The homotopy analysis for the nonlinear dynamics of planetary gear trains

Abstract

In this paper, the nonlinear oscillation of planetary gear trains is investigated by the homotopy analysis method. The nonlinearity of planetary gear trains due to the periodically time-varying mesh stiffness and contact loss are included. In contrast to the perturbation analysis, the homotopy analysis method is independent of the contact loss ratio, and then can be applied to both small and large contact loss ratios. In this article, firstly the closed-form approximations for the primary resonance, sub-harmonic resonance, and super-harmonic resonance are obtained by homotopy analysis method. The accuracy of homotopy analysis method solutions is evaluated by numerical integration simulations. Results indicate that with relatively large contact loss ratios, the amplitude–frequency curves obtained by homotopy analysis method agree better with the results obtained by numerical integration than those obtained by the method of multiple scales. This study lays a higher accurate foundation for more complex nonlinear dynamic analysis of planetary gear trains.

Keywords

Planetary gear trains homotopy analysis method nonlinear dynamics time-varying mesh stiffness contact loss

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