Analytical calculation of no-load air-gap magnetic field of surface permanent magnet motor

Based on the method of Schwarz-Christoffel transformation, this paper derives an air-gap relative specific permeance function, considering the slots in stator core. This function reflects the effect of slots in stator core on no-load air-gap magnetic field. In fact, the effect is variant with air-gap radius. Utilizing the analytical method for partial differential equations and neglecting saturation of the core, an analytical method to calculate the distribution of no-load air-gap magnetic field is proposed, which is suitable for surface permanent magnet brushless DC motors. Comparison between results derived by the 2D finite element method and the results by the proposed method confirms the accuracy and efficiency of the provided method. The presented work is a basic tool for the performance analysis of permanent magnet brushless DC motors.