accurately and well done, and the proportions of the same are of correct
design, so that the strain placed on the same in keying and coupling it
up does not distort it, the coupling and the shaft will run true,
because the strain due to the key pressure will not be (if properly
driven) sufficient to throw the coupling out of true. But the degree of
accuracy in workmanship necessary to attain this end is greater than can
be given to the work and compete in the market with work less accurately
made, because the difference in the quality of the workmanship will not
be discernible save to the most expert and experienced mechanic, and not
to him even unless the pieces be taken apart for examination. If the
bore of the coupling be true and smooth and of proper fit to the shaft
the key pressure, if the key fits on its top and bottom, will not, as
stated, be sufficient to throw the coupling out of true. It is true,
however, that such pressure is exerted on one half the bore _of the
coupling_ only, being the half bore opposite to the key. On the other
diametral side of the coupling the strain due to the key is exerted on
the top face of the key.
If, therefore, the key seats in the shaft and in the couplings are in
line or parallel, and both therefore in the same plane, the strain due
to the key may throw the coupling out of true to the amount that the key
pressure may relieve the bore of the coupling (on the half circumference
of the shaft of which the key is the centre) from contact or pressure
with the shaft. As a result, the coupling may run to that extent out of
true, but the shaft would run true nevertheless so long as the nature of
the surfaces on the shaft and on the coupling bore was such that the key
pressure caused no more compression or closer contact in the case of one
half coupling than in the case of the other.
It is obvious that a plate coupling will require at least as much force
to remove it from the shaft as it took to put it on, and sometimes, from
rusting of the keys, &c., it requires more. If it be removed by blows it
becomes damaged, and damage is likely to be also caused to the shaft,
while the surfaces having to slide in contact under the pressure of the
fit the surfaces abrade and compress, and the fit becomes impaired. But
in couplings such as shown in Fig. 2621, the gripping pieces are
relieved of pressure on the shaft by the removal of the bolts, and the
removal of the coupling becomes comparatively easy.
The interchangeability of plate couplings is further destroyed by the
fact already stated, that turned shafting is not, as a rule, of accurate
gauge diameter, and the least variation in the pressure or fit of the
coupling to its shaft is apt to cause a want of truth when the key bears
on its top and bottom. The fit of the coupling to its shaft may be, it
is true, relied on to do the main part of the driving duty, and the key
fitting on the sides only may be a secondary consideration, but in
proportion as the fit is relied on to drive, that fit must be tighter,
and the difficulty of application and removal is increased.
Another and important disadvantage of the plate coupling in any form is
that it necessitates the use of hangers open on one side to admit the
shaft, because the couplings must be fitted upon the shaft before the
same is erected and should not be removed after being fitted, as would
be necessary to slide the end of the shaft through the bearing.
When plate couplings are constructed as in Fig. 2617, the removal of a
section involves either the driving back of one-half of the coupling so
that the other half will clear it, or else the moving endwise of the
whole line to effect the same object.
With a plate coupling the half coupling on one end of the shaft must be
removed when it is required to put an additional pulley on the shaft,
unless, indeed, a split pulley be used, whereas with a clamp coupling,
such as shown in Fig. 2621, the half coupling at each end may be slacked
and moved back, one end of the shaft released, a solid pulley placed on
the shaft and the coupling replaced, when it will run as true as before,
and the pulley may be adjusted to its required position on the length of
shafting.
It is to be remarked, however, that a well-made plate coupling, such as
in Fig. 2618, makes a good and reliable permanent job that will not come
loose under any ordinary or proper conditions.
[Illustration: Fig. 2625.]
[Illustration: Fig. 2626.]
In Fig. 2625 is shown a patent self-adjusting compression clamp, which
is peculiarly adapted to connect shafting that is of proper gauge
diameter. It consists of a sleeve A made in two halves, each embracing
nearly one-half of the shaft circumference and being bored parallel and
slightly smaller than the diameter of the shaft ends. Over this sleeve
passes at each end a ring D E, bored conical and fitting a similar cone
on the external diameter of the sleeve. On each end of the sleeve is the
nut F G, which by forcing the cone ring up the taper of the sleeve
causes the two halves of the latter to close upon and grip the shaft.
For shafts less than two inches in diameter there are provided in the
sleeve two pins to enter holes in the shaft ends in place of keys, but
for sizes above that keys are employed. All parts of this coupling being
cylindrical it is balanced. The separate parts of this coupling are
shown in Fig. 2626.
[Illustration: Fig. 2627.]
[Illustration: Fig. 2628.]
[Illustration: Fig. 2629.]
[Illustration: Fig. 2630.]
In Figs. 2627 to 2630 are shown a side elevation and sectional view of
another form of shaft coupling. A is the sleeve, B B nuts on the ends of
the sleeve, and C C cones fitting taper holes in the sleeve. These cones
are split, as shown in Fig. 2629, to permit them to close upon the shaft
ends. The shaft ends themselves are matched with a half dovetail, as in
Fig. 2630, which dispenses with the employment of a key.
In coupling shafts of different diameters it is usual to reduce the
diameter of the end of the larger to that of the smaller shaft, and to
employ a size of coupling suitable for the smaller shaft; but in this
case it is necessary that the coupling be placed on the same side of the
hanger or bearing as the smaller shaft, otherwise it is obvious that the
strength of the larger would, between its bearings, be reduced to that
of the smaller shaft.
The couplings for line shafting are usually placed as near to the
bearings or hangers as will leave room for the removal of the couplings
by sliding them along the shaft.
The couplings on the length of shaft receiving power from the motor are
placed outside the bearings, hence on the succeeding lengths there will
be one coupling between each pair of bearings, the couplings being in
each case as close to each bearing as will allow the coupling to be
moved towards the bearing sufficiently to permit the length to be
removed without disconnecting the adjacent length from its bearings.
[Illustration: Fig. 2631.]
Fig. 2631 represents a very superior form of coupling for line shafts.
The ends of the line shaft are reduced to half diameters as shown, and
lapped with a horizontal joint at an angle to the axis of the shaft as
denoted by the dotted line, which prevents end motion; the ends of the
shaft and their abutting surfaces are dovetailed, as shown A and B, and,
therefore, perform driving duty. A sleeve envelops the whole joint and
is secured by a key. This coupling accomplishes all that can be desired,
but requires very accurate workmanship, and on this account is expensive
to make.
[Illustration: Fig. 2632.]
Fig. 2632 represents a form of coupling suitable for light shafting. It
consists of two halves A A, of cast iron, which are drawn together by
the bolt C; the centre of the coupling is recessed to enable the
coupling to take a better hold on the shaft, which is prevented turning
by the pins D D. This coupling has no projections to catch clothes or
belts, and is quickly applied or removed.
[Illustration: Fig. 2633.]
Fig. 2633[38] represents a form of coupling for heavy duty, the
transmitting capacity only being limited by the strength of the
projections A. If the shafts are not axially in line, this form of
coupling accommodates the error, since the projections A may slide in
their recesses, while if the axial lines of the shafts should vary from
flexure of the bearings or foundations, as in steamships, clearance
between the ends of A and the bottom of the recesses may be allowed, as
shown at B.
[38] From Rankine's "Machinery and Millwork."
[Illustration: Fig. 2634.]
In Fig. 2634 is shown a coupling (commonly known as the universal joint
coupling) which will transmit motion either in a straight line, or at
any angle up to 45°.
It is formed of two double eyes, such as A, connected to a yoke or
crosspiece B as shown at C. It is mainly used for connecting shafts or
arms carrying tools of some kind, such as rubbers for polishing stone,
tools for boring, or other similar purposes in which the tool requires
to be rotated at varying angles with the driving shaft.
CHAPTER XXXI.--PULLEYS.
Pulleys for the transmission of power by belt may be divided into two
principal classes, the solid and the split pulley. The former is either
cast in one entire piece, or the hub and arms are in one casting, and
the rim a wrought-iron band riveted on. The latter is cast in two halves
so that they may be the more readily placed upon or removed from the
shaft.
On account of the shrinkage strains in large pulley castings rendering
them liable to break, it is usual to cast pulleys of more than about 6
feet in halves or parts which are bolted together to form the full
pulley. On account of these same shrinkage strains it was formerly
considered necessary to cast even small pulleys with curved arms, so
that the strains might be accommodated or expended in bending or
straightening the curves of the respective arms. It is found, however,
that by properly proportioning the amount of metal in the hub, arms, and
rim of the pulley, straight arm pulleys may be cast to be as strong as
those with curved arms, and being lighter they are preferable, as
causing less friction on the shafting journals, and, therefore, being
easier to drive.
It is obvious that a pulley for a double belt requires to be stronger
than is necessary for a single one, but the difference is not
sufficiently great to give any practical advantage by making separate
pulleys for single and double belts; hence all pulleys are made strong
enough for double belts.
Pulleys are weaker in proportion to their duty as the speed at which
they rotate is increased, because the centrifugal force generated by the
rotation acts in a direction to burst the pulley asunder, so that if the
speed of rotation be continuously increased a point will ultimately be
reached at which the centrifugal force generated will be sufficient to
cause the wheel to burst asunder. But the speed at which pulleys are
usually run is so far within the limits of the pulley's strength, that
the element of centrifugal force is of no practical importance except in
the case of very large pulleys, and even then may be disregarded
provided that the pulleys be made in a sufficient number of pieces to
avoid undue shrinkage strains in the castings, but if solid pulleys are
rotated at high velocities the internal strains due to unequal cooling
in the mould has been known to cause the wheels to fly asunder when
under high speeds.
Fig. 2635 represents a solid pulley, the tapered arms meeting the rim in
a slightly rounded corner or fillet, and the rim being thickened at and
towards its centre. When the width of rim is excessive in proportion to
one set of arms a double set is employed as in Fig. 2636.
In some forms of pulley the arms and hub are cast in one piece and the
rim is formed of a band of wrought iron riveted to the arms. By this
means shrinkage strains are eliminated and a strong and light pulley is
obtained.
Fig. 2637 represents a split pulley in which the two halves are bolted
together after being placed on the shaft.
Variable motion may be transmitted by means of an oval driving pulley,
as in Fig. 2638, it being obvious that the belt velocity will vary
according to the position of the major axis of the oval. Arrangements of
this kind, however, are rarely met with in practice.
In Fig. 2639 is shown an expanding pulley largely employed on the drying
cylinders of paper machinery, and in other similar situations where
frequent small changes of revolution speed is required. Each arm of the
wheel carries a segment of the rim, and is moved radially to increase or
diminish the rim diameter by sliding in slots provided in the hub of the
wheel, a radial screw operated by bevel gears receiving motion from the
hand wheel and gear-wheels shown in the engraving. It is obvious that in
this case the driving belt must be made long enough to embrace the
pulley when expanded to its maximum diameter, the slack of the belt due
to reduction of diameter being taken up by a belt tightener.
[Illustration: Fig. 2640.]
[Illustration: Fig. 2641.]
[Illustration: Fig. 2642.]
In Fig. 2640 is shown a wooden pulley having a continuous web or disk
instead of arms. It is built up of segments, the web being secured to
the shaft as follows. In Figs. 2641 and 2642 A, B are clamping plates,
and C a split sleeve fitting easily to the shaft and passing through A,
B, while receiving the nut E on the other side. The web of the pulley
fits on the shoulder J, and the flange B fits on the shoulder K, so as
to keep these parts true or concentric to A. The bore of A is taper to
fit the taper of C; hence the nut E in drawing C through A, causes C to
close upon and grip the shaft, while the flanges A, B grip the pulley
and hold it to C.
In Figs. 2643 and 2644 are represented the Otis self-oiling loose
pulley, designed to automatically oil itself upon its starting or
stopping.
[Illustration: _VOL. II._ =EXAMPLES OF PULLEYS.= _PLATE XII._
Fig. 2635.
Fig. 2636.
Fig. 2637.
Fig. 2638.
Fig. 2639.]
[Illustration: Fig. 2643.]
[Illustration: Fig. 2644.]
The hub D is cored out in such manner as to form within it an annular
chamber or cavity B B, entirely surrounding the bore, and serving as a
reservoir to contain oil or other lubricating liquid.
This chamber or reservoir has no direct communication with the bore of
the hub, but a communication is formed between it and the bore through
one or more chambers C C, which are termed supply chambers, and which
are partitioned off within the bore from the reservoir B, by coring the
hub in a suitable manner.
These supply chambers have openings N N in their sides or ends
communicating with the reservoir B, and also openings C C communicating
with the bore of the pulley. These supply chambers are filled with wick
or other fibrous or capillary material, which is also inserted into the
openings N N, to draw the oil from the reservoir by capillary attraction
and supply it in moderate quantities between the bore of the pulley and
the shaft on which it runs. Three or more openings are provided in the
outer shell of the hub for the introduction of oil into the reservoir B,
which openings are closed by thumb-screws, plugs, or other stoppers E E.
There being three of these openings, one will always be at or near the
top when the pulley is at rest, and through this the oil may be
introduced without difficulty. It is not intended that the reservoir
should at any time contain more than one-third its capacity of oil, so
that whenever the pulley is at rest the surface of the oil will be below
the lowest point of the bore, thus preventing any waste of oil at such
times.
When the pulley is in motion, the centrifugal force imparted to the oil
in the reservoir throws it outwardly, causing it to be distributed in an
even layer against the inner surface of the shell which encloses and
forms the reservoir, thus preventing any possible waste when the pulley
is in motion.
But when the pulley is either stopped or started, the oil is caused to
change its position, and in so doing is brought into contact with the
wicks protruding from the small openings N N, by which it is conveyed
into the supply chamber, and thence to the shaft. By thus taking
advantage of what is a necessity in all business establishments in which
machinery is employed--to wit, the stopping and starting of the
machinery at regular intervals--to insure the supplying, at such times,
of a small quantity of oil to the bearings of the loose pulleys, the
makers claim that a perfect and reliable means is obtained for guarding
against any needless waste of the lubricant.
