Optimal rotor shape with third harmonic for maximizing torque and minimizing torque ripple in IPM motors

This paper presents optimal rotor shape design to increase the torque capability in IPM machines by introducing optimal 3rd harmonic to the inverse cosine shaped rotor. The impact of the optimal 3rd harmonic to the rotor shape on the electromagnetic performance is investigated by finite element method. It is demonstrated that under the same amount of permanent magnets as the inverse cosine shaped IPM machine, the average torque for the machine of inverse cosine with optimal 3rd harmonic shaped rotor can be improved by >5% while the torque ripple can be maintained almost the same. In addition, the inductance saliency ratio is also improved, which increases the average torque further. The impact of 3rd harmonic on stator and rotor iron and rotor eddy current magnet losses is also compared with the machine without 3rd harmonic in the rotor shape, which shows that the iron loss increases slightly. All results have been verified with finite element method.