[11] By E. S. Wicklin.
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.
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 flanges 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 class 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 class 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 circumference of the top of each wedge is greater than that of the bottom, and, in the case of the groove, the circumference of the top is greater than that of the bottom; and since the top or largest circumference of one contacts with the smallest circumference 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.
Fig. 222 shows the construction for a pair of bevel wheels on the same principle.
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 class 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 class 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.
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 pass through the circles will be points through which the pitch line of the cam may be drawn.
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.
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 retard 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 compasses 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 passes 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.
To compare the motions of the respective rollers along the line of motion a a we proceed as in Fig. 232, in which the two dots m and n are the same distance apart as are the centres of the two rollers b and c when in the positions they occupy in Fig. 228; hence a pair of compasses set to the radius from the axis of the cam to that of roller b will, if rested at n, strike the arc marked 1 above the line of motion a a, while a pair of compasses set to the radius from the axis of the cam to that of roller c in Fig. 228 will, if rested at m in Fig. 232, mark the arc 1 below the line of motion a a. Continuing this process, we set the compasses to the radius from the axis of the cam to that of roller b in Fig. 229, and mark this radius at arc 2 above the line a a in Fig. 232; hence the distance apart of these two arcs is the amount the roller travelled along the line a a while the cam moved from its position in Fig. 228 to its position in Fig. 229. Next we set the compasses from the axis of the cam to that of the large roller in Fig. 230, and then mark arc 3 above the line in Fig. 232, and repeat the process for Fig. 233, thus using the centre n for all the positions of the large roller and marking its motion above the line a a. To get the motion of the small roller c, we set the compasses to the radius from the axis of the cam to the small roller in Fig. 228, and then resting one point of these compasses on centre m in Fig. 232, we mark arc 1 below the line a a. Turning to Fig. 229 we set the compasses from the cam axis to the centre of roller c, and from centre n in Fig. 232 mark arc 2 below line a. From Figs. 230 and 231 proceed in the same way to get lines 3 and 4 below line a in Fig. 232, and we may at once compare the two motions. Thus we find that while the cam moved from the position in Fig. 228 to that in Fig. 229, the large roller moved twice as far as the small one, while at 230 the motions were rapidly equalizing again, the equalization being completed at 231.
We may now consider the return motion, and in Fig. 233 we find that the order of things is reversed, for the small roller has contact at o, while the large one has contact at p; hence the small one leads and gives the most rapid motion, which it continues to do, as is shown in Figs. 234, 235, and 236, and we may plot out the two motions as in Fig. 237—that for the large roller being above and that for the small one below the line a a. First we set a pair of compasses to the radius from the axis of the large and small roller when in the position shown in Fig. 231 (which corresponds to the same radius in Fig. 228), and mark two centres, m and n, as we did in Fig. 232. Of these n is the centre for plotting the motion of the large roller and m the centre for plotting the motion of the small one. We set a pair of compasses to the radius from the axis of the cam and that of the large roller in Fig. 231, and then resting the compasses at n we mark arc 5 above the line a a, Fig. 237. The compasses are then set from the cam to the roller axis in Fig. 233, and arc 6 is marked above line a a. From Figs. 234, 235, and 236 we get the radii to mark arcs 7, 8, 9 above a a, and the motion of the large roller is plotted. We proceed in the same way for the small one, but use the centre m, Fig. 237, to mark the arcs 5, 6, 7, 8, and 9 below the line a a, and find that the small roller has moved quickest throughout. It appears, then, that the larger the roller the quicker the forward motion and the slower the return one, which is advantageous, because the object is to move the roller out quickly and close it slowly, so that under a quick speed the cam shall not run away from the roller as it is apt to do in the absence of a return or backing cam, which consists of a separate cam for moving the roller on its return stroke, thus dispensing with the use of springs or weights to keep the roller upon the cam and making the motion positive.
The return or backing cam obviously depends for its shape upon the forward cam, and the latter having been determined, the requisite form for the return cam may be found as follows. In Fig. 238 let a represent the forward cam fastened in any suitable or convenient way to a disc of paper, or, what is better, sheet zinc, b. The cam is pivoted by a pin passing through it and the zinc, and driven into the drawing-board. A frame f is made to carry two rollers r and r′, whose width apart exactly equals the extreme length of the forward cam. The faces d d of the frame f are in a line with a line passing through the centres of the rolls r r′, and the cam is also pivoted on this line, so that when the four pins p are driven into the drawing-board, the frame f will be guided by them to move in a line that crosses the centre of the cam a. Suppose then that, the pieces occupying the position shown in the engraving, we slide f so that roller r touches the edge of cam a, and we may then take a needle and mark an arc or line around the edge of r′. We then revolve cam a a trifle, and, being fast to b, the two will move together, and with r against a we mark a second arc, coincident with the edge of roller r′. By continuing this process we mark the numerous short arcs shown upon b, and the crowns of these arcs give us the outline of the return cam. It is obvious that, while the edge of the cam a will not let roller r (and therefore frame f) move to the right, roller r′ being against the edge of the backing or return cam as marked upon b, prevents the frame f from moving to the left; hence neither roll can leave its cam.
