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Dynamic response of a single-mesh gear system with periodic mesh stiffness and backlash nonlinearity under uncertainty

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Abstract

Parametric uncertainties play a critical role in the response predictions of a gear system. However, accurately determining the effects of the uncertainty propagation in nonlinear time-varying models of gear systems is awkward and difficult. This paper improves the interval harmonic balance method (IHBM) to solve the dynamic problems of gear systems with backlash nonlinearity and time-varying mesh stiffness under uncertainties. To deal with the nonlinear problem including the fold points and uncertainties, the IHBM is improved by introducing the pseudo-arc length method in combination with the Chebyshev inclusion function. The proposed approach is demonstrated using a single-mesh gear system model, including the parametrically varying mesh stiffness and the gear backlash nonlinearity, excited by the transmission error. The results of the improved IHBM are compared with those obtained from the scanning method. Effects of parameter uncertainties on its dynamic behavior are also discussed in detail. From various numerical examples, it is shown that the results are consistent meanwhile the computational cost is significantly reduced. Furthermore, the proposed approach could be effectively applied for sensitivity analysis of the system response to parameter variations.

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Acknowledgements

The research work was supported by the Natural Science Foundation of China under Grant Nos. 11472170, 11632011, 51335006 and the China Postdoctoral Science Foundation under Grant No. 2016M601585.

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    S. Wei, X. J. Dong & Z. K. Peng

  2. Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, People’s Republic of China

    Q. K. Han & F. L. Chu

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  1. S. Wei
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  2. Q. K. Han
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  3. X. J. Dong
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  4. Z. K. Peng
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Correspondence to Z. K. Peng.

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Wei, S., Han, Q.K., Dong, X.J. et al. Dynamic response of a single-mesh gear system with periodic mesh stiffness and backlash nonlinearity under uncertainty. Nonlinear Dyn 89, 49–60 (2017). https://doi.org/10.1007/s11071-017-3435-z

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  • DOI: https://doi.org/10.1007/s11071-017-3435-z

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