Here we have two wheels having each 36 teeth; hence we may place one of them on the lathe spindle and one on the lead screw, as in Fig. 1239; and putting down the pitch of the lead screw, expressed in sixteenths as before, and beneath it the thread to cut also in sixteenths, we have:

the arrangement of the wheels being shown in Fig. 1239.

We may prove the correctness of this arrangement as follows: The 36 teeth on the lathe spindle will in a revolution cause the 24 wheel to make 1¹⁄₂ revolutions, because there are one and a half times as many teeth in the one wheel as there are in the other; thus: 36 ÷ 24 = 1¹⁄₂. Now, while the 24 wheel makes 1¹⁄₂, the 66 will also make 1¹⁄₂, because they are both on the same sleeve and revolve together. In revolving 1¹⁄₂ times the 66 will cause the 36 on the lead screw to make 2³⁄₄ turns, because 99 ÷ 36 = 2³⁄₄ (or expressed in decimals 2.75), and it thus appears that while the lathe spindle makes one turn, the lead screw will make 2³⁄₄ turns.

Now, the proportion between 1 and 2³⁄₄ is the same as that existing between the pitch of the lead screw and the pitch of the thread we want to cut, both being expressed in sixteenths; thus:

that is to say, 11 is 2³⁄₄ times 4.

Suppose it is required, however, to find what thread a set of gears already on the lathe will cut, and we have the following rule:

Rule.—Take either of the driven wheels and divide its number of teeth by the number of teeth in the wheel that drives it, then multiply by the number of teeth in the other driving wheel, and divide by the teeth in the last driven wheel. Then multiply by the pitch of the lead screw.

Example.—In Fig. 1240 are a set of change wheels, the first pair of which has a driving wheel having 36 teeth, and a driven wheel having 18 teeth. The second pair has a driving wheel of 66 teeth, and a driven wheel of 48.

Let us begin with the first pair and we have 36 ÷ 18 = 2, and this multiplied by 66 is 132. Then 132 ÷ 48 = 2.75, and 2.75 multiplied by 4 is 11, which is the pitch of thread that will be cut. Now, whether this 11 will be eleven threads per inch, or as in our previous examples a pitch of ¹¹⁄₁₆ inch from one thread to another or to the next one, depends upon what the pitch of the lead screw was measured in.

Taking now the second example as in Fig. 1240, and beginning from the first pair of gears, we have, according to the rule, 36 ÷ 48 × 66 ÷ 18 × 4 = 11 = pitch the gears will cut; or proceeding from the second pair of gears, we have by the rule, 66 ÷ 18 × 36 ÷ 48 × 4 = 11 = the pitch the gears will cut. It is not often, however, that it is required to determine what threads the wheels already on a lathe will cut, the problem usually being to find the wheels to cut some required pitch. But it may be pointed out that when the problem is to find the result produced by a given set of wheels, it is simpler to begin the calculation from the wheel already on the lathe spindle, rather than beginning with that on the lead screw, because in that case we begin at the first wheel and calculate the successive ones in the same order in which we find them on the lathe, instead of having to take the last pair in their reverse order, as has been done in the examples, when we began at the wheel on the lead screw, which we have termed the second pair.

The wheels necessary to cut a left-hand thread are obviously the same as those for a right-hand one having an equal pitch; all the alteration that is necessary is to employ an additional intermediate wheel, as at i in Fig. 1241, which will reverse the direction of motion of the lead screw. For a lathe such as shown in Fig. 1235, this intermediate wheel may be interposed between wheels d and i or between i and s. In Fig. 1236, it may be placed between d and i or between i and s, and in Fig. 1238 it may be placed between a and c or between d and s.

