Chapter XII: Examples in Lathe Work (4)

An excellent method of chucking a pulley, and one that with care avoids the disadvantages mentioned in the foregoing methods, is shown in Figs. 1232 and 1233. It consists of a clamping dog, Fig. 1234, that fastens to the lathe face plate, and secures the pulley by its arms, while supporting the rim and preventing it from chattering, if it is weak or slight.

This dog is bolted to the face plate by the two studs A and B. At C is a set screw for clamping the pulley arms against the screw D, and at F is a screw that steadies the pulley rim between the arms.

CUTTING SCREWS IN THE LATHE WITH SLIDE REST TOOLS.--In order to cut a thread in the lathe with a slide rest tool, it is necessary that the gear-wheels which transmit motion from the cone spindle to the feed screw shall be of the proportions necessary to give to the lathe carriage and slide rest sufficient lateral movement or traverse for lathe revolution to cut a thread of the desired pitch.

Suppose now that the feed screw makes a revolution in the same time that the cone spindle does, and it is evident that the thread cut by the slide rest tool will be of the same pitch as is the pitch of the lathe feed screw. If the feed screw gear-wheels of the lathe are what is called single geared (which means that no one stud in the change gearing carries more than one gear-wheel), it does not matter what are the sizes or how many teeth there are in the wheels used to convey or transmit motion from the cone spindle to the feed screw, for so long as the number of teeth on the cone spindle gear and that on the feed screw are equal, the feed screw will make one revolution in the same time as the cone spindle makes a revolution, and the cutting tool will travel a lateral distance equal to the pitch of the lead screw.

Suppose, for example, that Fig. 1235 represents the screw cutting gear or change wheels of a lathe, wheel D being the driver, I an intermediate wheel for transmitting motion from the driver D to the lead-screw wheel S. Suppose, also, that D has 32, I 80, and S 32 teeth, and we have a simple or single-geared lathe. In this case it may first be proved that we need not concern ourselves with the number of teeth in the intermediate I, because its number of teeth is of no consequence. For example, the 32 teeth in D will in a revolution move 32 of the teeth in I past the line of centres, and it is obvious that I will move the 32 teeth in S past the line of centres, causing it to make one revolution the same as D. If any other size of wheel be used for an intermediate, the effect will be precisely the same, the revolutions of D and of S remaining equal. Under these conditions the lathe would cut a thread whose pitch would be the same as that of the thread on the lead screw.

Now let us turn to Fig. 1236, representing an arrangement of gearing common in American practice, and we have within the lathe-head three gears, A, B, and C, which cannot be changed. Of these, B and C are simply intermediate wheels, the respective diameters of which have no effect upon the revolutions of the lead screw, except that they convey the motion to D. To demonstrate this, suppose the wheels to have the number of teeth marked respectively against them in the end view of the figure, C and D having each 20 teeth, and the one revolution of the live spindle wheel A will cause the lead-screw wheel to make one revolution, because A and S contain the same number of teeth. This may be made plain as follows: The 20 teeth in A will in one revolution cause B to make two revolutions, because B has but half as many teeth as A. The two revolutions of B will cause C to make but one revolution, because C has twice as many teeth as B has. Now, C and D are fast on the same shaft R; hence they revolve together, the one revolution of C simply being conveyed by the shaft R to D, and it is clear that the one revolution of A has been conveyed without change to D, and that, therefore, D may be considered to have simply taken the place of A, unaffected by the wheels B, C. Wheel I is again an intermediate, so that, whatever its diameter or number of teeth, one revolution of D will cause one revolution of S. Thus in this arrangement the lead screw will again revolve at the same speed as the live spindle, and the thread cut will be of the same pitch as the pitch of the lead screw. Practically, then, all the wheels between A and S, as thus arranged, act as simple intermediates, the same as though it were a single-geared lathe, which occurs because C and D have the same number of teeth, and we have, therefore, made no use of the shaft R to compound the gearing.

