As the carriage _C_ and the tool are moved by the lead-screw _S_ (see Fig. 2), which is geared to the spindle, the number of threads to the inch that are cut depends, in every case, upon the number of turns the work makes while the lead-screw is moving the carriage one inch. If the lead-screw has six threads per inch, it will make six revolutions while the carriage and the thread tool travel one inch along the piece to be threaded. Now if the change gears _a_ and _c_ (see also sketch _A_, Fig.

29) are so proportioned that the spindle makes the same number of revolutions as the lead-screw, in a given time, it is evident that the tool will cut six threads per inch. If the spindle revolved twice as fast as the lead-screw, it would make twelve turns while the tool moved one inch, and, consequently, twelve threads per inch would be cut; but to get this difference in speeds it is necessary to use a combination of gearing that will cause the lead-screw to revolve once while the lathe spindle and work make two revolutions.

[Ill.u.s.tration: Fig. 29. (A) Lathe with Simple Gearing for Thread Cutting. (B) Compound Geared Lathe]

Suppose that nine threads to the inch are to be cut and the lead-screw has six threads per inch. In this case the work must make nine revolutions while the lead-screw makes six and causes the carriage and thread tool to move one inch, or in other words, one revolution of the lead-screw corresponds to one and one-half revolution of the spindle; therefore, if the lead-screw gear _c_ has 36 teeth, the gear _a_ on the spindle stud should have 24 teeth. The spindle will then revolve one and one-half times faster than the lead-screw, provided the stud rotates at the same rate of speed as the main lathe spindle. The number of teeth in the change gears that is required for a certain pitch can be found by multiplying the number of threads per inch of the lead-screw, and the number of threads per inch to be cut, by the same trial multiplier. The formula which expresses the relation between threads per inch of lead-screw, threads per inch to be cut, and the number of teeth in the change gears, is as follows:

threads per inch of lead-screw teeth in gear on spindle stud ------------------------------ = ----------------------------- threads per inch to be cut teeth in gear on lead-screw

Applying this to the example given, we have 6/9 = 24/36. The values of 36 and 24 are obtained by multiplying 6 and 9, respectively, by 4, which, of course, does not change the proportion. Any other number could be used as a multiplier, and if gears having 24 and 36 teeth were not available, this might be necessary. For example, if there were no gears of this size, some other multiplier as 5 or 6 might be used.

Suppose the number of teeth in the change gears supplied with the lathe are 24, 28, 32, 36, etc., increasing by four teeth up to 100, and a.s.sume that the lead-screw has 6 threads per inch and that 10 threads per inch are to be cut. Then,

6 6 4 24 -- = ------ = -- 10 10 4 40

By multiplying both numerator and denominator by 4, we obtain two available gears having 24 and 40 teeth, respectively. The 24-tooth gear goes on the spindle stud and, the 40-tooth gear on the lead-screw. The number of teeth in the intermediate or "idler" gear _b_, which connects the stud and lead-screw gears, is not considered as it does not affect the ratios between gears _a_ and _c_, but is used simply to transmit motion from one gear to the other.

We have a.s.sumed in the foregoing that the spindle stud (on which gear _a_ is mounted) and the main spindle of the lathe are geared in the ratio of one to one and make the same number of revolutions. In some lathes, however, these two members do not rotate at the same speed, so that if equal gears were placed on the lead-screw and spindle stud, the spindle would not make the same number of revolutions as the lead-screw.

In that case if the actual number of threads per inch in the lead-screw were used when calculating the change gears, the result would be incorrect; hence, to avoid mistakes, the following general rule should be used as it gives the correct result, regardless of the ratios of the gears which connect the spindle and spindle stud:

_Rule.--First find the number of threads per inch that is cut when gears of the same size are placed on the lead-screw and spindle, either by actual trial or by referring to the index plate. Then place this number as the numerator of a fraction and the number of threads per inch to be cut, as the denominator; multiply both numerator and denominator by some trial number, until numbers are obtained which correspond to numbers of teeth in gears that are available._ The product of the trial number and the numerator (or "lathe screw constant") represents the gear _a_ for the spindle stud, and the product of the trial number and the denominator, the gear for the lead-screw.