Here it may be well to add instructions as to how to arrange the change wheels to cut threads in terms of the French centimètre. Thus, an inch equals ²⁵⁴⁄₁₀₀ of a centimètre, or, in other words, 1 inch bears the same proportion to a centimètre as 254 does to 100, and we may take the fraction ²⁵⁴⁄₁₀₀ and reduce it by any number that will divide both terms of the fraction without leaving a remainder; thus, ²⁵⁴⁄₁₀₀ ÷ 2 = ¹²⁷⁄₅₀. If, then, we take a pair of wheels having respectively 127 and 50 teeth, they will form a compound pair that if placed as in Fig. 1242 will enable the cutting of threads in terms of the centimètre instead of in terms of the inch.

Thus, for example, to cut 6 threads to the centimètre, we use the same change wheels on the stud and on the lead screw that would be used to cut 6 threads to the inch, and so on throughout all other pitches.

Cutting Double or other Multiple Threads in the Lathe.—In cutting a double thread the change wheels are obviously arranged for the pitch of the thread, and one thread, as a in Fig. 251 is cut first, and the other, b, afterwards. In order to insure that b shall be exactly midway between a, the following method is pursued. Suppose the pitch of the lead screw is 4 threads per inch, and that we require to cut a double thread, whose actual pitch is 8 per inch, and apparent pitch 16 per inch, then the lead screw requires to make half a turn to one turn of the lathe spindle; or what is the same thing, the lathe spindle must make two turns to one of the lead screw, hence the gears will be two to one, and in a single-geared lathe we may put on a 36 and a 72, as in Fig. 1243, in which the intermediate wheels are omitted, as they do not affect the case. With these wheels we cut a thread of 8 per inch and then, leaving the lead screw nut still engaged with the lead screw and the tool still in position to cut the thread already formed, we make on the change wheels a mark as at s t, and after taking off the driving gear we make a mark at space u, which is 18 teeth distant from s, or half-way around the wheel. We then pull the lathe around half a turn and put the driving gear on again with the space u engaged with the tooth t, and the lathe will cut the second thread exactly intermediate to the first one. If it were three threads that we require to cut, we should after the driving gear was taken off give the lathe one-third a revolution, and put it back again, engaging the twelfth space from s with tooth t, because one-third of 36 is 12.

It is obviously necessary, in cutting multiple threads in this way, to so select the change wheels that the driving gear contains a number of teeth that is divisible without leaving a remainder by the thread to be cut: thus, for a double thread the teeth must be divisible by two, hence a 24, 30, 34, 36, or any even number of teeth will do. For a triple thread the number of teeth in the driving gear must be divisible by 3, and so on.

But suppose the driving gear is fast upon the lathe spindle and cannot be taken off, and we may then change the position of the lead screw gear to accomplish the same object as moving the lathe spindle. Thus for a double thread we would require to remove the driving gear as before, and then pull round the lead screw so that the eighteenth tooth from t would engage with space s, which is obviously the same thing as moving the driving gear round 18 teeth.

In short work of small diameter the tool will retain its sharpness so long, that one tool will rough out and finish a number of pieces without requiring regrinding, and in this case the finishing cuts can be set by noting the position of the feed screw handle when the first piece is finished to size and the tool is touching the work, so that it may be brought to the same position in taking finishing cuts on the succeeding pieces; but the calipers should nevertheless be used, being applied to the threads as in Figs. 1244 and 1245, which is the best method when there is a standard to set the calipers by.

After a threading tool has carried its cut along the required length of the work, the carriage must be traversed back, so that the second cut may be started. In short work the overhead cross belt that runs the lathe backwards is sufficiently convenient and rapid for this purpose, but in long screws much time would be lost in waiting while the carriage runs back. In the Ames lathe there is a device that enables the carriage to be traversed back by hand, and the feed nut to be engaged without danger of cutting a double thread, or of the tool coursing to one side of the proper thread groove, which is a great convenience.

The construction of this device is shown in Fig. 574. In lathes not having a device for this purpose, the workman makes a chalk mark on the tail of the work driver, and another on the top of the lead screw gear, and by always moving the carriage back to the same point on the lathe bed, and engaging the lead screw nut when these two chalk marks are at the top of their paths of revolution, the tool will fall into its correct position and there will be no danger of cutting a double thread.

