Chapter VII: Details in Lathe Construction (3)

The feed nut should obviously remain axially true with the lead screw, as by reason of the extra weight of the front of the carriage, both it and the lathe shears wear most at the front, and the carriage, therefore, falls to the amount of its own wear and the wear of the shears. If the lead screw is used to feed with (as it should not be), the nut wears coincidently with the carriage and the shears, and the screw alignment is not impaired; but with an independent feed, only a small portion of the carriage traversing is done with the lead screw, hence the carriage lowers from the wear due to the independent feeding, and when the lead screw comes to be used its nut is not in true alignment with it. It is obviously preferable, then, to place the lead screw at the back, where the carriage and shears wear the least. Furthermore, this relieves the carriage front from the weight of the nut, &c., tending to equalize the back and front wear, while removing the nut-operating device from the front to the back of the shears, and thus reducing the number of handles in front, and thus avoid complication in small lathes.

LATHE LEAD SCREWS.--Lead screws have their pitches in terms of the inch throughout all parts of the world; or, in other words, the lead screws of all lathes contain so many full threads per inch of length.

Lead screws are usually provided with square threads of the usual form, or with threads whose sides have about fifteen degrees of angle, so that the two halves of the feed nut may be let together to take up the wear. It is obvious that in a [V]-thread or in a thread whose sides are at an angle, the feeding strain tends to force the two halves of the feed nut apart, and therefore places a strain on the feed-nut operating mechanism that does not exist in the case of a square thread. Furthermore it can be shown that with a [V]-thread the opportunities to lock the carriage on a wrong place, after traversing it back by hand in screw cutting, are increased, thus augmenting the liability to cut intermediate and improper threads.

In Fig. 615, for example, we have a pitch of lead screw of three threads per inch, and the gears arranged to cut six threads per inch on the work. As the bottom wheel has twice as many teeth as the top one, it is clear that, while the top one makes one, the bottom one will make half revolution, and the lead screw will make half a turn for every turn the work makes. Now, suppose the tool point to stand opposite to space A, and the nut (supposing it to have but one thread only, which is all that is required for our purpose), stand opposite to space D. Suppose, further, that the lathe makes one revolution, and space B on the work will have moved to occupy the position occupied by space A, or, rather, there will still be a place at A fully in front of the tool, as should be the case, but the lead screw will have made half revolution, the top _e_ of the thread coming opposite to the feed nut, as in the position of tool and nut shown in the figure at T and N; hence the nut would not engage, without moving the lathe carriage sideways, and thus throwing the tool to one side of the thread in the work. When, however, the work had made another revolution, both the feed screw and the work would again come into position for the tool and nut to engage properly, and it follows that in this case the tool will always fall into proper position for the nut to be locked.

It is obvious, however, that had the lead screw thread been a square one, and the nut thread to accurately fit to the lead screw thread, so as to completely fill it, then the nut could not engage with the lead screw until the lathe had made a complete revolution, at which time the work will have made two full or complete revolutions, and the tool would, therefore, fall into proper position to follow in the groove or part of a thread cut at the first tool traverse.

In Fig. 616, we have the same lead screw geared to cut five or an odd number of threads per inch. The tool and the nut are shown in position to properly engage, but suppose, the nut being disengaged, that the work makes one revolution, and during this period the lead screw will have made 3/5ths of a revolution, hence the nut will not be in position to engage properly, because, although space B will have travelled forward so as to occupy the position of space A in the figure (that is, there will be a space fairly in front of the tool point), yet the nut will not engage properly, because the nut point will not be opposite to the bottom of the lead screw thread. When the work has made its second revolution, and space C moves to the position occupied by A, the lead screw will have made 6/5 or 1-1/5 revolutions, and the nut cannot engage properly; when the lathe has made its third revolution, the lead screw will have made 1-4/5 revolutions and the nut will still fall to one side of the thread space, and will not lock properly. The work having made its fourth turn, the lead screw will have made 2-2/5 turns, and the nut will not be in position to lock fairly. The work having made its fifth turn, however, the lead screw will have made three turns, and the threads will fall into the same position that they occupy in the figure, and both tool and feed nut will fall into their proper positions in their respective threads. It does not follow, however, that, the lead screw having a [V]-shaped thread, the nut cannot be forced to engage but once in every five turns of the lead screw, because, were this the case, it would be impossible to lock the nut in an improper position.

