Modern Machine-Shop Practice Part 20

To obtain the forms of the teeth, therefore, take any convenient describing circle, and employ it to describe the teeth of the pinion by rolling within its pitch circle, and to describe the teeth of the wheel by rolling within and without its pitch circle, and the pinion will then work truly with the teeth of the wheel in both positions. The tooth at each extremity of the series must be a circular one, whose centre lies on the pitch line and whose diameter is equal to half the pitch.

[Ill.u.s.tration: Fig. 213.]

If the reciprocating piece move in a straight line, as it very often does, then the mangle-_wheel_ is transformed into a _mangle-rack_ (Fig.

213) and its teeth may be simply made cylindrical pins, which those of the mangle-wheel do not admit of on correct principle. B _b_ is the sliding piece, and A the driving pinion, whose axis must have the power of shifting from A to _a_ through a s.p.a.ce equal to its own diameter, to allow of the change from one side of the rack to the other at each extremity of the motion. The teeth of the mangle-rack may receive any of the forms which are given to common rack-teeth, if the arrangement be derived from either Fig. 210 or Fig. 211.

But the mangle-rack admits of an arrangement by which the shifting motion of the driving pinion, which is often inconvenient, may be dispensed with.

[Ill.u.s.tration: Fig. 214.]

B _b_ Fig. 214, is the piece which receives the reciprocating motion, and which may be either guided between rollers, as shown, or in any other usual way; A the driving pinion, whose axis of motion is fixed; the mangle rack C _c_ is formed upon a separate plate, and in this example has the teeth upon the inside of the projecting ridge which borders it, and the guide-groove formed within the ring of teeth, similar to Fig. 211.

This rack is connected with the piece B _b_ in such a manner as to allow of a short transverse motion with respect to that piece, by which the pinion, when it arrives at either end of the course, is enabled by shifting the rack to follow the course of the guide-groove, and thus to reverse the motion by acting upon the opposite row of teeth.

The best mode of connecting the rack and its sliding piece is that represented in the figure, and is the same which is adopted in the well-known cylinder printing-engines of Mr. Cowper. Two guide-rods K C, _k_ _c_ are jointed at one end K _k_ to the reciprocating piece B _b_, and at the other end C _c_ to the shifting-rack; these rods are moreover connected by a rod M _m_ which is jointed to each midway between their extremities, so that the angular motion of these guide-rods round their centres K _k_ will be the same; and as the angular motion is small and the rods nearly parallel to the path of the slide, their extremities C _c_ may be supposed to move at a right angle to that path, and consequently the rack which is jointed to those extremities will also move upon B _b_ in a direction at a right angle to its path, which is the thing required, and admits of no other motion with respect to B _b_.

[Ill.u.s.tration: Fig. 215.]

To multiply plane motion the construction shown in Fig. 215 is frequently employed. A and B are two racks, and C is a wheel between them pivoted upon the rod R. A crank shaft or lever D is pivoted at E and also (at P) to R. If D be operated C traverses along A and also rotates upon its axis, thus giving to B a velocity equal to twice that of the lateral motion of C.

The diameter of the wheel is immaterial, for the motion of B will always be twice that of C.

Friction gearing-wheels which communicate motion one to the other by simple contact of their surfaces are termed friction-wheels, or friction-gearing. Thus in Fig. 216 let A and B be two wheels that touch each other at C, each being suspended upon a central shaft; then if either be made to revolve, it will cause the other to revolve also, by the friction of the surfaces meeting at C. The degree of force which will be thus conveyed from one to the other will depend upon the character of the surface and the length of the line of contact at C.

[Ill.u.s.tration: Fig. 216.]

These surfaces should be made as concentric to the axis of the wheel and as flat and smooth as possible in order to obtain a maximum power of transmission. Mr. E. S. Wicklin states that under these conditions and proper forms of construction as much as 300 horse-power may be (and is in some of the Western States) transmitted.

In practice, small wheels of this cla.s.s are often covered with some softer material, as leather; sometimes one wheel only is so covered, and it is preferred that the covered wheel drive the iron one, because, if a slip takes place and the iron wheel was the driver, it would be apt to wear a concave spot in the wood covered one, and the friction between the two would be so greatly diminished that there would be difficulty in starting them when the damaged spot was on the line of centre.

