行星轮系固有频率的灵敏度分析
Natural Frequencies Sensitivity Analysis of Planetary Gear Train

建立了两级行星齿轮传动系统计算模型，推导了系统动力学微分方程，求解了行星齿轮传动系统的固有频率。采用矩阵摄动法，针对系统存在孤立特征值和重特征值，分别求解刚度参数变化对各阶固有频率的灵敏度。矩阵摄动法求解的结果与求导法求解的结果对比表明，基于两种方法求解的对各阶固有频率影响最大的参数基本一致，证明了矩阵摄动法求解结果的正确性。通过改变对固有频率灵敏度最大的刚度参数，可以修改固有频率，使其远离激励频率，避免共振的发生。
The computational model of two stage planetary gear train was established, the system's dynamical differential equations were derived, the inherent characteristics of planetary transmission were analyzed. Directing at system's distinct eigenvalues and multiple eigenvalues, the sensitivity of natural frequencies to stiffness parameters was solved by the method of matrix perturbation theory. The results of the matrix perturbation method and the results of derivation method were compared, the comparison results show that the greatest stiffness impact parameters solved by the two method are basically the same, which prove the results solved by the matrix perturbation method are correct. By changing the maximum stiffness parameters of natural frequencies sensitivity, Natural frequencies can be modified to be away from the excitation frequency, which avoids resonance