[Illustration: Fig. 2645.]
A crowning or crowned pulley is of largest diameter in the middle of its
width or face, the object being to cause the belt to run on the middle
of the pulley width. It would appear that this crowning would give to
the belt a greater degree of tension at its centre than at its edges,
but it is shown by experiment that if a piece of belt be clamped square
across its width at each end and stretched, the centre as section _b_,
in Fig. 2645, will stretch the most, and that if the piece be divided
along its centre lengthwise, and both halves again stretched, they will
again do so the most in the middle of their widths.
From this it appears that the crowning serves to produce a tension equal
across the pulley width, because it will stretch the belt the most in
the middle of its width, where it has the greatest capacity to stretch.
The amount of crowning employed in practice varies from about 3/16 to
3/8 inch per foot of width of pulley face, the minimum being employed
where the belt requires to be moved or slipped laterally from one pulley
to another of equal diameter, as from a fast to a loose pulley and _vice
versâ_. To relieve the belt of strain when on a loose pulley the loose
pulley is sometimes made of smallest diameter, and has a coned step up
which the belt moves when pressed against it. During this passage of the
belt, however, one edge is stretched more than the other, while in
passing from the large to the smaller pulley the same edge is under
tension, while the other is released from tension; hence, with the belt
passing either to or from the large pulley there is a tendency to unduly
stretch one of its edges. On the other hand, however, in cases where the
belt requires to run for long periods on the loose pulley relieving it
from tension is a great advantage.
In fixing pulleys so that they shall run true upon their shafts several
difficulties are met with. First, it is difficult to turn the shafts
quite parallel and to exact standard gauge diameter. Second, the bore of
the pulley must be made a sufficiently easy fit to enable their being
moved by hand along the shaft to the required location. As a result the
set-screw pressure throws the pulley out of true, unless the mandrel on
which the pulley is turned in the lathe be the same diameter as the
pulley shaft, and the pulley be held upon the mandrel by the set-screw
pressure, and not by driving the mandrel into the pulley bore. In this
case two set-screws must be used one on each end of the pulley hub, so
as to steady the pulley on the mandrel. A pulley thus trued will still
run out of true when on its shaft unless the shaft be of the same
diameter as the mandrel.
One means of obviating this difficulty is to reduce the diameter of the
shaft between the pulley seats sufficiently to allow the pulley to pass
easily, and to make the pulley bores a driving fit to their seats. This,
however, is only practicable in cases where the locations of the pulleys
are permanently fixed, and no occasion arises for the addition of new
pulleys.
[Illustration: Fig. 2646.]
To obviate this difficulty what is termed an internal clamp pulley has
been constructed. This pulley is shown in Fig. 2646. The bore is made
sufficiently smaller than the shaft diameter to be a forcing fit. A slot
in the form of an arc of a circle is formed in the hub as shown, and a
split runs from this arc into the bore. As a result a wedge driven
between the walls of the split will spring open the bore and permit its
easy passage along the shaft to its required location, when the removal
of the wedge will permit the bore to close upon the shaft. To secure the
pulley to the shaft four set-screws are employed, two of them being
shown in the cut, and the other two being similarly located on the other
side of the pulley.
By this means there will be less difference between the diameters of the
pulley bore and of the shaft should the latter be slightly less than its
standard diameter, and as a result the pulley will run more true.
Split pulleys are bored a tight fit to the shaft when the two halves are
bolted firmly together. They may, however, be made to grip the shaft in
two ways; first, if bored when bolted together the edges of the bore
will meet the shaft and clip it so firmly as to require each half bore
to spring open to permit it to pass on the shaft, but by inserting
between the two halves of the hub two thicknesses of writing paper, and
boring out the hole the thicknesses of the paper too large (which may be
done by placing two pieces of the same paper beneath the calipers or
gauge) the bore will be slightly oval when the paper is removed, and
will grip the shaft at the crown of each half bore, but the grip thus
obtained will not be so firm.
Pulleys of small diameter, as three feet or less in diameter, are
usually held to their shafts by set-screws, the consideration of their
shapes and position having been already treated of when referring to the
applications of keys and set-screws. Pulleys of large diameters, and
those which act as fly-wheels as well as pulleys, are usually held by
keys.
BALANCING PULLEYS.--A pulley (more especially those running at high
speed) should be balanced or in balance when rotating at the greatest
speed at which it is intended to run. This is necessary, because if the
centrifugal force generated by the pulley's rotation be greater on one
side than on another of the pulley, it will cause the pulley shaft to
vibrate and shake whenever the amount of unbalanced centrifugal force
becomes, on account of the speed of rotation, sufficient to bend the
shaft or deflect the framing holding the shaft.
The balancing of a pulley will not be correct unless the centrifugal
force is equal at all points on the perimeter in the same plane, as will
appear presently. In practice two methods of testing the balance of a
pulley are employed: first, the standing; and second, the running
balance. A standing balance does not in any sense balance a pulley, but
merely corrects the want of balance to a limited degree. A running
balance correctly balances a pulley when running up to the speed at
which the balance was made, but does not balance for greater speeds.
[Illustration: Fig. 2647.]
[Illustration: Fig. 2648.]
A standing balance is effected when the shaft being supported
horizontally and with as little friction as possible, the pulley will
remain at rest in any position in which it can be placed. Thus, in Fig.
2647 let C C represent the two centres of a lathe adjusted in their
distance apart so as to sustain the shaft S with just sufficient force
to prevent end movement or play of the shaft, and if the pulley P
remains motionless when arrested at any point of rotation it is in
standing balance. A common method of balancing is to set the pulley in
slow rotation several times in succession, and if the same part of the
pulley's circumference comes to rest in each case at the bottom as at B
then it is heaviest and its weight must be reduced, or weight must be
added on the diametrically opposite side of the pulley. Another method
is to rest the shaft horizontally on a pair of metallic strips as B B in
Fig. 2648, the strips resting on a flat horizontal surface D, the
testing being applied as before. Sometimes, however, cylindrical pieces
are used in place of the strips or pieces B B.
[Illustration: Fig. 2649.]
A pulley that is in balance thus tested, may not, however, be in balance
when rotated, or, as already stated, a standing balance may not be a
running balance, for the following reasons: In Fig. 2649 is a pulley
that if turned true inside and out would be of correct standing balance,
because the weight is equal on each side of the shaft; thus the point A,
though farther from the axis than B, would be counterbalanced by C,
while B would be counterbalanced by D, but as soon as the pulley was put
in rotation there would be more centrifugal force generated at A than
at B, and more at C than at D, because, though the weights would be
equal, the velocities of A and C would be greatest.
Now, suppose that instead of a continuous wide pulley several pulleys
were used, being out of true so as to be practically equal in shape to
Fig. 2649, and it is apparent that the fact of pulley A B being out of
balance is not removed by pulley C D being out in an opposite direction,
and that each pulley will tend to bend the shaft in the direction of its
excessive centrifugal force.
[Illustration: Fig. 2650.]
The effect of this inequality of centrifugal force will depend, in each
case, upon the strength of the shaft in comparison with the amount of
unbalanced centrifugal force. Suppose, for example, that the centrifugal
force at a point A in Fig. 2650 were 10 lbs. greater than at B at a
given velocity, and that the strength of the shaft be such that it will
bend 1/32 inch under a weight of 10 lbs., then the effort of the point A
will be to swing in a circle 1/16 inch larger than that due to its
diameter. Suppose, then, the stand be so firmly fixed at C as to be
motionless in a vertical direction under this effort, then the point A
will swing in an oval, as denoted by the dotted lines, the shaft
vibrating as denoted by the arrows.
[Illustration: Fig. 2651.]
Thus vibrations of the shaft, bearing, &c., occur whenever the excess of
centrifugal motion on one side of a pulley is sufficient to spring the
shaft, bearings, standard or foundation, as the case may be, and will
occur most in the direction in which those parts will most easily
succumb. From this it is evident that a pulley practically in balance,
so far as being free from vibration at a certain speed, may be
considerably out of balance at an increased speed. Thus, suppose a
pulley P, in Fig. 2651, has a rim of equal thickness, but the distance
of A from the axis of rotation is 6 inches, while the distance of B is 8
inches; then the centrifugal force at B will, at any speed of rotation,
be one-quarter more than that at A, because the distance is one-quarter
greater. Suppose, then, that its shaft, bearings, and foundation be
capable of resisting 100 lbs. without sensible flexure, but that
sensible flexure of those parts will occur under any pressure over 100
lbs.
The centrifugal force of 1 lb. at A and at B, respectively, may be
calculated by the following rule:--
_Rule._--Multiply the square of the number of revolutions per minute by
the diameter of the circle of rotation in feet, and divide the product
by 5,870. The quotient is the centrifugal force in terms of the weight
of the body.
In the case of A the pulley making, say, 200 revolutions per minute, we
have by the rule:
200^{2} × 1
----------- = 6.81 = the centrifugal force.
5,870
Likewise, centrifugal force at B = (200^{2} × 1.25)/5,870 = 8.51 = the
centrifugal force, 1 and 1.25 being diameters of circle of rotation of A
and B in feet.
Now, suppose the revolutions to be 2,000 per minute, we have in the case
of A 2,000 × 2,000 × 1 (= 4,000,000) ÷ 5,870 = 681 lbs. centrifugal
force. Add one-quarter more, or 170 lbs., to obtain the centrifugal
force at B = 851 lbs.; the unbalanced centrifugal force = 170 lbs.; and
this being 70 lbs. more than the shaft, bearings, &c., are capable of
resisting without flexure, a corresponding vibration will occur, whereas
at 200 revolutions the unbalanced centrifugal force was: Centrifugal
force at B = 8.51 lbs. less that at A = 6.81 = 1.70 lbs. unbalanced
centrifugal force, and it becomes apparent that while at 200 revolutions
the pulley would rotate without sensible vibration, at 2,000 revolutions
(in the same time), sensible vibration would occur; hence, the sensible
vibration of a pulley is in the proportion as the unbalanced centrifugal
motion is to the resistance of the shaft, bearings, &c., to flexure, and
further, as the unbalanced centrifugal motion increases with the
velocity, so also does the sensible vibration increase with the
velocity.
But there are two ways of increasing the velocity of a pulley: 1st, by
increasing the revolutions of a given pulley; 2nd, by employing a pulley
of a larger diameter, but making the same number of revolutions. In our
example we increased the speed tenfold (from 200 revolutions to 2,000)
but the centrifugal force was increased one hundredfold, according with
the law that the centrifugal force increases with the square of the
revolutions, and 10 × 10 = 100. But if the velocity had been increased
by augmenting the diameter of the pulley, the centrifugal force would
have increased in the same ratio as the pulley diameter was increased;
hence it appears that under equal velocities larger pulleys generate
less centrifugal force per unit of unbalanced weight than do smaller
ones.
[Illustration: Fig. 2652.]
A device for testing the balance of pulleys is shown in Fig. 2652; it
consists of a frame carrying a vertical spindle, which may be rotated by
suitable bevel-wheels, and the hand wheel shown. In this case it would
be preferable to balance the pulley at the greatest speed at which it
would be convenient to run it by hand with the wheel shown, because a
pulley balanced at any given speed will be balanced at any lesser speed,
although not at a greater one. But the pulley should not be driven by
the arms, because the pressure against the same will affect the balance.
It would be better therefore to let the spindle of the machine be small
enough in diameter to fit the smallest bore of pulley to be balanced, to
employ sleeves fitting the spindle and the bores of all larger bored
pulleys, and to obtain the most correct results the pulley should be
fastened to the sleeve by its set-screws, or keys of the pulley, as the
case might be, so that whatever error there might be induced by
tightening the same will be accounted for in the balancing. It is
obvious also that the pulley bore should fit the sleeve with the same
degree of tightness as it will fit the shaft to which it is to be fixed.
The heaviest side of the pulley will rotate through a circle of larger
diameter, and may be marked by a point, as a tool point moved up to it
by a slide rest, or roughly by a piece of chalk steadily moved up to it
by hand until it just touches the high side of the pulley.
[Illustration: Fig. 2653.]
The methods of correcting the balance are as follows: The heavy side of
the pulley having been found, a weight is attached to the diametrically
opposite side of the pulley; a convenient form of light weight for this
purpose is shown in Fig. 2653; it consists of what may be termed a
spring clamp, since it holds to the edge of the pulley rim, on which it
is forced by hand, by reason of the spring of the jaws. There are
numerous clamps of this form, each having a definite weight, as 2 ozs.,
3 ozs., 4 ozs., &c.; but for weights above about 1-1/2 lb. a clamp with
a set-screw is employed. For a running balance a set-screw is
indispensable. It is obvious that pulleys will be more easily and
correctly balanced when the inner side of their rim is turned up, as far
as the arms will permit, in the lathe; but on account of the expense
this is not usually done, except in the case of large pulleys.
In the best practice, however, the pulley is set in the lathe, so that
the inside of the rim runs as true as possible. Remarks on this subject
are given under the head of chucking pulleys.
When the balance is to be effected by adding weight to the pulley
mushroom-shaped pieces of metal are made for the purpose, their weights
varying by ounces; the stems are driven through holes drilled through
the rim to receive them, and riveted on the face side. The stems are of
wrought iron, while the heads may be of cast iron, but are better of
lead, because in that case they may be set with a hammer to fit the
inner surface of the pulley rim.
In some practice, protuberances, or a web in the middle of the pulley,
are cast on the pulley, and the balance is effected by cutting this away
to reduce the weight on the heavy side.
When pulleys are to revolve at very high speeds, as in the case of those
for emery-wheel spindles, the shafts themselves require to be balanced,
especially if of cast iron, because that part of the shaft uppermost in
the mould will be of less density and weight than that at the bottom of
the mould. The pulley should be balanced separately, and the whole again
balanced after being put together, because the weight of the key or
set-screw will be sufficient to destroy the balance under a sufficiently
high speed of rotation.
