Machinery's Handbook, 31st Edition
2182 Thread Cutting 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 met - ric threads, when using a lathe having an inch 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 inch 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: . . . 3 254 6 6 3 254 254 6 3 ÷ × = = The numerator and denominator of this fractional expression of the change gear ratio is 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 inch lead screw. The other gear required has 90 teeth. Thus: 25.4 5 6 3 5 127 90 # # # = Therefore, the following rule can be used to find the change gears for cutting metric pitches with an inch lead screw: Rule: Place the lathe screw constant multiplied by the lead of the required thread in mil limeters 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 inch lead screw. Rule: To find the change gears for cutting inch threads with a metric lead screw, place 127 in the numerator and the threads per inch to be cut, multiplied by the metric screw con stant 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. Threads per Inch Obtained with a Given Combination of Gears.— To determine the num- ber of threads per inch that will be obtained with a given combination of gearing, multiply the lathe screw constant by the number of teeth in the driven gear (or by the product of the numbers of teeth in both driven gears of compound gearing), and divide the product thus obtained by the number of teeth in the driving gear (or by the product of the two driving gears of a compound train). The quotient equals the number of threads per inch. Change Gears for Fractional Ratios.— When gear ratios cannot be expressed exactly in whole numbers that are within the range of ordinary gearing, the combination of gearing required for the fractional ratio may be determined quite easily, often by the “cancella - tion method.” To illustrate this method, assume that the speeds of two gears are to be in the ratio of 3.423 to 1. The number 3.423 is first changed to 3423 ∕ 1000 to clear it of decimals. Then, in order to secure a fraction that can be reduced, 3423 is changed to 3420;
1000 3420
100 342 = =
2 50 3 2 57 × × ×
1 50 3 57 × ×
=
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