There are a great many different systems used in indexing drawings, most
of which have some good points, but very few are sufficiently elastic to
cover a wide field. A plan based upon the decimal system of notation is
very simple, and, as there is no practical limit to the number of
subdivisions, it can be expanded indefinitely. Following are the main
outline features of the system as adapted to the needs of drawing
offices belonging to large works.
The main division numbers, 000, 100, 200, 300, etc., are used
respectively for all plans and general sheets referring to the division
concerned. 100 includes general plans covering more than one department,
and all small-scale plans with cross references to departments covered.
The class or tens divisions contain general drawings of the
subdivisions, the subclasses or units divisions being limited to details
only. Further subdivisions would probably be necessary in some cases. A
card index with cross references and written by someone who knew what to
do is an essential part of the system.
[Illustration: GEARING AND DESIGN]
[Illustration: Fig. 263.]
Gearing.
Under this heading the author has grouped some information relating to
a subject of wide interest and one sure to interest a student of
mechanical drawing.
The diagrams are intended for exercises in drawing, _i. e._, to be
redrawn as parts of practice; the text is to be studied not only for
the good to be gained from the study of gearing, but as an example of
the way in which written or printed descriptions are necessary to
explain a subject illustrated by drawings.
_A gear_ is primarily a toothed wheel; gearing is a train of toothed
wheels for transmitting motions; there are two chief sorts of toothed
gearing, viz., spur gearing and bevel gearing.
_A spur wheel_ has teeth around the edge pointing to the center;
commencing at the center, a spur wheel may be said to consist of a hole,
square, octagonal or round, for its axle or shaft; a hub; the web, body
or arms; a rim, and the teeth; see fig. 263.
_A spur wheel_ has teeth on its circumference which run parallel to its
shaft; wheels as shown in fig. 271 are termed _helical wheels_; these
are similar to spur wheels except their teeth are arranged upon
different angles to the shaft.
_A bevel_ is a slant or inclination of a surface from a right line,
hence a bevel wheel is one whose teeth stand beveling or at an oblique
angle to the shaft, or towards the center; see fig. 267.
_Miter wheels_ are bevel wheels of the same size, working at right
angles with one another; see fig. 268.
_The diameter of both spur and bevel wheels_ is measured and calculated
neither from the outside nor from the bottom of the teeth, but on the
pitch circle. When we speak of the diameter of a spur or bevel wheel, we
mean the diameter of the pitch circle, without any reference to the form
of tooth.
_The addendum circle_ of a toothed wheel is as shown in illustration,
fig. 264; _addendum_ means “something added,” and, as shown in the
figure, it is the part added beyond the pitch “line” or circle.
[Illustration: Fig. 264.]
_The pitch line_ is the most important one in gearing; the “pitch line”
or “pitch circle” is supposed to be the working circle. This is shown in
P--P in fig. 274.
_The periphery_ of a wheel is the extreme circumference, as N in fig.
274.
All parts of gear-wheels consist of portions, to which have been given
generally accepted names. Fig. 264 shows the “addendum circle” and the
“pitch line” as marked. The teeth and rim are shown in white, and the
other portions are indicated by the names.
_The circular pitch line_, as opposed to the diametral pitch, is the
same as the pitch circle. It is a line which bisects all the teeth of a
toothed wheel.
_The rolling circle_ is the same as the circular pitch line.
_Diametral_ means pertaining to a diameter or the length of a diameter;
hence a diametral pitch is a system of measures or enumeration based
upon the diameter instead of the circular pitch line; it is used very
generally in spacing for fine tooth gear. Wheels of this description
usually have their teeth cut in a gear-cutting machine, _i. e._, medium
and fine tooth gears.
[Illustration: Fig. 265.]
_A cog wheel_ is the general name for any wheel which has a number of
cogs placed around its circumference.
When the teeth of a wheel are made of the same material and formed of
the same piece as the body of the wheel, they are called _teeth_; when
they are made of wood or some other material and fixed to the
circumference of the wheel, they are called _cogs_; see fig. 265.
