faces of large
diameter, the lathe head should, when it is possible, be steadied for
end motion by placing a rod between the lathe centres, but if the radial
face is solid at the centre so that such a rod cannot be put in, the end
motion adjusting device of the lathe should be adjusted. The slides of
the lathe should also be set up to have good firm contact, and the tool
should be brought up to the work by putting the feed motion in gear and
operating it by hand at the cone pulley, or gear-wheel on the feed
spindle. If the lathe has no compound rest, the cut should be put on by
this means, but otherwise the tool may be brought near the work by the
feed motion and the cut put on by the compound rest, the object in both
cases being to take up all lost motion and hold the rest firmly or
steadily on the lathe shears, so that it shall not move back as the cut
proceeds.
Work of cast iron or brass and of small dimensions and irregular or
curved outline should be finished with scraping tools, such as shown in
Figs. 1303 and 1310, polished with emery cloth or paper. But whenever
scrapers are made with curves to suit the form of the work, such tool
curves should be so formed (for all metals) as not to cut along the
whole length of cutting edge at once, unless the curve be of very small
length as, say, 1/4 inch. This is necessary, because if the cutting edge
operates on too great a length it will jar or chatter.
For convex surfaces the curve on the scraper should be of greater radius
than that of the work, while in the case of concave curves the tool
should have a less radius. In both cases the tool will require a lateral
movement to cause it to operate over the full width of work curve.
If the work curves are sufficiently large, and the same is sufficiently
rigid that a slide rest tool may be used, the length of cutting edge may
be increased, so that under very favorable conditions of rigidity the
tool edge may cut along its whole length without inducing either jarring
or chattering, but the best results will always be obtained when with a
broad cutting edge the tool is of the spring tool form shown in Fig.
974.
Work of wrought iron or steel of small dimensions and of irregular form,
must also be finished by hand tools, such as the graver shown in Figs.
1285 and 1286, and the finishing tool shown in Figs. 1289 and 1292, the
shape of the tool varying to suit the shape of the work.
Round corners or sweeps cannot on any kind of work be finished by a
file, because the latter is apt to pin and cut scratches in the work.
For the final tool finishing of lathe work of plain cylindrical outline,
no tool equals the flat file if it be used under proper conditions,
which are, that the work be turned true and smooth with slide rest
tools, the marks left by these tools being exceedingly shallow and
smooth.
A dead smooth file that has been used enough to wear down the projecting
teeth (which would cut scratches) should then be used, the work rotating
at as fast a speed as the file teeth will stand without undue wear. The
file strokes should be made under a light pressure, which will prevent
the cuttings from clogging its teeth, and the cuttings should be cleaned
from the file after every few strokes. Under these conditions work of
moderate diameter may be turned to the greatest degree of smoothness and
truth attainable with steel cutting tools, providing that the work makes
several revolutions during each file stroke, and it therefore follows
that the file strokes may be more rapid as the diameter of the work
decreases, and should be more slow as that diameter increases. Allowing
the greatest speed of the filed surface permissible, without too rapid
destruction of the file teeth, to be 200 feet per minute, and the
slowest speed of file stroke that will prevent the file teeth from being
ground away or from becoming pinned (when used on wrought iron) to be
one stroke in two seconds, the greatest diameter of work that can be
finished by filing under the condition that the work must make more than
one rotation per file stroke, is about 25 inches in diameter, running
about 30 revolutions per minute. The same diameter and speed may be also
taken for cast iron, but brass may be filed under increased speed,
rendering it practicable to file it up to a diameter of about 36 inches
under the above conditions of work rotation and file stroke speed.
Supposing, however, that from hardness of the metal or from its
increased diameter the work cannot make a rotation per file stroke
unless that stroke be more slowly performed, then the cuttings gather in
the teeth of the file, become locked and form projections, termed pins,
above the file teeth, and these projections cut scratches in the work,
and this it is that renders it impracticable to hold the file still
while the work rotates. But suppose the file be applied to work of such
a diameter that, with a stroke in two seconds and the work surface
rotating at 200 feet per minute, each stroke acts on a fraction of the
circumference only, then there can be no assurance that the filed
surface will be cylindrical, because there is no means of applying the
file equally over the whole surface. But it is to be noted,
nevertheless, that the file acts with greater effect in proportion as
the area filed is decreased, and that as the tool marks are filed out
the area of surface operated upon is increased. Suppose, then, that
starting from any point on the work circumference a file stroke be
taken, and that it extends around one-third of the circumference, that
the second file stroke extends around one-third also, but that there is
an unfiled space of, say, two inches between the area of surface filed
by these two strokes, and that at the third file stroke the file starts
on the surface filed at the first stroke, passes over the two inches
previously unfiled and terminates on the surface filed by the second
stroke; then the conditions will be as follows:--
Part of the surface filed at the first stroke will have been filed
twice, part of the surface filed at the second stroke will also have
been filed twice, while the two inches will have been filed once only.
But this latter part will have had much more taken off it during the
third stroke than did the rest of the surface filed at that stroke,
because it operated on the ridges or tool marks where, being unfiled,
their area in contact with the file teeth was at a minimum. This
condition will prevail until the tool marks are effaced, and tends to
preserve the truth of the work up to that point, hence the necessity of
leaving very fine tool marks becomes obvious.
Apart from these considerations, however, there is the fact that filing
work in the lathe is a very slow operation, and therefore inapplicable
to large work; and furthermore, on large work the surface is not needed
to be so smooth as in small work; for example, tool feed marks 1/1000
inch deep would upon work of 1/2 inch diameter leave a surface appearing
very uneven, and the wearing away of those ridges or marks would destroy
the fit of the piece; but in a piece, say, six feet in diameter, tool
marks of that depth would not appear to much disadvantage, and their
wearing away would have but little effect upon the fit of the piece.
Finishing with the file, therefore, is usually applied to work of about
24 inches in diameter, and less, larger work being finished with the
cutting tool or by emery grinding, where a greater degree of finish is
required.
Small work--as, say, of six inches, or less, in diameter--may be
finished with the file so cylindrically true, that no error can be
discovered by measurement with measuring tools of the calipering class,
though the marks of contact if made apparent by gently forcing the work
through a closely fitting ring-gauge may not appear to entirely cover
the surface.
To produce filed work thus true, all that is necessary is to set the
cutting edge of the finishing tool at the horizontal centre of the work,
properly adjust the live spindle of the lathe for fit to its bearings,
adjust the slides of the slide rest so that there is no lost motion, and
follow the rules already given with reference to the shape of the tool
cutting edge, employing a cutting speed not so fast as to dull the tool
before it has finished its cut, using a fine feed except in the case of
cast iron, as already explained.
The requirement that the tool shall not become dull before it has
finished its cut, brings us to the fact that the length of work that can
be thus accurately turned is limited, as the diameter of the work
increases.
Indeed, the length of the work in proportion to its diameter is a very
important element. Thus, it would be very difficult indeed to turn up a
spindle of an inch in diameter and, say, 14 feet long, and finish it
cylindrically true, parallel, and smooth, because
1st. The slightness of the work would cause it to spring or deflect from
the pressure or strain due to the cut. This may to some extent be
remedied by steadying the work in a follower rest, but the bore of such
follower itself wears as the cut proceeds, though the amount may be so
small as to be almost inappreciable.
2nd. The work being better supported (by the lathe centres) at the two
ends than in the middle of its length, the duty placed on the follower
rest will increase as the middle of the work length is approached, hence
the spring or deflection of the follower rest will be a disturbing
element.
3rd. The tool gets duller as the cut proceeds, causing more strain from
the cut, and, therefore, placing more strain on the follower rest; and,
4th. It would be necessary, on account of the length of the cut, to
resharpen the tool before the cut was carried from end to end of the
spindle, and it would be almost impracticable to set the reground tool
to cut to the exact diameter.
The second, third, and fourth of the above reasons operate together in
causing increased work spring as the tool approaches the middle of the
work length; thus the deflection of the follower rest, the increased
weakness of the work, and the comparative dullness of the tool would all
operate to cause the work to gradually increase in diameter as the cut
proceeded towards the work centre (of length).
Suppose, for example, a cut to have been carried from the dead centre,
say, five feet along the work; at the end of this five feet the tool
will be at its dullest, the shaft at its weakest, and supported the
least from the dead centre and follower rest.
Suppose, then, that the reground tool be placed in the rest again and
set to just meet the turned surface without cutting it, then when it
meets the cut to carry it farther along the work the cut will produce
(on account of the tool being sharper) less strain on the work, which
will therefore spring or deflect less. Precisely what effect this may
have upon the diameter to which the tool will turn the work will depend
upon various conditions: thus, if the top face of the tool be
sufficiently keen to cause the strain due to bending the shaving cut or
chip to pull the work forward, the tool would turn to a smaller
diameter. If the depth of the cut be sufficient to cause the work to
endeavor to lift, and the tool edge be above the centre of the work, it
would be cut to smaller diameter. If the tool cutting edge were below
the centre, or if its top face be at an angle tending to force the work
away from the tool point, the diameter of the work would be increased.
From these considerations it is obvious that the finishing cut should be
started at the centre of the work length, and carried towards the lathe
centres, because in this case the tool will be sharpest, and therefore
will produce less tensional strain on the work at the point where the
latter is the weakest, while the resisting strength of the work would
increase as the cut proceeded, and the tool became dull from use.
Furthermore, if it were necessary to regrind the tool, it would be reset
nearer to the lathe centres, where the work would be more rigidly held;
hence the tool could be more accurately set to the diameter of the
finishing cut.
By following this plan, however, it becomes necessary to have the shaft
as near true and parallel as possible before taking the finishing cut,
for the following reasons:--
Let the diameter of the spindle before the finishing cut be 1-1/32
inches, leaving 1/32 inch to be taken off at the finishing cut, then the
ring in the follower rest must be at starting that cut 1-1/32 inch bore,
and if the rest is to follow the cut the bush must be changed (so soon
as it meets the finishing cut) to one of an inch bore. But if the
spindle be turned as true and parallel as possible before the finishing
cut the rest may lead the tool, in which case the bush need not be
changed. There are differences of opinion as to the desirability of
either changing the bush or letting the tool follow the rest, but there
can be no dispute that (from the considerations already given) a spindle
turned as true and parallel as may be with the tool started from the
dead centre and carried forward can be improved by carrying yet another
cut from the middle towards the dead centre. In any event, however, work
liable to spring or too long to be finished at one cut without removing
the tool to grind it, can be more accurately finished by grinding in a
lathe, such as was shown in Figs. 676 or 679, than by steel-cutting
tools, and for the following reasons:--
[Illustration: Fig. 1210.]
If it be attempted with steel tools to take a very fine cut, as, say,
one of sufficient depth to reduce a diameter, say 1/500 inch, the tool
is apt to turn an uneven surface. There appears, indeed, to be a
necessity to have the cut produce sufficient strain to bring the bearing
surfaces of the rest into close contact and to place a slight strain on
the tool, because under very light cuts, such as named above, the tool
will generally momentarily leave the cut or take a reduced cut, and
subsequently an increased one.
It may be accepted that from these causes a finishing cut taken with a
steel tool should not be less than that sufficient to reduce the
diameter of the work 1/64 inch. Now an emery-wheel will take a cut whose
fineness is simply limited by the wear of the wheel in the length of the
cut. Some experiments made by Messrs. J. Morton Poole and Sons, of
Wilmington, Delaware, upon this subject led to the conclusion that with
corundum wheels of the best quality the cut could be made so fine that a
12-inch wheel used upon a piece of work (a calender roll) 16 inches in
diameter and 6 feet long, would require about forty thousand traverses
to reduce the diameter of the work an inch, leading to the conclusion
that the wear of the wheel diameter was less than one eighty-thousandth
part of an inch per traverse.
Now the strain placed upon the work of an emery-wheel taking a cut of,
say, 1/1000 inch, is infinitely less than that caused by a cutting tool
taking a cut of 1/120 inch in diameter; hence the accuracy of grinding
consists as much in the small amount of strain and, therefore, of
deflection it places upon the work, as upon the endurance of the wheel
itself.
Since both in finishing and in polishing a piece of work the object is
to obtain as true and smooth a surface as possible, the processes are to
a certain extent similar, but there is this difference between the two:
where polishing alone is to be done, the truth of the work or refined
truth in its cylindrical form or parallelism may be made subservient to
the convenience of polish. Thus, in the case of the stem of the
connecting rod that has been turned and filed and finished as true as
possible, the polishing processes may be continued with emery-cloth,
&c., producing the finest of polish without impairing the quality of the
work, whereas the degree of error in straightness or parallelism induced
by the polishing may impair the degree of truth desirable for a piston
rod.
The degree of finish or polish for any piece of work is, therefore,
governed to some extent by the nature of its use. Thus a piston rod may
be finished and polished to the maximum degree consistent with
maintaining its parallelism and truth, while a connecting rod stem may
be polished to any required attainable degree.
In finishing for truth, as in the case of journal bearings, the work,
being turned as true and smooth as possible, may be filed with the
finest of cut files, and polished with a fine grade of emery-cloth or
paper; the amount of metal removed by filing and polishing being so
small as not to impair to any practically important degree the truth of
the work: a journal so finished will be as true as it is possible to
make it without the use of a grinding lathe.
Instead of using emery-paper, grain emery and oil may be used, but the
work will not be so true, because in this case much more metal will be
removed from the work in the finishing or polishing process.
When it is required to polish and to keep the work as true and parallel
as possible, these ends may be simultaneously obtained by means of
clamps, such as shown in Fig. 1210, which represents a form of grinding
and polishing clamp used by the Pratt and Whitney Company for grinding
their standard cylindrical gauges. A cast-iron cylindrical body A is
split partly through at B and entirely through at C, being closed by the
screw D to take up the wear. The split B not only weakens the body A and
enables its easy closure, but it affords ingress to the grinding
material. It may be noted that cast iron is the best metal that can be
used for this purpose, not only on account of the dead smooth surface it
will take, but also because its porosity enables it to carry the oil
better than a closer grained metal. For work of larger diameter, as,
say, 2 or 3 inches, the form of lap shown in Fig. 1211 is used for
external grinding, there being a hinge B C instead of a split, and
handles are added to permit the holding and moving of the lap. The bore
of this clamp is sometimes recessed and filled with lead. It is then
reamed out to fit the work and used with emery and oil, the lathe
running at about 300 feet per minute.
[Illustration: Fig. 1211.]
For grinding and polishing the bores of pieces, many different forms of
expanding grinding mandrels have been devised, in most of which the
mandrel has been given a slight degree of curvature in its length; or in
other words, the diameter is slightly increased as the middle of the
mandrel length is approached from either end. But with this curvature of
outline, as small as it may be, it rather increases the difficulty of
grinding a bore parallel instead of diminishing it. When expanding
mandrels are caused to expand by a wedge acting upon split sections of
the mandrel, they rarely expand evenly and do not maintain a true
cylindrical form.
Fig. 1212 represents a superior form of expanding mandrel for this
purpose. The length A is taper and contains a flute C. The lead is cast
on and turned upon the mandrel, the metal in the flute C driving the
lead. The diameter of the lap is increased by driving the taper mandrel
through it, and the lead is therefore maintained cylindrically true.
While these appliances are supplied with the flour emery and oil, their
action is to grind rather than to polish, but as they are used without
the addition of emery, the action becomes more a polishing one.
[Illustration: Fig. 1212.]
Fig. 1213 represents at A A a wooden clamp for rough polishing with
emery and oil. It consists of two arms hinged by leather at B and having
circular recesses, as C, D, to receive the work. At J J is represented a
similar grinding and polishing clamp for more accurate work. G and H are
screws passing through the top arm and threaded into the lower, while E,
F are threaded into the lower arm, and abut at their ends against the
face of the upper arm. It is obvious that by means of these screws the
clamp may be set to size, adjusted to give the required degree of
pressure, and held firmly together. Lead bushes may be inserted in the
bores as grinding laps. As this clamp is used by hand, it must be moved
along the work at an exactly even speed of traverse, or else it will
operate on the work for a longer period of time at some parts than at
others; hence the greatest care is necessary in its use.
The best method of polishing cylindrical work to be operated on entirely
in the lathe, the primary object being the polish, is by means of emery
paper, and as follows:--
In all polishing the lathe should run at a fast speed; hence special
high speeded lathes, termed speed lathes, are provided for polishing
purposes only.
The emery paper or cloth should be of a fine grade, which is all that is
necessary if the work has been properly filed, if cylindrical, and
scraped if radial or of curved outline.
In determining whether emery paper or cloth should be used, the
following is pertinent:--
The same grade of emery cuts more freely on cloth than on paper, because
the surface of the cloth is more uneven; hence the emery grains project
in places, causing them to cut more freely until worn down. If, then,
the surface is narrow, so that there is no opportunity to move the emery
cloth endways on the work, emery paper should be used. It should be
wrapped closely (with not more than one, or at least two folds) around a
_smooth_ file, and not a coarse one, whose teeth would press the emery
to the work at the points of its coarse teeth only. The file should be
given short, rapid, light strokes.
For work of curved outline emery cloth should be used, because it will
bend without cracking, and the cloth should be moved quickly backwards
and forwards across, and not round, the curve; and when the work is long
enough to permit it, the emery paper or cloth should be moved rapidly
backwards and forwards along the work so that its marks cross and
recross at an obtuse angle.
Now, suppose the grade of emery paper first used to be flour emery, and
the final polish is to be of the highest order, then 0000 French emery
paper will be required to finish, and it is to be observed that nothing
will polish a metal so exquisitely as an impalpable powder of the metal
itself: hence, while performing the earlier stages of polishing, it is
well to prepare the final finishing piece, so as to give it a glaze of
metal from the work surface.
When, therefore, all the file marks are removed by the use of the flour
emery cloth, the surface of the work should be slightly oiled and then
wiped, so as not to appear oily and yet not quite dry, with a piece of
rag or waste, then the piece of 0000 emery paper, or, what is equally as
good, a piece of crocus cloth, to be used for the final finishing should
be applied to the work, and the slightly oily surface will cause the
cuttings to clog and fill the crocus cloth. The cloth should be
frequently changed in position so as to bring all parts of its surface
in contact with the work and wear down all projections on the cloth as
well as filling it with fine cuttings from the work. Then a finer grade,
as, say, No. 0 French emery paper, must be used, moving it rapidly
endwise of the work, as before, and using it until all the marks left by
the flour emery have been removed.
One, or at most two drops of lard oil should then be put on the work,
and spread over as far as it will extend with the palm of the hand, when
the finishing crocus may again be applied and reversed as before in
every direction; 00 emery paper may then be used until all the marks of
the 0 are removed, and with the work left quite dry the crocus for final
finishing may again be applied; 000 emery paper may then be used to
efface all the marks left by the 00. This 000 emery paper should be used
until it is very much worn, the final finish being laid with the glazed
crocus.
If this crocus has been properly prepared, its whole surface will be
covered with a film of fine particles of metal, so that if the metal be
brass the crocus surface will appear like gold leaf. If cast iron, the
crocus surface will appear as though polished with plumbago or
blacklead, while in any case the crocus surface will be polished and
quite dry. The crocus should be pressed lightly to the work, so that its
polishing marks will not be visible to the naked eye.
If emery paper be applied to work finished to exact diameter it should
be borne in mind that the process reduces to some extent the size of the
work, and that the amount under proper conditions though small is yet of
importance, where preciseness of diameter is a requisite.
In the practice, however, of some of the best machine shops of the
United States, the lathe alone is not relied upon to produce the best of
polish. Thus, in the engine works of Charles H. Brown, of Fitchburg,
Massachusetts, whose engines are unsurpassed for finish and polish, and
which the majority of mechanics would suppose were finely silver plated,
the following is the process adopted for polishing connecting rods.
[Illustration: Fig. 1213.]
The rod is carefully tool-finished with a fine feed. The tool marks are
then erased with a fine smooth file, and these file marks by a
dead-smooth file, the work rotating at a quick speed, little metal being
left, so as to file as little as possible. Next comes _fine_ emery cloth
to smooth down and remove the file marks. The lathe is then stopped and
the rod stoned lengthwise with Hindostan stone and benzine, removing all
streaks. The Scotch stone used with water follows, until the surface is
without scratches or marks, as near perfect as possible. The next
process is, for the finest work, the burnisher used by hand. But if not
quite so exquisite a polish is required, the rod is finished by the use
of three grades of emery cloth, the last being very fine.
Sometimes, however, the streaks made by polishing with emery paper used
before the application of the stones are too difficult to remove by
them. In this case, for a very fine finish, the lathe is stopped and
draw-filing with the finest of files is performed, removing all streaks;
and the stones then follow the draw-filing. All stoning is done by hand
with the work at rest, as is also all burnishing.
After the burnisher comes fine imported crocus cloth, well worn, which
makes the surface more even and dead than that left by the burnisher.
The crocus is used with the lathe at its quickest speed, and is moved as
slowly and as evenly as possible, the slower and more even the crocus
movement along the rod, the more even the finish. If the rod has
filleted corners, such corners are in all cases draw-filed before the
stoning.
The method of polishing a cylinder cover at the Brown Engine Works is as
follows.
[Illustration: Fig. 1214.]
The finishing cut is taken with a feed of 32 lathe-revolutions per inch
of tool traverse, and at as quick a cutting speed as the hardness of the
iron will permit. This is necessary in order to have the tool-edge cut
the metal without breaking it out as a coarse one would do. With the
fine feed and quick speed the pores of the iron do not show; with a
coarse feed the pores show very plainly and are exposed for quite a
depth.
After the lathe-tool comes a well oil-stoned hand-scraper, with a piece
of leather between it and the tool rest to prevent the scraper from
chattering. The scraper not only smooths the surface, but it cuts
without opening the pores. It is used at a quick speed, as quick indeed
as it will stand, which varies with the hardness of the metal, but is
always greater than is possible with a slide-rest tool.
After the scraper the cover is removed from the lathe, and all flat
surfaces are filed as level as possible with a second-cut file, and then
stoned with soft Hindostan stone, used with benzine or turpentine, so as
to wash away the cuttings and prevent them from clogging the stone or
forming scratches. In using all stones the direction of motion is
frequently reversed so as to level the surface. Next comes stoning with
Scotch stone (Water of Ayr), used with water; in this part of the
operation great care must be taken, otherwise the cuttings will induce
scratches. When the Scotch stone marks have removed all those left by
the Hindostan stone, and left the surface as smooth as possible, the
cover is again put in the lathe and the grain is laid and finished with
very fine emery cloth and oil. The emery cloth is pressed lightly to the
work and allowed to become well worn so as to obtain a fine lustre
without leaving any streaks.
[Illustration: Fig. 1215.]
It will be noticed here that the use of the emery stick and oil is
entirely dispensed with; but for a less fine polish it may be used,
providing it be kept in quick motion radially on the work. The objection
to its use is that if there be any speck on the work it is apt to cut a
streak or groove following the spot like a comet's tail.
TURNING TAPERS.--There are five methods of turning outside tapers; 1st,
by setting over the tailstock of the lathe; 2nd, by the use of a former
or taper turning attachment such as was shown in Fig. 508; 3rd, by the
use of a compound slide rest; 4th, by means of a lathe in which the head
and tailstock are upon a bed that can be set at an angle to the lathe
shears on which the lathe carriage slides; and 5th, by causing the
cross-feed screw to operate simultaneously with the feed traverse.
Referring to the first method, it is objectionable, inasmuch as that the
work axis is thrown at an angle to the axis of the lathe centres, which
causes the work centres to wear rapidly, and this often induces them to
move their positions and throw the work out of true. Furthermore, the
tailstock has to be moved back in line with the live spindle axis for
turning parallel again, and this is a troublesome matter, especially
when the work is long.
Fig. 1214 shows the manner in which the lathe centres and the work
centres have contact, L being the live and B the dead centre; hence C C
is the axis of the live spindle which is parallel to the lathe shear
slides, which are represented by G; obviously A is the work axis. The
wear is greatest at the dead centre end of the work, but there is some
wear at the live centre end, because there is at that end also a certain
amount of motion of the work centre upon the live centre. Thus, in Fig.
1215, let _c_ represent the live centre axis, _a_ the work axis, D the
lathe face plate, and E F the plane of the driver or dog upon the work,
and it is obvious that the tail of the driver will when at one part of
the lathe revolution stand at E, while when diametrically opposite it
will stand at F; hence, during each work revolution the driver moves,
first towards and then away from the face plate D, and care must be
taken in adjusting the position of the driver to see that it has liberty
to move in this direction, for if obstructed in its motion it will
spring or bend the work.
[Illustration: Fig. 1216.]
To determine how much the tailstock of a lathe must be set over to turn
a given taper, the construction shown in Fig. 1216 may be employed. Draw
the outline of the work and mark its axis D, draw line C parallel to one
side of the taper end, and the distance A between this line and the work
axis is the amount the tailstock requires to be set over. This
construction is proved in Fig. 1217, in which the piece of work is shown
set over, C representing the line of the lathe ways, with which the side
F of the taper must be parallel. D is the line of the live spindle, and
E that of the work, and the distance B will be found the same as
distance A in Fig. 1216.
It may be remarked, however, that in setting the tailstock over it is
the point of the dead centre when set adjusted to the work length that
must be measured, and not the tailblock itself.
[Illustration: Fig. 1217.]
Other methods of setting tailstocks for taper turning are as follows: If
a new piece is to be made from an old one, or a duplicate of a piece of
work is to be turned, the one already turned, or the old piece as the
case may be, may be put in the lathe and we may put a tool in the tool
post and set the tailstock over until the tool traversed along the work
(the latter remaining stationary) will touch the taper surface from end
to end.
If, however, the taper is given as so much per foot, the distance to set
the tailstock over can be readily calculated.
Thus, suppose a piece of work has a taper part, having a taper of an
inch per foot, the work being three feet long, then there would be three
inches of taper in the whole length of the piece and the tailstock
requires to be set over one-half of the three inches, or 1-1/2 inches.
It will not matter how long the taper part of the work is, nor in what
part of the work it is, the rule will be found correct so long as the
tailstock is set over one-half the amount obtained by multiplying the
full length of the work per foot by the amount of taper per foot.
If we have no pattern we may turn at each end of the part that is to be
taper a short parallel place, truing it up and leaving it larger to the
same amount at each end than the finished size, and taking care that the
parallel part at the small end will all turn out in the finishing. We
then fasten a tool in the lathe tool post, place it so that it will
clear the metal of the part requiring to be turned taper, and placing it
at one extreme end of said part, we take a wedge, or a piece of metal
sufficiently thick, and place it to just contact with the turned part of
the work and the tool point (adjusting the tool with the cross-feed
screw), we then wind the rest to the other end of the required taper
part, and inserting same wedge or piece of iron, gauge the distance from
the tool point to the work, it being obvious that when the tool point
wound along is found to stand at an equal distance from each end of the
turned part, the lathe is set to the requisite taper.
[Illustration: Fig. 1218.]
Figs. 1218 and 1219 illustrate this method of setting. A represents a
piece of work requiring to be turned taper from B to C, and turned down
to within 1/32 inch of the required size at E and F. If then we place
the tool point H first at one end and then at the other, and insert the
piece I and adjust the lathe so that the piece of metal I will just fit
between the tool point and the work at each extreme end of the required
taper part, the lathe will be set to the requisite taper as near as
practicable without trying the work to the taper hole. The parallel part
at the small end of the work should be turned as true as possible, or
the marks may not be obliterated in finishing the work.
Fig. 1220 (from _The American Machinist_) represents a gauge for setting
the tailstock over for a taper. A groove is cut as at E and D, these
diameters corresponding to the required taper; a holder A is then put in
the tool point, and to this holder is pivoted the gauge B. The tailstock
is set over until the point of B will just touch the bottom of the
groove at each end of the work.
[Illustration: Fig. 1219.]
To try a taper into its place, we either make a chalked stripe along it
from end to end, smoothing the chalked surface with the finger, or else
apply red marking to it, and then while pressing it firmly into its
place, revolve it backwards and forwards, holding it the while firmly to
its seat in the hole; we move the longest outwardly projecting end up
and down and sideways, carefully noting at which end of the taper there
is the most movement. The amount of such movement will denote how far
the taper is from fitting the hole, while the end having the least
movement will require to have the most taken off it, because the fulcrum
off which the movement takes place is the highest part, and hence
requires the greatest amount of metal to be taken off.
Having fitted a taper as nearly as possible with the lathe tool, that is
to say, so nearly that we cannot find any movement or unequal movement
at the ends of the taper (for there is sure to be movement if the tapers
do not agree, or if the surfaces do not touch at more than one part of
their lengths), we must finish it with a fine smooth file as follows:
After marking the inside of the hole with a very light coat of red
marking, taking care that there is no dirt or grit in it, we press the
taper into the hole firmly, forcing it to its seat while revolving it
backwards and forwards.
By advancing it gradually on the forward stroke, the movement will be a
reciprocating and yet a revolving one. The work must then be run in the
lathe at a high speed, and a smooth file used to ease off the mark
visible on the taper, applying the file the most to parts or marks
having the darkest appearance, since the darker the marks the harder the
bearing has been. Too much care in trying the taper to its hole cannot
be taken, because it is apt to mark itself in the hole as though it were
a correct fit when at the same time it is not; it is necessary therefore
at each insertion to minutely examine the fit by the lateral and
vertical movement of projecting part of the taper, as before directed.
A taper or cone should be fitted to great exactitude before it is
attempted to grind it, the latter process being merely intended to make
the surfaces even.
For wrought-iron, cast-iron, or steel work, oil and emery may be used as
the grinding materials (for brass, burnt sand and water are the best).
The oil and emery should be spread evenly with the finger over the
surfaces of the hole and the taper; the latter should then be placed
carefully in its place and pressed firmly to its seat while it is being
revolved backwards and forwards, and slowly rotated forward by moving it
farther during the forward than during the backward movement of the
reciprocating motion.
After about every dozen strokes the taper should be carefully removed
from the hole and the emery again spread evenly over the surfaces with
the finger, and at and during about every fourth one of the back strokes
of the reciprocating movement the taper should be slightly lifted from
its bed in the hole, being pressed lightly home again on the return
stroke, which procedure acts to spread the grinding material and to make
the grinding smooth and even. The emery used should be about number 60
to 70 for large work, about 80 to 100 for small, and flour emery for
very fine work.
Any attempt to grind work by revolving it steady in one direction will
cause it to cut rings and destroy the surface.
[Illustration: Fig. 1220.]
Referring to the second method, all that is necessary in setting a
former or taper attachment bar is to set it out of line with the lathe
shears to half the amount of taper that is to be turned, the bar being
measured along a length equal to that of the work. Turning tapers with a
bar or taper-turning attachment possesses the advantage that the
tailstock not being set over, the work centres are not thrown out of
line with the live centres, and the latter are not subject to the wear
explained with reference to Fig. 1214. Furthermore, the tailstock being
kept set to turn parallel, the operator may readily change from turning
taper to turning parallel, and may, therefore, rough out all parts
before finishing any of them, and thus keep the work more true, whereas
in turning tapers by setting the tailstock over we are confronted by the
following considerations:--
If we turn up and finish the plain part first, the removing of the skin
and the wear of the centres during the operation of turning the taper
part will cause the work to run out of true, and hence it will not, when
finished, be true; or if, on the other hand, we turn up the taper part
first, the same effects will be experienced in afterwards turning the
plain part. We may, it is true, first rough out the plain part, then
rough out the taper part, and finish first the one and then the other;
to do this, however, we shall require to set the lathe twice for the
taper and once for the parallel part.
It is found in practice that the work will be more true by turning the
taper part the last, because the work will alter less upon the lathe
centres when changed from parallel to taper turning than when changed
from the latter to the former. In cases, however, in which the parts
fitting the taper part require turning, it is better to finish the
parallel part last, and to then turn up the work fastened upon the
taper part while it is fast upon its place: thus, in the case of a
piston rod and piston, were we to turn up the parallel part of the rod
first and the taper last, and the centres altered during the last
operation, when the piston head was placed upon the rod, and the latter
was placed in the lathe, the plain part or stem would not run true, and
we should require to true the centres to make the rod run true before
turning up the piston head. If, however, we first rough out the plain
part or stem of the rod, and then rough out and finish the taper part,
we may then fasten the head to its place on the rod, and turn the two
together; that is to say, rough out the piston head and finish its taper
hole; then rough out the parallel part of the rod, but finish its taper
end. The rod may then be put together and finished at one operation;
thus the head will be true with the rod whether the taper is true with
the parallel part of the rod or not. With a taper-turning attachment the
rod may be finished separately, which is a great advantage.
[Illustration: Fig. 1221.]
If, however, one part of the length of a taper turning attachment is
much more used than another, it is apt to wear more, which impairs the
use of the bar for longer work, as it affects its straightness and
causes the slide to be loose in the part most used, and on account of
the wear of the sliding block it is proper to wind the tool out from its
cut on the back traverse, or otherwise the tool may cut deeper on the
back than on the forward traverse, and thus leave a mark on the work
surface.
[Illustration: Fig. 1222.]
Referring to the third method, a compound slide rest provides an
excellent method of turning tapers whose lengths are within the capacity
of the upper slide of the compound rest, because that slide may be used
to turn the taper, while the ordinary carriage feed may be used for the
parallel parts of the work, and as the tailstock does not require to set
over, the work centres are not subject to undue wear.
If the seat for the upper slide of the rest is circular, and the taper
is given in degrees of angle, a mark may be made on the seat, and the
base of the upper slide may be marked in degrees of a circle, as shown
in Fig. 1221, which will facilitate the setting; or the following
construction, which is extracted from _Mechanics_, may be employed.
Measure the diameter of the slide rest seat, and scribe on a flat
surface a circle of corresponding diameter. Mark its centre, as A in
Fig. 1222, and mark the line A B. From the centre A mark the point B,
whose radius is that of the small end of the hole to be bored. Mark the
length of the taper to be turned on the line A G and draw the line G D
distant from A B equal to the diameter of the large end of the hole to
be bored. Draw the line B D. Then the distance E F is the amount the
rest must be swiveled to turn the required taper.
It is obvious that the same method may also be used for setting the
rest.
[Illustration: Fig. 1223.--Top View.]
Referring to the fourth method, by having an upper bed or base plate for
the head and tailstock, so that the line of lathe centres may be set at
the required angle to the [V]s or slides on which the carriage
traverses, it affords an excellent means of turning tapers, since it
avoids the disadvantages mentioned with regard to other systems, while
at the same time it enables the turning of tapers of the full length of
the carriage traverse, but it is obvious that the head and tailstock are
less rigidly supported than when they are bolted direct to the lathe
shears.
[Illustration: Fig. 1224.--End View.]
In turning tapers it is essential that the tool point be set to the
exact height of the work axis, or, in other words, level with the line
of centres. If this is not the case the taper will have a curved outline
along its length. Furthermore, it may be shown that if a straight taper
be turned and the tool be afterwards either raised or lowered, the
amount of taper will be diminished as well as the length being turned to
a curve.
Figs. 1223 and 1224 demonstrate that the amount of taper will be changed
by any alteration in the height of the tool. In Fig. 1223, A B
represents the line of centres of the spindle of a lathe, or, in other
words, the axis of the work W, when the lathe is set to turn parallel; A
C represents the axis of the work or cone when the lathe tailstock is
set over to turn the taper or cone; hence the length of the line C B
represents the amount the tailstock is set over. Referring now to Fig.
1224, the cone is supposed to stand level, as it will do in the end
view, because the lathe centres remain at an equal height from the lathe
bed or [V]s, notwithstanding that the tailstock is set over. The tool
therefore travels at the same height throughout its whole length of
feed; hence, if it is set, as at T, level with the line of centres, its
line of feed while travelling from end to end of the cone is shone by
the line A B. The length of the line A B is equal to the length of the
line B C Fig. 1223. Hence, the line A B, Fig. 1224, represents two
things: first, the line of motion of the point of tool T as it feeds
along the cone, and second its length represents the amount the work
axis is out of parallel with the line of lathe centres. Now, suppose
that the tool be lowered to the position shown at I; its line of motion
as it feeds will be the line C D, which is equal in length to the line A
B. It is obvious, therefore, that though the tool is set to the diameter
of the small end, it will turn at the large end a diameter represented
by the dotted circle H. The result is precisely the same if the taper is
turned by a taper-turning attachment instead of setting the tailstock
out of line.
[Illustration: Side View. Fig. 1225. End View.]
The demonstration is more readily understood when made with reference to
such an attachment as the one just mentioned, because the line A B
represents the line of tool feed along the work, and its length
represents the amount the attachment causes the tool to recede from the
work axis. Now as this amount depends upon the set-over of the
attachment it will be governed by the degree of that set over, and is,
therefore, with any given degree, the same whatever the length of the
tool travel may be. All that is required, then, to find the result of
placing the tool in any particular position, as at I in the end view, is
to draw from the tool point a line parallel to A B and equal in length
to it, as C D. The two ends of that line will represent in their
distances from the work axis the radius the work will be turned to at
each end with the tool in that position. Thus, at one end of the line C
D is the circle K, representing the diameter the tool I would turn the
cone at the small end, while at the other end the dotted circle H gives
the diameter at the large end that the tool would turn to when at the
end of its traverse. But if the tool be placed as at T, it will turn the
same diameter K at the small end, and the diameter of the circle P at
the large end.
We have here taken account of the diameters at the ends only of the
work, without reference to the result given at any intermediate point
along the cone surface, but this we may now proceed to do, in order to
prove that a curved instead of a straight taper is produced if the tool
be placed either above or below the line of lathe centres.
In Fig. 1225, D E F C represents the complete outline of a straight
taper, whose diameter at the ends is represented in the end view by the
outer and inner circles. Now, a line from A to B will represent the axis
of the work, and also the line of tool point motion or traverse, if that
point is set level with the axis. The line I K in the end view
corresponds to the line A B in the side view, in so far that it
represents the line of tool traverse when the tool point is set level
with the line of centres. Now, suppose the tool point to be raised to
stand level with the line G H, instead of at I K, and its line of feed
traverse be along the line G H, whose length is equal to that of I K. If
we divide the length of G H into six equal divisions, as marked from 1
to 6, and also divide the length of the work in the side view into six
equal divisions (_a_ to _f_), we shall have the length of line G H in
the first division in the end view (that is, the length from H to G),
representing the same amount or length of tool traverse as from the end
B of the cone to the line A in the side view. Now, suppose the tool
point has arrived at 1; the diameter of work it will turn when in that
position is evidently given by the arc or half-circle _h_, which meets
the point 1 on G H. To mark that diameter on the side view, we first
draw a horizontal line, as _h_ _p_, just touching the top of _h_; a
perpendicular dropped from it cutting the line A B, gives the radius of
work transferred from the end view to the side view. When the tool point
has arrived at 2 on G H in the end view, its position will be shown in
the side view at the line _b_, and the diameter of work it will turn is
shown in the end view by the half-circle _k_. To transfer this diameter
to the side view we draw the line _k_ _g_, and where it cuts the line
_b_ in the side view is the radius of the work diameter when the tool
has arrived at the point _b_ in the side view. Continuing this process,
we mark half-circles, as _l_, _m_, _n_, _o_, and the lines _l_ _r_, _m_
_s_, _n_ _t_, _o_ _u_, by means of which we find in the side view the
work radius when the tool has arrived at _c_, _d_, _e_, and _f_
respectively. All that remains to be done is to draw on the side view a
line, as _u_ E, that shall pass through the points. This line will
represent the outline of the work turned by the tool when its height is
that denoted by G H. Now, the line _u_ E is shown to be a curve, hence
it is proved that with the tool at the height G H a curved, and not a
straight, taper will be turned.