We have in this example supposed that the frame carrying the rollers is guided to move in a straight line, and it remains to give an example in which the rollers are carried on a pivoted shaft or rocking arm. In Fig. 239 we have the same cam a with a sheet of paper b fastened to it, the rollers r r′ being carried in a rock shaft pivoted at x. It is essential in this case that the rollers r and r′ and the centre upon which the cam revolves shall all three be in the arc of a circle whose centre is the axis of x, as is denoted by the arc d. The cam a is fastened to the piece of stiff paper or of sheet zinc b, and the two are pivoted by a pin passing through the axis e of the cam and into the drawing-board, while the lever is pivoted at x by a pin passing into the drawing-board. The backing or return cam is obviously marked out the same way as was described with reference to Fig. 238.
In Fig. 240 we have as an example the construction of a cam to operate the slide valve of an engine which is to have the steam supply to the cylinder cut off at one-half the piston stroke, and that will admit the live steam as quickly as a valve having steam lap equal to, say, three-fourths the width of the port. In Fig. 240 let the line a represent a piston stroke of 24 inches, the outer circle b the path of the outer edge of the cam, and the inner circle c the inner edge of the cam, the radius between these circles representing the full width of the steam port. Now, in a valve having lap equal to three-fourths the width of the steam port, and travel enough to open both ports fully, the piston of a 24-inch-stroke engine will have moved about 2 inches before the steam port is fully opened, and to construct a cam that will effect the same movement we mark a dot d, distant from the end e of piston stroke 2⁄26 of the length of the line a, and by erecting the line f we get at point g, the point at which the cam must attain its greatest throw. It is obvious, therefore, that as the roller is at r the valve will be in mid-position, as shown at the bottom of the figure, and that when point g of the cam arrives at e the edge p of the valve will be moved fair with edge s of the steam port t, which will therefore be full open. To cut off at half stroke the valve must again be closed by the time point n of the cam meets the roller r; hence we may mark point n. We may then mark in the cam curve from n to m, making it as short as it will work properly without causing the roller to fail to follow the curve or strike a blow when reaching the circle c. To accomplish this end in a single cam, it is essential to make the curve as gradual as possible from point m to o, so as to start the roller motion easily. But once having fairly started, its motion may be rapidly accelerated, the descent from o to q being rapid. To prevent the roller from meeting circle c with a blow, the curve from q to n is again made gradual, so as to ease and retard the roller motion. The same remarks apply to the curve from r to g, the object being to cause the roller to begin and end its passage along the cam curve as slowly as the length of cam edge occupied by the curve will permit. There is one objection to starting the curve slowly at g, which is that the port s will be opened correspondingly slowly for the live steam. This, however, may be overcome by giving the valve an increased travel, as shown in Fig. 241, which will simply cause the valve edge to travel to a corresponding amount over the inside edge of the port. The increased travel is shown by the circles y and z, and it is seen that the cam curve from w to r is more gradual than in Fig. 240, while the roller r will be moved much more quickly in the position shown in Fig. 241 than it will in that shown in Fig. 240, both positions being that when the piston is at the end of the stroke and the port about to open. While that part of the cam curve from g to m in Fig. 241 is moving past the roller r, the valve will be moving over the bridge, the steam port remaining wide open, and therefore not affecting the steam distribution. After point m, Fig. 241, has passed the roller, we have from m to t to start the roller gradually, so that when it has arrived at t and the port begins to close for the cut-off it may move rapidly, and continue to do so until the point n reaches the roller and the cut-off has occurred, after which it does not matter how slowly the valve moves; hence we may make the curve from n to the circle y as gradual as we like.
Fig. 242 represents a cam for a valve having the amount of lap represented by the distance between circles c and y, the cam occupying the position it would do with the piston at one end of the stroke, as at e. Obviously, a full port is obtained when point g reaches the roller, and as point n is distant from e three-quarters of the diameter of the outer circle, the cut-off occurs at three-quarter stroke, and we have from n to y to make the curve as gradual as we like, and from w to r in moving the valve to open the port. We cannot, however, give more gradual curves at g and at m without retarding the roller motion, and therefore opening and closing the port slower, and it would simply be a matter of increase of speed to cause the roller to fail to follow the cam surface at these two points unless a return cam be employed.
We have in these engine cams considered the steam supply and point of cut-off only, and it is obvious that a second and separate cam would be required to operate the exhaust valves.
