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The Homotopy Analysis for the Nonlinear Dynamics of Planetary Gear Trains

[+] Author Affiliations
Chao Xun, Sujuan Jiao, Yong Chen, Xinhua Long

Shanghai Jiao Tong University, Shanghai, China

Paper No. DETC2018-85478, pp. V006T09A034; 9 pages
doi:10.1115/DETC2018-85478
From:
  • ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Quebec City, Quebec, Canada, August 26–29, 2018
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5183-8
  • Copyright © 2018 by ASME

abstract

In this paper, the homotopy analysis method (HAM) is proposed to study the nonlinear oscillators of planetary gear trains, in which the periodically time-varying mesh stiffness and gear backlash are included through a nonlinear displacement function. In contrast to the traditional perturbation methods, the HAM does not require a small parameter in the equation under study, and then can be applied to both of the weakly and strongly nonlinear problems. In this article, firstly the closed-form approximations for the dynamic response of planetary gear trains are obtained by HAM. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. The accuracy of HAM solutions is evaluated by numerical integration simulations. Results indicate that with large tooth separation times, the amplitude-frequency curves obtained by HAM agree better with the results obtained by NI than those obtained by the MMS.

Copyright © 2018 by ASME

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