Modern Machine-Shop Practice, Volumes I and II

by Joshua Rose

The following table (from “Machine Tools,” by Wm. Sellers and Co.) gives the strength of round wrought iron as given by Clark:—

TABLE SHOWING STRENGTH OF ROUND WROUGHT-IRON SHAFTING.

Dia- meter of shaft.		Torsional Action.									Transverse Action.
		Ultimate resis- tance.		Working stress.		Work for one turn per minute.	Horse Power at the rate of one turn per minute.		Speed in turns per minute for one-horse power.		Under the gross distributed weight.			Under the net weight of shaft.
											Distance of bearings for the limiting deflection.		Gross weight for the span.	Distance of bearings for the limiting deflection.
1		2		3		4	5		6		7		8	9
Inches.		Stat’l. ft. tons.		Stat’l ft. lbs.		Ft. lbs.	H. P.		Turns.		Feet.		Lbs.	Feet.
1			.42	27	.7	174		.00526	190		6	.6	30	7	.9
1	1⁄4		.82	54	.1	340		.01028	97	.3	7	.7	55	9	.2
1	1⁄2	1	.42	93	.5	587		.01779	56	.2	8	.6	89	10	.3
1	5⁄8	1	.80	118	.9	746		.02259	44	.3	9	.2	112	11	.0
1	3⁄4	2	.25	148	.4	932		.02820	35	.4	9	.6	134	11	.5
1	7⁄8	2	.77	182	.6	1,147		.03469	28	.8	10	.1	163	12	.1
2		3	.36	221	.6	1,391		.04211	23	.7	10	.5	193	12	.7
2	1⁄8	4	.00	265	.8	1,669		.05062	19	.8	11	.0	227	13	.2
2	1⁄4	4	.80	315	.5	1,981		.05995	16	.7	11	.4	264	13	.7
2	3⁄8	5	.62	371	.1	2,330		.07051	14	.2	11	.8	305	14	.2
2	1⁄2	6	.56	432	.8	2,718		.08224	12	.2	12	.5	359	15	.0
2	3⁄4	8	.73	576	.1	3,618		.1094	9	.14	13	.0	450	15	.6
3		11	.3	747	.9	4,697		.1421	7	.04	13	.7	566	16	.5
3	1⁄4	14	.4	951	.0	5,972		.1807	5	.54	14	.5	701	17	.4
3	1⁄2	18	.0	1,188		7,458		.2257	4	.43	15	.2	854	18	.3
3	3⁄4	22	.1	1,461		9,173		.2775	3	.60	16	.0	1,029	19	.2
4		26	.9	1,773		11,136		.3368	2	.97	16	.7	1,225	20	.1
4	1⁄4	32	.2	2,127		13,345		.4040	2	.48	17	.4	1,439	20	.9
4	1⁄2	38	.2	2,524		15,851		.4796	2	.09	18	.1	1,679	21	.7
4	3⁄4	45	.0	2,969		18,635		.5642	1	.77	18	.8	1,943	22	.6
5		52	.5	3,463		21,750		.6579	1	.52	19	.4	2,220	23	.3
5	1⁄4	60	.7	4,008		25,177		.7616	1	.31	20	.0	2,525	24	.0
5	1⁄2	69	.8	4,609		28,936		.8758	1	.14	20	.6	2,854	24	.7
5	3⁄4	79	.8	5,266		33,077	1	.000	1	.00	21	.2	3,210	25	.4
6		90	.6	5,983		37,584	1	.137		.880	21	.6	3,600	26	.2
6	1⁄2	117		7,606		47,780	1	.445		.692	22	.9	4,421	27	.5
7		144		9,501		59,682	1	.805		.554	24	.2	5,426	29	.0
7	1⁄2	177		11,680		73,254	2	.220		.450	25	.3	6,518	30	.4
8		215		14,180		89,088	2	.694		.371	26	.5	7,774	31	.8
8	1⁄2	258		17,010		106,836	3	.232		.309	27	.6	9,133	33	.1
9		306		20,190		126,846	3	.837		.261	28	.7	10,650	34	.4
9	1⁄2	360		23,750		149,118	4	.512		.222	29	.8	12,320	35	.7
10		420		27,700		174,000	5	.260		.190	30	.8	14,100	36	.9
11		559		36,870		231,594	7	.005		.143	32	.8	18,180	39	.4
12		725		47,860		300,672	9	.095		.110	34	.7	22,880	41	.7
13		922		60,860		382,278	11	.83		.0865	36	.6	28,330	44	.0
14		1,152		76,010		477,456	14	.44		.0693	38	.5	34,560	46	.2
15		1,417		93,490		587,250	17	.76		.0563	40	.3	41,530	48	.4
16		1,720		113,500		712,704	21	.56		.0464	42	.1	49,330	50	.5
17		2,062		136,100		854,862	25	.86		.0387	43	.3	57,970	52	.6
18		2,447		161,500		1,014,768	30	.69		.0326	45	.5	67,490	54	.6
19		2,880		190,000		1,193,466	36	.10		.0277	47	.2	78,040	56	.6
20		3,360		221,600		1,392,000	42	.11		.0237	48	.8	80,660	58	.5
Note.—To find the corresponding values for shafts ofcast iron or steel, multiply the tabular values by the following multipliers:
Cast iron		2⁄5		2⁄3		2⁄3	2⁄3		1.5		.86		.81	.86
Steel		1.2		2.06		2.06	2.06		.48		1.05		1.07	1.05