_A pinion_ is a small wheel. When two toothed wheels act upon one
another, the smaller is generally called the pinion. The terms _trundle_
and _lantern_ are applied to small wheels having cylindrical bars
instead of teeth. The teeth in pinions are sometimes termed _leaves_; in
a trundle, _staves_. See fig. 273.
The wheel which acts is called a _leader_ or _driver_; and the wheel
which is acted upon by the former is called a _follower_ or the
_driven_. When a screw or _worm_ revolves in the teeth of a wheel, the
latter is termed a _worm wheel_ or _worm gear_; see fig. 270. When a
pinion acts with a rack having teeth, we speak of _rack_ and pinion.
When the teeth are on the inside of the rim, and not on the periphery,
the wheel is termed an _internal gear_; see fig. 272.
Two wheels acting upon one another in the same plane are called _spur
gear_; the teeth are parallel with the axis. When wheels act at an
angle, they are called _bevel gear_.
_Friction gear-wheels_ are those which communicate motion one to the
other by the simple contact of their surfaces.
In frictional gearing the wheels are toothless and one wheel drives the
other by means of the friction between the two surfaces which are
pressed together.
Grooved friction wheels are used to give greater cohesion than can be
obtained by the plain surface.
Fig. 263 shows a pair of spur-wheels in gear. The dotted circles which
meet are the rolling circles, called the “pitch line” or “pitch circle.”
[Illustration: Fig. 266.]
A spur mortise wheel is similarly shown in fig. 266; it is very like in
appearance to a spur wheel; it differs essentially in that the teeth are
separate cogs, fixed in singly to the rim; see also fig. 265, page 201.
NOTE.--The teeth of spur wheels cast from a pattern must of necessity
be larger at one side than at the other, because the teeth must have
taper to permit the extraction of the pattern from the mould;
therefore, in fixing wheels to gear, the large side of one should meet
the smaller side of the other; should the two large sides come
together the teeth will meet only at the large side, and the teeth
will probably break away from the excessive strain on that point.
_Skew gearing_ are bevel wheels working out of center; the teeth do not
form radial lines from the wheel center.
Fig. 267 shows a pair of bevel wheels in gear as described on page 199.
A bevel mortise wheel, _i. e._, one having cogs inserted in its rim
instead of teeth.
[Illustration: Fig. 267.]
A bevel wheel and pinion must be made to suit one another by both having
teeth forming together an angle of 90°, therefore they are pairs, or
proportioned in the number of teeth one to the other. Any other
proportion used would not exactly gear and would be termed a “bastard”
gear.
[Illustration: Fig. 268.]
Fig. 268 represents a pair of miter wheels in gear; it will be noted
that the shafts, when connected, will be at right angles to each other,
the wheels being in all particulars of the same dimensions; the figure
answers the purpose of a much longer description, if given in words.
A miter-wheel can easily be known by putting a square upon the face of
the teeth, which are always at an angle of 45° with one another,
irrespective of size.
_A miter-wheel_ is a particular kind of bevel-wheel, the bevel being
limited to an angle of 45° in each wheel.
The curve of the teeth in bevel-gears, when correctly formed, changes
constantly from one end of the tooth to the other, therefore bevel-gears
whose teeth are produced with a forced cutter are not theoretically
correct.
Fig. 269 represents a rack and pinion: the teeth in this form of gear
are shaped similarly to those in the spur wheel, shown on page 198, with
the difference that the teeth of one are on a circle and on the rack are
made on a straight line.
[Illustration: Fig. 269.]
A flange or addition to the end of a tooth and the rim connecting them
together is used to strengthen the teeth. This extends from the root to
pitch line when the wheel and pinion are both flanged: if only one is
flanged it extends from the root to the addendum.
[Illustration: Fig. 270.]
Fig. 270 illustrates a worm and a worm wheel, sometimes called screw
gears. This is a slow but powerful method of transmitting power, one
revolution of the worm only moving the wheel the distance of one tooth
and space.
_A worm gear_ is a spur wheel with teeth at an angle to the axis, so as
to work with a worm which is a _screw_, or has teeth shaped in the form
of a spiral wound round its circumference; the screw or worm is called
an endless screw, because it never comes to a stopping place in the
circumference of the wheel.
[Illustration: Fig. 271.]