In cutting V threads of very coarse pitch it will save time, if the thread is a round top and bottom one, to use a single-pointed slide rest tool, and cut up the thread to nearly the finished depth, leaving just sufficient metal for the chaser to finish the thread.

In using the single-pointed tool on the roughing cuts of very coarse pitches, it is an advantage to move the tool laterally a trifle, so that it will cut on one side or edge only. This prevents excessive tool spring, and avoids tool breakage.

This lateral movement should be sufficient to let the follower side or edge of the tool just escape the side of the thread, and all the cut be taken by the leading side or edge of the tool.

This is necessary because the tool will not cut so steadily on the follower as on the leading cutting edge, for the reason that the pressure of the cut assists to keep the feed screw nut against the sides of the feed screw thread, taking up the lost motion between them, whereas the pressure of a cut taken on the follower side of the thread tends to force the thread of the feed nut away from the sides of the feed screw thread and into the space between the nut thread afforded by the lost motion, and as a result the slide rest will move forward when the tool edges meet exceptionally hard places or spots in the metal of the work, while in any event the tool will not operate so steadily and smoothly.

If the screw is a long one, the cutting should be done with a liberal supply of oil or water to keep it cool, otherwise the contraction of the metal in cooling will leave the thread finer than it was when cut. This is of special importance where accuracy of pitch is requisite.

In cutting a taper thread in a lathe, it is preferable that the taper be given by setting over the lathe tailstock, rather than by operating the cross slider from a taper-turning attachment, because the latter causes the thread to be cut of improper pitch. Thus, in Fig. 1246 is a piece of work between the lathe centres, and it will be readily seen that supposing the lathe to be geared to cut, say, 10 threads per inch, and the length a of the work to be 2 inches long, when the tool has traversed the distance a it will have cut 20 threads, and it will have passed along the whole length of the side b of the work and have cut 20 threads upon it, but since the length of line b is greater than that of a, the pitch of the thread cut will be coarser than that due to the change wheels. The amount of the error is shown by the arc c, which is struck from d as a centre; hence from c to e is the total amount of error of thread pitch.

But if the lathe tailstock sets over as in Fig. 1247, then the pitch of the thread will be cut correct, because the length of b will equal the length of tool traverse; hence at each work revolution the tool would advance one-twentieth of the length of the surface on which the thread is cut, which is correct for the conditions.

Chapter XIII.—EXAMPLES IN LATHE WORK.

BALL TURNING.—One of the best methods of turning balls of the softer materials, such as wood, bone, or ivory, is shown in Figs. 1248 and 1249, in which are shown a blank piece of material and a tubular saw, each revolving in the direction denoted by the respective arrows. The saw is fed into the work and performs the job, cutting the ball completely off. In this case the saw requires to be revolved quicker than the work—indeed, as quickly as the nature of the material will permit, the revolving of the work serving to help the feed. Of course, the teeth of such a saw require very accurate sharpening if smooth work is to be produced, but the process is so quickly performed that it will pay to do whatever smoothing and polishing may be required at a separate operation. This method of ball cutting undoubtedly gave rise to the idea of using a single tooth, as in Fig. 1250. But when a single tooth is employed the work must revolve at the proper cutting speed, while the tooth simply advances to the feed. If the work was cut from a cylindrical blank the cutter would require to be advanced toward the work axis to put on a cut and then revolved to carry that cut over the work, when another cut may be put on, and so on until the work is completed. The diameter of ball that can be cut by one cutter is here obviously confined to that of the bore of the cutter, since it is the inside edge of the cutter that does the finishing.

