ROBERT GIBSON GRISWOLD

Perhaps the one feature above all others that makes the engine lathe so valuable and the " king of machine tools, " is its power of screw cutting. By means of the lead screw which is shown running along the front of the bed in the illustration given in Chapter I, the carriage, carrying the threading tool, may be moved along the ways at a predetermined rate, and the groove cut by the point of the tool will have a definite pitch per unit of length.

The lead screw is caused to revolve by a series of gears placed on adjustable studs at the left hand of the lathe-bed. These gears, shown piled one above the other on the floor, are called the "change gears, " and bear such a relation to one another that certain standard threads may be cut by their aid, and, by compounding them, many fine and fractional threads may be produced.

The formula for calculating the correct gears to use for cutting a certain thread is interesting, of value, and well worth the time in becoming acquainted with it. All lead screws are cut with a certain number of threads per inch; in small lathes it may be 10, while in larger types the pitch may be 5, 4, or even two threads per inch. Owing to the fact that a split nut has been provided in the apron of the tool carriage whereby the carriage may be moved along the ways when it is closed around the lead screw, this rate of movement may be modified by controlling ratio between the revolutions of the spindle and lead screw.

, Suppose that the lead screw has ten threads per inch ; one revo ution of the screw would move the carriage 1-10 in.; two revolutions 2-10, a half revolution would move it 1-20, and soon. If we have a piece between the centers upon which we wish to cut a thread of ten pitch, and the lead screw is provided with ten threads per inch, it is evident that if the spindle and screw revolve in unison the tool will be moved along the surface of the piece at the rate of 1-10 in. But perhaps we wish to cut fifteen threads per inch. In this case the lead screw must not advance the carriage so rapidly, but while the spindle is making fifteen revolutions, the lead screw must make only ten, so that the carriage will be moved just 1 in. The ratio of the revolutions, therefore, is 15 : 10 or 3 : 2. Now, if we placed a gear having 20 teeth on the spindle, and another having 30 teeth on the lead screw, the spindle would revolve three times while the lead screw' was revolving twice, since 3 x 20=2 x 30.

We are now in a position to derive our formula which may be applied to any lathe, and the amateur may make up his thread table for any number of threads within the capacity of the change gears. As we learned above, the number of threads cut depends upon the ratio existing between the revolutions of the spindle and those of the lead screw, and its pitch of thread. When the pitch to be cut is the same as that of the lead screw, the number of teeth in the spindle gear and those in the lead-screw gear must be the same. An idler gear placed between these two gears in no way affects their ratios of revolutions, but simply alters the direction of revolution. Therefore, the Pitch to be cut : Pitch of lead screw : : No. teeth in lead-screw gear : No. teeth in the spindle gear.

The ratios between the two pitches and the teeth of the two gears are inversely proportional. Then

Let p=pitch to be cut.

Lp = pitch of the lead screw.

Gl = number of teeth in the lead-screw gear.

Gs = number of teeth in the spindle gear.

Then P/LP = G1/Gs , and G1 = Gs X p / Lp

In this formula, three of the quantities maybe either determined or assumed, and by simple proportion the the fourth may be readily found. First determine the pitch of the lead-screw by counting the number of threads per inch ; then make a list of every gear that comes with the lathe. By simply substituting the different numbers of teeth in the formula, a table may be readily formed for every possible thread that can be out by this simple train of gears. This is what is known as simple gearing, and the rule may be expressed as follows:

"Where the spindle gear is either driven on the spindle direct, or on a separate stud that revolves in unison with the spindle, to cut a given number of threads per inch, select a certain gear for this stud; multiply the number of its teeth by the pitch to be. cut, and divide this product by the pitch of the lead screw; the quotient will be the number of teeth necessary in the lead-screw gear." Should this number be fractional, which would give a fractional number of teeth and is impossible, select some other gear for the spindle gear and repeat the operation until some gear is found that will give an even number of teeth for the lead-screw gear and one that is contained in the set.

You may readily reverse this process by selecting the gear for the lead-screw, multiply the number of teeth by the pitch of the lead screw, and divide this product by the number of theads per inch which you wish to cut. The quotient will be the number of teeth required in the spindle gear.

If the number of teeth in the gears supplied with the lathe increase by a constant number, that is, if the smallest gear has 20 teeth, the next largest 24, the next 28, 32, 36, etc., it is readily seen that the constant number by which they vary is 4; multiply 4, or any multiple of 4, by the number of threads per inch in the lead-screw. The product thus found will be the number of teeth in the spindle gear. Then multiply the same constant by the number of threads that you wish to cut, and this product will be the required number of teeth in the lead-screw gear.

It sometimes happens that the various makers of lathes adopt different methods of driving the first or spindle gear. Some place it directly on the tail of the spindle, others place it directly below, driving through a pair of spur gears, while others use a train of gears and alter the ratio of these gears from 1 :1 to 1 :2 or 2 : 3, thus making the spindle-gear setud revolve more slowly than the spindle.