“It is advantageous that the diameter of line shaft be kept as small as is possible with due regard to the duty, so as to avoid extra weight in the shafting hangers, pulley hubs and couplings, whose weights necessarily increase with the diameter of the shafting.

“Speeds For Shafting.—The speed at which shafting should run is determined within certain limits by the kind of machinery it is employed to drive. Shafting to drive wood-working machines may, for example, be made to rotate much faster than that employed to run metal-cutting machines, because the motions in the wood-working machines themselves are faster than those in metal-cutting machines. In a general sense, the rotation of shafting is greater in proportion as the movements of the machines driven require to run faster.

“This occurs because in proportion as the driving pulleys of the machines require to rotate faster than the line shaft, the diameters of the pulleys on the line shaft must be larger than the diameters of those on the machines; hence a great variation in speed would demand a corresponding increase of diameter of pulley on the line shaft, and the extra weight of this pulley would be so much added to the weight causing friction, as well as so much added to the cost. If small pulleys were used and countershafts employed to multiply the speed the cost would be increased, extra room would be taken up; indeed, this is so obvious as to require no discussion, further than to remark that the faster the shafting rotates the smaller may be its diameter to transmit a given horse-power. From deflection and weakness to resist transverse strains and other obvious causes it is not found in practice desirable to employ line shafts of less than about 1¹⁄₄ inches in diameter, and the diameters of shafting employed are usually arrived at from a calculated speed of about 120 revolutions per minute for metal-cutting machines such as used in machine shops, 250 revolutions per minute for wood-working machines, and from 300 to 400 revolutions per minute for cotton and woollen mills, and the countershafts for the machines usually have pulleys of the requisite diameters to convert this speed of rotation into that required to run each respective machine. Tubular or hollow shafting has been made to run at 600 revolutions per minute, but this kind of shafting has been of very limited application because of its expensiveness.

“It is obvious that since the speed of a line shaft is used as a multiplier in the calculation of the horse-powers of shafts, a given diameter of shaft will transmit more power in proportion as its speed is increased. Thus a shaft capable of transmitting 20 horse-power when making 120 revolutions per minute will transmit 40 horse-power if making 240 revolutions per minute.

“There are now running in some factories lines of shafting 1,000 feet long each. The power is generally applied to the shaft in the centre of the mill and the line extended each way from this. The head shaft being, say, 5 inches in diameter, the shafts extending each way are made smaller in proportion to the rate of distribution, so that from 5 inches they often taper down to 1³⁄₄.

“When very long lines of shafting are constructed of small or comparatively small diameter, such lines are liable to some irregularities in speed, owing to the torsion or twisting of the shaft as power is taken from it in more or less irregular manner. Shafts driving looms may at one time be under the strain of driving all the looms belted from them, but as some looms are stopped the strain on the shaft becomes relaxed, and the torsional strain drives some part of the line ahead, and again retards it when the looms are started up. This irregularity is in some cases a matter of serious consideration, as in the instance of driving weaving machinery. The looms are provided with delicate stop motion, whereby the breaking of a thread knocks off the belt shifter and stops the loom. An irregular driving motion is apt to cause the looms to knock off, as it is called, and hence the stopping of one or more may cause others near to them to stop also. This may in a measure be arrested by providing fly-wheels at intervals on the line shaft, so heavy in their rim as to act as a constant retardant and storer of power, which power is given back upon any reaction on the shaft, and thus the strain is equalized. We mention this, as at the present time it is occupying the thoughts of prominent millwrights, and the relative advantage and disadvantage of light and heavy fly-wheels are being discussed, and is influencing the proportions of shafting in mill construction.[36]”