Vibration Enhancement or Weakening Effect Caused by Permanent Magnet Synchronous Motor Radial and Tangential Force Formed by Tooth Harmonics

Abstract

This paper investigates the vibration enhancement or weakening effect caused by permanent magnet synchronous motor radial and tangential force formed by tooth harmonics. First, the analytical expressions of an air gap magnetic field are deduced based on a permanent magnet synchronous motor model. Then, the Maxwell stress tensor method is employed to calculate the radial and tangential force density produced by permanent magnet magnetomotive force harmonics and tooth harmonics. Moreover, the spatial phase difference between the minimum non-zero spatial order radial and tangential force waves under loading operation are also obtained. It is followed by stator vibration deformation induced by radial and tangential force waves, and the vibration enhancement or weakening effect is discussed. This study shows that the tangential force wave has a significant influence on the vibration performance similar to the radial force wave. At specific frequencies, superposition of the radial and tangential force waves can intensify the vibration while weakening each other to reduce the vibration at other specific frequencies. Numerical simulation and a vibration measurement experiment of the prototype motor were carried out to confirm the proposed theory, which can guide motor designers in selecting an appropriate pole and slot combination to apply the weakening effect between radial and tangential force waves and improve PMSM vibration performance.