Machinery's Handbook, 31st Edition
Thread Cutting
2181
Lathe Change Gears Change Gears for Thread Cutting.— To determine the change gears to use for cutting a thread of given pitch, first find what number of threads per inch will be cut when gears of the same size are placed on the lead screw and spindle stud, either by trial or by referring to the index plate; then multiply this number, called the “lathe screw constant,” by some trial number to obtain the number of teeth in the gear for the spindle stud, and multiply the threads per inch to be cut by the same trial number to obtain the number of teeth in the gear for the lead screw. Expressing this rule as a formula: Trial number threads per inch to be cut Trial number lathe screw constant teeth in gear on leadscrew teeth in gear on spindle stud × × = For example, suppose the available change gears supplied with the lathe have 24, 28, 32, 36 teeth, etc., the number increasing by 4 up to 100, and that 10 threads per inch are to be cut in a lathe having a lathe screw constant of 6; then, if the screw constant is written as the numerator, the number of threads per inch to be cut as the denominator of a fraction, and both numerator and denominator are multiplied by some trial number, say, 4, it is found that gears having 24 and 40 teeth can be used. Thus: 10 6 10 4 6 4 = The 24-tooth gear goes on the spindle stud and the 40-toothgear on the lead screw. The lathe screw constant is, of course, equal to the number of threads per inch on the lead screw, provided the spindle stud and spindle are geared in the ratio of 1 to 1, which, however, is not always so. 40 24 # # = Compound Gearing.— To find the change gears used in compound gearing, place the screw constant as the numerator and the number of threads per inch to be cut as the denom inator 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 suitable numbers of teeth for the change gears. (One factor in the numerator and one in the denominator make a “pair” of factors.) Example: —1 3 ∕ 4 threads per inch are to be cut in a lathe having a screw constant of 8; the available gears have 24, 28, 32, 36, 40 teeth. etc., increasing by 4 up to 100. Following the rule: = 1 4 3 8 2 × 4 1 4 1 3 × = (2 × 36) × (4 × 16) (1 × 36) × ( × 16) 1 4 3 72 × 64 = 36 × 28 The gears having 72 and 64 teeth are the driving gears and those with 36 and 28 teeth are the driven gears. 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:
8 3 1 1
8 3
3 8 2
3 2
÷ =
= =
To find the change gears to cut 2 2 ∕ 3 threads per inch in a lathe having a screw constant 8 and change gears ranging from 24 to 100 teeth, increasing in increments of 4, proceed as below: = 2 3 2 8 2 × 4 2 3 1 2 × = (2 × 36) × (4 × 24) (1 × 36) × ( × 24) 2 3 2 72 × 96 = 36 × 64
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