Modern Machine-Shop Practice Part 181

When the pulley is in motion, the centrifugal force imparted to the oil in the reservoir throws it outwardly, causing it to be distributed in an even layer against the inner surface of the sh.e.l.l which encloses and forms the reservoir, thus preventing any possible waste when the pulley is in motion.

But when the pulley is either stopped or started, the oil is caused to change its position, and in so doing is brought into contact with the wicks protruding from the small openings N N, by which it is conveyed into the supply chamber, and thence to the shaft. By thus taking advantage of what is a necessity in all business establishments in which machinery is employed--to wit, the stopping and starting of the machinery at regular intervals--to insure the supplying, at such times, of a small quant.i.ty of oil to the bearings of the loose pulleys, the makers claim that a perfect and reliable means is obtained for guarding against any needless waste of the lubricant.

[Ill.u.s.tration: Fig. 2645.]

A crowning or crowned pulley is of largest diameter in the middle of its width or face, the object being to cause the belt to run on the middle of the pulley width. It would appear that this crowning would give to the belt a greater degree of tension at its centre than at its edges, but it is shown by experiment that if a piece of belt be clamped square across its width at each end and stretched, the centre as section _b_, in Fig. 2645, will stretch the most, and that if the piece be divided along its centre lengthwise, and both halves again stretched, they will again do so the most in the middle of their widths.

From this it appears that the crowning serves to produce a tension equal across the pulley width, because it will stretch the belt the most in the middle of its width, where it has the greatest capacity to stretch.

The amount of crowning employed in practice varies from about 3/16 to 3/8 inch per foot of width of pulley face, the minimum being employed where the belt requires to be moved or slipped laterally from one pulley to another of equal diameter, as from a fast to a loose pulley and _vice versa_. To relieve the belt of strain when on a loose pulley the loose pulley is sometimes made of smallest diameter, and has a coned step up which the belt moves when pressed against it. During this pa.s.sage of the belt, however, one edge is stretched more than the other, while in pa.s.sing from the large to the smaller pulley the same edge is under tension, while the other is released from tension; hence, with the belt pa.s.sing either to or from the large pulley there is a tendency to unduly stretch one of its edges. On the other hand, however, in cases where the belt requires to run for long periods on the loose pulley relieving it from tension is a great advantage.

In fixing pulleys so that they shall run true upon their shafts several difficulties are met with. First, it is difficult to turn the shafts quite parallel and to exact standard gauge diameter. Second, the bore of the pulley must be made a sufficiently easy fit to enable their being moved by hand along the shaft to the required location. As a result the set-screw pressure throws the pulley out of true, unless the mandrel on which the pulley is turned in the lathe be the same diameter as the pulley shaft, and the pulley be held upon the mandrel by the set-screw pressure, and not by driving the mandrel into the pulley bore. In this case two set-screws must be used one on each end of the pulley hub, so as to steady the pulley on the mandrel. A pulley thus trued will still run out of true when on its shaft unless the shaft be of the same diameter as the mandrel.

One means of obviating this difficulty is to reduce the diameter of the shaft between the pulley seats sufficiently to allow the pulley to pa.s.s easily, and to make the pulley bores a driving fit to their seats. This, however, is only practicable in cases where the locations of the pulleys are permanently fixed, and no occasion arises for the addition of new pulleys.

[Ill.u.s.tration: Fig. 2646.]

To obviate this difficulty what is termed an internal clamp pulley has been constructed. This pulley is shown in Fig. 2646. The bore is made sufficiently smaller than the shaft diameter to be a forcing fit. A slot in the form of an arc of a circle is formed in the hub as shown, and a split runs from this arc into the bore. As a result a wedge driven between the walls of the split will spring open the bore and permit its easy pa.s.sage along the shaft to its required location, when the removal of the wedge will permit the bore to close upon the shaft. To secure the pulley to the shaft four set-screws are employed, two of them being shown in the cut, and the other two being similarly located on the other side of the pulley.

By this means there will be less difference between the diameters of the pulley bore and of the shaft should the latter be slightly less than its standard diameter, and as a result the pulley will run more true.

Split pulleys are bored a tight fit to the shaft when the two halves are bolted firmly together. They may, however, be made to grip the shaft in two ways; first, if bored when bolted together the edges of the bore will meet the shaft and clip it so firmly as to require each half bore to spring open to permit it to pa.s.s on the shaft, but by inserting between the two halves of the hub two thicknesses of writing paper, and boring out the hole the thicknesses of the paper too large (which may be done by placing two pieces of the same paper beneath the calipers or gauge) the bore will be slightly oval when the paper is removed, and will grip the shaft at the crown of each half bore, but the grip thus obtained will not be so firm.