Fig. 271 represents a gear with helical teeth. It is similar to a spur
wheel, and is used in place of same in heavy and slow moving machinery,
the formation of teeth preventing--in large measure--the jar or
concussion noticeable in common spur gears.
In recent years the speed at which gearing is run has been greatly
increased. A striking instance is that of a pair of _cast-iron_ helical
wheels, 6 ft. 3 in. diameter, 12 in. wide, making 220 revolutions per
minute, the speed of the pitch line being 4,319 feet per minute; these
wheels are running continuously and with little noise. There is also a
_cut_ gear in a mill in Massachusetts, 30 feet in diameter, and the
speed of pitch line is 4,670 feet per minute.
[Illustration: Fig. 272.]
_An internal or annular gear wheel_ is one in which the faces of the
teeth are within and the flank without the pitch circle, hence the
pinion operates within the wheel. See fig. 272.
In internal geared wheels there is almost an entire absence of friction
and consequent wear of the teeth, as compared to ordinary spur gearing.
Fig. 273 shows a _crown-wheel_ which has pin teeth which are fixed by
one end only, on its side face and gear into a trundle wheel.
[Illustration: Fig. 273.]
_A trundle wheel_ has no teeth, properly speaking. Instead of teeth, it
has pins as shown on illustration, fig. 273, arranged like the rungs of
a ladder between two walls. See page 201.
_Trains of Gears._--When two wheels mesh--that is, engage with each
other--as in fig. 263, one axle revolves in the opposite direction to
the other; but when internal gears mesh as shown in fig. 272, the shafts
revolve in the same direction; three or more gears running together are
often called _a train of gears_.
Maximum speed of gears under favorable conditions for safety is
comparatively--
Ordinary cast-iron wheels, 1,800 feet per minute.
Helical cast-iron wheels, 2,400 feet per minute.
Mortise wood cog wheels, 2,400 feet per minute.
Ordinary cast-steel wheels, 2,600 feet per minute.
Helical cast-steel wheels, 3,000 feet per minute.
Cast-iron machine cut wheels, 3,000 feet per minute.
It is not, however, advisable to run gears at their maximum speeds, as
great noise and vibration are caused.
Designing Gears.
This section is introduced into the work for a double purpose; 1, as
an exercise in drawing; 2, as a study in accurate measurements. It is
a sample of the work that the advanced student in mechanical drawing
will be confronted with as he puts in practice the theory of the art
of drawing.
Some sample rules are given in the following pages to aid in
calculations relating to gears, and still others are given under the
section “Useful Rules and Tables” at the end of the volume; these are
to be carefully studied.
To accurately divide the pitch circle of a gear wheel by hand requires
both patience and skill. On the accuracy of spacing lies the essential
requisite of a good gear wheel.
The drawing in plate, fig. 274, illustrates a pair of spur wheels, shown
in gear, the office instructions for which being:
“Required, _a detail plan_ of a pair of spur wheels; dimensions: wheel,
76 teeth, 3¹⁄₂ inches pitch, 7-inch eye, 6 arms; pinion, 19 teeth;
scale, 1¹⁄₂ inches = 1 foot.”
The drawing, as illustrated, is the result of the above instructions,
all pencil lines being removed, and this result is worked out as
follows:
76 teeth × 3¹⁄₂ inches, pitch = 266 inches in circum. = 7 ft. 0¹¹⁄₁₆ in.
diam. = 3 ft. 6¹¹⁄₃₂ in. radius; with this measurement as represented on
scale, draw line _P P_ on drawing. This is called the pitch line.
Draw next diameter line, produce or extend this diameter line for
pinion, and with radius of 10¹⁹⁄₃₂ (19 teeth × 3¹⁄₂) from pitch line of
wheel, draw pitch line of pinion.
Take any point in this pitch line of wheel, mark off 3¹⁄₂ inches as
represented on scale, mark this around the pitch line, it will be the
center of each of the 76 teeth; then the breadth of thickness of each
tooth (= pitch × 0.475) must be marked from these centers, then mark
from _P L_, length of tooth to point (= pitch × 0.35) and _P L_ to root
(= pitch × 0.4), draw circles for outside of teeth _N_ and root of tooth
_O_; now with compass set to the pitch (3¹⁄₂) of the wheel, draw the
outer portion from pitch line of tooth.
