Modern Machine-Shop Practice, Volumes I and II

by Joshua Rose

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.

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.
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			[middle of belt.
215		310		280	295		15		19	.7	5	.1	10	.2	168		1	.02			Sag 10′′ at
216		345	122	320	332	.5	12	.5	25	.8	9	.4	18	.8	164		1	.13			Finally slipped off.
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			Belt finally slipped off.
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.	Belt slip’d off.
229		418		360	389		29		13	.4	3		6		173			.859	15	m.	Continuing.
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.	After running 5 m. without load.
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.	Belt slipped off 2 m. later.
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.	[lat. Pul. warm.
253		790		680	735		55		13	.4	6	.3	12	.6	176			.845	5	m.	Belt sl. off 2 m.
254	100	100		44	72		28		2	.57		.6	1	.2	176			.307			Belt scraped.
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			Belt dres’d with preparation recommend’d by maker.
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.	Belt slipped off 3 m. later.
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.	Belt slipped off 3 m. later.
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.	Belt slipped off 2 m. later.
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			One day later.
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.	Belt slipp’d off.
284		770		640	705		65		10	.7	5	.4	10	.8	177			.767	1	m.	After 3 min. intermission.
285	300	350		240	295		55		5	.36	1	.2	2	.4	177			.543			Temp. 52°.
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.	[4 m. later.
300		270		240	255		15		17		9	.3	18	.6	168			.966	10	m.	Belt slipped off
303	100	110		40	75		35		2	.14		.1		.4	177			.246			20 in. pulleys.
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.	Temp. 56°.
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.	Temp. 42°.
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.	Temp. 46°.
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.	[lat. Pul. warm.
326		510		480	495		15		33		5		20		167		1	.20	5	m.	Belt sl. off 5 m.

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.