analytical model for predicting the magnetic field distribution in brushless permanent-magnet.pdf

IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 1, JANUARY 2002 229 Improved Analytical Model for Predicting the Magnetic Field Distribution in Brushless Permanent-Magnet Machines Z. Q. Zhu, Senior Member, IEEE, David Howe, and C. C. Chan, Fellow, IEEE Abstract—A general analytical technique predicts the magnetic field distribution in brushless permanent magnet machines equipped with surface-mounted magnets. It accounts for the effects of both the magnets and the stator windings. The technique is based on two-dimensional models in polar coordinates and solves the governing Laplacian/quasi-Poissonian field equations in the airgap/magnet regions without any assumption regarding the relative recoil permeability of the magnets. The analysis works for both internal and external rotor motor topologies, and either radial or parallel magnetized magnets, as well as for overlapping and nonoverlapping stator windings. The paper validates results of the analytical models by finite-element analyses, for both slotless and slotted motors. Index Terms—Electrical machines, magnetic field, permanent magnet. I. INTRODUCTION A N ACCURATE knowledge of the magnetic field dis- tribution is a prerequisite for predicting performance parameters, such as torque, back-emf, stator and rotor losses, demagnetization withstand, winding inductances, noise and vibration, etc., of brushless permanent magnet motors. Boules [1] formulated a two-dimensional (2-D) model in polar coor- dinates that utilized the concept of equivalent current-carrying coils to determine the airgap flux density distribution in a permanent magnet motor. The model could account for the effect of flux focusing in the magnets, as well as magnetization distribution, i.e., radial or parallel, on the flux per pole and the airgap flux density waveform. However, it only provided field solutions at the stator and rotor surfaces, which is usually insufficient for accurately predicting the performance of slot- less motor topologies. Laport