Suppose, for example, that we have in Fig. 617, the same piece of work and lead screw as in Fig. 616, and that a first groove, A, has been cut with the tool in the position shown, and the nut engaged in the position marked 1. Now, suppose the nut be disengaged and the work allowed to make one revolution, then the lead screw will, during this revolution, revolve 3/5 of a revolution, and the position of the nut point with relation to the lead screw will be as at position 2. If, then, the nut was forced into the lead screw thread, it would, acting on the wedge principle, move the carriage to the right sufficiently to permit the nut to engage fully in thread G, and the tool would then cut a second groove on thread B. If the nut then be withdrawn from thread G, and the work allowed to make another revolution, the nut will stand in a precisely similar position with relation to the lead screw thread as it did in position 2, and by forcing it down into thread H the carriage would be again forced to the right, causing a third thread, C, to be cut. By repeating the operation of withdrawing the nut, letting the work make another revolution and then engaging the nut again, it will seat in thread K, and a fourth thread D will be cut. On again repeating the operation, however, the nut will come into position 5, and, on being drawn home into thread, or, rather, into space L, the tool will fall into groove A again. Thus there will be four threads, each having a pitch equal to that of the lead screw. The second (B) of these four will fall to the left of thread A to an amount or distance equal to 2/5 of the pitch of the lead screw, because, in forcing the nut from position 2 down into the lead screw, the slide rest, and therefore the tool, will be moved to the right 2/5 of the pitch of the lead screw. The third thread C will fall to the left of thread B also to an amount equal to 2/5 of the pitch of the lead screw, because, in forcing the thread to seat itself into thread H from position 3, the slide rest was again moved (to that amount) to the right. The fourth thread D will fall to the left of thread C to the same amount and for the same reason.

But in this case, as before, if the lead screw had a square thread and the nut threads completely filled the spaces between the lead screw threads, then the nut could not engage at the 2nd, 3rd, or 4th work revolution, hence the false threads B, C, and D, could not have been cut, even though the feed nut was disengaged and the lathe carriage was traversed back by hand.

Now, suppose that two threads on the work measure less than the amount the lead screw advances during the time that the work makes a revolution, and if the lead screw has a [V]-shaped thread, the case is altered. We have, for example, in Fig. 618, a pitch of lead screw of 3 to cut 12 and 13 threads respectively. In the case of the 13 threads it will be seen that, supposing there to have been a first cut taken on the work, and the feed nut to be disengaged while the work makes a revolution, then the lead screw will revolve 3/13 revolution and the point A on the lead screw will have moved up to point B, and the nut point remaining at N, seating it in the thread, would cause it to engage with the same thread that it did before, and no second thread would be cut. If the nut be then released, the work allowed to make another revolution and the nut again closed, the operation would be the same as before, and no error would be induced, and so on. Suppose, further, that after the nut was disengaged the lathe was permitted to make two revolutions, and the lead screw would make 6/13, or less than half a turn, and closing it would still cause it to pass back into the same thread on the lead screw and produce correct work. But if after the nut was released the work made three turns, the lead screw would make 9/13 of a turn, and the nut would fall on the right-hand side of the lead screw thread, and in closing would move the lathe carriage to the right, causing the tool to cut a second thread. Now, the same operation that occurred with the first thread would during the next three trials occur with the second thread, and at the next or seventh trial a third thread would be cut, which would be again operated upon during the next succeeding three trials. At the eleventh trial a fourth thread would be cut, but on the next three trials the tool would again fall into the groove first cut and the work proceed correctly. In the case of the 12 threads, the thread cut at the first and second trials would be correct. At the third trial the nut would seat itself in the groove C of the lead screw, causing the carriage to move to the right to a distance equal to twice the pitch of thread being cut, but the tool would still fall into the same groove in the work, as it also would on the fourth. At the fifth trial the process would be repeated, and so on, so that no second thread would be cut.

It may now be noted that if we draw the lead screw and the thread to be cut as in the figure, and draw the dotted lines shown, then those that meet the bottom of the thread on the lead screw, and also meet the groove cut on the work, at the first trial, represent the cases in which the nut will fall naturally into its proper position for the tool to fall into the correct groove, while whenever the nut is being forced home it seats in a groove in the lead screw, the bottom of which groove meets a line drawn from the first thread cut; the results obtained will be made correct by reason of the movement given to the slide nut when artificially seating the nut. This is shown to be the case in Fig. 619, which represents a lead screw having an even number of threads per inch, and from which it appears that in cutting 12 threads (an even number also) the nut cannot be engaged wrong, whereas in the case of 13 threads it can be engaged right three times in 13 trials, and 10 times wrong, the latter causing the tool to cut three wrong threads.

To prevent end motion of a lead screw it should have collars on both sides of one bearing, and not one at each bearing. By this means the screw will be permitted to expand and contract under variations of atmospheric temperature, without binding against the bearing faces.

When a lead screw is long it requires to be supported, otherwise, either its weight will be supported or lifted by the feed nut in gear, or if that nut does not lift the screw, the thread cut will be finer than that due to the pitch of the lead screw, by reason of its deflection or sag.