If, however, the iron wheel ceased motion, the wooden one continuing to revolve, the damage would be spread over that part of the circ.u.mference of the wooden one which continued while the iron one was at rest, and if this occurred throughout a whole revolution of the wooden wheel its roundness would not be apt to be impaired, except in so far as differences in the hardness of the wood and similar causes might effect.

"To select the best material for driving pulleys in friction-gearing has required considerable experience; nor is it certain that this object has yet been attained. Few, if any, well-arranged and careful experiments have been made with a view of determining the comparative value of different materials as a frictional medium for driving iron pulleys. The various theories and notions of builders have, however, caused the application to this use of several varieties of wood, and also of leather, india-rubber, and paper; and thus an opportunity has been given to judge of their different degrees of efficiency. The materials most easily obtained, and most used, are the different varieties of wood, and of these several have given good results.

"For driving light machinery, running at high speed, as in sash, door, and blind factories, ba.s.swood, the linden of the Southern and Middle States (_Tilia Americana_) has been found to possess good qualities, having considerable durability and being unsurpa.s.sed in the smoothness and softness of its movement. Cotton wood (_Populus monilifera_) has been tried for small machinery with results somewhat similar to those of ba.s.swood, but is found to be more affected by atmospheric changes. And even white pine makes a driving surface which is, considering the softness of the wood, of astonishing efficiency and durability. But for all heavy work, where from twenty to sixty horse-power is transmitted by a single contact, soft maple (_Acer rubrum_) has, at present, no rival.

Driving pulleys of this wood, if correctly proportioned and well built, will run for years with no perceptible wear.

"For very small pulleys, leather is an excellent driver and is very durable; and rubber also possesses great adhesion as a driver; but a surface of soft rubber undoubtedly requires more power than one of a less elastic substance.

"Recently paper has been introduced as a driver for small machinery, and has been applied in some situations where the test was most severe; and the remarkable manner in which it has thus far withstood the severity of these tests appears to point to it as the most efficient material yet tried.

"The proportioning, however, of friction-pulleys to the work required and their substantial and accurate construction are matters of perhaps more importance than the selection of material.

"Friction-wheels must be most accurately and substantially made and kept in perfect line so that the contact between the surfaces may not be diminished. The bodies are usually of iron lagged or covered with wooden segments.

"All large drivers, say from four to ten feet diameter and from twelve to thirty inch face, should have rims of soft maple six or seven inches deep. These should be made up of plank, one and a half or two inches thick, cut into 'cants,' one-sixth, eighth, or tenth of the circle, so as to place the grain of the wood as nearly as practicable in the direction of the circ.u.mference. The cants should be closely fitted, and put together with white lead or glue, strongly nailed and bolted. The wooden rim, thus made up to within about three inches of the width required for the finished pulley, is mounted upon one or two heavy iron 'spiders,' with six or eight radial arms. If the pulley is above six feet in diameter, there should be eight arms, and two spiders when the width of face is more than eighteen inches.

"Upon the ends of the arms are flat 'pads,' which should be of just sufficient width to extend across the inner face of the wooden rim, as described; that is, three inches less than the width of the finished pulley. These pads are gained into the inner side of the rim; the gains being cut large enough to admit keys under and beside the pads. When the keys are well driven, strong 'lag' screws are put through the ends of the arm into the rim. This done, an additional 'round' is put upon each side of the rim to cover bolt heads and secure the keys from ever working out. The pulley is now put to its place on the shaft and keyed, the edges trued up, and the face turned off with the utmost exactness.

"For small drivers, the best construction is to make an iron pulley of about eight inches less diameter and three inches less face than the pulley required. Have four lugs, about an inch square, cast across the face of this pulley. Make a wooden rim, four inches deep, with face equal to that of the iron pulley, and the inside diameter equal to the outer diameter of the iron. Drive this rim snugly on over the rim of the iron pulley having cut gains to receive the lugs, together with a hard wood key beside each. Now add a round of cants upon each side, with their inner diameter less than the first, so as to cover the iron rim.

If the pulley is designed for heavy work, the wood should be maple, and should be well fastened by lag screws put through the iron rim; but for light work, it may be of ba.s.swood or pine, and the lag screws omitted.

But in all cases, the wood should be thoroughly seasoned.

