Chapter XXXII: Leather Belting (2)

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.

[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.

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.

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.

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.

---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
[A]|[B]|[C]|[D]|[E]| [F] | [G] | [H] | [I]| [J] | [K]| [L] | [M] |[N]
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
171|100|118| | 40| 79 | 39 | 2.03| .2| .8 |177°| .229| |
173| |140| | 80|110 | 30 | 3.67| .4| 1.6 |176 | .423| |
175| |168| |120|144 | 24 | 6 | .6| 2.4 |174 | .590| |
177| |202| |160|181 | 21 | 8.62| .8| 3.2 |172 | .661| |
179| |232| |200|216 | 16 | 13.5 | 1 | 4 |170 | .897| |
181| |268| |240|254 | 14 | 18.1 | 1.2| 4.8 |167 | .993| |
183| |302| |280|291 | 11 | 26.5 | 1.4| 5.6 |163 | 1.15 | |
184| |318|110|300|309 | 9 | 34.3 | 1.6| 6.4 |160 | 1.27 | |
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
185|100|150|115|140|145 | 5 | 29 | 1.6| 6.4 |180 | 1.02 | |[A]
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+
186|200|258| |240|249 | 9 | 27.4 | 1.2| 4.8 |180 | 1.05 | |
188| |290| |280|285 | 5 | 57 | 2.2| 8.8 |180 | 1.29 | |
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
189|300|412| |400|406 | 6 | 67.7 | 1.7| 6.8 |180 | 1.34 | |
190| |428| |420|424 | 4 |106 | 1.8| 7.2 |180 | 1.48 | |
191| |446|275|440|443 | 3 |148 | 3.3|13.2 |180 | 1.59 | |
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+
192|400|570|360|560|565 | 5 |113 | 2 | 8 |180 | 1.47 | |
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
329|100|110| | 40| 75 | 35 | 2.14| .3| .6 |177 | .246| |[B]
330| |135| | 80|107.5| 27.5| 3.90| .6| 1.2 |175 | .446| |
331| |198| |160|179 | 19 | 9.42| 1 | 2 |171 | .751| |
332| |275| |240|257.5| 17.5| 14.7 | 1.5| 3 |169 | .911| |
334| |345| |320|232.5| 12.5| 18.6 | 2 | 4 |165 | 1.01 | |
336| |420|110|400|410 | 10 | 41 | 3.2| 6.4 |162 | 1.31 | |
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
339|200|230| |160|195 | 35 | 5.86| .8| 1.6 |176 | .576| |
340| |360| |320|340 | 20 | 17 | 1.6| 3.2 |171 | .949| |
341| |435| |400|417.5| 17.5| 23.8 | 2 | 4 |169 | 1.07 | |
342| |505| |480|492.5| 12.5| 39.4 | 2.7| 5.4 |165 | 1.28 | |
343| |590|200|560|575 | 15 | 38.3 | 5 |10 |168 | 1.24 | |
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
344|300|400| |320|360 | 40 | 9 | 1.4| 2.8 |175 | .719| |
345| |450| |400|425 | 25 | 17 | 1.7| 3.4 |173 | .938| |
346| |520| |480|500 | 20 | 25 | 2.1| 4.2 |171 | 1.08 | |
347| |600| |560|570 | 10 | 57 | 3 | 6 |162 | 1.43 | 1 min.|
348| |600|280|560|570 | 10 | 57 | 3.4| 6.8 |162 | 1.43 | 5 min.|
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
350|400|500| |400|450 | 50 | 9 | 1.6| 3.2 |176 | .715| |
352| |605| |560|577.5| 17.5| 21.3 | 2.3| 4.6 |169 | 1.04 | |
353| |680| |640|660 | 20 | 33 | 3.2| 6.4 |171 | 1.17 | 1 min.|
354| |680| |640|660 | 20 | 33 | 3.7| 7.4 |171 | 1.17 | 5 min.|
355| |680| |640|660 | 20 | 33 | 4.1| 8.2 |171 | 1.17 |10 min.|
356| |680| |640|660 | 20 | 33 | 6.1|12.2 |171 | 1.17 |15 min.|[C]
357| |600| |560|580 | 20 | 29 |10 |20 |171 | 1.13 |20 min.|[D]
358| |600| |560|580 | 20 | 29 |17.2|34.4 |171 | 1.13 |25 min.|