The edges of pulley rims should be trued up in the lathe when the rim is
turned so that the pulleys to receive a belt may be set in line by
pressing a straight-edge, or setting a line to have contact with (as
near as possible) diametrically opposite points of the edge of one
pulley, and setting the other to have its corresponding edge in line.
Pulleys should run true so that the strain or tension of the belt shall
be equal at all parts of the revolution, and the transmitting power
shall be equal. The smoother and more polished the surface of the pulley
the greater its driving power.
The transmitting power of a pulley may be increased by covering the
pulley face with leather or rubber bands, but the thickness of these
should be equal both across the width and all around the circumference
so as to run true.
The amount of increase of driving power due to this covering is
variously stated, but may be taken at about 20 to 30 per cent. A cement
for fastening such pulley coverings may be made as follows: Take one
ounce of caoutchouc (pure or native rubber) and cut it into thin slices,
place it in a tinned sheet-iron vessel with six or seven ounces of
sulphide of carbon; the vessel is then to be placed in a water tank
previously heated to about 86° Fahr. To prevent the solution from
becoming thick and unmanageable, mix with a solution consisting of
spirits of turpentine, in which half an ounce of caoutchouc in shreds
has been dissolved over a slow fire, and then a quarter of an ounce of
powdered resin; from an ounce and a half to two ounces of turpentine
being afterwards stirred in, to be added in small quantities. This
cement must be kept in a large-mouthed bottle well corked, and in using
clean the parts to be united thoroughly with benzine; apply two coats of
cement, allowing each to dry before applying the next; when applying the
last coat allow the cement to dry so as to become very sticky, then
press the surfaces firmly together and allow to thoroughly dry. This is
waterproof.
A pulley that imparts motion to the belt enveloping or partly enveloping
it is termed a driving pulley or driver. A driven pulley is one that
receives motion from, or is driven by, the belt; hence in every pair of
pulleys connected by belt, one is termed the driver and the other the
driven. The revolutions of two pulleys connected by belt will vary in
the same proportion as their diameters, although their rim velocity will
be equal.
Suppose, for example, that a pulley of 7 in. diameter drives one of 14
in. diameter, then if there is no slip on either pulley both pulleys
will run at the same velocity as the belt, and this velocity must be
equal to the velocity of the driver, because the belt is moved by the
driver. Now, suppose the driver which is of 7 in. diameter makes one
revolution in a minute, and as it is only one-half the diameter of the
driven wheel, its circumference will also be half that of the driven, so
that it must make two revolutions to carry around length of belt enough
to pass once around the driven pulley. The revolutions of the two are,
therefore, in the same proportions as are their diameters, which in this
case is two to one. As the driven pulley is the largest diameter, it
will make one revolution in the same time that the driver makes two. But
suppose the driving pulley was 14 and the driven was 7 inches in
diameter, then the proportion would still be two to one, and the driven
would make two revolutions to every revolution of the driver.
[Illustration: Fig. 2654.]
If we are given the number of revolutions a driving pulley makes and the
diameter or circumference of both pulleys, and require to find the
number of revolutions the driven pulley will make to one or to any given
number of the driver, we may consider as follows: Suppose the
circumference of the driver to be 24 inches and that of the driven to be
18 inches, then in Fig. 2654 let circle A represent the driver, and
circle B the driven pulley. If we divide the circumference of A into
four equal divisions, as at 1, 2, 3, and 4, each of these divisions will
equal 6 inches, because the whole circumference being 24 inches, one
quarter of it will be 6. If we divide the circumference of B into
six-inch divisions there will be but three of them as marked, because
one-third of 18 (its circumference) is 6. Now three of the divisions at
A will move A a full revolution, and the remaining division on A will
move B through another one-third of a revolution, hence, each revolution
of A equals 1-1/3 revolutions on B. The proportions of the circumference
are, therefore, as 1-1/3 to 1, or as 133 is to 100, taking A as the
driver, and, therefore, as the basis of the proportion. But suppose we
take B as the basis of the proportion, and one revolution of B will
cause A to make three quarters of a revolution, or during 100
revolutions of B, A will make 75. But nevertheless during the period
that A is making 100 revolutions B will have made one-third more, or
133-1/3, because B makes 1-1/3 revolutions to cause A to make one
revolution. From this it will be seen that the proportion is as the
greater is to the lesser, and not as the lesser is to the greater, or,
in other words, it is in this case as 24 is to 18, which is one and
one-third times, for one-third of 18 is 6, and 18 + 6 = 24.
Suppose, now, we take the four divisions on A and the three on B to
consider their proportions, and we may say 4 is 1-1/3 times 3, or we may
with equal propriety say 3 is 3/4 of 4, hence 4 is not in the same
proportion to 3 that 3 is to 4. Let it now be supposed that a driven
pulley B is 18 inches in diameter, and requires to be driven one quarter
faster than the driver, what then must be the diameter of that driver?
As the revolutions require to be increased one-fourth the pulley
diameter must be increased one-fourth. Thus one quarter of 18 = 4-1/2,
and this added to 18 is 22-1/2, which is therefore the diameter of the
driving pulley, as may be proved as follows: Suppose the circumferences
instead of the pulley diameters to be 22-1/2 and 18 respectively, and
that the largest pulley makes 100 revolutions, then it will pass 2,250
(22-1/2 × 100 = 2,250) inches of belt over its circumference, and every
18 inches of this belt will cause the small pulley to make one
revolution; hence we divide 2,250 by 18, which gives us 125 as the
revolutions made by the small pulley, while the large one makes 100.
Thus it appears that we obtain the same result whether we take the
circumferences or the diameters of the pulleys, because it is their
relative proportions or relative revolutions that we are considering,
and their actual diameters do not affect their proportions one to the
other. Thus, if a 10-inch pulley drives a 30-inch one, the proportions
being three to one, the revolutions will be three to one, and the driven
being three times the largest, will make one revolution to every three
of the driver. If the driver was 3 inches in diameter and the driven 9,
the revolutions would be precisely the same as before, but with equal
revolutions the velocities would be different, because in each
revolution of the driver it will move a length of belt equal to its
circumference; hence, the greater the circumference the greater length
of belt it will move per revolution. To take the velocity into account,
we must take into consideration the number of revolutions made in a
given time by the driver. Suppose, for example, that the driver being 3
inches in diameter makes one revolution in a minute, then it will move
in that minute a length of belt equal to its circumference, so that the
circumference of the driver, multiplied by the number of its revolutions
per minute, gives its velocity per minute. Thus, if a pulley has a
circumference of 50 inches, and makes 120 revolutions per minute, then
its velocity will be 6,000 inches per minute, because 50 × 120 = 6,000.
The velocity of the belt, and therefore that of the driven wheel, will
also be 6,000 inches per minute, as has already been shown. From this
train of reasoning the following rules will be obvious:--
To find the diameter of the driving pulley when the diameter of the
driven pulley and the revolutions per minute of each are given:
_Rule._--Multiply the diameter of the driven by the number of its
revolutions, and divide the product by the number of revolutions of the
driver, and the quotient will be the diameter of the driver.
The diameter and revolutions of the driver in a given time being known,
to find the diameter of a driven wheel that shall make a given number of
revolutions in the same time:
_Rule._--Multiply the diameter of the driver by its number of
revolutions, and divide the product by the number of revolutions of the
driven. The quotient will be the diameter of the driven.
To find the number of revolutions of a driven pulley in a given time,
its diameter and the diameter and revolutions of the driver being given:
_Rule._--Multiply the diameter of the driver by the number of its
revolutions in the given time, and divide by the diameter of the driven,
and the quotient will be the number of revolutions of the driven in the
given time.
Suppose, however, that the speed of the shaft only is given, and we
require to find the diameter of both pulleys, as, for example, suppose a
shaft makes 150 revolutions per minute, and we require to drive the
pulley on a machine 600 revolutions per minute. Here we have two
considerations: first, the relative diameters of the two pulleys, and
secondly, the diameter of pulley and width of belt necessary to transmit
the amount of power necessary to drive the machine at the speed
required. Leaving the second to be discussed hereafter in connection
with the driving power of belts, we may proceed to determine the first
as follows: The pulley on the machine must be as much smaller than that
on the main shaft, as the speed of the pulley on the machine requires to
run faster than does the main shaft, hence we divide the 600 by 150 and
get four, which is the number of times smaller than the driver that the
driven pulley must be. Suppose then the driver is made a 24-inch pulley,
then the driven must be a 6-inch one, because 24 ÷ 4 = 6; or we may make
the driver 36, and the driven 9, because 36 ÷ 4 = 9; or the driver being
48 inches in diameter, the driven must be 12, because 48 ÷ 4 = 12. To
reverse the case, suppose the shaft to make 200 revolutions per minute,
and the machine pulley to make 50, then since 200 ÷ 50 = 4, the driven
(or machine pulley) must have a diameter four times that of the driver,
and any two pulleys of which one is four times the diameter of the other
may be used, as say: Pulley on line shaft 10 inches in diameter, pulley
on machine 40 inches in diameter; or, pulley on line shaft 20 inches in
diameter, pulley on machine 80 inches in diameter.
Now, in nearly all cases that are met with in practice, it would be
inconvenient to have so large a pulley as 80 inches in diameter to drive
a machine, and again in most cases a driving pulley of 10 inches in
diameter would be too small. So likewise in cases where the machine
pulley requires to run faster than the line shaft, a single pair of
pulleys will be found to give, where great changes of revolution are
required, too great a disproportion in the diameter of the pulleys; thus
in the case of a shaft making 150, and the machine requiring to make
600, we may use the following pairs of pulleys:--
On Main Shaft. On Machine Shaft.
First 32 inch diameter 8 inch diameter.
Second 40 " " 10 " "
Third 48 " " 12 " "
Fourth 60 " " 15 " "
But the machine may require so much power to drive it, that with the
width of belt it is desired to employ, a pulley larger than either of
these is necessary, as, say, one 20 inches in diameter. Now, with a
20-inch driven pulley, the driver would require to be 80 inches in
diameter, because 20 × 4 = 80. But there may not be room between the
shaft and the ceiling for a pulley of so large a diameter, or such a
large pulley may be too heavy to place on the shaft, or it may be too
costly, and to avoid these evils, countershafts are used.
By the employment of a countershaft we simply obtain--with two pairs of
pulleys and by means of small pulleys--that which could be obtained in a
single pair, providing the great difference in their diameters
(necessary to obtain great changes of rotation), were not objectionable;
all that is necessary, therefore, is to accomplish part of the required
change of rotation in one pair, and the remainder in the other. In
doing this, however, while the velocity of each driver and driven
will be equal (as was explained with reference to a single pair),
notwithstanding the difference in their diameters, yet the velocity of
one pair will necessarily differ from that of the other, so that the
pulley on the machine will vary in its velocity as well as in its
rotation from that of the first driver. The first driver is that on the
main or driving shaft, and the pulley it drives is the first driven. The
second driver is the second pulley on the countershaft, and the second
driven is the one it drives or that on the machine. Suppose, then, a
driving shaft makes 100 revolutions per minute, and the machine requires
to make 600, then the speed of rotation requires to be increased six
times. Now we may effect this change of six times in several ways; thus:
Suppose we increase the rotations three times in the first pair, then
the second pulley will make 300 rotations, or three times those of the
main shaft, and all we have to do is to make the second driven one-half
the diameter of the second driver, and its rotations will be double
those of the second driver, which will give the required speed of 600
revolutions. Suppose, however, we change the speed four times in the
first pair, and the 100 of the shaft becomes 400 on the countershaft,
and to increase this to 600 on the second driven, all that is required
is to make its diameter one-half less than that of the second driver,
because 600 is one-half more than 400. From this it will be perceived
that the number of changes or amount of increase or decrease of speed
being given, the proportion of diameters for both pairs of pulleys will
be represented by any two numbers which, multiplied together, will give
a sum equal to the number of increased revolutions required. Having
found the proportions for each pair, it remains to determine their
actual diameters, and they will be found to vary under different
conditions.
Suppose, for example, we have the following conditions: Main shaft runs
100; machine must run 600. The pulley on the line shaft is 36 inches in
diameter; required, the diameters for the other three pulleys.
To make three changes in the first pair, the first driven must be 1/3
the diameter of the first driver, which is 12 inches. Now the second
pair we may make any diameters that are two to one; and since the second
driver is to be the smallest, we may select as small a pulley as will
answer for the machine, and make its driver twice its diameter.
But suppose it is the diameter of the pulley on the machine that is
fixed, and the diameter of the other three require to be found. Let the
diameter of the second driven be 12; then its driver on the countershaft
must be 24. The other two must have diameters 3 to 1 as before, any
suitable wheels being selected.
Yet another condition may occur. Thus, suppose the countershaft is on
hand, and that it has on it two pulleys, as a 12 and a 24-inch; then a
36 on the inner shaft will be three times as large as the 12, and a
12-inch on the machine will be twice as small; or, what is the same, one
half as large as the 24.
When the principle is clearly understood the calculations can be
performed mentally with ease so far as the required diameters to attain
the necessary speed is concerned, but there are other considerations
that claim attention.
Thus, for example, to multiply the rotations 6 times we may proportion
the first pair as follows: Driver 48, driven 16; second pair, driver 30,
driven 15 inches in diameter.
Or we may proportion them as follows: First pair: driver 36, driven 12;
second pair: driver 28, driven 14 inches in diameter.
In the second arrangement of diameters the drivers are each 2 inches,
and the driven each 1 inch less in diameter than in the first; hence
their cost would be diminished, as would also be the wear of the
journals, on account of the reduced weight of the pulleys; hence, if the
driving capacity of each pulley is equal to the requirements the second
arrangement would be preferable.
In considering this part of the subject, first let it be shown that
although the horse-power transmitted by the two belts is equal whatever
be the proportions of the pulleys (provided, of course, that the belts
do not slip), yet the strain or wear and tear of the belts varies, and
the requirements for one belt are therefore different from those for the
other.
