This section is from the book "Machine Shop Work", by Frederick W. Turner, Oscar E. Perrigo, Howard P. Fairfield. Also available from Amazon: Machine shop work.
When the proper ratio cannot be obtained by the use of the change-gears at hand, or when the gears of the desired numbers of teeth would be too small to connect properly, or too large to put in place, the method called compounding is used. Assume that the ratio of 4 to 1 is required Referring to Fig. 98, a 36-toothed gear J is placed on the stud shaft, and a 72-toothed gear L on the lead-screw. On the sleeve stud are two gears, a 48-and a 24-toothed, fixed to each other by placing them on a splined compounding sleeve which runs loosely on the stud. The 36-gear is engaged with the 48-, and the 24- with the 72-toothed gear, as shown. Front and edge views of these gears are given to show clearly their relative positions.
The results of this combination are: If the 36-gear engaged the 72-gear, the ratio would be 2; and if the 24-gear engaged the 48-gear, the ratio would also be 2. These ratios multiplied would be 4, as required. As shown, the ratios are: 36 to 48, ratio l 1/3; and 24 to 72. ratio 3-which ratios multiplied together produce 4.
The effect, then, of introducing the 24- and 48-gears instead of a single intermediate (usually called an idler gear, as it does not affect ratios), is to double the ratio existing between the gear on the stud shaft and the gear on the lead-screw. The combination just described will cut a 16-pitch thread on a lathe having a 4-pitch lead-screw. (Usually a lathe will cut this thread without compounding. The gears shown and described are given merely as a simple example.)
Should the above order of arranging the gears be reversed, the effect will be to divide the thread ratio instead of multiplying it; and instead of cutting 16 threads per inch, the lead-screw threads of 4 to an inch will be divided by 4, producing 1, and the lathe will cut 1 thread per inch.
Lathes are usually provided with compounding gears of the ratios of 2 to 1-as 24 to 48, 36 to 72, and so on. But it is very convenient to have those of 3 to 1-as 24 to 72, 36 to 108, etc.
Fig. 99. End and Front Elevation of Rapid Change-Gear Device.
It is always advisable to use as large change-gears as possible, as the revolutions of the lead-screw will be more regular and steady, the strain on the gear teeth will be less, and smoother and more accurate work will result.