It may now be proved that if the tool point is placed level with the
line of centres, a straight taper will be turned. Thus its line of
traverse will be denoted by A B in the side view and the line I K in the
end view; hence we may divide I K into six equal divisions, and A B into
six equal divisions (as _a_, _b_, _c_, &c.). From the points of division
I K, we may draw half-circles as before, and from these half-circles
horizontal lines, and where the lines meet the lines of division in the
side view will be points in the outline of the work, as before. Through
these points we draw a line, as before, and this line C F, being
straight, it is proven that with the tool point level with the work
axis, it will turn a straight taper.
[Illustration: Top View. Fig. 1226. End View.]
It may now be shown that it is possible to turn a piece of work to a
curve of equal curvature on each side of the middle of the work length.
Suppose, for example, that the cutting tool stands on top of the work,
as in the end view in Fig. 1226, and that while the tool is feeding
along the work it also has a certain amount of motion in a direction at
right angles to the work axis, so that its line of motion is denoted by
the line B B in the top view. The outline of the work turned will be a
curve, as is shown in Fig. 1227, in which the line of tool traverse is
the line C D. Now the amount of tool motion that occurs during this
traverse in a direction at right angles to the work axis is represented
by the line F E, because the upper end is opposite to the upper end of C
D, while the lower end is opposite the lower end of C D. We may then
divide one-half of the length of F E into the divisions marked from 1 to
6. Now, as we have taken half the length of F E, we must also take half
the length of the work and divide it into six equal divisions marked
from _a_ to _f_. Now, suppose the tool point to stand in the line F S in
the end view, its position in the top view will be at C. When it is at 1
on the end view it will have arrived at _p_ in the top view. The radius
of work it will then turn is shown in the end view by the length of line
running from 1 to the work centre. Take this length, and from _a_ in the
work axis set it off on the line _a_ _h_, and make the length equal the
height of 1 S. In like manner, when the tool point has arrived at 2, the
radius it will cut the work is shown by the length of line _i_; hence
from 2 on the work axis we may set off the length of 2 S, making 2 S and
_b_ _i_ of equal length. Continuing this process, we make the length of
_c_ _k_ equal that of 3 S, the length of _d_ _l_ equal 4 S, and so on.
All that remains then is to draw a line, _o_ _g_, that shall meet the
tops of these lines. This line will show the curve to which that half of
the work length will be turned to. The other half of the work length
will obviously be turned to the same curvature.
[Illustration: Fig. 1227.]
[Illustration: Fig. 1228.]
It is obvious that the curvature of the work outline will be determined
by the proportion existing between the length of the work and the amount
of tool motion in a direction at right angles to the work axis, or, in
other words, between the length of the work and that of the line F E. It
is evident, also, that with a given amount of tool motion across the
work, the curvature of outline turned will be less in proportion as the
work length is greater. Now, suppose that the smaller and the larger
diameter of the work, together with its length, are given, and it is
required to find how much curvature the tool must have, we may find this
and work out the curve it will cut by the construction shown in Fig.
1228, in which the circle K is the smallest and the circle P the largest
diameter. The line _m_ C is drawn to just touch the perimeter of K, and
this at once gives the amount of cross-motion for the tool. Hence, we
may draw the line _m_ B and C B, and from their extremities draw the
line B B representing the path of traverse of the tool point. We may
then obtain the full curve on one side of the work by dividing one-half
the length of _m_ C into six equal divisions and proceeding as before,
except that we have here added the lines of division in the second half
as from _f_ to _l_. It will be observed that the centre of the curve is
at the point where the tool point crosses the axis of the work; hence,
by giving to the tool more traverse on one side than on the other of the
work axis, the location of the smallest point of work diameter may be
made to fall on one side of the middle of the work length.
In either turning or boring tapers that are to drive or force in or
together, the amount to be allowed for the fit may be ascertained, so
that the work may be made correct without driving each piece to its
place to try its fit.
Suppose, for example, that the pieces are turned, and the holes are to
be reamed, then the first hole reamed may be made to correct diameter by
fit and trial, and a collar may be put on the reamer to permit it to
enter the holes so far and no farther.
A taper gauge may then be made as in Fig. 1229, the line a representing
the bore of the hole, and line B the diameter of the internal piece, the
distance between the two being the amount found by trial to be necessary
for the forcing or driving. The same gauge obviously serves for testing
the taper of the holes reamed.
CHUCKED OR FACE PLATE WORK.--This class of work requires the most
skillful manipulation, because the order in which the work may most
advantageously proceed and the method of chucking are often matters for
mature consideration.
[Illustration: Fig. 1229.]
In a piece of work driven between the lathe centres, the truth of any
one part may be perceived at any time while operating upon the others,
but in chucked work, such is not always the case, and truth in the work
is then only to be obtained by holding it truly. Again, the work is apt
to be sprung or deflected by the pressure of the devices holding it, and
furthermore the removal of the skin or surface will in light work
sometimes throw it out of true as the work proceeds, the reason being
already given, when referring to turning plain cylindrical work.
TO TURN A GLAND.--There are three methods of turning a gland: first, the
hole and the face on the outside of the flange may be turned first, the
subsequent turning being done on a mandrel; second, the hole only may be
bored at the first chucking, all the remaining work being done on a
mandrel; and, third, the hole, hub, and one radial face may be turned at
one chucking, and the remaining face turned at a separate chucking.
If the first plan be adopted, any error in the truth of the mandrel will
throw the hole out of true with the hub, which would be a serious
defect, causing the gland to jamb against one side of the piston rod,
and also of the gland bore. The same evil is liable to result from the
second method; it is best, therefore, to chuck the gland by the hub in a
universal chuck, and simply face the outer face of the flange, and also
its edge. The gland may then be turned end for end, and the hole, the
hub, the inside radial flange face, and the hub radial face, may then
all be turned at one chucking; there is but one disadvantage in this
method, which is that the gland must be unchucked to try its fit in the
gland hole, but if standard gauges are used such trial will not be
necessary, while if such is not the case and an error of measurement
should occur, the gland may still be put on a mandrel and reduced if
necessary.
In either method of chucking, the fit of the hole to the rod it is
intended for cannot be tested without removing the gland from the chuck.
TO TURN A PLAIN CYLINDRICAL RING ALL OVER IN A UNIVERSAL CHUCK.--Three
methods may be pursued in doing this simple job: first, the hole may be
bored at one chucking, and the two radial faces and the circumference
turned at a second chucking; second, the diameter may be turned, first
on the hole and two radial faces turned at a second chucking; and third
the hole and one radial face may be turned at one chucking, and the
diameter and second radial face at a second chucking. The last method is
best for the following reasons. The tool can pass clear over the
surfaces at each chucking without danger of coming into contact with the
chuck jaws, which would cause damage to both; second, at the last
chucking, the chuck jaws being inside the ring, the latter may be tested
for truth with a pointer fixed in the tool rest, and therefore set quite
true.
It is obvious that at neither chucking should the ring be set so far
within the chuck jaws that there will be danger of the tool touching
them when turning the radial face.
In the case of a ring too thin to permit this, and of too large a bore
to warrant making a mandrel for it, the ring may be held on the outside
and bored, and both radial faces turned to within a short distance of
the chuck jaws; at the second chucking, the chuck jaws being within the
ring bore, the work may be set true with a pointer, as before, and
finished.
If, however, a number of such rings were to be turned, it would pay to
turn up another and thicker ring, and use it as a mandrel after the bore
and one radial face of the ring had been turned.
TO TURN AN ECCENTRIC STRAP AND ECCENTRIC.--The eccentric strap should be
turned first, because it can then be taken apart and its fit to the
eccentric tried while the latter is in the lathe, which is not the case
with the eccentric. The strap should first be held in a universal chuck
bolted to the face plate, or held in dogs such as shown in Fig. 893 at
C, and one face should be turned. It should then be turned round on the
chuck to bore it, and face the other side.
If the shape of the strap will admit it, it is best chucked by plates
and bolts holding the face first turned to the face plate, because in
this case there will be no pressure tending to spring the straps out of
their natural shape; otherwise, however, it may be held in a universal
or independent jaw chuck, or if too large for insertion in chucks of
this kind (which are rarely made for large lathes) it may be held in
dogs such as shown in Fig. 893 at C.
[Illustration: Fig. 1230.]
[Illustration: Fig. 1231.]
If after an eccentric strap is bored, and the bolts that hold its two
halves together have been slackened, its diameter at A and at C, Fig.
1230, be measured, it will be found that A is less than C. The cause of
this is partly explained under the head of tension of castings; but it
is necessary to add that the diameters at A and at C in the figure are
equal while the strap is in the lathe, or until the bolts holding the
two halves of the strap together are released, yet so soon as this is
done the diameter at A will reduce, the bore becoming an oval.[18]
[18] This occurs in all castings of similar form, as brasses, &c.
Now, it is obvious that the eccentric must be turned to the diameter at
C, or otherwise it will have lost motion in the strap. If, however, the
eccentric be turned to the diameter of C, the strap cannot be tried on,
as it will bind at the corners, as shown in Fig. 1231. To remedy this
evil it is usual to put a piece of sheet tin or metal between the joint
faces of the two halves of the eccentric straps before they are chucked
to turn them, and to bore them too large to the amount of the thickness
of sheet metal so employed. After the straps are bored these pieces of
metal are removed, and the strap halves bolted together as in Fig. 1230,
the diameter at C being that to which the eccentric must be turned.
If the sheet metal so inserted were thick enough, the strap bore will
measure the same at A as at C, Fig. 1230. If it were too thick the
diameter at A will be greatest, while if too thin the diameter at A will
be the least. There is no rule whereby the necessary thickness for a
given size of strap may be known, and the workman is usually governed by
his experience on castings of similar metal, or from the same moulding
shop.
He prefers, however, to be on the safe side by not putting in too great
a thickness, because it is easier to scrape away the bore at the joint
than it is to file away the joint faces. The following thicknesses for
the respective diameters may be considered safe for castings that have
not been reheated after casting.
Diameter Thickness of metal to
of place between the
bore. strap valves.
Inches. Inch.
6 1/64
12 1/32
18 3/64
24 1/8
In turning a new strap for an old eccentric, it will be necessary, when
taking the diameter of the eccentric, to take a piece of tin of the same
thickness as that placed between the eccentric lugs or jaws, and place
it between the caliper leg and the eccentric, so that the diameter of
the strap across C, Fig. 1230, may be made equal when the tin is removed
to the diameter of the eccentric.
In turning up the eccentric, the plain face should be faced first,
setting it true, or nearly so, with the circumference of the eccentric,
as will be the case if the circumference is held in a universal chuck,
but if the hub is so long that this cannot be done because the chuck
jaws cannot reach the circumference, the hub itself may be held in an
independent jaw chuck.
The face turned may then be turned round, so as to meet the face of the
chuck against which it should bed fairly, so as to run true. At this
chucking the hole bore, the hub, and the radial faces should be turned,
all these surfaces being roughed out before any one surface is finished.
The eccentric must then be again reversed, so that the face of the hub
meets, the face plate being held by bolts as shown for a crank in
figure, when the work being set to the lines marked (so as to give it
the correct amount of throw) may be turned to fit the bore of the strap,
the strap being taken apart so as to try it on, which this method of
chucking will readily permit.
Now, in an eccentric, the surfaces requiring to be most true one with
the other are those of the bore and of the circumference where the strap
fits, and since the latter was turned with the hub face to the chuck,
and that hub face was turned at the same chucking as the hole was bored
(and must, therefore, be true to the bore), the bore and circumference
will be as true as it is practicable to get them, because upon the truth
of the last chucking alone will the truth of the work depend.
Small eccentrics may be held for all their chuckings in jaw chucks, but
not so truly as if chucked on a face plate, because of the difficulty of
keeping the radial faces of such jaws true, which occurs by reason of
the causes explained with reference to Figs. 848 and 849.
Eccentrics having so much throw upon them as to render it difficult to
hold them for the last chucking by the method above given (by bolts
through the bore), usually have openings through them on the throw side,
and in this case parallel pieces may be placed behind the radial face
(on the hub side of the eccentric), such parallel pieces being thick
enough to keep the hub face clear of the chuck face, and bolts may be
passed through the said opening to hold the eccentric. Another method
would be as follows:--
The outside diameter of the eccentric may be gripped in a dog chuck, if
the dogs of the chuck project out far enough to reach it (otherwise the
dogs may grip the hub of the eccentric), while the hole is bored and the
plain face of the eccentric turned. The eccentric must then be reversed
in the lathe, and the hub and the radial face on that side must be
turned. Then the plain face of the eccentric must be bolted to the face
plate by plates placed across the spaces which are made to lighten the
eccentric, and by a plate across the face of the hub. The eccentric,
being set true to the lines, may then be turned on its outside diameter
to fit the strap; to facilitate which fitting, thin parallel strips may
be placed between the face plate and the plain face of the eccentric at
this last chucking. It will be observed that, in either method of
chucking, the outside diameter of the eccentric (that is to say, the
part on which the strap fits) is turned with the face which was turned
at the same chucking at which the hole was bored, clamped to the face
plate. In cases where a number of eccentrics having the same size of
bore and the same amount of throw are turned, there may be fitted to the
face plate of the lathe a disk (such as shown in Fig. 888), of
sufficient diameter to fit the hole of the eccentric, the said disk
being fastened to the face plate at the required distance from the
centre of the lathe to give the necessary amount of throw to the
eccentric. The best method of fastening such a disk to the face plate is
to provide it with a plain pin turned true with the disk, and let it fit
a hole (bored in the face plate to receive it) sufficiently tightly to
be just able to be taken in and out by the hand, the pin being provided
with a screw at the end, so that it can be screwed tight by a nut to the
face plate. The last chucking of the eccentric is then performed by
placing the hole of the eccentric on the disk, which will insure the
correctness of the throw without the aid of any lines on the eccentric
which may be set as true as the diameter of the casting will permit, and
then turned to fit the strap.
TO TURN A CYLINDER COVER.--A cylinder cover affords an example of
chucking in which the work done at one chucking requires to be very true
with that done at a subsequent chucking, thus the gland hole which is on
one side requires to be quite true with the diameter that fits into the
cylinder bore, this diameter being on the opposite side.
If the polished or gland side of the cover be turned first, the hole for
the packing ring and that for the gland may be bored with the assurance
that one will be true with the other, while the polished outside face
may be turned at the same chucking.
But when the cover is turned round in the lathe to turn the straight
face, though the hole may be set true as far as can be ascertained in
its short length, yet that length is too short to be an accurate guide,
and the hole for the packing ring may appear true, while that for the
gland, being longer, will have any error in the setting, multiplied by
reason of its greater length. It is better, therefore, to turn the plain
face first, gripping the cover by the gland flange so that the plain
radial face, the step that fits the cylinder bore, and the outer edge of
the cover flange may be turned at one chucking; then when the cover is
turned round in the chuck, the flat face may be set true by resting
against the radial surface of the chuck jaws, and the concentric truth
may be set by the outer edge of the flange, which, being of the extreme
diameter of the cover, will most readily show any want of truth in the
setting. If in this case a universal chuck be used, and the work does
not run quite true, it may be corrected by slacking the necessary dog or
jaw on one side, and tightening up again from the screw of the necessary
jaw on the other.
This occurs because from the wear, &c., there is always some small
amount of play or lost motion in the jaw screws, and in the mechanism
operating them, and by the above means this is taken advantage of to
true the work.
If from any cause the work cannot be held for the first chucking by
means of the gland hole flange, it must be held by the circumferential
edge of the cover, letting the jaws envelop as small a distance over
that edge as possible, the protruding part of it may then be turned up
as close to the chuck jaws as possible, and this turned part may still
be used to set the cover concentrically true at the second chucking.
In a very small cover the gland hole may have a mandrel fitted to it and
be turned therefrom on both radial faces, or on one face only, the other
being turned at the chucking at which the holes were bored.
In a cover too large to be held in a jaw chuck, the cover may be held in
chucking dogs such as shown at C in Fig. 893, the edge protruding as
much as possible from the dog screws, and being turned half way across
at one chucking, and finished at the second chucking. To set the radial
face at the second chucking, the surface gauge, applied as shown in Fig.
894, may be employed. If the bore of the packing ring or piston rod hole
is large enough to permit it, that hole and the gland hole may be bored
at the same chucking as that at which the plain face and step that fits
in the cylinder bore is turned, thus ensuring truth in all the essential
parts of the cover.
But in this case these operations should be performed at the last of the
two chuckings, so as to eliminate any error that might arise from the
casting altering its shape by reason of the removal of the metal on the
radial face of the gland hole side of the cover.
TO TURN A PULLEY.--A pulley affords an excellent example of lathe work,
because it may be operated upon by several different methods: thus, for
boring it may be held, if small, in a dog chuck, with the jaws inside
the rim; in a dog chuck with the jaws outside the rim; in a dog chuck by
the hub itself (if the hub is long enough). A larger pulley may be
chucked for boring by the rim held in a jaw chuck; by the rim held by
bolts and plates, or by the rim held by dogs, such as shown in Fig. 893,
or by the arms rested on pieces placed between them and the chuck, and
then bolts and plates applied to those arms.
The rim may be turned by placing the pulley on a mandrel and driving
that mandrel by a dog or carrier; by placing it on a mandrel and driving
it by a Clements driver such as shown in Fig. 753, and having two
diametrically opposite driving pins, placed to bear against
diametrically opposite arms; by holding the arms to the chuck as before
described, and performing the boring and facing at one chucking; or by
holding the rim on its inside by the chuck jaws, so as to turn and bore
the pulley at one chucking, which can be done when the inside of the rim
is parallel, or not sufficiently coned to cause it to slip off the jaws,
or when the jaws will reach to the centre of the rim width.
The advantages and disadvantages of these various methods are as
follows:--
From the weakness of the pulley rim it is apt to distort when held with
sufficient chuck-jaw pressure to enable the turning of the rim face and
edge. But this would not affect the truth of the hole; hence the rim may
be gripped in a chuck to bore the hole and face the hub. If so held it
should be held true to the inside face of the rim, so that the bore will
be true to the same, and then in turning the outside diameter it will be
made as true as possible with the rim, which will preserve the balance
of the pulley as much as possible. For these reasons the inside of the
rim should be the part set to run true, whatever method of chucking be
employed; hence, if the circumstances will permit of holding the hub to
bore it, an independent jaw chuck should be employed (that is, of
course, a chuck capable of independent jaw movement).
If the pulley be chucked by the arms, it is well-nigh impossible to
avoid springing those arms from the pressure of the bolts, &c., holding
them, and as a result the pulley face, though turned true, will not be
true of itself, nor true with the hole, when the arms are released from
such pressure.
If the pulley is of such a large size that its rim must be held by bolts
and plates while the boring is progressing, such bolts, &c., must be
placed on the outside of the rim, so as not to be in the way when
setting the pulley true to the inside of the rim.
A small pulley may be turned on a mandrel driven by a dog, which is the
truest method of turning, because the rim is in this case strained by
the pressure of the cut only. But a dog will not drive a cut at such a
leverage as exists at the rim of a pulley above about 18 inches in
diameter; furthermore, in a large wheel there would not be sufficient
friction between a mandrel and the pulley bore to drive the roughing cut
on the pulley face.
It is necessary, therefore, to drive the pulley from the arms, while
holding it on a mandrel, but if it be driven by one arm the whole strain
due to driving will fall on that one arm, and on one side of the pulley
only, and this will have a tendency to cause the rim at and near its
junction with that arm to spring or deflect from its natural position,
and, therefore, to be not quite true; all that can be done, therefore,
is to drive by two arms with a Clements driver, so as to equalize the
pressure on them.
An excellent method of chucking a pulley, and one that with care avoids
the disadvantages mentioned in the foregoing methods, is shown in Figs.
1232 and 1233. It consists of a clamping dog, Fig. 1234, that fastens to
the lathe face plate, and secures the pulley by its arms, while
supporting the rim and preventing it from chattering, if it is weak or
slight.
[Illustration: Fig. 1232.]
This dog is bolted to the face plate by the two studs A and B. At C is a
set screw for clamping the pulley arms against the screw D, and at F is
a screw that steadies the pulley rim between the arms.
[Illustration: Fig. 1233.]
CUTTING SCREWS IN THE LATHE WITH SLIDE REST TOOLS.--In order to cut a
thread in the lathe with a slide rest tool, it is necessary that the
gear-wheels which transmit motion from the cone spindle to the feed
screw shall be of the proportions necessary to give to the lathe
carriage and slide rest sufficient lateral movement or traverse for
lathe revolution to cut a thread of the desired pitch.
[Illustration: Fig. 1234.]
Suppose now that the feed screw makes a revolution in the same time that
the cone spindle does, and it is evident that the thread cut by the
slide rest tool will be of the same pitch as is the pitch of the lathe
feed screw. If the feed screw gear-wheels of the lathe are what is
called single geared (which means that no one stud in the change gearing
carries more than one gear-wheel), it does not matter what are the sizes
or how many teeth there are in the wheels used to convey or transmit
motion from the cone spindle to the feed screw, for so long as the
number of teeth on the cone spindle gear and that on the feed screw are
equal, the feed screw will make one revolution in the same time as the
cone spindle makes a revolution, and the cutting tool will travel a
lateral distance equal to the pitch of the lead screw.
[Illustration: Fig. 1235.]
Suppose, for example, that Fig. 1235 represents the screw cutting gear
or change wheels of a lathe, wheel D being the driver, I an intermediate
wheel for transmitting motion from the driver D to the lead-screw wheel
S. Suppose, also, that D has 32, I 80, and S 32 teeth, and we have a
simple or single-geared lathe. In this case it may first be proved that
we need not concern ourselves with the number of teeth in the
intermediate I, because its number of teeth is of no consequence. For
example, the 32 teeth in D will in a revolution move 32 of the teeth in
I past the line of centres, and it is obvious that I will move the 32
teeth in S past the line of centres, causing it to make one revolution
the same as D. If any other size of wheel be used for an intermediate,
the effect will be precisely the same, the revolutions of D and of S
remaining equal. Under these conditions the lathe would cut a thread
whose pitch would be the same as that of the thread on the lead screw.
[Illustration: Fig. 1236.]
Now let us turn to Fig. 1236, representing an arrangement of gearing
common in American practice, and we have within the lathe-head three
gears, A, B, and C, which cannot be changed. Of these, B and C are
simply intermediate wheels, the respective diameters of which have no
effect upon the revolutions of the lead screw, except that they convey
the motion to D. To demonstrate this, suppose the wheels to have the
number of teeth marked respectively against them in the end view of the
figure, C and D having each 20 teeth, and the one revolution of the live
spindle wheel A will cause the lead-screw wheel to make one revolution,
because A and S contain the same number of teeth. This may be made plain
as follows: The 20 teeth in A will in one revolution cause B to make two
revolutions, because B has but half as many teeth as A. The two
revolutions of B will cause C to make but one revolution, because C has
twice as many teeth as B has. Now, C and D are fast on the same shaft R;
hence they revolve together, the one revolution of C simply being
conveyed by the shaft R to D, and it is clear that the one revolution of
A has been conveyed without change to D, and that, therefore, D may be
considered to have simply taken the place of A, unaffected by the wheels
B, C. Wheel I is again an intermediate, so that, whatever its diameter
or number of teeth, one revolution of D will cause one revolution of S.
Thus in this arrangement the lead screw will again revolve at the same
speed as the live spindle, and the thread cut will be of the same pitch
as the pitch of the lead screw. Practically, then, all the wheels
between A and S, as thus arranged, act as simple intermediates, the same
as though it were a single-geared lathe, which occurs because C and D
have the same number of teeth, and we have, therefore, made no use of
the shaft R to compound the gearing.
[Illustration: Fig. 1237.]
The term "compounded" as applied to the change gears of a lathe, means
that there exists in it a shaft or some equivalent means by which the
velocity of the wheels may be changed. Such a shaft is shown at R in
Fig. 1236, and it affords a means of compounding by placing on its outer
end, as at D, a wheel that has a different number of teeth to that in
wheel C. In Fig. 1237 this change is made, wheel D having 40 teeth
instead of the 20 it had before. As in the former case, however, it will
make one revolution to one of C or one of A, but having 40 teeth it will
move 40 of the teeth in I past the line of centres, and this will cause
the lead screw wheel S to make two revolutions, because it has 20 teeth
only. Thus, the compounding of C and D on shaft R has caused S to make
two revolutions to one of A, or, what is the same thing, one revolution
of A will in this case cause S to make two revolutions, and the thread
cut would be twice as coarse as the lead-screw thread. In the case of a
lathe geared as in either Fig. 1235 or 1236, all the wheels that we
require to consider in calculating the change wheels are D and S. Now,
the shaft R is called the "mandrel," the "stud," or the "spindle," all
three terms being used, and the wheel D is the wheel on the stud,
mandrel, or spindle, while in every case S is that on the lead screw,
and the revolutions of this wheel D and those of the lead screw will be
in the same proportion as exists between their numbers of teeth. In
considering their revolutions it is to be borne in mind that when D has
more teeth than S the speed of the lead screw is increased, and the
lathe will cut a thread coarser than that of its lead screw, or when D
has less teeth than S the speed of the lead screw is diminished, and the
pitch of thread cut will be finer than that of the lead screw.
[Illustration: Fig. 1238.]
Another method of compounding is shown in Fig. 1238, the compounded pair
C D being on a stud carried in the swing frame F. Now, suppose A has 32,
C 64, D 32, and S 64 teeth, the revolution being in the same proportion
as the numbers of teeth, C will make one-half a revolution to one
revolution of A, and D, being fast to the same stud as C, will also make
one-half revolution to one revolution of A. This one-half revolution of
D will cause S to make one-quarter of a revolution; hence the thread cut
will be four times as fine as the pitch of the thread on the lead screw,
because while the lathe makes one turn the lead screw makes one-quarter
of a turn. In this arrangement we are enabled to change wheel C as well
as wheel D (which could not be done in the arrangement shown in Fig.
1236), and for this reason more changes can be made with the same number
of wheels. When the wheel C makes either more or less revolutions than
the driver A, it must be taken into account in calculating the change
wheels. As arranged in Fig. 1236, it makes the same number as A, which
is a very common, arrangement, but in Fig. 1238 it is shown to have
twice as many teeth as A; hence it makes half as many revolutions. In
the latter case we have two pairs of wheels, in each of which the driven
wheel is twice the size of the driver; hence the revolutions are reduced
four times.
Suppose it is required to cut a thread of eight to an inch on a lathe
such as shown in Fig. 1235, the lead screw pitch being four per inch,
and for such simple trains of gearing we have a very simple rule, as
follows:--
_Rule._--Put down the pitch of the lead screw as the numerator, and the
pitch of thread you want to cut as the denominator of a vulgar fraction,
and multiply both by the pitch of the lead screw, thus:
Pitch of
lead
screw. {the number of teeth for the
Pitch of lead screw 4 4 16 = {wheel on the spindle.
- × - = --
Pitch to be cut 8 4 32 = {the number of teeth for the
{wheel on the lead screw.
There are three things to be noted in this rule; and the first is, that
when the pitch of the lead screw and the pitch of thread you want to cut
is put down as a fraction, the numerator at once represents the wheel to
go on the stud, and the denominator represents the wheel to go on the
lead screw, and no figuring would require to be done providing there
were gear-wheels having as few teeth as there are threads per inch in
the lead screw, and that there was a gear-wheel having as many teeth as
the threads per inch required to be cut. For example, suppose the lathe
in Fig. 1236 to have a lead screw of 20 per inch, and that the change
wheels are required to cut a pitch 40, then we have 20/40, the 20 to go
on at D in Fig. 1236 and the 40 to go on the lead screw. But since lead
screws are not made of such fine pitch, but vary from two threads to
about six per inch, we simply multiply the fraction by any number we
choose that will give us numbers corresponding to the teeth in the
change wheels. Suppose, for example, the pitch of lead screw is 2, and
we wish to cut 6, then we have 2/6, and as the smallest change wheel
has, say, 12 teeth we multiply the fraction by 6, thus: 2/6 × 6/6 =
12/36. If we have not a 12 and a 36 wheel, we may multiply the fraction
by any other number, as, say, 8; thus: 2/6 × 8/8 = 16/48 giving us a 16
wheel for D, Fig. 1236, and a 48 wheel for the lead screw.
The second notable feature in this rule is that it applies just the same
whether the pitch to be cut is coarser or finer than the lead screw;
thus: Suppose the pitch of the lead screw is 4, and we want to cut 2. We
put these figures down as before 4/2, and proceed to multiply, say, by
8; thus: 4/2 × 8/8 = 32/16, giving a 32 and a 16 as the necessary
wheels.
The third feature is, that no matter whether the pitch to be cut is
coarser or finer than the lead screw, the wheels go on the lathe just as
they stand in the fraction; the top figure goes on top in the lathe, as,
for example, on the driving stud, and the bottom figures of the fraction
are for the teeth in the wheel that goes on the bottom of the lathe or
on the lead screw. No rule can possibly be simpler than this. Suppose
now that the pitch of the lead screw is 4 per inch and we want to cut
1-1/2 per inch. As the required pitch is expressed in half inches, we
express the pitch of the lead in half inches, and employ the rule
precisely as before. Thus, in four there are eight halves; hence, we put
down 8 as the numerator, and in 1-1/2 there are three halves, so we put
down 3 and get the fraction 8/3. This will multiply by any number, as,
say, 6; thus: (8/3) × (6/6) = (48/18), giving us 48 teeth for the wheel
D in Fig. 1236, and 18 for the lead screw wheel S.
In a lathe geared as in Fig. 1235 the top wheel D could not be readily
changed, and it would be more convenient to change the lead screw wheel
S only. Suppose, then, that the lead screw pitch is 2 per inch, and we
want to cut 8. Putting down the fraction as before, we have 2/8, and to
get the wheel S for the lead screw we may multiply the number of teeth
in D by 8 and divide it by 2; thus: 32 × 8 = 256, and 256 ÷ 2 = 128;
hence all we have to do is to put on the lead screw a wheel having 128
teeth. But suppose the pitch to be cut is 4-1/4, the pitch of the lead
screw being 2. Then we put both numbers into quarters, thus: In 2 there
are 8 quarters, and in 4-1/4 there are 17 quarters; hence the fraction
is 8/17. If now we multiply both terms of this 8/17 by 4 we get 32/68,
and all we have to do is to put on the lead screw a wheel having 68
teeth.
When we have to deal with a lathe compounded as in Fig. 1238, in which
the combination can be altered in two places--that is, between A and C
and between D and S--the wheel A remaining fixed, and the pitch of the
lead screw is 2 per inch, and it is required to cut 8 per inch--this
gives us the fraction 2/8, which is at once the proportion that must
exist between the revolutions of the wheel A and the wheel S. But in
this case the fraction gives us the number of revolutions that wheel S
must make while the wheel A is making two revolutions, and it is more
convenient to obtain the number that S requires to make while A is
making one revolution, which we may do by simply dividing the pitch
required to be cut by the pitch of the lead screw, as follows: Pitch of
thread required, 8; pitch of lead screw, 2; 8 ÷ 2 = 4 = the revolutions
S must make while A makes one. We have then to reduce the revolutions
four times, which we may do by putting on at C a wheel with twice as
many teeth in it as there are in A, and as A has 32, therefore C must
have 64 teeth. When we come to the second pair of wheels, D and S, we
may put any wheel we like in place of D, providing we put on S a wheel
having twice as many.
But suppose we require to cut a fractional pitch, as, say, 4-1/8 per
inch, the pitch of lead screw being 2, all we have to do is to put the
pitch of the lead screw into eighths, and also put the number of teeth
in A into eighths; thus: In two there are 16 eighths, and in the pitch
required there are 33 eighths; hence for the pitch of the lead screw we
use the 16, and for the thread required we use the 33, and proceed as
before; thus:
Pitch of thread Pitch of lead
required. screw.
33 ÷ 16 = 2-1/16 = the revolution which A
must make while wheel B
makes one revolution.
The simplest method of doing this would be to put on at C a wheel having
2-1/16 times as many teeth as there are in A. Suppose then that A has 32
teeth, and one sixteenth of 32 = 2, because 32 ÷ 16 = 2. Then twice 32
is 64, and if we add the 2 to this we get 66; hence, if we give wheel C
66 teeth, we have reduced the motion the 2-1/16 times, and we may put on
D and S wheels having an equal number of teeth. Or we may put on a wheel
at C having the same number as A has, and then put on any two wheels at
D and C, so long as that at S has 2-1/16 times as many teeth as that at
D.
Again, suppose that the pitch of a lead screw is 4 threads per inch, and
that it be required to find what wheels to use to cut a thread of 11/16
inch pitch, that is to say, a thread that measures 11/16 inch from one
thread to the other, and not a pitch of 11/16 threads per inch: First we
must bring the pitch of the lead screw and the pitch to be cut to the
same terms, and as the pitch to be cut is expressed in sixteenths we
must bring the lead screw pitch to sixteenths also. Thus, in an inch of
the length of the lead screw there are 16 sixteenths, and in this inch
there are 4 threads; hence each thread is 4/16 pitch, because 16 ÷ 4 =
4. Our pitch of lead screw expressed in sixteenths is, therefore, 4, and
as the pitch to be cut is 11/16 it is expressed in sixteenths by 11;
hence we have the fraction 4/11, which is the proportion that must exist
between the wheels, or in other words, while the lathe spindle (or what
is the same thing, the work) makes 4 revolutions the lead screw must
make 11.
Suppose the lathe to be single geared, and not compounded, and we
multiply this fraction and get--
4 × 4 16 = wheel to go on lead screw.
-- - = --
11 × 4 44 = " " stud or mandrel.
4 × 5 20 = wheel to go on lead screw.
Or, -- - = --
11 × 5 55 = " " stud or mandrel.
4 × 6 24 = wheel to go on lead screw.
Or, -- - = --
11 × 6 66 = " " stud or mandrel.
But suppose the lathe to be compounded as in Fig. 1235, and we may
arrange the wheels in several ways, and in order to make the problem
more practical, we may suppose the lathe to have wheels with the
following numbers of teeth, 18, 24, 36, 36, 48, 60, 66, 72, 84, 90, 96,
102, 108, and 132.
[Illustration: Fig. 1239.]
Here we have two wheels having each 36 teeth; hence we may place one of
them on the lathe spindle and one on the lead screw, as in Fig. 1239;
and putting down the pitch of the lead screw, expressed in sixteenths as
before, and beneath it the thread to cut also in sixteenths, we have:
4 × 6 24 = wheel to be driven by lathe spindle,
-- - = --
11 × 6 66 = " to drive lead screw wheel;
the arrangement of the wheels being shown in Fig. 1239.
We may prove the correctness of this arrangement as follows: The 36
teeth on the lathe spindle will in a revolution cause the 24 wheel to
make 1-1/2 revolutions, because there are one and a half times as many
teeth in the one wheel as there are in the other; thus: 36 ÷ 24 = 1-1/2.
Now, while the 24 wheel makes 1-1/2, the 66 will also make 1-1/2,
because they are both on the same sleeve and revolve together. In
revolving 1-1/2 times the 66 will cause the 36 on the lead screw to make
2-3/4 turns, because 99 ÷ 36 = 2-3/4 (or expressed in decimals 2.75),
and it thus appears that while the lathe spindle makes one turn, the
lead screw will make 2-3/4 turns.
Now, the proportion between 1 and 2-3/4 is the same as that existing
between the pitch of the lead screw and the pitch of the thread we want
to cut, both being expressed in sixteenths; thus:
Pitch of lead screw in sixteenths 4 }
}, and 11 ÷ 4 = 2-3/4;
" to be cut in sixteenths 11 }
that is to say, 11 is 2-3/4 times 4.
Suppose it is required, however, to find what thread a set of gears
already on the lathe will cut, and we have the following rule:
_Rule._--Take either of the driven wheels and divide its number of teeth
by the number of teeth in the wheel that drives it, then multiply by the
number of teeth in the other driving wheel, and divide by the teeth in
the last driven wheel. Then multiply by the pitch of the lead screw.
[Illustration: Fig. 1240.]
_Example._--In Fig. 1240 are a set of change wheels, the first pair of
which has a driving wheel having 36 teeth, and a driven wheel having 18
teeth. The second pair has a driving wheel of 66 teeth, and a driven
wheel of 48.
Let us begin with the first pair and we have 36 ÷ 18 = 2, and this
multiplied by 66 is 132. Then 132 ÷ 48 = 2.75, and 2.75 multiplied by 4
is 11, which is the pitch of thread that will be cut. Now, whether this
11 will be eleven threads per inch, or as in our previous examples a
pitch of 11/16 inch from one thread to another or to the next one,
depends upon what the pitch of the lead screw was measured in.
[Illustration: Fig. 1241.]
If it is a pitch of 4 threads per inch, the wheels will cut a thread of
11 per inch, while if it were a thread of 4/16 pitch, the thread cut
will be 11/16 pitch.
Let us now work out the same gears beginning from the lead screw pair,
and we have as follows:
Number of teeth in driver is 66, which divided by the number in the
driven, 48, gives 1.375. This multiplied by the number of teeth in the
driver of the other pair = 36 gives 49.5, which divided by the number of
teeth in the driven wheel of the first pair gives 2.75, which multiplied
by the pitch of the lead screw 4 gives 11 as before.
Taking now the second example as in Fig. 1240, and beginning from the
first pair of gears, we have, according to the rule, 36 ÷ 48 × 66 ÷ 18 ×
4 = 11 = pitch the gears will cut; or proceeding from the second pair of
gears, we have by the rule, 66 ÷ 18 × 36 ÷ 48 × 4 = 11 = the pitch the
gears will cut. It is not often, however, that it is required to
determine what threads the wheels already on a lathe will cut, the
problem usually being to find the wheels to cut some required pitch. But
it may be pointed out that when the problem is to find the result
produced by a given set of wheels, it is simpler to begin the
calculation from the wheel already on the lathe spindle, rather than
beginning with that on the lead screw, because in that case we begin at
the first wheel and calculate the successive ones in the same order in
which we find them on the lathe, instead of having to take the last pair
in their reverse order, as has been done in the examples, when we began
at the wheel on the lead screw, which we have termed the second pair.