[Illustration: Fig. 2655.]
In Fig. 2655 let A represent a 36-inch pulley on the driving shaft, B a
12-inch, and C a 24-inch pulley on a countershaft, and D a 12-inch
pulley on a machine shaft. Let the main shaft make 100 revolutions per
minute, and the machine requires a force to move it equal to 50 pounds
applied to the perimeter of D. Now the rotations of D will, with these
pulleys, be six to one of the main shaft or A, which gives D 600
revolutions per minute, thus: 100 × 6 = 600. The circumference of D is
about 37.69 inches, which, multiplied by 600 (the number of its
revolutions), gives 22,614 inches, or 1,884.5 feet as its speed per
minute. This multiplied by the 50 pounds it takes to move the machine at
the perimeter of D, gives 94,225 as the foot pounds per minute required
to drive the machine 600 revolutions per minute, and this, therefore, is
the amount of power transmitted by each belt. On the second belt this is
shown to be composed of 50 pounds moving 1,884-1/2 feet per minute,
hence we may now find how it is composed on the first belt, as
follows:--
The diameter of the first driver is 36 inches, and its circumference
113.09 inches, or 9.42 feet; this, multiplied by its revolutions per
minute, will give its speed, thus: 9.42 × 100 = 942 feet per minute. To
obtain the necessary amount of pull for this first belt, we must divide
this speed into the number of foot pounds it takes to drive the machine,
thus: 94,225 ÷ 942 = 100.02. The duties of the two belts are therefore
as follows:--
First belt, weight of pull 100.02
" speed per minute 942 feet.
Second belt, weight of pull 50.00
" speed per minute 1884.5 feet.
The duty in foot pounds being equal, as may be shown by multiplying the
feet per minute by the force or weight of the pull, leaving out the
fractions, thus:--
942 × 100 = 94,200.
1884 × 50 = 94,200.
The difference in the requirements is, then, that the first belt must
have as much more weight or force of pull than the second as its speed
is less than that of the second.
It is obvious that in determining the proportions of the pulleys this
difference in the requirements should be considered, and the manner in
which this should be done depends entirely upon the conditions.
Thus, in the case we have considered, the speed was increased, but the
object of the countershaft may be to decrease the speed, and in that
case the conditions would be reversed, inasmuch as though the foot
pounds transmitted by both belts would still be equal, yet the speed
would be greatest and the strain or pull the most on the second belt
instead of on the first.
It is obvious, then, that the proportions of the pulleys being
determined the actual diameters must be large enough to transmit the
required amount of power without unduly straining the belt.
CHAPTER XXXII.--Leather Belting.
The names of the various parts of a hide of leather as known to commerce
are as follows:--
[Illustration: Fig. 2656.]
In Fig. 2656 the oblong portion between the two belly parts marked G G
is known as the "butt," and when split down the ridge, as shown by the
dotted line down the centre, the two pieces are known as "bends;" the
two pieces marked Y are "belly offal;" D is known as "cheeks and faces."
The butt within the dotted line may extend in length from A to B, or
from A to C; if cut off between B and C that portion is called the
"range" or the whole from B to X may be cut in one piece and termed a
"shoulder."
Sometimes the range is cut off and the rest would be called a shoulder
with "cheeks and faces" on; or, again, the range and shoulder may be in
one nearly square piece. The manner of cutting this part depends upon
the spread and size of the hide.
[Illustration: Fig. 2657.]
The part of the hide that is used to manufacture the best belting is
shown in Fig. 2657, on which the characteristics of the various parts
are marked. The piece enclosed by the dotted lines is that employed in
the manufacture of the commonest belting, while that enclosed by the
full lines B, C, D is that used for the best belting. The former
includes the shoulder, which is more soft and spongy, while it contains
numerous creases, as shown. These creases are plainly discernible in the
belt when made up, and may be looked for near the belt points.
[Illustration: Fig. 2658.]
The centre of the length of the hide will stretch the least, and the
outer edges on each side of the length of the hide the most. Hence it
follows that the only strip of leather in the whole hide that will have
an equal amount of stretch on each edge is that cut parallel to line A,
and having that line as a centre of its width. All the remaining strips
will have more stretch on one edge than on the other, and it follows
that, to obtain the best results the leather should be stretched after
it is cut into strips, and not as a whole in the hide, or in that part
of it employed for the belt strips. It is found, indeed, that, even
though stretched in strips, the leather is apt in time to curve. Thus a
belt that is straight when rolled in the coil will, on being unrolled,
be found to be curved. It is to be observed, also, that each time the
width of the strips is reduced, this curving will subsequently take
place; thus, if a belt 8 inches wide and quite straight, be cut into two
belts of 4 inches wide, the latter will curve after a short time. The
reason of this is almost obvious, because it is plain that the edge that
was nearest the centre line of the hide offers the greatest resistance
to stretching; hence, when the strip is stretched straight, and an
equilibrium of tension is induced, reducing the width destroys to some
extent this equilibrium, and the leather resumes, to some extent, its
natural conformation. This, however, is not found to be of great
practical importance, so long as the outer curve of one piece is on the
same side as the outer curve of its neighbor, as shown on the left view
in Fig. 2658, in which case the belt will run straight, notwithstanding
its curve; but if the curves are reversed, as on the right in Fig. 2658,
the belt will run crooked, wabbling from side to side on the pulley. To
avoid this, small belts may be made continuous by cutting them from the
hide, as shown in Fig. 2659; but in this case it is better that the belt
be cut from the centre strip of the hide.
[Illustration: Fig. 2659.]
If the leather is stretched in strips after being cut from the hide, the
amount of the stretch is about 6 inches in a length of 4-1/2 feet of a
belt, say, 4 inches wide, but the stretch will be greater in proportion
as the width of the strip is reduced. But if stretched as a whole, the
amount of stretch will be about 1 inch per foot of length, the shoulder
end stretching one-third more.
If the leather has been properly stretched in strips the length of the
belt may be cut to the length of an ordinary tape line drawn tightly
over the pulleys, which allows the same stretch for the belt as there is
on the tape line, added to the degree of tension due to cutting the belt
too short to an amount equalling its thickness (as would be the case if
the belt is cut of the same length as the tape line); or if the belt is
a double one, the belt thus cut to length would be too short to an
amount equal to twice the thickness of the strips of leather of which it
is composed.
When the amount to which the leather has been stretched is an unknown
quantity (as is commonly the case), the workman cuts the belt too short,
to an amount dictated solely by judgment, following no fixed rule. If,
as in the case of narrow belts, the stretching be done by hand, the belt
is placed around the pulleys, stretched by hand, and cut too short to an
amount dictated by judgment, but which may be stated as about 2-1/2 per
cent. of its length.
But the stretch of a belt after it is put to work proceeds very much
more rapidly if it has been stretched in the piece and not in the strip,
hence it gets slack in the course of a few hours, or of a day or more,
according to how much it has been stretched; whereas one properly
stretched in the strip will last for weeks, and sometimes for months,
without getting too slack.
[Illustration: Fig. 2660.
+----------------+----------------+-----------------+----------------+
|2,000 1/4 3. |2,050 3/16 3.1|2,150 3/16 3.2 |2,175 1/4 3.3 |
+----------------+----------------+-----------------+----------------+
|1,400 9/32 2.12|2,000 1/8 3. |2,625 3/16 3.4 |2,325 7/32 3.4 |
+----------------+----------------+-----------------+----------------+
|2,000 1/4 2.11|2,075 3/16 3.1|2,375 7/32 3.4 |2,175 7/32 3.5 |
+----------------+----------------+-----------------+----------------+
|2,075 1/4 2.12|2,700 7/32 3.3|2,600 7/32 3.4 |2,275 5/32 3.7 |
+----------------+----------------+-----------------+----------------+
|2,450 1/4 2.13|3,025 9/32 3.7|2,575 11/32 3.8 |2,225 7/32 3.10|
+----------------+----------------+-----------------+----------------+
|2,475 1/4 3. |2,975 5/16 3.6|3,200 9/32 3.10|2,175 3/8 3.10|
+----------------+----------------+-----------------+----------------+
|2,575 11/32 3.2 |2,875 9/32 3.7|3,475 11/32 3.13|1,850 11/32 3.11|
+----------------+----------------+-----------------+----------------+
|2,675 11/32 3.2 |3,075 11/32 3.8|3,450 9/32 4. |1,950 1/4 3.11|
+----------------+----------------+-----------------+----------------+
|2,650 3/8 3.2 |2,900 9/32 3.6|3,150 3/16 3.15|2,225 1/4 3.10|
+----------------+----------------+-----------------+----------------+
|2,800 1/4 3.1 |3,050 5/16 3.6|2,850 1/4 3.13|2,275 3/16 3.7 |
+----------------+----------------+-----------------+----------------+
|2,700 1/4 3. |3,150 7/32 3.5|3,000 3/16 3.10|2,600 1/4 3.5 |
+----------------+----------------+-----------------+----------------+
|2,650 1/4 2.13|3,000 7/32 3.4|3,400 1/8 3.6 |2,550 1/4 3.4 |
+----------------+----------------+-----------------+----------------+]
The results of some experiments made by Messrs. J. B. Hoyt & Co. on the
strength of the various parts of a hide are given in Fig. 2660. One side
of the part of the hide used for leather belting was divided off into 48
equal divisions, each piece being 11-3/4 inches long, and two inches
wide, the results of each test being marked on the respective pieces.
The first column is the strain under which the piece broke; the second
column is the amount in parts of an inch that the piece stretched
previous to breaking; and the third column is the weight of the piece in
ounces and drachms.
From the table it appears that the centre of the hide which has the most
equal stretch has the least textile strength, while in general that
which has the most stretch has the greatest textile strength, but at the
same time the variations are in many cases abrupt.
A single belt is one composed of a single thickness of leather put
together, to form the necessary length, in pieces, riveted and cemented
together at the joint, or sewed or pegged as hereafter described.
A double belt is similarly constructed, but is composed of two
thicknesses of leather cemented and riveted, pegged, or sewed together
throughout its whole length, as hereafter described. The object of a
double belt is to increase the strength without increasing the width of
the belt. Belts are usually made in long lengths coiled up for ease of
transportation, the length of belt required being cut from the coil.
To find the length in a given coil that is closely rolled--Rule: the sum
of the diameter of the roll and the eye in inches, multiplied by the
number of turns made by the belt, and this product multiplied by the
decimal .1309, will equal length of the belt in feet.
[Illustration: Fig. 2661.]
The grain or smooth side of the leather is the weakest, as may be
readily found by chamfering it to a thin edge, when it will tear like
paper, and a great deal more easily than will the flesh side under
similar treatment. Again, it will crack much more readily: thus, take a
piece of leather and double it close with the grain side outward, and it
will crack, as shown in Fig. 2661 at C, whereas if doubled, however
closely, on the flesh side no cracks will appear. If the edge of a
clean-cut piece of leather be examined, there will be found extending
from the grain side inward a layer of lighter color than the remainder
of the belt; and this whole layer is less fibrous and much weaker than
the body of the belt, the strongest part of which is on the flesh side.
If the grain side is shaved off thin and stretched slightly with the
fingers it will exhibit a perfect network of small holes showing where
the hair had root. Here, then, we have weakness and excessive liability
to crack on the grain side of the leather, and it is obvious that if
this side is the outside of the belt, as in Fig. 2662, at A, the
tendency is to stretch and crack it, especially in the case of small
pulleys, whereas if the grain side were next to the pulley the tendency
would be to compress it, and therefore, rather to prevent either
cracking or tearing. Furthermore, very little of the belt's strength is
lost by wearing away its weakest side.
[Illustration: Fig. 2662.]
Another and important consideration is, that the grain side will lie
closest and have most contact over a given area with the pulley surface.
In making double belts of extra good quality, it is not uncommon to cut
away or shave off the grain side of both belts, and place those surfaces
together in making up the belts.
If the grain side of a belt is the outside when on the pulleys, and a
crack should consequently start, the destruction of the belt proceeds
rapidly, because the line of crack is the weakest part of the belt, and
the belt has less elasticity as a continuous body, and more at the line
of crack. Cracking may, to some extent, be provided against by oiling
the belt, and for this purpose nothing is better than castor oil. In the
manufacture of belts, extra pliability is induced by an application of
fish oil and tallow, applied when the belt (after having been wetted),
is in a certain stage of progress toward drying. The oil and tallow are
supposed to enter the pores of the leather and supply the place of the
evaporated water.
LENGTH OF BELTS.--Since the stretch of a belt is variable in different
belts of the same length, no rule can be given for the amount to which a
belt should be cut shorter than the measured length around the pulleys,
and it follows, therefore, that the length of a belt cannot be obtained
precisely by calculation. In practice the necessary length for a belt to
pass around pulleys already in their places upon the shaft is usually
obtained by passing a tape line or cord around the pulleys, the stretch
of the tape line being allowed as that necessary for the belt. Then when
the belt is placed around the pulleys it is shortened if it should
appear to require more tension. If, however, the belt length for pulleys
not in position is required, it may be obtained as follows, the error
being so slight as to be within the margin of difference of stretch in
different belts, and therefore of no practical moment:--
[Illustration: Fig. 2663.]
For open belts let the distance between the shaft centres, as _a_ _b_ in
Fig. 2663, be the base of a right angle triangle, and the difference
between the semi-diameters, as _b_ _c_, the perpendicular. Square the
base and the perpendicular, and the square root of the sum of the two
will give the hypothenuse, and this multiplied by 2 and added to
one-half the circumference of each pulley is the required length for the
belt. This will give a belt too long to the amount to be cut out of the
belt to give it the necessary tension when on the pulleys.
