Modern Machine-Shop Practice Part 177

"The process of cold rolling produces a very marked change in the physical properties of the iron thus treated.

"It increases the tenacity from 25 to 40 per cent., and the resistance to transverse stress from 50 to 80 per cent.

"It elevates the elastic limit under torsional as well as tensile and transverse stresses, from 80 to 125 per cent....

"It gives the iron a smooth bright surface, absolutely free from the scale of black oxide unavoidably left when hot rolled.

"It is made exactly to gauge diameter, and for many purposes requires no further preparation.

"The cold-rolled metal resists stresses much more uniformly than does the untreated metal. Irregularities of resistance exhibited by the latter do not appear in the former; this is more particularly true for transverse stress.

"This treatment of iron produces a very important improvement in uniformity of structure, the cold-rolled iron excelling common iron in density from surface to centre, as well as in its uniformity of strength from outside to the middle of the bar.

"This great increase of strength, stiffness, elasticity, and resilience is obtained at the expense of some ductility, which diminishes as the tenacity increases. The modulus of ultimate resilience of the cold-rolled iron is, however, above 50 per cent. of that of the untreated iron.

"Cold-rolled iron thus greatly excels common iron in all cases where the metal is to sustain maximum loads without permanent set or distortion."

From this it appears that cold-rolled iron is peculiarly adapted for line shafting. Suppose, for example, a given quant.i.ty of power to transmit, and that a length of cold-rolled and a length of hot-rolled iron be connected together to form the line. Then the diameters of the two being such as to have equal torsional strength, we have--

1st. That the weight of the cold rolled will be the least, and it will, therefore, produce less friction in the hanger bearings.

2nd. That the cold rolled will be harder, and will therefore suffer less from abrasion of the journals.

3rd. That being of smaller diameter the journals are more easily and perfectly lubricated.

The resistance to transverse stress (say) 50 per cent.; but the elastic limit under transverse stress is increased from 80 to 125 per cent., accepting the lesser amount we have in the case of the two shafts.

4th. That the resistance to permanent set or bend will be 30 per cent.

more in the cold rolled.

5th. The accuracy to gauge diameter enables the employment of a coupling having a continuous sleeve, and gives an equal bearing along the entire coupling bore.

6th. The reduction of shaft diameter enables the employment of a smaller and lighter coupling; and

7th. The hubs of the pulleys may be made smaller and lighter, are easier to bore, and may be bored to gauge diameter with the a.s.surance that they will fit the shaft.

The friction between the journals of a line shafting and its bearings depends so intimately upon the distance apart of the bearings, upon the alignment of the same, upon the accurate bedding of the shaft journals to the bearings, and upon the amount of transverse strain; and this latter is so influenced by the amount of power that may be delivered from one side of the shaft more than from another, that the application of rules for determining the said friction under conditions of perfect alignment rigidity would be practically useless. The conditions found in actual practice are so widely divergent and so rarely alike, or even nearly alike, that the consideration of this part of the subject would, in the opinion of the author, be of no practical value. The reader, however, is referred to the remarks made with reference to the friction of journals.

To prevent end motion to a line of shafting it is necessary that there be fixed at some part of the line two shoulders, or collars, on relatively different sides of a bearing, or of the bearings, these collars meeting the side faces of the bearing. If shoulders are produced by reducing the diameter of the journal bearing of the shaft, the strength of the shafting is reduced to that at the reduced bearing, because the strength of the whole can be no greater than its strength at the weakest part. If collars are placed one on each end of the line of shafting, the difficulty is met that the collars will permit end motion to the shaft whenever the temperature of the shaft is greater than that which obtained at the time at which the collars were adjusted, which occurs on account of the increased expansion of the shaft. On the other hand the collars will bind against the side faces of the bearing boxes whenever the shaft is at a lower temperature than it was at the time of setting the shaft, because of the contraction of the shaft's length, and this would cause undue friction, abrasion, and wear.

It is preferable, therefore, to place such collars one on each side of one bearing, so that the difference in contraction and expansion from varying temperatures shall be confined to the difference in expansion between the metal of which the bearing and shaft respectively are composed in the length of the bearing only, instead of being extended to the difference in expansion between the shaft throughout its whole length and that of the framework to which the hangers, or bearings, are bolted.

[Ill.u.s.tration: Fig. 2593.]