A lead screw should preferably be as near as possible to the middle of the lathe shears, and as close to the surface as possible, so as to bring it as nearly in line with the strain on the tool as possible, but on account of the cuttings, which falling upon the screw would cause it to wear rapidly, it is usual to locate it on one side, so as to protect it from the cuttings. It is better to locate it on the front side of the lathe rather than on the back, because the strain of the cut falls mainly on the front side (especially in work of large diameter when this strain is usually greatest) and it is desirable to pull the carriage as near in a line with the resistance of the cut as possible, because the farther off the feed nut from the cutting tool point, the greater the tendency to twist the carriage on the shears.

To preserve the nut from wear, it should be made as long as convenient, as, say, five or six times the diameter of the lead screw; it is usually made, however, three or four diameters.

It is obvious that the pitch of the thread should be as accurate as possible, but it has not as yet been found practicable to produce a screw so accurate that it would not show an error, if sufficient of its length be tested, as, say, several feet.

If the error in a screw be equal, and in the same direction at all parts of its length, various devices may be employed to correct it. Thus Fig. 620 represents a device employed by the Pratt and Whitney Co.

It was first ascertained by testing the lathe that its lead screw was too short by 7/100ths of a revolution in a length of 2 feet, the pitch of its thread being 6 to an inch. Now in 2 feet of the screw there would be 144 threads, and since 7/100ths (the part of a revolution the thread was too short) × 1/6 (the pitch of the thread) = 7/600ths (which was called 1/85th), the error amounted to 1/85th inch in 144 turns of the screw. The construction of the device employed to correct this error is as follows: In Fig. 620, A represents the bearing of the feed screw of the lathe, and B _b_ a sleeve, a sliding fit upon A, prevented from revolving by the pin _h_, while still having liberty to move endways. C represents a casing affording journal bearing to B _b_, having a fixed gear-wheel at its end C´, and an external thread upon a hub at that end. D is the flange of C to fasten the device to the shears of the latter, being held by screws. E represents an arm fast upon the collar of the feed screw, and carrying the pinion F, the latter being in gear with the pinion C´, and also with G, which is a pinion containing two internal threads, one fitting to B at _b_, and the other fitting to C at _c_, the former having a pitch of 27 threads to an inch, the latter a pitch of 25 to an inch.

The operation is as follows:--The ordinary change wheels are connected to the feed screw, or lead screw, as it is sometimes termed, at J in the usual manner. The arm E being fast to the feed screw will revolve with it, and cause the pinion F to revolve around the stationary gear-wheel C´. F also gears with G. Now, F is of 12 diametrical pitch and contains 26 teeth, C´ is of 12 diametrical pitch and contains 37 teeth, and G is of 12 diametrical pitch and contains 36 teeth. It follows that the pinion F, while moving around the fixed gear C´, will revolve the pinion G (which acts as a nut), to an amount depending upon the difference in the number of its teeth and those of fixed gear C´ (in this case as 36 is to 37), and upon the difference in the pitches of the two threads, so that at each revolution G will move the feed screw ahead of the speed imparted by the change gears, the end of the sleeve B abutting against the collar of the feed screw to move it forward.

In this case there are 36 turns of the feed screw A for one turn of the nut pinion G, the thread on sleeve B being 27, and that on the hub of C being 25 to the inch; hence, 36 turns of the feed screw gives an end motion to the sleeve B of 1/25 minus 1/27 = 2/675, and 1/36 of that = 1/12150 of an inch = the amount of sliding motion of the sleeve _b_, for each revolution of the lathe feed screw. By varying the proportions between the number of teeth in C´ and G and the pitches of the two threads in a proper and suitable ratio, the device enables the cutting of a true thread from any untrue one in which the variation is regular.

It is usual to fasten to the side of the lathe head stock a brass plate, giving a table of threads, and the wheels that will cut them, and obviously such tables vary according to the pitch of the lead screw, but a universal table may be constructed, such as the following table (prepared by the author) that will serve for any lathe.

At the top of the table is the number of teeth in wheels, advancing by four from 12 to 80 teeth, but it may be carried as much beyond 80 as desired. On the left hand of the table is a column of the same wheels. At the bottom of the scale are pitches of lead screw from 3 up to 20 threads per inch. Over each lead screw pitch are thread pitches, thus on lead screw pitch 4 we have 20, 19, 18, and so on.

The use of the table is as follows:--

Find the pitch of the lead screw, and at the head of that column is the number of teeth for the lathe stud or mandril. Then find in that column the number of threads to be cut, and on the same line, but at the left hand, will be found the number of teeth for the lead screw.

NUMBERS OF TEETH FOR WHEEL TO GO ON LATHE SPINDLE, LATHE STUD, OR MANDRIL.