This naturally suggests the employment of a single-pointed and removable tool, such as in Fig. 1251, which can be set to turn the required diameter of ball, and readily resharpened. To preserve the tool for the finishing cut several of such tools and holders may be carried in a revolving head provided to the lathe or machine, as the case may be. In any event, however, a single-pointed tool will not give the smoothness and polish of the ball cutter shown in Fig. 1252, which produces a surface like a mirror. It consists of a hardened steel tube c, whose bore is ground cylindrically true after it has been hardened. The ball b is driven in a chuck composed of equal parts of tin and lead, and the cutter is forced to the ball by hand. The ball requires to revolve at a quick speed (say 100 feet per minute for composition brass), while the cutter is slowly revolved.

A simple attachment for ball turning in an ordinary lathe is shown in Fig. 1253. It consists of a base a, carrying a plate b, which is pivoted in a; has worm-wheel teeth provided upon its circumference and a slideway at s, upon which slides a tool rest r, operated by the feed-screw handle h. The cut is put on by operating h, and the feed carried around by means of the screw at w. The base plate a may be made suitable to bolt on the tool rest, or clamped on in place of the tool, as the circumstances may permit; or in some cases it might be provided with a stem to fit in place of the dead centre. For boring the seats for balls or other curved internal surfaces the device shown in Fig. 1254 may be used. It consists of a stem or socket s, fitting to the dead spindle in place of the dead centre, and upon which is pivoted a wheel w, carrying a tool t. r is a rack-bar that may be held in the lathe tool post and fed in to revolve wheel w and feed the tool to its cut. At p is a pin to maintain the rack in gear with the wheel. Obviously, a set-screw may be placed to bear against the end of the tool to move it endwise and put on the cut. An equivalent device is shown in Fig. 1255, in which the tool is pivoted direct into the stem and moved by a bar b, held in the tool post. The cut is here put on by operating the tail spindle, a plan that may also be used in the device shown in Fig. 1254. The pins p upon the bar are for moving or feeding the tool to its cut. It is obvious that in all these cases the point of the tool must be out of true vertically with the axis of the work.

In turning metal balls by hand it is best to cast them with a stem at each end, as in Fig. 1257.

To rough them out to shape, a gauge or template, such as in Fig. 1256, is used, being about ¹⁄₃₂ inch thick, which envelops about one-sixth of the ball’s circumference. After the ball is roughed out as near as may be to the gauge, the stems may be nicked in, as in Fig. 1257, and broken off, the remaining bits, a, b, being carefully filed down to the template. The balls are then finished by chucking them in a chuck such as shown in Fig. 1258,[19] and a narrow band, shown in black in the figure, is scraped, bringing the ball to the proper diameter. The ball is then reversed in the chuck, as in Fig. 1259, and scraped by hand until the turning marks cross those denoted by the black band. The ball is then reversed, so that the remaining part of the black band that is within the chuck in Fig. 1259 may be scraped down, and when by successive chuckings of this kind the lightest of scrape marks cross and recross each other when the ball is reversed, it may be finished by the ball cutter, applied as shown in Fig. 1252, and finally ground to its seat with the red-burnt sand from the foundry, which is better than flour emery or other coarser cutting grinding material.

Cutting Cams in the Lathe.—Fig. 1260 represents an end view of cam to be produced, having four depressions alike in form and depth, and arranged equidistant round the circumference, which is concentric to the central bore. The body of a cam is first turned up true, and one of the depressions is filed in it to the required form and curvature. On its end face there is then drilled the four holes, a, b, c, d, Fig. 1261, these being equidistant from the bore e. A similar piece is then turned up in the lathe, and in its end is fitted a pin of a diameter to fit the holes a, b, &c., it being an equal distance from bore e. These two pieces are then placed together, or rather side by side, on an arbor or mandrel, with the pin of the one fitting into one of the holes, as a. Two tool posts are then placed in position, one carrying a dull-pointed tool or tracer, and the other a cutting tool. The dull-pointed tracer is set to bear against the cam shown in Fig. 1262, while the cutting tool is set to take a cut off the blank cam piece. The cross feed screw of the lathe is disengaged, and a weight w, Fig. 1262, attached to the slider to pull the tracer into contact with the cam f. As a result, the slide rest is caused to advance to and recede from the line of lathe centres when the cam depression passes the tracer point, the weight w maintaining contact between the two. Successive cuts are taken until the tool cuts a depression of the required depth. To produce a second cam groove, the piece is moved on the mandrel so that the pin will fall into a second hole (as, say, b, Fig. 1261), when, by a repetition of the lathe operation, another groove is turned. The whole four grooves being produced by the same means, they must necessarily be alike in form, the depths being equal, provided a finishing cut were taken over each without moving the cutting tool.