The wheels necessary to cut a left-hand thread are obviously the same as
those for a right-hand one having an equal pitch; all the alteration
that is necessary is to employ an additional intermediate wheel, as at I
in Fig. 1241, which will reverse the direction of motion of the lead
screw. For a lathe such as shown in Fig. 1235, this intermediate wheel
may be interposed between wheels D and I or between I and S. In Fig.
1236, it may be placed between D and I or between I and S, and in Fig.
1238 it may be placed between A and C or between D and S.
[Illustration: Fig. 1242.]
Here it may be well to add instructions as to how to arrange the change
wheels to cut threads in terms of the French centimètre. Thus, an inch
equals 254/100 of a centimètre, or, in other words, 1 inch bears the
same proportion to a centimètre as 254 does to 100, and we may take the
fraction 254/100 and reduce it by any number that will divide both terms
of the fraction without leaving a remainder; thus, 254/100 ÷ 2 = 127/50.
If, then, we take a pair of wheels having respectively 127 and 50 teeth,
they will form a compound pair that if placed as in Fig. 1242 will
enable the cutting of threads in terms of the centimètre instead of in
terms of the inch.
Thus, for example, to cut 6 threads to the centimètre, we use the same
change wheels on the stud and on the lead screw that would be used to
cut 6 threads to the inch, and so on throughout all other pitches.
CUTTING DOUBLE OR OTHER MULTIPLE THREADS IN THE LATHE.--In cutting a
double thread the change wheels are obviously arranged for the pitch of
the thread, and one thread, as A in Fig. 251 is cut first, and the
other, B, afterwards. In order to insure that B shall be exactly midway
between A, the following method is pursued. Suppose the pitch of the
lead screw is 4 threads per inch, and that we require to cut a double
thread, whose actual pitch is 8 per inch, and apparent pitch 16 per
inch, then the lead screw requires to make half a turn to one turn of
the lathe spindle; or what is the same thing, the lathe spindle must
make two turns to one of the lead screw, hence the gears will be two to
one, and in a single-geared lathe we may put on a 36 and a 72, as in
Fig. 1243, in which the intermediate wheels are omitted, as they do not
affect the case. With these wheels we cut a thread of 8 per inch and
then, leaving the lead screw nut still engaged with the lead screw and
the tool still in position to cut the thread already formed, we make on
the change wheels a mark as at S T, and after taking off the driving
gear we make a mark at space _u_, which is 18 teeth distant from S, or
half-way around the wheel. We then pull the lathe around half a turn and
put the driving gear on again with the space _u_ engaged with the tooth
T, and the lathe will cut the second thread exactly intermediate to the
first one. If it were three threads that we require to cut, we should
after the driving gear was taken off give the lathe one-third a
revolution, and put it back again, engaging the twelfth space from S
with tooth T, because one-third of 36 is 12.
[Illustration: Fig. 1243.]
It is obviously necessary, in cutting multiple threads in this way, to
so select the change wheels that the driving gear contains a number of
teeth that is divisible without leaving a remainder by the thread to be
cut: thus, for a double thread the teeth must be divisible by two, hence
a 24, 30, 34, 36, or any even number of teeth will do. For a triple
thread the number of teeth in the driving gear must be divisible by 3,
and so on.
But suppose the driving gear is fast upon the lathe spindle and cannot
be taken off, and we may then change the position of the lead screw gear
to accomplish the same object as moving the lathe spindle. Thus for a
double thread we would require to remove the driving gear as before, and
then pull round the lead screw so that the eighteenth tooth from T would
engage with space S, which is obviously the same thing as moving the
driving gear round 18 teeth.
In short work of small diameter the tool will retain its sharpness so
long, that one tool will rough out and finish a number of pieces without
requiring regrinding, and in this case the finishing cuts can be set by
noting the position of the feed screw handle when the first piece is
finished to size and the tool is touching the work, so that it may be
brought to the same position in taking finishing cuts on the succeeding
pieces; but the calipers should nevertheless be used, being applied to
the threads as in Figs. 1244 and 1245, which is the best method when
there is a standard to set the calipers by.
[Illustration: Fig. 1244.]
After a threading tool has carried its cut along the required length of
the work, the carriage must be traversed back, so that the second cut
may be started. In short work the overhead cross belt that runs the
lathe backwards is sufficiently convenient and rapid for this purpose,
but in long screws much time would be lost in waiting while the carriage
runs back. In the Ames lathe there is a device that enables the carriage
to be traversed back by hand, and the feed nut to be engaged without
danger of cutting a double thread, or of the tool coursing to one side
of the proper thread groove, which is a great convenience.
The construction of this device is shown in Fig. 574. In lathes not
having a device for this purpose, the workman makes a chalk mark on the
tail of the work driver, and another on the top of the lead screw gear,
and by always moving the carriage back to the same point on the lathe
bed, and engaging the lead screw nut when these two chalk marks are at
the top of their paths of revolution, the tool will fall into its
correct position and there will be no danger of cutting a double thread.
[Illustration: Fig. 1245.]
In cutting [V] threads of very coarse pitch it will save time, if the
thread is a round top and bottom one, to use a single-pointed slide rest
tool, and cut up the thread to nearly the finished depth, leaving just
sufficient metal for the chaser to finish the thread.
In using the single-pointed tool _on_ the roughing cuts of very coarse
pitches, it is an advantage to move the tool laterally a trifle, so that
it will cut on one side or edge only. This prevents excessive tool
spring, and avoids tool breakage.
This lateral movement should be sufficient to let the follower side or
edge of the tool just escape the side of the thread, and all the cut be
taken by the leading side or edge of the tool.
This is necessary because the tool will not cut so steadily on the
follower as on the leading cutting edge, for the reason that the
pressure of the cut assists to keep the feed screw nut against the sides
of the feed screw thread, taking up the lost motion between them,
whereas the pressure of a cut taken on the follower side of the thread
tends to force the thread of the feed nut away from the sides of the
feed screw thread and into the space between the nut thread afforded by
the lost motion, and as a result the slide rest will move forward when
the tool edges meet exceptionally hard places or spots in the metal of
the work, while in any event the tool will not operate so steadily and
smoothly.
If the screw is a long one, the cutting should be done with a liberal
supply of oil or water to keep it cool, otherwise the contraction of the
metal in cooling will leave the thread finer than it was when cut. This
is of special importance where accuracy of pitch is requisite.
[Illustration: Fig. 1246.]
In cutting a taper thread in a lathe, it is preferable that the taper be
given by setting over the lathe tailstock, rather than by operating the
cross slider from a taper-turning attachment, because the latter causes
the thread to be cut of improper pitch. Thus, in Fig. 1246 is a piece of
work between the lathe centres, and it will be readily seen that
supposing the lathe to be geared to cut, say, 10 threads per inch, and
the length A of the work to be 2 inches long, when the tool has
traversed the distance A it will have cut 20 threads, and it will have
passed along the whole length of the side B of the work and have cut 20
threads upon it, but since the length of line B is greater than that of
A, the pitch of the thread cut will be coarser than that due to the
change wheels. The amount of the error is shown by the arc C, which is
struck from D as a centre; hence from C to E is the total amount of
error of thread pitch.
[Illustration: Fig. 1247.]
But if the lathe tailstock sets over as in Fig. 1247, then the pitch of
the thread will be cut correct, because the length of B will equal the
length of tool traverse; hence at each work revolution the tool would
advance one-twentieth of the length of the surface on which the thread
is cut, which is correct for the conditions.
[Illustration: _VOL. I._ =METHODS OF BALL TURNING.= _PLATE XIII._
Fig. 1248.
Fig. 1249.
Fig. 1250.
Fig. 1251.
Fig. 1252.
Fig. 1253.
Fig. 1254.
Fig. 1255.]
CHAPTER XIII.--EXAMPLES IN LATHE WORK.
BALL TURNING.--One of the best methods of turning balls of the softer
materials, such as wood, bone, or ivory, is shown in Figs. 1248 and
1249, in which are shown a blank piece of material and a tubular saw,
each revolving in the direction denoted by the respective arrows. The
saw is fed into the work and performs the job, cutting the ball
completely off. In this case the saw requires to be revolved quicker
than the work--indeed, as quickly as the nature of the material will
permit, the revolving of the work serving to help the feed. Of course,
the teeth of such a saw require very accurate sharpening if smooth work
is to be produced, but the process is so quickly performed that it will
pay to do whatever smoothing and polishing may be required at a separate
operation. This method of ball cutting undoubtedly gave rise to the idea
of using a single tooth, as in Fig. 1250. But when a single tooth is
employed the work must revolve at the proper cutting speed, while the
tooth simply advances to the feed. If the work was cut from a
cylindrical blank the cutter would require to be advanced toward the
work axis to put on a cut and then revolved to carry that cut over the
work, when another cut may be put on, and so on until the work is
completed. The diameter of ball that can be cut by one cutter is here
obviously confined to that of the bore of the cutter, since it is the
inside edge of the cutter that does the finishing.
This naturally suggests the employment of a single-pointed and removable
tool, such as in Fig. 1251, which can be set to turn the required
diameter of ball, and readily resharpened. To preserve the tool for the
finishing cut several of such tools and holders may be carried in a
revolving head provided to the lathe or machine, as the case may be. In
any event, however, a single-pointed tool will not give the smoothness
and polish of the ball cutter shown in Fig. 1252, which produces a
surface like a mirror. It consists of a hardened steel tube C, whose
bore is ground cylindrically true after it has been hardened. The ball B
is driven in a chuck composed of equal parts of tin and lead, and the
cutter is forced to the ball by hand. The ball requires to revolve at a
quick speed (say 100 feet per minute for composition brass), while the
cutter is slowly revolved.
A simple attachment for ball turning in an ordinary lathe is shown in
Fig. 1253. It consists of a base A, carrying a plate B, which is pivoted
in A; has worm-wheel teeth provided upon its circumference and a
slideway at S, upon which slides a tool rest R, operated by the
feed-screw handle H. The cut is put on by operating H, and the feed
carried around by means of the screw at W. The base plate A may be made
suitable to bolt on the tool rest, or clamped on in place of the tool,
as the circumstances may permit; or in some cases it might be provided
with a stem to fit in place of the dead centre. For boring the seats for
balls or other curved internal surfaces the device shown in Fig. 1254
may be used. It consists of a stem or socket S, fitting to the dead
spindle in place of the dead centre, and upon which is pivoted a wheel
W, carrying a tool T. R is a rack-bar that may be held in the lathe tool
post and fed in to revolve wheel W and feed the tool to its cut. At P is
a pin to maintain the rack in gear with the wheel. Obviously, a
set-screw may be placed to bear against the end of the tool to move it
endwise and put on the cut. An equivalent device is shown in Fig. 1255,
in which the tool is pivoted direct into the stem and moved by a bar B,
held in the tool post. The cut is here put on by operating the tail
spindle, a plan that may also be used in the device shown in Fig. 1254.
The pins P upon the bar are for moving or feeding the tool to its cut.
It is obvious that in all these cases the point of the tool must be out
of true vertically with the axis of the work.
[Illustration: Fig. 1256.]
[Illustration: Fig. 1257.]
In turning metal balls by hand it is best to cast them with a stem at
each end, as in Fig. 1257.
[Illustration: Fig. 1258.]
[Illustration: Fig. 1259.]
To rough them out to shape, a gauge or template, such as in Fig. 1256,
is used, being about 1/32 inch thick, which envelops about one-sixth of
the ball's circumference. After the ball is roughed out as near as may
be to the gauge, the stems may be nicked in, as in Fig. 1257, and broken
off, the remaining bits, A, B, being carefully filed down to the
template. The balls are then finished by chucking them in a chuck such
as shown in Fig. 1258,[19] and a narrow band, shown in black in the
figure, is scraped, bringing the ball to the proper diameter. The ball
is then reversed in the chuck, as in Fig. 1259, and scraped by hand
until the turning marks cross those denoted by the black band. The ball
is then reversed, so that the remaining part of the black band that is
within the chuck in Fig. 1259 may be scraped down, and when by
successive chuckings of this kind the lightest of scrape marks cross and
recross each other when the ball is reversed, it may be finished by the
ball cutter, applied as shown in Fig. 1252, and finally ground to its
seat with the red-burnt sand from the foundry, which is better than
flour emery or other coarser cutting grinding material.
[19] From _The American Machinist_.
[Illustration: Fig. 1260.]
[Illustration: Fig. 1261.]
CUTTING CAMS IN THE LATHE.--Fig. 1260 represents an end view of cam to
be produced, having four depressions alike in form and depth, and
arranged equidistant round the circumference, which is concentric to the
central bore. The body of a cam is first turned up true, and one of the
depressions is filed in it to the required form and curvature. On its
end face there is then drilled the four holes, A, B, C, D, Fig. 1261,
these being equidistant from the bore E. A similar piece is then turned
up in the lathe, and in its end is fitted a pin of a diameter to fit the
holes A, B, &c., it being an equal distance from bore E. These two
pieces are then placed together, or rather side by side, on an arbor or
mandrel, with the pin of the one fitting into one of the holes, as A.
Two tool posts are then placed in position, one carrying a dull-pointed
tool or tracer, and the other a cutting tool. The dull-pointed tracer is
set to bear against the cam shown in Fig. 1262, while the cutting tool
is set to take a cut off the blank cam piece. The cross feed screw of
the lathe is disengaged, and a weight W, Fig. 1262, attached to the
slider to pull the tracer into contact with the cam F. As a result, the
slide rest is caused to advance to and recede from the line of lathe
centres when the cam depression passes the tracer point, the weight W
maintaining contact between the two. Successive cuts are taken until the
tool cuts a depression of the required depth. To produce a second cam
groove, the piece is moved on the mandrel so that the pin will fall into
a second hole (as, say, B, Fig. 1261), when, by a repetition of the
lathe operation, another groove is turned. The whole four grooves being
produced by the same means, they must necessarily be alike in form, the
depths being equal, provided a finishing cut were taken over each
without moving the cutting tool.
[Illustration: Fig. 1263.]
It will be observed that this can be done in any lathe having a slide
rest, and that the grooves cut in one piece will be an exact duplicate
of that in the other, or guide groove, save such variation as may occur
from the thickness of the tracer point, which may be allowed for in
forming the guide or originating groove. From the wear, however, of the
tracer point, and from having to move the cutting tool to take
successive depths of cut, this method would be undesirable for
continuous use, though it would serve excellently for producing a single
cam. An arrangement for continuous use is shown in Fig. 1263, applied to
a lathe having a feed spindle at its back, with a cam G upon it. This
cam G may be supposed to have been produced by the method already
described. A tracer point H, or a small roller, may be attached to the
end of the slide-rest and held against G by the weight W, which may be
within the lathe shears if they have no cross girts, as in the case of
weighted lathes. The slide-rest may be arranged to have an end motion
slightly exceeding the motion, caused by the cam, of the tracer H.
Change gears may then be used to cause the cam G to make one rotation
per lathe rotation, cutting four recesses in the work; or by varying the
rotations of G per lathe rotation, the number of recesses cut by the
tool T may be varied. Successive depths of cut may then be put on by
operating the feed screw in the ordinary manner. In this arrangement the
depth and form of groove cut upon the work will correspond to the form
of groove upon the cam-roller G; or each groove upon G being of a
different character, those cut on the work will correspond. The wear on
the cross slide will, in this case, be considerable, however, in
consequence of the continuous motion of the tool-carrying slider, and to
prevent this another arrangement may be used, it being shown in Fig.
1264 as applied to a weighted and elevating slide rest. The elevating
part of the slide rest is here pivoted to the lathe carriage at I, the
weight W preventing play (from the wear) at I. A bracket J is shown fast
to the elevating slide of the rest, carrying a roller meeting the
actuating cam G. In this arrangement the cut may be put on by the feed
screw traversing the slider in the usual manner, or the elevating screw
K may be operated, causing the roller at the end of J to gradually
descend as each cut is put on into more continuous contact with G as the
latter rotates. The form of groove cut by the tool does not, in this
case, correspond to the form on G, because the tool lifts and falls in
the arc of a circle of which pivot I is the centre of motion, and its
radius from I being less than the radius of G, its motion is less. But
in addition to this the direction of its motion is not that of
advancing and receding directly toward and away from the line of lathe
centres, and the cam action is reduced by both these causes.
[Illustration: Fig. 1264.]
[Illustration: Fig. 1265.]
The location of pivot I is of considerable importance, since the nearer
it is to the line of centres the less the action of the cam G is reduced
upon the work. As this is not at first sight apparent, a few words may
be said in explanation of it. It is obvious that the farther the pivot I
is from the tool point the greater will be the amount of motion of the
tool point, but this motion is not in a direction to produce the
greatest amount of effect upon the work, as is demonstrated in Fig.
1265; referring to which, suppose line A B C to represent a lever
pivoted at B, and that end A be lifted so that the lever assumes the
position denoted by the dotted lines D and E, then the end of C will
have moved from circle F to circle G, as denoted by arc H; arm C of the
lever being one-half the length of arm A B, and from circle F to circle
G, measured along the line H, being one-half the distance between A and
the end of the line D, the difference in the diameters of circles F and
G will represent the effect of the cam motion on the tool under these
conditions. Now, suppose A J is a lever pivoted at K, and that end A is
raised to the dotted line D, then arm J, being one-half the length of A
K, will move half as much as end A, and will assume the position denoted
by dotted line L, and the difference in the diameter of circles F and M
will represent the cam motion upon the tool motion under these
conditions. From this it appears that the more nearly vertical beneath
the tool point the pivoted point is, the greater the effect produced by
a given amount of cam motion. On this account, as well as on account of
the direction of motion, the shape of the actuating cam may be more
nearly that of the form required to be produced in proportion as the
pivoted centre falls directly beneath the tool point. But, on the other
hand, the wear of the pivot, if directly beneath the tool point, would
cause more unsteadiness to the tool; hence it is desirable that it be
somewhere between points K and B, the location being so made that (B
representing the pivoted point of the rest) the line B C forms an angle
of 50° with the line B A. It is obvious that when the work is to be
cam-grooved on a radial face the pivoted design is unsuitable, and
either that in Fig. 1262 or 1263 is suitable.
Similar cam motions may be given to the cross feed of a lathe: thus, the
Lane and Bodley Company of Cincinnati, Ohio, employ the following method
for turning the spherical surfaces of their swiveling bearings for line
shafting.
[Illustration: Fig. 1266.]
[Illustration: Fig. 1267.]
The half bearing B, Fig. 1266, is chucked upon a half-round mandrel, C
being the spherical surface to be turned, a sectional view of C being
shown in Fig. 1267.
[Illustration: Fig. 1268.]
In Fig. 1268 is a plan view of the chuck, work, and lathe rest; D is a
former attachment bolted to the slider of the rest, and E a rod passing
through the lathe block. The weight W, Fig. 1269, is suspended by a cord
attached to the slide rest so as to keep the former D firmly against the
end of E.
As the slider is operated, the rest is caused by E to slide upon the
lathe bed, and the cutting tool forms a spherical curve corresponding to
the curve on the former D. The weight W of course lifts or falls
according to the direction of motion of the slider.
The cut is put on by operating handle G, thus causing E to advance.
The weight W causes any play between the slider and the cross slide to
be taken up in the same direction as the tool pressure would take it up,
hence the cut taken is a very smooth one. The half-round mandrel being
fixed to the lathe face plate will remain true, obviating the liability
of the centre of the spherical surface being out of line with the axis
of the bearing-bore.
A method of producing cams without a lathe especially adopted for the
purpose is shown in Figs. 1270 and 1272, which are extracted from
_Mechanics_. The apparatus consists of a frame E, which fits on the
cross ways of an ordinary lathe. The cross-feed screw is removed, so
that E may slide backwards and forthwards freely. The frame E carries
the worm-wheel A and the worm-gear B, which is operated by the crank F.
The cam C to be cut is bolted on to the face of the worm-wheel, which
faces the headstock of the lathe. The form for the cam, which may be
made of sheet steel, or thicker material, according to the wear it is to
have, is fastened to the face of the cam.
[Illustration: Fig. 1269.]
[Illustration: Fig. 1270.]
[Illustration: Fig. 1271.]
[Illustration: Fig. 1272.]
A cutter, like a fluted reamer, such as is shown in Fig. 1271, is then
put in the live centre of the lathe. Care must be taken that the shank
is the same size as the fluted part, and that the flutes are not cut up
farther than the thickness that the cam grooves are to be cut in the
blank. Having attached a cord to the back of E, pass it over a pulley H,
fastened on the rear of the lathe, and hang on a weight G. Fig. 1272 is
an edge view of the device, looking from the back of the lathe. It shows
the worm A, blank C, and former D all bolted together, while the cutter
I is ready in its place on a line with the centre of the worm, and just
at back of the former. The machine is operated by turning the crank F,
which causes the worm A, also C and D, to revolve slowly, while the
cutter I has a rather rapid rotation. The weight causes the cutter to be
held firmly against the form F, and to follow its curves in and out.
[Illustration: Fig. 1273.]
[Illustration: Fig. 1274.]
[Illustration: Fig. 1275.]
KNURLING OR MILLING TOOLS.--In Fig. 1273 is shown the method of using
the knurling tool in the slide rest of a lathe. It represents the tool
at work producing the indentations which are employed to increase the
hand grip of screw heads, or of cylindrical bodies, as shown in the
figure by the crossed lines. Fig. 1274 is an end view of the tool, which
consists of a holder to go in the slide rest tool post, and carrying two
small hardened steel wheels, each of which is serrated all round its
circumference, the serrations of one being in an opposite direction to
those of the other. The method of using the tool is shown in Fig. 1275,
where it is represented operating upon a cylindrical piece of work. If
the knurling is to be carried along the work to a greater length than
the thickness of the knurl wheels, the lathe slide rest is slowly
traversed the same as for a cutting tool.
As the knurling tool requires to be forced against the work with
considerable pressure, there is induced a strain tending to force the
tool directly away from the work, as denoted by the arrow in Fig. 1276,
and this, in a weighted lathe, acts to raise the lathe carriage and
weight. This is avoided by setting the tool at an angle, as in Fig.
1277, so that the direction of strain is below and not above the pivot
on which the cross slide rests. This is accomplished by pivoting the
piece carrying the wheels to the main body of the stem, as shown in Fig.
1277.
For use by hand the knurling or milling tool is fitted to a holder and
handle, as in Fig. 1278, and the hand tool rest is placed some little
distance from the work so that the knurl can pass over it, and below the
centre of the work.
Knurls for screw heads are made convex, concave, or parallel, to fit the
heads of the screws, and may be indented with various patterns.
[Illustration: Fig. 1276.]
[Illustration: Fig. 1277.]
[Illustration: Fig. 1278.]
WINDING SPIRAL SPRINGS IN THE LATHE.--Spiral springs whose coils are
close, and which therefore act on distension only, may be wound by
simply starting the first coil true, and keeping the wire as it winds on
the mandrel close to that already wound thereon.
[Illustration: Fig. 1279.]
Spiral springs with open coils may be best wound as shown in Fig. 1279,
in which is shown a mandrel held between the lathe centres and driven by
a dog that also grips one end of the wire W, of which the spring is to
be made. The wire is passed through two blocks B, which, by means of the
set-screw in the lathe tool post, place a friction on it sufficient to
place it under a slight tension which keeps it straight. The change
gears of the lathe are arranged as they would be to cut a screw of a
pitch equal to the thickness of the wire added to the space there is to
be between the coils of the spring. The first turn of the lathe should
wind a coil straight round the mandrel when the self-acting feed motion
is put in operation and the winding proceeds, and when the spring is
sufficiently long, the feed motion is disconnected, and the last coil is
allowed to wind straight round the mandrel, thus giving each end of the
spring a flat or level end.
If the wire is of brass it will be necessary to close it upon the
mandrel with blows from a lead mallet to prevent it from uncoiling on
the mandrel when the end is released, which it will do to some extent in
any event.
[Illustration: Fig. 1280.]
If it is of steel it may be necessary to heat the coil red-hot to
prevent its uncoiling, and in the coiling it will, if of stout wire,
require to be bent against the mandrel during winding with a piece of
steel placed in the tool post, as in Fig. 1280, in which A represents
the mandrel, B the spring wire, and D the lathe tool post.
[Illustration: Fig. 1281.]
[Illustration: Fig. 1282.]
In the absence of a lathe with a self-acting feed motion, the mandrel
may have a spiral groove in it and the piece of steel or other hard
metal shown in figure must be used, the feed screw of the slide rest
being removed so that the wire can feed itself along as the mandrel
rotates. Near one end of the mandrel a small hole is drilled through,
there being sufficient space between the hole and the end of the mandrel
to admit of a loose washer being placed thereon; the bore of this washer
requires to be rather larger in diameter than the outside diameter of
the spring, when wound upon the mandrel, and also requires to be
provided with a keyway and key. The washer D (Fig. 1281), is slipped
over the mandrel, the end of the wire C is inserted in the hole B and
the spring being wound, the washer is passed up to the end, and the key
driven home as in Fig. 1282; when the wire is cut off and the mandrel
may be taken from the lathe with the spring closely wound round it to be
hammered if of brass, and heated if of steel. The hammering should be
done over the whole circumference, not promiscuously, but beginning at
one end and following along the wire with the blows delivered not more
than 1/4 of an inch apart; for unless we do this we cannot maintain any
definite relation between the size of the mandrel and the size of the
spring.
When a grooved mandrel is used, its diameter should be slightly less
than the required diameter of spring, as when released the coils expand
in diameter.
[Illustration: Fig. 1283.]
If it is not essential that the coils be exactly true, take a plain
mandrel, such as shown in Fig. 1283, and a hook, such as shown at A,
fasten the end of the wire either round the lathe dog, or in a hole in
the mandrel as before, and wind one full coil of the spring upon the
mandrel, then force this coil open until the hook end of A can be
inserted between it and over the mandrel, the other end hanging down
between the lathe shears, which will prevent it from rotating, starting
the lathe while holding the unwound end of the wire against the hook
with a slight pressure, and the winding will proceed as shown in the
figure, the thickness of A regulating the width apart of the coils. It
is obvious that if the coil is to be a right-handed one and is started
at the carrier end, the lathe must revolve backwards.
Spiral springs for railroad cars are wound while red-hot in special
spring-winding lathes and with special appliances.
TOOLS FOR HAND TURNING.--Many of the tools formerly used in hand turning
have become entirely obsolete, because they were suitable for larger
work than any to which hand turning is now applied; hence, reference to
such tools will be omitted, and only such hand tools will be treated of
as are applicable to foot lathes and wood turning, their purposes being
those for which hand tools are now used.
To the learner, practice with hand tools is especially advantageous,
inasmuch as the strain due to the cut is felt by the operator; hence,
the effects of alterations in the shape of the tools, its height or
position with relation to the work, and also the resistance of the metal
to severance, are more readily understood and appreciated than is the
case where the tool is held in a slide rest or other mechanical device.
If under certain conditions the hand tool does not operate to advantage,
these conditions may be varied by a simple movement of the hands,
altering the height of the tool to the work, the angle of the cutting
edges to the work, or the rate of feed, as the case may be, and
instantly perceiving the effects; whereas with tools held by mechanical
means, such alterations would involve the expenditure of considerable
time in loosening, packing, and fastening the tool, and adjusting it to
position.
Small work that is turned by hand may, under exceptionally expert
manipulation, be made as interchangeable and more accurate in dimensions
than it could be turned by tools operated in special machines. That is
to say, it is possible to turn by hand a number of similar small pieces
that will be when finished as true, more nearly corresponding in
dimensions, and have a finer finish, than it is practicable to obtain
with tools operated or guided by parts of a machine. This occurs because
of the wear of the cutting tools, which upon small work may be
compensated for in the hand manipulation in cases where it could not be
in machine manipulation. But with ordinary skill, and under ordinary
conditions, the liability to error in hand work induces greater
variation in the work than is due to the wear of the tool cutting edges
in special machine work; hence, the practical result is that work made
by special machinery is more uniform and true to size and shape than
that made by hand, while also the quantity turned out by special
machines is very much greater.
[Illustration: Fig. 1284.]
The most desirable form of tool for taking a heavy hand cut is the heel
tool shown in Fig. 1284, which, it may be remarked, is at present but
little used on account of the greater expedition of tools held in slide
rests. It consists of a steel bar, about 3/8 or 1/2 inch square, forged
with a heel at F, so that it may firmly grip the hand rest, and having a
cutting edge at E. This bar is about 8 inches long, and is held in a
groove in a wooden stock by a strap passing over it, and having a stem
which passes down through the handle D, in which is fixed a nut, so that
by screwing up or unscrewing D the bar is gripped or released, as the
case may be, in a groove in the stock. In use, the end H of the stock is
held firmly against the operator's shoulder, the left hand grasps the
stock and presses the tool firmly down upon the face of the hand rest,
while with the right the handle D is moved laterally, causing the tool
to move to its cut. The depth of the cut is put on and regulated by
elevating the end H of the stock. The heel F is placed close enough to
the work to keep E F nearly vertical, for if it inclines too much in any
direction the tool gets beyond the operator's control. The position of
the heel F is moved from time to time along the hand rest to carry the
cut along.
A cut of 1/8 inch deep, that is, reducing the work diameter 1/4 inch,
may readily be taken with this tool, which, however, requires skilful
handling to prevent it from digging into the work.
The shorter the distance from the face E to the heel F the more easily
the tool can be controlled; hence, as F serves simply as a sharp and
gripping fulcrum it need not project much from the body of the steel;
indeed, in many cases it is omitted altogether, the bottom of the steel
bar being slightly hollowed out instead. No oil or water is required
with the heel tool.
The hand rest should be so adjusted for height that the cutting edge of
the tool stands slightly above the horizontal level of the work, a rule
which obtains with all hand tools used upon wrought iron and steel.
[Illustration: Fig. 1285.]
The graver is the most useful of all hand turning tools, since it is
applicable to all metals, and for finishing as well as roughing out the
work. It is formed by a square piece of steel whose end is ground at an
angle, as shown in the top and the bottom view, Fig. 1285, A A being the
cutting edges, C C the points, and D D the heels.
It is held in a wooden handle, which should be long enough to grasp in
both hands, so that the tool may be held firmly. For cutting off a
maximum of metal in roughing out the work the graver is held as in Fig.
1286, the heel being pressed down firmly upon the tool rest. The cut is
carried along the work by revolving the handle upon its axis, and from
the right towards the left, at the same time that the handle is moved
bodily from the left towards the right. By this combination of the two
movements, if properly performed, the point of the graver will move in a
line parallel to the centres of the lathe, because, while the twisting
of the graver handle causes the graver point to move away from the
centre of the diameter of the work, the moving of the handle bodily from
left to right causes the point of the graver to approach the centre of
that diameter; hence the one movement counteracts the other, producing a
parallel movement, and at the same time enables the graver point to
follow up the cut, using the heel as a pivotal fulcrum, and hence
obviating the necessity of an inconveniently frequent moving of the heel
of the tool along the rest. The most desirable range of these two
movements will be very readily observed by the operator, because an
excess in either of them destroys the efficacy of the heel of the graver
as a fulcrum, and gives it less power to cut, and the operator has less
control over the tool.
[Illustration: Fig. 1286.]
[Illustration: Fig. 1287.]
[Illustration: Fig. 1288.]
For finishing or smoothing the work the graver is held as in Fig. 1287,
the edge being brought parallel to the work surface. For brass work the
top faces of the graver should be slightly bevelled in the direction
shown in Fig. 1288.
The graver cuts most efficiently with the work revolving at a fast
speed, or, say, at about 60 feet per minute, and for finishing wrought
iron or steel requires an application of water.
[Illustration: Fig. 1289.]
To finish work that has been operated upon by a heel tool or by a
graver, the finishing tool shown in Fig. 1289 may be employed. It is
usually made about 5/8 or 3/4 inch wide, as the graver is employed for
shorter work. It is ground so as not to let the extreme corners cut, and
is used at a slow speed with water. The edge of this tool is sometimes
oilstoned, causing it to cut with a clean polish. The tool is held
level, brought up to the work, and a cut put on by elevating the handle
end. To carry the cut forward, the tool is moved along the hand rest to
nearly the amount of its width, and is brought to its cut by elevating
the handle as before. When the work has been finished as near as may be
with this tool, it may be finished by fine filing, the lathe running at
its quickest speed; or the file may be used to show the high spots while
using the finishing tool.
[Illustration: Fig. 1290.]
For facing the ends of work the tool shown in Fig. 1290, or that shown
in Fig. 1291, may be used, either of them being made from an old
three-cornered file. The cutting edge at A, Fig. 1290, should be
slightly curved, as shown. The point of the tool is usually brought to
cut at the smallest diameter of the work, with the handle end of the
tool somewhat elevated. As the cut is carried outwards the handle end of
the tool is depressed, and the point correspondingly elevated. It may be
used dry or with water, but the latter is necessary for finishing
purposes.
[Illustration: Fig. 1291.]
Another form of this tool is shown in Fig. 1291. It has two cutting
edges A A, one of which rests on the hand rest while the other is
cutting, the tool being shown in position for cutting a right-and a
left-hand face, the face nearest to the work being shown in the lower
view. This face should be placed against the radial face of the work,
and the cut put on by turning the upper edge over towards the work while
pressing the tool firmly to the lathe rest.
[Illustration: Fig. 1292.]
For cutting out a round corner the tool shown in Fig. 1292, employed
either for roughing or smoothing purposes (water being used with it for
the latter), the heel causes it to grip the hand rest firmly, and acts
as a pivotal fulcrum from which the tool may be swept right and left
round the curve, or a portion of it.
This tool, as in the case of all tools used upon wrought iron or steel,
should not cut all round its edge simultaneously, as in that case,
unless indeed it is a very narrow tool, the force placed upon it by the
cut will be too great to enable the operator to hold and control it;
hence the cut should be carried first on one side and then on the other,
and then at the point, or else the handle end should be moved laterally,
so that the point sweeps round the work. It should be brought to its cut
by placing its heel close to the work, and elevating the handle end
until the cutting edge meets the work.
The point or nose of the tool may obviously be made straight or square,
as it is termed, to suit the work, the top rake being omitted for brass
work.
[Illustration: Fig. 1293.]
In using this tool for cutting a groove it is better (if it be a deep
groove, and imperative if it be a broad one, especially if the work be
slight and apt to spring) to use a grooving tool narrower in width than
the groove it is to cut, the process being shown in Fig. 1293, in which
W represents a piece of work requiring the two grooves at A and B cut in
it. For a narrow groove as A the tool is made about half as wide as the
groove, and a cut is taken first on one side as at C, and then on the
other as at D. For a wider groove three or more cuts may be made, as at
E, F, G. In all cases the tool while sinking the groove is allowed to
cut on the end face only; but when the groove is cut to depth, the side
edges of the tool may be used to finish the sides of the groove, but the
side and end edge must not cut simultaneously, or the tool will be
liable to rip into the work.
[Illustration: Fig. 1294.]
HAND TOOLS FOR BRASS WORK.--In addition to the graver as a roughing-out
tool for brass work, we have the tool shown in Fig. 1294, the cutting
edge being at the rounded end A. It is held firmly to the rest, which is
not placed close to the work (as in the case of other tools), so as to
give the tool a wide range of movement, and hence permit of the cut
being carried farther along without moving its position on the rest. It
may be used upon either internal or external work.
For finishing brass work, tools termed scrapers are employed.
[Illustration: Fig. 1295.]
Fig. 1295 represents a flat scraper, the two end edges A and the side
edges along the bevel forming the cutting edges.
[Illustration: Fig. 1296.]
[Illustration: Fig. 1297.]
[Illustration: Fig. 1298.]
[Illustration: Fig. 1299.]
In this tool the thickness of the end A is of importance, since if it be
too thin it will jar or chatter. This is especially liable to occur when
a broad scraper is used, having a great length of cutting edge in
operation. This may be obviated to some extent by inclining the scraper
as in Fig. 1296, which has the same effect as giving the top face
negative rake, causing the tool to scrape rather than cut. The dividing
line between the cutting and scraping action of a tool is found in the
depth of the cut, and the presentation of the tool to the work, as well
as in the shape of the tool. Suppose, for example, that we have in Fig.
1297, a piece of work W and a tool S, and the cut being light will be a
scraping one. Now suppose that the relative positions of the size of the
work and of the tool remain the same, but that the cut be deepened as in
Fig. 1298, and the scraping action is converted into that class of
severing known as shearing, or we may reduce the depth of cut as in Fig.
1299, and the action will become a cutting one.
[Illustration: Fig. 1300.]
But let the depth of cut be what it may, the tool will cut and not
scrape whenever the angle of its front face is more than 90° to the line
of tool motion if the tool moves, or of work motion if the work moves to
the cut. In Fig. 1300, for example, the tool is in position to cut the
angle of the front face, being 110° to the direction of tool motion.
We may consider this question from another stand-point, however,
inasmuch as that the tool action is a cutting one whenever the pressure
of the cut is in a direction to force the tool deeper into the work, and
a scraping one whenever this pressure tends to force the tool away from
the work, assuming of course that the tool has no front rake, and that
the cut is light or a "mere scrape," as workmen say. This is illustrated
in Fig. 1301, the tool at A acting to cut, and at B to scrape, and the
pressure of the cut upon A acting to force the tool into the work as
denoted by the arrow D, while that upon B acts to force it in the
direction of arrow C, or away from the work.
In addition to these distinctions between a cutting and a scraping
action we have another, inasmuch as that if a tool is pulled or dragged
to its cut its action partakes of a scraping one, no matter at what
angle its front face may stand with relation to the work.
The end face of a flat scraper should be at a right angle to the body of
the tool, so that both edges may be equally keen, for if otherwise, as
in Fig. 1302, one edge as A will be keener than the other and will be
liable to jar or chatter.
[Illustration: Fig. 1301.]
[Illustration: Fig. 1302.]
The flat scraper can be applied to all surfaces having a straight
outline, whether the work is parallel or taper, providing that there is
no obstruction to prevent its application to the work.
[Illustration: Fig. 1303.]
[Illustration: Fig. 1304.]
[Illustration: Fig. 1305.]
[Illustration: Fig. 1306.]