------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
Lead |12|16|20|24|28|32|36| 40| 44| 48| 52| 56| 60| 64| 68| 72| 76| 80
Screw.| | *| | | | | | | | | | | | | | | |
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
12 | 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
16 | 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
20 | 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
24 | 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
28 | 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
32 | 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
36 | 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
40 |10|10|10|10|10|10|10| 10| 10| 10| 10| 10| 10| 10| 10| 10| 10| 10
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
44 |11|11|11|11|11|11|11| 11| 11| 11| 11| 11| 11| 11| 11| 11| 11| 11
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
48 |12|12|12|12|12|12|12| 12| 12| 12| 12| 12| 12| 12| 12| 12| 12| 12
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
*52 |13|13|13|13|13|13|13| 13| 13| 13| 13| 13| 13| 13| 13| 13| 13| 13
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
56 |14|14|14|14|14|14|14| 14| 14| 14| 14| 14| 14| 14| 14| 14| 14| 14
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
60 |15|15|15|15|15|15|15| 15| 15| 15| 15| 15| 15| 15| 15| 15| 15| 15
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
64 |16|16|16|16|16|16|16| 16| 16| 16| 16| 16| 16| 16| 16| 16| 16| 16
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
68 |17|17|17|17|17|17|17| 17| 17| 17| 17| 17| 17| 17| 17| 17| 17| 17
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
72 |18|18|18|18|18|18|18| 18| 18| 18| 18| 18| 18| 18| 18| 18| 18| 18
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
76 |19|19|19|19|19|19|19| 19| 19| 19| 19| 19| 19| 19| 19| 19| 19| 19
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
80 |20|20|20|20|20|20|20| 20| 20| 20| 20| 20| 20| 20| 20| 20| 20| 20
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---
Lead | | | | | | | | | | | | | | | | | |
Screw |3.|4.|5.|6.|7.|8.|9.|10.|11.|12.|13.|14.|15.|16.|17.|18.|19.|20.
Pitch | | | | | | | | | | | | | | | | | |
------+--+--+--+--+--+--+--+---+---+---+---+---+---+---+---+---+---+---

EXAMPLE.--The lead screw has a pitch of 4, and I require to cut 13 threads per inch. At the head of the column is 16, and on a line with the 13 of the column, but on the left is 52, each number being marked by a * hence the 16 and 52 are the wheels; if we have not those wheels, multiply both by 2 and 32, and 104 will answer.

If the pitch of the lead screw is 2 threads per inch, the wheels must advance by 6 teeth, as indicated below:--

NUMBERS OF TEETH FOR WHEEL TO GO ON LATHE STUD, LATHE SPINDLE OR MANDRIL.

+-----+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| |Lead |12|18|24|30|36|42|48|54|60|66|72|78|84|90|96|
| |Screw. | | | | | | | | | | | | | | | |
|NUM- +--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
|BER | 12 | 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2| 2|
|OF | 18 | 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3| 3|
|TEETH| 24 | 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4| 4|
|FOR | 30 | 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5| 5|
|WHEEL| 36 | 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6| 6|
|TO | 42 | 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7| 7|
|GO | 48 | 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8| 8|
|ON | 54 | 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9| 9|
|LEAD | 60 |10|10|10|10|10|10|10|10|10|10|10|10|10|10|10|
|SCREW+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| |Pitch of| | | | | | | | | | | | | | | |
| |Lead | 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|
| |Screw. | | | | | | | | | | | | | | | |
+-----+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+

This table may be used for compound lathes by simply dividing the pitch of the lead screw by the ratio of the compounded pair of wheels. For example, for the wheels to cut 8 threads per inch, the pitch of lead screw being 4 and the compounded gears 2 to 1, as the ratio of the compounded pair is 2 to 1, we divide the pitch of lead screw by 2, which gives us 2, and we thus find the wheels in the column of pitch of lead screw 2, getting 12 and 48 as the required wheels, the 12 going on top of the lathe because it is at the top of the table, and the 48 on the lead screw because it is at the left-hand end of the table, and the lead screw gear is at the left-hand end of the lathe.

The table may be made for half threads as well as whole ones by simply advancing the left-hand column by two teeth, instead of by four, thus:--

+------+--------------------------------------------------------------+
|Teeth | Teeth for Wheel on Stud. |
| for |------+------+------+------+------+------+------+------+------+
|Wheel | | | | | | | | | |
| on | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 |
| Lead | | | | | | | | | |
|Screw.| | | | | | | | | |
+------+------+------+------+------+------+------+------+------+------+
| 12 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
+------+------+------+------+------+------+------+------+------+------+
| 14 | 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2| 3-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 16 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
+------+------+------+------+------+------+------+------+------+------+
| 18 | 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2| 4-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 20 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
+------+------+------+------+------+------+------+------+------+------+
| 22 | 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2| 5-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 24 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |
+------+------+------+------+------+------+------+------+------+------+
| 26 | 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2| 6-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 28 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |
+------+------+------+------+------+------+------+------+------+------+
| 30 | 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2| 7-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 32 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |
+------+------+------+------+------+------+------+------+------+------+
| 34 | 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2| 8-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 36 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 |
+------+------+------+------+------+------+------+------+------+------+
| 38 | 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2| 9-1/2|
+------+------+------+------+------+------+------+------+------+------+
| 40 |10 |10 |10 |10 |10 |10 |10 |10 |10 |
+------+------+------+------+------+------+------+------+------+------+
| 42 |10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|10-1/2|
+------+------+------+------+------+------+------+------+------+------+
|Pitch | | | | | | | | | |
| of | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10 |11 |
| Lead | | | | | | | | | |
|Screw.| | | | | | | | | |
+------+------+------+------+------+------+------+------+------+------+

For quarter threads we advance the left-hand column by one tooth, or for thirds of threads by three teeth, and so on.

