A general formulation for the calculation of the load sharing and transmission error under load of spiral bevel and hypoid gears

Abstract

This paper presents the basis of a Loaded Tooth Contact Analysis (LTCA) program predicting the motion error of spiral bevel gear sets under load, and explores some of the influences of the unloaded motion error curve shape and amplitude over the kinematical behaviour under load. The effects of tooth composite deflection caused by bending and shearing, tooth contact deformation and initial profile separation due to profile mismatch are considered in the development. Due to the complex geometry of spiral bevel gear teeth, the tooth bending stiffness is calculated by finite elements. Classical Hertz theory is used to calculate the contact deformation. Numerical examples are presented to illustrate the behaviour of spiral bevel gear motion error under load as the unloaded motion error is modified. Results show that under general circumstances, low contact ratio spiral bevel gears with parabolic unloaded motion error may produce undesirable kinematics under load, while parabolic motion error high contact ratio spiral bevel gears are likely to produce acceptable kinematics under a larger load range. It is also shown that the governing factors, in loaded motion error, are the contact ratio, thus combined mesh stiffness, and the amplitude of unloaded motion error curve which is linked to load sharing between adjacent tooth pairs.