K-H-V型摆线钢球传动扭转振动建模与刚度激励分析

Analysis of the Torsional Vibration Modeling and Rigidity Excitation of K-H-V Cycloid Steel Ball Transmission

综合考虑传动过程中啮合力方向变化和多钢球啮合等影响因素,建立了K-H-V型摆线钢球传动系统的扭转振动模型。通过分析各啮合力间的相对位置关系和各构件间的相对位移关系,推导出系统的运动微分方程及各传动盘间的无量纲等效啮合刚度关系式,进而对啮合刚度激励进行频谱分析,并探讨了系统传动比和摆线短幅系数对啮合刚度激励的影响,最后给出算例,计算了系统的固有频率、主振型与稳态响应。研究结果表明,摆线钢球传动为参变系统,其中心盘和行星盘间的啮合刚度激励具有周期时变性特征,且相应的频谱中存在高次谐波成分。

A torsional vibration model of the K - H - V cycloid steel ball transmission system is established with considering the direction changing of engagement force and the multi - balls engagement in transmission process. By analyzing the position relationships of each engagement force and the displacement relationships of each component, the governing differential equations of the system and the dimensionless equivalent engagement rigidities of each transmission disc are derived. And then, the frequency spectrum of the engagement rigidity excitation is analyzed, and the influences of the system transmission ratio and the cycloid curtate coeffi- cient to the engagement rigidity excitation are discussed. At last, the natural frequency, the principal mode and the steady - state response of system are calculated. The results show that the cycloid steel ball transmission system is a parametric vibration system. The engagement rigidity excitation between the center disc and the planetary disc is a periodic and time -variant function, and the high -order harmonic components are included in the frequency spectrum.