Analytical Determination of Optimal PM-Arc Ratio of Consequent-Pole Permanent Magnet Machines

This paper analytically derives the optimal permanent magnet (PM) arc ratio of the consequent-pole PM (CPM) machines to improve the utilization of rare earth PM material and maximize the output torque. The relationship between the output torque and the PM-arc ratio is established. Moreover, the optimal PM-arc ratio is analytically derived and confirmed by finite element (FE) analysis. It is found that the optimal PM-arc ratio is determined by the ratio of the airgap length to the PM thickness, and its influence on the optimal PM-arc ratio is investigated as well. The electromagnetic performances of the CPM machine with the optimal PM-arc ratio, including the open-circuit airgap flux density, the back EMFs, the average torque, and the torque ripple, are compared with those of the conventional surface-mounted PM (SPM) machine. It is demonstrated that the CPM machine with optimal PM-arc ratio features 33% reduction of PM volume and its torque ripple is almost unchanged compared with the conventional SPM machine. Although the output torque is decreased by 8%, the torque per PM volume is improved by 38%. Finally, a 12-slot/10-pole CPM machine is prototyped and tested to validate the analyses.