If we require to find what wheels to provide for a lathe, we take the pitch of the lead screw for the numerator, and the pitch required for the denominator, and multiply them first by 2, then by 3, then by 4, and so on, continuing until the numerator or denominator is as large as it can be to give the required proportion of teeth, and not exceed the greatest number that the largest wheel can contain.

For example: A lathe has single gear, and its lead screw pitch is 8 per inch, what wheels will cut 18, 17, 16, 15, 14, or 13 threads per inch?

Wheels.

Pitch of lead screw 8 16 24 32
-- × 2 = -- -- --
Pitch required 18 36 54 72

Pitch of lead screw 8 16 24 32
-- " -- -- --
Pitch required 17 34 51 68

Pitch of lead screw 8 16 24 32
-- " -- -- --
Pitch required 16 32 48 64

Pitch of lead screw 8 16 24 32
-- " -- -- --
Pitch required 15 30 45 60

Pitch of lead screw 8 16 24 32
-- " -- -- --
Pitch required 14 28 42 56

Pitch of lead screw 8 16 24 32 40
-- " -- -- -- --
Pitch required 13 26 39 52 65

If we suppose that the greatest number of teeth permissible in one wheel is not to exceed 100, then in this table we have all the combinations of wheels that can be used to cut the given pitches; and having made out such a table, comprising all the pitches to be cut, we may select therefrom the least number of wheels that will cut those pitches. The whole table being made out it will be found, of course, that the numerators of the fractions are the same in each case; that is, in this case, 16, 18, 24, 32, and so on as far as we choose to carry the multiplication of the numerator. We shall also find that the denominators diminish in a regular order: thus taking the fractions whose numerators are in each case 16, we find their denominators are, as we pass down the column, 36, 34, 32, 30, 28, and 26, respectively, thus decreasing by 2, which is the number we multiplied the left-hand column by to obtain them. Similarly in the fractions whose numerators are 24, the denominators diminish by 3, being respectively 54, 51, 48, 45, 42, and 39; hence the construction of such a table is a very simple matter so far as whole numbered threads are concerned, as no multiplication is necessary save for the first line representing the finest pitch to be cut.

For fractional threads, however, instead of using the pitch of the lead screw for the numerator, we must reduce it to terms of the fraction it is required to cut. For example, for 5-1/2 threads we proceed as follows. The pitch of the lead screw is 8, and in 8 there are 16 halves, hence we use 16 instead of 8, and as in the 5-1/2 there are 11 halves we use the fraction 16/11 and multiply it first by 2, then by 3, and then by 4, and so on, obtaining as follows: 16/11, 32/22, 48/33, 64/44, obtaining as before three sets of wheels either of which will cut the required pitch. In selecting from such a table the wheels to cut any required number of pitches, the set must, in order to cut a thread of the same pitch as the lead screw, contain two wheels having the same number of teeth.

Now, suppose that the pitch of the lead screw was 6 instead of 8 threads per inch, and the table will be as follows:--

6 12 18 24
-- -- -- --
18 36 54 72

6 12 18 24
-- -- -- --
17 34 51 68

6 12 18 24
-- -- -- --
16 32 48 64

6 12 18 24
-- -- -- --
15 30 45 60

6 12 18 24
-- -- -- --
14 28 42 56

6 12 18 24
-- -- -- --
13 26 39 52

Here, again, we find that in the first vertical column the denominators decrease by two for each thread less per inch, in the second column they decrease by three, and in the third by four; this decrease equalling the number the first fraction was multiplied by.

But suppose the lead screw pitch is an odd one, as, say, 3 threads per inch, and we construct the table as before, thus--

Pitch of lead screw 3 6 9 12 15
-- -- -- -- --
Pitch to be cut 18 32 54 72 90

Now it is useless to multiply by 2 or by 3, because they give a less number of teeth than the smallest wheel should have, hence the first multiplier should be 4, giving the following table:--

3 12 15 18
-- -- -- ---
18 72 90 108

3 12 15 18
-- -- -- ---
17 68 85 102

3 12 15 18
-- -- -- --
16 64 80 96

3 12 15 18
-- -- -- --
15 60 75 90

By continuing the table for other pitches we shall find that in the first vertical column the denominators diminish by 4, the second column by 5, and the third by 6; and it is seen that by diminishing the pitch of the lead screw, we have rendered necessary one of two things, which is, that either larger wheels containing more teeth must be used, or the change gears must be compounded.

