Analytical Average Torque Optimization Method of Parallel MagnetizedSurface-Mounted Permanent-MagnetMachine withThird-OrderHarmonic Shaping Method

On the basis of existing studies presented in literature on optimizing permanent magnet (PM) shaping with third harmonic for the tile-shaped magnetic poles under radial magnetization, this paper proposes a method for PM shape optimization using third harmonic for bread-shaped magnetic pole under parallel magnetization. Furthermore, the optimal value of third harmonic that should be injected for achieving maximum torque output of a surface-mounted permanent-magnet (SPM) motor under parallel magnetization is obtained. The accuracy of the analytical calculation is verified using the finite element method. Furthermore, electromagnetic properties, including back-EMF waveform, cogging torque, average torque, and torque ripple of the SPM motor obtained under different PM shaping conditions, i.e., without PM shaping, sinusoidal PM shaping, and sinusoidal PM shaping with third harmonic are compared. The comparison results indicate that injecting the optimal value of third harmonic into the PM being subject to sinusoidal shaping can greatly improve the average torque and power density of the SPM motor without increasing the torque ripple. (c) 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.