The Magnetic Field Analytical Calculation of Permanent Magnet Vernier Synchronous Machine With Saddle-Shaped Permanent Magnets

This article proposes a novel permanent magnet Vernier synchronous machine (PMVSM) with saddle-shaped PMs. The torque of the PMVSM with saddle-shaped PMs is increased by 35.4% and 45.6% compared with the PMVSM with V-shaped PMs and tile-shaped PMs, respectively. The torque ripple of the PMVSM with saddle-shaped PMs is reduced by 0.1% and 1.7% compared with the PMVSM with V-shaped PMs and tile-shaped PMs, respectively. To facilitate the analysis, the saddle-shaped PMs are equivalently transformed to the fan-shaped PMs, which ensures that the pole arc angles and air-gap magnetic flux are unchanged. The rotor flux saturation region is modeled to improve the analytical calculation accuracy. The Laplace and Poisson equations are established for each part of the machine, the general solutions of the respective parts are solved, and the boundary conditions and intersection conditions are utilized to solve the factors. Compared with the finite-element method (FEM) results, the torque difference is $0.32~ \mathrm {N}\cdot \mathrm {m}$ , and the torque ripple difference is 0.2%. The correctness of the analytical calculation is verified by comparing with the FEM results. The auxiliary slot angle and slot depth can be optimized, resulting in a higher torque and a lower torque ripple.