_Example._--Let the distance between centres in Fig. 2663 be 48 inches;
diameter of large pulley 24 inches; diameter of small pulley 4 inches--
Here distance between centres 48
" " " 48
---
384
192
----
2304
Square of perpendicular 100
----
2404 Square root of 2404 = 49.03
Multiply by 2 2
-----
98.06
Half circumference of large pulley 37.699
-------
135.759
Half circumference of small pulley 6.283
-------
Length of belt 142.042
A simpler rule which gives results sufficiently accurate for practical
purposes is as follows:--
_Rule._--Add the diameter of the two pulleys together, divide the result
by 2, and multiply the quotient by 3-1/4, then add this product to twice
the distance between the centres of the shafts, and you have the length
required.
When the length of a crossed belt is required, and the pulleys are not
erected upon the shafts, it is, on account of the abstruseness of a
calculation for the purpose, preferred in workshop practice to mark off
by lines the pulleys set at their proper distance apart (either full
size or to scale), and measure the length of the side of the belt,
supposing the belt to envelop one-half the circumference only of each
pulley, and to add to this one-half the circumference of each pulley; or
if there is a great difference between the relative diameters of the
pulleys and the distance apart of the shafts is unusually small, the
lengths of the straight sides of the belt are measured and the arcs of
contact around the pulleys are stepped around by compasses, the set of
the compasses being not more than about one-tenth the circumference of
the pulleys. This gives a more near result than that obtained by
calculation, because although it will give a belt shorter than by
calculation, yet the belt will be too long on account of the stretch
necessary to the tension required for ordinary conditions.
[Illustration: Fig. 2664.]
In narrow belts, as, say, three inches and less in width, the belt may
be cut to the length of a tape line passed over the pulleys, and when
placed over the pulleys it may be strained under a hand pull and cut as
much shorter as the tension under hand pressure indicates as being
necessary.
But if the belt is a wide one a stretching clamp, such as shown in Fig.
2664, is employed, the screws being right hand at one end and left hand
at the other, so that operating them draws the clamps, and therefore the
ends of the belt, together.
The stretch of a belt not stretched in the piece proceeds slowly when
the belt is at work, hence if laced at first to a proper degree of
tension it will get slacker in a few hours or in a day or so, and must
be tightened, or taken up as it is termed, by cutting a piece out. For
this purpose a butt joint possesses the advantage that the piece to be
taken out may be less, and still leave the end clear for new holes to be
punched, than is the case with a lap joint, which occurs because the
butt joint occupies a shorter length of the belt than is the case with a
lap joint.
[Illustration: Fig. 2665.]
[Illustration: Fig. 2666.]
When a belt is under tension upon two pulleys and at rest, the friction
or grip of the belt upon the respective pulleys (supposing them to be of
the same diameter and therefore to have the same arc and area of
contact) will depend upon the relative positions of the pulleys; thus
suppose one pulley to be above the other as in Fig. 2665, the upper
pulley P will have the grip due to the tension of the belt added to that
due to the weight of the belt, whereas if placed horizontally, as in
Fig. 2666, the weight of the belt will fall equally on the two pulleys,
and for this reason vertical belts of a given width require to have a
greater tension to transmit the same amount of power as the same belt
would if placed horizontally. But as soon as motion was transmitted, by
the belt, from one pulley to the other, the belt on one side of the
pulley would be under greater tension then that on the other.
[Illustration: Fig. 2667.]
Suppose, for example, a belt to transmit motion and power from pulley A
in Fig. 2667, to pulley B, then the side C of the belt is that which
drives or pulls B, and it is therefore called the driving side of the
belt, the resistance to rotation offered by B causing the driving side
of the belt to be the most strained; and hence the straightest, whereas
the side D will be free of the tension due to the resistance of B.
[Illustration: Fig. 2668.]
But if the direction of motion be reversed as in Fig. 2668, A still
being the driving pulley, the side D will be the one most tightly
strained, and therefore, the driving side of the belt; or, in other
words, the driving side of a belt is always that side which approaches
the driving pulley, and the slack side is always that which recedes from
the driving pulley. In horizontal belts, however, the driving side of
the belt is not a straight line, because of the belt sagging from its
own weight no matter how tightly it may be strained, but the shorter the
belt the less the sag.
[Illustration: Fig. 2669.]
It is always, therefore, desirable, so far as the driving power of the
belt is concerned, to have the lower half (of belts running
horizontally) the driving side, because in that case the sag of the belt
causes it to envelop a greater arc of the pulley, which increases its
driving power. If the circumstances will not permit this and the sag of
the belt operates to practically incapacitate the belt for its duty,
what is termed an idle wheel or idler may be employed as shown in Fig.
2669 at E, serving to prevent the sag and to cause the belt on the
driving side to envelop a greater portion of the pulley's circumference,
and hence increase its friction on the pulley and therefore its driving
power. In the example the two pulleys A and B are of equal diameters;
hence the idle wheel is placed midway between them, but when such is not
the case the idle wheel should be located according to the circumstances
and the following considerations. The idle wheel requires a certain
amount of power to drive it, and this amount will be greater as the idle
wheel is nearer to the smallest wheel of the pair connected; but on the
other hand, the closer the idle wheel to the small pulley (all other
factors being equal) the greater the arc of small pulley surface
enveloped by the belt, and hence the greater the belt's driving power.
When therefore a maximum increase of driving power is required, the
idler must be placed near to the smallest pulley, the desired effect
being paid for in the increased amount of motive power required to
rotate the driving pulley.
But under equal conditions the larger the diameter of the idle wheel the
less the power required to drive it, because the less its friction on
its journal bearing. A belt tightener should whenever practicable be
placed on the slack side of the belt.
Belt tighteners are sometimes used to give intermittent motion, as in
the case of trip hammers; the belt being vertical is made long enough to
run loose, until the tightening pulley closes the belt upon the pulley,
taking up its slack and increasing the arc of contact.
[Illustration: Fig. 2670.]
When the direction of rotation of the driven pulley requires to be
reversed from that of the driving pulley, the belt is crossed as in Fig.
2670. A crossed belt has a greater transmitting power than one uncrossed
(or, as it is termed, than an "open belt") because it envelops a greater
arc of both pulleys' circumference. This is often of great advantage
where the two pulleys are of widely varying diameter, especially if the
small pulley requires to transmit much power, and be of very small
diameter.
But a crossed belt is open to the objection that the surfaces of the
belt rub against each other at the point of crossing, which tends to
rapidly wear out the laced joint of the belt. By crossing a vertical
belt the lower pulley receives part of the weight of the belt.
When a belt connects two pulleys whose respective planes of revolution
are at an angle one to the other, it is necessary that the centre line
of the length of the belt shall approach the pulley in the plane of the
pulley's revolution, which is sufficient irrespective of the line of
motion of the belt when receding from the pulley. This is shown in Fig.
2671, which represents what is known as a quarter twist; A, B are two
pulleys having their planes of revolution at a right angle, the belt
travelling as denoted by the arrows, then the centre line C of the belt
being in the plane of rotation of A on the side on which it advances to
A, the belt will continue to run upon the same section of A. If the
pulley positions be reversed, as in Fig. 2672, the same rule applies,
and the side D in the figure being that which advances upon B must
travel to B in the plane of B´s rotation, otherwise the belt would run
off the pulley; hence it is obvious that the belt motion must occur in
the one direction only.
[Illustration: Fig. 2671.]
[Illustration: Fig. 2672.]
[Illustration: Fig. 2673.]
Shafts at any angle one to another may have motion communicated from one
to the other by a similar belt connection, providing that a line at a
right angle to the axis of one shaft forms also a right angle with the
axis of the other. Thus in Fig. 2673 the axis of shaft A may be set at
any required angle to the plane of rotation of pulley B, provided that
the axial line of A be made to lie at a right angle to the imaginary
line _l_, which is at a right angle to the axis of the shaft of B, and
that the side of the driving pulley which delivers the belt (as C, Fig.
2671) is in line with the centre line of the driven pulley, as denoted
by the dotted line C.
[Illustration: Fig. 2674.]
But when this provision cannot be carried out, pulleys to guide the
direction of motion of the belt must be employed; thus in Fig. 2674 are
an elevation and plan[39] of an arrangement of these guide or mule
pulleys; A B is the intersection of the middle planes E E and F F of the
pulleys P and P´ to be connected by belt. Select any two points, A and
B, on this line and draw tangents A C, B D to the principal pulleys.
Then C A C and D B D are suitable directions for the belt. The guide
pulleys must be placed with their middle planes coinciding with the
planes C A C, D B D, and the belt will then run in either direction.
[39] From Unwin's "Elements of Machine Design."
[Illustration: Fig. 2675.]
In Fig. 2675 is an arrangement of guide pulleys by which two pulleys not
in the same plane are connected, while the arc of contact of the smaller
pulley C is increased by the idlers or guide pulleys A B, while either C
or D may be driven running in either direction.
[Illustration: Fig. 2676.]
In Fig. 2676 is shown Cresson's adjustable mule pulley stand, which is a
device for carrying guide pulleys, and admitting of their adjustment in
any direction. Thus the vertical post being cylindrical, the brackets
can be swung around upon it and fastened in the required position by the
set-screws shown. The brackets carrying the pulleys are also capable of
being swung in a plane at a right angle to the axis of the guide
pulleys, and between these two movements any desired pulley angle may be
obtained. It is obvious that by moving the brackets along the
cylindrical post their distance apart may be regulated.
When a belt is stretched upon two pulleys and remains at rest there will
be an equal tension on all parts of the belt (that is to say,
independent of its weight, which would cause increased tension as the
points of support on the pulleys are approached from the centre of the
belt between the two pulley shafts); but so soon as motion begins and
power is transmitted this equality ceases, for the following reasons:--
[Illustration: Fig. 2677.]
In the accompanying illustration, Fig. 2677, A is the driving and B the
driven pulley, rotating as denoted by the arrows; hence C is the driving
and D the slack side of the belt. Now let us examine how this slackness
is induced. It is obvious that pulley A rotates pulley B through the
medium of the side C only of the belt, and from the resistance offered
by the load on B, the belt stretches on the side C. The elongation of
the belt due to this stretch, pulley A takes up and transfers to side D,
relieving it of tension and inducing its slackness. The belt therefore
meets pulley B at the point of first contact, E, slack and unstretched,
and leaves it at F, under the maximum of tension due to driving B.
While, therefore, a point in the belt is travelling from E to F, it
passes from a state of minimum to one of maximum tension. This tension
proceeds by a regular increment, whose amount at any given point upon B
is governed by the distance of that point from E. The increase of
tension is, of course, accompanied by a corresponding degree of belt
stretch, and therefore of belt length; and as a result, the velocity of
that part of the belt on pulley B is greater than the velocity of any
part on the slack side of the belt; hence the velocity of the pulley is
also greater than that of the slack side of the belt. In the case of
pulley A the belt meets it at G under a maximum of tension, and
therefore of stretch, but leaves it at H under a minimum of tension and
stretch, so that while passing from G to H the belt contracts, creeping
or slipping back on the pulley, and therefore effecting a reduction of
belt velocity below that of the pulley. To summarize, then, the velocity
of the part of the belt enveloping A is less than that of A to the
amount of the creep; hence the velocity of the slack side of the belt is
that of A minus the belt creep on A. The velocity of the part of the
belt on B is equal to that of the slack side of the belt plus the
stretch of the belt while passing over B; and it follows that if the
belt or slip creep on one pulley is equal in amount to the belt stretch
on the other, the velocities of the two pulleys will be equal.
[Illustration: Fig. 2678.]
Now (supposing the elasticity of the belt to remain constant, so that no
permanent stretch takes place) it is obvious that the belt-shortening
which accompanies its release from tension can only equal the amount of
elongation which occurs from the tension; hence, no matter what the size
of the pulleys, the creep is always equal in amount to the stretch, and
the velocity ratio of the driven pulley will (after the increase of belt
length due to the stretch is once transferred to the slack side of the
belt) always be equal to that of the driving pulley, no matter what the
relative diameters of the pulleys may be. In Fig. 2678, for example, are
two pulleys, A and B, the circumference of A being 10 inches, while that
of B is 20; and suppose that the stretch of the belt is an inch in a
revolution of A (A being the driving pulley). Suppose the revolutions of
a to be one per minute, then the velocity of the belt where it envelops
A and B, and on the sides C and D, will be as respectively marked.
Thus the creep being an inch per revolution of A, the belt velocity on
the side C will be nine inches per minute, and its stretch on B being an
inch, the velocity of B will be ten inches per minute, which is equal to
the velocity of the driving pulley.
It is to be observed, however, that since A receives its motion
independently of the belt, its motion is independent of the creep, which
affects the belt velocity only: but in the case of B, which receives its
motion from the belt, it remains to be seen if stretch is uniform in
amount from the moment it meets this pulley until it leaves it, for
unless this be the case, the belt will be moving faster than the pulley
at some part of the arc of contact.
[Illustration: Fig. 2679.]
Thus suppose P, Fig. 2679, represents a driven pulley, whose load is
1,000 pounds, and that from A to B, from B to C, from C to D, and from D
to E, represent equal arcs of contact between belt and pulley, then arc
A B will have on it the amount of stretch due to a pull of 250 pounds at
B, diminishing to nothing at A. Arc C B will have on it the amount of
stretch due to a pull of 500 pounds at C and 250 at B; arc D C will have
on it the amount of stretch due to a load of 750 at D, and 500 at C; and
arc D E will have the tension due to a load of 1,000 pounds at E, and
750 pounds at D. Suppose, then, that the amount of belt stretch is
greater between B and C than it is between D and E, then the belt will
travel faster between B C than between D E to an amount equal to the
difference in stretch, and will at B C slip over the pulley to that
amount; or if the friction of the belt at B C is sufficient to move the
pulley in accordance with the stretch, then the belt must move the
pulley at a greater velocity than the belt motion from D to E.
But since the friction of the belt is greatest at D E, it will hold the
pulley with the greatest force, and hence the velocity of the belt and
pulley will be uniform, or at least the most uniform, at D E.