359| |530| |480|505 | 25 | 20.2 | 5.2|10.4 |173 | .955|30 min.|
360| |530|350|480|505 | 25 | 20.2 | 2.8| 5.6 |173 | .955|35 min.|
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
361|500|570| |400|485 | 85 | 5.71| 1.3| 2.6 |178 | .561| |
364| |700| |640|670 | 30 | 22.3 | 2.3| 4.6 |174 | 1.02 | |
365| |755| |720|637.5| 17.5| 36.4 | 3.2| 6.4 |169 | 1.22 | |
366| |820| |800|810 | 10 | 81 | 6.6|13.2 |162 | 1.55 +-------+[E]
367| |750| |720|735 | 15 | 49 | 5.1|10.2 |168 | 1.32 | 1 min.|
368| |750| |720|735 | 15 | 49 |11 |22 |168 | 1.32 | 5 min.|
369| |690| |640|665 | 25 | 26.6 |12 |24 |173 | 1.09 +-------+[F]
370| |610| |560|585 | 25 | 23.4 |14.4|28.8 |173 | 1.05 | 1 min.|
371| |610| |560|585 | 25 | 23.4 |20 |40 |173 | 1.05 | 4 min.|
372| |550| |480|515 | 35 | 14.7 | 7.4| 14.8|175 | .880| 1 min.|
373| |550|410|480|515 | 35 | 14.7 | 2.3| 4.6|175 | .880| 5 min.|
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
374|600|680| |480|580 |100 | 5.8 | 1.5| 3 |178 | .566| |
376| |755| |640|697.5| 57.5| 12.1 | 2.1| 4.2 |177 | .807| |
378| |850| |800|825 | 25 | 33 | 2.8| 5.6 |173 | 1.16 | 1 min.|
379| |850| |800|825 | 25 | 33 | 3.5| 7 |173 | 1.16 | 5 min.|[G]
380| |780| |720|750 | 30 | 25 | 8.8|17.6 |174 | 1.06 | 1 min.|
381| |680| |560|620 | 60 | 10.3 |11.2|22.4 |177 | .755| 5 min.|
382| |680| |560|620 | 60 | 10.3 | 2 | 4 |177 | .755+-------+[H]
383| |730| |640|685 | 45 | 15.2 | 2.5| 5 |176 | .886| 1 min.|
384| |730| |640|685 | 45 | 15.2 | 2.4| 4.8 |176 | .886| 5 min.|
385| |780| |720|750 | 30 | 25 | 4.6| 9.2 |174 | 1.06 | 1 min.|
388| |780|550|720|750 | 30 | 25 | 8.8|17.6 |174 | 1.06 | 5 min.|
389| |780| |720|750 | 30 | 25 | 4 | 8 |174 | 1.06 | 1 min.|[I]
390| |780| |720|750 | 30 | 25 | 6.4|12.8 |174 | 1.06 | 5 min.|[E]
391| |730| |640|685 | 45 | 15.2 | 3.7| 7.4 |176 | .886| 1 min.|
392| |730|550|640|685 | 45 | 15.2 | 3.9| 7.8 |176 | .886| 5 min.|
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
396|600|680| |400|540 |140 | 3.86| 2 | .45|170 | .432| |[J]
397| |820| |720|770 | 50 | 15.4 |17.2| 3.87|176 | .890| |
398| |750| |640|695 | 55 | 12.6 |15 | 3.37|177 | .874| |
399| |700| |560|630 | 70 | 9 | 9.4| 2.17|177 | .711| |
400| |670| |480|575 | 95 | 6.05| 4.5| 1.12|178 | .579| |
401| |630|550|400|515 |115 | 4.48| 3.5| .75|178 | .483| |
402| |830| |720|775 | 55 | 14.1 |26 | 5.85|177 | .856| |
403| |630| |320|475 |155 | 3.06| 1.5| .30|179 | .358| |
404| |610| | 60|335 |275 | 1.22| .7| .16|180 | .063| |
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---
408|600|610| |120|365 |245 | 1.49| .2| .09|180 | .127| |[K]
413| |660| |400|530 |130 | 4.08| 1 | .45|179 | .450| |
415| |710| |560|635 | 75 | 8.46| 1.9| .86|177 | .691| |
416| |750| |640|695 | 55 | 12.6 | 3.2| 1.44|177 | .820| |
417| |800| |720|760 | 40 | 19 | 3.8| 1.71|175 | .964| |
418| |340| |200|274 | 70 | 3.91| .6| .27|177 | .441| |
419|300|380| |280|330 | 50 | 6.6 | 1.2| .54|176 | .614| |
421| |450| |400|425 | 25 | 17 | 3.2| 1.44|173 | .938| |
423| |515| |480|497.5| 17.5| 28.4 | 4 | 1.8 |169 | 1.13 | |
425| |580| |560|570 | 10 | 57 | 5 | 2.25|162 | 1.43 | |
427| |695| |680|687.5| 7.5| 91.7 | 7 | 3.15|155 | 1.67 | |
---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---