The term "compounded" as applied to the change gears of a lathe, means that there exists in it a shaft or some equivalent means by which the velocity of the wheels may be changed. Such a shaft is shown at R in Fig. 1236, and it affords a means of compounding by placing on its outer end, as at D, a wheel that has a different number of teeth to that in wheel C. In Fig. 1237 this change is made, wheel D having 40 teeth instead of the 20 it had before. As in the former case, however, it will make one revolution to one of C or one of A, but having 40 teeth it will move 40 of the teeth in I past the line of centres, and this will cause the lead screw wheel S to make two revolutions, because it has 20 teeth only. Thus, the compounding of C and D on shaft R has caused S to make two revolutions to one of A, or, what is the same thing, one revolution of A will in this case cause S to make two revolutions, and the thread cut would be twice as coarse as the lead-screw thread. In the case of a lathe geared as in either Fig. 1235 or 1236, all the wheels that we require to consider in calculating the change wheels are D and S. Now, the shaft R is called the "mandrel," the "stud," or the "spindle," all three terms being used, and the wheel D is the wheel on the stud, mandrel, or spindle, while in every case S is that on the lead screw, and the revolutions of this wheel D and those of the lead screw will be in the same proportion as exists between their numbers of teeth. In considering their revolutions it is to be borne in mind that when D has more teeth than S the speed of the lead screw is increased, and the lathe will cut a thread coarser than that of its lead screw, or when D has less teeth than S the speed of the lead screw is diminished, and the pitch of thread cut will be finer than that of the lead screw.

Another method of compounding is shown in Fig. 1238, the compounded pair C D being on a stud carried in the swing frame F. Now, suppose A has 32, C 64, D 32, and S 64 teeth, the revolution being in the same proportion as the numbers of teeth, C will make one-half a revolution to one revolution of A, and D, being fast to the same stud as C, will also make one-half revolution to one revolution of A. This one-half revolution of D will cause S to make one-quarter of a revolution; hence the thread cut will be four times as fine as the pitch of the thread on the lead screw, because while the lathe makes one turn the lead screw makes one-quarter of a turn. In this arrangement we are enabled to change wheel C as well as wheel D (which could not be done in the arrangement shown in Fig. 1236), and for this reason more changes can be made with the same number of wheels. When the wheel C makes either more or less revolutions than the driver A, it must be taken into account in calculating the change wheels. As arranged in Fig. 1236, it makes the same number as A, which is a very common, arrangement, but in Fig. 1238 it is shown to have twice as many teeth as A; hence it makes half as many revolutions. In the latter case we have two pairs of wheels, in each of which the driven wheel is twice the size of the driver; hence the revolutions are reduced four times.

Suppose it is required to cut a thread of eight to an inch on a lathe such as shown in Fig. 1235, the lead screw pitch being four per inch, and for such simple trains of gearing we have a very simple rule, as follows:--

_Rule._--Put down the pitch of the lead screw as the numerator, and the pitch of thread you want to cut as the denominator of a vulgar fraction, and multiply both by the pitch of the lead screw, thus:

Pitch of
lead
screw. {the number of teeth for the
Pitch of lead screw 4 4 16 = {wheel on the spindle.
- × - = --
Pitch to be cut 8 4 32 = {the number of teeth for the
{wheel on the lead screw.

There are three things to be noted in this rule; and the first is, that when the pitch of the lead screw and the pitch of thread you want to cut is put down as a fraction, the numerator at once represents the wheel to go on the stud, and the denominator represents the wheel to go on the lead screw, and no figuring would require to be done providing there were gear-wheels having as few teeth as there are threads per inch in the lead screw, and that there was a gear-wheel having as many teeth as the threads per inch required to be cut. For example, suppose the lathe in Fig. 1236 to have a lead screw of 20 per inch, and that the change wheels are required to cut a pitch 40, then we have 20/40, the 20 to go on at D in Fig. 1236 and the 40 to go on the lead screw. But since lead screws are not made of such fine pitch, but vary from two threads to about six per inch, we simply multiply the fraction by any number we choose that will give us numbers corresponding to the teeth in the change wheels. Suppose, for example, the pitch of lead screw is 2, and we wish to cut 6, then we have 2/6, and as the smallest change wheel has, say, 12 teeth we multiply the fraction by 6, thus: 2/6 × 6/6 = 12/36. If we have not a 12 and a 36 wheel, we may multiply the fraction by any other number, as, say, 8; thus: 2/6 × 8/8 = 16/48 giving us a 16 wheel for D, Fig. 1236, and a 48 wheel for the lead screw.