Here arises another consideration, in that the stretch of the leather is
not uniform, and the section of belt at C B may stretch more or less
under its load than section C D does under its load, in which event the
velocities of the respective belt sections cannot be uniform, and to
whatever amount belt slip ensues the velocity of the driven wheel will
be less than that of the driver.
Attention has thus far been directed to the relative velocities of the
pulleys while under continuous motion. But let us now examine the
relative velocities when the two pulleys are first put in motion.
Suppose, then, the belt and pulley to be at rest with an equal degree of
tension (independently of the weight of the belt, as before) on both
sides of the belt. On motion being imparted to the driving pulley, the
amount of belt elongation due to the stress of the load on the driving
pulley has first to be taken up and transferred to the slack side of the
belt, and during such transfer a creep is taking place on the arc of
belt contact on the driving pulley.
[Illustration: Fig. 2680.]
Furthermore, let it be noted that while under continuous motion the belt
first receives full stress at point F, Fig. 2677; at starting it first
receives it at point E, and there will be a period of time during which
the belt stretch will proceed from E towards F, the pulley remaining
motionless. The length of duration of this period will, in a belt of a
given width, and having a given arc of contact on the driven pulley,
depend on the amount of the load. Thus, referring to Fig. 2680, if the
amount of the load is such that the arc of contact between the top and
the point B is sufficient to drive the pulley, the pulley will receive
motion when the belt stretch has proceeded from A to B; but if the load
on the pulley be increased the belt stretch will require to proceed
farther towards C.
At the top the stretch will proceed simultaneously with that of the
driving side of the belt, between the points F G, Fig. 2677; but from
the friction between the belt and pulley, the stretch of the part
enveloping the pulley will be subsequent and progressive from F towards
E, Fig. 2677.
It follows, then, that the velocity of the driven wheel will be less
than that of the driver at first starting than when in continuous
motion.
As the length of the belt is increased, the gross amount of stretch,
under any given condition, increases, and hence the longer the belt, the
greater the variation of velocity at first starting between the driven
pulley and the driver.
From what has been said, it follows that when a mathematically equal
velocity ratio is essential, belts cannot be employed, but the
elasticity that disturbs the velocity ratio possesses the quality of
acting as a cushion, modifying on one pulley any shocks, sudden strains,
or jars existing on the other, while the longer the belt and less
strained within the limit of elasticity, the greater this power of
modification; furthermore in case of a sudden or violent increase of
load, the belt will slide on the pulley, and in most cases slip off it,
thus preventing the breakage of parts of the driving gear or of the
machine driven that would otherwise probably ensue. Furthermore, belt
connections are lighter and cheaper than gear-wheel or other rigid and
positive connections, and hence the wide application of leather belts
for the transmission of power, notwithstanding the slight variations of
pulley velocity ratio due to the unequal elasticity of the various parts
of the leather composing the belt.
[Illustration: Fig. 2681.]
The ends of belts are joined by two principal methods, the butt and the
lap joint. In butt joints the holes are pierced near the ends of the
belts, and the ends of the belt are brought together by means of a
leather lace threaded through these holes. If the duty is light a single
row of holes is all that is necessary. An example of this kind is shown
in Fig. 2681, in which there are five holes on one side, and four on the
other of the joint, the extra hole coming in the middle of its end of
the belt. The lace is drawn half-way through this extra hole, and laced
each way to the side and back again to the middle, the ends being tied
on the outside of the belt, which does not come in contact with the
pulley surface. By this means the lacing is double through all the
holes, and if the knot should slip the slackness will begin at the
middle of the belt and extend gradually towards the edges; whereas, if
the lacing terminated at one side, and the knot or fastening should
slip, all the tension would be thrown on one edge of the belt, unduly
stretching it, and rendering it liable to tear. By this method of lacing
the lace is not crossed on either side of the belt, which is desirable,
because it is found in practice that a crossed lace does not operate so
well as an uncrossed one.
[Illustration: Fig. 2682.]
If the power to be transmitted is so much as to render it desirable to
have the strength of the laced joint more nearly approach that of the
solid belt than is obtainable with a single row of holes, a double row
is provided, as shown in Fig. 2682.
For belts of about 3 inches wide and over, these holes are made as
follows: A, B, and C, D, E, about an inch apart and 5/8 inch from the
line of joint; F, G, H, and I, J, being about 1/2 inch behind A, B, and
C, D, E, respectively.
For thinner belts the holes may be closer together, and to the edges of
the belt the exact distances permissible being closer together as the
duty is lighter; but however narrow the width of the belt, it should
contain at least two holes on each side of the joint. The sizes of these
holes are an important element, since the larger the hole the more the
belt is weakened. The following are the sizes of holes employed in the
best practice:--
Width of Belt. Size of Punched Hole.
Up to 4 inches 1/4 inch.
From 4 to 8 inches 5/16 "
From 8 inches upwards 3/8 "
[Illustration: Fig. 2683.]
The holes are usually made round, but from the pliability of the lace,
which enables it to adapt itself to the form of the hole to a remarkable
degree, it is not unusual to preserve the strength of a belt by making
an oblong hole, as in Fig. 2683 at A, or a mere slit, as at B, which,
from removing less material from the belt, leaves it to that extent
stronger.
[Illustration: Fig. 2684.]
[Illustration: Fig. 2685.]
The ends of the belt should be cut quite square, and at a right angle to
the edges, so that when the two ends are drawn together by the lace the
edges of the belt will remain straight, and not curved, as they would do
if either end of the belt were not cut at a right angle. Suppose, for
example, that the ends of a belt were cut aslant, as in Fig. 2684, when
laced up the edge of the belt would come as in Fig. 2685.
[Illustration: Fig. 2686.]
The holes must be punched exactly opposite to each other, or lacing the
belt will bring the edges out of fair, as shown in Fig. 2686, the
tension of the lace drawing the holes opposite to each other,
irrespective of where the edges of the belt will come. If some of the
holes are opposite and others are not, the latter will throw the edges
of the belt out of line to some extent, especially if the lace is first
entered in the holes that are not opposite, because, in that case,
drawing the lace tight at once throws the belt edges out, and the
subsequent lacing has but a limited effect in correcting the error,
unless, indeed, the majority of the holes are opposite, and but one or
two are out of line.
The lace should be drawn sufficiently tight to bring the ends of the
belt firmly together, and should be laced with an even tension
throughout, and for a belt doing heavy duty should have its ends tied in
a knot at the back, and in the middle of the belt.
The width of the lace is usually about as follows:--
Width of Belt. Width of Lace.
24 inches and over 1/2 inch
6 to 24 inches 3/8 "
2 to 4 inches 5/16 "
2 inches and less 1/4 "
Since belts are tightened by cutting a piece off one end (preferably the
end which shows the holes most stretched), it is obvious that a
butt-joint possesses an advantage, because as less of the belt length is
occupied by the holes they may be cut quite out and new ones punched,
whereas, in some cases, the length of the belt occupied by the holes in
a lap-joint is more than the length of belt required to be cut out to
tighten it.
[Illustration: Fig. 2687.]
[Illustration: Fig. 2688.]
[Illustration: Fig. 2689.]
There are many different methods of lacing a belt, but those here
described are generally preferred. Thus referring to Fig. 2687 the lace
is first passed through holes G and D, the ends being of equal length
from the belt and emerging on the side that is to be the outside of the
belt, thence each end of the lace is laced towards the edge of the belt,
the dotted lines in the cut showing the path of the lace. It is then
laced back to the middle of the belt, the second inside lacing exactly
overlaying the first, the laces never crossing; the outside appearing as
in Fig. 2688. The ends are in some cases tied in a knot on the outside,
and in others fastened as shown in Fig. 2689, in which case the ends are
merely held by friction, which will serve very well unless for a belt
that is tightly strained.
By this method of lacing all the crossing of the lace is on the outside
of the belt, which is an advantage, because from the creep of the belt
the lace undergoes considerable friction, which is apt to rapidly wear
out the lace, especially if it be crossed on the side of the bed that
meets the pulley surface.
[Illustration: Fig. 2690.]
Fig. 2690 shows a method of lacing in which the crossing of the lace is
entirely avoided, the knot being on the outside at _a_ _a_. The path of
the lace on one side of the belt is shown in full lines, and on the
other side in dotted lines.
The objections to lacing are that the lace lifts the belt from the
pulley surface, which throws all the wear on the lace, causing it
eventually to break, and which also reduces the area of belt (at the
joint) in contact with the pulley surface and reduces the driving power
of the belt at the time the joint is passing over the pulley. In fact,
in running belts this reduction of transmitting capacity is not great,
because of the rapidity with which the joint passes over the pulley,
but in slow moving belts slip is very apt to occur when the lace meets
the pulley, especially if the power transmitted is great in proportion
to the width of the belt.
[Illustration: Fig. 2691.]
[Illustration: Fig. 2692.]
There are considerable movement and friction between the lace and the
belt, more especially when the latter passes over a pulley of small
diameter, and this with the friction due to whatever amount of slip the
belt may experience, wears away the lace so that in time it breaks.
Sometimes a cover is employed as shown in Fig. 2691 at A, to protect the
lace, the cover being riveted or cemented to the belt on the side that
is to meet the pulley surface. A similar means is also sometimes
employed to make a butt joint. Thus in Fig. 2692 A is the cover riveted
or cemented to the two ends B C, of the belt so as to dispense with
lacing.
[Illustration: Fig. 2693.]
Fig. 2693 represents an excellent method of joining very thin belts, the
operation being as follows:--
Place the two ends of the belt together with the edges fair one with the
other, and with an awl make a row of holes at _a_, through both ends;
then take about half a yard of strong twine (in some cases a lace or gut
is better) and draw half the length through the first hole, then pass
each end of the twine through the second hole, one end to the right and
the other to the left, and draw both tight at the same time, and so on
until the last hole is reached, when one end only of the twine is passed
through; the two ends of the twine are then knotted tight together and
the excess cut off.
The middle sketch shows the joint when the belt is stretched. The lower
sketch shows it passing over a small pulley, where it will be seen that
in the act of bending over the curve there is no friction between the
lace and the belt, and this is the reason of its superiority over other
methods, where there is always more or less friction between the lace
and the belt when bending over a curve. Another advantage is, that in
this system the lace does not come into contact with the pulley, so that
whatever friction or slipping may take place between the belt and the
pulley, the lacing is perfectly unaffected by it.
[Illustration: Fig. 2694.]
A lap joint is one in which the two ends of the belt overlap, as in Fig.
2694. The overlap is cut down to a plain bevel so as to reduce the joint
to nearly or quite the same thickness as the main body of the belt. The
lap joint is employed to join together the strips of leather forming the
belt, and to fasten the ends of the finished belt together. In making
the belt the overlap is cemented and riveted, while in joining the ends
it may be cemented, or riveted, or laced.
The advantage of rivets lies simply in that they are easily applied.
Their disadvantages are that they grip but a small area of the belt,
namely, that portion beneath the rivet head and washer surface; hence,
when rivets are used the joint should always be cemented also. A more
important defect is, however, that the heat generated by the compression
of the rivet while riveting it is sufficiently great to _burn the
leather_ beneath the rivet-head. The reason that the leather under the
head and not under the washer or burr at the riveted end of the rivet
burns is, that although the heat due to riveting is most at the burr end
of the rivet, its passage from the rivet to the washer is less rapid
than it is through the body of the rivet, because in the one case it has
to be transferred from one body to another (from the rivet to the burr),
while in the other its passage is uninterrupted and continuous.
[Illustration: Fig. 2695.]
Rivets for lap joints are usually placed about, as in Fig. 2695, the
rows A and C being about 1/2 inch from the edges B and D respectively,
and the row F about 3/8 inch from the edge F of the lap, while the
rivets are about 5/8 inch apart in the rows.
For comparatively narrow belts as, say, four inches wide, a single row G
would be placed in the middle, additional middle rows should for wider
belts be about 1-1/4 inches apart.
The rivet holes should be a close fit to the rivets, the latter being
left just long enough to hold the washer or burr and sink with it, in
the riveting, to the level surface of the belt.
The heads of the rivets should be on the side of the belt that is to run
next to the pulley.
The strongest method of forming a belt is by means of small taper wooden
pegs, such as are used in boot and shoe manufacture, the joint being
cemented, and the pegs inserted. In this case the belt is merely pierced
with an awl, hence none of the leather is removed.
[Illustration: Fig. 2696.]
The arrangement of wooden pegs should be as in Fig. 2696, the rows A and
B being respectively about 5/8 inch from the edges C D, the row E being
about 1/4 inch from the edge of the joint, and H about 3/4 inch from
that edge. The pegs are placed about 1/2 inch apart in the rows.
A cemented and pegged joint is the strongest made, and it preserves a
more equal tension throughout the belt than any other, while the belt is
strong, since the hole for the pegs may be pierced with an awl, which
does not remove any leather from the belt, as is the case with punched
holes.
The length of the lap in some of the best practice is as follows:
When the strips of leather are cut from the hide in such lengths that
the part termed the shoulder of the hide is utilised, a uniform lap of 8
inches is employed for all widths of belt. When the strips do not
contain the shoulder of the hide, the following are the respective
lengths of lap:--
Width of single belt. Length of lap.
1 to 4-1/2 inches 4-1/4 inches.
5 inches 5 "
6 to 8 inches 6 "
9 inches 6-1/2 "
10 to 14 inches 7 "
15 to 24 " 8 "
All double belts are given a 6 inch lap.
[Illustration: Fig. 2697.]
Another and excellent method of joining a belt, or of fastening two
thicknesses together to form a double belt, is to sew it together with
lace leather, as shown in Fig. 2697. The lace is in this case about 1/4
inch wide, the holes being pierced so as to have the lace diagonal, as
shown in the cut. Sometimes four rivets are added at the joint as shown
in the cut.
[Illustration: Fig. 2698.]
