Analytical Model of a Spoke-Type Permanent Magnet Synchronous In-Wheel Motor With Trapezoid Magnet Accounting for Tooth Saturation

This paper presents an analytical model for the prediction of the performance in a spoke-type permanent magnet synchronous in-wheel motor with a trapezoid magnet accounting for tooth saturation. The impact of magnet shape on modeling is considered. To match the standard boundary conditions, the trapezoid magnet is simplified to sector magnets. According to the invariance principle of the magnetic field created by the magnet, the dimension of the sector magnet is calculated with a lumped magnetic circuit model. Then, the motor is divided into six subdomains, i.e., shaft, inner sector magnet, outer sector magnet, rotor slot, air-gap, and stator slot. Based on the boundary conditions, the magnetic field, back electromotive force, and torque are obtained by solving Poisson's and Laplace's equations. The effect of tooth saturation is considered. The finite-element method and experiments are employed to validate the accuracy of the analytical model. In addition, the proposed method can also be used to evaluate the performance of the spoke-type motor with any irregular magnet.