Legend Remarks: [A] = Slack side of belt running on a board to prevent
sagging.
[B] = 10" cast-iron pulleys.
[C] = Belt slipped off 4 m. later.
[D] = Continuing.
[E] = Belt slipped off 2 m. later.
[F] = Belt slipped off 3 m. later.
[G] = Belt slipped off 5 m. later.
[H] = After running 5 minutes at _T_ - _t_ = 560.
[I] = Belt scraped.
[J] = 18 r. p. m. 10" cast-iron pulleys.
[K] = 20" cast-iron pulleys. 18 r. p. m.

These experiments, however, are subject to an error arising from the friction of the belt upon the board, the amount of which was not determined. All of the experiments, in fact, are subject to slight errors which were extremely difficult to eliminate or properly allow for, but an effort has been made throughout to obtain results which should approximate as closely as possible to the truth. The sum of the tensions, as determined by measuring scales, was subject only to errors in observation. This part of the apparatus was carefully tested by a horizontal pull of known amount and made to register correctly.

The difference of the tensions _T_ - _t_, as computed from the reading of the scales, was measured by the force of an equivalent moment at 20" radius. This moment, divided by the radius of the pulley was taken to be the difference _T_ - _t_.

In this calculation, it will be noticed that two slight corrections have been omitted which are opposite in effect and about equal in degree. One is the friction of the brake shaft in its bearings, which of course was not recorded on the scales, and the other is the thickness of the belt which naturally increases the effective radius of the pulley. Both of these errors are somewhat indefinite, but the correctness of the results obtained was tested in a number of cases by the sag of the belt, and the tension _t_, as calculated from the sag, was found to agree closely with the tension calculated by the adopted method.

As the limiting capacity of the belt was reached, the difficulty of obtaining simultaneous and accurate observations was increased by the vibrations of the scale beams. This was apparently due to irregularity in the slip, and it was only by the use of heavily loaded beams and a dash-pot that readings could then be taken at all. The dash-pot consisted of a large flat plate suspended freely in a bucket of water by a fine wire from the scale beam. This provision, however, was applied only to the scales on which the vibrations were more pronounced.

TABLE IV.

DOUBLE OAK-TANNED LEATHER BELT 4" WIDE BY 5/16" THICK AND 30 FT. LONG, WEIGHING 17 LBS., ON 10" CAST-IRON PULLEYS. 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] = Duration of run at time of experiment.
[N] = Remarks.