"In the early use of friction-gearing, when it was used only as backing gear in saw-mills, and for hoisting in grist-mills, the pulleys were made so as to present the head of the wood to the surface; and we occasionally yet meet with an instance where they are so made. But such pulleys never run so smoothly nor drive so well as those made with the fibre more nearly in a line with the work."[11]

[11] By E. S. Wicklin.

[Ill.u.s.tration: Fig. 217.]

[Ill.u.s.tration: Fig. 218.]

The driving friction may be obtained from contact of the radial surfaces in two ways: thus, Fig. 217 represents three discs, A, B, and C; the edge of A being gripped by and between B and C, which must be held together by a spiral spring S or other equivalent device. These wheels may be made to give a variable speed of rotation by curving the surfaces of the pair B C as in the figure. By means of suitable lever-motion A may be made to advance towards or recede from the centre of B and C, giving to their shaft an increased or diminished speed of revolution.

[Ill.u.s.tration: Fig. 219.]

A similar result may be obtained by the construction shown in Fig. 218, in which D and E are two discs fast upon their respective shafts, and C are discs of leather clamped in E. It is obvious that if D be the driver the speed of revolution of E will be diminished in proportion as it is moved nearer to the centre of D, and also that the direction of revolution of D remaining constant, that of E will be in one direction if on the side B of the centre of D, and in the other direction if it is on the side A of the centre of D, thus affording means of reversing the motion as well as of varying its speed. A similar arrangement is sometimes employed to enable the direction of rotation of the driver shaft to be reversed, or its motion to cease. Thus, in Fig. 219, R is a driving rope driving the discs A, B, and _c_, _d_, _e_, _f_, _g_ are discs of yellow pine clamped between the f.l.a.n.g.es _h_ _i_; when these five discs are forced (by lifting shaft H), against the face of a motion occurs in one direction, while if forced against B the direction of motion of H is reversed.

For many purposes, such as hoisting, for example, where considerable power requires to be transmitted, the form of friction wheels shown in Fig. 220 is employed, the object being to increase the line of contact between wheels of a given width of face. In this case the strain due to the length of the line of contact partly counteracts itself, thus relieving to that extent the journals from friction. Thus in Fig. 221 is shown a single wedge and groove of a pair of wheels. The surface pressure on each side will be at a right angle to the face, or in the direction described by the arrows A and B. The surface contact acts to thrust the bearings of the two shafts apart. The effective length of surface acting to thrust the bearings apart being denoted by the dotted line C. The relative efficiency of this cla.s.s of wheel, however, is not to be measured by the length of the line C, as compared to that of the two contacting sides of the groove, because it is increased from the wedge shape of the groove, and furthermore, no matter how solid the wheels may be, there will be some elasticity which will operate to increase the driving power due to the contact. It is to preserve the wedge principle that the wedges are made flat at the top, so that they shall not bottom in the grooves even after considerable wear has taken place. The object of employing this cla.s.s of gear is to avoid noise and jar and to insure a uniform motion. The motion at the line of contact of such wheels is not a rolling, but, in part, a sliding one, which may readily be perceived from a consideration of the following. The circ.u.mference of the top of each wedge is greater than that of the bottom, and, in the case of the groove, the circ.u.mference of the top is greater than that of the bottom; and since the top or largest circ.u.mference of one contacts with the smallest circ.u.mference of the other, it follows that the difference between the two represents the amount of sliding motion that occurs in each revolution. Suppose, for example, we take two of such wheels 10 inches in diameter, having wedges and grooves 1/4 inch high and deep respectively; then the top of the groove will travel 31.416 inches in a revolution, and it will contact with the bottom of the wedge which travels (on account of its lesser diameter) 29.845 inches per revolution.

[Ill.u.s.tration: Fig. 220.]

[Ill.u.s.tration: Fig. 221.]

Fig. 222 shows the construction for a pair of bevel wheels on the same principle.

[Ill.u.s.tration: Fig. 222.]

[Ill.u.s.tration: Fig. 223.]

[Ill.u.s.tration: Fig. 224.]

A form of friction-gearing in which the journals are relieved of the strain due to the pressure of contact, and in which slip is impossible, is shown in Fig. 223. It consists of projections on one wheel and corresponding depressions or cavities on the other. These projections and cavities are at opposite angles on each half of each wheel, so as to avoid the end pressure on the journals which would otherwise ensue.

