Vibration Reduction and Torque Improvement of Integral-slot SPM Machines Using PM Harmonic Injection

This study aimed to improve the vibration and torque of an integral-slot surface-mounted permanent magnet (SPM) machine by optimizing the shape of the harmonically injected permanent magnet (PM). First, the effect of the third harmonic injected into the sinusoidal PM shape on the electromagnetic performance of a 36-slot/12-pole SPM machine was investigated, including the torque performance and vibration response. It was found that the Sin+3rd harmonic-shaped PM had a contrary effect on the torque and vibration performance of the integral-slot machine, which improved the torque capability but worsened the vibration performance. Second, the response surface model and Barebones multi-objective particle swarm optimization algorithm based on a trade-off between the average torque and vibration were implemented to determine the optimal harmonic injection. Subsequently, the performances of the optimal Sin+3rd-shaped and eccentric PM machines were compared, showing the excellent torque and vibration performance of the adopted method. Finally, a prototype was manufactured and tested to verify the results of the theoretical analysis.