Electromagnetic Forces and Vibrations Under Stator and Rotor Reference Frames in Permanent Magnet Synchronous Machines

ABSTRACT The electromagnetic force plays a significant role in contributing to torque ripple and electromagnetic vibration in permanent magnet synchronous machines (PMSMs), thereby impacting the noise, vibration, and harshness (NVH) performance. However, in most cases, existing design and analysis approaches predominantly focus on torque ripple, radial force and vibration under the stator reference frame, which is not sufficiently comprehensive. To address this gap, this paper presents the derivation of the spatial and temporal orders of force harmonics under both the stator stationary reference frame and the rotor rotating reference frame. Through theoretical analysis and finite element method (FEM) simulations, this paper highlights the differences in force harmonics and vibrations between the two reference frames. Furthermore, it explores the relationship between torque ripple and vibrations under different reference frames. Additionally, the superposition and cancellation effects of radial and tangential forces in producing vibrations are investigated. Finally, to validate the theoretical analysis, two prototypes of PMSMs with 6 poles and 9 slots have been manufactured and subjected to performance testing.