Fig. 243 represents a groove-cam, and it is to be observed that the roller cannot be maintained in a close fit in the groove, because the friction on its two sides endeavours to drive it in opposite directions at the same time, causing an abrasion that soon widens the groove and reduces the roller diameter; furthermore, when the grooves are made of equal width all the way down (and these cams are often made in this way) the roller cannot have a rolling action only, but must have some sliding motion. Thus, referring to Fig. 243, the amount of sliding motion will be equal to the differences in the circumferences of the outer circle a and the inner one b. To obviate this the groove and roller must be made of such a taper that the axis of the cam and of the roller will meet on the line of the cam axes and in the middle of the width, as is shown in Fig. 244; but even in this case the cam will grind away the roller to some extent, on account of rubbing its sides in opposite directions. To obviate this, Mr. James Brady, of Brooklyn, N. Y., has patented the use of two rollers, as in Fig. 245, one acting against one side and the other against the other side of the groove, by which means lost motion and rapid wear are successfully avoided.
In making a cam of this form, the body of the cam is covered by a sleeve. The groove is cut through the sleeve and into the body, and is made wider than the diameter of the roller. When the rollers are in place on the spindle or journal, the sleeve is pushed forward, or rather endways, and fastened by a set-screw. This gives the desired bearing on both sides of the groove, while each roller touches one side only of the groove. The edges of the sleeve are then faced off even with the cam body, the whole appearing as in the figure.
Chapter IV.—SCREW THREAD.
Screw threads are employed for two principal purposes—for holding or securing, and for transmitting motion. There are in use, in ordinary machine shop practice, four forms of screw thread. There is, first, the sharp V-thread shown in Fig. 246; second, the United States standard thread, the Sellers thread, or the Franklin Institute thread, as it is sometimes called—all three designations signifying the same form of thread. This thread was originally proposed by William Sellers, and was afterward recommended by the Franklin Institute. It was finally adopted as a standard by the United States Navy Department. This form of thread is shown in Fig. 247. The third form is the Whitworth or English standard thread, shown in Fig. 248. It is sometimes termed the round top and bottom thread. The fourth form is the square thread shown in Fig. 249, which is used for coarse pitches, and usually for the transmission of motion.
The sharp V-thread, Fig. 246, has its sides at an angle of 60° one to the other, as shown; or, in other words, each side of the thread is at an angle of 60° to the axial line of the bolt. The United States Standard, Fig. 247, is formed by dividing the depth of the sharp V-thread into 8 equal divisions and taking off one of the divisions at the top and filling in another at the bottom, so as to leave a flat place at the top and bottom. The Whitworth thread, Fig. 248, has its sides at an angle of 55° to each other, or to the axial line of the bolt. In this the depth of the thread is divided into 6 equal parts, and the sides of the thread are joined by arcs of circles that cut off one of these parts at the top and another at the bottom of the thread. The centres from which these arcs are struck are located on the second lines of division, as denoted in the figure by the dots. Screw threads are designated by their pitch or the distance between the threads. In Fig. 250 the pitch is 1⁄4 inch, but it is usual to take the number of threads in an inch of length; hence the pitch in Fig. 250 would generally be termed a pitch of 4, or 4 to the inch. The number of threads per inch of length does not, however, govern the true pitch of the thread, unless it be a “single” thread.
A single thread is composed of one spiral projection, whose advance upon the bolt is equal in each revolution to the apparent pitch. In Fig. 251 is shown a double thread, which consists of two threads. In the figure, a denotes one spiral or thread, and b the other, the latter being carried as far as c only for the sake of illustration. The true pitch is in this case twice that of the apparent pitch, being, as is always the case, the number of revolutions the thread makes around the bolt (which gives the pitch per inch), or the distance along the bolt length that the nut or thread advances during one rotation. Threads may be made double, treble, quadruple and so on, the object being to increase the motion without the use of a coarser pitch single thread, whose increased depth would weaken the body of the bolt.
The “ratchet” thread shown in Fig. 252 is sometimes used upon bolts for ironwork, the object being to have the sides a a of the thread at a right angle to the axis of the bolt, and therefore in the direct line of the strain. Modifications of this form of thread are used in coarse pitches for screws that are to thread direct into woodwork.
A waved or drunken thread is one in which the path around the bolt is waved, as in Fig. 253, and not a continuous straight spiral, as it should be. All threads may be either left hand or right, according to their direction of inclination upon the bolt; thus, Fig. 254 is a cylinder having a right-hand thread at a and a left-hand one at b. When both ends of a piece have either right or left-hand threads, if the piece be rotated and the nuts be prevented from rotating, they will move in the same direction, and, if the pitches of the threads are alike, at the same rate of motion; but if one thread be a right and the other a left one, then, under the above conditions, the nuts will advance toward or recede from each other according to the direction of rotation of the male thread.