A Study of Third-harmonic Shaping in Surface-mounted Permanent Magnet Machine with Bread-shape Magnetic Pole

Abstract

This work proposes a method to utilizing the third-harmonic magnet shaping to increase the output torque but not the torque ripple in a radial magnetized surface-mounted permanent magnet (SPM) machine with the sinusoidal magnetic pole. The optimal amplitude of the third harmonic injected into the sinusoidal magnetic pole can be obtained through finite element (FE) scanning or analysis. As for the magnetic pole of the SPM machine, it can be arc-shaped or bread-shaped. For the radial magnetized SPM machine with the arc-shaped pole, the optimal amplitude of the third harmonic injected into sinusoidal magnetic pole is 1/6 of the fundamental wave0, while for the radial magnetized SPM machine of the bread-shaped pole, the optimal value varies with the number of pole pairs (p), magnet thickness and rotor radius. Therefore, the previously-derived third-harmonic analytical model is not accurate enough to be useful for the SPM machine with the bread-shaped magnetic pole. For this reason, this paper presents an analytical model for injecting the optimal third harmonic into the sinusoidal bread-shaped pole of the radial magnetized SPM machine. The model can improve the torque to the largest extent without increasing the torque ripple. The model is proved to be accurate by the FE analytical method.