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Quasi-static analysis of the nonlinear behavior of a railway vehicle gear system considering time-varying and stochastic excitation

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Abstract

The gearboxes of machines generally operate under a time-varying state rather than under steady-state conditions. However, it is difficult to investigate the nonlinear dynamics of a time-varying gear system. A gear system model of a railway vehicle was proposed in consideration of its time-varying mesh stiffness, nonlinear backlash, transmission error, time-varying external excitation, and rail irregularity. To obtain the nonlinear behaviors of a time-varying stochastic gear system, a quasi-static analysis was performed to observe its doubling-periodic bifurcation, chaotic motion, and transition from a lower to a higher power periodic motion. Based on the energy comparison results, the time-varying stochastic gear system was degraded to a time-varying system to simplify the calculation. Furthermore, the nonlinear response of the time-varying system was computed using the Runge–Kutta method and was compared with the results of a quasi-static analysis that employed a short-time Fourier transform method. The results of the quasi-static analysis were consistent with the results of the time–frequency analysis for the time-varying gear system except for the result at 3180 r/min, which represented a short period wherein the process transitioned to chaos. Hence, the comparison demonstrates the applicability of the quasi-static analysis for the nonlinear behavior analysis of a time-varying stochastic system.

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Acknowledgements

The authors are very grateful to the six reviewers and the editors for their valuable comments and suggestions that have helped improve this paper. This paper has been supported by Great Scholars Training Project (CIT&TCD20150312), Open Research Fund Program of Beijing Key Laboratory of Performance Guarantee on Urban Rail Transit Vehicles (06080915001), Beijing Recognized Talent Project (2014018), and National Natural Science Foundation of China (51175028). Besides, the first author would like to thank his wife, Yunlei Lin, for her continued love and support.

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Authors and Affiliations

  1. School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, No. 3 Shang Yuan Cun, Hai Dian District, Beijing, 100044, China

    Jinhai Wang, Jianwei Yang & Qiang Li

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  1. Jinhai Wang
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  2. Jianwei Yang
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  3. Qiang Li
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Correspondence to Jianwei Yang.

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Wang, J., Yang, J. & Li, Q. Quasi-static analysis of the nonlinear behavior of a railway vehicle gear system considering time-varying and stochastic excitation. Nonlinear Dyn 93, 463–485 (2018). https://doi.org/10.1007/s11071-018-4204-3

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  • DOI: https://doi.org/10.1007/s11071-018-4204-3

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