Dynamics of a hypoid gear pair considering the effects of time-varying mesh parameters and backlash nonlinearity

A generalized nonlinear time-varying (NLTV) dynamic model of a hypoid gear pair with backlash nonlinearity is formulated which is also applicable to spur, helical, spiral bevel and worm gears. Firstly, the fundamental harmonic form of time-varying mesh parameters is used to study the effects of mesh parameter variations on the dynamic response, and the interactions between them and backlash nonlinearity. The analysis also examines the effects of mean load and mesh damping. Secondly, based on a three-dimensional quasi-static tooth contact analysis, a new significantly more exact time-varying mesh model is proposed, which describes the true mesh characteristics of hypoid gear pairs. The enhanced time-varying mesh model is applied to perform further dynamic analysis. Computational results reveal numerous interesting nonlinear characteristics, such as jump discontinuities, sub-harmonic and chaotic behaviors, especially for lightly loaded and lightly damped cases.