Calculation of the Air-Gap Field Distribution in Surface-Mounted Permanent-Magnet Synchronous Motors Using the Finite Difference Method

A quick calculation of the air-gap held distribution in surface-mounted permanent-magnet synchronous motors (PMSMs) is significant. Knowing the flux density distribution, one can calculate quantities such as magnetic loading, static torque, and inductances. This paper aims to provide a fast numerical procedure to calculate the air-gap field in surface PMSMs using the finite difference method (FDM), being a good tool before running comprehensive non-linear finite element simulations. Several analytic methods exist in the literature, and most of these, center on the separation of variables and Fourier series. That makes their formulations cumbersome. The proposed method in this work centers itself on the FDM with a straightforward implementation. We can use this with the finite element method (FEM) for the optimal design of surface PMSMs. A 10-pole/12-slot fractional slot surface-mounted PMSM is selected as a benchmark. We calculate its field distribution due to both magnets (no-load condition) and armature excitation using the proposed method and FEM. Results corresponding to each case are presented, and we show that the proposed method has enough accuracy compared with the finite element analysis.