Magnetic Field Analysis of Inset and Surface-Mounted Permanent-Magnet Synchronous Motors Using Schwarz–Christoffel Transformation

In this paper, we apply an original numerical Schwarz-Christoffel (SC) transformation to analyze magnetic field originating from permanent magnets and the armature winding currents in a slotted air gap of an inset permanent-magnet synchronous motor. We obtained the solution of the SC integral numerically using Matlab SC Toolbox. We used this field solution to calculate both cogging torque and electromagnetic torque by integrating the Maxwell stress tensor inside the air gap. The case without inter-polar piece, which is equivalent to a surface-mounted permanent-magnet motor, is also treated. The accuracy of the developed method is verified by comparing its results with those obtained from the developed numerical finite-element models.