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 circumference, 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 quantity 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 quantity, 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.

“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]”

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.

An excellent form of countershaft hanger is shown in Fig. 2594, the guide for the slide being adjustable along the arm, and fixed in its adjusted position by means of the set-screws. The bearing is self-adjusting horizontally for alignment. The countershaft is shown in Fig. 2595, a b being the bearings, c the cone pulley, d the fast and e the loose pulley, which is placed next to the bearing, so that it may be oiled without having to reach past the belt and fast pulley. By reducing the journal for the loose pulley no collar is needed, the shaft shoulder and the face of the bearing serving instead.

When the direction of rotation of the cone pulley on the countershaft requires to be occasionally reversed, there are two belts, an open one and a crossed one, from the line shaft to the countershaft, and there are three pulleys on the countershaft, their arrangement being as shown in Fig. 2596. l l′ are two loose pulleys, one receiving the open and the other the crossed belt, both these pulleys being a little more than twice the width of the belt; f is a fast pulley. By operating the belt skipper or shifter in the requisite direction either the open or the crossed belt is brought upon the fast pulley, the other belt merely moving across the width of its loose pulley, which must be twice that of the fast one. In the position of the belt shifter shown in the cut, both belts would be upon the loose pulleys l l′, hence the countershaft would remain at rest. If the direction of rotation of one pulley is required to be quicker than the other, two fast pulleys, each slightly more than twice the width of the belt, may be placed upon the line shaft, one of them being of enlarged diameter, to give the requisite increased velocity.

In Fig. 2597 Pratt’s patent friction clutch is shown applied to a countershaft requiring to rotate in both directions, but quicker in one direction than in the other; hence, one of the pulleys is of smaller diameter than the other. The pulleys are free to rotate upon the countershaft unless engaged by the clutch, which is constructed as follows:—

The inside surface of the pulley rim is bored and the end surface of the shoes is turned to correspond. The shoes are in the form of a bell crank, upon the exposed end of which is provided a small lug, clearly shown in the cut. To prevent end motion of the pulley a collar is placed on one side of it and secured to the countershaft, while, on the other, the sleeve to which the shoes are pivoted is also secured to the countershaft; upon the shaft between the two pulleys there is a sleeve, having at each end a conical hub. When this sleeve is moved to the right, its right-hand coned hub passes between the lugs on the exposed ends of the shoes, forcing these lugs apart and causing the shoes to grip the bore of the large pulley, which thereupon rotates the shaft through the medium of the sleeve upon which the shoes are pivoted. Similarly, if the engaging (and disengaging) sleeve be moved to the left it will pass between the lugs of the shoes on the left-hand pulley, which will, therefore, be caused to drive the shaft. In the position shown in the cut the engaging sleeve is clear of the ends of all the shoes, hence the pulleys would be caused to rotate (by their belts), but the shafts, &c., would remain stationary.

In yet another form the inner face of the pulley rim is coned, and in place of shoes a disk, whose circumference is coned to fit the pulley rim, is fast upon the shaft. The shaft is provided with a fixed collar, and from this collar, as a fulcrum, the pulley and disk are (by means of short levers attached to a sleeve upon the countershaft) brought into contact, the thrust on the other side of the pulley being sustained by a conical surface on the sleeve, fitting to a similar cone on the hub of the pulley. Thus the pulley is gripped between two coned surfaces, one on each side, and is released by moving the sleeve laterally so as to relieve the grip, which it does noiselessly.

By this means motion to the shaft is communicated from the pulley without the sudden shock incidental to the impact of two fixed pieces, because the grip of the cones is gradual, and a certain amount of slip may occur until such time as the grip of the surfaces is sufficient to drive by friction.

Fig. 2598[37] represents a cone friction clutch pulley. The outer half is a working fit upon the shaft, but is secured against end motion by the collar d. The sliding half is coned and covered with leather as shown at c c, the outer half being coned to correspond. The sliding half is driven by a feather fast in its bore, and sliding in a feather-way or spline in the shaft.

The driving power of the device is obtained by means of the friction of the coned surfaces. The less the angle x of the cones the more power transmitted with a given pressure of the internal to the external cone.

