General analytical solution of magnetic field in slotted surface-mounted permanent magnet machines

This paper presents a general analytical method taking into account the slotting effect for the open-circuit magnetic field in surface-mounted permanent-magnet machines with any pole and slot combinations. A new analytical solution based on 2-D analysis in polar coordinates and suitable for radial/parallel magnetization, internal/external rotor topologies is developed. In order to accurately calculate the magnetic field and cogging torque, unlike previous introduced a relative permeance function and conformal transformation, the boundary conditions is used to consider the influence of interaction between slots. The radial and tangential flux density is obtained by using the Fourier´s series and the method of separating variables. The cogging torque characteristic is deduced by calculating the Maxwell tensors. The analytical results are in very good agreement with those obtained by the FEM, confirmed the accuracy of the analytical method. The model is used to analyze the cogging torque developed in surface-mounted permanent-magnet machines when the design parameters vary in wide ranges. The model is useful in design and optimization of permanent magnet motors.