It will be observed that this can be done in any lathe having a slide rest, and that the grooves cut in one piece will be an exact duplicate of that in the other, or guide groove, save such variation as may occur from the thickness of the tracer point, which may be allowed for in forming the guide or originating groove. From the wear, however, of the tracer point, and from having to move the cutting tool to take successive depths of cut, this method would be undesirable for continuous use, though it would serve excellently for producing a single cam. An arrangement for continuous use is shown in Fig. 1263, applied to a lathe having a feed spindle at its back, with a cam g upon it. This cam g may be supposed to have been produced by the method already described. A tracer point h, or a small roller, may be attached to the end of the slide-rest and held against g by the weight w, which may be within the lathe shears if they have no cross girts, as in the case of weighted lathes. The slide-rest may be arranged to have an end motion slightly exceeding the motion, caused by the cam, of the tracer h. Change gears may then be used to cause the cam g to make one rotation per lathe rotation, cutting four recesses in the work; or by varying the rotations of g per lathe rotation, the number of recesses cut by the tool t may be varied. Successive depths of cut may then be put on by operating the feed screw in the ordinary manner. In this arrangement the depth and form of groove cut upon the work will correspond to the form of groove upon the cam-roller g; or each groove upon g being of a different character, those cut on the work will correspond. The wear on the cross slide will, in this case, be considerable, however, in consequence of the continuous motion of the tool-carrying slider, and to prevent this another arrangement may be used, it being shown in Fig. 1264 as applied to a weighted and elevating slide rest. The elevating part of the slide rest is here pivoted to the lathe carriage at i, the weight w preventing play (from the wear) at i. A bracket j is shown fast to the elevating slide of the rest, carrying a roller meeting the actuating cam g. In this arrangement the cut may be put on by the feed screw traversing the slider in the usual manner, or the elevating screw k may be operated, causing the roller at the end of j to gradually descend as each cut is put on into more continuous contact with g as the latter rotates. The form of groove cut by the tool does not, in this case, correspond to the form on g, because the tool lifts and falls in the arc of a circle of which pivot i is the centre of motion, and its radius from i being less than the radius of g, its motion is less. But in addition to this the direction of its motion is not that of advancing and receding directly toward and away from the line of lathe centres, and the cam action is reduced by both these causes.

The location of pivot i is of considerable importance, since the nearer it is to the line of centres the less the action of the cam g is reduced upon the work. As this is not at first sight apparent, a few words may be said in explanation of it. It is obvious that the farther the pivot i is from the tool point the greater will be the amount of motion of the tool point, but this motion is not in a direction to produce the greatest amount of effect upon the work, as is demonstrated in Fig. 1265; referring to which, suppose line a b c to represent a lever pivoted at b, and that end a be lifted so that the lever assumes the position denoted by the dotted lines d and e, then the end of c will have moved from circle f to circle g, as denoted by arc h; arm c of the lever being one-half the length of arm a b, and from circle f to circle g, measured along the line h, being one-half the distance between a and the end of the line d, the difference in the diameters of circles f and g will represent the effect of the cam motion on the tool under these conditions. Now, suppose a j is a lever pivoted at k, and that end a is raised to the dotted line d, then arm j, being one-half the length of a k, will move half as much as end a, and will assume the position denoted by dotted line l, and the difference in the diameter of circles f and m will represent the cam motion upon the tool motion under these conditions. From this it appears that the more nearly vertical beneath the tool point the pivoted point is, the greater the effect produced by a given amount of cam motion. On this account, as well as on account of the direction of motion, the shape of the actuating cam may be more nearly that of the form required to be produced in proportion as the pivoted centre falls directly beneath the tool point. But, on the other hand, the wear of the pivot, if directly beneath the tool point, would cause more unsteadiness to the tool; hence it is desirable that it be somewhere between points k and b, the location being so made that (b representing the pivoted point of the rest) the line b c forms an angle of 50° with the line b a. It is obvious that when the work is to be cam-grooved on a radial face the pivoted design is unsuitable, and either that in Fig. 1262 or 1263 is suitable.