Other methods of fastening the ends of leather belts are by means of
metal hooks of various forms. Fig. 2698 represents a fastening of this
kind, the appearance of both sides of the joint being shown in the
figure. In this case considerable leather is removed from the belt, but
this is to some extent compensated for, because the hook holds each end
of the belt in two places; that is to say, in the crook of the hook as
well as at the end. This, however, while it has the effect of increasing
the grip of the hook on the belt, still leaves the belt as a whole
weaker, by reason of the removal of leather to form the holes.
[Illustration: Fig. 2699.]
[Illustration: Fig. 2700.]
In Figs. 2699 and 2700 is shown a belt screw, intended to take the place
of rivets, and thus avoid the burning of the leather which accompanies
the use of rivets. It consists of two screws, one having a right and the
other a left-hand thread. The former is of bronze, and has a coarse
exterior thread cut conically, while it is hollow with a fine thread
tapped inside. The latter is of steel, and has a conical shoulder
underneath. The heads of both screws are slightly rounded and formed
with circular grooves on the under side, to give them a firm grip on the
leather. The conical screw is first run into the leather, and the steel
screw is then introduced. The belt is run with the head of the latter on
the inner side.
If the body of a narrow belt is riveted it contains two rows only of
rivets; but as the width of the belt increases, other rows are
introduced, all the rows running the entire length of the belt. In some
cases two separate single belts running one over or outside the other
are employed in place of an ordinary double belt, and the arrangement
works well.
Two single belts applied in this manner are especially preferable to a
double belt when used upon a small pulley, because they will bend to the
curvature of the pulley more readily, being more pliable; whereas a
double belt will from its resistance to bending not envelop as much of
the circumference of the belt as is due to the relative sizes of the
pulleys, and the distance apart of their axes.
Round leather belts are made in two forms, the solid and the twisted.
The first consists of a simple leather cord, hence its diameter cannot
exceed the thickness of the leather. The second consists of a strip of
leather twisted into cylindrical form, the grain side of the leather
being outside.
The ends of round belts are usually joined by means of cylindrical hooks
and eyes, which are threaded so as to screw on to the end of the belt,
but for twisted round belts it is better to place in the centre of the
belt a small core of soft wood. The ends of the belt should be slightly
tapered, and the hook and eye screwed firmly home. Sometimes from the
smallness of the pulleys the inflexibility of the hook and eye becomes
objectionable, and a simple hook is employed on solid round belting.
The length of twisted round belting may be altered by twisting or
untwisting it, which renders it unnecessary to cut the belt for a small
amount of shortening.
Round belts should bear upon the sides, and not on the bottom of the
pulley-groove, which increases their transmitting power. Thus, if the
groove is a semicircle of the same radius as is the belt when new, the
stretch of the belt as it wears decreasing its diameter, it will then
touch only on the bottom of the groove. Furthermore, when the belt bears
on the sides only of the groove it becomes wedged to a certain extent in
the sides of the pulley groove.
[Illustration: Fig. 2701.]
[Illustration: Fig. 2702.]
[V]-belting is formed of strips of leather welted together, as shown in
Figs. 2701 and 2702, the latter showing the joint or splice of the belt.
The pulleys are [V]-grooved as shown. The tension of the belt causes it
to grip the sides of the groove on the wedge principle, and the belt is
flat at the apex of the [V] so that it shall not bottom in the groove,
which would impair its wedging action. This class of belt is largely
employed for connecting shafts at an angle, especially in cases where
the distance between the shafts is small, in which case it will last
much longer than a flat belt.
From the construction, the rivets joining the pieces forming the belt do
not come into contact with the surfaces of the pulley, and from the
tension of the belt causing it to wedge into the sides of the pulley
groove, the driving power is greater than that simply due to the area of
contact and the tension of the belt.
[Illustration: Fig. 2703.]
A belt will run to the largest diameter of a pulley, thus in Fig. 2703,
the belt would, unless guided, gradually creep up to the side A of
pulley P, and following this action would move to side C of pulley D.
[Illustration: Fig. 2704.]
If the pulleys are parallel, but the axis of their shafts are not in
line, then the belt will run towards that side on which the axes are
closest; thus in Fig. 2704 the belt would run towards the side P of the
large pulley, because the belt B will meet the pulley surface at _a_,
and if a point on the belt at _b_ travelled coincident with the point on
the pulley with which it took contact, its plane of rotation, while on
the pulley, would be as denoted by the dotted line _b_.
But to follow this plane of rotation, the belt would require to bend
edgeways, as denoted by the dotted line _b_, which it does to some
extent, carrying the belt with it.
CHANGING OR SLIPPING BELTS ON PULLEYS.--To change a belt on a stepped
cone, proceed as follows:--
Suppose the belt to be on the small step of the driving cone, and to
require to run on the largest step. Throw the belt on the smallest step
of the lower cone and place the palm of the hand on the inside face of
the belt on the side on which it approaches that cone. Draw the belt
tight enough (with the palm of the right hand) to take up the slack and
cause the lower cone to rotate. When it is in full motion place the palm
of the left hand against the inside face of the other side of the belt
(while still keeping the pressure of the right hand against the slack
side of the belt).
Release suddenly the pressure of the right hand and immediately with a
quick and forcible lateral motion of the left hand force the belt
towards the larger step of the upper cone, which will cause it to mount
the next step, when the operation may be repeated for each succeeding
step.
If the steps of the cone are too steep, or the belt is too long for this
method, a wooden rod may be used, its end being applied to the side of
the belt that runs on the upper cone and close to the cone. Then lift
the belt with the rod, while the lower end of the rod is inclined away
from the step the belt is to mount, when the belt will mount the step of
the rotating cone.
In the case of broad heavy belts it is best to stop the running pulley
and place the belt on it, then lift the belt edge on the stationary
pulley at the point where the belt will first meet it when in motion,
forcing the belt on by hand as far as possible. Take a strong cord, as,
say 3/8 inch diameter, and double it, pass the loop between the pulley
arms around the belt and over the pulley face. Pass the two free ends of
the cord through the loop (formed by doubling the cord) and pull the
free ends as tight as possible by hand. While standing on the side of
the pulley opposite to that of the belt, communicate slow motion to the
driving pulley and release the ends of the cords as soon as the belt is
on. The belt, in travelling from the pulley, will then undo the cord of
itself.
A belt may be taken off a pulley, either by pressing it in the required
direction and as close to the pulley as possible, or by holding the two
sides of the belt together, which should be done as far from the running
pulley as possible, or as far from the pulley the belt is required to
come off as possible.
[Illustration: Fig. 2705.]
In Fig. 2705 is shown a device for automatically replacing a belt that
has slipped off a pulley. A is the pulley and B the device, which has a
curved projection which is of the full width of the device at one end,
where it comes even with the perimeter of A, and tapers laterally
towards the outside edge of the device. As a result the belt will easily
pass on the broad end and cause the device to rotate, the belt running
up the curved projection and therefore lifting clear of the pulley A,
but on account of the taper of the projection the belt finally has
contact with the projection on one edge only, and therefore tips over to
the other side, and as a result falls on A, because it is under tension
and naturally adjusts itself to be in line with the pulley at the other
end of the belt. It would appear that the belt, if running, would move
on the pulley, driving it, and this would be the case if sufficient time
were allowed for it to do so, but the action of the device is too quick,
and furthermore, when the belt is off one pulley and therefore loose its
motion is apt to become greatly reduced, which retards its moving
laterally on the pulley driving it.
It is obvious that the device must be applied to that side of the pulley
on which the belt is found to run off, but it may be noted that belts
are not apt to run off the loose pulley, but off the driving one, and
only at times when from excessive resistance or duty the velocity of the
pulley is reduced below that of the belt, or the velocity of the belt is
less than that of the pulley driving it; hence the device must be
applied on the outside of the fast or tight pulley.
The driving power of a belt is determined principally by the amount of
its pull upon the pulley, and the speed at which it travels.
The amount of pull is determined by its tension, or in other words, the
degree with which it grips the pulley and the closeness with which it
lies to the pulley surface. The amount of tension a single belt is
capable of withstanding with a due regard to its durability has been
fixed by various experimenters at 66-2/3 lbs. per inch of its width. The
pull of the belt under this degree of tension will vary as follows:--
It will be more with the grain or smooth side than it will with the
flesh or fibrous side of the belt in contact with the pulley face, some
authorities stating the amount of difference to be about 20 per cent. It
will be more with a smooth and polished surface on the pulley than with
one less smooth and polished. At high speeds it will be diminished by
the interposition of air between the belt and pulley surface, and from
the centrifugal force generated by the passage of the belt around the
pulley. It will be more when the pulley is covered with leather rubber
or other cushioning substance than when the pulley is bare, even though
it be highly polished, some authorities stating this difference to be
about 20 per cent.
It will be increased in proportion as the belt envelops a greater
proportion of the pulley circumference, the part of the pulley enveloped
by the belt when the pulley is at rest (or what is the same thing, at
any point of time when it is in motion) being termed the arc of contact.
It is obvious that the arc of contact taken to calculate the belt power
must be the least that exists on either the driving or the driven
pulley, because when the belt slips it ceases to transmit the full
amount of the power it receives, the remainder being expended in the
friction caused by the belt slipping over the pulley.
The speed at which a belt may run is limited only by reason of the
centrifugal force generated during its passage around the pulley, this
force tending to diminish its pressure upon the pulley. The maximum of
speed at which it is considered advisable to run a belt is about 6,000
feet per minute; but the amount of centrifugal force generated at this
speed depends upon the diameter of the pulley, because the centrifugal
force increases in direct proportion as the number of revolutions is
increased, or in other words it increases in the same proportion as the
velocity; but in a given circle it increases as the square of the
velocity. Suppose, then, that it be required to double the velocity of a
belt, and that the same pulley be used running at twice the velocity,
this will increase fourfold the centrifugal force generated; but if the
diameter of the pulley be doubled the centrifugal force generated will
be simply doubled; hence it appears that the larger the pulley the less
the centrifugal force of the belt in proportion to its velocity. This
will be apparent when it is considered that the larger the pulley the
nearer will the curve of its circumference approach to a straight line.
The following experiments on the transmission of power by belting were
made Messrs. Wm. Sellers & Co.
[40]These experiments were undertaken with a view to determine, under
actual working conditions, the internal resistances to be overcome, the
percentage of slip, and the coefficient of friction on belt surface.
They were conducted, during the spring of 1885, under the direction of
Mr. J. Sellers Bancroft.
[40] From a paper read before the American Society of Mechanical
Engineers by Wilfred Lewis.
These experiments seemed to show that the principal resistance to
straight belts was journal friction, except at very high speeds, when
the resistance of the air began to be felt. The resistance from
stiffness of belt was not apparent, and no marked difference could be
detected in the power required to run a wide double belt or a narrow
light one for the same tension at moderate speeds. With crossed and
quarter-twist belts the friction of the belt upon itself or upon the
pulley in leaving it was frequently an item of more importance, as was
shown by special experiments for that purpose.
In connection with the experiments upon internal resistances, some
interesting points were noted. Changes in tension were made while the
belt was running, commencing with a very slack belt and increasing by
definite amounts to the working strength. As this point was approached,
it was found necessary, to maintain a constant tension, that the
tightening bolt should be constantly operated on account of stretch in
the belt. Then, again, as the tension was reduced from this limit, it
was found that at lower tensions the belt would begin to shrink and
tighten for a fixed position of the sliding frame. This stretching and
tightening would continue for a long time, the tightening being, of
course, limited, but the stretching indefinite and unlimited.
The first series of experiments was made upon paper-coated pulleys 20"
diameter, which carried an old 5-1/2" open belt 3/16" to 1/4" thick and
34 ft. long, weighing 16 lbs. The arc of contact on the pulleys has been
calculated approximately from the tension on slack side, and for this
purpose the width and length of the belt were taken. The percentage of
slip must be considered as equally divided between the two pulleys, and
from observations made it is easy to calculate the velocity of sliding
when the speed is given.
Some of the most important results obtained with this belt are given in
Table I. in which the experiments have been selected to avoid
unnecessary repetition. In all cases the coefficient of friction is
shown to increase with the percentage of slip. The adhesion on the
paper-covered pulleys appears to be greater than on the cast-iron
surfaces, but this difference may possibly have been due to some change
in the condition of the belt surfaces.
After a fresh application of the belt dressing known as "Beltilene," the
results obtained are even higher on cast iron than on paper surfaces,
but after a time it was found that the adhesive property of this
substance became sensibly less and less. Flakes of a tarry nature rolled
up from the belt surface and deposited, themselves on the pulleys, or
scaled off.
So much was found to depend upon the condition of the belt surface and
the nature of the dressing used, that the necessity was felt for
experiments upon some standard condition which could be easily realized
and maintained. For this purpose a belt was taken from a planing machine
when it had become perfectly dried by friction. The results of
experiments upon this belt are given in Table II. When dry, as used on
the planer, the coefficients for any given percentage of slip were much
smaller than those given in Table I. This was naturally to be expected,
and the experiments were continued to note the effect of a belt dressing
in common use, known as "Sankey's Life of Leather," which was applied to
the belt while running. At first, the adhesion was very much diminished,
but it gradually increased as the lubricant became absorbed by the
leather, and in a short time the coefficient of friction had reached the
unprecedented figures of 1.44 and 1.37.
TABLE I.
STRAIGHT OPEN BELT 5-1/2" WIDE BY 7/32" THICK AND 34 FT. LONG, WEIGHING
16 LBS., IN GOOD PLIABLE CONDITION, WITH HAIR SIDE ON PULLEYS 20 IN.
DIAM. RUNNING AT 160 R. P. M., OR ABOUT 800 FT. PER MINUTE.
Legend column headings: [A] = No. of Experi'nt.
[B] = Sum of Tensions. _T_ + _t_ Initial.
[C] = Sum of Tensions. _T_ + _t_ Working.
