a pinion with the number of teeth N of 20 meshes........?

Question

a pinion with the number of teeth N of 20 meshes with a gear having a number of teeth N2 of 55. The spur gear set has the diametral pitch P of 6 teeth per inch. Determine the pinion d1 pitch diameter and the gear d2 pitch diameter.

Answer 1

For known diametral pitch (6 per inch), Pitch diameter is number of teeth divided by diametral pitch.

Therefore - pitch diameter for 20 teeth is 20/6 or 3.333 inches

Pitch diameter for 55 teeth is 55/6 or 9.167 inches.

Note that the pitch diameter is a theoretical value; it cannot be physically measured from the gear itself. It is the effective diameter used to calculate torques and reaction forces for the gear system, using the pressure angle for the patricular type of involute tooth system being used.