Modern Machine-Shop Practice Part 189

432| |105| | 20| 62.5|42.5|1.47| .3| .14|179 |.123| |m.

433| |112| | 50| 81 |31 |2.61| 3.5| 1.57|178 |.309| | ---+---+---+---+---+-----+----+----+----+------+----+----+------+--- 435|200|204| | 40|132 |82 |1.61| .2| .09|180 |.152| | 436| |206| | 60|133 |73 |1.82| .7| .32|180 |.191| | 437| |208| | 80|144 |64 |2.25| 1.8| .81|179 |.260| | 438| |210| |100|155 |55 |2.82| 3.7| 1.66|179 |.332| | 439| |212| |120|166 |40 |3.61| 7.7| 3.47|179 |.411| | 440| |215| |140|177.5|37.5|4.73|18.4| 8.28|179 |.497| | ---+---+---+---+---+-----+----+----+----+------+----+----+------+--- 442|100|110| | 60| 85 |25 |3.40| .3| 7.12|178 |.394| |950 443| |120| | 80|100 |20 |5 | .7| 16.62|178 |.518| |r.

445| |125| | 90|107.5|17.5|6.14| 3 | 71.25|177 |.587|Start.|p.

446| |125| | 90|107.5|17.5|6.14|25 |593.7 |177 |.587|min. |m.

---+---+---+---+---+-----+----+----+----+------+----+----+------+--- 448|200|200| | 80|140 |60 |2.33| .4| 9.5 |179 |.271| | 449| |200| |100|150 |50 |3 | .5| 11.87|179 |.352| | 450| |195|175|120|157.5|37.5|4.20| .8| 19 |179 |.459| | ---+---+---+---+---+-----+----+----+----+------+----+----+------+--- 451|150|175| |120|147.5|27.5|5.36| .9| 21.38|178 |.540| | ---+---+---+---+---+-----+----+----+----+------+----+----+------+--- 452|135|160| |120|140 |20 |7 |20 |475 |178 |.626| | ---+---+---+---+---+-----+----+----+----+------+----+----+------+---

It may here be mentioned that the sum of the tensions was the horizontal pressure of the belt against the pulleys, and that no allowance was necessary for the effect of the centrifugal force. At the speed here used, the tension indicated in the belt at rest was about 50 lbs.

greater than when in motion.

TABLE VI.

SHOWING THE AVERAGE COEFFICIENT OF FRICTION AND VELOCITY OF SLIP FOR A NUMBER OF EXPERIMENTS IN WHICH THE SLIP APPROXIMATED 2 PER CENT.

-------------------------------------+--------------+----------------- No. exper'ts in av'ge. | | |Percentage of Slip. | | | |Veloc. of Sl. in ft. per m. | | | | |Coefficient of Fric- | | | | |tion. | | | | | | Belt. | Pulleys. | Remarks.

--+----+-----+-----+-----------------+--------------+----------------- 3|1.4 | 5.6 | .661|5-1/2" old belt. |20" diam. |Belt in nor.

| | | |Table I |pap. cov'd |w'k'g con.

--+----+-----+-----+-----------------+--------------+ 2|1.7 | 6.8 | .44 |5-1/2" old belt. |20" di. | " "

| | | |Table I |cast-iron sur.| --+----+-----+-----+-----------------+--------------+----------------- 2|1.55| 6.2 | .575|5-1/2" old belt. |20" di. |Belt dressed | | | |Table I |cast-iron sur.|with "Beltiline."

--+----+-----+-----+-----------------+--------------+----------------- 5|1.7 | 6.8 | .452|2-1/4" dbl. belt.|20" di. |B't dry as us.

| | | |Table II |cast-iron sur.|on plan'r.

--+----+-----+-----+-----------------+--------------+----------------- 2|1.5 | 6 | .818|2-1/4" dbl. belt.|20" di. |Belt dressed | | | |Table II |cast-iron sur.|with "Sankey's | | | | | |Life of Leather."

--+----+-----+-----+-----------------+--------------+----------------- 2|1.7 | 6.8 |1.38 |4" r'hide b. |20" di. |Belt in nor.

| | | |Table III |cast-iron sur.|w'k'g con.