The collars may be shrunk on to the shaft so as to avoid the necessity of set-screws, or if set-screws are used they should be as short as is practicable so as to avoid the liability to catch against the lacings, &c., of belts, which, on slipping off the pulley may come into contact with the set-screw head. The Lane and Bodley Co., of Cincinnati, employ a collar (for loose pulleys, &c.) in which the radius of the collar for a width equal to the diameter of the set-screw head, is equal to that of the set-screw head thus projecting from the centre of the collar circ.u.mference, a slot in the ring affording access to the set-screw head, as shown in Fig. 2593. By this means the head of the set-screw is protected from contact with a belt, in case the latter should be off the pulley and resting upon the shaft.

As a rule it is preferable that the collars, to prevent end motion to the shaft, be placed at the bearing nearest to the engine or motor; and this is especially desirable where bevel-wheels are employed to drive the shaft, because in that case the pitch lines of the wheels are kept to coincide as nearly as practicable, and the teeth are prevented from getting too far into or out of gear.

DIAMETERS OF LINE SHAFTING.--The necessary diameters of the various length of the shafts composing a line of shafting, should be proportioned to the quant.i.ty of power delivered by each respective length, and in this connection the position of the various pulleys upon the length and the amount of power given off by the pulley is an important consideration. Suppose, for example, that a piece of shafting delivers a certain amount of power, then it is obvious that the shaft will deflect or bend less if the pulley transmitting that power be placed close to a hanger or bearing than if it be placed midway between the two hangers or bearings.

The strength of a shaft to resist torsion is the cube of its diameter in inches, multiplied by the strength of the material of which the shaft is composed, per square inch of cross-sectional area, giving the strength in statical foot-pounds. The application of this rule is to find the necessary strength of the shaft to convey power irrespective of the distance from its centre at which it delivers such power.

But since the point at which the power to produce torsion is applied is at the rim of the pulley, the amount of torsion produced upon a shaft by a given stress must be obtained by multiplying the given amount of stress by the radius of the pulley in inches and parts of an inch.

Example: the static stress upon a pulley, 24 inches diameter, is 100 lbs., what static torsion does it exert upon the shaft?

Here, stress 100 12 (radius of the pulley) = 1200 = static torsional stress.

In the following rules for finding the necessary diameters and strengths of shafts, the margin of extra diameter for strength necessary for safety is included, so that the given sizes are working diameters.

To find the necessary diameter of shaft from a given torsional stress.--Rule, divide the torsional stress expressed in statical foot lbs., by 57.2 for steel, by 27.7 for wrought iron, or by 18.5 for cast iron, and the cube root of the quotient is the required working diameter of shaft expressed in inches.

To find the maximum amount of horse-power capable, within good working limits, of being transmitted by a _shaft_ of a given diameter.--Rule, multiply the cube of the diameter of the shaft, in inches, by its revolutions per minute and divide by 92 for steel, by 190 for wrought-iron, or by 285 for cast-iron shafts, and the quotient is the amount of horse-power.

Since, in this rule, the horse-power is a given quant.i.ty, the diameter of the pulley is of no consequence, since with a given stress it must have been taken into account in obtaining the horse-power.

To find the revolutions per minute a shaft will require to make to transmit a given amount of horse-power.--Rule, multiply the given amount of horse-power by 92 for steel, by 190 for wrought-iron, or by 285 for cast-iron shafts, and divide the product by the cube of the diameter of the shaft expressed in inches, and the quotient is the required revolutions per minute for the shaft.

The rule adopted by William Sellers and Co. to determine the size of shafts to transmit a given horse-power is:--Rule, divide the cube root of the horse-power by the revolutions per minute and multiply the quotient by 125, the product is the diameter of shaft required.

This gives a shaft strong enough to resist flexure, if the bearings are not too far apart. The distance apart that the bearings should be placed is an important consideration. Modern millwrights differ slightly in opinion in this respect: some construct their mills with beams 9 feet 6 inches apart, and put one hanger under each of the beams; others say 8 feet apart gives a better result. We are clearly of opinion that with 8 feet distance, and shafting lighter in proportion, the best result is obtained.

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.