Assuming that the pitch of the lead screw was 5 per inch, the table would be as follows:--

5 15 20 25
-- × 3 = -- -- --
18 54 72 90

5 15 20 25
-- " -- -- --
17 51 68 85

5 15 20 25
-- " -- -- --
16 48 64 80

The wheels in the first column here decrease by 3, the second by 4, and the third by 5.

In nearly all lathes the advance or decrease is by 4 or by 6. In determining this rate of advance or decrease, there are several elements, among which are the following. Suppose the lathe to be geared without compounding, then the distance between the lathe spindle and the lead screw will determine what shall be the diameters of the largest and of the smallest wheel in the set, it being understood that the smallest wheel must not contain less than 12 teeth. Assume that in a given case the distance is 10 inches, and it is obvious that the pitch of the teeth at once commands consideration, because the finer the pitch the smaller the wheel that will contain 12 teeth, and the larger the wheel on the lead screw may be made. Of course the pitch must be coarse enough to give the required tooth strength.

Let it be supposed that the arc pitch is 3/4-inch, then the pitch circumference of a 12-toothed wheel would be 9 inches and its radius 1.432 in.; this subtracted from the 10 leaves 8.568 in. as the radius, or 17.136 in. as the largest diameter of wheel that can be used on the lead screw, supposing there to be no intermediate gears. Now a wheel of this diameter would be capable of containing more than 75 teeth, but less than 76. But from the foregoing tables it will be seen that it should contain a number of teeth divisible either by 4 or by 6 without leaving a remainder, and what that number should be is easily determined by means of a table constructed as before explained. Thus from the tables it would be found that 72 teeth would be best for a lead screw having a pitch of either 8, 6, 5, or 3 threads per inch, and the screw-cutting capacity of the lathe would (unless compounded) be confined to such pitches as may be cut with wheels containing between 12 and 72 teeth both inclusive.

But assume that an arc pitch of 3/8-inch be used for the wheel teeth, and we have as follows: A wheel of this pitch and containing 12 teeth will have a radius of 7-16/1000 inches, leaving 9.284 in. as the radius of the largest wheel, assuming it to gear direct with the 12-tooth pinion. With this radius it would contain 155 teeth and a fraction of a tooth; we must, therefore, take some less number, and from what has been said, it will be obvious that this lesser number should be one divisible by either 4 or 6. If made divisible by 6, the number will be 150, because that is the highest number less than 155 that is divisible by 6 without leaving a remainder. But if made divisible by 4, it may contain 152 teeth, because that number is divisible by 4 without leaving a remainder. With 150 teeth the latter could cut a thread 12-1/2 times as fine as the lead screw, because the largest wheel contains 12-1/2 times as many teeth as the smallest one; or it would cut a thread 12-1/2 times as coarse as the lead screw, if the largest wheel be placed on the mandril and the smallest on the lead screw. With 152 teeth the lathe would be able to cut a thread 12-84/100 times as fine or as coarse as the lead screw. Unless, however, the lathe be required to cut fractional pitches, it is unnecessary that the largest wheel have more teeth than divisible, without leaving a remainder, by the number of teeth in the smallest wheel, which being 12 we have 144 as the number of teeth for the largest wheel. In the United States standard pitches of thread, however, there are several pitches in fractions of an inch, hence it is desirable to have wheels that will cut these pitches.

LATHE SHEARS OR BEDS.--The forms of the shears and beds may be classified as follows.

The term shear is generally applied when the lathe is provided with legs, while the term bed is used when there are no legs; it may be noted, however, that by some workmen the two terms of _shear_ and _bed_ are used indiscriminately.

The forms of shears in use on common lathes are, in the United States, the raised [V], the flat shear and the shear, with the edge at an angle of 90° or with parallel edges. In England and on the continent of Europe, the flat shear is almost exclusively employed.

Referring to the raised [V] it possesses an important advantage in that, first, the slide rest does not get loosely guided from the wear; and second, the wear is in the direction that least affects the diameter of the work.

