The homotopy analysis for the nonlinear dynamics of planetary gear trains

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 analy...

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Bibliographic Details
Published in:Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Journal of mechanical engineering science, 2020-08, Vol.234 (16), p.3154-3165
Main Authors: Xun, Chao, Jiao, Sujuan, Dai, He, Long, Xinhua
Format: Article
Language:English
Subjects:
Computer simulation
Contact loss
Finite element method
Gear trains
Multiscale analysis
Nonlinear analysis
Nonlinear dynamics
Nonlinearity
Numerical integration
Perturbation methods
Resonance
Stiffness
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Summary: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.
ISSN:0954-4062
2041-2983
DOI:10.1177/0954406220913327