Improved method for field analysis of surface permanent magnet machines using Schwarz-Christoffel transformation

Air gap field solution for an outer rotor permanent magnet (PM) machine is derived based on numerical Schwarz-Christoffel (SC) transformation of a single slot geometry and analytical solution of a point wire field in the rectangular canonical domain. This approach takes into account geometrical distortions of PM edges and field evaluation points located along the air gap centre, which occur due to conformal mapping of the slotted air gap into a slotless domain and impair the accuracy of the existing analytical field solutions using SC transformation and complex relative air gap permeance. The increased accuracy of the improved solution is confirmed by comparing the air gap flux density waveforms produced by the PMs and armature winding, cogging torque, and total torque with the results of time-stepping transient finite element simulation.