Thus, in Fig. 1303 we have a piece of work taper at _a_ and C, parallel
at _e_, and with a collar at _d_, the scraper S being shown applied to
each of these sections, and it is obvious that it cannot be applied to
section _a_ because the collar _d_ is in the way. This is remedied by
grinding the scraper as in Fig. 1304, enabling it to be applied to the
work as in Fig. 1305. Another example of the use of a bevelled scraper
is shown in Fig. 1306, the scraper S having its cutting edge parallel to
the work and well clear of the arm H.
[Illustration: Fig. 1307.]
The round-nosed scraper is used for rounding out hollow corners, or may
be made to conform to any required curve or shape. It is limited in
capacity, however, by an element that affects all scraping tools, that
if too great a length of cutting edge is brought into action at one
time, chattering will ensue, and to prevent this the scraper is only
made of the exact curvature of the work when it is very narrow, as at S
in Fig. 1307.
For broad curves it is made of more curvature, so as to limit the length
of cutting edge, as is shown in the same figure at S´, and is swept
round the work so as to carry the cut around the curve.
There are, however, other means employed to prevent chattering, and as
these affect the flat scraper as well as the round-nosed one, they may
as well be explained with reference to the flat one.
First, then, a thin scraper is liable to chatter, especially if used
upon slight work. But the narrower the face on the end of the scraper,
the easier it is to resharpen it on the oilstone, because there is less
area to oilstone. A fair thickness is about 1/20 inch; but if the
scraper was no thicker than this throughout its whole length, it would
chatter violently, and it is for this reason that it is thinned at its
cutting end only. Chattering is prevented in small and slight work by
holding the scraper as in Fig. 1308, applying it to the top of the work;
and to reduce the acting length of cutting edge, so as to still further
avoid chattering, it is sometimes held at an angle as in the top view in
Fig. 1309, S being the scraper and R the tool rest.
When the scraper is applied to side faces, or in other cases in which a
great length of cutting edge is brought into action, a piece of leather
laid beneath the scraper deadens the vibration and avoids chattering.
[Illustration: Fig. 1308.]
[Illustration: Fig. 1309.]
[Illustration: Fig. 1310.]
It is obvious that the scraper may be given any required shape to meet
the work, Fig. 1310 representing a scraper of this kind; but it must in
this case be fed endways only to its cut, if the work is to be cut to
fit the scraper.
[Illustration: Fig. 1311.]
[Illustration: Fig. 1312.]
In Fig. 1311 is shown a half-round scraper, which is shown in Fig. 1312
in position to scrape out a bore or hole. This tool is made by grinding
the flat face and the two edges of a worn-out half-round smooth file,
and is used to ease out bores that fit too tightly. The cutting edges
are carefully oilstoned, and the work revolved at a very quick feed.
[Illustration: Fig. 1313.]
[Illustration: Fig. 1314.]
[Illustration: Fig. 1315.]
When a number of small pieces of duplicate form are to be turned by
hand, a great deal of measuring may be saved and the work very much
expedited by means of the device shown in Fig. 1313. It consists of a
tool stock or holder, the middle of which, denoted by A, is square, and
contains three or four square slots, with a set-screw to each slot to
hold different turning tools. Each end of the stock is turned parallel,
as denoted by B, C. In Figs. 1313 and 1314, D, E, and F are the tools,
and G, H, are the set-screws.
Fig. 1315 represents top and side view of a plate, of which there must
be two, one to fasten on the headstock and one on the tailstock of the
lathe, as shown in Fig. 1316. In Fig. 1317 the manner of using the tool
is shown, similar letters of reference denoting similar parts in all the
figures.
The plates P P are bolted by screws to the headblock H and the tailstock
T of the lathe. The tool holder is placed so that the cylindrical ends
B, C, rest on the ends of these plates, and in the angles P´ P´. The
cutting tool D is sustained, as shown, upon the lathe rest R. In use the
operator holds the stock A in his hands in the most convenient manner,
using the tool E as a handle when there is a tool in the position of E.
The cutting point of the tool is pressed up to the work W, and the feed
is carried along by hand. It is obvious, however, that when the
perimeters of A B meet the shoulders O O, Fig. 1315, of the plates P P,
the tool cannot approach any nearer to the diametrical centre of the
work; hence the diameter to which the tool will turn is determined by
the distance of the shoulder O of the plate P from the centre of the
lathe centres, as shown in Fig. 1316 by the line L. In carrying the cut
along it is also obvious that the lateral travel of the stock or holder
must end when the end of the square part A comes against the side face
of either of the plates. In the engraving we have shown the tool D
cutting a groove in the work W, while the shoulder of the holder is
against the plate fastened to the lathe tailstock T; and so long as the
operator, in each case, keeps the shoulder against that plate, the
grooves upon each piece of work will be cut in the same position, for it
will be observed that the position in the length of the work performed
by each tool is determined by the distance of the cutting part of each
tool from the end of the square part A of the tool holder. All that is
necessary, then, is to adjust each tool so that it projects the proper
distance to turn the requisite diameter and stands the required distance
from the shoulders of the square to cut to the desired length, and when
once set error cannot occur.
[Illustration: Fig. 1316.]
This plain description of the device, however, does not convey an
adequate idea of its importance. Suppose, for example, that it is
required to turn a number of duplicate pieces, each with a certain
taper: all that is necessary is to adjust the plates P in their
distances from the lathe centres. If the large end of the taper on the
work is required to stand nearest the lathe headstock A, the plate P on
the headstock must be moved until its shoulder O is farther from the
lathe centre. If, however, the work requires to be made parallel, the
plates P must be set the same distance for the axial line of the
centres. If it be desired to have a parallel and a taper in proximity
upon the same piece of work, the tool must have one of its cylindrical
ends taper and use it upon the taper part of the work.
[Illustration: Fig. 1317.]
In Fig. 1317 the tool D is shown cutting a square groove. The tool at F
serves to turn the parallel part X, and the tool E would cut the
[V]-shaped groove I.
All kinds of irregular work may be turned by varying the parallelism and
form of the cylindrical ends B C; but in this event the shoulders O O,
Fig. 1315, should be made [V]-shaped and hardened to prevent them from
rapid wear.
[Illustration: Fig. 1318.]
[Illustration: Fig. 1319.]
SCREW CUTTING WITH HAND TOOLS.--Screw threads are cut by hand in the
lathe with chasers, of which there are two kinds, the outside and the
inside chaser. In Fig. 1319 is shown an outside, or male, and in Fig.
1318 an inside, or female chaser. The width of a chaser should be
sufficient to give at least four teeth, and for the finer thread pitches
it is better to have six or eight teeth, the number increasing as the
pitch is finer, and the length of the work will permit. The leading
tooth should be a full one, or otherwise it will break off, and if in
cutting up the chaser a half or less than a full tooth is formed it
should be ground off. The tooth points should not be in a plane at a
right angle to the chaser length, but slightly diagonal thereto, as in
Fig. 1319, so that the front edge of the chaser will clear a bolt head
or shoulder, and permit the leading tooth to pass clear up to the head
without fear of the front edge of the steel meeting the shoulder.
[Illustration: Fig. 1320.]
[Illustration: Fig. 1321.]
[Illustration: Fig. 1322.]
The method of producing a chaser from a hob is shown in Fig. 1320, in
which H is a hob, which is a piece of steel threaded and serrated, as
shown, to give cutting edges to act, as the hob rotates, upon the chaser
C. If the chaser is cut while held in a constant horizontal plane, its
teeth will have the same curvature as the hob, or, in other words, they
will fit its circumference. Suppose that the chaser, being cut up by the
hob and then hardened, is applied to a piece of work of the same
diameter as the hob and held in the same vertical plane, as in Fig.
1320, it is obvious that, there being no clearance, the teeth cannot
cut. Or, suppose it be applied to a piece of work of smaller diameter,
as in Fig. 1324, it cannot cut unless its position be lowered, as in
Fig. 1322, or else it must be elevated, as in Fig. 1323. In either case
the angle of the thread cut will be different from the angle of the
sides of the chaser teeth, and the thread will be of improper depth.
Thus, on referring to Fig. 1321, it will be seen that the chaser C has a
tooth depth corresponding to that on the work W along the horizontal
dotted line E only, because the true depth of thread on the work is its
depth measured along a radial line, as line F or G, and the chaser teeth
are, at the cutting edge, of a different angle. This becomes more
apparent if we suppose the chaser thickness to be extended up to the
dotted line H, and compare that part of its length that lies within the
two circles I J, representing the top and bottom of the thread, with the
length of radial line G, that lies within these circles. If, then, the
chaser be lowered, to enable it to act, it will cut a thread whose sides
will be of more acute angle than are the sides of the chaser teeth or of
the hob from which it was cut. The same effect is caused by using a
chaser upon a larger diameter of work than that of the hob from which
the chaser was cut, because the increased curvature of the chaser teeth
acts to give the teeth less contact with the work, as is shown in Fig.
1325, for the teeth cannot cut without either the lower corners A of the
teeth being forced into the metal, or else the chaser being tilted to
relieve them of contact. To obviate these difficulties and enable a
chaser to be used upon various diameters of work, it is, while being cut
up by the hob, moved continuously up and down, as denoted in Fig. 1326,
by A and B, which represent two positions of the chaser. The amount of
this movement is sufficient to make the chaser teeth more straight in
their lengths, and to give them a certain amount of clearance, an
example of the form of chaser thus produced being shown in Fig. 1327,
applied to two different diameters of work, as denoted by the circle A
and segment of a circle B, C representing the chaser.
[Illustration: Fig. 1323.]
[Illustration: Fig. 1324.]
[Illustration: Fig. 1325.]
[Illustration: Fig. 1326.]
To obtain the most correct results with such a chaser, it must be
applied to the work in such a way that it has as little clearance as
will barely enable it to cut, because it follows from what has been said
with reference to single-pointed threading tools that to whatever amount
the chaser has clearance, a corresponding error of thread angle and
depth is induced. In hand use, therefore, it does not matter at what
height the chaser is applied so long as it is elevated sufficiently to
barely enable it to cut.
[Illustration: Fig. 1327.]
[Illustration: Fig. 1328.]
After the chaser is cut on the hob, its edges, as at C, and the corner,
as at D, in Fig. 1328, should be rounded off, so that they may not catch
in any burr which the heel of the hand tools may leave on the surface of
the hand rest.
[Illustration: Fig. 1329.]
For roughing out the threads on wrought iron or steel the top face
should be hollowed out, as shown in Fig. 1328, which will enable the
chaser to cut very freely. For use on cast iron the top face should be
straight, as shown in Fig. 1328 at A, while for use on soft metal, as
brass, the top face must be ground off, as shown in Fig. 1329.
[Illustration: Fig. 1330.]
The Pratt and Whitney Co. cut up chasers by the following method: In
place of a hob, a milling cutter is made, having concentric rings
instead of a thread. The cutters are revolved on a milling machine in
the ordinary manner. The chaser is fastened in a chuck fixed on the
milling machine table, and stands at an angle of 15°. It is traversed
beneath the milling cutter, and thus cut up with teeth whose lengths are
at a right angle to the top and bottom faces of the chaser; hence the
planes of the length of the teeth are not in the same plane as that of
the grooves of the thread to be cut. Thus, let _a_, _b_, _c_, and _d_,
Fig. 1330, represent the planes of the thread on the work, and _e_, _f_,
_g_, _h_, will be the planes of the lengths of the chaser teeth.
The chaser, however, is given 15° of bottom rake or clearance, and this
causes the sides of the chaser teeth to clear the sides of the thread.
[Illustration: Fig. 1331.]
Now, suppose the top face A, Fig. 1331, of the chaser to be parallel
with the face of the tool steel, and to lie truly horizontal and in the
same plane as the centre of the work. This clearance will cause the
thread cut by the chaser to be deeper than the natural depth of the
chaser teeth. Thus, in Fig. 1331 is shown a chaser (with increased
clearance to illustrate the point desired), the natural depth of whose
thread is represented by the line F, but it is shown on the section of
work that the thread cut by the tool will be of the depth of the line D,
which is greater than the length or depth of F, as may be more clearly
observed by making a line E, which, being parallel to A, is equal in
length to D, but longer than F. Hence, the clearance causes the chaser
under these conditions to cut a thread of the same pitch, but deeper
than the grooves of the hub, and this would alter the angles of the
thread. This, however, is taken into account in forming the angles of
the thread upon the milling cutter, and, therefore, of the chaser, which
are such that with the tool set level with the work centre, the thread
cut will be of correct angle, notwithstanding the clearance given to the
teeth.
[Illustration: Fig. 1332.]
In order to enable the cutting of an inside chaser from a hub, it
requires to be bent as in Fig. 1332, in which H is the hub, R the lathe
rest, and C the chaser. After the chaser is cut, it has to be
straightened out, as shown in Fig. 1318, in which is represented a
washer being threaded and shown in section; C is the chaser and R the
lathe rest, while P is a pin sometimes let into the lathe rest to act as
a fulcrum for the back of the chaser to force it to its cut, the handle
end of the chaser being pressed inwards.
[Illustration: Fig. 1333.]
[Illustration: Fig. 1334.]
When an inside chaser is cut from a hub (which is the usual method) or
male thread, its teeth slant the same as does the male thread on the
side of the hub on which it is cut, and in an opposite direction to that
of the thread on the other side of the hub. Thus, in Fig. 1333, H is the
hub, C the chaser, and R the lathe rest. The slope of the chaser-teeth
is shown by the dotted line B. Now, the slant of the thread on the half
circumference of the hub not shown or seen in the cut will be in an
opposite direction, and in turning the chaser over from the position in
which it is cut (Fig. 1333) to the position in which it is used (Fig.
1334), and applying it from a male to a female thread, we reverse the
direction with relation to the work in which the chaser-teeth slant; or,
in other words, whereas the teeth of the chaser should lie as shown in
Fig. 1334 at A A, they actually lie as denoted in that figure by the
dotted line B B. As a consequence, the chaser has to be tilted over
enough to cause the sides of the chaser-teeth to clear the sides of the
thread being cut, which, as they lie at opposite angles, is sufficient
to cause the female thread cut by the chaser to be perceptibly shallower
than the chaser-teeth, for reasons which have been explained with
reference to Fig. 1321. It may be noted however, that an inside chaser
cannot well be used with rake, hence the tilting in this case makes the
thread shallower instead of deeper.
To obviate these difficulties the hub for cutting a right-hand inside
chaser should have a left-hand thread upon it, and _per contra_, an
inside chaser for cutting a left-hand thread should be cut from a hub
having a right-hand thread.
The method of starting an outside thread upon wrought iron or steel to
cut it up with a chaser is as follows:--
[Illustration: Fig. 1335.]
The work is turned up to the required diameter, and the [V]-tool shown
in Fig. 1335 is applied; the lathe is run at a quick speed, and the heel
of the tool is pressed firmly to the face of the lathe rest, the handle
of the tool must be revolved from right to left at the same time as it
is moved laterally from the left to the right, the movement being
similar to that already described for the graver, save that it must be
performed more rapidly. It is in fact the relative quickness with which
these combined movements are performed which will determine the pitch of
the thread. The appearance of the work after striking the thread will be
as shown in Fig. 1336, A being the work, and B a fine groove cut upon it
by the [V]-tool.
The reason for running the lathe at a comparatively fast speed is that
the tool is then less likely to be checked in its movement by a seam or
hard place in the metal of the bolt, and that, even if the metal is soft
and uniform in its texture, it is easier to move the tool at a regular
speed than it would be if the lathe ran comparatively slowly.
[Illustration: Fig. 1336.]
If the tool is moved irregularly or becomes checked in its forward
movement, the thread will become waved or "drunken"--that is, it will
not move forward at a uniform speed;[20] and if the thread is drunken
when it is started, the chaser will not only fail to rectify it, but, if
the drunken part occurs in a part of the iron either harder or softer
than the rest of the metal, the thread will become more drunken as the
chaser proceeds. It is preferable, therefore, if the thread is not
started truly, to try again, and, if there is not sufficient metal to
permit of the starting groove first struck being turned out, to make
another farther along the bolt. It takes much time and patience to learn
to strike the requisite pitch at the first trial; and it is therefore
requisite for a beginner to leave the end of the work larger in diameter
than the required finished size, as shown in Fig. 1336, so as to have
sufficient metal to turn out the groove cut by the [V]-tool at the first
trial cut, and try again.
[20] See Fig. 253, Plate II., Vol. I.
If the thread is to be cut on brass the [V]-tool must not have any top
rake. Some turners start threads upon brass by placing the chaser itself
against the end of the work and sweeping it rapidly from left to right
(for a right-hand thread), thus obviating the use of the [V]-tool.
In all cases the work should be rounded off at the end to prevent the
chaser-teeth from catching.
In applying the chaser to the groove cut by the [V]-tool the leading
tooth should be held just clear of the work at first, and only be
brought to touch the work after the rear teeth have found and are
traversing in the groove. By this means the chaser will carry the thread
forward more readily and true. The thread must be carried forward but a
short distance at each passage of the chaser, gradually deepening the
thread while carrying it forward.
To start an inside thread the corner of the hole at its entrance should
be rounded off and the back teeth of the chaser placed to touch the bore
while the front teeth are clear. The lathe is to be run at a quick
speed, and the chaser moved forward at as near the proper speed as can
be judged. When the chaser is moved at the proper speed, the rear teeth
will fall into the fine grooves cut by the advance ones, and start a
thread, while otherwise promiscuous grooves only will be cut. It is an
easy matter, however, to start a double thread with an inside chaser;
hence, when the thread is started the lathe should be stopped and the
thread examined.
The chaser should be placed with its top face straight above the
horizontal level of the work and held quite horizontal, and the handle
end then elevated just sufficient to give the teeth clearance enough to
enable them to cut; otherwise, with a chaser having top rake, the thread
cut will be too deep, and its sides will be of improper angle one to the
other.
[Illustration: Fig. 1337.]
Thus, in Fig. 1337, W represents a piece of work, R the lathe rest, and
T the chaser. The depth of the thread cut in this case will be from the
circle A to the circle B; whereas the depth of the chaser teeth, and
therefore the proper depth for the thread, is from C to D. Thus tilting
the handle end of the chaser too much has caused the chaser teeth to cut
a thread too deep. If on brass work the chaser has its top face ground
off as in figure, tilting the handle too much will cause the thread cut
to be too shallow, and in both cases the error in thread depth induces a
corresponding error in the angles of the sides of the thread one to the
other and relative to the axial line of the bolt or work.
If the chaser teeth are held at an angle to the work surface, the thread
cut will be of finer pitch than the chaser, and the angles of the sides
of the thread on the work will not be the same as those of the teeth. It
is permissible, however, during the early cuts taken with a hand chaser
to give the chaser a slight degree of such angle, because it diminishes
the length of cutting edge, and causes the chaser to cut more freely,
especially when the pitch of the thread is coarse and the chaser is
becoming dull.
In the case of a taper thread the same rule, that the thread may be
roughed out with the chaser teeth at an angle to the surface lengthways
of the work, but must be finished with the teeth parallel to the
surface, holds good.
[Illustration: Fig. 1338.]
Thus, in Fig. 1338 is a taper plug fitting in a ring having a threaded
taper bore, the threads matching, and having the thread sides in both
cases at an equal angle to the surface, lengthways of the work, though
the tops and bottoms of the thread are not parallel with the axial line
of the work.
WOOD TURNING TOOLS.--Wood turning in the ordinary lathe is generally
performed by hand tools, and of these the principal is the gouge, which
in skillful hands may be used to finish as well as to rough out the work
(although there are other more useful finishing tools to be hereafter
described).
It is used mainly, however, to rough out the work and to round out
corners and sweeps. The proper form for this tool is shown in Fig. 1339,
the bevel on the end of the back or convex side being carried well round
at the corners, so as to bring those corners up to a full sharp cutting
edge on the convex or front side.
The proper way to hold a gouge is shown in Fig. 1340, in which the cut
taken by the tool is being carried from right to left, the face plate of
the lathe being on the left side, so that by holding it in the manner
shown the body and arms are as much as possible out of the way of the
face plate, which is a great consideration in short work. But if the cut
is to be carried from left to right, the relative position of the hands
may be changed.
When the work runs very much out of true, or has corners upon it, as in
the case of square wood, the forefinger may be placed under the hand
rest, and the thumb laid in the trough of the gouge, pressing the latter
firmly against the lathe rest to prevent the tool edge from entering the
work too far, or, in other words, to regulate the depth of the cut, and
prevent its becoming so great as to force the tool from the hands or
break it, as is sometimes the case under such circumstances. When the
gouge is thus held, its point of rest upon the lathe rest may be used as
a fulcrum, the tool handle being moved laterally to feed it to the cut,
which is a very easy and safe plan for learners to adopt, until practice
gives them confidence. The main point in the use of the gouge is the
plane in which the trough shall lie. Suppose, for example, that in Fig.
1341 is shown a piece of work with three separate gouge cuts being taken
along it, that on the right being carried in the direction of the arrow.
Now the gouge merely acts as a wedge, and the whole of the pressure
placed by the cut on the trough side or face of the gouge is tending to
force the gouge in the direction of the arrow, and therefore forward
into its cut, and this it does, ripping along the work and often
throwing it out of the lathe. To avoid this the gouge is canted, so that
when cutting from right to left it lies as shown at B, in which case the
pressure of the cut tends rather to force the gouge back from the cut,
rendering a slight pressure necessary to feed it forward. The gouge
trough should lie nearly horizontal lengthwise, the cutting edge being
slightly elevated. The gouge should never (for turning work) be ground
in the trough (as the concave side is termed), and should always be
oilstoned, the trough being stoned with a slip of stone lying flat along
the trough, the back being rotated upon a piece of flat stone, and held
with the ground surface flat on the surface of the stone, and so pressed
to it as to give most pressure at and near the cutting edge.
[Illustration: Fig. 1339.]
[Illustration: Fig. 1340.]
[Illustration: Fig. 1341.]
[Illustration: Fig. 1342.]
For finishing flat surfaces, the chisel shown in Fig. 1342 is employed.
It should be short, as shown. It should be held to the work in a
horizontal position, or it is apt to dig or rip into the work,
especially when it is used upon soft wood. Some expert workmen hold it
at an angle for finishing purposes, which makes it cut very freely and
clean, but increases the liability to dig into the work; hence learners
should hold it as shown.
[Illustration: Fig. 1343.]
[Illustration: Fig. 1344.]
Another excellent finishing tool is the skew-chisel, Fig. 1343, so
called because its cutting edge is at an angle, or askew with the body
of the tool. This tool will cut very clean, leaving a polish on the
work. It also has the advantage that the body of the tool may be kept
out of the way of flanges or radial faces when turning cylindrical work,
or may, by turning it on edge, be used to finish radial faces. It is
shown in Fig. 1343 by itself, and in Fig. 1344 turning up a stem. It is
held so that the middle of the edge does the cutting, and this tends to
keep it from digging into the work. The bevels forming the cutting edge
require to be very smoothly oilstoned.
The whole secret of the skillful and successful use of this valuable
tool lies in giving it the proper inclination to the work. It is shown
in Fig. 1344, at E, in the proper position for taking a cut from right
to left, and at F in position for taking a cut from left to right. The
face of the tool lying on the work must be tilted over, for E as denoted
by line A, and for F as denoted by the line B, the tilt being only
sufficient to permit the edge to cut. If tilted too much it will dig
into the work; if not tilted, the edge will not meet the work, and
therefore cannot cut. For cutting down the ends of the work, or down a
side face, it must be tilted very slightly, as denoted in figure by C D,
the amount of the tilt regulating the depth of the cut, so that when the
cutting edge of the tool has entered the wood to the requisite depth,
the flat face of the tool will prevent the edge from entering any
deeper. In cutting down a radial face the acute corner of the tool leads
the cut, whereas in in plain cylindrical work the obtuse is better to
lead.
For cutting down the ends, for getting into small square corners, and
especially for small work, the skew chisel is more handy than the
ordinary chisel, and leaves less work for the sand-paper to do.
Beginners will do well to practise upon black walnut, or any wood that
is not too soft, roughly preparing it with an axe to something near a
round shape.
[Illustration: Fig. 1345.]
For finishing hollow curves the tool shown in Fig. 1345 is employed, the
cutting edge being at B; the degree of the curve determines the width of
the tool, and, for internal work the tool is usually made long and
without a handle.
[Illustration: Fig. 1346.]
[Illustration: Fig. 1347.]
The tool shown in Fig. 1346 is employed in place of the gouge in cases
where the broad cutting edge of the latter would cause tremulousness. It
may be used upon internal or external work, being usually about two feet
long. For boring purposes, the tools shown in Fig. 1347 are employed,
the cutting edges being from the respective points along the edges C, D,
respectively. But when the bore is too small to admit of the application
of tools having their cutting edges on the side, the tool shown in Fig.
1347 at E is employed, which has its cutting edge on the end.
[Illustration: _VOL. I._ =THE ROGERS-BOND UNIVERSAL COMPARATOR.= _PLATE
XIV._
Fig. 1348.
Fig. 1349.]
CHAPTER XIV.--MEASURING MACHINES, TOOLS, AND DEVICES.
Measurements are primarily derived in Great Britain and her colonies,
and in the United States, from the English Imperial or standard yard.
This yard is marked upon a bar of "Bailey's metal" (composed of 16 parts
copper, 2-1/2 parts tin, and 1 part zinc), an inch square and 38 inches
long. One inch from each end is drilled a hole about three-quarters
through the whole depth of the bar, into which are fitted gold plugs,
whose upper end faces are level with the axis of the bar. Across each
plug is marked a fine line, and the distance between these lines was
finally made the standard English yard by an Act of Parliament passed in
1855. A copy of this bar is in the possession of the United States
Government at Washington, and all the standard measuring tools for feet,
inches, &c., are derived from subdivisions of this bar.
The standard of measurement in France and her colonies, Italy, Germany,
Portugal, British India, Mexico, Roumania, Greece, Brazil, Peru, New
Granada, Uruguay, Chili, Venezuela, and the Argentine Confederation, is
the French mètre, which is also partially the standard in Austria,
Bavaria, Wurtemberg, Baden, Hesse, Denmark, Turkey, and Switzerland. It
consists of a platinum bar, called the "mètre des archives," whose end
faces are parallel, and the length of this bar is the standard mètre.
But as measuring from the ends of this bar would (from the wear) impair
its accuracy, a second bar, composed of platinum and iridium, has been
made from the "mètre des archives." This second bar has ruled upon it
two lines whose distance apart corresponds to the length of the "mètre
des archives," and from the distance between these lines the
subdivisions of the mètre have been obtained.
As all metals expand or contract under variations of temperature, it is
obvious that these standards of length can only be accurate when at some
given temperature: thus the English bar gives a standard yard when it is
at a temperature of 62° Fahr., while the French standard bar is standard
at a temperature of 32° Fahr., which corresponds to 0 in the centigrade
thermometer. But if a bar is copied from a standard, and is found to be
too short, it is obvious that if its amount of expansion under an
increase of temperature be accurately known, it will be an accurate
standard at some higher temperature, or in other words, at a temperature
sufficiently higher to cause it to expand enough to compensate for its
error, and no more.
As all bars of metal deflect from their own weight, it is obvious that
the bar must be supported at the same points at which it rested when the
lines were marked, and it has been determined by Sir George Airy, that
the best position for the points of support for any bar may be obtained
as follows: Multiply the number of the points of support by itself (or,
as it is commonly called, "square it"), and from the sum so obtained
subtract 1. Then subtract the square root of the remainder, which gives
a sum that divided into the length of the bar will represent the
distance apart for the points of support. It will be obvious that the
points of support must be at an equal distance from each end of the bar.
Measurement may be compared in two ways, by sight and by the sense of
feeling. Measurement by sight is made by comparing the coincidence of
lines, and is called "line measurement." Measurement by feeling or touch
is called "end measurement," because the measurement is taken at the
ends. If, for example, we measure the diameter of a cylindrical bar, it
is an end measurement, because the measurement is in a line at a right
angle to the axis of the bar, and the points of touch on each side of
the bar are the ends of the measurement, which is supposed to have no
width.
In measuring by sight we may, for rude measurements, trust to the
unaided eye, as in using the common foot rule, but for such minute
comparisons as are necessary in subdividing or transferring a standard,
we may call in the aid of the microscope.
The standard gauges, &c., in use in the United States have been obtained
from Sir Joseph Whitworth, or duplicated from those made by him with the
aid of measuring and comparing machines. It has been found, however,
that different sets of these gauges did not measure alike, the
variations being thus given by Mr. Stetson, superintendent of the Morse
Twist Drill and Machine Co.
At the time the Government established the use of the standard system of
screw threads in the navy yards, ten sets of gauges were ordered from a
manufacturer. His firm procured a duplicate set of these and took them
to the navy yard in Boston and found that they were practically
interchangeable. He also took them to the Brooklyn Yard Navy. The
following tabular statement shows the difference between them:--
---------------------------------------------------------------
| |Morse Twist|
|Navy Yard |Drill and | Morse Twist Drill and
Size. |Male Gauge. |Machine Co.| Machine Co.
| |Male Gauge.| Female Gauge.
-------+------------+-----------+------------------------------
1/4 | 0.25 | 0.25 | Interchanged
5/16 | .313 | .313 | "
3/8 | .375 | .3759 |
7/16 | .437 | .437 | Interchanged
1/2 | .505 | .505 | "
9/16 | .562 | .564 (-)| "
5/8 | Damaged | .626 | "
3/4 | .7505 | .751 | "
7/8 | .876 | .8758 | "
1 | 1.00075 | 1.00075 | "
| | | { Navy Yard M. T. D. & M. Co.
1-1/8 | 1.125 (+)| 1.125 (-)| { --------- -----------------
| | | { (+) (-)
1-1/4 | 1.25 | 1.25 | Interchanged
1-3/8 | 1.375 | 1.375 | "
1-1/2 | 1.5 | 1.5 (-)| (-)
1-5/8 | 1.6245 | 1.624 | (-)
1-3/4 | 1.749 | 1.749 | Interchanged
1-7/8 | 1.8745 | 1.874 | (-)
2 | 1.999 | 1.999 |
---------------------------------------------------------------
The sign (-) means that the piece is small, but not enough to measure.
The sign (+) means that the piece is large, but not enough to measure.
The advantages to be derived from having universally accepted standard
subdivisions of the yard into inches and parts of an inch are as
follows:--
When a number of pieces of work of the same shape and size are to be
made to fit together, then, if their exact size is not known and there
is no gauge or test piece to fit them to, each piece must be fitted by
trial and correction to its place, with the probability that no two
pieces will be of exactly the same size. As a result, each piece in a
machine would have to be fitted to its place on that particular machine,
hence each machine is made individually.
Furthermore, if another lot of machines are afterwards to be made, the
work involved in fitting the parts together in the first lot of machines
affords no guide or aid in fitting up the second lot. But suppose the
measurements of all the parts of the first lot are known to within the
one ten-thousandth part of an inch, which is sufficiently accurate for
practical purposes, then the parts may be made to measurement, each part
being made in quantities and kept together throughout the whole process
of manufacture, so that when all the parts are finished they may go to
the assembling or erecting room, and one piece of each part may be taken
indiscriminately from each lot, and put together to make a complete
machine. By this means the manufacture of the machine may be greatly
simplified and cheapened, and the fit of any part may be known from its
size, while at the same time a new part may be made at any time without
reference to the machine or the part to which it is to fit.
Again, work made to standard size in one shop will fit to that made to
standard size in another, providing the standard gauges agree.
The Pratt and Whitney Company, of Hartford, Connecticut, in union with
Professor Rogers, of Cambridge University, in Massachusetts, determined
to inspect the Imperial British yard, to obtain a copy of it, and to
make a machine that would subdivide this copy into feet and inches, as
well as transfer the line measurements employed in the subdivisions into
end measures for use in the workshops, the degree of accuracy being
greater than is necessary in making the most refined mechanism, made
under the interchangeable or standard gauge system. The machine made
under these auspices is the Rogers-Bond Universal Comparator; Mr. Bond
having been engaged in conjunction with Professor Rogers in its
construction.
The machine consists of two cylindrical guides, upon which are mounted
two heads, carrying microscopes which may be reversed in the heads, so
as to be used at the front of the machine for line measurements and on
the back for end measurements.
Fig. 1348 is a front, and Fig. 1349 a rear view of the machine, whose
details of construction are more clearly shown in the enlarged views,
Fig. 1350 and 1352.
[Illustration: Fig. 1350.]
[Illustration: Fig. 1351.]
[Illustration: Fig. 1352.]
Fig. 1350 is a top view, and Fig. 1352 a front view, the upper part of
the machine being lifted up for clearness of illustration. X, X, are the
cylindrical guides, upon which are the carriages I, K, for the
microscopes. The construction of these carriages is more fully seen in
Fig. 1351, which represents carriage K. It is provided with a hand-wheel
R, operating a pinion in a rack (shown at T in the plan view figure of
the machine) and affording means to traverse the carriage along the
cylindrical guides. The microscope may be adjusted virtually by the
screw M^{4}. The base upon which the microscope stands is adjustable
upon a plate N, by means of the two slots and binding screws shown, and
the plate N fits in a slideway running across the carriage. U is one of
the stops used in making end measurements, the other being fixed upon
the frame of the machine at V in the plan view, Fig. 1350. The
micrometric arrangement for the microscope is shown more clearly in Fig.
1353. The screw B holds the box in position, the edge of the circular
base on which it sits being graduated, so that the position of M may be
easily read. In the frame M is a piece of glass having ruled upon it the
crossed lines, or in place of this a frame may be used, having in it
crossed spider web lines. These lines are so arranged as to be exactly
in focus of the upper glass of the microscope, this adjustment being
made by means of the screw S. The lines upon the bar are in the focus of
the lower glass; hence, both sets of lines can be seen simultaneously,
and by suitable adjustment of the microscope can be brought to coincide.
[Illustration: Fig. 1353.]
Beneath the cylindrical guides, and supported by the rack T that runs
between and beneath them, are the levers P, in Fig. 1352, upon which
weights may be placed to take up the flexure or sag of the cylindrical
guides.
In Fig. 1352, H, H, are heads that may be fixed to the cylindrical
guides at any required point, and contain metallic stops, against which
corresponding stops on the microscope carriages may abut, to limit and
determine the amount to which these carriages may be moved along the
cylindrical guides.
The pressure of contact between the carriage and the fixed stops is
found to be sufficiently uniform or constant if the carriage is brought
up to the stops (by means of the hand-wheel R, Fig. 1351) several times,
and a microscope reading taken for each time of contact. But this
pressure of contact may be made uniform or constant for all readings by
means of an electric current applied to the carriage through the
metallic stops on heads H, H, and those on the carriage.
We have now to describe the devices for supporting the work and
adjusting it beneath the microscopes.
[Illustration: Fig. 1354.]
Referring, then, to Fig. 1352, E is a bed or frame that may be raised or
lowered by means of the hand-wheel C, so as to bring the plate S (on
which rests the bar whose line measure is to be compared) within range
of the microscopes. The upper face of E is provided with raised [V]
slideways, which are more clearly seen in the end view of this part of
the machine shown in Fig. 1354. Upon these raised [V]s are the devices
for adjusting the height of the eccentric rollers S^{3}, upon which the
bars to be tested are laid, S^{2} representing one of these bars. To
adjust the bars in focus under the microscope, these eccentric rollers
are revolved by means of levers S^{4}. At S^{5} is a device for giving
to the table a slight degree of longitudinal movement in the base plate
that rests upon the raised [V]s; on the upper face of E and at S^{6} is
a mechanism for adjusting the height of that end of the plate S. The
base plate may be moved along the raised [V]s of E by the hand-wheel D.
To test whether the cylindrical guides are deflected by their own weight
or are level, a trough of mercury may be set upon the eccentric rollers
S^{3}, Fig. 1352, and the fine particles of dust on its surface may be
brought into focus in the microscope, whose carriage may then be
traversed to various positions along the cylindrical guides, and if
these dust particles remain in focus it is proof that the guides are
level with the mercury surface.
[Illustration: Fig. 1355.]
The methods of using the machine are as follows: The standard bar has
marked upon its upper face (which is made as true as possible and highly
polished) a line B (Fig. 1355), which is called the horizontal line, and
is necessary in order to set the bar parallel to the cylindrical guides
of the machine. The lines A, A, are those defining the measurement as a
yard, a foot, or whatever the case may be, and these are called the
vertical lines or lines of measurement. Now, suppose we require to test
a bar with the standard and the lines on its face are marked to
correspond to those on the standard.
The first operation will be to set the standard bar on the eccentric
rollers S^{3} in Fig. 1352, and it and the microscopes are so adjusted
that the spider web lines in the microscope exactly intersect the lines
A and B on the standard, when the microscope carriage abuts against the
heads H, Fig. 1352. The standard bar is then replaced by the bar to be
tested, which is adjusted without altering the microscope adjustment or
the heads H, and if the spider web lines in the microscope exactly
coincide with and intersect the lines A and B, the copy corresponds to
the standard. But if they do not coincide, then the amount of error may
be found by the micrometer wheel G, Fig. 1353.
[Illustration: Fig. 1356.]
In this test the carriage is moved up against the stops H several times,
and several readings or tests are made, so as to see that the force of
the contact of the carriage against the stops H is uniform at each test,
and if any variation is found, the average of a number of readings is
taken. It is found, however, that with practice the carriage may be
moved against the head H by means of the hand-wheel with such an equal
degree of force that an error of not more than one fifty-thousandth of
an inch is induced. It is found, however, that if too much time is
occupied in this test, the heat of the operator's body will affect the
temperature of the bars, and therefore expand them and vitiate the
comparison. But in this connection it may be noted that if a bar is at a
temperature of 40°, and is placed in an ice bath, it does not show any
contraction in less than one minute, and that when it does so, the
contraction is irregular, taking place in sudden movements or impulses.
Professor Rogers' methods of testing end measures are as follows: To
compare a line with an end measure, a standard bar is set upon the
machine, its horizontal and vertical lines being adjusted true to the
cylindrical guides by the means already described, and the microscope
carriage is so adjusted that the spider web lines of the microscope
coincide with the horizontal and vertical lines marked on the standard,
while at the same time the stop (U, Fig. 1350) on the carriage K has
contact with the fixed stop (V, Fig. 1350.) Carriage K is then moved
along the cylindrical guides so as to admit the bar (whose end measure
is to be compared with the lines on the standard) between the two stops,
and if, with the bar touched by both stops U and V, the microscope
spider lines intersect the vertical and horizontal line on the standard
bar, then the end measure corresponds to the line measure; whereas, if
such is not the case, the amount of error may be found by noting how
much movement of the micrometer wheel of the microscope is required to
cause the lines to intersect.
It is obvious that in this test, if the cylindrical guides had a
horizontal curvature, the test would not be perfect.