The second notable feature in this rule is that it applies just the same whether the pitch to be cut is coarser or finer than the lead screw; thus: Suppose the pitch of the lead screw is 4, and we want to cut 2. We put these figures down as before 4/2, and proceed to multiply, say, by 8; thus: 4/2 × 8/8 = 32/16, giving a 32 and a 16 as the necessary wheels.

The third feature is, that no matter whether the pitch to be cut is coarser or finer than the lead screw, the wheels go on the lathe just as they stand in the fraction; the top figure goes on top in the lathe, as, for example, on the driving stud, and the bottom figures of the fraction are for the teeth in the wheel that goes on the bottom of the lathe or on the lead screw. No rule can possibly be simpler than this. Suppose now that the pitch of the lead screw is 4 per inch and we want to cut 1-1/2 per inch. As the required pitch is expressed in half inches, we express the pitch of the lead in half inches, and employ the rule precisely as before. Thus, in four there are eight halves; hence, we put down 8 as the numerator, and in 1-1/2 there are three halves, so we put down 3 and get the fraction 8/3. This will multiply by any number, as, say, 6; thus: (8/3) × (6/6) = (48/18), giving us 48 teeth for the wheel D in Fig. 1236, and 18 for the lead screw wheel S.

In a lathe geared as in Fig. 1235 the top wheel D could not be readily changed, and it would be more convenient to change the lead screw wheel S only. Suppose, then, that the lead screw pitch is 2 per inch, and we want to cut 8. Putting down the fraction as before, we have 2/8, and to get the wheel S for the lead screw we may multiply the number of teeth in D by 8 and divide it by 2; thus: 32 × 8 = 256, and 256 ÷ 2 = 128; hence all we have to do is to put on the lead screw a wheel having 128 teeth. But suppose the pitch to be cut is 4-1/4, the pitch of the lead screw being 2. Then we put both numbers into quarters, thus: In 2 there are 8 quarters, and in 4-1/4 there are 17 quarters; hence the fraction is 8/17. If now we multiply both terms of this 8/17 by 4 we get 32/68, and all we have to do is to put on the lead screw a wheel having 68 teeth.

When we have to deal with a lathe compounded as in Fig. 1238, in which the combination can be altered in two places--that is, between A and C and between D and S--the wheel A remaining fixed, and the pitch of the lead screw is 2 per inch, and it is required to cut 8 per inch--this gives us the fraction 2/8, which is at once the proportion that must exist between the revolutions of the wheel A and the wheel S. But in this case the fraction gives us the number of revolutions that wheel S must make while the wheel A is making two revolutions, and it is more convenient to obtain the number that S requires to make while A is making one revolution, which we may do by simply dividing the pitch required to be cut by the pitch of the lead screw, as follows: Pitch of thread required, 8; pitch of lead screw, 2; 8 ÷ 2 = 4 = the revolutions S must make while A makes one. We have then to reduce the revolutions four times, which we may do by putting on at C a wheel with twice as many teeth in it as there are in A, and as A has 32, therefore C must have 64 teeth. When we come to the second pair of wheels, D and S, we may put any wheel we like in place of D, providing we put on S a wheel having twice as many.

But suppose we require to cut a fractional pitch, as, say, 4-1/8 per inch, the pitch of lead screw being 2, all we have to do is to put the pitch of the lead screw into eighths, and also put the number of teeth in A into eighths; thus: In two there are 16 eighths, and in the pitch required there are 33 eighths; hence for the pitch of the lead screw we use the 16, and for the thread required we use the 33, and proceed as before; thus:

Pitch of thread Pitch of lead
required. screw.
33 ÷ 16 = 2-1/16 = the revolution which A
must make while wheel B
makes one revolution.

