将太阳轮、行星轮和行星架视为刚体,内齿圈视为柔性体,构建了行星齿轮系统的刚柔耦合纯扭转模型,根据运动约束条件,推导出了柔性内齿圈的运动方程.经过对柔性运动方程进行分离变量和积分处理后,得到了内齿圈的柔性变形方程和刚性扭转位移方程,并与其他刚性构件的运动方程进行结合,构造出了整个行星齿轮系统的运动微分方程.通过数值分析,归纳出了三种典型的振动模式:扭转振动模式、行星轮振动模式和内齿圈振动模式;与刚体模型相比,系统的固有频率出现下降但阶数增多;内齿圈的柔性越大,系统的固有频率越高.%The sun, the planet and the carrier are regarded as the rigid body, and the ring is treated as the flexible body, so the rigid flexibility hybrid pure torsional model is established, according to the constraints of the motion, the kinematic equation of the flexible ring is deduced. Through the separation of variable and the integration of the ring's equation, getting the flexible deformation equation and the rigid torsional displacement equation of the ring gear, and combining the kinematic equations of the other rigid body, the kinematic differential equations of the planetary gear system are constructed. Through the numerical analysis, we can summarize three typical vibration mode: the torsional vibration mode, the planet vibration mode and the ring vibration mode;comparing with the rigid model, the natural frequencies of the system decreased but the order of the natural frequencies increase;and the more flexible the ring is, the higher the natural frequency of the system is.
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