=Lathes with Compound Gearing.=--When gearing is arranged as shown at _A_, Fig. 29, it is referred to as simple gearing, but sometimes it is necessary to introduce two gears between the stud and screw as at _B_, which is termed compound gearing. The method of figuring compound gearing is practically the same as that for simple gearing. To find the change gears used in compound gearing, place the "screw constant"

obtained by the foregoing rule, as the numerator, and the number of threads per inch to be cut as the denominator of a fraction; resolve both numerator and denominator into two factors each, and multiply each "pair" of factors by the same number, until values are obtained representing numbers of teeth in available change gears. (One factor in the numerator and one in the denominator make a "pair" of factors.)

Suppose the lathe cuts 6 threads per inch when gears of equal size are used, and that the number of teeth in the gears available are 30, 35, 40 and so on, increasing by 5 up to 100. If 24 threads per inch are to be cut, the screw constant 6 is placed in the numerator and 24 in the denominator. The numerator and denominator are then divided into factors and each pair of factors is multiplied by the same number to find the gears, thus:

6 2 3 (2 20) (3 10) 40 30 -- = ----- = ------------------- = ------- 24 4 6 (4 20) (6 10) 80 60

The last four numbers indicate the gears which should be used. The upper two having 40 and 30 teeth are the _driving_ gears and the lower two having 80 and 60 teeth are the _driven_ gears. The driving gears are gear _a_ on the spindle stud and gear _c_ on the intermediate stud, meshing with the lead-screw gear, and the driven gears are gears _b_ and _d_. It makes no difference which of the driving gears is placed on the spindle stud, or which of the driven is placed on the lead-screw.

=Fractional Threads.=--Sometimes the lead of a thread is given as a fraction of an inch instead of stating the number of threads per inch.

For example, a thread may be required to be cut, having 3/8-inch lead.

The expression "3/8-inch lead" should first be transformed to "number of threads per inch." The number of threads per inch (the thread being single) equals:

1 3 8 --- = 1 - = - = 2-2/3 3/8 8 3

To find the change gears to cut 2-2/3 threads per inch in a lathe having a screw constant of 8 and change gears varying from 24 to 100 teeth, increasing by 4, proceed as follows:

8 2 4 (2 36) (4 24) 72 96 ----- = --------- = ----------------------- = ------- 2-2/3 1 2-2/3 (1 36) (2-2/3 24) 36 64

As another ill.u.s.tration, suppose we are to cut 1-3/4 thread per inch on a lathe having a screw constant of 8, and that the gears have 24, 28, 32, 36, 40 teeth, etc., increasing by four up to one hundred. Following the rule:

8 2 4 (2 36) (4 16) 72 64 ----- = --------- = ----------------------- = ------- 1-3/4 1 1-3/4 (1 36) (1-3/4 16) 36 28

The gears having 72 and 64 teeth are the _driving_ gears, and those with 36 and 28 teeth are the _driven_ gears.

=Change Gears for Metric Pitches.=--When screws are cut in accordance with the metric system, it is the usual practice to give the lead of the thread in millimeters, instead of the number of threads per unit of measurement. To find the change gears for cutting metric threads, when using a lathe having an English lead-screw, first determine the number of threads per inch corresponding to the given lead in millimeters.

Suppose a thread of 3 millimeters lead is to be cut in a lathe having an English lead-screw and a screw constant of 6. As there are 25.4 millimeters per inch, the number of threads per inch will equal 25.4 3. Place the screw constant as the numerator, and the number of threads per inch to be cut as the denominator:

6 25.4 6 3 ------- = 6 ---- = ----- 25.4 3 25.4 ---- 3

The numerator and denominator of this fractional expression of the change-gear ratio are next multiplied by some trial number to determine the size of the gears. The first whole number by which 25.4 can be multiplied so as to get a whole number as the result is 5. Thus, 25.4 5 = 127; hence, one gear having 127 teeth is always used when cutting metric threads with an English lead-screw. The other gear required in this case has 90 teeth. Thus:

6 3 5 90 --------- = --- 25.4 5 127

Therefore, the following rule can be used to find the change gears for cutting metric pitches with an English lead-screw:

_Rule.--Place the lathe screw constant multiplied by the lead of the required thread in millimeters multiplied by 5, as the numerator of the fraction, and 127 as the denominator. The product of the numbers in the numerator equals the number of teeth for the spindle-stud gear, and 127 is the number of teeth for the lead-screw gear._

If the lathe has a metric pitch lead-screw, and a screw having a given number of threads per inch is to be cut, first find the "metric screw constant" of the lathe or the lead of thread in millimeters that would be cut with change gears of equal size on the lead-screw and spindle stud; then the method of determining the change gears is simply the reverse of the one already explained for cutting a metric thread with an English lead-screw.

_Rule.--To find the change gears for cutting English threads with a metric lead-screw, place 127 in the numerator and the threads per inch to be cut, multiplied by the metric screw constant multiplied by 5, in the denominator; 127 is the number of teeth on the spindle-stud gear and the product of the numbers in the denominator equals the number of teeth in the lead-screw gear._

=Quick Change-gear Type of Lathe.=--A type of lathe that is much used at the present time is shown in Fig. 30. This is known as the quick change-gear type, because it has a system of gearing which makes it unnecessary to remove the change gears and replace them with different sizes for cutting threads of various pitches. Changes of feed are also obtained by the same mechanism, but the feeding movement is transmitted to the carriage by the rod _R_, whereas the screw _S_{1}_ is used for screw cutting. As previously explained, the idea of using the screw exclusively for threading is to prevent it from being worn excessively, as it would be if continually used in place of rod _R_, for feeding the carriage when turning.

[Ill.u.s.tration: Fig. 30. Lathe having Quick Change-gear Mechanism]

[Ill.u.s.tration: Fig. 31. End and Side Views of Quick Change-gear Mechanism]

The general construction of this quick change gear mechanism and the way the changes are made for cutting threads of different pitch, will be explained in connection with Figs. 30, 31 and 32, which are marked with the same reference letters for corresponding parts. Referring to Fig.

30, the movement is transmitted from gear _s_ on the spindle stud through idler gear _I_, which can be moved sidewise to mesh with either of the three gears _a_, _b_ or _c_, Fig. 31. This cone of three gears engages gears _d_, _e_ and _f_, any one of which can be locked with shaft _T_ (Fig. 32) by changing the position of k.n.o.b _K_. On shaft _T_ there is a gear _S_ which can be moved along the shaft by hand lever _L_ and, owing to the spline or key _t_, both the sliding gear and shaft rotate together. Shaft _T_, carrying gears _d_, _e_ and _f_ and the sliding gear _S_, is mounted in a yoke _Y_, which can be turned about shaft _N_, thus making it possible to lower sliding gear _S_ into mesh with any one of a cone of eight gears _C_, Fig. 31. The shaft on which the eight gears are mounted has at the end a small gear _m_ meshing with gear _n_ on the feed-rod, and the latter, in turn, drives the lead-screw, unless gear _o_ is shifted to the right out of engagement, which is its position except when cutting threads.

[Ill.u.s.tration: Fig. 32. Sectional Views of Quick Change-gear Mechanism]

With this mechanism, eight changes for different threads or feeds are obtained by simply placing gear _S_ into mesh with the various sized gears in cone _C_. As the speed of shaft _T_ depends on which of the three gears _d_, _e_ and _f_ are locked to it, the eight changes are tripled by changing the position of k.n.o.b _K_, making twenty-four. Now by shifting idler gear _I_, three speed changes may be obtained for gears _a_, _b_ and _c_, which rotate together, so that the twenty-four changes are also tripled, giving a total of seventy-two variations without removing any gears, and if a different sized gear _s_ were placed on the spindle stud, an entirely different range could be obtained, but such a change would rarely be necessary. As shown in Fig. 30, there are eight hardened steel b.u.t.tons _B_, or one for each gear of the cone _C_, placed at different heights in the casing. When lever _L_ is shifted sidewise to change the position of sliding gear _S_, it is lowered onto one of these b.u.t.tons (which enters a pocket on the under side) and in this way gear _S_ is brought into proper mesh with any gear of the cone _C_. To shift lever _L_, the handle is pulled outward against the tension of spring _r_ (Fig. 32), which disengages latch _l_ and enables the lever to be lifted clear of the b.u.t.ton; yoke _Y_ is then raised or lowered, as the case may be, and lever _L_ with the sliding gear is shifted laterally to the required position.

