Analytical Method for Calculating the Magnetic Field of Spoke-Type Permanent Magnet Machines Accounting for Eccentric Magnetic Pole

This article proposes an analytical method to calculate the magnetic field, back electromotive force (BEMF), inductance, and torque of spoke-type permanent magnet machine (PMM) accounting for eccentric magnetic pole. The magnetic field in the slotted spoke-type PMM is predicted according to conformal mapping, flux continuity theorem, double reaction theory, superposing principle, and complex relative air-gap permeance. Then, BEMF, inductance, and torque are obtained according to the results of magnetic field. A spoke-type PMM with eccentric magnetic pole is used to verify the analytical model. The harmonics of BEMF and torque ripple of spoke-type PMM with eccentric magnetic pole are very slight. Results of magnetic field, BEMF, inductance, and torque by the analytical model are verified by finite element. The validation to calculate BEMF and electromagnetic torque with analytical model is confirmed by experimental result. The analytical method proposed in this article can be applied to the spoke-type PMM with all kinds of magnetic-pole shape.