The air-gap eccentricity will produce unbalanced magnetic pull and cause vibrations and noises in a motor. In this study, the dynamic behavior of a synchronous motorized spindle with inclined eccentricity is investigated. A semi-analytical method is proposed to model the unbalanced magnetic pull and the electromagnetic torque of a rotor with inclined eccentricity, and the semi-analytical method is verified by the finite element method. The dynamic model of a spindle-bearing system is built by taking the centrifugal force and gyroscopic effects into account. Then, the vibration response of dynamic displacement eccentricity, inclined eccentricity including displacement eccentricity and angle eccentricity, rotating speed, and unbalanced mass eccentricity in both time domain and frequency domain are simulated and analyzed. The results show that the eccentricities can lead to fluctuations in amplitudes of the dynamic displacement response and the angle response. The frequency components of the dynamic responses are the combination of rotating frequency, VC frequency, and power frequency. It is indicated that the coupling interactions of bearing forces, unbalanced mass force, and unbalanced magnetic pull have an obvious effect on the spindle-bearing system.

气隙偏心会产生不平衡的磁拉力，并在电机中引起振动和噪音。在这项研究中，研究了具有倾斜偏心的同步电主轴的动态行为。提出了一种模拟偏心转子不平衡磁拉力和电磁转矩的半解析方法，并通过有限元方法对半解析方法进行了验证。考虑离心力和陀螺效应建立主轴-轴承系统的动力学模型。然后，在时域和频域对动态位移偏心、包括位移偏心和角偏心的倾斜偏心、转速和不平衡质量偏心的振动响应进行了仿真分析。结果表明，偏心会导致动态位移响应和角度响应的幅度波动。动态响应的频率分量是旋转频率、VC 频率和电源频率的组合。结果表明，轴承力、不平衡质量力和不平衡磁拉力的耦合相互作用对主轴-轴承系统有明显的影响。