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
[A]|[B]|[C]|[D]|[E]| [F] | [G] | [H] | [I]| [J] | [K]| [L] | [M] |[N]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
209|120|120| | 48| 84 | 36 | 2.33| .4| .8 |176°| .275| |
210| |140| | 80|110 | 30 | 3.67| .6| 1.2 |175 | .426| |
211| |168| |120|144 | 24 | 6 | .9| 1.8 |174 | .590| |
212| |198| |160|179 | 19 | 9.42| 1.6| 3.2 |170 | .756| |
213| |235| |200|217.5| 17.5|12.4 | 2.3| 4.6 |174 | .829| |
214| |270| |240|255 | 15 |17 | 3.2| 6.4 |168 | .966| |
215| |310| |280|295 | 15 |19.7 | 5.1|10.2 |168 |1.02 | |[A]
216| |345|122|320|332.5| 12.5|25.8 | 9.4|18.8 |164 |1.13 | |[B]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
217|200|200| | 48|124 | 76 | 1.63| .4| .8 |179 | .156| |
219| |240| |160|200 | 40 | 5 | 1 | 2 |176 | .524| |
220| |360| |320|340 | 20 |17 | 2.7| 5.4 |170 | .954| |
221| |430| |400|415 | 5 |27.7 |15 |30 |167 |1.13 | |
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
222|300|318| |160|239 | 79 | 3.03| .8| 1.6 |179 | .354| |
223| |350| |240|295 | 55 | 5.36| 1.2| 2.4 |177 | .543| |
224| |400| |320|360 | 40 | 9 | 2 | 4 |175 | .719| |
225| |470| |440|455 | 15 |30.3 | 8 | 1.6 |167 |1.17 | |[C]
226| |450| |400|425 | 25 |17 | 4 | 8 |172 | .943| 1 m.|
227| |450| |400|425 | 25 |17 | 8 |16 |172 | .943| 5 m.|
228| |450| |400|425 | 25 |17 |17.3|34.6 |172 | .943| 10 m.|[D]
229| |418| |360|389 | 29 |13.4 | 3 | 6 |173 | .859| 15 m.|[E]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
230|400|405| |160|282.5|122.5| 2.30| .8| 1.6 |179 | .267| |
232| |455| |320|387.5| 67.5| 5.74| 1.4| 2.8 |177 | .566| |
233| |495| |400|447.5| 47.5| 9.42| 1.9| 3.8 |176 | .730| 1 m.|
234| |495|370|400|447.5| 47.5| 9.42| 2.1| 4.2 |176 | .730| 5 m.|
235| |560| |480|520 | 40 |13 | 2.7| 5.4 |175 | .859|Start.|
236| |560| |480|520 | 40 |13 | 4.5| 9 |175 | .859| 5 m.|
237| |560| |480|520 | 40 |13 | 7.5|15 |175 | .859| 10 m.|
238| |550|380|480|465 | 85 | 5.47|20 |40 |178 | .547| 15 m.|
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
239|400|560| |480|520 | 40 |13 | 3.4| 6.8 |175 | .859| 1 m.|[F]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
240|500|610| |480|545 | 65 | 8.38| 2.1| 4.2 |177 | .688| 1 m.|
241| |610| |480|545 | 65 | 8.38| 2.5| 5 |177 | .688| 5 m.|
242| |660| |560|610 | 50 |12.2 | 3.2| 6.4 |176 | .814| 1 m.|
243| |655| |560|607.5| 47.5|12.8 | 8.4|16.8 |176 | .830| 5 m.|[G]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
244|600|700| |560|630 | 70 | 9 | 1.9| 3.8 |177 | .711| 1 m.|
245| |700| |560|630 | 70 | 9 | 2.1| 4.2 |177 | .711| 5 m.|
246| |690|550|560|625 | 65 | 9.69| 2.3| 4.6 |177 | .735| 10 m.|
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
247|600|750| |600|675 | 75 | 9 | 2.2| 4.4 |177 | .771| 1 m.|
248| |740|585|600|670 | 70 | 9.57| 2.4| 4.8 |177 | .731| 5 m.|
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
249|600|770| |640|705 | 65 |10.8 | 2.5| 5 |177 | .770| 1 m.|
250| |765| |640|702.5| 62.5|11.2 | 3.5| 7 |177 | .782| 5 m.|
251| |770|600|640|685 | 85 | 8.06| 4.2| 8.4 |178 | .672| 10 m.|
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
252|600|790| |680|735 | 55 |13.4 | 4.3| 8.6 |176 | .845| 1 m.|
253| |790| |680|735 | 55 |13.4 | 6.3|12.6 |176 | .845| 5 m.|[H]
---+---+---+---+---+-----+-----+-----+-----+-----+----+-----+------+---
254|100|100| | 44| 72 | 28 | 2.57| .6| 1.2 |176 | .307| |[I]
256| |160| |120|140 | 20 | 7 | 2.1| 4.2 |172 | .648| |
257| |200| |160|180 | 20 | 9 | 4 | 8 |171 | .736| |
258| |230| |200|215 | 15 |14.3 | 6.6|13.2 |168 | .907| 1 m.|
259| |230|100|200|215 | 15 |14.3 | 7.2|14.4 |168 | .907| 5 m.|
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
261|100|100| | 44| 72 | 28 | 2.57| .6| 1.2 |176 | .307| |[J]
263| |160| |120|140 | 20 | 7 | 2.8| 5.6 |172 | .648| |
264| |200| |160|180 | 20 | 9 | 5.1|10.2 |171 | .736| |
265| |230| |200|215 | 15 |14.3 | 7.3|14.6 |168 | .907| 1 m.|
266| |230| |200|215 | 15 |14.3 | 7.9|15.8 |168 | .907| 5 m.|
