Analysis and Reduction of Radial Vibration of FSCW PMSM Considering the Phase of Radial, Tangential Forces, and Tooth Modulation Effect

In this study, the causes of significant radial vibration at pole frequency in an 18-slot 16-pole (18S16P) permanent magnet synchronous motor (PMSM) are thoroughly analyzed, and an improved model is proposed. First, the spatial phase relationship of the lowest order radial and tangential air-gap electromagnetic force densities (AEFDs) of the 18S16P PMSM is derived analytically. Then, using 3-D structural finite element analysis (FEA), the radial vibration-enhancing effect of the lowest order radial and tangential AEFDs is revealed. Furthermore, the tooth modulation effect of the 18S16P PMSM is investigated. The analysis results show that the modulated radial vibration is also enhanced by the radial vibration caused by the lowest order radial and tangential AEFDs, leading to significant pole-frequency radial vibrations. Afterward, a vibration reduction model is proposed to minimize the tooth modulation effect and utilize the vibration suppression effect caused by the lowest order radial and tangential AEFDs considering the spatial phase relationships. As a result, radial vibrations are greatly reduced, and the results are validated through simulations and tests.