Their shapes may be formed at will, providing that the tops of the projections are narrower than their bases, which is necessary to enable the projections to enter and leave the cavities. In this cla.s.s of positive gear great truth or exactness is possible, because both the projections and cavities may be turned in a lathe. Fig. 224 represents a similar kind of gear with the projections running lengthways of the cylinder approaching more nearly in its action to toothed gearing, and in this case the curves for the teeth and groves should be formed by the rules already laid down for toothed gearing. The action of this latter cla.s.s may be made very smooth, because a continuous contact on the line of centres may be maintained by reason of the longitudinal curve of the teeth.

[Ill.u.s.tration: Fig. 225.]

Cams may be employed to impart either a uniform, an irregular, or an intermittent motion, the principles involved in their construction being as follows:--Let it be required to construct a cam that being revolved at a uniform velocity shall impart a uniform reciprocating motion. First draw an inner circle O, Fig. 225, whose radius must equal the radius of the shaft that is to drive it, plus the depth of the cam at its shallowest part, plus the radius of the roller the cam is to actuate.

Then from the same centre draw an outer circle S, the radius between these two circles being equal to the amount the cam is to move the roller. Draw a line O P, and divide it into any convenient numbers of divisions (five being shown in the figure), and through these points draw circles. Divide the outer circle S into twice as many equal divisions as the line O P is divided into (as from 1 to 10 in the figure), and where these lines pa.s.s through the circles will be points through which the pitch line of the cam may be drawn.

[Ill.u.s.tration: Fig. 226.]

Thus where circle 1 meets line 1, or at point A, is one point in the pitch line of the cam; where circle 2 meets line 2, or at B, is another point in the pitch line of the cam, and so on until we reach the point E, where circle 5 meets line 5. From this point we simply repeat the process, the point E where line 6 cuts circle 4, being a point on the pitch line, and so on throughout the whole 10 divisions, and through the points so obtained we draw the pitch line.

[Ill.u.s.tration: Fig. 227.]

[Ill.u.s.tration: Fig. 228.]

If we were to cut out a cam to the outline thus obtained, and revolve it at a uniform velocity, it would move a point held against its perimeter at a uniform velocity throughout the whole of the cam revolution. But such a point would rapidly become worn away and dulled, which would, as the point broadened, vary the motion imparted to it, as will be seen presently. To avoid this wear a roller is used in place of a point, and the diameter of the roller affects the action of the cam, causing it to accelerate the cam action at one and r.e.t.a.r.d it at another part of the cam revolution, hence the pitch line obtained by the process in Fig. 225 represents the path of the centre of the roller, and from this pitch line we may mark out the actual cam by the construction shown in Fig.

226. A pair of compa.s.ses are set to the radius of the roller R, and from points (such as at A, B, E, F), as the pitch line, arcs of circles are struck, and a line drawn to just meet the crowns of these arcs will give the outline of the actual cam. The motion of the roller, however, in approaching and receding from the cam centre C, must be in a straight line G G that pa.s.ses through the centre C of the cam. Suppose, for example, that instead of the roller lifting and falling in the line G G its arm is horizontal, as in Fig. 227, and that this arm being pivoted the roller moves in an arc of a circle as D D, and the motion imparted to the arm will no longer be uniform. Furthermore, different diameters of roller require different forms of cam to accomplish the same motion, or, in other words, with a given cam the action will vary with different diameters of roller. Suppose, for example, that in Fig. 228 we have a cam that is to operate a roller along the line A A, and that B represents a large and C a small roller, and with the cam in the position shown in the figure, C will have contact with the cam edge at point D, while B will have contact at the point E, and it follows that on account of the enlarged diameter of roller B over roller C, its action is at this point quicker under a given amount of cam motion, which has occurred because the point of contact has advanced upon the roller surface--rolling along it, as it were. In Fig. 229 we find that as the cam moves forward this action continues on both the large and the small roller, its effect being greater upon the large than upon the small one, and as this rolling motion of the point of contact evidently occurs easily, a quick roller motion is obtained without shock or vibration. Continuing the cam motion, we find in Fig. 230 that the point of contact is receding toward the line of motion on the large roller and advancing upon the small one, while in Fig. 231 the two have contact at about the same point, the forward motion being about completed.