Consider a pair of standard, 12 diametral pitch, 20 degree pressure angle steel

Question

Consider a pair of standard, 12 diametral pitch, 20 degree pressure angle steel gears with a 1 inch face width. The pinion has 20 teeth and the mating gear has 42 teeth. When installed at the nominal center distance, the pinion exhibits 1/2 degree angular backlash. For both nominal center distance installation and 1/16 inch larger center distance installation, estimate the average gear rotational speed ratios (more commonly called the gear ratio) gear ratio variations pinion and gear pitch diameters pinion and gear base circle diameters pressure angles backlashes. Technical notes from a manufacturer such as Boston Gear may help. Cite your source. Also be careful with units; backlash may be expressed in angular units or linear units. Please convert your final answer to angular units, as given. Estimate the minimum center distance which is possible for the two gear assembly without causing some interference?

Explanation / Answer

i) gear ratio = input speed / output speed = N2/N1 = D1/D2 = T1/T2 = 20 / 42 = 0.476

ii) gear ratio variation is gue to the 1/2 degree angular backlash.

iii) module = D/T = 1/diametral pitch = 1/12

so, pitch dia of pinion = 20/12 = 1.67

and pitch dia of gear = 42/12 = 3.5

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