Similar cam motions may be given to the cross feed of a lathe: thus, the Lane and Bodley Company of Cincinnati, Ohio, employ the following method for turning the spherical surfaces of their swiveling bearings for line shafting.

The half bearing b, Fig. 1266, is chucked upon a half-round mandrel, c being the spherical surface to be turned, a sectional view of c being shown in Fig. 1267.

In Fig. 1268 is a plan view of the chuck, work, and lathe rest; d is a former attachment bolted to the slider of the rest, and e a rod passing through the lathe block. The weight w, Fig. 1269, is suspended by a cord attached to the slide rest so as to keep the former d firmly against the end of e.

As the slider is operated, the rest is caused by e to slide upon the lathe bed, and the cutting tool forms a spherical curve corresponding to the curve on the former d. The weight w of course lifts or falls according to the direction of motion of the slider.

The cut is put on by operating handle g, thus causing e to advance.

The weight w causes any play between the slider and the cross slide to be taken up in the same direction as the tool pressure would take it up, hence the cut taken is a very smooth one. The half-round mandrel being fixed to the lathe face plate will remain true, obviating the liability of the centre of the spherical surface being out of line with the axis of the bearing-bore.

A method of producing cams without a lathe especially adopted for the purpose is shown in Figs. 1270 and 1272, which are extracted from Mechanics. The apparatus consists of a frame e, which fits on the cross ways of an ordinary lathe. The cross-feed screw is removed, so that e may slide backwards and forthwards freely. The frame e carries the worm-wheel a and the worm-gear b, which is operated by the crank f. The cam c to be cut is bolted on to the face of the worm-wheel, which faces the headstock of the lathe. The form for the cam, which may be made of sheet steel, or thicker material, according to the wear it is to have, is fastened to the face of the cam.

A cutter, like a fluted reamer, such as is shown in Fig. 1271, is then put in the live centre of the lathe. Care must be taken that the shank is the same size as the fluted part, and that the flutes are not cut up farther than the thickness that the cam grooves are to be cut in the blank. Having attached a cord to the back of e, pass it over a pulley h, fastened on the rear of the lathe, and hang on a weight g. Fig. 1272 is an edge view of the device, looking from the back of the lathe. It shows the worm a, blank c, and former d all bolted together, while the cutter i is ready in its place on a line with the centre of the worm, and just at back of the former. The machine is operated by turning the crank f, which causes the worm a, also c and d, to revolve slowly, while the cutter i has a rather rapid rotation. The weight causes the cutter to be held firmly against the form f, and to follow its curves in and out.

Knurling or Milling Tools.—In Fig. 1273 is shown the method of using the knurling tool in the slide rest of a lathe. It represents the tool at work producing the indentations which are employed to increase the hand grip of screw heads, or of cylindrical bodies, as shown in the figure by the crossed lines. Fig. 1274 is an end view of the tool, which consists of a holder to go in the slide rest tool post, and carrying two small hardened steel wheels, each of which is serrated all round its circumference, the serrations of one being in an opposite direction to those of the other. The method of using the tool is shown in Fig. 1275, where it is represented operating upon a cylindrical piece of work. If the knurling is to be carried along the work to a greater length than the thickness of the knurl wheels, the lathe slide rest is slowly traversed the same as for a cutting tool.