THE HORIZONTAL CURVATURE.--The copy or bar to be tested may be set
between the stops, and the standard bar may be placed on one side of it,
as in Fig. 1356, and the test be made as already described. It is then
set the same distance from the bar to be tested, but on the other side
of it, as in figure, and again adjusted for position and tested, and if
the readings on the standard bar are the same in both tests, it is proof
that the measurements are correct.
Suppose, for example, that the cylindrical guides were curved as in Fig.
1356, it is evident that the vertical lines would appear closer together
on the standard bar when in the first position than when in the second
position.
In the Rogers machine the amount of error due to curvature in the
cylindrical guides in this direction is found to be about 1/5000 part of
an inch in 39 inches, corresponding to a radius of curvature of five
miles.
[Illustration: Fig. 1357.]
[Illustration: Fig. 1358.]
Another method of testing an end with a line measure is as follows: The
bar to be measured is shaped as in Fig. 1357, the end measurement being
taken at A, and the projection B at each end serving to preserve the end
surfaces A from damage. The standard bar is then set upon the machine
and its horizontal and vertical lines adjusted in position as before
described. In connection with this adjustment, however, the bar to be
tested is set as in Fig. 1358; C being a block of metal (having marked
centrally upon it horizontal and vertical lines), placed between the bar
and the fixed stop U, its vertical line being in line with the vertical
line on the standard. This adjustment being made, the block C is removed
and placed at the other end of the bar, as shown in Fig. 1359, when, if
the end measure on the bar corresponds with the line measure on the
standard, the vertical line at the other end of the standard will
correspond with the vertical line on block C.
[Illustration: Fig. 1359.]
To prove that the vertical line is exactly equidistant from each end of
the block C, all that is necessary is to place it between the bar and
the fixed stop U, Fig. 1350, adjust the microscope to it and then turn
it end for end, and if its vertical line is still in line with the
spider web of the microscope it is proof that it is central on the
block, while if it is not central the necessary correction may be made.
It is obvious that it is no matter what the length of C may be so long
as its vertical line is central in its length.
In this process the coincidence of the vertical lines on the standard
and on the piece C are employed to test the end measure on the bar with
the line measure on the standard.
[Illustration: Fig. 1360.--General View.]
[Illustration: Fig. 1361.--Plan.]
Figs. 1360 and 1361 represent the Whitworth Millionth Measuring Machine,
in which the measurement is taken by the readings of an index wheel, and
the contact is determined from the sense of touch and the force of
gravity.
It is obvious that in measuring very minute fractions of an inch one of
the main difficulties that arise is that the pressure of contact between
the measuring machine and the surfaces measured must be maintained
constant in degree, because any difference in this pressure vitiates the
accuracy of the measurement. This pressure should also be as small as is
consistent with the assurance that contact actually exists, otherwise
the parts will spring, and this would again impair the accuracy of the
measurement.
If the degree of contact is regulated by devices connected with the
moving mechanism of the machine it is indirect, and may vary from causes
acting upon that mechanism. But if it is regulated between the work and
the moving piece that measures it, nothing remains but to devise some
means of making its degree or amount constant for all measurements; so
that if a duplicate requires to be compared with a standard, the latter
may first be measured and the duplicate be afterwards measured for
comparison.
All that is essential is that the two be touched with an equal degree
of contact, and the most ingenious and delicate method yet devised to
accomplish this result is that in the Whitworth machine, whose
construction is as follows:--
In a box frame A, is provided a slide-way for two square bars, B, C,
which are operated by micrometer screws, one of which is shown at J (the
cap over B being removed to expose B and J to view). The bars B, C, are
made truly square, and each side a true plane. The groove or slide-way
in which they traverse is made with its two sides true planes at a right
angle to each other; so that the bars in approaching or receding from
each other move with their axes in a straight line. At the two ends of
the frame the micrometer screws are afforded journal bearings. The ends
of the bars B, C, are true planes at a right angle to the axes of B, C.
Bar B is operated as follows: Its operating screw J has a thread of 1/20
inch pitch; or in other words, there are twenty threads in an inch of
its length. It is rotated by the hand-wheel F, whose rim-face is
graduated by 250 equidistant lines of division. Moving F through a
distance equal to that between, or from centre to centre of its lines of
division, moves B through a distance equal to one five-thousandth part
of an inch.
The screw in head I for operating bar C also has a pitch of 1/20 inch
(or twenty threads in an inch of its length), and is driven by a
worm-wheel W, having 200 teeth. This worm-wheel W is driven by a worm or
tangent-screw H, having upon its stem a graduated wheel G, having 250
equidistant lines marked upon the face of its rim.
Suppose, then, that wheel G be moved through a distance equal to that
between its lines of division, that is 1/250th of a rotation, then the
worm H will move through 1/250th of a rotation, and the worm-wheel on
the micrometer screw will be rotated 1/250th part of its pitch expressed
in inches; because a full rotation of G would move the worm one
rotation, and thus would move the worm-wheel on the screw one tooth
only, whereas it has 200 teeth in its circumference; hence it is obvious
that moving graduated wheel G, through a distance equal to one of its
rim divisions will move the bar C the one-millionth of an inch; because:
Pitch of Rotation of Rotation of
thread worm-wheel graduated wheel
1/20 inch × 1/200 × 1/250 = 1/1000000
[Illustration: Fig. 1362.]
Fixed pointers, as K, Fig. 1362, enable the amount of movement or
rotation of the respective wheels F, G, to be read.
A peculiarly valuable feature of this machine is the means by which it
enables an equal pressure of contact to be had upon the standards, and
the duplicates to be tested therewith. This feature is of great
importance where fine and accurate measurements are to be taken. The
means of accomplishing this end are as follows:--
In the figures, D is a piece in position to be measured, and between it
and the bar C is a feeler consisting of a small flat strip of steel, E
E, having parallel sides, which are true planes.
When the pressure of contact upon this piece E E is such that if one end
be supported independently the other will just be supported by friction,
and yet may be easily moved between D and C by a touch of the finger,
the adjustment is complete. At the sides of the frame A are two small
brackets, shown at K, in the end view, Fig. 1362, E E being shown in
full lines resting upon them, and in dotted lines with one end
suspended. The contact-adjustment may thus be made with much greater
delicacy and accuracy than in those machines in which the friction is
applied to the graduated wheel-rim, because in the latter case, whatever
friction there may be is multiplied by the difference in the amount of
movement of the graduated rim and that of the bar touching the work.
All that is necessary in the Whitworth machine is to let E E be easy of
movement under a slight touch, though capable of suspending one end by
friction, and to note the position of the lines of graduation on C with
reference to its pointer. By reason of having two operative bars, B, C,
that which can be most readily moved may be operated to admit the piece
or to adjust the bars to suit the length of the work, while that having
the finer adjustive motion, as C, may be used for the final measuring
only, thus preserving it from use, and therefore from wear as much as
possible; or coarser measurements may be made with one bar, and more
minute ones with the other.
So delicate and accurate are the measurements taken with this machine,
that it is stated by C. P. B. Shelley, C.E., in his "Workshop
Appliances," that if well protected from changes of temperature and from
dust, a momentary contact of the finger-nail will suffice to produce a
measurable expansion by reason of the heat imparted to the metal. In an
iron bar 36 inches long, a space equal to half a division on the wheel G
having been rendered distinctly measurable by it, this space indicating
an amount of expansion in the 36-inch bar equals the one two-millionth
part of an inch!
The following figures, which are taken from _Mechanics_, represent a
measuring machine made by the Betts Machine Company, of Wilmington,
Delaware.
[Illustration: Fig. 1363.]
Fig. 1363 shows a vertical section through the length of the machine,
which consists of a bed carrying a fixed and an adjustable head, the
fixed head carrying the measuring screw and vernier while the adjustable
one carries a screw for approximate adjustment in setting the points of
the standard bars.
These screws have a pitch of ten threads per inch, and the range of the
measuring screw has a range of 4 inches, and the machine is furnished
with firm standard steel bars (4-inch, 6-inch, 18-inch, and 24-inch).
The measuring points of the screws are of hardened steel, secured
axially in line with the screws, and of two forms, with spherical and
flat points, one set of each being used at a time. The larger wheel C is
indexed to 1000 divisions, each division representing the ten-thousandth
of an inch at the points; the smaller wheel has 100 divisions, each
representing the one-thousandth part of an inch at the points. Beside,
and almost in contact with, the larger wheel is a movable or adjustable
pointer E, upon which the error of the screw is indexed for each inch of
its length; the screw error is of the utmost importance when positive
results are desired. The screw is immersed in oil to maintain a uniform
temperature throughout its length, and to avoid particles of dust
accumulating on its surface.
[Illustration: Fig. 1364.]
As stated above, the readings are indexed to the ten-thousandth part of
an inch, but variations to the hundred-thousandth part of an inch can be
indicated. The machine will take in pieces to 24 inches in length, and
to 4 inches in diameter. In measuring, the points are brought into easy
contact and then expanded by turning the larger wheel, counting the
revolutions or parts of revolutions to determine the distance between
the points or the size of what is to be measured. The smaller machine is
constructed so as to indicate by means of vernier attachment to the
ten-thousandth part of an inch, and is of value in tool-rooms where
standard and special tools are continually being prepared. By its use,
gauges and other exact tools can be made, and at the same time keep
gauges of all kinds to standard size by detecting wear or derangement.
The machine consists of a frame with one fixed head; the other head is
moved by a screw; on both heads are hardened steel points. As with the
larger machine, the screw error is indicated in such a manner as to
permit the operator to guard against reproducing its error in its work.
These machines are used for making gauges, reamers, drills, mandrels,
taps, and so on.
The errors that may exist in the pitch of the measuring screw are taken
into account as follows: The points of the measuring machine should be
brought into light contact, the position of index-wheel, vernier, and
the adjustable pointer which has the screw error indexed upon it should
be as in Fig. 1364; that is, the zeros on index-wheel and vernier should
be in exact line, the vernier covering half of the zero line on pointer.
To measure 1/2 inch, for illustration, five complete revolutions of
index-wheel should produce 1/2 inch, and would if we had a perfect
screw, but the screw is not perfect, and we must add to the measurement
already obtained one-half of the space, stamped upon corrective devise,
0-1. This space 0-1 represents the whole error in the screw from zero to
1 inch. The backlash of the screw should always be taken up.
[Illustration: Fig. 1365.]
[Illustration: Fig. 1366.]
[Illustration: Fig. 1367.]
[Illustration: Fig. 1368.]
The details of this machine are as follows:--
In Fig. 1363 the points G are those between which the measuring is done,
and the slide held by the nut K in position is adjusted by means of inch
bars to the distance to be measured; H, the hand-wheel for moving one
point, and F the wheel which moves the other. Fig. 1366 is a cross
section of the movable head through the nut K and stud M, by which the
movable head is adjusted, and Fig. 1365 is a cross section through the
fixed head. The bars used in setting the machine are shown in Fig. 1367,
and in Fig. 1368 the points of the measuring screws are shown on a large
scale. The other figures show various details of the machine and their
method of construction. The vernier, it will be observed, is a double
one. This is shown in Fig. 1364, and is so arranged that the zero is
made movable in order to correct the errors of the screw itself. These
errors are carefully investigated and a record made of each. Thus, in
Fig. 1363 the arm E is graduated so as to show the true zero for
different parts of the screw; D can then be adjusted to a correct
reading, and the divisions on the large wheel will then be correct to an
exceedingly small fraction. This method of construction enables the
machine to be used for indicating very minute variations of length.
[Illustration: Fig. 1369.]
In Fig. 1369 is shown a measuring machine designed by Professor John E.
Sweet, late of Cornell University. The bed of the machine rests on three
feet, so that the amount of support at each leg may remain the same,
whether the surface upon which it rests be a true plane or otherwise.
This bed carries a headstock and a tailstock similar to a lathe. The
tailstock carries a stationary feeler, and the headstock a movable one,
operated horizontally by a screw passing through a nut provided in the
headstock, the axial lines of the two feelers being parallel and in the
same plane. The diameters of the two feelers are equal at the ends, so
that each feeler shall present the same amount of end area to the work.
The nut for the screw operating the headstock feeler is of the same
length as the screw itself, so that the wear of the screw shall be
equalized as near as possible from end to end, and not be the most at
and near the middle of its length, as occurs when the thread on the
screw is longer than that in the nut.
The pitch of the thread on the screw is 16 threads in an inch of length,
hence one revolution of the screw advances the feeler 1/16 inch. The
screw carries a wheel whose circumference is marked or graduated by 625
equidistant lines of division. If, therefore, this wheel be moved
through a part of a rotation equal to one of these divisions, the feeler
will move a distance equal to 1/625 of the 1/16th of an inch, which is
the ten thousandth part of an inch, and as the bed of the machine is
long enough to permit the feelers to be placed 12 inches apart, the
machine will measure from zero to 12 inches by the ten-thousandth of an
inch.
To assist the eye in reading the lines of division, each tenth line is
marked longer than the rest, and every hundredth, still longer. The
pitch of the screw being 16 threads to an inch enables the feeler to be
advanced or retired (according to the direction of the rotation of the
wheel) a sixteenth inch by a simple rotation of the wheel, an eighth
inch by two wheel rotations, a thirty-second inch by a quarter rotation,
and so on; and this renders the use of that machine very simple for
testing the accuracy of caliper gauges, that are graduated to 1/8, 1/16,
1/32, 1/64th inch, and so on, such a gauge being shown (in the cut)
between the feelers.
The bar or arm shown fixed to the headstock and passing over the
circumference of the wheel at the top affords a fixed line or point
wherefrom to note the motion of the wheel, or in other words, the number
of graduations it moves through at each wheel movement. It is evident
that in a machine of this kind it is essential that the work to be
measured have contact with the feelers, but that it shall not be
sufficient to cause a strain or force that will spring or deflect either
the work itself (if it be slight) or the parts of the machine. It is
also essential that at excessive measurements the feelers shall touch
the work with the same amount of force. The manner of attaining this end
in Professor Sweet's machine is as follows: Upon the same shaft as the
wheel is an arm having contact at both ends with the edge of the wheel
rim whose face is graduated. This arm is free to rotate upon the shaft
carrying the graduated wheel, which it therefore drives by multiple
friction on its edges at diametrically opposite points; by means of a
nut the degree of this friction may be adjusted so as to be just
sufficient to drive the wheel without slip when the wheel is moved
slowly. So long, then, as the feelers have no contact with the piece to
be measured, the arm will drive the graduated wheel, but when contact
does take place the wheel will be arrested and the arm will slip. The
greatest accuracy will therefore be obtained if the arm be moved at an
equal speed for all measurements.
[Illustration: Fig. 1370.]
Fig. 1370 represents a Brown and Sharpe measuring machine for sheet
metal. It consists of a stand A with a slotted upright having an
adjusting screw C above, and a screw D, with a milled head and carrying
a dial, passing through its lower part. One turn of the screw, whose
threads are 1/10th inch apart, causes one rotation of the dial, the edge
of which is divided into one hundred parts, enabling measurements to be
made to thousandths of an inch. The sheet-metal to be gauged is inserted
in the slot of the upright. The adjusting-screw is set so that when the
points of the two screws meet, the zero of the dial shall be opposite an
index or pointer which shows the number of divisions passed over, and is
firmly secured by a set-screw.
Next in importance to line and end measurements is the accurate division
of the circle, to accomplish which the following means have been taken.
What is known as "Troughton's" method (which was invented by Edward
Troughton about 1809) is as follows: A disk or circle of 4 feet radius
was accurately turned, both on its face and its inner and outer edges. A
roller was next provided of such diameter that it revolved sixteen times
on its own axis, while rolling once round the outer edge of the circle.
This roller was pivoted in a framework which could be slid freely, yet
tightly, along the circle, the roller meanwhile revolving by frictional
contact on the outer edge. The roller was also, after having been
properly adjusted as to size, divided as accurately as possible into
sixteen equal parts by lines parallel to its axis. While the frame
carrying the roller was moved once round along the circle, the points of
contact of the roller divisions with the circle were accurately observed
by two microscopes attached to the frames, one of which commanded the
ring on the circle near its edge, which was to receive the divisions,
and the other viewed the roller divisions. The exact points of contact
thus ascertained were marked with faint dots, and the meridian circle
thereby divided into 256 very nearly equal parts.
The next part of the operation was to find out and tabulate the errors
of these dots, which are called apparent errors, because the error of
each dot was ascertained on the supposition that all its neighbors were
correct. For this purpose two microscopes, which we shall call A and C,
were taken with cross-wires and micrometer adjustments, consisting of a
screw and head divided into 100 divisions, 50 of which read in the one
and 50 in the opposite direction. These microscopes, A and B, were fixed
so that their cross-wires respectively bisected the dots 0 and 128,
which were supposed to be diametrically opposite. The circle was now
turned half way round on its axis, so that dot 128 coincided with the
wire of A, and should dot 0 be found to coincide with B, then the dots
were sure to be 180° apart. If not, the cross-wire of B was moved till
it coincided with the dot 0 and the number of divisions of micrometer
head noted. Half this number gave clearly the error of dot 128 and was
tabulated plus or minus according as the arcual distance between 0 and
128 was found to exceed or fall short of the removing part of the
circumference. The microscope B was now shifted, A remaining opposite
dot 0 as before, till its wire bisected dot 64, and by giving the circle
one-quarter of a turn on its axis, the difference of the arcs between
dots 0 and 64, and between 64 and 128 was obtained. The half of this
distance gave the apparent error of dot 64, which was tabulated with its
proper sign. With the microscope A still in the same position, the error
of dot 192 was obtained, and in the same way, by shifting B to dot 32,
the errors of dots 32, 96, 160 and 224 were successively ascertained. By
proceeding in this way the apparent errors of all the 256 dots were
tabulated.
In order to make this method fully understood, we have prepared the
accompanying diagrams, which clearly show the plan pursued.
[Illustration: Fig. 1371.]
Fig. 1371 illustrates the plan of dividing the large circle by means of
the roller B.
[Illustration: Fig. 1372.]
Fig. 1372 shows the general adjustment of the microscope for the purpose
of proving the correctness of the divisions.
[Illustration: Fig. 1373.]
Fig. 1373 shows the location of the microscope over the points 0 and
128.
[Illustration: Fig. 1374.]
Fig. 1374 shows the circle turned half-way round, the points 0 and 128
coinciding with the cross threads of the microscope.
[Illustration: Fig. 1375.]
Fig. 1375 shows a similar reading, in which the points do not coincide
with the cross threads of the microscope.
[Illustration: Fig. 1376.]
Fig. 1376 shows the microscope adjusted for testing by turning the
circle a quarter revolution.
Fig. 1377 represents one of the later forms of Ramsden's dividing
engine.[21] It consists first of a three-legged table, braced so as to
be exceedingly stiff. Upon this is placed a horizontal wheel with deep
webs, and a flat rim. The webs stiffen the wheel as much as possible,
and one of these webs, which runs round the wheel about half-way between
the centre and the circumference, rests upon a series of rollers which
support it, and prevent, as far as possible, the arms from being
deflected by their own weight. An outer circle, which receives the
graduation, is laid upon the rim of the wheel and secured in place. The
edge of this circle is made concave. A very fine screw, mounted in boxes
and supported independently, is then brought against this hollow edge,
and, being pressed against it, the screw, when revolved, of course cuts
a series of teeth in the circumference, and this tooth-cutting,
facilitated by having the screw threads made with teeth, was continued
until perfect [V]-shaped teeth were cut all around the edge of the
wheel. This Mr. Ramsden calls ratching the wheel. The number of teeth,
the circumference of the wheel, and the pitch of the screw were all
carefully adjusted, so that by using 2160 teeth, six revolutions of the
screw would move the wheel the space of 1°. When this work was finished,
and the adjustment had been made as perfect as possible, a screw without
teeth--that is, one in which the thread was perfect--was put in the
place of that which had cut the teeth from the wheel, and the machine
was perfected. The wheel A B C in the drawings is made of bell metal,
and turns in a socket under the stand, which prevents the wheel from
sliding from the supporting or friction rolls Z, Z. The centre R,
working against the spindle M, is made so as to fit instruments of
various sizes. The large wheel has a radius of 45 inches, and has 10
arms. The ring B is 24 inches in diameter by 3 inches deep. The ring C
is of very fine brass, fitting exactly on the circumference of the
wheel, and fastened by screws, which, after being screwed home, were
well riveted. Great care was taken in making the centre on which the
wheel worked exceedingly true and perfect, and in making the socket for
the wheel fit as exactly as possible. The revolving mechanism is all
carried on the pillar P, resting on the socket C´. We may state here
that the machine, as shown in the engravings, now in the possession of
the Stevens Institute, is in some respects slightly improved on that
shown in the original drawings published in "Rees' Cyclopædia" in 1819.
After the wheel was put on its stand, and the pulleys in place, the
instrument was ready for the turning mechanism. The upper part of this
pillar P carries the framework in which the traversing screw revolves.
[21] From _Mechanics_.
In Fig. 1378 D is the head of this pillar, P the screw which turns the
wheel. E^{1} E^{1} are the boxes, which are made conical so as to
prevent any shake and to hold the screw firmly. Circles of brass, F and
V, are placed on the arbor of the screw, and as their circumference is
divided into 60 parts, each division consequently amounts to a motion of
the wheel of 10 seconds, and 60 of them will equal 1 minute. Revolution
is given to the screw by means of the treadle B´ and the cord Y, which
runs over the guiding screw W, Fig. 1379, and is finally attached to the
box U. A spring enclosed in the box U causes it to revolve, and winds up
the slack of the cord whenever the treadle is relieved. In the original
drawing the head of the pillar P was carried in a parallel slip in the
piece surrounding its head. The construction as shown in Fig. 1379 is
somewhat different. The result attained, however, is identical, and the
spindles and attachments are held so as to have no lateral motion. The
wheels V and X have stops upon them, so arranged that the screw may be
turned definitely to a given point and stopped. These wheels are at the
opposite ends of the screw W. A detail of one of them is shown at V in
Fig. 1380, where X is the ratchet-wheel. This figure also illustrates
the construction of the bearings for the screw arbor. We have not space
to explain the method by which the perfection of the screw was obtained,
nor to discuss the means by which was obtained the success of so
eliminating the errors as to make the division of the instrument more
perfect than anything which had been attempted previously. Success,
however, was obtained, and by means of the first or tooth-cutting screw
the teeth were brought to such a considerable uniformity that, together
with the fact that the screw took hold of a number of teeth at one time,
most of the errors which would have been expected from this method of
operation were eliminated. The method of ruling lines upon the
instrument was most ingenious. The frame L L, is connected to the head
D, of the pillar P in front, by the clamps I and K, and to the centre M
by the block R. A frame N N stiffens the back. The blocks O, O on the
frame Q´ are secured to the frame L L, by set-screws C, C.
[Illustration: Fig. 1377.]
Fig. 1381 shows a side view of the frame Q´, which it is seen carries a
[V]-shaped piece Q, which in turn carries another [V]-shaped piece S,
Fig. 1378. The piece Q is supported on pointed screws _d_, _d_, and the
piece S is supported on two similar screws _f_, _f_. The point of this
piece S carries the cutting tool E, Fig. 1378. Of course S can move only
in a radial line from the centre M towards the circumference. If the
sextant, octant, or other instrument be fastened to the large wheel A,
with its centre at M, and the large wheel be rotated by the screw, all
lines drawn upon it by E will be radial, and the distances apart will be
governed by the number of turns made by the screw. This improvement, we
think, was originated by Mr. Ramsden, and was a very great advance over
the old method of the straight-edge, and has been used in some of the
Government comparators and dividing engines. The following is Mr.
Ramsden's own description of the graduation of the machine, and of his
method of operating it. It shows the extreme care which he took in
correcting the mechanical errors in the construction:--
"From a very exact centre a circle was described on the ring C, about
4/10 inch within where the bottom of the teeth would come. This circle
was divided with the greatest exactness I was capable of, first into
five parts, and each of these into three. These parts were then bisected
four times; that is to say, supposing the whole circumference of the
wheel to contain 2160 teeth, this being divided into five parts, and
these again divided into three parts, each third part would contain 144,
and this space, bisected four times, would give 72, 36, 18, 9;
therefore, each of the last divisions would contain 9 teeth. But, as I
was apprehensive some error might arise from quinquesection and
trisection, in order to examine the accuracy of the divisions, I
described another circle on the ring C, Fig. 1378, 1/10 inch within the
first, and divided it by continual bisection, as 2160, 1080, 540, 270,
135, 67-1/2, 33-3/4, and, as the fixed wire (to be described presently)
crossed both the circles, I could examine their agreement at every 135
revolutions (after ratching could examine it at every 33-3/4); but not
finding any sensible difference between the two sets of divisions, I,
for ratching, made choice of the former, and, as the coincidence of the
fixed wire with an intersection could be more exactly determined with a
dot or division, I therefore made use of intersections on both sides,
before described.
"The arms of the frame L, Fig. 1381, were connected by a thin piece of
brass, 3/4 inch broad, having a hole in the middle 4/10 inch in
diameter; across this hole a silver wire was fixed, exactly in a line to
the centre of the wheel; the coincidence of this wire with the
intersections was examined by a lens of 1/10 inch focus, fixed in a tube
which was attached to one of the arms L. Now (a handle or winch being
fixed on the end of the screw) the division marked 10 on the circle F
was set to its index, and, by means of a clamp and adjusting-screw for
that purpose, the intersection marked I on the circle C´ was set exactly
to coincide with the fixed wire. The screw was then carefully pressed
against the circumference of the wheel by turning the finger-screw _h_;
then, removing the clamp, I turned the screw by its handle nine
revolutions, till the intersection marked 240 came nearly to the wire.
Then, turning the finger-screw _h_, I released the screw from the wheel,
and turned the wheel back till the intersection marked 2 exactly
coincided with the wire, and by means of the clamp before mentioned, the
division 10 on the circle being set to its index, the screw was pressed
against the edges of the wheel by the finger-screw _h_, the clamps were
removed, and the screw turned nine revolutions, till the intersection
marked I nearly coincided with the fixed wire; the screw was released
from the wheel by turning finger-screw _h_ as before, the wheel was
turned back till intersection marked 3 coincided with the fixed wire;
the division 10 in the circle being set to its index, the screw was
pressed against the wheel as before, and the screw turned nine
revolutions, till intersection 2 was nearly coincident with the fixed
wire, and the screw released, and I proceeded in this manner till the
teeth were marked round the whole circumference of the wheel. This was
repeated three times round to make the impressions deeper. I then
ratched the wheel round continuously in the same direction, without ever
disengaging the screw, and, in ratching the wheel about 300 times round,
the teeth were finished.
[Illustration: Fig. 1378.]
"Now, it is evident that if the circumference of the wheel was even one
tooth, or ten minutes, greater than the screw would require, this error
would, in the first instance, be reduced by 1/240 part of a revolution,
or two seconds and a half, and these errors or inequalities of the teeth
were equally distributed round the wheel at the distance of nine teeth
from each other. Now, as the screw in ratching had continual hold of
several teeth at the same time and thus constantly changing, the
above-mentioned irregularities soon corrected themselves, and the teeth
were reduced to a perfect equality. The piece of brass which carried the
wire was now taken away, and the cutting-screw was also removed, and a
plain one put in its place. At one end of the screw arbor, or mandrel
was a small brass circle F, having its edge divided into 60 parts,
numbered at every sixth division, as before mentioned. On the other end
of the screw is a ratchet-wheel V (X, Fig. 1380) having 60 teeth,
covered by the hollow circle (V, Fig. 1380), which carries two clicks
that catch upon opposite sides of the ratchet-wheel. When the screw is
to be moved forward, the cylinder W turns on a strong steel arbor E´´,
which passes through the piece X´; this piece, for greater firmness, is
attached to the screw-frame by the braces _w_. A spiral groove or thread
is cut upon the outside of the cylinder W, which serves both for holding
the string and also giving motion to the lever I on its centre, by means
of a steel tooth _v_, that works between the threads of the spiral. To
the lever is attached a strong steel pin _m_, on which a brass socket
turns; this socket passes through a slit in the piece _u_, and may be
tightened in any part of the slit by the finger-nut _y_. This piece
serves to regulate the number of revolutions of the screw for each tread
of the treadle B´."
[Illustration: Fig. 1379.]
[Illustration: Fig. 1380.]
[Illustration: Fig. 1381.]
[Illustration: Fig. 1382.]
Figs. 1382, 1383, and 1384 represent a method adopted to divide a circle
by the Pratt and Whitney Company. The principle of the device is to
enable the wheel to be marked, to be moved through a part of a
revolution equal to the length of a division, and to test the accuracy
of the divisions by the coincidence of the line first marked with that
marked last when the wheel has been moved as many times as it is to
contain divisions. By this means any error in the division multiplies,
so that the last division marked will exhibit it multiplied by as many
times as there are divisions in the whole wheel. The accuracy of this
method, so long as variations of temperature are avoided, both in the
marking and the drilling of the wheel, appears to be beyond question. In
the figures, W represents a segment of the wheel to be divided, and C
what may be termed a dividing chuck. The wheel is mounted on an arbor in
a gear-cutting machine. On the hub of the wheel (which has been turned
up for the purpose) there is fitted, to a close working fit, a bore at
the end of an arm, the other end of the arm being denoted by A in the
figures. The dividing chuck is fitted to the slide S of the gear-cutting
machine, and is of the following construction.
Between two lugs, B and B´, it receives the end of arm A. These lugs are
provided with set-screws, the distance between the ends of which
regulate the amount of movement of the end of arm A. Upon A is the slide
D, carrying the piece E, in which is the marking tool F, the latter
being lifted by a spring G, and, therefore, having no contact with the
wheel surface until the spring is depressed. H is an opening through the
arm A to permit the marking tool F to meet the wheel face, as shown in
Fig. 1384, which is an end view of the slide showing the arm A in
section. The face of the wheel rests upon the chuck on each side of the
arm at the points I, J, and may be clamped thereto by the clamps K. The
arm may be clamped to the wheel by the clamp shown dotted in at L, the
bolt passing up and through the screw handle M. N is simply a lever with
which to move the arm A, or arm A and the wheel. Suppose all the parts
to be in the position shown in the cuts, the clamps being all tightened
up, the slide D may be moved forward towards K, while the spring is
depressed, and F will mark a line upon the wheel. The handle M may then
be released and arm A moved until it touches the set-screw in B´, when M
may be tightened and another line marked. Clamps K are then tightened,
and the wheel, with the arm A fast to it, moved back to the position
shown in the cut, when the clamps may be tightened again and another
line marked, the process being continued all round the wheel. To detect
and enable the correction of any discoverable error in a division, there
is provided the plate P, having upon it three lines of division (which
have been marked simultaneously with three of the lines marked on the
wheel). This plate is supported by an arm or bracket Q, on the rear edge
of which are three notches R to hold a microscope, by means of which the
lines on P may be compared with those on the wheel face, so that if any
discrepancy should appear it may be determined which line is in error.
The labor involved in the operation of marking a large wheel is very
great. Suppose, for example, that a wheel has 200 lines of division, and
that after going round the wheel as described it is found that the last
division is 100th inch out; then in each division the error is the
two-hundredth part of this 100th inch, and that is all the alteration
that must be made in the distance between set-screws B and B´.
[Illustration: Fig. 1383.]
[Illustration: Fig. 1384.]
Figs. 1385 and 1386 represent a method of originating an index wheel,
adopted by R. Hoe and Co., of New York City.
In this method the plan was adopted of fitting round a wheel 180
tapering blocks, which should form a complete and perfect circle. These
blocks were to serve the same purpose as is ordinarily accomplished by
holes perforated on the face of an index wheel. In their construction,
means of correcting any errors that might be found, without the
necessity of throwing away any portion of the work done, would also be
provided. Further, this means would provide for taking up wear, should
any occur in the course of time, and thus restore the original truth of
the wheel.
Fig. 1385 of the engravings shows the originating wheel mounted upon a
machine or cutting engine. Upon the opposite end of the shaft is the
worm-wheel in the process of cutting. After the master worm-wheel has
been thus prepared by means of the originating wheel, it is used upon
the front end of the shaft, in the position now occupied by the
originating wheel, and operated by a worm in the usual manner.
Subdivisions are made by change wheels. The construction of the
originating wheel will be understood by the smaller engravings.
Fig. 1386 is an enlarged section of a segment of the wheel, while Fig.
1387 is an edge view of this segment. Fig. 1388 is a view of one of the
blocks employed in the construction of the wheel, drawn to full size.
In the rim of the originating wheel there was turned a shoulder, C, Fig.
1387, 5 feet in diameter. Upon this shoulder there were clamped 180
blocks, of the character shown in Fig. 1386, as indicated by the
section, Fig. 1387. These blocks were secured to the face of the wheel D
by screws E, and were held down to the shoulder by the screw and clamp G
F, shown in Fig. 1387. (They are omitted in Fig. 1385 for clearness of
illustration.) In the preparation of these blocks each was fitted to a
template T, in Fig. 1388, and was provided with a recess B, to save
trouble in fitting and to insure each block seating firmly on the
shoulder C. The shoulder, after successive trials, was finally reduced
to such a diameter that the last block exactly filled the space left for
it when it was fully seated on the shoulder C. The wheel thus prepared
was mounted on a Whitworth cutting engine, as shown in Fig. 1385. The
general process of using this wheel is as follows: The blocks forming
the periphery of the originating wheel are used in place of the holes
ordinarily seen in the index plates. One of them is removed to receive a
tongue, shown in the centre of Fig. 1385, which, exactly filling the
opening or notch thus made, holds the wheel firmly in place. After a
tooth has been cut in the master worm-wheel, shown at the back of Fig.
1385, the block in the edge of the originating wheel corresponding to
the next tooth to be cut is removed. The tongue is withdrawn from the
first notch, the wheel is revolved, and the tongue is inserted in the
second position. The block first removed is then replaced, and the
cutting proceeds as before. This operation is repeated until all the
teeth in the master wheel have been cut. The space being a taper, the
tongue holds the originating wheel more firmly than is possible by means
of cylindrical pins fitting into holes. The number of blocks in the
originating wheel being 180, the teeth cut in the master wheel may be
180 or some exact divisor of this number.
The advantages of this method of origination are quite evident. Since
180 blocks were made to fill the circle, the edges of each had 2° taper.
This taper enabled the blocks to be fitted perfectly to the template,
because any error in fit would be remedied by letting the block farther
down into the template. Hence, it was possible to correct any error that
was discovered without throwing the block away. Further, as the blocks
themselves are removed to form a recess for locking the originating
wheel in position while cutting the worm-wheel, the truth of the work is
not subject to the errors that creep in when holes or notches require to
be pierced in the originating wheel. Such errors arise from the heating
due to the drilling or cutting, from the wear of the tools or from their
guides, from soft or hard spots in the metal and other similar causes.
To avoid any error from the heating due to the cut on the worm-wheel, in
producing master wheels, Messrs. Hoe and Co. allowed the wheel to cool
after each cut. The teeth were cut in the following order: The first
three were cut at equidistant points in the circumference of the wheel.
The next three also were at equidistant points, and midway between
those first cut. This plan was continued until all the teeth were cut,
thus making the expansion of the wheel from the heat as nearly equal as
possible in all directions.
There is one feature in this plan that is of value. It is that a certain
number of blocks, for example six, may be taken out at two or three
different parts of the originating wheel and interchanged, thus
affording a means of testing that does not exist in any other method of
dividing.
The tools applied by the workmen to measure or to test work may be
divided into classes.
1st. Those used to determine the actual size or dimension of the work,
which may be properly termed measuring tools.
2nd. Those used as standards of a certain size, which may be termed
gauges.
3rd. Those used to compare one dimension with another, as in the common
calipers.
4th. Those used to transfer measurements or distances defined by lines.
5th. Those used to test the accuracy of plane or flat surfaces, or to
test the alignment of one surface to another.
Referring to the first, their distinctive feature is that they give the
actual dimensions of the piece, whether it be of the required dimension
or not.
The second determine whether the piece tested is of correct size or not,
but do not show what the amount of error is, if there be any.
The third show whatever error there may be, but do not define its
amount; and the same is true of the fifth and sixth.
Fig. 1389 represents a micrometer caliper for taking minute end
measurements. This instrument is capable of being set to a standard
measurement or of giving the actual size of a piece, and is therefore
strictly speaking a combined measuring tool and a gauge. The [U]-shaped
body of the instrument is provided with a hub _a_, which is threaded to
receive a screw C, the latter being in one piece with the stem D, which
envelops for a certain distance the hub _a_. The thread of C has a pitch
of 40 per inch; hence one revolution of D causes the screw to move
endways 1/40 of an inch.
The vertical lines of division shown on the hub _a_ are also 1/40 of an
inch apart, hence the bevelled edge of the sleeve advances one of the
divisions on _a_ at each rotation.
This bevelled edge is divided into 25 equal divisions round its
circumference, as denoted by the lines marked 5, 10, &c. If, then, D be
rotated to an amount equal to one of its points of division, the screw
will advance 1/25 of 1/40 of an inch. In the cut, for example, the line
5 on the sleeve coincides with the zero line which runs parallel to the
axial line of the hub. Now suppose sleeve D to be rotated so that the
next line of division on the bevelled edge of D comes opposite to the
zero line, then 1/25 part of a revolution of D will have been made, and
as a full revolution of D would advance the screw 1/40 of an inch, then
1/25 of a revolution will advance it 1/25 of 1/40 inch, which is 1/1000
inch.
The zero line being divided by lines of equal division into 40ths of an
inch, then, as shown in the cut, the instrument is set to measure
3/40ths and 5/25ths of a fortieth.
It is to be observed that to obtain correct measurements the work must
be held true with the face of the foot B, and the contact between the
end of screw _c_ and the work must be just barely perceptible, otherwise
the pressure of the screw will cause the [U]-piece to bend and vitiate
the accuracy of the measurement. Furthermore, if the screw be rotated
under pressure upon the work, its end will wear and in time impair the
accuracy of the instrument. To take up any wear that may occur, the
foot-piece B is screwed through the hub, holding it so that it may be
screwed through the hub to the amount of the wear.
To avoid wear as much as possible, the screws of instruments of this
kind are sometimes hardened, and to correct the error of pitch induced
in the hardening, each screw is carefully tested to find in what
direction the pitch of the hardened thread has varied, and provision is
made for the correction as follows:--
The zero line on the hub _a_ stands, if the thread is true to pitch,
parallel to the axis of the screw C, but if the pitch of the thread has
become coarser from hardening, this zero line is marked at an angle, as
shown in Fig. 1390, in which A A represents the axial line of the screw
and B the zero line.
