An Improved Conformal Mapping Method for Electromagnetic Vibration Analysis in PMSMs With Rotor Eccentricity

The temporal and spatial distribution of electromagnetic force is significantly deteriorated in the permanent magnet synchronous motors (PMSMs) due to rotor eccentricity. Therefore, the noise radiation of PMSMs will inevitably increase, which greatly increases the probability of abnormal operation. In order to accurately and quickly analyze the magnetic field under rotor eccentricity, a two-dimensional (2D) analytical model to predict the eccentric magnetic field of PMSMs using improved conformal mapping method is presented in this article. The 2D analytical model can accurately account for the stator slotting, the winding arrangement, the armature reaction and the rotor eccentricity. Firstly, the topology of rotor eccentricity and stator slot is mapped to the topology of no eccentricity and no slot by using conformal mapping and fractional linear mapping. Then, the magnetic field in the topology without eccentricity and slot is solved analytically. After the inverse transformation, the magnetic field in the original topology is obtained. Finally, the 2D analytical model is validated by finite element method (FEM) and vibration response experiment. The results indicate that the improved conformal mapping method is accurate enough and timesaving.