Machinery's Handbook, 31st Edition
Thread Cutting
2185
Inch Threads on Metric Lead-Screw Lathes:
driven gears driving gears
5 gearbox setting in mm pitch thds/in to be cut 127 #
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# Odd Metric Pitch Threads on Metric Lead-Screw Lathes:
Standard driven gear gearbox setting in mm pitch Standard driving gear mm pitch to be cut # #
driven gears driving gears
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Finding Accurate Gear Ratios.— Tables included in the 23rd and earlier editions of this Handbook furnished a series of logarithms of gear ratios as a quick means of finding ratios for all gear combinations having 15 to 120 teeth. The ratios thus determined could be factored into sets of 2, 4, 6, or any other even numbers of gears to provide a desired overall ratio. Although the method of using logarithms of gear ratios provides results of suitable accu racy for many gear-ratio problems, it does not provide a systematic means of evaluating whether other, more accurate ratios are available. In critical applications, especially in the design of mechanisms using reduction gear trains, it may be desirable to find many or all possible ratios to meet a specified accuracy requirement. The methods best suited to such problems use Continued Fractions and Conjugate Fractions as explained in the ADDITIONAL material in the Machinery’s Handbook 31 Digital Edition and illustrated in the worked-out example provided there for a set of four change gears. As an example, if an overall reduction of 0.31416 is required, a fraction must be found such that the factors of the numerator and denominator may be used to form a four-gear reduction train in which no gear has more than 120 teeth. By using the method of conju - gate fractions, the ratios listed above and their factors are found to be successively closer approximations to the required overall gear ratio. Ratio Numerator Factors Denominator Error Factors 11 ∕ 35 11 5 × 7 +0.00013 16 ∕ 51 2 × 2 × 2 × 2 3 × 17 − 0.00043 27 ∕ 86 3 × 3 × 3 2 × 43 − 0.00021 38 ∕ 121 2 × 19 11 × 11 − 0.00011 49 ∕ 156 7 × 7 2 × 2 × 3 × 13 − 0.00006 82 ∕ 261 2 × 41 3 × 3 × 29 +0.00002 224 ∕ 713 2 × 2 × 2 × 2 × 2 × 7 23 × 31 +0.000005 437 ∕ 1391 19 × 23 13 × 107 +0.000002 721 ∕ 2295 7 × 103 3 × 3 × 3 × 5 × 17 +0.000001 1360 ∕ 4329 2 × 2 × 2 × 2 × 17 3 × 3 × 13 × 53 +0.0000003 1715 ∕ 5459 5 × 7 × 7 × 7 53 × 103 +0.0000001 3927 ∕ 12500 3 × 7 × 11 × 17 2 × 2 × 5 × 5 × 5 × 5 × 5 0 Lathe Change-Gears.— To calculate the change gears to cut any pitch on a lathe, the “con stant” of the machine must be known. For any lathe, the ratio C : L = driver:driven gear, in which C = constant of machine and L = threads per inch. For example, to find the change gears required to cut 1.7345 threads per inch on a lathe having a constant of 4, the formula:
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