+--------+---------------------------------------------------------+ | | TORSIONAL ACTION. | | +----------+------------+-----------+----------+----------+ | Dia- | Ultimate | Working | Work for | Horse | Speed in | | meter | resist- | stress. | one turn | Power at | turns | | of | ance. | | per | the rate | per | | shaft. | | | minute. | of one | minute | | | | | | turn per | for | | | | | | minute. | one- | | | | | | | horse | | | | | | | power. | +--------+----------+------------+-----------+----------+----------+ | =1= | =2= | =3= | =4= | =5= | =6= | +--------+----------+------------+-----------+----------+----------+ | Inches.| Stat'l. | Stat'l ft. | Ft. lbs. | H. P. | Turns. | | |ft. tons. | lbs. | | | | | 1 | .42 | 27.7 | 174 | .00526 | 190 | | 1-1/4 | .82 | 54.1 | 340 | .01028 | 97.3 | | 1-1/2 | 1.42 | 93.5 | 587 | .01779 | 56.2 | | 1-5/8 | 1.80 | 118.9 | 746 | .02259 | 44.3 | | 1-3/4 | 2.25 | 148.4 | 932 | .02820 | 35.4 | | 1-7/8 | 2.77 | 182.6 | 1,147 | .03469 | 28.8 | | 2 | 3.36 | 221.6 | 1,391 | .04211 | 23.7 | | 2-1/8 | 4.00 | 265.8 | 1,669 | .05062 | 19.8 | | 2-1/4 | 4.80 | 315.5 | 1,981 | .05995 | 16.7 | | 2-3/8 | 5.62 | 371.1 | 2,330 | .07051 | 14.2 | | 2-1/2 | 6.56 | 432.8 | 2,718 | .08224 | 12.2 | | 2-3/4 | 8.73 | 576.1 | 3,618 | .1094 | 9.14 | | 3 | 11.3 | 747.9 | 4,697 | .1421 | 7.04 | | 3-1/4 | 14.4 | 951.0 | 5,972 | .1807 | 5.54 | | 3-1/2 | 18.0 | 1,188 | 7,458 | .2257 | 4.43 | | 3-3/4 | 22.1 | 1,461 | 9,173 | .2775 | 3.60 | | 4 | 26.9 | 1,773 | 11,136 | .3368 | 2.97 | | 4-1/4 | 32.2 | 2,127 | 13,345 | .4040 | 2.48 | | 4-1/2 | 38.2 | 2,524 | 15,851 | .4796 | 2.09 | | 4-3/4 | 45.0 | 2,969 | 18,635 | .5642 | 1.77 | | 5 | 52.5 | 3,463 | 21,750 | .6579 | 1.52 | | 5-1/4 | 60.7 | 4,008 | 25,177 | .7616 | 1.31 | | 5-1/2 | 69.8 | 4,609 | 28,936 | .8758 | 1.14 | | 5-3/4 | 79.8 | 5,266 | 33,077 | 1.000 | 1.00 | | 6 | 90.6 | 5,983 | 37,584 | 1.137 | .880 | | 6-1/2 | 117 | 7,606 | 47,780 | 1.445 | .692 | | 7 | 144 | 9,501 | 59,682 | 1.805 | .554 | | 7-1/2 | 177 | 11,680 | 73,254 | 2.220 | .450 | | 8 | 215 | 14,180 | 89,088 | 2.694 | .371 | | 8-1/2 | 258 | 17,010 | 106,836 | 3.232 | .309 | | 9 | 306 | 20,190 | 126,846 | 3.837 | .261 | | 9-1/2 | 360 | 23,750 | 149,118 | 4.512 | .222 | | 10 | 420 | 27,700 | 174,000 | 5.260 | .190 | | 11 | 559 | 36,870 | 231,594 | 7.005 | .143 | | 12 | 725 | 47,860 | 300,672 | 9.095 | .110 | | 13 | 922 | 60,860 | 382,278 | 11.83 | .0865 | | 14 | 1,152 | 76,010 | 477,456 | 14.44 | .0693 | | 15 | 1,417 | 93,490 | 587,250 | 17.76 | .0563 | | 16 | 1,720 | 113,500 | 712,704 | 21.56 | .0464 | | 17 | 2,062 | 136,100 | 854,862 | 25.86 | .0387 | | 18 | 2,447 | 161,500 | 1,014,768 | 30.69 | .0326 | | 19 | 2,880 | 190,000 | 1,193,466 | 36.10 | .0277 | | 20 | 3,360 | 221,600 | 1,392,000 | 42.11 | .0237 | | | | NOTE.--To find the corresponding values for shafts of cast iron | | or steel, multiply the tabular values by the following | | multipliers: | | | | Cast | | | | | | | iron | 2/5 | 2/3 | 2/3 | 2/3 | 1.5 | | Steel | 1.2 | 2.06 | 2.06 | 2.06 | .48 | +--------+----------+------------+-----------+----------+----------+

