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摆线钢球行星传动系统为多自由度的参数振动系统,其时变啮合刚度激励会对系统的动态特性产生较大影响。该文首先综合考虑时变啮合刚度及轴承支承刚度等影响因素,建立了摆线钢球行星传动系统的平移-扭转耦合动力学模型,并推导出系统的动力学方程。然后将动力学方程转换为正则模态方程,并利用多尺度法对系统进行动力稳定性分析,推导出系统的组合共振频率及稳定性条件。最后利用摄动法计算出系统的稳态响应。研究结果表明:当偏心轴的输入转速接近和型组合共振频率时,系统将发生参数共振;当偏心轴的输入转速接近差型组合共振频率时,系统总是稳定的;系统的稳态响应中包含多种组合频率成分,并表现出多频响应叠加的特性。
The cycloid ball planetary transmission system is a multi-degree-of-freedom parametric vibration system whose time-varying meshing stiffness excitation has a great influence on the dynamic characteristics of the system. In this paper, firstly, considering the influence factors such as time-varying meshing stiffness and bearing support stiffness, the translational-torsional coupling dynamics model of cycloidal ball planetary drive system is established and the dynamic equation of the system is deduced. Then, the dynamic equations are transformed into regular modal equations, and the dynamic stability of the system is analyzed by multi-scale method. The combined resonant frequency and stability conditions of the system are deduced. Finally, using the perturbation method to calculate the steady-state response of the system. The results show that the system will resonate when the input speed of the eccentric shaft approaches the resonance frequency of the combined type, and the system will always be stable when the input speed of the eccentric shaft approaches that of the differential combined resonant frequency. Contains a variety of combinations of frequency components, and shows the multi-frequency response superimposed characteristics.