Chapter XXXII: Leather Belting (1)

The names of the various parts of a hide of leather as known to commerce are as follows:--

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.

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.

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.

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.

+----------------+----------------+-----------------+----------------+
|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.

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.

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:--

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.

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.

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.

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.

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.

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.

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.

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.

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."

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.

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:--

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.

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.

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.

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.

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.

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 "

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.