+--------+---------------------------+ | | TRANSVERSE ACTION. | | +-----------------+---------+ | | Under | Under | | | the gross | the net | | | distributed |weight of| | Dia- | weight. | shaft. | | meter |-----------------+---------+ | of |Distance| Gross |Distance | | shaft. |of bear-| weight |of bear- | | |ings for| for |ings for | | | the | the | the | | |limiting| span. |limiting | | |deflec- | |deflec- | | | tion. | | tion. | +--------+--------+--------+---------+ | =1= | =7= | =8= | =9= | +--------+--------+--------+---------+ | Inches.| Feet. | Lbs. | Feet. | | | | | | | 1 | 6.6 | 30 | 7.9 | | 1-1/4 | 7.7 | 55 | 9.2 | | 1-1/2 | 8.6 | 89 | 10.3 | | 1-5/8 | 9.2 | 112 | 11.0 | | 1-3/4 | 9.6 | 134 | 11.5 | | 1-7/8 | 10.1 | 163 | 12.1 | | 2 | 10.5 | 193 | 12.7 | | 2-1/8 | 11.0 | 227 | 13.2 | | 2-1/4 | 11.4 | 264 | 13.7 | | 2-3/8 | 11.8 | 305 | 14.2 | | 2-1/2 | 12.5 | 359 | 15.0 | | 2-3/4 | 13.0 | 450 | 15.6 | | 3 | 13.7 | 566 | 16.5 | | 3-1/4 | 14.5 | 701 | 17.4 | | 3-1/2 | 15.2 | 854 | 18.3 | | 3-3/4 | 16.0 | 1,029 | 19.2 | | 4 | 16.7 | 1,225 | 20.1 | | 4-1/4 | 17.4 | 1,439 | 20.9 | | 4-1/2 | 18.1 | 1,679 | 21.7 | | 4-3/4 | 18.8 | 1,943 | 22.6 | | 5 | 19.4 | 2,220 | 23.3 | | 5-1/4 | 20.0 | 2,525 | 24.0 | | 5-1/2 | 20.6 | 2,854 | 24.7 | | 5-3/4 | 21.2 | 3,210 | 25.4 | | 6 | 21.6 | 3,600 | 26.2 | | 6-1/2 | 22.9 | 4,421 | 27.5 | | 7 | 24.2 | 5,426 | 29.0 | | 7-1/2 | 25.3 | 6,518 | 30.4 | | 8 | 26.5 | 7,774 | 31.8 | | 8-1/2 | 27.6 | 9,133 | 33.1 | | 9 | 28.7 | 10,650 | 34.4 | | 9-1/2 | 29.8 | 12,320 | 35.7 | | 10 | 30.8 | 14,100 | 36.9 | | 11 | 32.8 | 18,180 | 39.4 | | 12 | 34.7 | 22,880 | 41.7 | | 13 | 36.6 | 28,330 | 44.0 | | 14 | 38.5 | 34,560 | 46.2 | | 15 | 40.3 | 41,530 | 48.4 | | 16 | 42.1 | 49,330 | 50.5 | | 17 | 43.3 | 57,970 | 52.6 | | 18 | 45.5 | 67,490 | 54.6 | | 19 | 47.2 | 78,040 | 56.6 | | 20 | 48.8 | 80,660 | 58.5 | | | | NOTE.--To find the corresponding | | values for shafts of cast iron or | | steel, multiply the tabular values | | by the following multipliers: | | | | Cast | | | | | iron | .86 | .81 | .86 | | Steel | 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 1-1/4 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 1-3/4.

"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 r.e.t.a.r.ds 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 s.h.i.+fter 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 r.e.t.a.r.dant 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]"

[36] From "Machine Tools," by William Sellers and Co.

Countershafts are separate sections of shafting (usually a short section) employed to increase or diminish belt speed, to alter the direction of belt motion, to carry a loose as well as a fast pulley (so that by moving the belt on to the loose pulley it may cease to communicate motion to the machine driven), and for all these purposes combined.

[Ill.u.s.tration: Fig. 2594.]

[Ill.u.s.tration: Fig. 2595.]