--+----+-----+-----+-----------------+--------------+ 11|1.8 | 3.6 | .861|4" r'hide b. |10" diameter. | " "

| | | |Table III | | --+----+-----+-----+-----------------+--------------+ 1|2 | .45| .432|4" r'hide b. |10" diameter. | " "

| | | |Table III | | --+----+-----+-----+-----------------+--------------+ 1|1.9 | .86| .691|4" r'hide b. |20" diameter. | " "

| | | |Table III | | --+----+-----+-----+-----------------+--------------+ 7|1.94| 3.88| .617|4" o.tan'd b. |10" diameter. | " "

| | | |Table IV | | --+----+-----+-----+-----------------+--------------+ 4|1.85| 7.40| .906|4" o.tan'd b. |20" diameter. | " "

| | | |Table IV | | --+----+-----+-----+-----------------+--------------+----------------- 2|1.5 | .67| .251|2" o.tan'd b. |20" diameter. |B't dry as us. on | | | |Table V | |plan'r.

--+----+-----+-----+-----------------+--------------+ 2| .8 |38 | .529|2" o.tan'd b. |20" diameter. | " "

| | | |Table V | | --+----+-----+-----+-----------------+--------------+-----------------

The conclusion to be drawn from this series of experiments is the great importance of high speed in the economy of belt transmission. The friction of belts on pulleys is evidently dependent on the velocity of sliding, and, as a general rule, the greater the velocity the greater the friction. There are but few apparent exceptions to this rule, and investigation of them has led to the inference that in all such cases, the condition of the belt or pulley surface had undergone a change either by heating or by deposit from the belt on the pulley. The percentage of slip is the measure of the power lost in transmission by the belt itself, and the higher the speed the less this becomes. There is a limit, however, to the power which may be transmitted as the speed is increased, and this limit is caused by the reduction in pressure against the pulley arising from the action of centrifugal force.

This point has been clearly demonstrated in a paper read before this Society by Mr. A. F. Nagle on the "Horse Power of Leather belts,"[43]

and the formula there developed is written thus:

_HP_ = _CVtw_(_S_ - .012_V_^{2}) 550, (1.)

in which _C_ is a constant to be determined from the arc of contact and coefficient of friction as expressed in the equation:

_C_ = 1 - 10^{-.00758_f[alpha]_}, (2.)

_V_ = velocity of belt in feet per second.

_t_ = thickness of the belt in inches.

_w_ = width " "

_S_ = working strength of leather in lbs. per square inch.

_f_ = coefficient of friction.

_[alpha]_ = arc of contact in degrees.

[43] Transactions A. S. M. E., Vol. II., page 91. See also Mr. Nagle's Tables I., II., and III., in Appendix VI. to this paper for values of _C_ and _H.P._

The velocity at which the maximum amount of power can be transmitted by any given belt is independent of its arc of contact and coefficient of friction, and depends only upon the working strength of the material and its specific gravity.

From equation (1.) we obtain for the maximum power of leather belts the condition:

_____ _V_ = /28_S_, (3.)

and for any other material whose specific gravity is _y_, we find

____ /_S_ _V_ = / --- / _y_

The coefficient of friction .40, adopted by Mr. Nagle, appears from these experiments to be on the safe side for all working requirements, except in cases where dry belts are run at slow speeds.

If we a.s.sume 2 per cent. as the greatest allowable slip, and select within this limit the coefficient corresponding to the nearest approximations to it, we can form some idea of the coefficients which can be relied upon at different speeds.

Table VI. gives the average results obtained for this maximum allowance of slip, and shows an extreme variation in the coefficient of friction from .251 for a dry oak-tanned belt at the slow speed of 90 feet per minute to 1.38 for a rawhide belt at the moderate speed of 800 feet per minute.

