Analytical Model for Calculating Magnetic Field of Nonlinear Spoke-Type Permanent-Magnet Motors Considering Rotor Eccentricity and Pole Shape

This paper proposes an analytical method to calculate magnetic field of nonlinear spoke-type permanent-magnet motors (STPMM) considering static, dynamic, mixed rotor eccentricities and pole shape. First of all, eccentricity problem within two circular boundaries is handled by using bilinear mapping to transform two eccentric circles in S-plane to two concentric circles in T-plane. Then magnetic field in the slotted STPMM with concentric rotor is predicted according to conformal mapping, double reaction theory, superposing principle complex relative air-gap permeance, and nonlinear magnetic network. After that, back electromotive force (BEMF) and torque are obtained according to the results of magnetic field. The calculating results show that open-circuit and on-load air-gap flux density, cogging torque, BEMF, and static torque of STPMM considering rotor eccentricity and pole shape by the proposed analytical method are in good agreement with those predicted by finite-element method. Analytical results of BEMF and static torque are also similar with experimental results. The finite-element and experimental results confirm that the developed analytical method has high accuracy for predicting magnetic field of nonlinear STPMM considering rotor eccentricities and pole shape.