General mathematical model of spiral bevel gears of continuous pure-rolling contact

Abstract

Sliding contact has negative influence for the performance of gears in most situations, such as frictional loss, pitting, micro-pitting, etc. To avoid sliding contact, this paper discusses the fundamental geometrical characteristics of spiral bevel gears of continuous pure-rolling contact. Differential geometry, gearing kinematics, and conjugate curve meshing method are used to derive the general mathematical model of spiral bevel gears of continuous pure-rolling contact. Simplified equations that continuous pure-rolling contact bevel gears must satisfy are derived. An example is represented to explain and verify this model. The theoretical results benefit further studies on design and manufacturing of spiral bevel gears of heavy loads and high efficiency.