Modern Machine-Shop Practice Part 47

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 f.l.a.n.g.e 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.

[Ill.u.s.tration: Fig. 620.]

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 ab.u.t.ting 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 bra.s.s 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 pa.s.s 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