A Descriptive Geometry-Based Solution to a Geometrical Problem in Rotary Shaving of a Shoulder Pinion

Abstract

A novel descriptive-geometry-based (DGB) approach for determining of limitation on parameters of rotary shaving operation of shoulder gear is reported in the paper. The paper covers determination: (a) of the maximum feasible outside diameter of the shaving cutter; (b) of the minimum required overlap in rotary shaving operation; and (c) of the minimum required face-width of the shaving cutter. Insufficiency of location, and migration of the pivot point is investigated as well. It is proven that instead of consideration of the pivot point itself, it is required to consider size and relative disposition of the auxiliary rack of the pinion, and of the auxiliary rack of the shaving cutter. The developed solution is the exact and not an approximate one. Due to that it is still valid for any value of the crossed-axis angle, even in cases where it exceeds 10 deg. The results are valid for all four basic methods of rotary shaving. Application of the results enables avoiding of the pinion tooth bias. Taken as a whole, the topic covered in this paper will enable one determination of proper values of parameters (a) through (c) of rotary shaving operation, which are the dominating limiting factors of rotary shaving operation. The developed DGB approach can be readily put into practice.