[D] = Sum of Tensions. _T_ + _t_ Final.
[E] = _T_ - _t_ Working.[41]
[F] = _T_[41]
[G] = _t_[41]
[H] = _T_/_t_[41]
[I] = Percentage of Slip.
[J] = Velocity of Slip in ft. per min.
[K] = Arc of contact.
[L] = Coefficient of Friction.
[M] = Remarks.
---+---+---+---+---+-----+-----+-----+----+----+----+----+---
[A]|[B]|[C]|[D]|[E]| [F] | [G] | [H] | [I]| [J]| [K]|[L] |[M]
---+---+---+---+---+-----+-----+-----+----+----+----+----+---
17|200|210| |100|155 | 55 | 2.82| .4| 1.6|177°|.336|[A]
19| |220| |140|180 | 40 | 4.50| .6| 2.4|176 |.490|
21| |246| |180|213 | 33 | 6.45| 1.2| 4.8|175 |.610|
22| |260| |200|230 | 30 | 7.67| 2.6|10.4|174 |.671|
23| |270|180|220|245 | 25 | 9.80| 7.9|31.6|173 |.756|
---+---+---+---+---+-----+-----+-----+----+----+----+----+
24|300|316| |200|258 | 58 | 4.45| .7| 2.8|177 |.483|
27| |344| |260|302 | 42 | 7.20| 1.0| 4 |176 |.643|
28| |350| |280|315 | 35 | 9 | 1.8| 7.2|175 |.719|
29| |364| |300|332 | 32 |10.4 | 2.8|11.2|175 |.784|
30| |380|260|320|350 | 30 |11.7 | 5.5|22 |175 |.805|
---+---+---+---+---+-----+-----+-----+----+----+----+----+
31|400|422| |200|211 |111 | 1.90| .5| 2 |179 |.205|
33| |440| |280|360 | 80 | 4.50| .8| 3.2|178 |.484|
35| |470| |360|415 | 55 | 7.54| 1.1| 4.4|177 |.654|
36| |506| |400|453 | 53 | 8.54| 2.1| 8.4|177 |.694|
37| |520|380|420|470 | 50 | 9.40| 5 |20 |177 |.725|
---+---+---+---+---+-----+-----+-----+----+----+----+----+---
60|200|205| | 80|147.5| 67.5| 2.18| .5| 2 |178 |.251|[B]
61| |210| |100|155 | 55 | 2.82| .9| 3.6|177 |.336|
62| |215| |120|167.5| 47.5| 3.52| 1.7| 6.8|177 |.407|
63| |220| |140|180 | 40 | 4.50| 3 |12 |176 |.490|
65| |246|180|180|213 | 33 | 6.45|12 |48 |175 |.610|
---+---+---+---+---+-----+-----+-----+----+----+----+----+
66|300|300| |120|210 | 90 | 2.33| .5| 2 |179 |.270|
68| |310| |160|235 | 75 | 3.13| .8| 3.2|179 |.365|
69| |315| |180|247.5| 67.5| 3.67| 1 | 4 |178 |.418|
70| |320| |200|260 | 60 | 4.33| 1.7| 6.8|178 |.472|
71| |325| |220|272.5| 52.5| 5.19| 2.6|10.4|177 |.545|
72| |340| |240|290 | 50 | 5.80| 3.8|15.2|177 |.569|
73| |350| |260|305 | 45 | 6.77| 5.5|22 |176 |.623|
74| |360| |280|320 | 40 | 8 | 8.6|34.4|176 |.677|
75| |375| |300|337.5| 37.5| 9 |15.2|60.8|175 |.719|
---+---+---+---+---+-----+-----+-----+----+----+----+----+---
76|400|420| |200|310 |110 | 2.82| .6| 2.4|179 |.336|[C]
78| |460| |280|370 | 90 | 4.11| 1 | 4 |179 |.452|
81| |480| |340|410 | 70 | 5.86| 1.5| 6 |178 |.569|
84| |510| |400|455 | 55 | 8.27| 2.2| 8.8|177 |.684|
86| |535| |440|487.5| 47.5|10.2 | 4.5|18 |177 |.760|
88| |560|385|480|520 | 40 |13 | 8.4|33.6|176 |.834|
---+---+---+---+---+-----+-----+-----+----+----+----+----+
89|300|320| |120|220 |100 | 2.20| .4| 1.6|179 |.252|
93| |350| |200|275 | 75 | 3.67| .8| 3.2|178 |.418|
97| |390| |280|335 | 55 | 6 | 1.6| 6.4|177 |.580|
101| |440| |360|400 | 40 |10 | 3.1|12.4|176 |.750|
104| |470|310|420|445 | 25 |17.8 | 8.6|34.4|173 |.953|
---+---+---+---+---+-----+-----+-----+----+----+----+----+---
Legend Remarks: [A] = Paper-covered pulleys.
[B] = Cast-iron surfaces.
[C] = Belt dressed with "Beltilene."
[41] _T_ represents the tension on the tight part, and _t_ on the sag
part of the belt.
An interesting feature of these and subsequent experiments is the
progressive increase in the sum of the belt tensions during an increase
in load. This is contrary to the generally accepted theory that the sum
of the tensions is constant, but it may be accounted for to a large
extent by the horizontal position of the belt, which permitted the
tension on the slack side to be kept up by the sag. That this is only a
partial explanation of the phenomenon, and that the sum of the tensions
actually increases as their difference increases for even a vertical
position of the belt, will be shown by a special set of experiments. If
a belt be suspended vertically, and stretched by uniformly increasing
weights, it will also be found that the extension is not uniform, but
diminishes as the load is increased, or, as already stated, the stress
increases faster than the extension. A little reflection will show that
when this is the case the tensions must necessarily increase with the
load transmitted.
TABLE II.
DOUBLE BELT 2-1/4" WIDE BY 5/16" THICK, AND 32 FT. LONG, WEIGHING 9-1/2
LBS., ON 20" CAST-IRON PULLEYS. THIS BELT HAD BEEN USED ON A PLANING
MACHINE, WAS QUITE PLIABLE, DRY, AND CLEAN. 160 R. P. M.
Legend column headings: [A] = No. of Experi'nt.
[B] = Sum of Tensions. _T_ + _t_ Initial.
[C] = Sum of Tensions. _T_ + _t_ Working.
[D] = Sum of Tensions. _T_ + _t_ Final.
[E] = _T_ - _t_ Working.
[F] = _T_
[G] = _t_
[H] = _T_/_t_
[I] = Percentage of Slip.
[J] = Velocity of Slip in ft. per min.
[K] = Arc of contact.
[L] = Coefficient of Friction.
[M] = Remarks.
---+---+---+---+---+-----+-----+-----+----+----+----+-----+---
[A]|[B]|[C]|[D]|[E]| [F] | [G] | [H] | [I]| [J]| [K]| [L] |[M]
---+---+---+---+---+-----+-----+-----+----+----+----+-----+---
105|100|104| | 40| 72 | 32 | 2.25| .3| 1.2|177°| .263|
106| |110| | 60| 85 | 25 | 3.40| .8| 3.2|177 | .395|
107| |122| | 80| 101 | 21 | 4.81| 1.7| 6.8|176 | .511|
108| |138| |100| 119 | 19 | 6.26| 4.3|17.2|175 | .600|
---+---+---+---+---+-----+-----+-----+----+----+----+-----+---
109|200|208| | 80| 144 | 64 | 2.25| .4| 1.6|179 | .260|
110| |212| |100| 156 | 56 | 2.81| .7| 2.8|179 | .331|
111| |216| |120| 168 | 48 | 3.50| 1 | 4 |179 | .401|
112| |220| |140| 180 | 40 | 4.50| 1.8| 7.2|178 | .484|
113| |230| |160| 195 | 35 | 5.57| 4.4|17.6|178 | .553|
---+---+---+---+---+-----+-----+-----+----+----+----+-----+---
114|300|308| |120| 214 | 94 | 2.28| .4| 1.6|180 | .262|
116| |316| |160| 238 | 78 | 3.05| .8| 3.2|180 | .355|
118| |322| |200| 261 | 61 | 4.28| 1.6| 6.4|179 | .465|
119| |330|285|220| 275 | 55 | 5 | 2.6|10.4|179 | .516|
---+---+---+---+---+-----+-----+-----+----+----+----+-----+---
121|400|404| |160| 282 |122 | 2.31| .7| 2.8|180 | .267|
124| |410| |220| 315 | 95 | 3.37| 1.5| 6 |180 | .387|
125| |412| |240| 326 | 86 | 3.79| 2.3| 9.2|180 | .424|
126| |414| |260| 338 | 78 | 4.33| 3.7|14.8|179 | .469|
127| |416|370|280| 348 | 68 | 5.12|10.1|40.4|179 | .523|[A]
---+---+---+---+---+-----+-----+-----+----+----+----+-----+
128|500|516| |200|358 |158 | 2.27| .5| 2 |180 | .261|
131| |520| |260|390 |130 | 3 | 1.1| 4.4|180 | .350|
133| |525| |300|412.5|112.5| 3.67| 1.8| 7.2|180 | .414|
134| |525| |320|422.5|102.5| 4.11| 2.7|10.8|180 | .450|
135| |525|460|340|432.5| 92.5| 4.67| 5.1|20.4|180 | .490|
---+---+---+---+---+-----+-----+-----+----+----+----+-----+---
136|100|105| | 40| 72.5| 32.5| 2.02| .2| .8|177 | .228|[B]
137| |110| | 60| 85 | 25 | 3.40| .4| 1.6|177 | .396|
138| |125| | 80|102.5| 22.5| 4.56| .6| 2.4|176 | .494|
140| |150| |120|135 | 15 | 9 | 1.8| 7.2|174 | .723|
141| |164| |140|152 | 12 |12.7 | 2.8|10.8|172 | .779|
142| |180| |160|170 | 10 |17 | 5 |20 |170 | .954|
144| |215| |200|207.5| 7.5|27.7 | 7.3|29.2|166 |1.15 |
146| |250| |240|245 | 5 |49 |10.6|42.4|158 |1.41 |
147| |270| 90|260|265 | 5 |53 |17.7|70.8|158 |1.44 |
---+---+---+---+---+-----+-----+-----+----+----+----+-----+---
149|100|105| | 40| 72.5| 32.5| 2.02| .2| .8|177 | .228|[C]
150| |110| | 60| 85 | 25 | 3.40| .3| 1.2|177 | .396|
151| |120| | 80|100 | 20 | 5 | .4| 1.6|176 | .524|
153| |150| |120|135 | 15 | 9 | .7| 2.8|174 | .723|
155| |182| |160|171 | 11 |15.5 | 1.2| 4.8|172 | .913|
156| |202| |180|191 | 11 |17.3 | 3 |12 |172 | .950|
157| |216| |200|208 | 8 |26 | 5.8|23.2|167 |1.12 |
158| |232| |220|226 | 6 |37.3 | 7 |28 |161 |1.29 |
159| |252| |240|246 | 6 |41 | 9.8|39.2|161 |1.32 |
161| |292| |280|286 | 6 |47.7 |13.7|54.8|161 |1.37 |
---+---+---+---+---+-----+-----+-----+----+----+----+-----+---
Legend Remarks: [A] = Belt almost slipped off.
[B] = Here the belt was coated with "Sankey's Life of
Leather," and run until in good working
condition before noting experiments.
[C] = Three days later without any additional
dressing.
A piece of belting 1 sq. in. in section and 92 ins. long was found by
experiment to elongate 1/4 in. when the load was increased from 100 to
150 lbs., and only 1/8 in. when the load was increased from 450 to 500
lbs. The total elongation from 50 to 500 lbs. was 1-11/16", but this
would vary with the time of suspension, and the measurements here given
were taken as soon as possible after applying the loads. In a running
belt the load is applied and removed alternately for short intervals of
time, depending upon the length and speed of the belt, and the time for
stretching would seldom be as great as that consumed in making the
experiments just mentioned.
The differences between the initial and final tensions unloaded, as
given in the tables, show the effect of extension or contraction during
the course of the experiments made at a fixed position of the pulleys.
The percentage of elongation which a belt undergoes in passing from its
loose to its tight side, is the measure of the slip which must
necessarily take place in the transmission of power. This is a direct
loss, and within the assumed working strength of 500 lbs. per sq. in.
for cemented belts without lacings, experiment indicates that it should
not exceed 1-1/2 or 2 per cent. When, therefore, an experiment shows
less than 2 per cent. of slip, the amount may be considered as allowable
and proper, and the belt may be relied upon to work continuously at the
figures given.
Table III. gives the results of experiments upon a soft and pliable
rawhide belt made by the Springfield Glue and Emery Co. This belt had
been used by the Midvale Steel Co. for a period of seven months, at its
full capacity, and was sent in its usual working condition to be tested.
It had been cleaned and dressed with castor oil at intervals of three
months, and was received three weeks after the last dressing. Commencing
with the light initial tension of 50 lbs. on a side, it was found
impossible with the power at command to reach a limit to the pulling
power of the belt, and in order to do so the experiment was made of
supporting the slack side of the belt upon a board to prevent sagging.
TABLE III.
RAWHIDE BELT 4" WIDE BY 9/32" THICK AND 31 FT. LONG, WEIGHING 15 LBS.
160 R. P. M. ON 20" CAST-IRON PULLEYS.
Legend column headings: [A] = No. of Experi'nt.
[B] = Sum of Tensions. _T_ + _t_ Initial.
[C] = Sum of Tensions. _T_ + _t_ Working.
[D] = Sum of Tensions. _T_ + _t_ Final.
[E] = _T_ - _t_ Working.
[F] = _T_
[G] = _t_
[H] = _T_/_t_
[I] = Percentage of Slip.
[J] = Velocity of Slip in ft. per min.
[K] = Arc of contact.
[L] = Coefficient of Friction.
[M] = Duration of run at time of experiment.
[N] = Remarks.