摆线钢球行星传动系统参数振动特性研究

RESEARCH ON PROPERTIES FOR PARAMETRIC VIBRATION OF CYCLOID BALL PLANETARY TRANSMISSION SYSTEM

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 parametric vibration system with multi-freedom, and the dynamic characteristics are affected by the engagement rigidity excitation. Firstly, the translational-torsional coupling dynamic model of the system is established, which includes the factors such as the time-variant engagement rigidity and the bearing rigidity, and the dynamic equations of the system are derived. And then, the dynamic equations are converted to the canonical modal equations. The dynamic stability of the system is analyzed using the multi-scale method, and the combination resonance frequencies as well as the stability conditions are present. Finally, the steady-state response of the system is solved using the perturbation method. The results show that the parametric resonance is generated as the input rotational speed approaches the summation resonance frequencies; the system is stable as the input rotational speed approaches the difference resonance frequencies; the steady-state response of the system is the superposition of multi-response with different combination frequencies.