Comparison of alternate analytical models for predicting cogging torque in surface-mounted permanent magnet machines

Permanent magnet brushless machines exhibit high efficiency and torque density, and have already been employed in hybrid electric vehicles. However, one of their disadvantages is the inherent cogging torque, which is a kind of torque ripple and always desirable to minimize. Six analytical models for cogging torque prediction are presented and compared in this paper. These analytical models are progressively refined and differ in methods for calculating the permeance due to stator slotting (i.e. with/without considering the slot leakage), the airgap field distribution due to permanent magnets (i.e. with/without considering the inter-pole leakage and/or curvature effect), and the cogging torque (based on the energy method or the net lateral force acting on the stator teeth). Developed analytical models are used to predict the cogging torque waveforms, the optimal magnet pole-arc to pole-pitch ratio and the optimal slot opening in three machines having different combinations of slot number and pole number, viz. 18/24, 9/8, and 24/16, respectively, and are extensively validated by the finite element analyses. It shows that accounting for the slot leakage and/or magnet interpole leakage can significantly improve the accuracy of cogging torque prediction, while the method for predicting the cogging torque based on the calculation of net lateral force acting on the stator teeth exhibits a higher accuracy than that based on the energy method.