The simplest method of doing this would be to put on at C a wheel having 2-1/16 times as many teeth as there are in A. Suppose then that A has 32 teeth, and one sixteenth of 32 = 2, because 32 ÷ 16 = 2. Then twice 32 is 64, and if we add the 2 to this we get 66; hence, if we give wheel C 66 teeth, we have reduced the motion the 2-1/16 times, and we may put on D and S wheels having an equal number of teeth. Or we may put on a wheel at C having the same number as A has, and then put on any two wheels at D and C, so long as that at S has 2-1/16 times as many teeth as that at D.

Again, suppose that the pitch of a lead screw is 4 threads per inch, and that it be required to find what wheels to use to cut a thread of 11/16 inch pitch, that is to say, a thread that measures 11/16 inch from one thread to the other, and not a pitch of 11/16 threads per inch: First we must bring the pitch of the lead screw and the pitch to be cut to the same terms, and as the pitch to be cut is expressed in sixteenths we must bring the lead screw pitch to sixteenths also. Thus, in an inch of the length of the lead screw there are 16 sixteenths, and in this inch there are 4 threads; hence each thread is 4/16 pitch, because 16 ÷ 4 = 4. Our pitch of lead screw expressed in sixteenths is, therefore, 4, and as the pitch to be cut is 11/16 it is expressed in sixteenths by 11; hence we have the fraction 4/11, which is the proportion that must exist between the wheels, or in other words, while the lathe spindle (or what is the same thing, the work) makes 4 revolutions the lead screw must make 11.

Suppose the lathe to be single geared, and not compounded, and we multiply this fraction and get--

4 × 4 16 = wheel to go on lead screw.
-- - = --
11 × 4 44 = " " stud or mandrel.

4 × 5 20 = wheel to go on lead screw.
Or, -- - = --
11 × 5 55 = " " stud or mandrel.

4 × 6 24 = wheel to go on lead screw.
Or, -- - = --
11 × 6 66 = " " stud or mandrel.

But suppose the lathe to be compounded as in Fig. 1235, and we may arrange the wheels in several ways, and in order to make the problem more practical, we may suppose the lathe to have wheels with the following numbers of teeth, 18, 24, 36, 36, 48, 60, 66, 72, 84, 90, 96, 102, 108, and 132.

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:

4 × 6 24 = wheel to be driven by lathe spindle,
-- - = --
11 × 6 66 = " to drive lead screw wheel;

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 1-1/2 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 = 1-1/2. Now, while the 24 wheel makes 1-1/2, the 66 will also make 1-1/2, because they are both on the same sleeve and revolve together. In revolving 1-1/2 times the 66 will cause the 36 on the lead screw to make 2-3/4 turns, because 99 ÷ 36 = 2-3/4 (or expressed in decimals 2.75), and it thus appears that while the lathe spindle makes one turn, the lead screw will make 2-3/4 turns.

Now, the proportion between 1 and 2-3/4 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:

Pitch of lead screw in sixteenths 4 }
}, and 11 ÷ 4 = 2-3/4;
" to be cut in sixteenths 11 }

that is to say, 11 is 2-3/4 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.

If it is a pitch of 4 threads per inch, the wheels will cut a thread of 11 per inch, while if it were a thread of 4/16 pitch, the thread cut will be 11/16 pitch.

Let us now work out the same gears beginning from the lead screw pair, and we have as follows:

Number of teeth in driver is 66, which divided by the number in the driven, 48, gives 1.375. This multiplied by the number of teeth in the driver of the other pair = 36 gives 49.5, which divided by the number of teeth in the driven wheel of the first pair gives 2.75, which multiplied by the pitch of the lead screw 4 gives 11 as before.

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.

Fig. 1248.

Fig. 1249.

Fig. 1250.

Fig. 1251.

Fig. 1252.

Fig. 1253.

Fig. 1254.

Fig. 1255.]