The radius will center in the pitch line of next tooth where thickness
of tooth has been marked; after finishing outer portion of both sides of
teeth, set the compass from _center_ of tooth with radius to the
thickness marked on pitch line and draw the portion of tooth from pitch
line to root.
Now mark off with dividers and draw thickness of rim (= pitch × 0.5),
divide this line into six parts, draw radii for centers of arms; draw
the bore hole 7″ and the thickness of metal for hub same as pitch.
On radii lines of arms, draw the breadth of arm at rim (= pitch and
thickness of tooth), increase in breadth approaching the center (1″ per
foot), draw the thickness of feather of arm (= pitch × 0.35); draw web
on inside of rim (= pitch × 0.375); fill in arcs for the joining of arms
in rim and hub (radii = pitch × 0.8) and feather to rim and hub (radii =
pitch × 0.37).
Proceed in similar manner, completing the teeth of pinion, and when
pencil lines are all in, ink the drawing, erasing all needless lines.
_P P_ shows the pitch line; _B_, thickness of tooth; _c_, breadth of
space; _A_, the pitch; _E_, clearance at root; _N_, the addendum of
tooth; _O_, the root of tooth; _H_, length of tooth from pitch line to
point; _I_, length of tooth pitch line to root; _G_, whole length of
tooth; _F_, thickness of rim; _J_, web or feather on rim; _K_, breadth
of arm; _L_, thickness of feather; _M_, hub, or thickness round the eye.
NOTE.--It must be remembered that no fixed standard has ever been
agreed upon for these proportions, and workshops differ considerably
in practice.
[Illustration: Fig. 274.]
The number of teeth, their proportions, pitch and diameter of pitch
circle are frequently determined on the “Manchester” principle. This
system originated in Manchester (Eng.), and is now generally used in the
United States for determining diameters and number of teeth, which, of
course, regulate speeds. The principle is not applicable to large
wheels, but is limited in its application to small wheels, or wheels
having “fine pitch,” as will be seen in the following explanation, which
is introduced as very useful and indispensable knowledge for the
acquisition of the student in mechanical drawing.
[Illustration: Fig. 275.]
The “pitch” of teeth has already been stated to be the distance from
center of one tooth to the center of another on the “pitch line,”
measured on the chord of the arc. In determining the number of teeth or
pitch of wheels on this principle, the pitch is reckoned on the
_diameter_ of the wheel, _in place of the circumference_, and
distinguished as wheels of “4 pitch,” “6 pitch,” “8 pitch,” etc. In
other words, this means that there are four, six, or eight teeth in the
circumference of the wheel for every inch of diameter.
In designing gears to transmit power the stress on a tooth is
calculated; it determines the breadth or width and also the thickness of
the tooth on pitch line; the space between the teeth is in proportion to
the thickness of tooth, and the thickness of both combined (one tooth
and one space), measured on the pitch line or circle, is the pitch of
the wheel.
From the pitch all the proportions and measurements for the sizes and
strength of the parts of the wheel are taken _by rule_, and a
symmetrical form is produced.
In machine drawing the practice is to represent wheels by circles only;
the teeth are never shown except on enlarged details and then only in
very rare instances; the circles drawn are always the _pitch lines_ or
the rolling points of contact of the wheels.
The addendum circle is seldom if ever used in practical drawing. Should
it be necessary to show it in an exceptional case, the circle would be
represented by “dotted” line.
The shape of tooth and mode of constructing it, as practiced in drawing
offices, differs from the true theoretical curve of the tooth, although
very minutely.
In all calculations for the speed of toothed gears the estimates are
based upon the pitch line, the latter standing in the same place as the
circumference of a pulley.
To find the _diameter of a gear-wheel_ multiply the number of teeth by
the pitch, divide by 3.1416.
To find the _pitch of a gear-wheel_ multiply the diameter by 3.1416 and
divide by the number of teeth.
To find the _number of teeth in a gear-wheel_ multiply the diameter by
3.1416 and divide by the pitch.
