Optimal magnet shaping with third order harmonic for maximum torque in brushless AC machines

This paper describes the optimal magnet shaping techniques to increase the torque capability in brushless AC machines by utilising the 3^rd order harmonic in inverse cosine shape airgap and sinusoidal shape magnet. It is analytically found that for different types of magnet shaping methods, the optimal magnitude of the 3^rd order harmonic is always 1/6 of that of the fundamental, which is validated by the finite element analysis. By utilising the optimal 3^rd order harmonic, the average torque of two 10-pole/12-slot machine can be increased by ~11%, while their torque ripple is only slightly increased by less than 1.5%, compared to machines employing magnet shaping techniques without the 3^rd order harmonic.