Pulleys of small diameter, as three feet or less in diameter, are usually held to their shafts by set-screws, the consideration of their shapes and position having been already treated of when referring to the applications of keys and set-screws. Pulleys of large diameters, and those which act as fly-wheels as well as pulleys, are usually held by keys.

BALANCING PULLEYS.--A pulley (more especially those running at high speed) should be balanced or in balance when rotating at the greatest speed at which it is intended to run. This is necessary, because if the centrifugal force generated by the pulley's rotation be greater on one side than on another of the pulley, it will cause the pulley shaft to vibrate and shake whenever the amount of unbalanced centrifugal force becomes, on account of the speed of rotation, sufficient to bend the shaft or deflect the framing holding the shaft.

The balancing of a pulley will not be correct unless the centrifugal force is equal at all points on the perimeter in the same plane, as will appear presently. In practice two methods of testing the balance of a pulley are employed: first, the standing; and second, the running balance. A standing balance does not in any sense balance a pulley, but merely corrects the want of balance to a limited degree. A running balance correctly balances a pulley when running up to the speed at which the balance was made, but does not balance for greater speeds.

[Ill.u.s.tration: Fig. 2647.]

[Ill.u.s.tration: Fig. 2648.]

A standing balance is effected when the shaft being supported horizontally and with as little friction as possible, the pulley will remain at rest in any position in which it can be placed. Thus, in Fig.

2647 let C C represent the two centres of a lathe adjusted in their distance apart so as to sustain the shaft S with just sufficient force to prevent end movement or play of the shaft, and if the pulley P remains motionless when arrested at any point of rotation it is in standing balance. A common method of balancing is to set the pulley in slow rotation several times in succession, and if the same part of the pulley's circ.u.mference comes to rest in each case at the bottom as at B then it is heaviest and its weight must be reduced, or weight must be added on the diametrically opposite side of the pulley. Another method is to rest the shaft horizontally on a pair of metallic strips as B B in Fig. 2648, the strips resting on a flat horizontal surface D, the testing being applied as before. Sometimes, however, cylindrical pieces are used in place of the strips or pieces B B.

[Ill.u.s.tration: Fig. 2649.]

A pulley that is in balance thus tested, may not, however, be in balance when rotated, or, as already stated, a standing balance may not be a running balance, for the following reasons: In Fig. 2649 is a pulley that if turned true inside and out would be of correct standing balance, because the weight is equal on each side of the shaft; thus the point A, though farther from the axis than B, would be counterbalanced by C, while B would be counterbalanced by D, but as soon as the pulley was put in rotation there would be more centrifugal force generated at A than at B, and more at C than at D, because, though the weights would be equal, the velocities of A and C would be greatest.

Now, suppose that instead of a continuous wide pulley several pulleys were used, being out of true so as to be practically equal in shape to Fig. 2649, and it is apparent that the fact of pulley A B being out of balance is not removed by pulley C D being out in an opposite direction, and that each pulley will tend to bend the shaft in the direction of its excessive centrifugal force.

[Ill.u.s.tration: Fig. 2650.]

The effect of this inequality of centrifugal force will depend, in each case, upon the strength of the shaft in comparison with the amount of unbalanced centrifugal force. Suppose, for example, that the centrifugal force at a point A in Fig. 2650 were 10 lbs. greater than at B at a given velocity, and that the strength of the shaft be such that it will bend 1/32 inch under a weight of 10 lbs., then the effort of the point A will be to swing in a circle 1/16 inch larger than that due to its diameter. Suppose, then, the stand be so firmly fixed at C as to be motionless in a vertical direction under this effort, then the point A will swing in an oval, as denoted by the dotted lines, the shaft vibrating as denoted by the arrows.

[Ill.u.s.tration: Fig. 2651.]

Thus vibrations of the shaft, bearing, &c., occur whenever the excess of centrifugal motion on one side of a pulley is sufficient to spring the shaft, bearings, standard or foundation, as the case may be, and will occur most in the direction in which those parts will most easily succ.u.mb. From this it is evident that a pulley practically in balance, so far as being free from vibration at a certain speed, may be considerably out of balance at an increased speed. Thus, suppose a pulley P, in Fig. 2651, has a rim of equal thickness, but the distance of A from the axis of rotation is 6 inches, while the distance of B is 8 inches; then the centrifugal force at B will, at any speed of rotation, be one-quarter more than that at A, because the distance is one-quarter greater. Suppose, then, that its shaft, bearings, and foundation be capable of resisting 100 lbs. without sensible flexure, but that sensible flexure of those parts will occur under any pressure over 100 lbs.

The centrifugal force of 1 lb. at A and at B, respectively, may be calculated by the following rule:--

_Rule._--Multiply the square of the number of revolutions per minute by the diameter of the circle of rotation in feet, and divide the product by 5,870. The quotient is the centrifugal force in terms of the weight of the body.