The _breadth of wheels_, where practicable, should be at least three
times the pitch.
[Illustration: Fig. 276.]
Fig. 276 shows a scale for proportions of teeth; it is divided into
tenths and used thus:
Say wheel is 2″ pitch, then from pitch circle to addendum will be 3¹⁄₂
tenths, and from pitch circle to root of tooth will be 4 tenths measured
at the 2″ line on scale, and so on.
The decimal proportions already given in example, page 210, are adopted
in many workshops. Many others use the proportions approved of by Sir
William Fairbairn, which are:
Table of proportion of gears:
Depth of tooth above pitch line .35 of the pitch.
Depth of tooth below pitch line .40 of the pitch.
Working depth of tooth .70 of the pitch.
Total depth of tooth .75 of the pitch.
Clearance at root .05 of the pitch.
Thickness of tooth .45 of the pitch.
Width of space .55 of the pitch.
The diameter of a wheel or pinion is invariably the diameter measured on
pitch circle, except it is specially described otherwise, thus the
diameter “over all,” etc.
The shape of the curved face of the teeth of gears extending from the
root to the addendum is the curve conforming to the passage of the teeth
described on its fellow entering and leaving, as they rotate or roll
together on their pitch circles.
The curve of teeth outside the pitch circle is called “the face,” and
the curve from pitch circle to root is called “the flank.”
The difference between the width of a space and the thickness of a tooth
is called clearance or side clearance.
The play or movement permitted by clearance is called the backlash;
clearance is necessary to prevent the teeth of one wheel becoming locked
in the spaces of the other.
Wheels are in gear or geared together when their pitch lines engage, _i.
e._, when the pitch circles meet.
Wheels to be geared together must have their teeth spaced the same
distance apart, or in other words, of the same pitch.
The teeth of spur wheels are arranged on its periphery parallel to the
wheel axis, or shaft on which it is hung.
The teeth of a bevel wheel or bevel gears are always arranged at an
angle to the shaft.
When the _teeth_ of bevel gears form an angle of 45° they are called
miter wheels.
Miter wheels to gear must be of equal sizes.
A crown wheel is a disc that has teeth which are on its side face; that
is, teeth on a flat circular surface all parallel to the axis of the
wheel.
A rack has teeth on a flat surface or plane all parallel to one another.
A gear cut by machine is called a _cut gear_. It has teeth with less
clearance than cast wheels, which are not so true or perfect, and
therefore require more clearance.
A worm with even a light load is liable to heat and cut if run at over
300 feet of rubbing surface travel. The wheel teeth will keep cool, as
they form part of a large radiating surface; the worm itself is so small
that its heat is dissipated slowly.
A worm throws a severe end thrust or strain on its shaft.
_Steel Gears._--There is great economy in the use of cast-steel over
cast-iron in gears; the average life of the former is nearly twice as
great as of cast-iron gears. And, apart from their longer life and
efficiency, there is less danger of breaking.
The most accurate teeth, strongest and most uniform in wearing, are to
be found in steel gears cut from solid stock, or made by cutters of
proper shape.
Fig. 275 shows an elevation and a vertical section of a spur wheel. From
these views the various parts in spur gears can be better understood, as
they are represented here in combination, and the wheel in its entirety.
_AA_ is the horizontal center line, _BB_, _BB_ the vertical center
lines, _II_ and _II_ the pitch lines, _N_ thickness of tooth, _O_ space
of tooth, _D_ total depth of tooth, _C_ breadth of face, _F_ diameter on
pitch line, _P_ diameter over all, _G_ diameter of hub, _E_ diameter of
hole, _H_ depth of hole, _L_ thickness of rim, _M_ thickness of web.
Much has been and still is being written on gearing. No general rule is
followed by the writers; the elementary principles given will enable the
student to master spur gearing, and bevel and combinations of many kinds
of wheels will afterwards be found easier to delineate than the numerous
lines seem to indicate.
[Illustration: WORKING DRAWINGS]
[Illustration: Fig. 277.]
Working Drawings.