If the screw pitch becomes finer from hardening, the zero line is made
at an angle in the opposite direction, as shown in Fig. 1391, the amount
of the angle being that necessary to correct the error in the screw
pitch. The philosophy of this is, that if the pitch has become coarser a
less amount of movement of the screw is necessary, while if it has
become finer an increased movement is necessary. It is obvious, also,
that if the pitch of the thread should become coarser at one end and
finer at the other the zero line may be curved to suit.
[Illustration: Fig. 1392.]
[Illustration: Fig. 1393.]
[Illustration: _VOL. I._ =DIVIDING ENGINE AND MICROMETER.= _PLATE XV._
Fig. 1385.
Fig. 1386.
Fig. 1387.
Fig. 1388.
Fig. 1389.
Fig. 1390.
Fig. 1391.]
Fig. 1392 represents a vernier caliper, in which the measurement is read
by the coincidence of ruled lines upon the following principle. The
vernier is a device for subdividing the readings of any equidistant
lines of division. Its principle of action may be explained as follows:
Suppose in Fig. 1393 A to be a rule or scale divided into inches and
tenths of an inch, and B a vernier so divided that its ten equidistant
divisions are equal to nine of the divisions on A; then the distance
apart of the lines of division on A will be 1/10 inch; but, as the whole
ten divisions on B measure less than an inch, by 1/10 inch, then each
line of division is a tenth part of the lacking tenth less than 1/10
inch apart. Thus, were we to take a space equal to the 1/10 inch between
9 and 10 on A, and divide it into 10 equal parts (which would give ten
parts each measuring 1/100th of an inch) and add one of said parts to
each of the distances between the lines of division on B, then the whole
of the lines on A would coincide with those on B. It becomes evident,
then, that line 1 on B is 1/100 inch below line 1 on A, that line 2 on B
is 2/100 inch below line 2 on A, line 3 on the vernier B is 3/100 inch
below line 3 on the rule A, and so on, until we arrive at line 10 on the
vernier, which is 10/100 or 1/10 inch below line 10 on A. Suppose, then,
the rule or scale to rest vertically on a truly surfaced plate, and a
piece of metal be placed beneath B, the thickness of the piece will be
shown by which of the lines on B coincides with a line on A. For more
minute divisions it is simply necessary to have more lines of division
in a given length on A and B. Thus, if the rule be divided into inches
and fiftieths, and the vernier is so divided that it has 20 equidistant
lines of division to 19 lines on the rule, it will then lack one
division, or 1/50 inch in 20/50 inch, each division on the vernier will
then be the one-twentieth of a fiftieth too short, and as 1/20 of 1/50
is 1/1000, the instrument will read to one-thousandth of an inch.
Let it now be noted that, instead of making the lines of division closer
together to obtain minute measurements, the same end may be obtained by
making the vernier longer. For example, suppose it be required to
measure to 1/2000 part of an inch, then, if the rule or scale be
graduated to inches and fiftieths, and the vernier be graduated to have
40 equidistant lines of division, and 39 of the lines on the scale, the
reading will be to the 1/2000 part of an inch. But, in any event, the
whole of the readings on the vernier may be read, or will be passed
through, while it is traversing a division equal to one of the divisions
on the scale or rule.
In Fig. 1392 is shown a vernier caliper, in which the vernier is
attached to and carried by a slide operating against the inside edge of
the instrument. The bar is marked or graduated on one side by lines
showing inches and fiftieths of an inch, with a vernier graduated to
have 20 equidistant lines of division in 19 of the lines of division on
the bar, and therefore measuring to the 1/1000th of an inch, while the
other side is marked in millimètres with a vernier reading to 1/40th
millimètre, there being also 20 lines of division on the vernier to 19
on the bar.
The inside surfaces of the feet or jaws are relieved from the bar to
about the middle of their lengths, so as to confine the measuring
surfaces to dimensions sufficiently small to insure accurate
measurement, while large enough to provide a bearing area not subject to
rapid wear. If the jaw surface had contact from the point to the bar, it
would be impossible to employ the instrument upon a rectangular having a
burr, or slight projection, on the edge. Again, by confining the bearing
area to as small limits as consistent with the requirements of
durability a smaller area of the measured work is covered, and the
undulations of the same may be more minutely followed.
To maintain the surface of the movable jaw parallel with that of the
bar-jaw, it is necessary that the edge of the slide carrying the vernier
be maintained in proper contact with the edge of the instrument, which,
while adjusting the vernier, should be accomplished as follows:--
The thumb-screw most distant from the vernier should be set up tight, so
that that jaw is fixed in position. The other thumb-screw should be set
so as to exert, on the small spring between its end and the edge of the
bar, a pressure sufficient to bend that spring to almost its full limit,
but not so as to let it grip the bar. The elasticity of the spring will
then hold the edge of the vernier slide sufficiently firmly to the under
edge of the bar to keep the jaw-surfaces parallel; to enable the correct
adjustment of the vernier, and to permit the nut-wheel to move the slide
without undue wear upon its thread, or undue wear between the edge of
the slide and that of the bar, both of which evils will ensue if the
thumb-screw nearest the vernier is screwed firmly home before the final
measuring adjustment of the vernier is accomplished.
When the measurement is completed the second thumb-screw must be set
home and the reading examined again, for correctness, to ascertain if
tightening the screw has altered it, as it would be apt to do if the
thumb-screw was adjusted too loose.
The jaws are tempered to resist wear, and are ground to a true plane
surface, standing at a right angle to the body of the bar. The method of
setting the instrument to a standard size is as follows:--
The zero line marked 0 on the vernier coincides with the line 0 on the
bar when the jaws are close together; hence, when the 0 line on the
vernier coincides with the inch line on the bar, the instrument is set
to an inch between the jaws. When the line next to the 0 line on the
vernier coincides with the line to the left of the inch line on the bar,
the instrument is set to 1-1/1000 inches. If the vernier slide then be
moved so that the second line on the vernier coincides with the second
line, on the left of the inch on the bar, the instrument is set to
1-2/1000 inches, and so on, the measurement of inches and fiftieths of
an inch being obtained by the coincidence of the zero line on the
vernier with the necessary line on the bar, and the measurements of
one-thousands being taken as described.
But if it is required to measure, or find the diameter of an existing
piece of work, the method of measuring is as follows:--
The thumb-screws must be so adjusted as to allow the slide to move
easily or freely upon the work without there being any play or looseness
between the slide and the bar. The slide should be moved up so as to
very nearly touch the work when the latter is placed between the jaws.
The thumb-screw farthest from the vernier should then be screwed home,
and the other thumb-screw operated to further depress the spring without
causing it to lock upon the bar. The nut-wheel is then operated so that
the jaws, placed squarely across the work, shall just have perceptible
contact with it. (If the jaws were set to grip the work tight they would
spring from the pressure, and impair the accuracy of the measurements.)
The thumb-screw over the vernier may then be screwed home, and the
adjustment of the instrument to the work again tried. If a correction
should be found necessary, it is better to ease the pressure of the
thumb-screw over the vernier before making such correction, tightening
it again afterwards. The reading of the measurement is taken as
follows:--
If the 0 line on the vernier coincides with a line on the bar, the
measurement will, of course, be shown by the distance of that line from
the 0 line on the bar, the measurement being in fiftieths of inches, or
inches and fiftieths (as the case may be), but if the 0 line on the
vernier does not coincide with any line of division on the bar, then the
measurement in inches and fiftieths will be from the next line (on the
bar) to the right of the vernier, while the thousandths of an inch may
be read by the line on the vernier which coincides with a line on the
bar.
Suppose, for example, that the zero line of the vernier stands somewhere
between the 1 inch and the 1-1/50 inch line of division on the bar, then
the measurement must be more than an inch, but less than 1-1/50 inches.
If the tenth or middle line on the vernier is the one that coincides
with a line on the bar, the reading is 1-10/1000 inches. If the line
marked 5 on the vernier is the one that coincides with a line on the
bar, the measurement is an inch and 5/1000, and so on.
For measuring the diameters of bores or holes, the external edges of the
jaws are employed; the width of the jaw at the ends being reduced in
diameter to enable the jaw ends to enter a small hole. These edges are
formed to a circle, having a radius smaller than the smallest diameter
of hole they will enter when the jaws are closed, which insures that the
point of contact shall be in the middle of the thickness of each jaw. In
this case the outside diameter of the jaws must be deducted from the
measurement taken by the vernier, or if it be required to set the
instrument to a standard diameter, the zero line on the vernier must be
set to a distance on the bar less than that of the measurement required
to an amount equal to the diameter of the jaw edges when the jaws are
closed. This diameter is, as far as possible, made to correspond to the
lines of division on the bar. Thus in the instrument shown in Fig. 1392,
these lines of division are 1/50 inch; hence the diameter across the
closed bars should, to suit the reading (for internal measurements) on
the bar, be measurable also in fiftieths of an inch; but the other side
of the bar is divided into millimètres, hence to suit internal
measurements (in millimètres or fractions thereof) the width of the
jaws, when closed, should be measurable in millimètres; hence, it
becomes apparent that the diameter of the jaws used for internal
measurements can be made to suit the readings on one side only of the
bar, unless the divisions on one side are divisible into those on the
other side of the bar. When the diameter of the jaws is measurable in
terms of the lines of division on the bar, the instrument may be set to
a given diameter by placing the zero of the vernier as much towards the
zero on the bar as the width of the jaws when closed. Thus, suppose that
width (or diameter, as it may be termed) be 10/50 of an inch, and it be
required to set the instrument for an inch interval or bore measurement,
then the zero on the vernier must be placed to coincide with the line on
the bar which denotes 40/50 of an inch, the lacking 10/50 inch being
accounted for in the diameter or width of the two jaws.
But when the width of the jaws when closed is not measurable in terms
of the lines of division on the bar, the measurement shown by the
vernier will, of course, be too small by the amount of the widths of the
two jaws, and the measurement shown by the vernier must be reduced to
the terms of measurement of the width of the jaws, or what is the same
thing, the measurement of the diameter of the jaws must be reduced to
the terms of measurement on the bar, in order to subtract one from the
other, or add the two together, as the case may require.
For example: Suppose the diameter of the jaws to measure, when they are
close together, 250/1000 of an inch, and that the bar be divided into
inches and fiftieths. Now set the zero of the vernier opposite to the
line denoting 49/50 inch on the bar. What, then, is the measurement
between the outside edges of the jaws? In this case we require to add
the 250/1000 to the 49/50 in order to read the measurement in terms of
fiftieths and thousandths of an inch, or we may read the measurement to
one hundredths of an inch, thus: 49/50 equal 98/100, and 250/1000 equal
25/100, and 98/1000 added to 25/100 are 123/100, or an inch and 23/100.
To read in 1/1000ths of an inch, we have that 49/50 of an inch are equal
to 980/1000, because each 1/50 inch contains 20/1000 inch, and this
added to 250/1000 makes 1230/1000, that is 1-230/1000 inches.
The accuracy of the instrument may be maintained, notwithstanding any
wear which may in the course of time take place on the inside faces of
the jaws, by adjusting the zero line on the vernier to exactly coincide
with the zero line on the bar, but the fineness of the lines renders
this a difficult matter with the naked eye, hence it is desirable to
read the instrument with the aid of a magnifying glass. If the outer
edges of the jaws should wear, it is simply necessary to alter the
allowance made for their widths.
[Illustration: Fig. 1394.]
Fig. 1394 represents standard plug and collar gauges. These tools are
made to represent exact standard measurements, and obviously do no more
than to disclose whether the piece measured is exactly to size or not.
If the work is not to size they will not determine how much the error or
difference is, hence they are gauges rather than measuring tools. It is
obvious, however, that if the work is sufficiently near to size, the
plug or male gauge may be forced in, or the collar or female gauge may
be forced on, and in this case the tightness of the fit would indicate
that the work was very near to standard size. But the use of such gauges
in this way would rapidly wear them out, causing the plug gauge and also
the collar to get smaller than its designated size, hence such gauges
are intended to fit the work without friction, and at the same time
without any play or looseness whatever. Probably the most accurate
degree of fit would be indicated when the plug gauge would fit into the
collar sufficiently to just hold its own weight when brought to rest
while within the collar, and then slowly fall through if put in motion
within the collar. It is obvious that both the plug and the collar
cannot theoretically be of the same size or one would not pass within
the other, but the difference that is sufficient to enable this to be
done is so minute that it is practically too small to measure and of no
importance.
[Illustration: Fig. 1395.]
When these gauges are used by the workmen, to fit the work to their wear
is sufficient to render it necessary to have some other standard gauge
to which they can be from time to time referred to test their accuracy,
and for this purpose a standard such as in Fig. 1395 may be employed. It
consists of a number of steel disks mounted on an arbor and carefully
ground after hardening each to its standard size.
But a set of plug and collar gauges provide within themselves to a
certain extent the means of testing them. Thus we may take a collar or
female gauge of a certain size and place therein two or three plug
gauges whose added diameters equal that of the female or collar gauge.
[Illustration: Fig. 1396.]
In Fig. 1396, for example, the size of the female gauge A being 1-1/2
inches, that of the male B may be one inch, and that of C 1/2 an inch,
and the two together should just fit the female. On the other hand, were
we to use instead of B and C two males, 7/8 and 5/8 inches respectively,
they should fit the female; or a 1/2 inch, a 5/8 inch and a 3/8 inch
male gauge together should fit the female. By a series of tests of this
description, the accuracy of the whole set may be tested; and by
judicious combinations, a defect in the size of any gauge in the set may
be detected.
The wear of these gauges is the most at their ends, and the fit may be
tested by placing the plug within the collar, as in Fig. 1397, and
testing the same with the plug inserted various distances within the
collar, exerting a slight pressure first in the direction of A and then
of B, the amount of motion thus induced in the plug denoting the
closeness of the fit.
In trying the fit of the plug by passing it well into or through the
collar, the axis of the plug should be held true with that of the
collar, and the plug while being pressed forward should be slightly
rotated, which will cause the plug to enter more true and therefore more
easily. The plug should be kept in motion and not allowed to come to
rest while in the collar, because in that case the globules of the oil
with which the surfaces are lubricated maintain a circular form and
induce rolling friction so long as the plug is kept in motion, but
flatten out, leaving sliding friction, so soon as the plug is at rest,
the result being that the plug will become too tight in the collar to
permit of its being removed by hand.
[Illustration: Fig. 1397.]
The surfaces of both the plug and the collar should be very carefully
cleaned and oiled before being tried together, it being found that a
film of oil will be interposed between the surfaces, notwithstanding the
utmost accuracy of fit of the two, and this film of oil prevents undue
abrasion or wear of the surfaces.
When great refinement of gauge diameter is necessary, it is obvious that
all the gauges in a set should be adjusted to diameter while under an
equal temperature, because a plug measuring an inch in diameter when at
a temperature of, say, 60° will be of more than an inch diameter when
under a temperature of, say, 90°.
It follows also that to carry this refinement still farther, the work to
be measured if of the same material as the standard gauge should be of
the same temperature as the gauge, when it will fit the gauge if applied
under varying temperatures; but if a piece of work composed, say, of
copper, be made to true gauge diameter when both it and the gauge are at
a temperature of, say, 60°, it will not be to gauge diameter, and will
not fit the gauge, if both be raised to 90° of temperature, because
copper expands more than steel.
To carry the refinement to its extreme limit then, the gauge should be
of the same metal as the work it is applied to whenever the two fitting
parts of the work are of the same material. But suppose a steel pin is
to be fitted as accurately as possible to a brass bush, how is it to be
done to secure as accurate a fit as possible under varying temperatures?
The two must be fitted at some equal temperature; if this be the lowest
they will be subject to, the fit will vary by getting looser, if the
highest, by getting tighter; in either case all the variation will be in
one direction. If the medium temperature be selected, the fit will get
tighter or looser as the temperature falls or rises. Now in workshop
practice, where fit is the object sought and not a theoretical standard
of size, the range of variation due to temperature and, generally, that
due to a difference between the metals, is too minute to be of practical
importance. To the latter, however, attention must, in the case of work
of large diameter, be paid: thus, a brass piston a free fit at a
temperature of 100° to a 12-inch cast-iron cylinder, will seize fast
when both are at a temperature of, say, 250°. In such cases an allowance
is made in conformity with the co-efficients of expansion.
In the case of the gauges, all that is practicable for ordinary
work-shop variation of temperature is to make them of one kind and
quality of material--as hard as possible and of standard diameter, when
at about the mean temperature at which they will be when in use. In this
case the limit of error, so far as variation from temperature is
concerned, will be simply that due to the varying co-efficients of
expansion of the metals of which the work is composed.
[Illustration: Fig. 1398.]
To provide a standard of lineal measurement which shall not vary under
changes of temperature it has been proposed to construct a gauge such as
shown in Fig. 1398, in which A and B are bars of different metals whose
lengths are in the inverse ratio of their co-efficients of expansion. It
is evident that the difference of their lengths will be a constant
quantity, and that if the two bars be fastened together at one end, the
distance from the free end of B to the free end of A will not vary with
ordinary differences in temperature.
Plug and collar gauges may be used for taper as well as for parallel
fits, the taper fit possessing the advantage that the bolt or pin may be
let farther into its hole to take up the wear. In a report to the Master
Mechanics Association upon the subject of the propriety of recommending
a standard taper for bolts for locomotive work, Mr. Coleman Sellers
says:--
"As the commission given to me calls for a decision as to the taper of
bolts used in locomotive work, it presupposes that taper bolts are a
necessity. In our own practice we divide bolts into several classes, and
our rule is that in every case where a through bolt can be used it must
be used. If we cannot use a through bolt we use a stud, and where a stud
cannot be used we put in a tap bolt, and the reason why a tap bolt comes
last is because it is part and parcel of the machine itself. There are
also black bolts and body bound bolts, the former being put into holes
1/16 inch larger than the bolt. It is possible in fastening a machine or
locomotive together to use black bolts and body bound bolts. With body
bound bolts it is customary for machine builders to use a straight
reamer to true the hole, then turn the bolt and fit it into its place.
It is held by many locomotive builders that the use of straight bolts is
objectionable, on the score that if they are driven in tight there is
much difficulty in getting them out, and where they are got out two or
three times they become loose, and there is no means of making them
tighter.
"There is no difficulty in making two bolts of commercially the same
size. But there is a vast difference between absolute accuracy and
commercial accuracy. Absolute accuracy is a thing that is not
obtainable. What we have to strive for, then, is commercial accuracy.
What system can we adopt that will enable workmen of limited capacity to
do work that will be practically accurate? The taper bolt for certain
purposes presents a very decided advantage. Bolts may be made
practically of the same diameter, but holes cannot be made practically
of the same diameter. Each one is only an approximation to correctness.
We have here an ordinary fluted reamer (showing an excellent specimen of
Betts Machine Company's make). That reamer is intended to produce a
straight hole, but having once passed through a hole the reamer will be
slightly worn. The next time you pass it through it is a little duller,
and every time you pass it through the hole must become smaller. There
have been many attempts made to produce a reamer that should be
adjustable. That, thanks to the gentlemen who are making such tools a
speciality, has added a very useful tool to the machine shop--a reamer
where the cutters are put in tapered and can be set up and the reamer
enlarged and made to suit the gauge. This will enable us to make and
maintain a commercially uniform hole in our work. But the successful use
of a reamer of this kind depends upon the drill that precedes this
reamer being made as nearly right as possible, so that the reamer will
have little work to do. The less you give a reamer to do the longer it
will maintain its size.
"The question of tapered bolts involves at once this difficulty: that we
have to drill a straight hole, then the tapered reamer must take out all
the metal that must be removed in order to convert a straight into a
tapered hole. The straight hole is maintained in its size by taking out
the least amount of metal. It follows that the tapered reamer would be
nearest right which would also take out the least amount of metal.
"Then you come to the question of the shape of the taper. When I was
engaged building locomotives in Cincinnati, a great many years ago, we
used bolts the taper of which was greater than I shall recommend to you.
In regard to the compression that would take place in bolts, no piece of
iron can go into another piece of iron without being smaller than the
hole into which it is intended to go. If it is in any degree larger, it
must compress the piece itself or stretch the material that is round
it. So, if you adopt a tapered bolt, you cannot adopt a certain distance
that it shall stand out before you begin to drive it, for there will be
more material to compress in a large piece than in a small one. Metal is
elastic. Within the elastic limit of the metal you may assume the
compression to be a spring. In a large bolt you have a long spring, and
in a short one you have a short spring. If you drive a half-inch bolt
into a large piece of iron, it is the small bolt which you compress;
therefore the larger the bolt the more pressure you can give to produce
the same result. Hence, if you adopt the taper bolt, you will have to
use your own discretion, unless you go into elaborate experiments to
show how far the bolt head should be away from the metal when you begin
to drive it.
[Illustration: Fig. 1399.]
"Certain builders of locomotives put their stub ends together with
tapered bolts, but do not use tapered bolts in any other part of the
structure. The Baldwin Works use tapered bolts wherever they are body
bound bolts. They make a universal taper of 1/16 inch to the foot. An
inch bolt 12 inches long would be 1-1/16 inches diameter under the head.
They make all their bolts under 9 inches long 1/16 larger under the head
than the name of the bolt implies. Thus a 3/4 inch bolt would be 13/16
inch under the head, provided it was 9 inches long or under. Anything
over 9 inches long is made 1/8 inch larger under the head, and still
made a taper of 1/16 inch to the foot. A locomotive builder informs me
that a taper of 1/8 inch to the foot is sometimes called for, and the
Pennsylvania road calls for 3/32 inch to the foot. But the majority of
specifications call for 1/16 inch to the foot. The advantage of 1/16
inch taper lies in the fact that a bolt headed in the ordinary manner
can be made to fill the requirements, provided it is made of iron. You
may decide that bolts should be tapered, for the reason that when a
tapered bolt is driven into its place it can be readily knocked loose,
or if that bolt, when in its place, proves to be too loose, you have
merely to drive it in a little farther: these are arguments in favor of
tapered bolts, showing their advantage. It is easier to repair work that
has tapered bolts than work that has straight bolts. If you adopt a
tapered bolt, say, with a taper of 1/16 inch to the foot, you are going
to effect the making of those bolts and the boring of those holes in a
commercially accurate manner, so that they can be brought into the
interchangeable system. To carry this out, you require some standard to
start with, and the simplest system that one can conceive is this: Let
us imagine that we have a steel plug and grind it perfectly true. We
have the means of determining whether that is a taper of 1/16 inch,
thanks to the gentlemen who are now making these admirable gauges. We
have a lathe that can turn that taper. I think if you go into the
manufacture of these bolts, you will be obliged to use a lathe which
will always turn a uniform taper. Having made a female gauge, Fig. 1399,
8 inches long and 1-1/16 inches diameter with a taper of 1/16 inch to
the foot, this is the standard of what? The area of the bolt, not of the
hole it goes into. We now make a plug, Fig. 1399. Taking that tapered
plug we should be able to drop it into the hole. Your taper reamer is
made to fit this, but you require to know how deep the hole should be.
Remember, I said this is the gauge that the bolts are made by. Now let
us suppose that we have this as a standard, and to that standard these
reamers are made. We decide by practice how much compression we can put
upon the metal. For inch bolts, and, say, all above 1/2 inch, we might,
say, allow the head to stand up 1/8 of an inch. Let us make another
female gauge like Fig. 1399, but turned down 1/8 of an inch shorter. We
then shall have the hole smaller than it was before. It is this degree
smaller, .0065 of an inch; that is a decimal representing how much
smaller that hole is when you have gone down 1/8 of an inch on a taper
of 1/16 inch to the foot.
[Illustration: Fig. 1400.]
"Having got this tapered plug, you then must have the means of making
the bolts commercially accurate in the shop. For that purpose you must
have some cast-iron plugs. Those are reamed with a reamer that has no
guard on it, but is pushed into it until the plug--this standard
plug--is flush with the end of it. If you go in a little too far it is
no matter. Having produced that gauge, we gauge first the one that is
used on the lathe for the workman to work by, and he will fit his bolt
in until the head will be pushed up against it. If you have a bolt to
make from a straight piece of iron, I should advise its being done in
two lathes. Here are those beautiful gauges of the Pratt and Whitney
Company, which will answer the present purpose; one of these gauges
measuring what the outside of the bolt will be, the other gauge 1/16 of
an inch larger will mark the part under the head. Messrs. Baldwin have a
very good system of gauges. All the cast-iron plugs which they use for
this purpose are square. Holes are cut in the blocks the exact size of
the bolts to be turned up, as shown in Fig. 1400. The object of this is
that there shall be no mistake as to what the gauge is. These gauges can
be readily maintained, because they have to go back into the room to the
inspector. He puts this plug in. If it goes in and fits flush, it is all
right. If the plug goes in too far, it is worn. He then turns a little
off the end and adjusts it.
"Now practically through machine shops we find that we have to use
cast-iron gauges. We take, for instance, 2-inch shafting. Shafting can
only be commercially accurate. Therefore we make cast-iron rings and if
those rings will go on the shafting it is near enough accurate for
merchantable purposes. But this ring will wear in a certain time.
Therefore it must not be used more than a certain number of days or
hours. Here you have a system that is simple in the extreme. You have
all this in two gauges, one gauge being made as a mere check on that
tapered plug which is the origin of all things, the origin being 1/8 or
7/16, or 1/4 of an inch shorter if the bolt is very large. There is
where you have to use your own judgment. But having adopted something
practical you then can use your reamer which is necessary to produce a
hole of a given size. If this reamer wears, you then turn off this
wrought-iron collar far enough back to let it go in that much farther. I
know of no other way by which you can accomplish this result so well as
by that in use at the Baldwin Locomotive Works. I think that the system
originated with Mr. Baldwin himself.
"I do not feel disposed to recommend to you any particular taper to be
adopted, because it is not a question like that of screw-threads. In
screw-threads we throw away the dies that are used upon bolts, which are
perishable articles. The taper that has once been adopted in locomotive
establishments is a perpetual thing. If the Pennsylvania railroad and
all its branches have adopted 3/32, it is folly to ask them to change it
to 1/16 of an inch, because their own connections are large enough to
make them independent of almost any other corporation, and the need of
absolute uniformity in their work would cause them to stick to that
particular thing. Any of you having five, six, seven, or two or three
hundred engines, must make up your minds what you will do. When we adopt
a standard for screw-threads, a screw-thread is adopted which has a
manifest advantage. A bolt that has one screw thread can be used on any
machine. But once having adopted a taper on a road, it is very difficult
to make a change; and whether it is wisdom for this Association to say
that thus-and-so shall be the standard taper, is a question I am unable
to answer. Therefore I am unwilling to present any taper to you, and
only present the facts, but will say that 1/16 inch is enough. The less
taper you have the less material you have to cut away. But to say that
1/16 inch is preferable to 1/32 inch is folly, because no human being
could tell the difference. If a bolt has 5° taper on the side, it may
set in place; if it has 7°, it may jump out. That is the angle of
friction for iron or other metals. Five degrees would be an absurd angle
for a taper bolt. Anything, then, that will hold; that is, if you drive
the bolt it will set there.
"This presentation may enable you to arrive at some conclusion. Nothing
is more desirable than an interchangeable system. In making turning
lathes we try to make all parts interchangeable, and we so fit the
sliding spindle. Every sliding spindle in the dead head of the lathe has
to be fitted into its own place. We know of no method of making all
holes of exactly the same size that shall be commercially profitable.
The only way we could surmount that difficulty was to put two conical
sleeves in that should compress. We have so solved the problem. We now
make spindles that are interchangeable, and we do not fit one part to
the other. But that is not the case with bolts. You cannot put the
compressing thimbles on them, therefore, you have to consider the
question, How can you make holes near enough, and how can you turn the
bolts near enough alike?"
[Illustration: Fig. 1401.]
Fig. 1401 represents, and the following table gives the taper adopted by
the Baldwin Locomotive Works.
Bolt threads, American standard, except stay bolts and boiler studs,
[V]-threads, 12 per inch; valves, cocks and plugs, [V]-threads, 14 per
inch, and 1/8 inch taper per 1 inch.
Standard bolt taper 1/16 inch per foot.
Length of bolts from head to end of thread equals A.
Diameter of bolt under the head as follows:--
3/64 inch larger at B for 9 inch and under
1/16 " " over 9 inch to 12 inch
3/32 " " " 12 " to 18 "
1/8 " " " 18 " to 24 "
5/32 " " " 24 " to 30 "
3/16 " " " 30 " to 36 "
[Illustration: Fig. 1402.]
It is obvious that a plug or collar gauge simply determines what is the
largest dimension of the work, and that although it will demonstrate
that a piece of work is not true or round yet it will not measure the
amount of the error. The work may be oval or elliptical, or of any other
form, and yet fit the gauge so far as the fit can be determined by the
sense of feeling. Or suppose there is a flat place upon the work, then
except in so far as the bearing marks made upon the work by moving it
within the gauge may indicate, there is no means of knowing whether the
work is true or not. Furthermore, in the case of lathe work held between
the lathe centres it is necessary to remove the work from the lathe
before the collar gauge can be applied, and to obviate these
difficulties we have the caliper gauge shown in Fig. 1402. The caliper
end is here shown to be for 3/4 inch, and the plug end for 13/16 inch.
If the two ends were for the same diameter one gauge only would be used
for measuring external and internal work of the same diameter, but in
this case the male cannot be tested with the female gauge; whereas if
the two ends are for different diameters the end of one gauge may be
tested with that of another, and their correctness tested, but the
workman will require two gauges to measure an external and internal
piece of the same diameter.
[Illustration: Fig. 1403.]
For small lathe work of odd size as when it is required to turn work to
fit holes reamed by a worn reamer that is below the standard size, a
gauge such as in Fig. 1403, is sometimes used, the mouth A serving as a
caliper and the hole B as a collar gauge for the same diameter of work.
It is obvious that such a gauge may be applied to the work while it is
running in the lathe, and that when the size at A wears too large the
jaw may be closed to correct it; a plan that is also pursued to rectify
the caliper gauge shown in Fig. 1402.
[Illustration: Fig. 1404.]
On large work, as, say, of six inches in diameter, a gauge, such as in
Fig. 1404, is used, being short so that it may be light enough to be
conveniently handled; or sometimes a piece such as in Fig. 1405 is used
as a gauge, the ends being fitted to the curvature of the bore to be
tested. Gauges of these two kinds, however, are generally used more in
the sense of being templates rather than measuring tools, since they
determine whether a bore is of the required size rather than determine
what that size is.
[Illustration: Fig. 1405.]
[Illustration: Fig. 1406.]
[Illustration: Fig. 1407.]
For gauging work of very large diameter, as, say, several feet, to
minute fractions of an inch, as is necessary, for example, for a
shrinkage fit on a locomotive tire, the following method is employed. In
Fig. 1406 let A represent a ring, say, 5 feet bore, and requiring its
bore to be gauged to within, say, 1/100 inch. Then R represents a rod
made, say, 1/2 inch shorter than the required diameter of bore, and W,
Fig. 1407, represents a wedge whose upper surface C D is curved, its
lower surface being a true plane. The thickness at the end C is made,
say, 51/100 inch, while that at D is 48/100 inch; or in other words,
there is 3/100 of an inch taper in the length of the wedge. Suppose then
that the rod R is placed in the bore of A as in figure, and that the
wedge just has contact with the work bore and with the end of the rod
when it has entered as far as E in Fig. 1407, and that point E is
one-third of the length of the wedge, then the bore of A will measure
the length of the rod R plus 49/100 of an inch. But if the wedge passed
in to line F, the latter being two-thirds the length of the wedge from
D, then the bore would be 50/100 larger than the length of the rod R. It
is obvious that with this method the work may be measured very minutely,
and the amount of error, if there be any, may be measured.
The rod must be applied to the work in the same position in which its
measurement was made, otherwise its deflection may vitiate the
measurement. Thus, if the rod measures 4 feet 11-1/2 inches when
standing vertical, it must be applied to the work standing vertical; but
if it was measured lying horizontal, it must be applied to the work
lying horizontal, as there will be a difference in its length when
measured in the two positions, which occurs on account of variations in
its deflection from its own weight.
[Illustration: Fig. 1408.]
[Illustration: Fig. 1409.]
For simply measuring a piece of work to fit it to another irrespective
of its exact size as expressed in inches and parts of an inch the common
calipers are used. Fig. 1408 represents a pair of spring calipers, the
bow acting as a spring to keep the two legs apart, and the screw and nut
being used to close them against the spring pressure. The slightness of
the legs enables these calipers to be forced or to spring over the work,
and thus indicate by the amount of pressure it requires to pass them
over the work how much it is above size, and therefore how much it
requires to be reduced. But, on the other hand, this slightness renders
it somewhat difficult to measure with great correctness. A better form
of outside calipers is shown in Fig. 1409, in which in addition to the
stiffness of the pivoted joint a bow spring acts to close the caliper
legs, which are operated, to open or close them, by operating the hand
screw shown, the nuts in which the screw operates being pivoted to the
caliper legs. The advantage of this form is that the calipers may be set
very readily, while there is no danger of the set or adjustment of the
calipers altering from any slight blow or jar received in laying them
down upon the bench.
[Illustration: Fig. 1410.]
Fig. 1410 gives views of a common pair of outside calipers such as the
workman usually makes for himself. When this form is made with a
sufficiently large joint, and with the legs broad and stiff as in the
figure, they will serve for very fine and accurate adjustments.
[Illustration: Fig. 1411.]
Fig. 1411 represents a pair of inside calipers for measuring the
diameters of holes or bores. The points of these calipers should be at
an angle as shown in the Fig. 1412, which will enable the points to
enter a long distance in a small hole, as is denoted by the dotted lines
in the figure. This will also enable the extreme points to reach the
end of a recess, as in Fig. 1413, which the rounded end calipers, such
as in this figure, will not do.
[Illustration: Fig. 1412.]
[Illustration: Fig. 1413.]
[Illustration: Fig. 1414.]
Fig. 1414 represents a pair of inside calipers with an adjustment screw
having a right-hand screw at A and a left-hand one at B, threaded into
two nuts pivoted into the arms, so that by operating the screw the legs
are opened or closed, and are locked in position, so that they cannot
move from an accidental blow. But as the threads are apt to wear loose,
it is preferable to provide a set screw to one of the nuts so as to take
up the wear and produce sufficient friction to prevent looseness of the
legs.
[Illustration: Fig. 1415.]
[Illustration: Fig. 1416.]
Calipers are sometimes made double, that is to say, the inside and the
outside calipers are provided in the one tool, as in Fig. 1415, which
represents a pair of combined inside and outside calipers having a set
screw at C to secure the legs together after the adjustment is made. The
object of this form is to have the measuring points equidistant from the
centre of the pivot A in Fig. 1416, so that when the outside legs are
set to the diameter of the work as at B, the inside ones will be set to
measure a hole or bore of the same diameter as at C.
This, however, is not a desirable form for several reasons, among which
are the following:--
In the first place outside calipers are much more used than inside ones,
hence the wear on the points are greatest. Again, the pivot is apt to
wear, destroying the equality of length of the points from the centre of
the pivot; and in the third place the shape of the points of calipers as
usually made vitiates the correctness of the measurements.
[Illustration: Fig. 1417.]
Fig. 1417, for example, represents the ordinary form, the points being
rounded; hence, when the legs are closed the point of contact between
the inside and outside calipers will be at A, while when they are opened
out to their fullest the points of contact will be at B. This may,
however, be remedied to a great extent by bevelling off the ends from
the outside as shown in Fig. 1416.
[Illustration: Fig. 1418.]
The end faces of outside calipers should be curved in their widths, as
in Fig. 1418, so that contact shall occur at the middle, and it will
then be known just where to apply the points of the inside calipers when
testing them with the outside ones.
Inside and outside calipers are capable of adjustment for very fine
measurements; indeed, from some tests made by the Pratt and Whitney
Company among their workmen it was found that the average good workman
could take a measurement with them to within the twenty-five thousandth
part of an inch. But the workman of the general machine shop who has no
experience in measuring by thousandths has no idea of the accuracy with
which he sets two calipers in his ordinary practice. The great
difference that the one-thousandth of an inch makes in the fit of two
pieces may be shown as in Fig. 1419, which represents a collar gauge of
5/8 inch in diameter, and a plug 1/1000 inch less in diameter, and it
was found that with the plug inserted 1/8 inch in the collar it could be
moved from A to B, a distance of about 5/16 inch, which an ordinary
workman would at once recognise as a very loose fit.
If the joints of outside calipers are well made the calipers may upon
small work be closed upon the work as in Fig. 1420, and the adjustment
may be made without requiring to tap or lightly knock the caliper legs
against the work as is usually done to set them. But to test the
adjustment very finely the work should be held up to the light, as in
Fig. 1421, the lower leg of the calipers rested against the little
finger so as to steady it and prevent it from moving while the top leg
is moved over the work, and at the same time moving it sideways to find
when it is held directly across the work. For testing the inside and
outside calipers together they should for small diameters be held as in
Fig. 1422, the middle finger serving to steady one inside and one
outside leg, while one leg only of either calipers is grasped in the
fingers.
[Illustration: Fig. 1419.]
[Illustration: Fig. 1420.]
[Illustration: Fig. 1421.]
[Illustration: Fig. 1422.]
For larger dimensions, as six or eight inches, it is better, however, to
hold the calipers as in Fig. 1423, the forefinger of the left hand
serving to rest one leg of each pair on the contact being thus tested
between the legs that are nearest to the operator.
The adjustment of caliper legs should be such that contact between the
caliper points and the work is scarcely, if at all, perceptible. If with
the closest of observation contact is plainly perceptible, the outside
calipers will be set smaller than the work, while in the case of inside
calipers, they would be set larger; and for this reason it follows that
if a bore is to be measured to have a plug fitted to it, the inside
calipers should have barely perceptible contact with the work bore, and
the outside calipers should have the same degree of contact, or, if
anything, a very minute degree of increased contact. On the other hand,
if a bore is to be fitted to a cylindrical rod the outside calipers
should be set to have the slightest possible contact with the rod, and
the inside ones set to have as nearly as possible the same degree of
contact with the outside ones, or, if anything, slightly less contact.
For if in any case the calipers have forcible contact with the work the
caliper legs will spring open and will therefore be improperly set.
Calipers should be set both to the gauge and to the work in the same
relative position. Let it be required, for example, to set a pair of
inside calipers to a bore, and a pair of outside calipers to the inside
ones, and to then apply the latter to the work. If the legs of the
inside calipers stand vertical to the bore for setting they should stand
vertical while the outside calipers are set to them, and if the outside
calipers are held horizontally while set to the inside ones they should
be applied horizontally to the work, so as to eliminate any error due to
the caliper legs deflecting from their own weight.
[Illustration: Fig. 1423.]