In Fig. 621, for example, is a section of a lathe shear, with a slide rest shown in place, and it will be observed that the wear of the [V] upon the lathe bed, and of the [V]-groove in the slide rest, will cause the rest to fall in the direction of arrow A, and that a given amount of motion in that direction will have less effect in altering the diameter than it would in any other direction. This is shown on the right hand of the figure as follows: Suppose the cutting point of the tool is at _a_, and the work will be of the diameter shown by the full circle in the figure. If we suppose the tool point to drop down to _f_, the work would be turned to the diameter denoted by dotted arc _g_, while if the tool were moved outwards from _a_ to _c_ the work would be turned to the diameter _e_. Now since _f_ and _c_ are equidistant from the point _a_, therefore the difference in the diameters of _e_ and _g_ represents the difference of effect between the wear letting the rest merely fall, or moving it outwards, and it follows that, as already stated, the diameter of the work is less affected by a given amount of wear, when this wear is in the direction of A, than when it is in the direction of B. When the carriage is held down by a weight as is shown in Figs. 577 and 578, there is therefore no lost motion or play in the carriage, which therefore moves steadily upon the shears, unless the pressure of the cut is sufficient in amount, and also in a direction to lift the carriage (as it is in the case of boring with boring tools); but to enable the carriage to remain firm upon the shears under all conditions, it is necessary to provide means to hold it down upon the [V]s, which is done by means of gibs G, G, which are secured to the carriage, and fit against the bottom of the bed flange as shown.

Now since lathes are generally used much more frequently on short than on long work, therefore the carriage traverses one part of the shears more than another, and the [V]s wear more at the part most traversed, and it follows that if gibs G are set to slide properly at some parts they will not be properly set at another or other parts of the length of the shears; hence the carriage will in some parts have liberty to move from the bed, there being nothing but the weight of the carriage, &c., to hold it down to the [V]s. Now, the wear in the direction of A acts directly to cause this inequality of gib fit, whereas that in the direction of B does so to a less extent, as will appear hereafter.

Meantime it may be noted that when the carriage is held down by a suspended weight the shears cannot be provided with cross girts, and are therefore less rigid and more subject to torsion under the strain of the cut; furthermore the amount of the weight must be sufficient to hold the carriage down under the maximum of cut, and this weight acts continuously to wear the [V]s, whether the carriage is under cutting duty or not, but the advantage of keeping the carriage firmly down upon the [V]s is sufficiently great to cause many to prefer the weighted carriage for light work driven between the lathe centres.

Fig. 622 represents the flat shear, the edges being at an angle and the fit of the carriage to the shears being adjusted by the gibs at _a_ _a_, which are set up by bolts _c_ _c_ and _d_ _d_. In this case there is a large amount of wearing surface at _b_ _b_, to prevent the fall of the carriage _c_, but the amount of end motion (in the direction of B, Fig. 621), permitted to the carriage by reason of the wear of the gibs and shear edges, is greater than the amount of the wear because of the edges being at an angle. It is true that the amount of fall of the carriage on the raised [V] is also (on account of the angle of the [V]) greater than the actual amount of the wear, but the effect upon the work diameter is in this case much greater, as will be readily understood from what has already been said. The wearing surface of the raised [V] may obviously be increased by providing broader [V]s, or two [V]s instead of having four. This would tend to keep the lathe in line, because the wear due to moving the tailblock would act upon those parts of the shear length that are less acted upon by the carriage, and since the front journal and bearing of the live spindle wear the most, the alignment of the lathe centres would be more nearly preserved.

Fig. 623 represents another form of parallel edged shears in which the fit of the carriage to the shears is effected at the front end only, the other or back edge being clear of contact with the carriage, but provided with a gib to prevent the carriage from lifting. This allows for any difference in expansion and contraction between the carriage and the shears, while maintaining the fit of the carriage to the bed.

A modification of this form (both these forms being taken from "Mechanics") is shown in Fig. 624, in which the underneath side of the front edge is beveled so that but one row of screws is required to effect the adjustment.

Fig. 625 represents a form of bed in which the fit adjustment is also made at the front end only of the bed, and there is a flange or slip at _a_, which receives the thrust outwards of the carriage; and a similar design, but with a bevelled edge, is shown in Fig. 626.

In Fig. 627 is shown a lathe shear with parallel edges, the fit being adjusted by a single gib D, set up by set-screws S. In this case the carriage will fall or move endwise, to an amount equal to whatever the amount of the wear may be, and no more, but it may be observed that in all the forms that admit of wear endways (that is to say in the direction of B in Fig. 621), the straightness of the shears is impaired in proportion as its edges are more worn at one part than at another.

A compromise between the flat and the raised [V]-shear is shown in Fig. 628, there being a [V]-guide on one side only, as at J. When the carriage is moved by mechanism on the front side of the lathe, and close to the [V], this plan may be used, but if the feed screw or other mechanism for traversing the carriage is within the two shears, the carriage should be guided at each end, or if the operating mechanism is at the back of the lathe, the carriage should be guided at the back end, if not at both ends.

In flat shear lathes the tailstock is fitted between the inside edges of the two shears, and the alignment of the tailstock depends upon maintaining a proper fit notwithstanding the wear that will naturally take place in time. The inside edges of the shears are sometimes tapered; this taper makes it much easier to obtain a correct fit of the tailstock to the shears, but at the same time more hard to move the tailstock along the bed. To remedy this difficulty, rollers are sometimes mounted upon eccentrics having journal bearing in the tailstock, so that by operating these eccentrics one half a turn, the rollers will be brought down upon the upper face of the shears, lifting the tailstock and enabling it to be easily moved along the bed to its required position.

