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Nonlinear dynamic characteristics of a spur gear pair considering extended tooth contact and coupling effect between gear neighboring teeth

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Abstract

The bifurcation of the gear transmission system is very important for the stability and safety characteristics of the system from the perspective of nonlinear dynamics. Meanwhile, the extended tooth contact and the coupling effect between gear neighboring teeth are focused on the establishment of the dynamic models of the gear transmission system. However, there has been nearly no literature revealing the effect of the extended tooth contact and the coupling effect between gear neighboring teeth on the bifurcation characteristics of the gear system. In this paper, a dynamic model of spur gear pair is established by considering the extended tooth contact, the coupling effect between gear neighboring teeth, and some time-varying parameters. The extended tooth contact and coupling effect between gear neighboring teeth are directly involved in the calculation of the dynamic meshing force. Then, a solving method with two loop statements is proposed to numerically solve the gear dynamic model. Besides, two new Poincaré mapping sections are established to unify the characterization of system motion and extended tooth contact. Finally, the bifurcation characteristics of the system are studied by using the established Poincaré mapping sections, bifurcation diagrams with multi-mapping sections, phase portraits, Poincaré mapping points, and contact forces. The results show that the system bifurcation and chaotic motion become more severe due to the coupling effect between neighboring teeth. The contact of the extended teeth is accentuated by the system bifurcation. But more extended tooth contact decreases the parameter range of system bifurcation. The connection between system bifurcation, extended tooth contact, and coupling effect between gear neighboring teeth is revealed. This paper can also provide a reference for the stability of the gear transmission system.

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Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This investigation is financially supported by the National Natural Science Foundation of China (Grant Nos. 52022083, 52275132, 51735012).

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Authors and Affiliations

  1. State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Zhengfa Li, Zaigang Chen & Wanming Zhai

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  1. Zhengfa Li
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  2. Zaigang Chen
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  3. Wanming Zhai
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Correspondence to Zaigang Chen.

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Li, Z., Chen, Z. & Zhai, W. Nonlinear dynamic characteristics of a spur gear pair considering extended tooth contact and coupling effect between gear neighboring teeth. Nonlinear Dyn 111, 2395–2414 (2023). https://doi.org/10.1007/s11071-022-07963-w

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  • DOI: https://doi.org/10.1007/s11071-022-07963-w

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