and for any other material whose specific gravity is y, we find
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 assume 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
experi-
m’nt. | Ten-
sion. T + t | Moment
in inch
lbs. | Dia-
meter
of
pul-
leys. | Revo-
lut’s
per
min. | Width
of
Belt. | Thick-
ness
of
Belt. | Manner of Driving. | Remarks. |
| 1 | 100 | 20 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Straight open belt. | |
| 3 | 300 | 25 | |
| 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 belt. |
| 165 | 300 | 25 | |
| 167 | 500 | 30 | |
| 169 | 700 | 35 | |
| 194 | 100 | 17 | .5 | 10′′ | 160 | 4′′ | 5⁄16′′ | Straight open belt. |
| 196 | 300 | 27 | .5 |
| 198 | 500 | 40 | |
| 200 | 700 | 55 | |
| 202 | 900 | 70 | |
| 203 | 1000 | 80 | |
| 327 | 100 | 20 | | 10′′ | 18 | 4′′ | 5⁄16′′ | Straight open belt. |
| 328 | 1000 | 80 | |
| 393 | 100 | 20 | |
| 394 | 1000 | 100 | |
| 395 | 600 | 60 | |
| 405 | 100 | 20 | | 20′′ | 18 | 4′′ | 9⁄32′′ | Straight open belt. |
| 406 | 1000 | 160 | |
| 407 | 600 | 100 | |
| 428 | 100 | 20 | | 20′′ | 18 | 2′′ | 9⁄32′′ | Straight open belt. |
| 434 | 200 | 25 | |
| 441 | 100 | 25 | | 20′′ | 950 | 2′′ | 3⁄16′′ | Straight open belt. |
| 447 | 200 | 30 | |
| 453 | 100 | 25 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Crossed belt. | 14′ 6′′ between pulleys. |
| 454 | 500 | 60 | |
| 455 | 1000 | 110 | | 14′ 6′′ bet. pul’ys. |
| 459 | 100 | 15 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Straight open belt. | 14′ 6′′ between pulleys. |
| 460 | 500 | 25 | |
| 461 | 1000 | 65 | |
| 462 | 100 | 25 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Straight open belt. | With 8′′ tightener. |
| 463 | 500 | 60 | |
| 464 | 1000 | 110 | |
| 465 | 100 | 45 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Crossed belt. | 8 feet between pulleys. |
| 466 | 500 | 105 | |
| 467 | 1000 | 180 | |
| 470 | 100 | 25 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Quarter turn belt on 16′′ diameter mule pulleys. |
| 471 | 500 | 80 | |
| 472 | 750 | 145 | |
| 473 | 1000 | 250 | |
| 474 | 750 | 170 | |
| 475 | 500 | 110 | |
| 476 | 1000 | 220 | |
| 477 | 1000 | 140 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Quarter turn belt on 16′′ diameter mule pulleys. | Freshly oiled. |
| 478 | 750 | 100 | |
| 479 | 500 | 70 | |
| 480 | 100 | 20 | |
| 481 | 50 | 60 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Quarter turn on 16′′ mule pulleys. | Belt rub. against low. guide m. pul. |
| 482 | 25 | 120 | |
| 483 | 100 | 20 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Quarter turn on 16′′ mule pulleys. | Well oiled, after a run of 2 hrs. at T + t = 100. |
| 484 | 500 | 50 | |
| 485 | 750 | 70 | |
| 486 | 1000 | 105 | |
| 495 | 250 | 30 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Half turn belt on 16′′ mule pulleys. | |
| 496 | 500 | 50 | |
| 497 | 750 | 90 | |
| 498 | 1000 | 170 | |
| 503 | 1000 | 260 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Quarter twist. | 10 feet between pulleys. |
| 504 | 750 | 190 | |
| 505 | 500 | 130 | |
| 506 | 250 | 80 | |
| 507 | 100 | 30 | |
| 513 | 100 | 50 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Quarter twist. | 7′ 6′′ between pulleys. |
| 514 | 250 | 105 | |
| 515 | 500 | 200 | |
| 516 | 750 | 290 | |
| 517 | 1000 | 380 | |
| 523 | 100 | 25 | | 20′′ | 160 | 4′′ | 1⁄4′′ | Quarter twist. | 10 feet between pulleys. |
| 524 | 250 | 50 | |
| 525 | 500 | 95 | |
| 526 | 750 | 145 | |
| 527 | 1000 | 210 | |
| 528 | 100 | 65 | | 20′′ | 160 | 4′′ | 1⁄4′′ | Quarter twist. | 6 feet between pulleys. |
| 529 | 250 | 135 | |
| 530 | 500 | 245 | |
| 531 | 750 | 380 | |
| 533 | 100 | 25 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Quarter twist. | 16′ 6′′ between pulleys. |
| 534 | 250 | 40 | |
| 535 | 500 | 75 | |
| 536 | 750 | 105 | |
| 537 | 1000 | 165 | |
| 539 | 1000 | 130 | | 20′′ | 160 | 6′′ | 7⁄32′′ | Quarter twist with 16′′ diameter carrying pulley. | 7′6′′ between pulleys. |
| 540 | 750 | 110 | |
| 541 | 500 | 90 | |
| 542 | 250 | 60 | |
| 543 | 100 | 40 | |
| 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 belt. | |
| 571 | 500 | 55 | |
| 572 | 750 | 70 | |
| 573 | 1000 | 90 | |