267| |270| |240|255 | 15 |17 |10.7|21.4 |168 | .966| 1 m.|[K]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
268|300|350| |240|295 | 55 | 5.36| 1.4| 2.8 |177 | .544| |
269| |400| |320|360 | 40 | 9 | 3 | 6 |175 | .719| |
270| |450| |400|425 | 25 | 17 | 6.8|13.6 |172 | .943| 1 m.|[K]
271| |418| |360|389 | 29 |13.4 | 8.8|17.6 |173 | .859| 1 m.|
272| |418| |360|389 | 29 |13.4 |15.6|31.2 |173 | .859| 5 m.|[G]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
273|600|700| |560|630 | 70 | 9 | 6.3|12.6 |177 | .711| |
274| |650| |480|565 | 85 | 6.65| 3.1| 6.2 |178 | .610| 1 m.|
275| |650| |480|565 | 85 | 6.65| 3.9| 7.8 |178 | .610| 5 m.|
276| |650| |480|565 | 85 | 6.65| 4.4| 8.8 |178 | .610| 10 m.|
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
277|600|652| |400|526 |126 | 4.17| 1.4| 2.8 |178 | .460| |[L]
279| |715| |560|637.5| 77.5| 8.23| 2.4| 4.8 |177 | .682| |
280| |705| |560|632.5| 72.5| 8.72| 2.8| 5.6 |177 | .701| |
281| |700|560|560|630 | 70 | 9 | 3 | 6 |177 | .711| |
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
282|560|750| |640|695 | 55 |12.6 | 4.1| 8.2 |176 | .824| 1 m.|
283| |735|535|640|682.5| 47.5|14.3 |22 |44 |176 | .866| 5 m.|[M]
284| |770| |640|705 | 65 |10.7 | 5.4|10.8 |177 | .767| 1 m.|[N]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
285|300|350| |240|295 | 55 | 5.36| 1.2| 2.4 |177 | .543| |[O]
286| |400| |320|360 | 40 | 9 | 1.8| 3.6 |175 | .719| |
287| |430| |360|395 | 35 |11.3 | 2.7| 5.4 |174 | .798| |
289| |465| |400|432.5| 32.5|13.3 | 5.3|10.6 |174 | .852| |
290| |455| |400|427.5| 27.5|15.5 | 7.3|14.6 |173 | .907| |
291| |460| |400|430 | 30 |14.3 |11.6|23.2 |173 | .881| |
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
292|100|100| | 44| 72 | 28 | 2.57| .5| 1 |176 | .307| |
293| |125| | 80|102.5| 22.5| 4.55| .8| 1.6 |173 | .502| |
294| |165| |120|142.5| 22.5| 6.33| 1.2| 2.4 |173 | .611| |
295| |200| |160|180 | 20 | 9 | 2.1| 4.2 |171 | .736| |
296| |230| |200|215 | 15 |14.3 | 3.4| 6.8 |168 | .907| |
297| |230| |200|215 | 15 |14.3 | 3.9| 7.8 |168 | .907| |
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
298|100|270| |240|225 | 15 |17 | 5.7|11.4 |168 | .966| 1 m.|
299| |270| |240|255 | 15 |17 | 7.6|15.2 |168 | .966| 5 m.|
300| |270| |240|255 | 15 |17 | 9.3|18.6 |168 | .966| 10 m.|[P]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
303|100|110| | 40| 75 | 35 | 2.14| .1| .4 |177 | .246| |[Q]
304| |132| | 80|106 | 26 | 4.08| .4| 1.6 |174 | .463| |
305| |160| |120|140 | 20 | 7 | 1 | 4 |172 | .648| |
306| |195| |160|177.5| 17.5|10.1 | 1.9| 7.6 |169 | .814| |
307| |230| |200|215 | 15 |14.3 | 3 |12 |168 | .907| 1 m.|
308| |230| 90|200|215 | 15 |14.3 | 3.5|14 |168 | .907| 5 m.|
309| |270| |240|255 | 15 |17 | 4.5|18 |168 | .966| 1 m.|
310| |270| |240|255 | 15 |17 | 5.8|23.2 |168 | .966| 5 m.|
311| |270| |240|255 | 15 |17 | 6.2|24.8 |168 | .966| 10 m.|
312| |270| |240|255 | 15 |17 | 6.2|24.8 |168 | .966| 15 m.|[R]
313| |270| |240|255 | 15 |17 | 2 | 8 |168 | .966| 1 m.|
314| |270| |240|255 | 15 |17 | 2.1| 8.4 |168 | .966| 5 m.|[S]
315| |305| |280|292.5| 12.5|23.4 | 3.4|13.6 |165 |1.09 | 1 m.|
316| |305|100|280|292.5| 12.5|23.4 | 3.5|14 |165 |1.09 | 5 m.|
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
317|100|335| |320|327.5| 7.5|43.7 | 5.2|20.8 |152 |1.42 | 1 m.|
318| |335| |320|327.5| 7.5|43.7 | 6.5|26 |152 |1.42 | 5 m.|
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
319|300|380| |320|350 | 30 |11.7 | 1.3| 5.2 |173 | .814| 1 m.|
320| |380| |320|350 | 30 |11.7 | 1.4| 5.6 |173 | .814| 5 m.|
321| |440| |400|420 | 20 |21 | 2.1| 8.4 |170 |1.03 | 1 m.|
322| |440|260|400|420 | 20 |21 | 2.4| 9.6 |170 |1.03 | 5 m.|
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---
323|300|480| |440|460 | 20 |23 | 2.8|11.2 |170 |1.06 | 1 m.|[T]
324| |480|285|440|460 | 20 |23 | 3 |12 |170 |1.06 | 5 m.|
325| |510| |480|495 | 15 |33 | 3.2|12.8 |167 |1.20 | 1 m.|
326| |510| |480|495 | 15 |33 | 5 |20 |167 |1.20 | 5 m.|[U]
---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+---

