中文摘要：

建立了电机柔性转子非线性动力学模型，并使用多尺度法计算了系统的一次近似主共振响应。通过定常解分析发现转子主共振响应中存在幅频曲线左偏这一软非线性现象，并且不平衡磁拉力的线性部分使系统固有频率下降，非线性部分使主共振峰左偏量增大。使用 MATLAB 软件中的“o de23”函数绘制出系统的时间历程图及相图，数值积分的结果验证了解析解的正确性。从理论上揭示了转子长度、转子外径以及平均气隙长度等电机参数对非线性振动的影响，为电机的优化设计和控制提供了理论依据。

英文摘要：

A multiple scale approach was applied to the nonlinear dynamics model of the flexible rotor in a motor ,to study the first approximate primary resonance of the rotor .T he results show that the formant makes a left shifting in the frequency response curve .In addition ,the linear part of the unbalanced magnetic pull will decrease the natural frequency in the system ,and the nonlinear part will increase the left shifting of the formant .The numerical simulation was carried out to verify the results obtained through the analytical method .The results given here make a foundation for further optimi-zation and control of permanent magnet synchronous motors .