To adjust calipers so finely that a piece of work may be turned by
caliper measurement to just fit a hole; a working or a driving fit
without trying the pieces together, is a refinement of measurement
requiring considerable experience and skill, because, as will be readily
understood from the remarks made when referring to gauge measurements,
there are certain minute allowances to be made in the set of the
calipers to obtain the desired degree of fit.
In using inside calipers upon flat surfaces it will be found that they
can be adjusted finer by trusting to the ear than the eye. Suppose, for
example, we are measuring between the jaws of a pillow-block. We hold
one point of the calipers stationary, as before, and adjust the other
point, so that, by moving it very rapidly, we can just detect a scraping
sound, giving evidence of contact between the calipers and the work. If,
then, we move the calipers slowly, we shall be unable, with the closest
scrutiny, to detect any contact between the two.
Calipers possess one great advantage over more rigid and solid gauges,
in that the calipers may be forced over the work when the degree of
force necessary to pass them on indicates how much the work is too
large, and therefore how much it requires reducing. Thus, suppose a
cylindrical piece of work requires to be turned to fit a hole, and the
inside calipers are set to the bore of the latter, then the outside
calipers may be set to the inside ones and applied to the work, and when
the work is reduced to within, say, 1/100 inch the calipers will spring
open if pressed firmly to the work, and disclose to the workman that the
work is reduced to nearly the required size. So accustomed do workmen
become in estimating from this pressure of contact how nearly the work
is reduced to the required diameter, that they are enabled to estimate,
by forcing the calipers over the work, the depth of the cut required to
be taken off the work, with great exactitude, whereas with solid gauges,
or even caliper gauges of solid proportions, this cannot be done,
because they will not spring open.
The amount to which a pair of calipers will spring open without altering
their set depends upon the shape: thus, with a given joint they will do
so to a greater extent in proportion as the legs are slight, whereas
with a given strength of leg they will do so more as the diameter of the
joint is large and the fit of the joint is a tight one. But if the joint
is so weak as to move too easily, or the legs are so weak as to spring
too easily, the calipers will be apt in one case to shift when applied
to the work, and in the other to spring so easily that it will be
difficult to tell by contact when the points just touch the work and yet
are not sprung by the degree of contact. For these reasons the points of
calipers should be made larger in diameter than they are usually made:
thus, for a pair of calipers of the shape shown in Fig. 1410, the joint
should be about 1-1/4 inches diameter to every 6 inches of length of
leg. The joint should be sufficiently tight that the legs can just be
moved when the two legs are taken in one hand and compressed under heavy
hand pressure.
[Illustration: Fig. 1424.]
For measuring the distance of a slot or keyway from a surface, the form
of calipers shown in Fig. 1424 is employed; the straight leg has its
surface a true plane, and is held flat against the surface B of the slot
or keyway, and the outside or curved leg is set to meet the distance of
the work surface measuring the distance C. These are termed keyway
calipers.
There are in general machine work four kinds of fit, as follow: The
working or sliding fit; the driving fit; the hydraulic press fit; and
the shrinkage fit. In the first of these a proper fit is obtained when
the surfaces are in full contact, and the enveloped piece will move
without undue friction or lost motion when the surfaces are oiled. In
the second, third, and fourth, the enveloped piece is made larger than
the enveloping piece, so that when the two pieces are put together they
will be firmly locked.
It is obvious that in a working or sliding fit the enveloped piece must
be smaller than that enveloping it, or one piece could not pass within
the other. But the amount of difference, although too small to be of
practical importance in pieces of an inch or two in diameter and but few
inches in length, is appreciable in large work, as, say, of two or more
feet in diameter. A journal, for example, of 1/10 inch diameter, running
in a bearing having a bore of 1/1000 inch larger diameter, and being two
diameters in length, would be instantly recognised as a bad fit; but a
journal 6 inches in diameter and two diameters or 12 inches long would
be a fair fit in a bearing having a bore of 6-1/1000 inches. In the one
case the play would be equal to one one-hundredth of the shaft's
diameter, while in the other case the play would equal but one
six-thousandth part of the shaft's diameter. In small work the limit of
wear is so small, and the length of the pieces so short, that the 1/1000
of an inch assumes an importance that does not exist in larger work.
Thus, in watch work, an error of 1/1000 inch in diameter may render the
piece useless; in sewing machine work it may be the limit to which the
tools are allowed to wear; while in a steamship or locomotive engine it
may be of no practical importance whatever.
A journal 1/10 inch in diameter would require to run, under ordinary
conditions, several years to become 1/1000 inch loose in its bearing.
Some of this looseness, and probably nearly one half of it, will occur
from wear of the bearing bore; hence, if a new shaft of the original
standard diameter be supplied the looseness will be reduced by one-half.
But a 6-inch journal and bearing would probably wear nearly 1/1000 inch
loose in wearing down to a bearing which may take but a week or two, and
for these reasons among others, standard gauges and measuring tools are
less applicable to large than to small work.
The great majority of fits made under the standard gauge system consist
of cylindrical pieces fitting into holes or bores. Suppose then that we
have a plug and a collar gauge each of an inch diameter, and a reamer to
fit the collar gauge, and we commence to ream holes and to turn plugs to
fit the collar gauge, then as our work proceeds we shall find that as
the reamer wears, the holes it makes will get smaller, and that as the
collar gauge wears, its bore gets larger, and it is obvious that the
work will not go together. The wear of the gauge obviously proceeds
slowly, but the wear of the reamer begins from the very first hole that
it reams, although it may perform considerable duty before its wear
sensibly affects the size of the hole. Theoretically, however, its size
decreases from the moment it commences to perform cutting duty until it
has worn out, and the point at which the wearing-out process may have
proceeded to its greatest permissible limit is determined by its
reduction of size rather than by the loss of its sharpness or cutting
capacity. Obviously then either the reamer must be so made that its size
may be constantly adjusted to take up the wear, as in the adjustable
reamer, or else if solid reamers are used there must be a certain limit
fixed upon as the utmost permissible amount of wear, and the reamer must
be made above the standard size to an amount equal to the amount of this
limit, so that when the reamer has worn down it will still bore a hole
large enough to admit the plug gauge. To maintain the standard there
should be in this case two sets of gauges, one representing the correct
standard and the other the size to which the reamer is to be made when
new or restored to its proper size.
The limit allowed for reamer wear varies in practice from 1/1000 to
1/10000 of an inch, according to the requirements of the work. As
regards the wear of the standard gauges used by the workmen they are
obviously subject to appreciable wear, and must be returned at intervals
to the tool room to be corrected from gauges used for no other purpose.
To test if a hole is within the determined limit of size a limit gauge
may be used. Suppose, for example, that the limit is 1/1000 of an inch,
then a plug gauge may be made that is 1/1000 of an inch taper, and if
the large end of this plug will enter the hole, the latter is too large,
while if the small end will not enter, the hole is too small.
When only a single set of plug and collar gauges are at hand the plug or
the collar gauge may be kept to maintain the standard, the other being
used to work to, both for inside and outside work. Suppose, for example,
that a plug and collar gauge are used for a certain piece of work and
that both are new, then the reamer may be made from either of them,
because their sizes agree, but after they have become worn either one or
the other must be accepted as the standard of size to make the reamer
to. If it be the collar gauge, then the plug gauge is virtually
discarded as a standard, except in that if the plug gauge be not used at
all it may be kept as a standard of the size to which the collar gauge
must be restored when it has worn sufficiently to render restoration to
size necessary. If this system be adopted the size of the reamer will be
constantly varying to suit the wear of the collar gauge, and the
difficulty is encountered that the standard lathe arbors or mandrels
will not fit the holes produced, and it follows that if standard
mandrels are to be used the reamers must when worn be restored to a
standard size irrespective of the wear of the gauges, and that the
standard mandrels must be made to have as much taper in their lengths as
the limit of wear that is allowed to the reamers. Suppose, for example,
that it is determined to permit the reamer to wear the 1/2000 of an inch
before restoring it to size, then in an inch mandrel the smallest end
may be made an inch in diameter and the largest 1-1/2000 inch in
diameter, so that however much the reamer may be worn within the limit
allowed for wear the hole it produces will fit at some part in the
length of the standard mandrel. But as the reamer wears smaller its size
must be made as much above its designated standard size as the limit
allowed for wear; hence, when new or when restored to size, the reamer
would measure 1-1/2000 inches, and the hole it produced would fit the
large end of the mandrel. But as the reamer wore, the hole would be
reamed smaller and would not pass so far along the mandrel, until
finally the limit of reamer wear being reached the work would fit the
small end of the mandrel. The small end of the mandrel is thus the
standard of its size, and the wear of the collar gauge is in the same
direction as that of the reamer. Thus, so long as the collar gauge has
not worn more than the 1/2000 of an inch it will, if placed upon the
mandrel, fit it at some part of its length.
Now suppose that the plug gauge be accepted as the standard to which the
reamer is to be made, and that to allow for reamer wear the reamer is
made, say, 1/2000 inch larger than the plug gauge, the work being made
to the collar gauge. Then with a new reamer and new or unworn gauges the
hole will be reamed above the standard size to the 1/2000 inch allowed
for reamer wear. As the reamer wears, the hole it produces will become
smaller, and as the collar gauge wears, the work turned to it will be
larger, and the effect will be that, to whatever extent the collar gauge
wears, it will reduce the permissible amount of reamer wear, so that
when the collar gauge had worn the 1/2000 inch the work would not go
together unless the reamer was entirely new or unworn.
In a driving fit one piece is driven within the other by means of hammer
blows, and it follows that one piece must be of larger diameter than the
other, the amount of the difference depending largely upon the diameter
and length of the work.
It is obvious, however, that the difference may be so great that with
sufficiently forcible blows the enveloping piece may be burst open. When
a number of pieces are to be made a driving fit, the two pieces may be
made to fit correctly by trial and correction, and from these pieces
gauges may be made so that subsequent pieces may be made correct by
these gauges, thus avoiding the necessity to try them together.
In fitting the first two pieces by fit and trial, or rather by trial and
correction, the workman is guided as to the correctness of the fit by
the sound of the hammer blows, the rebound of the hammer, and the
distance the piece moves at each blow. Thus the less the movement the
more solid the blow sounds, and the greater the rebound of the hammer
the tighter the fit, and from these elements the experienced workman is
enabled to know how tightly the pieces may be driven together without
danger of bursting the outer one.
What the actual difference in diameter between two pieces may require to
be to make a driving fit is governed, as already said, to a great extent
by the dimensions of the pieces, and also by the nature of the material
and the amount of area in contact. Suppose, for example, that the plug
is 6 inches long, and the amount of pressure required to force it within
the collar will increase with the distance to which it is enveloped by
the collar. Or suppose one plug to be 3 inches and another to be 6
inches in circumference, and each to have entered its collar to the
depth of an inch, while the two inside or enveloped pieces are larger
than the outside pieces by the same amount, the outside pieces being of
equal strength in proportion to their plugs, so that all other elements
are equal, and then it is self-evident that the largest plug will
require twice as much power as the small one will to force it in another
inch into the collar, because the area of contact is twice as great. It
is usual, therefore, under definite conditions to find by experiment
what allowance to make to obtain a driving or a forcing fit. Thus, Mr.
Coleman Sellers, at a meeting of the Car Builders Association, referring
to the proper amount of difference to be allowed between the diameters
of car axles and wheel bores in order to obtain a proper forcing or
hydraulic fit, said, "Several years ago some experiments were made to
determine the difference which should be made between the size of the
hole and that of the axle. The conclusion reached was that if the axle
of standard size was turned 0.007 inch larger than the wheel was bored
it would require a pressure of about 30 tons to press the axle into the
wheel." The wheel seat on the axle here referred to was 4-7/8 inches in
diameter and 7 inches long. It is to be remarked, however, that the
wheel bore being of cast iron and the axle of wrought iron the friction
between the surfaces was not the same as it would be were the two
composed of the same metal. This brings us to a consideration of what
difference in the forcing fit there will be in the case of different
metals, the allowance for forcing being the same and the work being of
the same dimensions.
Suppose, for example, that a wrought-iron plug of an inch in diameter is
so fitted to a bore that when inserted therein to a distance of, say, 2
inches, it requires a pressure of 3 lbs. to cause it to enter farther,
then how much pressure would it take if the bore was of cast iron, of
yellow brass, or of steel, instead of wrought iron. This brings us to
another consideration, inasmuch as the elasticity and the strength of
the enveloping piece has great influence in determining how much to
allow for a driving, forcing, or a shrinkage fit.
Obviously the allowance can be more if the enveloping piece be of
wrought iron, copper, or brass, than for cast iron or steel, because of
the greater elasticity of the former. Leaving the elasticity out of the
question, it would appear a natural assumption that the pieces, being of
the same dimensions, the amount of force necessary to force one piece
within the other would increase in proportion as the equivalents of
friction of the different metals increased.
This has an important bearing in practice, because the fit of pieces not
made to standard gauge diameter is governed to a great extent by the
pressure or power required to move the pieces. Thus, let a steel
crosshead pin be required to be as tight a fit into the crosshead as is
compatible with its extraction by hand, and its diameter in proportion
to that of the bore into which it fits will not be the same if that bore
be of wrought iron, as it would be were the bore of steel, because the
coefficient of friction for cast steel on cast iron is not the same as
that for steel on wrought iron. In other words, the lower the
coefficient of friction on the two surfaces the less the power required
to force one into the other, the gauge diameters being equal. In this
connection it may be remarked that the amount of area in contact is of
primary importance, because in ordinary practice the surfaces of work
left as finished by the steel cutting tools are not sufficiently true
and smooth to give a bearing over the full area of the surfaces.
This occurs for the following reasons. First, work to be bored must be
held (by bolts, plates, chuck-jaws, or similar appliances) with
sufficient force to withstand the pressure of the cut taken by the
cutting tool, and this pressure exerts more or less influence to spring
or deflect the work from its normal shape, so that a hole bored true
while clamped will not be so true when released from the pressure of the
holding clamps.
To obviate this as far as possible, expert workmen screw up the holding
devices as tight as may be necessary for the heavy roughing cuts, and
then slack them off before taking the finishing cuts.
Secondly, under ordinary conditions of workshop practice, the steel
cutting tools do not leave a surface that is a true plane in the
direction of the length of the work, but leave a spiral projection of
more or less prominence and of greater or less height, according to the
width of that part of the cutting edge which lies parallel to the line
of motion of the tool feed, taken in proportion to the rate of feed per
revolution of the work.
Let the distance, Fig. 1424A, A to B lie in the plane of motion of the
tool feed, and measure, say, 1/4 inch, the tool moving, say, 5/16 inch
along the cut per lathe revolution. Suppose the edge from B to D to lie
at a minute angle to the line of tool traverse, and the depth of the cut
to be such that the part from B to C performs a slight cutting or
scraping duty, then the part from B to C will leave a slight ridge on
the work plainly discernible to the naked eye in what are termed the
tool marks.
The obvious means of correcting this is to have the part A B of greater
width than the tool will feed along the cut, during one revolution of
the work (or the cutter, as the case may be); but there are practicable
obstacles to this, especially when applied to wrought iron, steel, or
brass, because the broader the cutting edge of a tool the more liable it
is to spring, as well as to jar or chatter, leaving a surface showing
minute depressions lying parallel to the line of tool feed.
If the cutting tool be made parallel and cylindrical on its edges, and
clearance be given on the front end of its diameter only, so as to cut
along a certain distance only of its cylindrical edge, the rest being a
close fit to the bore of the work, the part having no cutting edge, that
is, the part without clearance, will be apt to cause friction by rubbing
the bore of the work as the tool edge wears, and the friction will cause
heat, which will increase as the cut proceeds, causing the hole to
expand as the cut proceeds, and to be taper when cooled to an equal
degree all over. This may be partly obviated by giving the tool a slow
rate of cutting speed, and a quick rate of feed, which will greatly
reduce the friction and consequently the heating of the tool and the
work. On cast iron it is possible to have a much broader cutting edge to
the tool, without inducing the chattering referred to, than is the case
with wrought iron, steel, or brass, especially when the finishing cut is
a very light one. If the finishing cut be too deep, the surface of the
work, if of cast iron, will be pitted with numerous minute holes, which
occur because the metal breaks out from the strain placed on it (and due
to the cut) just before it meets the cutting edge of the tool.
Especially is this the case if the tool be dull or be ground at an
insufficiently acute angle.
When the work shows the tool marks very plainly, or if of cast iron
shows the pitting referred to (instead of having a smooth and somewhat
glossy appearance), there will be less of its surface in contact with
the surface to which it fits, and the fit will soon become destroyed,
because the wearing surface or the gripping surface, as the case may be,
will the sooner become impaired, causing looseness of the fit. In the
one case the abrasion which should be distributed over the whole area of
the fitting parts is at first confined to the projections having
contact, which, therefore, soon wear away. In the other case the
projecting area in contact compresses, causing looseness of the fit.
Hydraulic press or forcing fits.--For securing pieces together by
forcing one within the other by means of an hydraulic press, the plug
piece is made a certain amount larger than the bore it is to enter, this
amount being termed the allowance for forcing. What this allowance
should be under any given conditions for a given metal, will depend upon
the truth and smoothness of the surfaces, and on this account no
universal rule obtains in general practice. From some experiments made
by William Sellers & Co., it was determined that if a wheel seat (on an
axle) measuring 4-7/8 inches in diameter and 7 inches long was turned
7/1000 of an inch larger than the wheel bore, it would require a
pressure of about thirty tons to force the wheel home on the axle.
At the Susquehanna shops of the Erie railroad the measurements are
determined by judgment, the operatives using ordinary calipers. If an
axle 3-1/2 diameter and 6 inches long requires less than 25 tons it is
rejected, and if more than 35 tons it is corrected by reducing the axle.
In order to insure a proper fit of pieces to be a driven or forced fit
it is sometimes the practice to make them taper, and there is a
difference of opinion among practical mechanics as to whether taper or
parallel fits are the best. Upon this point it may be remarked that it
is much easier to measure the parts when they are parallel than when
they are taper, and it is easier to make them parallel than taper.
On the elevated railroads in New York city, the wheel bores being 4-1/8
inches in diameter and 5 inches long, the measurements are taken by
ordinary calipers, the workmen judging how much to allow, and the rule
is to reject wheels requiring less than about 26 tons, or more than
about 35 tons, to force them on. These wheels form excellent examples,
because of the excessive duty to which they are subjected by reason of
the frequency of their stoppage under the pressure of the vacuum brake.
The practice with these wheels is to bore them parallel, finishing with
a feed of 1/4 inch per lathe revolution, and to turn the axle seats
taper just discernible by calipers.
This may, at first sight, seem strange, but examination makes it
reasonable and plain. Let a wheel having a parallel bore be forced upon
a parallel axle, and then forced off again, and the bore of the wheel
will be found taper to an appreciable amount, but increasing in
proportion as the surface of the hole varied from a dead smoothness; in
other words, varying with the depth of the tool marks in the bore and
the smoothness of the cut.
Let the length of the wheel bore be 7 inches long, and the amount
allowed for forcing be .004 inch, and one end of the wheel bore will
have been forced (by the time it is home on the axle) over the length of
7 inches of the axle-seat, whose diameter was .004 larger than the bore:
a condensation, abrasion, or smoothing of the metal must have ensued.
[Illustration: Fig. 1424A.]
Now the other end of the same bore, when it takes its bearing on the
shaft, is just iron, and iron without having suffered any condensation.
If the tool marks be deep, those on one end will be smoothed down while
those at the other remain practically intact. Clearly then, for a
parallel hole, a shaft having as much taper as the wheel bore will get
in being forced over the shaft best meets the requirements; or, for a
parallel shaft or seat, and a taper hole (the taper being proportioned
as before), the small end of the taper hole should be first entered on
the shaft, and then when home both the axle and the wheel-bore will be
parallel.
It may be remarked that the wheel seat on the axle will also be
affected, which is quite true, but the axle is usually of the hardest
metal and has the smoothest surface, hence it suffers but little; not an
amount of any practical importance.
In an experiment upon this point made in the presence of the author by
Mr. Howard Fry and the master mechanic of the Renovo shops of the
Philadelphia and Erie railroad, an axle seat finished by a Whitney
"doctor," and parallel in diameter, was forced into a wheel having a
parallel bore, and removed immediately. On again measuring the axle, the
wheel-seat was found to be 1/1000 taper in its length.
The wheel-bore was found to be but slightly affected in its diameter,
which is explained because it being very smooth, while the turning marks
in the axle were plainly visible, the abrasion fell mainly upon the
latter.
When the enveloping piece or bore is not solid or continuous, but is
open on one side, the degree of the fit may be judged from the amount
that it opens under the pressure of the plug piece.
[Illustration: Fig. 1425.]
Thus the axle brasses of American locomotives are often made circular at
the back, as shown in Fig. 1425, and are forced in endways by hydraulic
pressure. The degree of tightness of the brass within the box may, of
course, be determined by the amount of pressure it requires to force it
in, but another method is to mark a centre punch dot as at J, and before
the brass is put in mark from this dot as a centre an arc of a circle as
L L. When the brass is home in the box a second arc K is marked, the
distance between L and K showing how much the brass has sprung the box
open widening at H. In an axle box whose bore is about 4 inches to 5
inches in diameter, and 6 inches long, 1/32 inch is the allowance
usually made.
Shrinkage fits are employed when a hole or bore requires to be very
firmly and permanently fastened to a cylindrical piece as a shaft. The
bore is turned of smaller diameter than its shaft, and the amount of
difference is termed the allowance for shrinkage. The enveloping piece
is heated so as to expand its bore; the shaft is then inserted and the
cooling of the bore causes it to close or contract upon the shaft with
an amount of force varying of course with the amount allowed for
contraction. If this allowance is excessive, sufficient strain will be
generated to burst the enveloping piece asunder, while if the allowance
for shrinking is insufficient the enveloping piece may become loose.
The amount of allowance for shrinkage varies with the diameter
thickness, and kind of the material; but more may be allowed for wrought
iron, brass, and copper, than for cast iron or steel.
Again, the smoothness and truth of the surfaces is an important element,
because the measurement of a bore will naturally be taken at the tops of
the tool marks, and these will compress under the shrinkage strain,
hence less allowance for contraction is required in proportion as the
bore is smoother.
In ordinary workshop practice, therefore, no special rule for the amount
of allowance for shrinkage obtains, the amount for a desultory piece of
work generally being left to the judgment of the workman, while in cases
where such work is often performed on particular pieces, the amount of
allowance is governed by experience, increasing it if the pieces are
found in time to become loose, and decreasing it if it is found
impossible to get the parts together without making the enveloping piece
too hot, or if it is found to be liable to split from the strain.
The strength of the enveloping piece is again an element to be
considered in determining the amount to be allowed for shrinkage. It is
obvious, for example, that a ring of 8 inches thick, and having a bore
of, say, 6 inches diameter, would be less liable to crack from the
strain due to an allowance of 1/50 inch for contraction, than would a
ring of equal bore and one inch thick having the same allowance. The
strength or resistance to compression of the piece enveloped in
proportion to that enveloping it, is yet another consideration.
The tires for railway wheels are usually contracted on, and Herr Krupp
states the allowance for contraction to be for steel tires 1/100 inch
for every foot of diameter; in American practice, however, a greater
amount is often employed. Thus upon the Erie railroad a 5 foot tire is
given 1/16 inch contraction. The allowance for wrought iron or brass
should be slightly more than it is for steel or cast iron, on account of
the greater elasticity of those metals.
Examples of the practice at the Renovo shops of the Pennsylvania road
are as follows:
Class E, diameter of wheel centre, 44 inches; bore of steel tire,
43-15/16 inches.
Class D, diameter of wheel, 50 inches; bore of tire, 49-9/16 inches.
It is found that the shrinkage of the tire springs or distorts the wheel
centre, hence the tires are always shrunk on before the crank-pin holes
are bored.
Much of the work formerly shrunk on is now forced on by an hydraulic
press. But in many cases the work cannot be taken to an hydraulic press,
and shrinkage becomes the best means. Thus, a new crank pin may be
required to be shrunk in while the crank is on the engine shaft, the
method of procedure being as follows: In heating the crank, it is
necessary to heat it as equally as possible all round the bore, and not
to heat it above a _very dark_ red. In heating it some dirt will
necessarily get into the hole, and this is best cleaned out with a piece
of emery paper, wrapped round a half-round file, carefully blowing out
the hole after using the emery paper. Waste or rag, whether oiled or
not, is not proper to clean the hole with, as the fibres may burn and
lodge in the hole; indeed, nothing is so good as emery paper.
It is desirable to heat the crank as little as will serve the purpose,
and it is usual to heat it enough to allow the pin to push home by hand.
It is better, however, to overheat the crank than to underheat it,
providing that the heat in no case exceeds a barely perceptible red
heat. If, however, the crank once grips the pin before it is home, in a
few seconds the pin will be held so fast that no sledge hammer will move
it. It is well, therefore, to have a man stationed on each side of the
crank, each with a sledge hammer, and to push the crank pin in with a
slam, giving the man in front orders to strike it as quickly as possible
at a given signal; but if the pin does not move home so rapidly at each
blow as to make it appear certain that it will go home, the man at the
rear, who should have a ten-pound sledge, should be signalled to drive
out the crank pin as quickly as he possibly can for every second is of
consequence. All this should be done so quickly that the pin has not
had time to get heated to say 100° at the part within the crank.
So soon as the pin is home, a large piece of wetted cotton waste should
be wrapped round its journal, and a stream of water kept running on it,
to keep the crank pin cold. At the other end water should be poured on
the pin end in a fine stream, but in neither case should the water run
on the crank more than can be avoided. Of course, if the crank is off
the shaft, the pin may be turned downward, and let project into water.
The reasons for cooling the pin and not the crank are as follows: If the
crank be of cast iron, sudden cooling it would be liable to cause it to
split or crack. If the crank pin is allowed to cool of itself, the pin
will get as hot as the crank itself, and in so doing will expand,
placing a strain on the crank that will to some extent stretch it.
Indeed, when the pin has become equally hot with the crank it is as
tight a fit as it will ever be, because after that point both pieces
will cool together, and shrink or contract together, and hence the fit
will be a looser or less tight one to the amount that the pin expanded
in heating up to an equal temperature with the crank.
The correct process of shrinking is to keep the plug piece as cold as
possible, while the outside is cooled as rapidly as can be without
danger of cracking or splitting.
The ends of crank pins are often riveted after being shrunk in, in which
case it is best to recess the end, which makes the riveting easier, and
causes the water poured upon its face to be thrown outward, thus keeping
it from running down the crank face and causing the crank to crack or
split.
It sometimes becomes necessary and difficult to take out a piece that
has been shrunk in, and in this event, as also in the case of a piece
that has become locked before getting fully home in the shrinking
process, there is no alternative but to reheat the enveloping piece
while keeping the enveloped piece as cold as can be by an application of
water.
The whole aim in this case is to heat the enveloping piece as quickly as
possible, so that there shall be but little time for its heat to be
transmitted to the piece enveloped. To accomplish this end melted metal,
as cast iron, is probably the most efficient agent; indeed it has been
found to answer when all other means failed.
[Illustration: Fig. 1426.]
[Illustration: Fig. 1427.]
The fine measurements necessary for shrinkage purposes render it
necessary, where pieces of the same form and kind are shrunk on, to
provide the workmen with standard gauges with which the work may be
correctly gauged. These often consist of simple rods or pieces of iron
wire of the required length. Figs. 1426 and 1427, however, represent an
adjustable shrinkage gauge designed by H. S. Brown, of Hartford,
Connecticut. Fig. 1427 is a sectional, and Fig. 1426 a plan side view of
the gauge. A is a frame, containing at its lower end a fixed measuring
piece B, and provided at its upper end with a threaded and taper split
hub to receive externally the taper-threaded screw cap C, and threaded
internally to receive a tube E, which is plugged at the bottom by the
fixed plug F. The adjustable measuring leg G is threaded with the tube
E, so as to be adjustable for various diameters of boxes, but it is
locked when adjusted by the jamb-nut H. The operation is as follows: The
cap-nut C and jamb-nut H are loosened and screwed back, allowing stem G
and tube E to be adjusted to the exact size of the shaft for which a
shrinkage fit is to be bored, as, say, in an engine crank. In setting
the gauge to the diameter of the shaft, the cap end C and jamb-nut H are
screwed home, so as to obtain a correct measurement while all parts are
locked secure. The cap-nut C draws the split hub upon the tube E, and
the jamb-nut H locks up G to E, so that the shaft measurement is taken
with all lost motion, play and spring of the mechanism taken into
account, so that they shall not vitiate the measurement. This being
done, C is loosened so that E can be rotated, and raised up (by
rotating) to admit the shrinkage gauge-piece J, whose thickness equals
the amount to be allowed for the size of borer to be shrunk on the
shaft. J being inserted, E is rotated back so as to bind J between the
end of E and the foot piece B, when C is screwed down, clamping E again.
Thus the measuring diameter of the gauge is increased to an amount due
to the thickness of the gauge-piece J. At the right of Fig. 1426 an edge
and side elevation of J is shown, the 12/1000 indicating its thickness,
which is the amount allowed for shrinkage, and the 6-inch indicating
that this gauge-piece is to be used for bores of 6 inches in diameter.
The dotted circle K K L L represents a bore to which the gauge is shown
applied.
The system of shrinking employed at the Royal Gun Factory at Woolwich,
England, is thus described by Colonel Maitland, superintendent of that
factory:--
"The inside diameter of the outer tube, when cold, must be rather
smaller than the outside diameter of the inner tube: this difference in
the diameter is called the 'shrinkage.' While the outer coil is cooling
and contracting it compresses the inner one: the amount by which the
diameter of the inner coil is decreased is termed the 'compression.'
Again, the outer coil itself is stretched on account of the resistance
of the inner one, and its diameter is increased; this increase in the
diameter of an outer coil is called 'extension.' The shrinkage is equal
to compression plus the extension, and the amount must be regulated by
the known extension and compression under certain stresses and given
circumstances. The compression varies inversely as the density and
rigidity of the interior mass; the first layer of coils will therefore
undergo more compression than the secondhand the second more than the
third, and so on.
"Shrinking is employed not only as an easy and efficient mode of binding
the successive coils of a built-up gun firmly together, but also for
regulating as far as possible the tension of the several layers, so that
each and all may contribute fairly to the strength of the gun.
"The operation of shrinking is very simple; the outer coil is expanded
by heat until it is sufficiently large to fit easily over the inner coil
or tube (if a large mass, such as the jacket of a Fraser gun, by means
of a wood fire, for which the tube itself forms a flue; if a small mass,
such as a coil, in a reverberatory furnace at a low temperature, or by
means of gas). It is then raised up by a travelling crane overhead and
dropped over the part on to which it is to be shrunk, which is placed
vertically in a pit ready to receive it.
"The heat required in shrinking is not very great. Wrought iron, on
being heated from 62° Fahr. (the ordinary temperature) to 212°, expands
linearly about 1-1000th part of its length; that is to say, if a ring of
iron 1000 inches in circumference were put into a vat of boiling water,
it would increase to 1001 inches, and according to Dulong and Petit the
coefficient of expansion, which is constant up to 212°, increases more
and more from that point upward, so that if the iron ring were raised
150° higher still (_i.e._ to 362°) its circumference would be more than
1002 inches. No coil is ever shrunk on with so great a shrinkage as the
2-1000th part of its circumference or diameter, for it would be strained
beyond its elastic limit. Allowing, therefore, a good working margin, it
is only necessary to raise a coil to about 500° Fahr.,[22] though in
point of fact coils are often raised to a higher degree of temperature
than this in some parts, on account of the mode of heating employed.
Were a coil plunged in molten lead or boiling oil (600° Fahr.) it would
be uniformly and sufficiently expanded for all the practical purposes of
shrinking, but as shrinkings do not take place in large numbers or at
regular times, the improvised fire or ordinary furnace is the more
economical mode, and answers the purpose very well.
[22] The temperature may be judged by color; at 500° F. iron has a
blackish appearance; at 575° it is blue; at 775° red in the dark; at
1,500° cherry red, and so on, getting lighter in color, until it
becomes white, or fit for welding, at about 3,000°.
"Heating a coil beyond the required amount is of no consequence,
provided it is not raised to such a degree of temperature that scales
would form; and in all cases the interior must be swept clean of ashes,
&c., when it is withdrawn from the fire. With respect to the modes of
cooling during the process of shrinking, care must be taken to prevent a
long coil or tube cooling simultaneously at both ends, for this would
cause the middle portion to be drawn out to an undue state of
longitudinal tension. In some cases, therefore, water is projected on
one side of a coil so as to cool it first. In the case of a long tube of
different thickness, like the tube of a R. M. L. gun, water is not only
used at the thick end, but a ring of gas or a heated iron cylinder is
applied at the thin or muzzle end, and when the thick end cools the gas
or cylinder is withdrawn from the muzzle, and the ring of water raised
upward slowly to cool the remainder of the tube gradually.
"As a rule, the water is supplied whenever there is a shoulder, so that
that portion may be cooled first and a close joint secured there; and
water is invariably allowed to circulate through the interior of the
mass to prevent its expanding and obstructing or delaying the operation;
for example, when a tube is to be shrunk on a steel barrel, the latter
is placed upright on its breech end, and when the tube is dropped down
on it, a continual flow of cold water is kept up in the barrel by means
of a pipe and syphon at the muzzle. The same effect is produced by a
water jet underneath, when it is necessary to place the steel tube
muzzle downward for the reception of a breech coil. As to the absolute
amount of shrinkage given when building up our guns, let us take the
12-1/2-inch muzzle-loading gun of 38 tons as an example.
SHRINKAGES OF COILS OF 12.5 INCH R. M. L. GUNS.
-------------+---------------------------+---------------------------
| Shrinkages. |
+-------------+-------------+
| | In terms of |
Coils. | In Inches. | diameter. | Remarks.
+------+------+------+------+
| Rear.|Front.| Rear.|Front.|
-------------+------+------+------+------+---------------------------
| | | D | D |
Breech-piece| .022 | .026 | --- | --- | Shrunk on A tube.
| | | 857 | 807 |
| | | | |
| | | D | D |
B coil | .055 | .01 | --- | --- | " "
| | | 561 | 190 |
| | | | |
| | | D | |
B tube | .035 | nil. | --- | nil. | " "
| | | 668 | |
| | | | |
| | | D | D |
C coil | .03 | .06 | ---- | --- | Shrunk on to breech piece
| | | 1134 | 729 | and rear end of 1 B coil."
-------------+------+------+------+------+---------------------------
The objections to fitting work by contraction where accuracy is required
in the work are, that if the enveloping piece is of cast iron its form
is apt to change from being heated. Furthermore, if the enveloping
piece, which is always the piece to be heated, is of unequal thickness
all round the bore, the thin parts are apt to become heated the most,
and to therefore give way to the strain induced by contraction when
cooling, which, while not, perhaps, impairing the fit, may vitiate the
alignment of parts attached to it. Thus, a crank pin may be thrown out
of true by the alteration of form induced first by unequal heating of
the metal round the crank eye, enveloping the shaft; and secondly,
because of the weakest side of the eye giving way, to some extent, to
the pressure of the contracting strain. To counteract this, the
strongest part of the enveloping piece should be heated the most, or if
the enveloping piece be of equal strength all round its bore, it should
be heated equally all round. To effect this object heated liquids, as
boiling water, or heated fluids, as melted lead, may advantageously be
employed.
In some practice, locomotive wheel tires are heated for shrinking in
boiling water. The allowance for shrinkage is from .075 millimètre to
every mètre in diameter, which is .02952 inch to every 39.37079 inches
of diameter.
The employment of hot water, however, necessitates that the tires be
bored very smoothly and truly, and that the wheel rim be similarly true
and smooth, otherwise the amount of expansion thus obtained will be
insufficient to maintain a permanent fit under the duty to which a wheel
tire is submitted.
Shrinking is often employed to strengthen a weak place or part, or one
that has cracked. The required size is, in this case, a cylindrical
surface that is not a true cylinder, obtained by a rolling wheel rotated
by friction over the surface to be enveloped by the band. Or if the
surface is of a nature not to admit of this, a strip of lead or piece of
lead wire may be lapped round it to get the necessary measurements.
The bands for this purpose are usually of wrought iron, and require in
the case of irregular surfaces to be driven on by hammer blows, so that
the fit may be correct. As the band is forced on a heavy hammer is held
against it, to prevent its moving back and off the work as the other
parts are forced on.
[Illustration: Fig. 1428.]
Very slight bands may be forced on by levers: thus, wagon makers use a
lever or jack, such as in Fig. 1428, for forcing the tires on their
wheels. The wheel is laid horizontally on a table as shown, and the tire
A forced out by the vertical lever, the arm B affording a fulcrum for
the lever, and itself resting against the hub C of the wheel.
The following extracts are from a paper read by Thomas Wrightson, before
the Iron and Steel Institute of Great Britain.
"The large amount of attention bestowed upon the chemical properties of
metals, and the scientific methods adopted for their investigation, have
led to the most brilliant results in the history of iron and steel
industries. It must not, however, be overlooked that iron and steel have
highly important properties other than those which can be examined by
chemical methods. The cause for so little having been done in accurate
observation of the physical properties of iron is twofold: 1. The
molecular changes of the metals are so slow, when at ordinary
temperatures and when under ordinary conditions of strain, that reliable
observations, necessarily extending over long periods, are difficult to
obtain: 2. When the temperatures are high--at which times the greatest
and most rapid molecular changes are occurring--the difficulties of
observation are multiplied to such an extent that the results have not
the scientific accuracy which characterizes the knowledge we have of the
chemical properties of metals.
"The object of the present paper is to draw attention to some phenomena
connected with the physical properties of iron and steel, and to record
some experiments showing the behavior of these metals under certain
conditions.
"In experimenting the author has endeavored to adopt methods which
would, as far as possible, eliminate the two great difficulties
mentioned.
"It is obvious that the possible conditions under which experiments may
be made are so numerous that all which any one experimenter can do is to
record faithfully and accurately his observations, carefully specifying
the exact conditions of each observation, and this must eventually lead
to a more complete knowledge of the physical properties of the metals.
"The author's observations have been led in the following directions:--
"1. The changes in wrought and cast iron when subjected to repeated
heatings and coolings.
"2. The effect upon bars and rings when different parts are cooled at
different rates.
"3. These changes occurring in molten iron when passing from the solid
to the liquid state, and _vice versâ_.
PART I.
"To illustrate the practical importance of knowing the effects of
reiterated heating and cooling on iron plates, one of the most obvious
examples is the action of heat upon the plates of boilers which are
alternately heated and cooled, as in use or otherwise. When in use, the
plates above the fire are subjected to the fierce flame of the furnace
on one side, and on the other side to a temperature approximating to
that of the steam and water in the boiler. Where the conducting surfaces
of the metal are thickened at the riveted seams, a source of danger is
frequently revealed in the appearance of what are known as 'seam-rips.'