In the case of A the pulley making, say, 200 revolutions per minute, we have by the rule:

200^{2} 1 ----------- = 6.81 = the centrifugal force.

5,870

Likewise, centrifugal force at B = (200^{2} 1.25)/5,870 = 8.51 = the centrifugal force, 1 and 1.25 being diameters of circle of rotation of A and B in feet.

Now, suppose the revolutions to be 2,000 per minute, we have in the case of A 2,000 2,000 1 (= 4,000,000) 5,870 = 681 lbs. centrifugal force. Add one-quarter more, or 170 lbs., to obtain the centrifugal force at B = 851 lbs.; the unbalanced centrifugal force = 170 lbs.; and this being 70 lbs. more than the shaft, bearings, &c., are capable of resisting without flexure, a corresponding vibration will occur, whereas at 200 revolutions the unbalanced centrifugal force was: Centrifugal force at B = 8.51 lbs. less that at A = 6.81 = 1.70 lbs. unbalanced centrifugal force, and it becomes apparent that while at 200 revolutions the pulley would rotate without sensible vibration, at 2,000 revolutions (in the same time), sensible vibration would occur; hence, the sensible vibration of a pulley is in the proportion as the unbalanced centrifugal motion is to the resistance of the shaft, bearings, &c., to flexure, and further, as the unbalanced centrifugal motion increases with the velocity, so also does the sensible vibration increase with the velocity.

But there are two ways of increasing the velocity of a pulley: 1st, by increasing the revolutions of a given pulley; 2nd, by employing a pulley of a larger diameter, but making the same number of revolutions. In our example we increased the speed tenfold (from 200 revolutions to 2,000) but the centrifugal force was increased one hundredfold, according with the law that the centrifugal force increases with the square of the revolutions, and 10 10 = 100. But if the velocity had been increased by augmenting the diameter of the pulley, the centrifugal force would have increased in the same ratio as the pulley diameter was increased; hence it appears that under equal velocities larger pulleys generate less centrifugal force per unit of unbalanced weight than do smaller ones.

[Ill.u.s.tration: Fig. 2652.]

A device for testing the balance of pulleys is shown in Fig. 2652; it consists of a frame carrying a vertical spindle, which may be rotated by suitable bevel-wheels, and the hand wheel shown. In this case it would be preferable to balance the pulley at the greatest speed at which it would be convenient to run it by hand with the wheel shown, because a pulley balanced at any given speed will be balanced at any lesser speed, although not at a greater one. But the pulley should not be driven by the arms, because the pressure against the same will affect the balance.

It would be better therefore to let the spindle of the machine be small enough in diameter to fit the smallest bore of pulley to be balanced, to employ sleeves fitting the spindle and the bores of all larger bored pulleys, and to obtain the most correct results the pulley should be fastened to the sleeve by its set-screws, or keys of the pulley, as the case might be, so that whatever error there might be induced by tightening the same will be accounted for in the balancing. It is obvious also that the pulley bore should fit the sleeve with the same degree of tightness as it will fit the shaft to which it is to be fixed.

The heaviest side of the pulley will rotate through a circle of larger diameter, and may be marked by a point, as a tool point moved up to it by a slide rest, or roughly by a piece of chalk steadily moved up to it by hand until it just touches the high side of the pulley.

[Ill.u.s.tration: Fig. 2653.]

The methods of correcting the balance are as follows: The heavy side of the pulley having been found, a weight is attached to the diametrically opposite side of the pulley; a convenient form of light weight for this purpose is shown in Fig. 2653; it consists of what may be termed a spring clamp, since it holds to the edge of the pulley rim, on which it is forced by hand, by reason of the spring of the jaws. There are numerous clamps of this form, each having a definite weight, as 2 ozs., 3 ozs., 4 ozs., &c.; but for weights above about 1-1/2 lb. a clamp with a set-screw is employed. For a running balance a set-screw is indispensable. It is obvious that pulleys will be more easily and correctly balanced when the inner side of their rim is turned up, as far as the arms will permit, in the lathe; but on account of the expense this is not usually done, except in the case of large pulleys.

In the best practice, however, the pulley is set in the lathe, so that the inside of the rim runs as true as possible. Remarks on this subject are given under the head of chucking pulleys.

When the balance is to be effected by adding weight to the pulley mushroom-shaped pieces of metal are made for the purpose, their weights varying by ounces; the stems are driven through holes drilled through the rim to receive them, and riveted on the face side. The stems are of wrought iron, while the heads may be of cast iron, but are better of lead, because in that case they may be set with a hammer to fit the inner surface of the pulley rim.

In some practice, protuberances, or a web in the middle of the pulley, are cast on the pulley, and the balance is effected by cutting this away to reduce the weight on the heavy side.

