Modeling and analysis of electromagnetic force in interior permanent magnet synchronous motor used for electric vehicles

Abstract

The accurate prediction and analysis of electromagnetic excitation source is the pre-condition for the investigation of electromagnetic vibration and noise. In this work, an analytical model for electromagnetic (EM) force calculation of interior permanent magnet synchronous motors (IPMSMs) is proposed by coupling the 2-D model in polar coordinates and the Maxwell stress tensor method (MSTM). In the modeling, the boundary conditions for solving the air-gap magnetic field are firstly simplified based on the equivalent conversion of permanent magnets (PMs). Then, the magnetic field is acquired by solving the governing equation based on the simplified boundary conditions. Finally, the EM force is obtained according to the MSTM. The effectiveness is fully verified by finite element (FE) analysis that the analytical model can be applied not only for the calculation of radial EM force of IPMSMs with/without load but also for the calculation of tangential EM force. Besides, the tangential EM force is further analyzed by 2-D Fourier decomposition, and the relationship between tangential EM force and torque fluctuation is also clarified. The results show that the radial EM force harmonics and the tangential EM force harmonics have the same spatiotemporal characteristics no matter under no-load or load. Moreover, the high-frequency components of tangential EM force harmonics with low spatial orders, which have the highest contribution to vibration and noise, are comparable to those of radial EM force harmonics. Meanwhile, the torque fluctuation of IPMSMs with/without load only comes from the zero-order tangential EM force harmonics in space.