"The long egg-ended boilers, much used in the North of England, are very
subject to this breaking away of the seams. From some tests made by the
writer on iron cut from the plates of two different boilers which had
ripped at the seams, and one of which seam-rips had led to an explosion
resulting in the destruction of much property, though happily of no
lives, it was found that the heat acting on the bottom of the boiler
had, through time, so affected the iron at the seam as to make it
brittle, apparently crystalline in fracture, and of small tensile
strength. Farther from the seam the iron appeared in both cases less
injuriously affected. But although the alternate heating and cooling of
the plates over a long period had produced this change in the molecular
condition of the iron, a method of restoration presents itself in the
process of annealing. In subjecting the pieces cut from the seam-rips to
a dull red heat, and then allowing them to cool slowly in sawdust, the
writer found that the fibrous character of the iron appeared again, and
renewed testing showed that the ductility and tensile strength were
restored.
"The same process of annealing is equally effectual in restoring the
tenacity of iron in chains rendered brittle, and apparently crystalline,
by long use, and is periodically applied where safety depends upon
material in this form. Thus the heating and cooling of iron may be
looked upon as the bane or the antidote according to the conditions
under which the process is carried out. This affords an example of the
importance of the physical effects produced by repeated changes of
temperature. The change effected by one heating and cooling is so small
that a cumulative method of experiment is the only one by which an
observable result can be obtained, and this is the method adopted by the
writer in the investigation now to be described.
"It is well known that if a wrought-iron bar be heated to redness, a
certain expansion takes place, which is most distinctly observed in the
direction of its length. It is also known, although not generally so,
that if a bar be thus heated and then suddenly cooled in water, a
contraction in length takes place, the amount of this contraction
exceeding that of the previous expansion, insomuch that the bar when
cooled is permanently shorter than it originally was. If this process of
heating and cooling be repeated, a further amount of contraction is
found to follow for many successive operations.
"Experiments Nos. 1 and 2 were made to verify this, and to show the
increment of contraction after each operation.
"EXPERIMENTS ON WROUGHT-IRON BARS 1-1/8 IN. SQUARE BY 30.05 IN. LONG,
HEATED TO A DULL RED, THEN COOLED SUDDENLY IN WATER.
------------------+------------------------+------------------------
| EXPERIMENT NO. 1. | EXPERIMENT NO. 2.
| Common Iron. | Best Iron.
+------------+-----------+------------+-----------
| |Percentage | |Percentage
|Contraction.|on original|Contraction.|on original
| | length. | | length.
------------------+------------+-----------+------------+-----------
| Inches. | | Inches. |
After 1st cooling | .04 | .13 | .04 | .13
" 2nd " | .10 | .33 | .10 | .33
" 3rd " | .16 | .53 | .14 | .46
" 4th " | .17 | .56 | .16 | .53
" 5th " | .23 | .76 | .20 | .66
" 6th " | .28 | .93 | .24 | .80
" 7th " | .31 | 1.03 | .27 | .89
" 8th " | .33 | 1.10 | .30 | 1.00
" 9th " | .40 | 1.33 | .33 | 1.10
" 10th " | .47 | 1.56 | .39 | 1.30
" 11th " | .52 | 1.73 | .42 | 1.40
" 12th " | .54 | 1.80 | .47 | 1.56
" 13th " | .58 | 1.93 | .51 | 1.70
" 14th " | .62 | 2.06 | .54 | 1.80
" 15th " | .68 | 2.26 | .56 | 1.86
------------------+------------+-----------+------------+-----------
"The Table of Experiment No. 5 shows that at the twenty-fifth cooling a
contraction of 3.05 per cent. had taken place, or an average of .122 per
cent. after each cooling. This is almost identically the same average
result as shown in Experiment No. 1 with straight bars.
"The above experiments only having reference to the permanent
contraction of the iron in the direction of its length, the author made
the following experiments to ascertain the effect in the other
dimensions, and to see whether the specific gravity of the iron was
affected in the reduction of dimensions.
[Illustration: Fig. 1429.]
"_Experiment No. 6._--Wrought-iron plate, .74 inch thick, planed on both
surfaces and all edges to a form nearly rectangular, and of the
dimensions given in Fig. 1429.
"_Specific Gravity._--Two small samples were cut out of different parts
of the same piece of plate from which the experimental piece was planed,
and the specific gravity determined as follows:--
No. 1 piece 7.629 }
No. 2 piece 7.651 } Mean, 7.64.
"_Quality._--Subjecting a piece to tensile strain in the direction of
the grain, it broke at 21.2 tons per square inch of section, the
ductility being such that an elongation of 8.3 per cent. occurred before
fracture, with a reduction of 9.6 per cent. of the area of fracture.
This may be looked upon as representing a fairly good quality of iron.
"A bar of wrought iron, 1-1/8 inches square and 30.00 inches long, was
heated to redness, and then allowed to cool gradually in air.
Measurements after each of five coolings showed no perceptible change of
length.
"_Experiment No. 4._--Wrought-iron bar, 1-1/8 inches square by 30 inches
long, heated to a white heat and cooling gradually in air.
------------------+------------+----------------+----------------
|Contraction.| Percentage on | Remarks.
| |original length.|
------------------+------------+----------------+----------------
| Inches. | |
After 1st cooling | No change. | | ----
" 2nd " | " | | ----
" 3rd " | .02 | .07 | ----
" 4th " | .05 | .17 | ----
" 5th " | .05 | .17 | ----
------------------+------------+----------------+----------------
"It may be remarked, that if the bars be heated to white heat a slight
contraction does occur, as shown by Experiment No. 4, where a bar of the
same dimensions as No. 3 contracted .17 per cent. after the fifth
cooling. As, however, the further remarks on this subject have only
reference to bars heated to redness and then cooled, the writer would
summarize the results of Experiments Nos. 1, 2, and 3, by stating that
wrought-iron bars heated to redness permanently contract in their length
along the fibre when cooled in water of ordinary temperature; but when
cooled in air, they remain unchanged in length.
"To show that this is true as applied to circular hoops, Experiment No.
5 was made upon a wrought-iron bar of 1-1/8 inches square in section,
welded into a circular hoop, 57.7 inches outside circumference.
"_Experiment No. 5._--Wrought-iron hoop, 1-1/8 inches square by 57.7
inches outside circumference, heated to a dull red, then cooled suddenly
in water.
------------------+------------+--------------+-----------------------
| |Percentage of |
|Contraction.| original | Remarks.
| |circumference.|
------------------+------------+--------------+-----------------------
| Inches. | |
After 1st cooling | .06 | .10 | Red heat.
" 2nd " | .06 | .10 | This was nearly white,
" 3rd " | .16 | .28 | but before cooling
" 4th " | .26 | .45 | red hot.
" 5th " | .35 | .61 |
" 6th " | .46 | .80 |
" 7th " | .54 | .93 |
" 8th " | .60 | 1.04 |
" 9th " | .68 | 1.18 |
" 10th " | .76 | 1.32 |
" 11th " | .80 | 1.38 |
" 12th " | .87 | 1.51 |
" 13th " | .94 | 1.63 |
" 14th " | 1.00 | 1.73 |
" 15th " | 1.08 | 1.90 |
" 20th " | 1.30 | 2.25 | On opposite edge 1.66;
" 25th " | 1.76 | 3.05 | hoop splitting.
------------------+------------+--------------+-----------------------
"This hoop was heated to redness and cooled in water twenty-five times,
the circumference of the hoop being accurately measured after each
cooling.[23]
[23] The lengths of circumference were taken, in this and other hoops,
after each cooling, by encircling the periphery with a very fine piece
of "crinoline" steel, the ends of which were made just to meet round
the original hoop. By again encircling the hoop with the same piece of
steel the expansion was shown by a gap between the ends, and a
contraction by an overlap, either of which was measured with great
accuracy by means of a finely divided scale.
"Two wrought-iron bars, 1-1/8 inches square and 30.05 inches long, were
selected.[24] No. 1 was of common "Crown" quality; No. 2 of a superior
quality known as "Tudhoe Crown." These bars were heated to redness in a
furnace and then plunged into water of ordinary temperature, the length
being accurately measured after each cooling. After fifteen heatings and
coolings the permanent contraction on No. 1 bar was 2.26 per cent. of
the original length, and that on No. 2 bar 1.86 per cent., or an average
on the two bars of about .13 per cent. after each cooling, the increment
of contraction being nearly equal after each successive operation. It is
noticeable that after the first two coolings the better quality of iron
did not contract quite so much as the common quality, and that in the
latter the contraction was going on as vigorously at the fifteenth as at
the first cooling.
[24] In some of these experiments the original sizes of the iron were
only measured with an ordinary foot-rule, in which case the dimensions
are given in the ordinary fraction used in expressing the mercantile
sizes of iron. When accurate measurement was taken decimals are
invariably used both in this paper and the Tables of Experiment.
"Similar bars of wrought iron, heated to redness and then allowed to
cool in air at ordinary temperature, do not appear to suffer any
permanent change in their length.
"Experiment No. 3 was made to verify this.
"_Experiment No. 3._--Wrought-iron bar, 1-1/8 inches square by 30 inches
long heated to a dull red and cooled gradually in air.
------------------+------------+----------------+-----------
|Contraction.| Percentage on |
| |original length.| Remarks.
------------------+------------+----------------+-----------
After 1st cooling | No change. | ---- | ----
" 2nd " | " | ---- | ----
" 3rd " | " | ---- | ----
" 4th " | " | ---- | ----
" 5th " | " | ---- | ----
------------------+------------+----------------+-----------
[Illustration: _Wrought iron rectangular plate. 14" thick × 11" 995 ×
598 planed on both surface and edges. Heated to redness, and cooled in
water 50 times. The dotted lines show original form, the black lines the
form after the experiment._
(Two-ninths of full size.)
Fig. 1430.]
The plate was subjected to fifty heatings to redness and subsequent
coolings in water of ordinary temperature. At every tenth cooling
accurate measurements were taken of the contraction in superficial
dimensions, and Fig. 1430 shows the final form after fifty coolings. The
intermediate measurements at every tenth cooling showed a uniform and
gradual decrease in the superficial dimensions, but the thicknesses were
only measured after the fifty coolings had been completed. The thickness
appears to have varied considerably; in some places, notably towards the
centre and outside edges, being much reduced. Between the centre and
outside edges the thickness appears to have increased, and in some few
places the plate has been split open. The average dimensions in inches
before and after the experiment were as follows (dimensions of cracks
being allowed for):--
----------------------+---------+----------+----------+-----------
| | | | Cubic
| Average | Average | Average | inches
| length. | breadth. |thickness.|capacity.
+---------+----------+----------+----------
| Inches. | Inches. | Inches. |
Original | 11.995 | 5.98 | .74 | 53.08
After 50 coolings | 11.25 | 5.59 | .774 | 48.72
Per cent. variation { |Decrease |Decrease | Increase | Decrease
from original { | of | of | of | of
{ |6.2 p. c.|6.52 p. c.| 4.6 p. c.| 8.2 p. c.
----------------------+---------+----------+----------+----------
"Three triangular pieces of iron were then cut out of the plate from
positions indicated on the diagram; No. 1A from the part most reduced in
thickness, No. 3A from the part most increased in thickness, and No. 2A
from a part where the thickness was a mean between the thickest and
thinnest part. The specific gravities were accurately determined as
follows:--
No. 1A 7.552 thinnest part.
No. 2A 7.574 average thickness.
No. 3A 7.560 thickest part.
"The average of these specific gravities is 7.562.
"The average before experiment was 7.64. Hence the average loss in
specific gravity has been 1.02 per cent.
"The small triangular piece No. 1A, specific gravity 7.552 (already
subjected to fifty heatings when forming part of the solid plate), was
next heated and cooled fifty times more. The specific gravity at the end
of the one hundred total coolings was 7.52, being .43 per cent. lower
than after fifty heatings in plate, and 1.57 per cent. lower than 7.64,
the original mean specific gravity of the plate.
"The same piece, 1A, was then heated twenty-five times more, making 125
in all. On taking the specific gravity it was found to be 7.526, or
practically the same as after 100 total heatings and coolings.
"It thus appears that there is an undoubted decrease in specific gravity
on repeated heating and cooling as described up to one hundred coolings,
the specific gravity decreasing as much as 1.57 per cent.; that this
percentage appears to be less when the pieces of iron operated upon are
very small; that while there is a decrease of specific gravity there is
also a decrease of total volume.
[Illustration: Fig. 1431.]
"From the above it was evident that the volume was affected by several
causes:--
"1. By the permanent contraction of the outer skin, either the volume
would be lessened, or relief by bulging out the sides must occur.
"2. By the decrease of specific gravity an increase of volume must
occur, which could also find relief in bulging.
"3. A diminution of the whole mass must occur through scaling of the
surface.
"Having determined the change in specific gravity by Experiment 6, we
only now want to determine the loss of volume due to surface scaling,
and we can then infer the actual contraction of the outer skin.
"_Experiment No. 7._--To ascertain the amount of scaling which took
place in heating and cooling under same conditions as Experiment No. 6,
a wrought-iron plate was cut from the same piece as No. 6, thickness .74
in., planed on both surfaces and all edges to a form nearly rectangular,
and to the dimensions given in Fig. 1431.
"The only difference (except the very small difference in the
dimensions) between this and 1430, was that the principal grain of the
iron was in 1431 in the direction of the arrow, whereas in the other it
was lengthwise of the plate.
"This piece was subjected to fifty heatings to redness and sudden
coolings in water of ordinary temperature, as in the case of No. 6. The
change in form was exactly the same in general character, but the
contraction was not quite so great either in length or breadth; the
increase in thickness, however, was proportionately greater, the volume
(measured by displacement of water) after fifty heatings being 48.6
cubic inches, which is nearly the same as in No. 6 after the same number
of heatings. The weight of the piece:--
Avoirdupois.
lbs. oz. dr.
Before heating 14 10 15
After fifty heatings 13 5 10
------------
Difference 1 1 5
"This represents a loss of 9.07 per cent. of the original weight by
scaling, and upon the whole original surface (sides and edges)
represents a thickness of .0284 of an inch for the fifty immersions, or
.00057 of an inch for the thickness of the film lost at each immersion
over the whole surface.
"Calculating the weight of No. 6 before and after experiment from the
volumes and specific gravities, we find the following:--
Mean Weight of
specific cubic inch
Volume. gravity. water. Pounds.
Weight before heating should be 53.08 × 7.64 × .036 = 14.599
" after " " 48.72 × 7.562 × .036 = 13.262
------
Difference in weight 1.337
the ascertained difference in the case of No. 7 being 1.332, thus
sufficiently accounting for the discrepancy between specific gravity and
change of volume by the scaling.
"By Experiment 7 it has been shown that the loss of thickness due to
scaling after fifty immersions was .0284 inch over the whole surface
(sides and edges.) Therefore, assuming this scaling as uniform over the
surface, the girth, whether measured lengthwise or breadthwise, should
be eight times .0284, or .23 inch less after immersion than before. Now
the gross loss of girth is:--
--------------------------------------+-----------+------------
|Lengthwise.|Breadthwise.
--------------------------------------+-----------+------------
| Inches. | Inches.
In No. 6 | 1.38 | .86
In No. 7 | 1.2 | .52
+-----------+------------
Or for both experiments a mean of | 1.29 | .69
Deducting from them the loss of | |
girth due to scaling | .23 | .23
+-----------+------------
Net contraction after fifty immersions| 1.06 | .46
Or in percentage of original girths, | |
which were | 25.46 | 13.43
| per cent. | per cent.
We have a percentage of | 4.16 | 3.42
Or for each immersion an average of | .083 | .07
--------------------------------------+-----------+------------
"Comparing these results with those of Experiments Nos. 1, 2, and 5, we
find that the contraction of the skin of the plate is less for each
immersion than that of a bar or hoop, in the proportion of .125 to .083.
This is what might be expected, as the contraction of the plate is
resisted by the volume of heated matter inside, which is eventually
displaced by bulging, while the bar finds relief endwise without having
to displace the interior.
"We have now before us the following facts, substantiated by the
experiments described:--
"1. That in heating to redness, and then cooling suddenly in water at
ordinary temperatures, bars and plates of wrought iron, a reduction of
specific gravity takes place, the amount being about 1 per cent. after
fifty immersions, and 1.57 per cent. after one hundred immersions,
further heatings and coolings not appearing to produce further change.
"2. That a reduction of the surface takes place after each heating and
cooling, this being due to two causes:--
"_a._ The scaling of the surface, which is shown to amount to a film
over the (sides and edges) entire area of .00057 inch in thickness for
each immersion, or 0.284 inch for fifty immersions (Experiment 7).
"_b._ A persistent contraction, which takes place after each immersion.
This varies according to the form of the iron, being in plates from .07
per cent. to 0.83 per cent. (Experiment 6), while in long bars it varies
from .122 to .15 per cent. (Experiments 1, 2, and 5). This contraction
continues vigorously up to fifty immersions, and probably much farther.
"3. That in the case of plates a bulging takes place on the largest
surfaces, increasing the thickness towards the centres, although the
edges diminish in thickness.
"4. That wrought-iron bars heated to redness, and allowed to cool slowly
in air, do not show any change in dimensions (Experiment 3).
"The reduction of specific gravity, and the bulging out of the sides,
have been explained as follows by the learned Secretary of the Royal
Society, Professor Stokes, who has taken considerable interest in these
experiments, and who has kindly allowed the author to publish the
explanation:
"'When the heated iron is plunged into water, the skin tends everywhere
to contract. It cannot, however, do so to any significant extent by a
contraction which would leave it similar to itself, because that would
imply a squeezing in of the interior metal, which is still expanded by
heat, and is almost incompressible. The endeavor, then, of the skin to
contract is best satisfied, consistently with the retention of volume of
the interior, by a contraction of the skin in the two longish lateral
directions, combined with a bulging out in the short direction. The
still plastic state of the interior permits of this change.
"'Conceive an india-rubber skin of the form of the plate in its first
state, the skin being free from tension, and having its interior filled
with water, treacle, or pitch. I make abstraction of gravity. It would
retain its shape. But suppose, now, the india-rubber to be endowed with
a tension the same everywhere similar to that of india-rubber that has
been pulled out, what would take place? Why, the flat faces of
considerable area, being comparatively weak to resist the interior
pressure, would be bulged out, and the vessel would contract
considerably in the long directions, increasing in thickness. This is
just what takes place with the iron in the first instance. But when the
cooling has made further progress, and the solidified skin has become
comparatively thick and strong, the further cooling of the interior
tends to make it contract. But this it cannot well do, being encased in
a strong hide, and accordingly the interior tends to be left in a porous
condition.'
"The reduction by scaling does not require any explanation. The only
fact which appears unaccounted for is this persistent contraction of the
cooled iron skin, which does not appear to be explicable on any
mechanical grounds; and we are, therefore, obliged to look upon it as
the result of a change in the distance of the molecules of the iron,
caused by the sudden change of temperature in the successive coolings.
"Our next subject is the curious effect of cooling bars or rings by
partial immersion in water. Bearing in mind the results at which we have
arrived, viz., that wrought iron contracts when immersed in water after
heating, and that when allowed to cool in air it remains of the same
dimensions, let us ask what would be the behavior of a bar or circular
hoop of iron cooled half in water and half in air, the surface of the
water being parallel to the fibre and at right angles to the axis of the
hoop?
"Arguing from the results of Experiments 1, 2, and 5, it might be
expected that the lower portion cooled in water would suffer permanent
contraction; and, arguing from Experiment 3, that the upper or
air-cooled edge would not alter. This apparently legitimate conclusion
is completely disproved by experiments. This will be seen by a reference
to Experiments 8, 9, and 10.
[Illustration: Fig. 1432.--Experiments with a circular hoop of wrought
iron. Appearance of the hoop at the beginning.]
"In No. 8 a circular hoop of wrought iron was forged out of a 3-1/2-inch
by 1/2-inch bar, the external diameter being about 18 inches, the
breadth, 1/2 inch, being parallel to the axis of the hoop. This hoop,
Fig. 1432, was heated to redness, then plunged into cold water half its
depth, the upper half cooling in air. The changes in the external
circumference of the hoop were accurately measured after each of twenty
successive coolings, at the end of which the external circumference of
the water-cooled edge had increased 1.24 inches, or 2.14 per cent. of
its original length, and the air-cooled edge had contracted 7.9 inches,
or 13.65 per cent.
"_Experiment No. 8._--Wrought-iron hoop, 3-1/2 inches by 1/2 inch by
about 18 inches in diameter, or exactly 57.85 inches in circumference at
top, and 57.95 inches at bottom edge.
-------------+--------------------+--------------------+--------------
| Top Edge. | Bottom Edge. |
+--------+-----------+--------+-----------+
|Contrac-|Percentage | Expan- |Percentage |
| tion. |of original| sion. |of original|
| | circum- | | circum- | Remarks.
| | ference. | | ference. |
-------------+--------+-----------+--------+-----------+--------------
| Ins. | | Ins. | |
After 1st dip| .50 | .86 | .08 | .14 |
" 2nd " | .99 | 1.71 | .08 | .14 |
" 3rd " | 1.47 | 2.54 | .26 | .45 |
" 4th " | 1.92 | 3.32 | .30 | .52 |
" 5th " | 2.30 | 3.97 | .34 | .59 |
" 6th " | 2.60 | 4.49 | .40 | .70 |Slight crack
| | | | |in expanded
| | | | |edge.
" 7th " | 2.94 | 5.25 | .44 | .76 |
" 8th " | 3.40 | 5.98 | .50 | .86 |
" 9th " | 3.70 | 6.39 | .56 | .96 |
" 10th " | 4.40 | 7.60 | .62 | 1.07 |
" 11th " | 4.42 | 7.64 | .66 | 1.14 |
" 12th " | 4.85 | 8.40 | .70 | 1.22 |
" 13th " | 5.24 | 9.02 | .78 | 1.34 |
" 14th " | 5.74 | 9.92 | .80 | 1.39 |
" 15th " | 6.00 | 10.37 | .86 | 1.49 |
" 20th " | 7.90 | 13.65 | 1.24 | 2.14 |After de-
| | | | |ducting for a
| | | | |crack .06 inch
| | | | |wide which
| | | | |appeared at
| | | | |sixth dip.
-------------+--------+-----------+--------+-----------+--------------
"It will be observed that we have here two remarkable phenomena: 1. The
reversal of the expansion and contraction as described. 2. The very
large amount of contraction on the upper edge compared with what was
exhibited in Experiment 5 of entire submersion.
"The table showing Experiment 5 gives a contraction of 2.25 per cent.
after the twentieth cooling, whereas the contraction on the air-cooled
edge of Experiment 8 is 13.65 per cent., or six times the contraction of
an entirely submerged hoop.
[Illustration: Fig. 1433.--Condition of the hoop after the twentieth
cooling.]
"To ascertain whether these unexpected phenomena had any connection with
the circular form of the hoop, Experiment 9 was made with a straight bar
of iron 3-1/2 inches deep by 1/2 inch thick by 28.4 inches long.
"_Experiment No. 9._--Wrought-iron bar, 3-1/2 inches by 1/2 inch by 28.4
inches long, heated to a dull red, then quenched half its depth in
water.
------------------+--------------------+--------------------
| Bottom Edge. | Top Edge.
+--------+-----------+--------+-----------
| Expan- |Percentage |Contrac-|Percentage
| sion. |on original| tion. |on original
| | length. | | length.
------------------+--------+-----------+--------+-----------
| Inches.| | Inches.|
After 1st cooling | .05 | .18 | .26 | .91
" 2nd " | .10 | .35 | .43 | 1.51
" 3rd " | .10 | .35 | .54 | 1.90
" 4th " | .14 | .49 | .75 | 2.64
" 5th " | .20 | .70 | .92 | 3.24
" 6th " | .30 | 1.05 | 1.25 | 4.40
" 7th " | .34 | 1.20 | 1.50 | 5.28
" 8th " | .38 | 1.34 | 1.56 | 5.53
" 9th " | .39 | 1.37 | 1.66 | 5.84
" 10th " | .40 | 1.40 | 1.76 | 6.19
" 11th " | .41 | 1.43 | 1.84 | 6.48
" 12th " | .44 | 1.55 | 1.96 | 6.90
------------------+--------+-----------+--------+-----------
"This was cooled half in air and half in water, and the length of the
two edges measured accurately after each of twelve coolings. At the end
of this experiment the air-cooled edge had contracted 6.9 per cent.,
while the water-cooled edge had expanded 1.55 per cent. of the original
length. The effect on the bar was to make it gradually curve, the
water-cooled or extended edge becoming convex, the air-cooled or
contracted edge concave.
[Illustration: Fig. 1434.--Experiments with a wrought-iron bar.
Appearance of the piece before heating.]
"Experiment No. 10 was made in order to show the effect of reversing
this cooling process. After five coolings, a bar of iron, 28 inches
long, 3-1/2 inches deep, and 1/2 inch thick, was curved so that the
versed sine of its air-cooled edge was 1-1/2 inches. The coolings were
then reversed, what was the air-cooled edge being then immersed in
water. After five more coolings the bar was restored to within 1/8 inch
of being straight, and the eleventh cooling threw the concavity on the
other side of the bar.
[Illustration: Fig. 1435.--Appearance of the bar after the twelfth
cooling.]
"_Experiment No. 10._--Wrought-iron flat bar, 28 inches long by 3-1/2
inches by 1/2 inch, heated to dull red, then quenched half its depth in
water, up to five heats, then the opposite edge dipped.
-----------+-----------+------------+------------------
| | | Reversed Cooling.
| | +------------------
|Versed sine| | Versed sine
|of concave,| | of concave,
| _i.e._ | | _i.e._ now
|air-cooled | | water-cooled
| edge. | | edge.
-----------+-----------+------------+------------------
| Inches. | | Inches.
1st cooling| 5/16 | 6th cooling| 1-3/16
2nd " | 9/16 | 7th " | 7/8
3rd " | 13/16 | 8th " | 3/4 scant.
4th " | 1-3/8 | 9th " | 3/8 full.
5th " | 1-1/2 |10th " | 1/8
| |11th | Brought concavity
| | | 1/8 in. on other
| | | side.
-----------+-----------+------------+------------------
[Illustration: Fig. 1436.--After the preceding experiment the same bar
was reheated and reversed in the water, the eleventh cooling resulting
in the above form, the bar bending in the opposite direction from that
previously shown.]
"When the author had proceeded thus far, these curious results were
shown to several leading scientific men, who expressed interest in the
subject, which encouraged the author to extend his experiments under
varied conditions with a view of ascertaining the cause for these
anomalous effects. These experiments (Nos. 11 to 17) are fully recorded,
and the results shown on the diagrams; the actual rings are also on the
table before you.
"_Experiment No. 11._--Wrought-iron hoop, turned and bored, 37.1 inches,
outside circumference, by 2.95 inches deep by .44 inch thick, the grain
of the iron running the short way of the bar from which the hoop was
made, heated to redness, then cooled half its depth in water (see Fig.
1437 at A for final form of hoop after ten heatings and coolings).
-----------------+--------------------+--------------------
| Top Edge. | Bottom Edge.
+--------+-----------+--------+-----------
|Contrac-|Percentage | Expan- |Percentage
| tion. |on original| sion. |on original
| | length. | | length.
-----------------+--------+-----------+--------+-----------
| Inches.| | Inches.|
After 1st cooling| .3 | .83 | .05 | .13
" 2nd " | .64 | 1.72 | .12 | .32
" 3rd " | 1.02 | 2.75 | .22 | .60
" 4th " | 1.38 | 3.72 | .30 | .80
" 5th " | 1.62 | 4.37 | .37 | 1.00
" 10th " | 3.14 | 8.46 | .76 | 2.05
-----------------+--------+-----------+--------+-----------
"_Experiment No. 12._--Wrought-iron hoop, turned and bored, 6 inches
diameter (18.85 inches circumference) outside, by 2 inches deep by .375
inch thick, heated to redness, then cooled, with lower edge barely
touching the water (see Fig. 1437 at B for final form of hoop after
twenty heatings and coolings).
-----------------+--------------------+--------------------
| Top Edge. | Bottom Edge.
+--------+-----------+--------+-----------
|Contrac-|Percentage |Contrac-|Percentage
| tion. |of original| tion. |of original
|Outside | circum- |Outside | circum-
|circum- | ference. |circum- | ference.
|ference.| |ference.|
-----------------+--------+-----------+--------+-----------
| Inches.| | Inches.|
After 5th cooling| .10 | .53 | .16 | .85
" 10th " | .22 | 1.17 | .34 | 1.80
" 15th " | .32 | 1.70 | .48 | 2.54
" 20th " | .48 | 2.54 | .62 | 3.30
-----------------+--------+-----------+--------+-----------
"_Experiment No. 13._--Wrought-iron hoop, turned and bored, 6 inches
diameter (18.85 inches circumference) outside by 2 inches deep by .375
inch thick, heated to redness, then cooled one-fourth its depth in water
(see Fig. 1437 at C for final form of hoop after twenty heatings and
coolings).
-----------------+--------------------+--------------------------------
| Top Edge. | Bottom Edge.
+--------+-----------+-------------------+-----------
|Contrac-|Percentage | |Percentage
| tion. |of original| |of original
| | circum- | Extension. | circum-
| | ference. | | ference.
-----------------+--------+-----------+-------------------+-----------
| Inches.| | Inches. |
After 1st cooling| .06 | .32 | .02 | .10
" 5th " | .28 | 1.50 {|A hair's breadth |
| | {|contraction. |
" 10th " | .56 | 3.00 { |Returned to origi- |
| | { |nal circumference. |
" 15th " | .78 | 4.14 | .02 contraction. | .10
" 20th " | 1.12 | 6.00 | .02 contraction. | .10
-----------------+--------+-----------+-------------------+-----------
"_Experiment No. 14._--Wrought-iron hoop, turned and bored. 6 inches
diameter (18.85 inches circumference) outside by 2 inches deep by .375
inch thick, heated to redness, then cooled one-half its depth in water
(see Fig. 1437 at D for final form of hoop after twenty heatings and
coolings).
-----------------+--------------------+--------------------
| Top Edge. | Bottom Edge.
+--------+-----------+--------+-----------
|Contrac-|Percentage | Expan- |Percentage
| tion. |of original| sion. |of original
|Outside | circum- |Outside | circum-
|circum- | ference. |circum- | ference.
|ference.| |ference.|
-----------------+--------+-----------+--------+-----------
| Inches.| | Inches.|
After 5th cooling| .46 | 2.44 | .06 | .32
" 10th " | .96 | 5.00 | .09 | .48
" 15th " | 1.34 | 7.10 | .18 | .96
" 20th " | 1.80 | 9.10 | .26 | 1.38
-----------------+--------+-----------+--------+-----------
"_Experiment No. 15._--Wrought-iron hoop turned and bored, 6 inches in
diameter (18.85 inches circumference) outside by 2 inches deep by .375
inch thick, heated to redness, then cooled three-fourths its depth in
water (see Fig. 1437 at E for final form of hoop after twenty heatings
and coolings).
-----------------+--------------------+-------------------------------
| Top Edge. | Bottom Edge.
+--------+-----------+-------------------+-----------
|Contrac-|Percentage | |Percentage
| tion. |of original| |of original
| | circum- | Expansion. | circum-
| | ference. | | ference.
-----------------+--------+-----------+-------------------+-----------
| Inches.| | Inches. |
After 1st cooling| .05 | .26 | .015 | .08
" 5th " | .30 | 1.60 | .02 | .10
" 10th " | .56 | 3.00 {| A hair's breadth |
| | {| contraction. |
" 15th " | .74 | 3.92 { | .02 |} .10
| | { | contraction. |}
" 20th " | 1.02 | 5.40 {| .03 | } .10
| | {| contraction. | }
-----------------+--------+-----------+-------------------+-----------
"_Experiment No. 16._--Cast-copper ring, turned and bored to same
dimensions as Nos. 12, 13, 14, and 15, heated to redness, then cooled
half its depth in water (see Fig. 1437 at F for final form of hoop after
twenty heatings and coolings).
-----------------+--------------------+--------------------
| Top Edge. | Bottom Edge.
+--------+-----------+--------+-----------
|Contrac-|Percentage | Expan- |Percentage
| tion. |of original| sion. |of original
| | circum- | | circum-
| | ference. | | ference.
-----------------+--------+-----------+--------+-----------
| Inches.| | Inches.|
After 1st cooling| .01 | .05 | .05 | .26
" 2nd " | .01 | .05 | .08 | .42
" 3rd " | .02 | .10 | .14 | .75
" 4th " | .02 | .10 | .17 | .90
" 5th " |} No change from | .22 | 1.17
" 10th " |} original size | .40 | 2.13
" 15th " |} from 5th to | .56 | 3.00
" 20th " |} 20th cooling. | .70 | 3.70
-----------------+--------------------+--------+-----------
[Illustration: Fig. 1437.]
"It will be unnecessary to occupy much time in analyzing the
experiments, as any one who takes a practical interest in the subject
will have full information in the diagrams and tables. Professor Stokes
drew attention to the fact that, in 1863, similar phenomena had been
noticed by Colonel Clark, of the Royal Engineers. His experiments, made
at the Royal Arsenal, Woolwich, were published in the 'Proceedings of
the Royal Society,' and Professor Stokes had himself attached an
explanatory note, the outline of which was as follows:--
"Imagine a cylinder divided into two parts by a horizontal plane at the
water-line, and in this state immersed after heating. The under part,
being in contact with water, would rapidly cool and contract, while the
upper part would cool but slowly. Consequently by the time the under
part had pretty well cooled, the upper part would be left jutting out;
but when both parts had cooled their diameters would again agree. Now in
the actual experiments the independent motion of the two parts is
impossible on account of the continuity of the metal; the under part
tends to pull in the upper, and the upper to pull out the under. In this
contest the cooler metal, being the stronger, prevails, and so the upper
part gets pulled in a little above the water-line while still hot. But
it has still to contract in cooling, and this it will do to the full
extent due to its temperature, except in so far as it may be prevented
by its connection with the rest. Hence, on the whole, the effect of this
cause is to leave a permanent contraction a little above the water-line,
and it is easy to see that the contraction must be so much nearer to the
water-line as the thickness of the metal is less, the other dimensions
of the hollow cylinder and the nature of the metal being given. When the
hollow cylinder is very short, so as to be reduced to a mere hoop, the
same cause operates, but there is not room for more than a general
inclination of the surface, leaving the hoop bevelled.
"The expansion of the bottom edge was not noticed in Colonel Clark's
paper, perhaps owing to the much smaller hoops which he used in
experimenting. Accepting Professor Stokes' explanation of the top
contraction, it appears that expansion of the bottom may be accounted
for by the reacting strain put on the cooled edge when forcing in the
top edge, acting in such a way as to prevent the cooled edge coming
quite to its natural contraction, and this, when sufficiently great,
expresses itself in the form of a slight expansion.
"_Experiment No. 14._--Forged steel hoop, turned and bored, 18.53 inches
in circumference outside by 2.375 inches deep by .27 inch thick, heated
to redness, then cooled one-half its depth in water (see Fig. 1437 at G
for final form of hoop after three heatings and coolings).
-----------------+--------------------+-------------------+-------------
| Top Edge. | Bottom Edge. |
+--------+-----------+-------+-----------+
|Contrac-|Percentage | Expan-|Percentage |
| tion. |of original| sion. |of original|
| | length. | | length. |
-----------------+--------+-----------+-------+-----------+-------------
| Inches.| |Inches.| |
| | | | {|Cracked at
| | | | {|water-
After 1st cooling| .06 | .32 | -- | -- {|cooled
| | | | {|edge one-
| | | | {|third depth
| | | | {|of ring.
| | | | |
" 2nd " | .12 | .64 | -- | -- |
| | | | |
| | | | {|After allow-
| | | | {|ing for
" 3rd " | .20 | 1.08 | .05 | .27 {|three small
| | | | {|cracks in
| | | | {|bottom edge."
-----------------+--------+-----------+-------+-----------+-------------
The shrinkage of iron and steel by cooling rapidly is sometimes taken
advantage of by workmen to refit work, the principles involved in the
process being as follows:--
Suppose in Fig. 1438 _a_ _a_ represents a piece of wrought-iron tube
that has been heated to a bright red and immersed in cold water _c_ _c_
from the end B to D, _until that end is cold_. The part submerged and
cold will be contracted to its normal diameter and have regained its
normal strength, while the part above the water, remaining red-hot,
will be expanded and weak. There will be, then, a narrow section of the
tube, joining the heated and expanded part to the cooled and contracted
part, and its form will be conical, as shown at D D. Now, suppose the
tube to be slowly lowered in the water, the cold metal below will
compress the heated metal immediately above the water-line, the cone
section D being carried up into the metal before it has had time to
cool; and the tube removed from the water when cold will be as shown in
Fig. 1438, from _c_ to D, representing the part first immersed and
cooled. To complete the operation the tube must be heated again from the
end _c_ to a short distance past D, and then immersed from E nearly to
D, and held still until the submerged part is cold, when the tube must
be slowly lowered to compress the end _c_ D, making the tube parallel,
but smaller in diameter and in bore, while leaving it of its original
length, but thickening its wall.
[Illustration: Fig. 1438.]
[Illustration: Fig. 1439.]
This process may, in many cases, be artificially assisted. Suppose, for
example, a washer is too large in its bore; it should have its hole and
part of its radial faces filled with fire-clay, as shown in Fig. 1439,
in which A is the washer and B B the clay, _c_ _c_ being pieces of wire
to hold the fire-clay and prevent its falling off. The washer should be
heated to a clear red and plunged in the water D D, which will cool and
shrink the exterior and exposed metal in advance of the interior, which
will compress to accommodate the contraction of the outer metal, hence
the hole will be reduced. This operation may be repeated until the hole
be entirely closed.
[Illustration: Fig. 1440.]
[Illustration: Fig. 1441.]
Another method of closing such a piece as an eye of large diameter
compared to its section, is shown in Fig. 1440; first dipping the heated
eye at A and holding it there till cold and then slowly lowering it into
the water, which would close the diameter across C, and, after
reheating, dipping at D till cold, and then slowly immersing, which
would close the eye across E. To shrink a square ring, the whole ring
would require to be heated and a side of the square dipped, as shown in
Fig. 1441, until quite cold, and then immersed slowly for about an inch,
the operation being performed with a separate heating for each side.
Connecting rod straps, wheel-tires, and a large variety of work may be
refitted by this process, but in each case the outside diameter will be
reduced.