When pulleys are to revolve at very high speeds, as in the case of those for emery-wheel spindles, the shafts themselves require to be balanced, especially if of cast iron, because that part of the shaft uppermost in the mould will be of less density and weight than that at the bottom of the mould. The pulley should be balanced separately, and the whole again balanced after being put together, because the weight of the key or set-screw will be sufficient to destroy the balance under a sufficiently high speed of rotation.

The edges of pulley rims should be trued up in the lathe when the rim is turned so that the pulleys to receive a belt may be set in line by pressing a straight-edge, or setting a line to have contact with (as near as possible) diametrically opposite points of the edge of one pulley, and setting the other to have its corresponding edge in line.

Pulleys should run true so that the strain or tension of the belt shall be equal at all parts of the revolution, and the transmitting power shall be equal. The smoother and more polished the surface of the pulley the greater its driving power.

The transmitting power of a pulley may be increased by covering the pulley face with leather or rubber bands, but the thickness of these should be equal both across the width and all around the circ.u.mference so as to run true.

The amount of increase of driving power due to this covering is variously stated, but may be taken at about 20 to 30 per cent. A cement for fastening such pulley coverings may be made as follows: Take one ounce of caoutchouc (pure or native rubber) and cut it into thin slices, place it in a tinned sheet-iron vessel with six or seven ounces of sulphide of carbon; the vessel is then to be placed in a water tank previously heated to about 86 Fahr. To prevent the solution from becoming thick and unmanageable, mix with a solution consisting of spirits of turpentine, in which half an ounce of caoutchouc in shreds has been dissolved over a slow fire, and then a quarter of an ounce of powdered resin; from an ounce and a half to two ounces of turpentine being afterwards stirred in, to be added in small quant.i.ties. This cement must be kept in a large-mouthed bottle well corked, and in using clean the parts to be united thoroughly with benzine; apply two coats of cement, allowing each to dry before applying the next; when applying the last coat allow the cement to dry so as to become very sticky, then press the surfaces firmly together and allow to thoroughly dry. This is waterproof.

A pulley that imparts motion to the belt enveloping or partly enveloping it is termed a driving pulley or driver. A driven pulley is one that receives motion from, or is driven by, the belt; hence in every pair of pulleys connected by belt, one is termed the driver and the other the driven. The revolutions of two pulleys connected by belt will vary in the same proportion as their diameters, although their rim velocity will be equal.

Suppose, for example, that a pulley of 7 in. diameter drives one of 14 in. diameter, then if there is no slip on either pulley both pulleys will run at the same velocity as the belt, and this velocity must be equal to the velocity of the driver, because the belt is moved by the driver. Now, suppose the driver which is of 7 in. diameter makes one revolution in a minute, and as it is only one-half the diameter of the driven wheel, its circ.u.mference will also be half that of the driven, so that it must make two revolutions to carry around length of belt enough to pa.s.s once around the driven pulley. The revolutions of the two are, therefore, in the same proportions as are their diameters, which in this case is two to one. As the driven pulley is the largest diameter, it will make one revolution in the same time that the driver makes two. But suppose the driving pulley was 14 and the driven was 7 inches in diameter, then the proportion would still be two to one, and the driven would make two revolutions to every revolution of the driver.

[Ill.u.s.tration: Fig. 2654.]

If we are given the number of revolutions a driving pulley makes and the diameter or circ.u.mference of both pulleys, and require to find the number of revolutions the driven pulley will make to one or to any given number of the driver, we may consider as follows: Suppose the circ.u.mference of the driver to be 24 inches and that of the driven to be 18 inches, then in Fig. 2654 let circle A represent the driver, and circle B the driven pulley. If we divide the circ.u.mference of A into four equal divisions, as at 1, 2, 3, and 4, each of these divisions will equal 6 inches, because the whole circ.u.mference being 24 inches, one quarter of it will be 6. If we divide the circ.u.mference of B into six-inch divisions there will be but three of them as marked, because one-third of 18 (its circ.u.mference) is 6. Now three of the divisions at A will move A a full revolution, and the remaining division on A will move B through another one-third of a revolution, hence, each revolution of A equals 1-1/3 revolutions on B. The proportions of the circ.u.mference are, therefore, as 1-1/3 to 1, or as 133 is to 100, taking A as the driver, and, therefore, as the basis of the proportion. But suppose we take B as the basis of the proportion, and one revolution of B will cause A to make three quarters of a revolution, or during 100 revolutions of B, A will make 75. But nevertheless during the period that A is making 100 revolutions B will have made one-third more, or 133-1/3, because B makes 1-1/3 revolutions to cause A to make one revolution. From this it will be seen that the proportion is as the greater is to the lesser, and not as the lesser is to the greater, or, in other words, it is in this case as 24 is to 18, which is one and one-third times, for one-third of 18 is 6, and 18 + 6 = 24.