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Nonlinear dynamics analysis of gear system considering time-varying meshing stiffness and backlash with fractal characteristics

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Abstract

The microscopic topography of tooth surface affects the nonlinear dynamic characteristics of the gear system. However, few studies have fully taken into account the effects of microscopic topography on time-varying meshing stiffness (TVMS) and backlash in gear dynamics. In this context, this study derives TVMS and time-varying backlash with fractal characteristics based on fractal theory and introduced them into a 6-DOF nonlinear dynamic model. With various nonlinear dynamics analysis tools, the dynamic characteristics of the gear system under different fractal parameters are investigated. The results indicate that the increase in the fractal dimension or the decrease in the characteristic scale coefficient leads to a smoother tooth surface, larger TVMS, and smaller amplitude of backlash. The effect of fractal dimension is more sensitive than characteristic scale coefficient. Furthermore, in the low-speed region, the increase in fractal dimension has a positive effect on the dynamic response of the system and can reduce the amplitude of dynamic transmission error. In the high-speed region, the opposite is true. It is worth pointing out that the influence of fractal dimension on gear dynamic characteristics is nonlinear. Considering the machining cost and dynamic response of gear, the fractal dimension of 1.5 is the best choice. The influence of characteristic scale coefficient on system dynamics is similar to that of fractal dimension, but the intensity is much weaker.

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The authors declare that the data supporting the findings of this study are available within the article.

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Funding

This work is supported in part by the National Natural Science Foundation of China (52175122 and 52075456), the Sichuan Science and Technology Program (2023NSFSC0362 and 2023NSFSC0371), and the Sichuan Province Innovative Talent Funding Project for Postdoctoral Fellows (BX202214).

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Authors and Affiliations

  1. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Heng Xia, Fanshan Meng, Xin Zhang, Jiaxu Wang & Yulin Jin

  2. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, 400044, People’s Republic of China

    Jiaxu Wang

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  1. Heng Xia
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  2. Fanshan Meng
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  3. Xin Zhang
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  4. Jiaxu Wang
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by HX, FSM and XZ. Review and editing were performed by XZ, JXW and YLJ. The first draft of the manuscript was written by HX and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Xin Zhang.

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Xia, H., Meng, F., Zhang, X. et al. Nonlinear dynamics analysis of gear system considering time-varying meshing stiffness and backlash with fractal characteristics. Nonlinear Dyn 111, 14851–14877 (2023). https://doi.org/10.1007/s11071-023-08649-7

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