Fig. 2679Fig. 2679.
Fig. 2679.
Thus supposep,Fig. 2679, represents a driven pulley, whose load is 1,000 pounds, and that fromatob, frombtoc, fromctod, and fromdtoe, represent equal arcs of contact between belt and pulley, then arca bwill have on it the amount of stretch due to a pull of 250 pounds atb, diminishing to nothing ata. Arcc bwill have on it the amount of stretch due to a pull of 500 pounds atcand 250 atb; arcd cwill have on it the amount of stretch due to a load of 750 atd, and 500 atc; and arcd ewill have the tension due to a load of 1,000 pounds ate, and 750 pounds atd. Suppose, then, that the amount of belt stretch is greater betweenbandcthan it is betweendande, then the belt will travel faster betweenb cthan betweend eto an amount equal to the difference in stretch, and will atb cslip over the pulley to that amount; or if the friction of the belt atb cis 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 fromdtoe.
But since the friction of the belt is greatest atd 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, atd e.
Here arises another consideration, in that the stretch of the leather is not uniform, and the section of belt atc bmay stretch more or less under its load than sectionc ddoes 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 transfera creep is taking place on the arc of belt contact on the driving pulley.
Fig. 2680Fig. 2680.
Fig. 2680.
Furthermore, let it be noted that while under continuous motion the belt first receives full stress at pointf,Fig. 2677; at starting it first receives it at pointe, and there will be a period of time during which the belt stretch will proceed frometowardsf, 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 toFig. 2680, if the amount of the load is such that the arc of contact between the top and the pointbis sufficient to drive the pulley, the pulley will receive motion when the belt stretch has proceeded fromatob; but if the load on the pulley be increased the belt stretch will require to proceed farther towardsc.
At the top the stretch will proceed simultaneously with that of the driving side of the belt, between the pointsf 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 fromftowardse,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.
Fig. 2681Fig. 2681.
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 inFig. 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.
Fig. 2682Fig. 2682.
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 inFig. 2682.
For belts of about 3 inches wide and over, these holes are made as follows:a,b, andc,d,e, about an inch apart and5⁄8inch from the line of joint;f,g,h, andi,j, being about1⁄2inch behinda,b, andc,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 bestpractice:—
Fig. 2683Fig. 2683.
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 inFig. 2683ata, or a mere slit, as atb, which, from removing less material from the belt, leaves it to that extent stronger.
Fig. 2684Fig. 2684.
Fig. 2684.
Fig. 2685Fig. 2685.
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 inFig. 2684, when laced up the edge of the belt would come as inFig. 2685.
Fig. 2686Fig. 2686.
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 inFig. 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 asfollows:—
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.
Fig. 2687Fig. 2687.
Fig. 2687.
Fig. 2688Fig. 2688.
Fig. 2688.
Fig. 2689Fig. 2689.
Fig. 2689.
There are many different methods of lacing a belt, but those here described are generally preferred. Thus referring toFig. 2687the lace is first passed through holesgandd, 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 inFig. 2688. The ends are in some cases tied in a knot on the outside, and in others fastened as shown inFig. 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. 2690Fig. 2690.
Fig. 2690.
Fig. 2690shows a method of lacing in which the crossing of the lace is entirely avoided, the knot being on the outside ata 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 jointpasses 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.
Fig. 2691Fig. 2692Fig. 2691.Fig. 2692.
Fig. 2691.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 inFig. 2691ata, 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 inFig. 2692ais the cover riveted or cemented to the two endsb c, of the belt so as to dispense with lacing.
Fig. 2693Fig. 2693.
Fig. 2693.
Fig. 2693represents an excellent method of joining very thin belts, the operation being asfollows:—
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 ata, 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.
Fig. 2694Fig. 2694.
Fig. 2694.
A lap joint is one in which the two ends of the belt overlap, as inFig. 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 toburn the leatherbeneath 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.
Fig. 2695Fig. 2695.
Fig. 2695.
Rivets for lap joints are usually placed about, as inFig. 2695, the rowsaandcbeing about1⁄2inch from the edgesbanddrespectively, and the rowfabout3⁄8inch from the edgefof the lap, while the rivets are about5⁄8inch apart in the rows.
For comparatively narrow belts as, say, four inches wide, a single rowgwould be placed in the middle, additional middle rows should for wider belts be about 11⁄4inches 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.
Fig. 2696Fig. 2696.
Fig. 2696.
The arrangement of wooden pegs should be as inFig. 2696, the rowsaandbbeing respectively about5⁄8inch from the edgesc d, the rowebeing about1⁄4inch from the edge of the joint, andhabout3⁄4inch from that edge. The pegs are placed about1⁄2inch 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 oflap:—
Fig. 2697Fig. 2697.
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 inFig. 2697. The lace is in this case about1⁄4inch 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.
Fig. 2698Fig. 2698.
Fig. 2698.
Other methods of fastening the ends of leather belts are by means of metal hooks of various forms.Fig. 2698represents 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.
Fig. 2699Fig. 2699.
Fig. 2699.
Fig. 2700Fig. 2700.
Fig. 2700.
InFigs. 2699and2700is 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 twistingor 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.
Fig. 2701Fig. 2701.
Fig. 2701.
Fig. 2702Fig. 2702.
Fig. 2702.
V-belting is formed of strips of leather welted together, as shown inFigs. 2701and2702, the latter showing the joint or splice of the belt. The pulleys areV-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 theVso 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.
Fig. 2703Fig. 2703.
Fig. 2703.
A belt will run to the largest diameter of a pulley, thus inFig. 2703, the belt would, unless guided, gradually creep up to the sideaof pulleyp, and following this action would move to sidecof pulleyd.
Fig. 2704Fig. 2704.
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 inFig. 2704the belt would run towards the sidepof the large pulley, because the beltbwill meet the pulley surface ata, and if a point on the belt atbtravelled 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 lineb.
But to follow this plane of rotation, the belt would require to bend edgeways, as denoted by the dotted lineb, 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 asfollows:—
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, say3⁄8inch 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 byholding 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.
Fig. 2705Fig. 2705.
Fig. 2705.
InFig. 2705is shown a device for automatically replacing a belt that has slipped off a pulley.ais the pulley andbthe 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 ofa, 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 pulleya, 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 ona, 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 662⁄3lbs. per inch of its width. The pull of the belt under this degree of tension will vary asfollows:—
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.
[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 51⁄2′′ open belt3⁄16′′ to1⁄4′′ 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 inTable 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 onpaper 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 inTable II. When dry, as used on the planer, the coefficients for any given percentage of slip were much smaller than those given inTable 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.