For continuous working, it is probable that the coefficient 1.38 is too high, but still it is certain that a coefficient of 1.00 can be steadily maintained for an indefinite length of time, and we may say that in actual practice the coefficient of friction may vary from .25 to 1.00 under good working conditions. This extreme variation in the coefficient of friction does not give rise, as might at first be supposed, to such a great difference in the transmission of power. It will be seen by reference to formula (1.) that the power transmitted for any given working strength and speed is limited only by the value of _C_, which depends upon the arc of contact and the coefficient of friction.

For the usual arc of contact, 180, the power transmitted when _f_ = .25 is about 24 per cent. less than when _f_ = .40, and when _f_ = 1.00, the power transmitted is about 33 per cent. more, from which it appears that in extreme cases the power transmitted may be 1/4 less or 1/3 more than will be found from the use of Mr. Nagle's coefficient of .40.

TABLE VII.

SHOWING THE TORSIONAL MOMENT IN LBS. REQUIRED TO OVERCOME JOURNAL FRICTION AND OTHER INTERNAL RESISTANCES, FOR BELTS AT VARIOUS SPEEDS AND TENSIONS ON DIFFERENT ARRANGEMENTS OF PULLEYS.

------+-----+-------+-----+-----+-----+------+-------------+-------------- No. of|Ten- |Moment |Dia- |Revo-|Width|Thick-| | exper-|sion.|in inch|meter|lut's| of | ness | Manner of | im'nt.|_T_ +| lbs. | of |per |Belt.| of | Driving. | Remarks.

| _t_ | |pul- |min. | |Belt. | | | | |leys.| | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 1 | 100| 20 | 20" | 160 | 6" |7/32" |Straight open| 3 | 300| 25 | | | | |belt. | 5 | 500| 30 | | | | | | 7 | 700| 35 | | | | | | 10 | 1000| 45 | | | | | | 45 | 100| 15 | | | | | | 47 | 300| 22.5 | | | | | | 49 | 500| 27.5 | | | | | | 51 | 700| 35 | | | | | | 54 | 1000| 50 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 163 | 100| 17.5 | 20" | 160 | 4" |9/32" |Straight open| 165 | 300| 25 | | | | |belt. | 167 | 500| 30 | | | | | | 169 | 700| 35 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 194 | 100| 17.5 | 10" | 160 | 4" |5/16" |Straight open| 196 | 300| 27.5 | | | | |belt. | 198 | 500| 40 | | | | | | 200 | 700| 55 | | | | | | 202 | 900| 70 | | | | | | 203 | 1000| 80 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 327 | 100| 20 | 10" | 18 | 4" |5/16" |Straight open| 328 | 1000| 80 | | | | |belt. | 393 | 100| 20 | | | | | | 394 | 1000| 100 | | | | | | 395 | 600| 60 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 405 | 100| 20 | 20" | 18 | 4" |9/32" |Straight open| 406 | 1000| 160 | | | | |belt. | 407 | 600| 100 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 428 | 100| 20 | 20" | 18 | 2" |9/32" |Straight open| 434 | 200| 25 | | | | |belt. | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 441 | 100| 25 | 20" | 950 | 2" |3/16" |Straight open| 447 | 200| 30 | | | | |belt. | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 453 | 100| 25 | 20" | 160 | 6" |7/32" |Crossed belt.|14' 6" between 454 | 500| 60 | | | | | |pulleys.

455 | 1000| 110 | | | | | |14' 6" bet.

| | | | | | | |pul'ys.

------+-----+-------+-----+-----+-----+------+-------------+-------------- 459 | 100| 15 | 20" | 160 | 6" |7/32" |Straight open|14' 6" between 460 | 500| 25 | | | | |belt. |pulleys.

461 | 1000| 65 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 462 | 100| 25 | 20" | 160 | 6" |7/32" |Straight open|With 8"

463 | 500| 60 | | | | |belt. |tightener.

464 | 1000| 110 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 465 | 100| 45 | 20" | 160 | 6" |7/32" |Crossed belt.|8 feet between 466 | 500| 105 | | | | | |pulleys.