[Ill.u.s.tration: Fig. 33. Index Plate showing Position of Control Levers for Cutting Threads of Different Pitch]

The position of lever _L_ and k.n.o.b _K_ for cutting threads of different pitches is shown by an index plate or table attached to the lathe and arranged as shown in Fig. 33. The upper section _a_ of this table shows the different numbers of threads to the inch that can be obtained when idler gear _I_ is in the position shown by the diagram _A_. Section _b_ gives the changes when the idler gear is moved, as shown at _B_, and, similarly, section _c_ gives the changes for position _C_ of the idler.

The horizontal row of figures from 1 to 8 below the word "stops"

represents the eight positions for lever _L_, which has a plate _p_ (Fig. 30) just beneath it with corresponding numbers, and the column to the left shows whether k.n.o.b _K_ should be out, in a central position, or in.

In order to find what the position of lever _L_ and k.n.o.b _K_ should be for cutting any given number of threads to the inch, find what "stop"

number is directly above the number of threads to be cut, which will indicate the location of lever _L_, and also what position should be occupied by k.n.o.b _K_, as shown in the column to the left. For example, suppose the lathe is to be geared for cutting eight threads to the inch.

By referring to section a we see that lever _L_ should be in position 4 and k.n.o.b _K_ in the center, provided the idler gear _I_ were in position _A_, as it would be ordinarily, because all standard numbers of threads per inch (U. S. standard) from 1/4 inch up to and including 4 inches in diameter can be cut with the idler gear in that position. As another ill.u.s.tration, suppose we want to cut twenty-eight threads per inch. This is listed in section _c_, which shows that lever _L_ must be placed in position 3 with k.n.o.b _K_ pushed in and the idler gear shifted to the left as at _C_.

The simplicity of this method as compared with the time-consuming operation of removing and changing gears is apparent. The diagram _D_ to the right shows an arrangement of gearing for cutting nineteen threads per inch. A 20-tooth gear is placed on the spindle stud (in place of the regular one having 16 teeth) and one with 95 teeth on the lead-screw, thus driving the latter direct as with ordinary change gears. Of course it will be understood that the arrangement of a quick change-gear mechanism varies somewhat on lathes of different make.

CHAPTER V

TURRET LATHE PRACTICE

Turret lathes are adapted for turning duplicate parts in quant.i.ty. The characteristic feature of a turret lathe is the turret which is mounted upon a carriage and contains the tools which are successively brought into the working position by indexing or rotating the turret. In many instances, all the tools required can be held in the turret, although it is often necessary to use other tools, held on a cross-slide, for cutting off the finished part, facing a radial surface, knurling, or for some other operation. After a turret lathe is equipped with the tools needed for machining a certain part, it produces the finished work much more rapidly than would be possible by using an ordinary engine lathe, princ.i.p.ally because each tool is carefully set for turning or boring to whatever size is required and the turret makes it possible to quickly place any tool in the working position. Turret lathes also have systems of stops or gages for controlling the travel of the turret carriage and cross-slide, in order to regulate the depth of a bored hole, the length of a cylindrical part or its diameter; hence, turning machines of this type are much more efficient than ordinary lathes for turning duplicate parts, unless the quant.i.ty is small, in which case, the advantage of the turret lathe might be much more than offset by the cost of the special tool equipment and the time required for "setting up" the machine. (See "Selecting Type of Turning Machine.")

[Ill.u.s.tration: Fig. 1. Bardons & Oliver Turret Lathe of Motor-driven Geared-head Type]