On the other hand, however, this angle may be so little that the external cone will not release the internal one when the end pressure on the latter is removed.

The object is, therefore, to so proportion the angle x of the cones that their friction will be a maximum, while the internal cone may be moved endwise and unlocked from the external without undue effort or strain at the moving clutch bar e. If the angle be 30 degrees, the clutch will release itself when the lateral pressure is removed. If the angle be 25 degrees the internal cone will require a slight lateral pressure to release it. If the angle be 20 degrees, the internal cone cannot be released by end pressure applied by hand.

The transmitting capacity of the clutch depends upon the pressure applied to maintain the cones in contact, and therefore upon the leverage of the clutch bar, whose fork end is shown in section at e.

It is desirable that the end pressure be as small as possible, because of the friction between e and the hub of the sliding half of the pulley.

The hangers which carry the bearing boxes supporting shafting may be divided into four principal classes:—Those in which the bearing boxes are permitted to swivel, and to a certain extent to adjust themselves, to the axial line of the shafting, and having means to adjust the vertical height of the bolts.

Those in which the bearings are incapable of such adjustments.

Those in which the bearing boxes are supported on each side; and those in which the bearing is supported on one side only, so that the shafting may be taken down without disturbing the couplings.

The first named are desirable in that they eliminate to a certain extent the strains due to the extra journal bearing friction which occurs when the shafting is sprung out of its true alignment, and obviate to a great extent the labor involved in fitting the bore of the bearing boxes to the journals of the shafting, so as to hold the same with its axis in a straight line, while they permit of vertical movement to attain vertical alignment.

Fig. 2599 represents Wm. Sellers & Co.’s ball-and-socket hanger which has come into extensive use throughout the United States: a represents the frame of the hanger threaded to receive the cylindrical threaded plungers d e, which therefore by rotation advance or recede respectively from the centre of the bearing boxes b c.

The ends of these plungers are concave, and the top and bottom halves of the bearing boxes are provided with a spheroidal section fitting into the concaves of the plungers, so that when the plungers are adjusted to fit (a working fit) against the boxes, the latter are held in a ball-and-socket or universal joint, which permits motion in any direction, the centre of such motion being central to the spherical concaves on the ends of plungers e d.

To adjust the vertical height of the bearings or boxes, it is simply necessary to rotate the plungers d e, in the threaded holes in the frame. f is simply a dish to catch the lubricating oil after it has passed through the bearing.

It is obvious that if a shaft be aligned axially true, and held in a box of this design, the centre of a length of shaft on either side of the box may be sprung or deflected out of alignment, and that the box will adjust itself so that its bore will be parallel with the axis of the shaft thus deflected, hence the friction between the shaft journal and the bearing box will be at all times a minimum.

This feature of self-adjustment permits of the employment of longer bearings, which reduces the wear, as well as the friction, and by providing sufficient bearing and wearing area, enables the bearings to be composed of cast iron, which is the cheapest as well as the very best material of which a bearing can be made, provided that its area of bore is sufficiently large in proportion to the duty, or load, to have a pressure of not more than about 60 lbs. per square inch of area.

Again, if the alignment of the shaft should require readjustment from the warping or sinking of beams, as is a very common occurrence where hangers are fixed to the joists of ceilings, the adjustment is readily and easily effected by means of the plungers, nor need the boxes be fitted to the shaft more than to see that when free from the hangers they bed firmly down until the crowns of their bore have contact with the shaft. The hangers themselves require no refinement of alignment, because that may be secured by means of the plungers, and the boxes require no fitting to the shafts after the hangers are erected.

In hangers in which the self-adjusting ball-and-socket feature is omitted, the bottom hangers must not only be accurately aligned, but the boxes must, to avoid friction and undue wear, all be fitted to the shaft, and the latter must, during such fitting, be tried in the boxes; the operation, if properly performed, costing far more in labor than is equivalent to the difference in the first cost of the ball-and-socket adjustable hangers and those solid or not self-adjustable, especially if the boxes be long ones, as about, or not less than, three times the diameter of the shaft, as they should be.