467 | 1000| 180 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 470 | 100| 25 | 20" | 160 | 6" |7/32" |Quarter turn | 471 | 500| 80 | | | | |belt on 16" | 472 | 750| 145 | | | | |diameter mule| 473 | 1000| 250 | | | | |pulleys. | 474 | 750| 170 | | | | | | 475 | 500| 110 | | | | | | 476 | 1000| 220 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 477 | 1000| 140 | 20" | 160 | 6" |7/32" |Quarter turn |Freshly oiled.

478 | 750| 100 | | | | |belt on 16" | 479 | 500| 70 | | | | |diameter mule| 480 | 100| 20 | | | | |pulleys. | 481 | 50| 60 | 20" | 160 | 6" |7/32" |Quarter turn |Belt rub.

482 | 25| 120 | | | | |on 16" mule |against low.

| | | | | | |pulleys. |guide m. pul.

------+-----+-------+-----+-----+-----+------+-------------+-------------- 483 | 100| 20 | 20" | 160 | 6" |7/32" |Quarter turn |Well oiled, 484 | 500| 50 | | | | |on 16" mule |after a run of 485 | 750| 70 | | | | |pulleys. |2 hrs. at _T_ 486 | 1000| 105 | | | | | |+ _t_ = 100.

------+-----+-------+-----+-----+-----+------+-------------+-------------- 495 | 250| 30 | 20" | 160 | 6" |7/32" |Half turn | 496 | 500| 50 | | | | |belt on 16" | 497 | 750| 90 | | | | |mule pulleys.| 498 | 1000| 170 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 503 | 1000| 260 | 20" | 160 | 6" |7/32" |Quarter |10 feet 504 | 750| 190 | | | | |twist. |between 505 | 500| 130 | | | | | |pulleys.

506 | 250| 80 | | | | | | 507 | 100| 30 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 513 | 100| 50 | 20" | 160 | 6" |7/32" |Quarter |7' 6" between 514 | 250| 105 | | | | |twist. |pulleys.

515 | 500| 200 | | | | | | 516 | 750| 290 | | | | | | 517 | 1000| 380 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 523 | 100| 25 | 20" | 160 | 4" | 1/4" |Quarter |10 feet 524 | 250| 50 | | | | |twist. |between 525 | 500| 95 | | | | | |pulleys.

526 | 750| 145 | | | | | | 527 | 1000| 210 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 528 | 100| 65 | 20" | 160 | 4" | 1/4" |Quarter |6 feet between 529 | 250| 135 | | | | |twist. |pulleys.

530 | 500| 245 | | | | | | 531 | 750| 380 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 533 | 100| 25 | 20" | 160 | 6" |7/32" |Quarter |16' 6" between 534 | 250| 40 | | | | |twist. |pulleys.

535 | 500| 75 | | | | | | 536 | 750| 105 | | | | | | 537 | 1000| 165 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 539 | 1000| 130 | 20" | 160 | 6" |7/32" |Quarter twist|7' 6" between 540 | 750| 110 | | | | |with 16" |pulleys.

541 | 500| 90 | | | | |diameter | 542 | 250| 60 | | | | |carrying | 543 | 100| 40 | | | | |pulley. | 544 | 100| 30 | | | | | | 545 | 250| 55 | | | | | | 546 | 500| 90 | | | | | | 547 | 750| 120 | | | | | | 548 | 1000| 170 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+-------------- 569 | 100| 25 | 20" | 160 | 6" |7/32" |Straight open| 571 | 500| 55 | | | | |belt. | 572 | 750| 70 | | | | | | 573 | 1000| 90 | | | | | | ------+-----+-------+-----+-----+-----+------+-------------+--------------

The percentage of slip is the most important factor affecting the efficiency of belt transmission, but in addition to this we have journal friction, the resistance of the air, and with crossed belts the friction of the belt upon itself. These have been termed internal resistances, and their values for some of the most common arrangements of pulleys are given in Table VII. From this table it appears that the moment required to run a straight belt varies from 15 to 25 inch lbs. at 100 lbs.

tension for all speeds. At 160 revolutions per minute and 1,000 lbs.

tension, the required moment varied from 45 to 90 inch lbs., and at 18 revolutions per minute and at the same tension it varied from 80 to 150 inch lbs.