Legend Remarks: [A] = Sag 10" at middle of belt.
[B] = Finally slipped off.
[C] = Belt finally slipped off.
[D] = Belt slip'd off.
[E] = Continuing.
[F] = After running 5 m. without load.
[G] = Belt slipped off 2 m. later.
[H] = Belt sl. off 2 m. lat. Pul. warm.
[I] = Belt scraped.
[J] = Belt dres'd with preparation recommend'd by
maker.
[K] = Belt slipped off 3 m. later.
[L] = One day later.
[M] = Belt slipp'd off.
[N] = After 3 min. intermission.
[O] = Temp. 52°.
[P] = Belt slipped off 4 m. later.
[Q] = 20 in. pulleys.
[R] = Temp. 56°.
[S] = Temp. 42°.
[T] = Temp. 46°.
[U] = Belt sl. off 5 m. lat. Pul. warm.

A peculiar and important feature of Tables III. and IV. is the effect of time upon the percentage of slip. In previous experiments the percentage of slip was measured at once after the load was applied, but it was accidentally discovered that repeated measurements seldom agreed, and investigation showed that these discrepancies were principally due to the duration of the experiment. The continual slipping of the belt was found to cause a deposit of a thick black substance upon the surface of the pulley, which, acting as a lubricant, continued to increase the slip still further.

Upon removing the load on brake-wheel, this deposit would be again absorbed by the belt, and the original adhesion would be restored. The temperature was also found to affect the slipping, and, in general, the colder the weather the slower would this deposit take place.