In many of the watchmakers' lathes the outer edges are beveled off as in Fig. 629, the bearing surfaces being on the faces _b_ as well as on the edges _a_. As a result, edges _a_ are relieved of weight, and therefore to some extent of wear also, and whatever wear faces _b_ have helps the fit at _a_ _a_.

In the Barnes lathe, as in several other forms in which the lathe is made (as, for example, in screw-making lathes) the form of bed in Fig. 630 is employed. The tailblock may rest on the surfaces A, A´, B, C, D, and E, or as in the Barnes lathe the tailstock may fit to angles A B, but not to E D, while the carriage fits to B E, and C D, but not to A, the intention being to equalize the wear as much as possible.

The shears of lathes require to be as rigid as possible, because the pressure of the cut, as well as the weight of the carriage, slide rest, and tailstock, and of the work, tends to bend and twist them.

The pressure of the dead centre against the end of the work considered individually, is in a direction to bend the lathe shears upward, but the weight of the work itself acts in an opposite direction.

The strain due to the cut falls in a direction variable with the shape of the cutting tool, but mainly in a direction towards the operator, and, therefore, tending to twist the shears. To resist these strains, lathe shears are usually given the [I] form shown in the cuts.

Figs. 631 and 632 represent the ribbing in the Putnam Tool Company's lathe; a middle rib running the entire length, which greatly stiffens it.

The legs supporting lathe shears are, in lathes of ordinary length, placed at each end of the bed, so that the weight of the two heads, that of the work, and that of the carriage and slide rest, as well as the downward pressure of the cut, act combined to cause it to deflect or bend. It is necessary, therefore, in long beds to provide intermediate resting or supporting points to prevent this deflection.

Professor Sweet has pointed out that a lathe shears will be more truly supported on three than on four resting points, if the foundation on which the legs rest do not remain permanently level, and in lathes designed by him has given the right-hand end of the shears a single supporting point, as shown at _a_ in Fig. 633.

J. Richards in an article in "Engineering," has pointed out also that, when the lathe legs rest upon a floor that is liable from moving loads upon it to move its level, it is preferable that the legs be shaped as in Fig. 634, being narrowest at the foot, whereas when upon a permanent foundation, in which the foundation is intended to impart rigidity to the legs, they should be broader at the base, as in Fig. 635.

The rack on a lathe bed should be a cut one, and not simply a cast one, because when a cutting tool is running up to a corner as against a radial face, the self-acting motion must be stopped and the tool fed into the corner by hand. As a very delicate tool movement is required to cut the corner out just square, it should be capable of easy and steady movement, but in the case of cast racks, the rest will, from defects in the rack teeth, move in little jumps, especially if the pitch of the teeth be coarse. On the other hand it is difficult to cast fine pitches of teeth perfectly, hence the racks as well as the gear teeth should be cut gear and of fine pitch.

The tailblock of a lathe should be capable of easy motion for adjustment along the shears, or bed of the lathe, and readily fixable in its adjusted position. The design should be such as to hold the axial line of its spindle true with the axial line of the live spindle. If the lathe bed has raised [V]s there are usually provided two special [V]s for the tailblock to slide on, the slide rest carriage sliding on two separate ones. In this case the truth of the axial line of the tail spindle depends upon the truth of the [V]s.

If the lathe bed is provided with ways having a flat surface, as was shown in Fig. 622, the surfaces of the edges and of the projection are apt in time to wear, permitting an amount of play which gives room for the tailblock to move out of line. To obviate this, various methods are resorted to, an example being given in the Sellers lathe, Fig. 518.

In wood turners' lathes, where tools are often used in place of the dead centre, and in which a good deal of boring is done by such use of the tail spindle, it is not unusual to provide a device for the rapid motion of that spindle. Such a device is shown in Fig. 636; it consists of an arm A to receive the end C of the lever B, C being pivoted to A. The spindle is provided with an eye at E, the wheel W is removed and a pin passed through D and E, so that by operating the handle the spindle can be traversed in and out without any rotary motion of the screw.

When the tailblock of a lathe fits between the edges of the shears, instead of upon raised [V]s, it is sometimes the practice to give them a slight taper fitting accurately a corresponding taper on the edges of the shears. This enables the obtenance of a very good fit between the surfaces, giving an increased area of contact, because the surfaces can be filed on their bearing marks to fit them together; but this taper is apt to cause the tailstock to fit so tightly between the shears as to render it difficult to move it along them, and in any event the friction is apt to cause the fit to be destroyed from the wear. An excellent method of obviating these difficulties is by the employment of rollers, such as shown at R in Figs. 637 and 638, which represent the tailstock of the Putnam Tool Company's lathe. In some cases such rollers are carried on eccentric shafts so that they may be operated to lift the tailstock from the bed when moving it.