Analytical calculation of no-load air gap magnetic field of surface mounted permanent magnet motor based on Schwarz-Christoffel transformation

In this paper, the complex air gap region of surface mounted permanent magnet synchronous motor (PMSM) with equal thickness poles is transformed into a simple single infinite plane region by using the Schwarz-Christoffel (S-C) transformation. The transformation relation can be obtained accurately by using the SC toolbox. Next, the permanent magnet (PM) is converted into surface current and then equivalent to multiple line currents. According to the S-C mapping, the equivalent currents are transformed into a simple plane, and the magnetic field distribution in a single infinite plane is obtained by using the superposition principle. Then, the magnetic field distribution of PMSM is calculated by inverse S-C transformation. Finally, finite element (FE) simulation is used to verify the analytical results, and the results prove the accuracy of the analytical calculation.