Nonlinear dynamic characteristics of a spur gear pair considering extended tooth contact and coupling effect between gear neighboring teeth
Nonlinear dynamic characteristics of a spur gear pair considering extended tooth contact and coupling effect between gear neighboring teeth
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考虑扩展齿接触和齿轮相邻齿间耦合效应的正齿轮副非线性动态特性
DOI：
10.1007/s11071-022-07963-w
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发表时间：
2022-10
影响因子：
5.6
通讯作者：
Wanming Zhai
中科院分区：
文献类型：
--
作者：
Zhengfa Li;Zaigang Chen;Wanming Zhai
从非线性动力学的角度来看，齿轮传动系统的分叉对于系统的稳定性和安全性是非常重要的。同时，建立了齿轮传动系统的动力学模型，重点研究了轮齿接触扩展和相邻轮齿间的耦合效应。然而，几乎没有文献揭示扩展齿接触和齿轮邻齿间的耦合效应对齿轮系统分叉特性的影响。本文建立了直齿圆柱齿轮副的动力学模型，该模型考虑了轮齿接触扩展、相邻轮齿间的耦合效应以及一些时变参数的影响。在动态啮合力的计算中，直接考虑了齿轮邻齿间的扩展接触和耦合效应。在此基础上，提出了一种双环语句的求解方法，对齿轮动力学模型进行数值求解。此外，还建立了两个新的Poincaré映射截面，统一了系统运动和扩展齿接触的表征。最后，利用所建立的Poincaré映射截面、多映射截面分叉图、相图、Poincaré映射点和接触力研究了系统的分叉特性。结果表明，由于邻齿间的耦合作用，系统的分叉和混沌运动更加严重。系统分叉加强了延伸齿的接触。但过大的齿面接触减小了系统分叉的参数范围。揭示了系统分叉、扩展齿接触与齿轮邻齿间的耦合效应之间的关系。本文还可为齿轮传动系统的稳定性提供参考。
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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