Experiments 353 to 360 inclusive were made to determine the limit at which the belt would run continuously without increasing its percentage of slip. After the pulleys had become well coated and the slip had reached a high per cent., the load on the brake-wheel was gradually removed until a marked improvement was reached, as shown by experiments 359 and 360. The highest allowable coefficient of friction for this belt is therefore estimated to be somewhere between 1.13 and .995, or we may safely say 1. The highest coefficient obtained was 1.67, but, of course, this was temporary. The diameter of the pulley also appears to affect the coefficient of friction to some extent. This is especially to be noticed at the very slow speed of 18 revolutions per minute on 10 in. and 20 in. pulleys, where the adhesion on the 20 in. pulleys is decidedly greater; but, on the other hand, at 160 revolutions per minute the adhesion on the 10 in. pulleys is often as good, and sometimes better, than appears for the 20 in. at the same velocity of sliding.

It might be possible to determine the effect of pulley diameter upon adhesion for a perfectly dry belt, where the condition of its surface remains uniform, but for belts as ordinarily used it would be very difficult, on account of the ever-changing condition of surface produced by slip and temperature. It is generally admitted that the larger the diameter the greater the adhesion for any given tension, but no definite relation has ever been established, nor, indeed, does it seem possible to do so except by the most elaborate and extensive experiments.

It should be observed, however, that such a variation, if true, implies a corresponding variation in the coefficients of friction for different intensities of pressure upon the same pulleys, and that, consequently, our experiments should show higher coefficients under the lighter loads for the same velocity of sliding. Referring to Table II., where the condition of the belt is dry and uniform for a large range of tensions, we find that this inference is generally sustained, although there are some few exceptions.

Experiment 106 may be compared with 116, and 112 with 133, also 108, 113, and 135, all showing great reductions in the coefficients of friction for increments in tension. The exceptions are all to be found under the smallest velocities of sliding, and appear only in the third decimal place, so that the weight of their record against the probability of such a law is light. By a similar inference it should also follow that a wide belt would drive a little more at a given tension than a narrow one, on account of the reduction in pressure per square inch against the pulley. The mean intensity of pressure of a belt against its pulley may be considered as proportional to the sum of the tensions divided by the product of pulley diameter and width of belt, and an analysis of the experiments referred to will show the relation there existing between intensity of pressure and coefficient of friction.

If we let [Iota] = intensity of pressure, and [phi] = coefficient of friction, we shall find that [phi] is approximately proportional to [Iota]^{-.15}, or, in other words that doubling the width of belt or diameter of pulley would apparently increase the coefficient of friction about 10 per cent. of its original value. This relation is not proved, of course, and it is given only as a suggestion toward the solution of the question. If the coefficient of friction does vary with the intensity of pressure, the problem of determining the driving power of a belt on strictly mathematical principles will indeed be complicated.

The coefficient of friction in the tables has been calculated by a well-known formula, developed upon the assumption of a uniform coefficient around the arc of contact, but this could no longer be considered as correct if the coefficient is known to vary with the pressure. Referring from Table II. to Table III., we shall find at once the proof and contradiction of the inferences drawn from Table II., and we are left as much in the dark as ever respecting the value of pressure intensity.

Practical millwrights all know, or think they know, that an increase of pulley diameter increases the drive, and it is a matter of common observation that when large and small pulleys are connected by a crossed belt, the smaller pulley will invariably slip first.

On one side a great deal of testimony can be adduced to show that pressure intensity should be an important factor in the theory of belt transmission, and, on the other hand, we have strong evidence to the contrary. I may refer, in this connection, to the experiments of Mr. Holman in _Journal of Franklin Institute_ for September, 1885, in which there is no indication that the coefficient of friction varies at all with the pressure. The coefficients obtained by Mr. Holman follow the variations in slip like our own, and it gives us pleasure to observe that our general results and conclusions are so strongly corroborative of each other. There is at the same time a great difference in the methods pursued in arriving at the same results. In his experiments, the velocity of sliding was the fixed condition upon which the coefficient of friction was determined, while, in ours, the conditions were those of actual practice in which the percentage of slip was measured. Our least amount of slip, with a dry belt running at the extremely slow speed of 90 feet per minute, was 1.08 inches, and ten times this would be perfectly proper and allowable. A great many of Mr. Holman's experiments are taken at rates below 1" per minute, and the coefficients obtained are very much below the average practice, as himself seems to believe.