Investigation on Radial Vibration of FSCW PMSM According to Pole/Slot Combination Considering Phase of Radial, Tangential Force and Moment

In this study, the radial vibration of fractional-slot concentrated winding (FSCW) permanent magnet synchronous motor (PMSM) was analyzed according to pole/slot combination considering phase relationship of modulated radial, tangential forces, and moment. First, to calculate the modulated forces and moment according to pole/slot combination, the amplitude and phase of modulated radial, tangential force and moment converted by radial air-gap electromagnetic force density (AEFD) are analytically derived. Since the lever arm effect by tangential force varies according to the tooth length, tangential force was translated on the yoke and an equivalent modulated moment was derived. Subsequently, to analyze the radial vibration caused by modulated forces and moment, the radial displacement response owing to a unit radial AEFD is calculated using 3D structural finite element analysis by applying unit modulated forces and moment. It was found out that the tooth modulation effect hardly varied with pole/slot combination and shape of the PMSM such as tooth length. Rather, it was confirmed that the tooth modulation effect was significantly influenced by the slot opening width. Especially, it was analyzed that the radial vibration of PMSM is not simply reduced by optimizing the slot opening width with reduced modulated radial force, but the amplitude and phase of the modulated tangential force and moment should also be considered. Finally, four prototypes of the PMSM with different slot opening widths of two 12-slot 10-pole and two 12-slot 14-pole are fabricated, and the test and simulation results are compared and verified.