Analytical Prediction and Optimization of Cogging Torque in Surface-Mounted Permanent Magnet Machines With Modified Particle Swarm Optimization

An analytical method is proposed to predict and optimize cogging torque accurately. It is derived by the exact subdomain model, equivalent current sheet of magnet, and modified particle swarm optimization (PSO), in surface-mounted permanent magnet machines (SPMs) accounting for the effect of stator slotting and tooth-tips. The analysis works for internal/external rotor motor topologies, radial/parallel magnetization, as well as for any combinations of pole and slot numbers. Then, four important design parameters, viz. magnet thickness, air-gap length, slot-opening to slot pitch ratio, and pole-arc to pole-pitch ratio, are adopted as optimal variables, and the peak of fundamental order of the radial component of the air-gap flux density is constrained to optimize cogging torque by modified PSO based on forgoing model. Finally, the cogging torque of two prototype machines with both radial and parallel magnetizations is optimized notably. The paper validates the results of analytical prediction by finite-element analysis.