Analytical Modeling and Design Optimization of a Vernier Permanent Magnet Motor

In this paper, we present the analysis and design optimization of a Vernier permanent magnet (VPM) motor for direct-drive applications. A subdomain-based analytical model is developed for fast calculation of the electromagnetic performances, including air-gap flux, torque ripple, and power factor. Built on the analytical model, we investigate the trade-off between torque generation and power factor of the VPM motor, and conduct multi-objective optimization for key design parameters of the VPM motor. Flux density in different regions of the stator core is calculated using the analytical model, based on which a constraint is set in the objective functions to take the saturation effect into account. The design optimization process is implemented for a multi-objective optimization of the VPM motor. The optimized machine achieves over $1.8\times$ torque output compared with a commercially-available surface-mount permanent magnet direct-drive motor with the exact inner and outer dimensions at the same operating speed.