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Modern Machine-Shop Practice, Volumes I and II

Chapter 93: TABLE II.
By Joshua Rose
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About This Book

The work presents a comprehensive, practical manual for machine-shop operations, with step-by-step instruction on constructing and using machine tools, work-holding devices, hand tools, and the management of steam engines and boilers. It emphasizes approved workshop practices over theory, provides simple arithmetic calculations, many illustrated examples and tables, and detailed chapters on topics such as gear-tooth geometry and gear trains. Material is organized progressively for apprentices and experienced mechanics alike, and includes numerous engravings, practical rules, sample computations, and a technical vocabulary to aid self-instruction and shop reference.

[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 21⁄4′′ WIDE BY 5⁄16′′ THICK, AND 32 FT. LONG, WEIGHING 91⁄2 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.
No.
of
Exper-
i’nt.		 Sum of Tensions T + t T - t
Work-
ing.		 T t T ⁄ t Per-
cent-
age
of
Slip.		 Velocity
of Slip
in ft.
per
min.		 Arc
of
con-
tact.		 Coef-
ficient
of
Friction.		 Remarks.
Initial. Work-
ing.		 Final.
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 Belt almost slipped off.
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 Here the belt was coated with “Sankey’s Life of Leather,” and run until in good working condition before noting experiments.
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 Three days later without any additional dressing.
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

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 111⁄16′′, 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 11⁄2 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.
No.
of
Exper-
i’nt.		 Sum of Tensions T + t T - t
Work-
ing.		 T t T ⁄ t Per-
cent-
age
of
Slip.		 Velocity
of Slip
in ft.
per
min.		 Arc
of
con-
tact.		 Coef-
ficient
of
Friction.		 Dura-
tion
of run
at time
of
experi-
ment.		 Remarks.
Initial. Work-
ing.		 Final.
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       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   Slack side of belt running on a board to prevent sagging.
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       180   1 .47  
329 100 110   40 75   35   2 .14   .3   .6 177     .246   10′′ cast-iron pulleys.
330   135   80 107 .5 27 .5 3 .90   .6 1 .2 175     .446  
331   198   160 179   19   9 .42 1       171     .751  
332   275   240 257 .5 17 .5 14 .7 1 .5     169     .911  
334   345   320 232 .5 12 .5 18 .6 2       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       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     .0 168   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       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. [4 m. later.
356   680   640 660   20   33   6 .1 12 .2 171   1 .17 15 min. Belt slipped off
357   600   560 580   20   29     .0   .0 171   1 .13 20 min. Continuing.
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   Belt slipped off 2 m. later.
367   750   720 735   15   49   5 .1 10 .2 168   1 .32 1 min.
368   750   720 735   15   49     .1   .2 168   1 .32 5 min.
369   690   640 665   25   26 .6   .2   .4 173   1 .09   Belt slipped off 3 m. later.
370   610   560 585   25   23 .4 14 .4 28 .8 173   1 .05 1 min.
371   610   560 585   25   23 .4   .0   .0 173   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     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     173   1 .16 5 min. Belt slipped off 5 m. later.
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       177     .755   After running 5 minutes at T - t = 560.
383   730   640 685   45   15 .2 2 .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       174   1 .06 1 min. Belt scraped.
390   780   720 750   30   25   6 .4 12 .8 174   1 .06 5 min.
391   730   640 685   45   15 .2 3 .7 7 .4 176     .886 1 min. Belt slipped off 2 m. later.
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   18 r. p. m. 10′′ cast-iron pulleys.
397   820   720 770   50   15 .4 17 .2 3 .87 176     .890  
398   750   640 695   55   12 .6   .5 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   .6 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   20′′ cast-iron pulleys. 18 r. p. m.
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