From the “plans” made in the office are produced “working
drawings”--which represent in detail the work to be done to exact
measurement and of material, as indicated, by the pattern-maker, the
foundry, the forge, the shop, and finally, by the erector of the
completed mechanism.
How to satisfactorily fulfill the directions contained in these
drawings, representing only a part of the work, so that it will fit,
with needed accuracy, to all other parts of the design, is the task
before each separate worker.
It is by means of this division of the process of manufacture through
these drawings, that scores and hundreds of men can be employed at the
same time upon a single engine or machine; thus, while handwork has been
superseded by machines in many quarters, the art of drawing has not been
narrowed nor diminished, for no drawings or designs have yet been made
by machinery, nor are they likely to be.
It is thus that a good designer and draughtsman “projects” or extends
himself, to the advantage of many fellow workers.
The drawing, fig. 277, shows a simple form of pillar crane: it consists
of an upright cast-iron pillar, which is bolted on a cap stone, under
which is the foundation plate not shown in the drawing; the boom is of
rolled steel, supported by steel tie rods, and provided with rollers at
the base; the hoisting gear is shown in broken lines and circles; all as
seen in the drawing.
[Illustration: Fig. 278.--Fig. 279.]
[Illustration: Fig. 280.]
Figs. 278, 279 and 280 show a drawing of a “hydraulic beam bending
machine” in three views; fig. 280 is a plan, fig. 278 is an end
elevation, and fig. 279 a side elevation, and a portion of the latter in
section shows the interior construction.
NOTE.--These three views are a practical illustration of drawings for
a machine of the following dimensions: this machine has a bed 3 × 5
feet in area, with 27 holes in each side for the bending pins. The
frame and cylinders are made of cast iron, the rams of machinery
steel, and the slides for holding the bending blocks, of steel
casting. The distance between the bending blocks is 17 inches. The
cylinders are copper lined, 8 inches diameter, and the rams have a
6-inch stroke. The rams, which are independent and single acting, are
returned by counterweights placed as shown under the table. The
cylinders can be operated independently from either side of the
machine by an arrangement of valves and levers. The machine complete
weighs about 7,500 lbs.
[Illustration: Fig. 281.--Fig. 282.--Fig. 283.]
The drawing, page 222, shows three views of a power punching press.
Fig. 282 is a side elevation.
Fig. 283 a front elevation.
Fig. 281 a vertical sectional view; from these views the proportion,
general arrangement and disposition of the automatic devices can be
easily understood; it may be well to call particular attention to the
automatic clutch on the top shaft and the tripping device.
[Illustration: Fig. 284.]
This drawing, fig. 284, shows a side elevation in section of a
self-adjusting piston-rod packing.
_A_ is the gland, _B_ is the piston rod, _C_ is a brass sleeve which
contains the packing _D_, _E_ is the cylinder cover, _F_ is a coil
spring. It will be seen that the spring _F_ abuts on a bushing in the
bottom of the stuffing box and is prevented from scoring the piston rod
by stepping over the ends of the bushing and follower. All as shown in
the drawing.
The drawing, fig. 285, shows a sectional view of a large pulley fixed on
a “quill,” or hollow shaft: the driving shaft passes through the hollow
shaft and is attached to the friction clutch shown at the right-hand
end; this friction clutch drives the hollow shaft and pulley.
[Illustration: Fig. 285.]
Fig. 286 shows the mechanism, called the link-motion, employed to
reverse an engine, or to enable it to be run in either direction. Many
forms of link-motion have been devised, but the Stephenson form, as
shown in the figure, is, however, the one in almost universal use.
[Illustration: Fig. 286.
This drawing shows shading and the mode of figuring the parts for
identification.]
[Illustration: Fig. 287.--Fig. 288.--Fig. 289.]
Figs. 287 to 289 represent a bumping-post for the end of railway tracks,
reproduced on an enlarged scale from the columns of the _Engineering
News_.
In addition to the lettering and dimensions, admirably shown in the
drawings, the following description is appended to show how printed text
and mechanical drawings mutually aid in practical--or commercial--usage.
The unique feature of the arrangement shown, is that the center line of
the post does not coincide with the track, thus adapting itself to the
nature of the blows of a car-bumper, as received in the single-post
style of the mechanism.