Analytical Prediction of Halbach Array Permanent Magnet Machines Considering Finite Tooth Permeability

The most significant assumption of conventional analytical methods (e.g., the subdomain technique) is that the stator and rotor iron cores are infinitely permeable. The magnetic saturation is ignored, resulting in an overestimation of the flux density. This article presents an analytical model of permanent magnet (PM) machines with segmented Halbach arrays (PMMSHA). It considers the finite magnetic permeabilities of the stator teeth and tooth tips (STTT) and can study the tooth saturation effect. The permeability variation in the slots and teeth is solved via Cauchy's product theorem. Based on magnetic vector potential and the Maxwell-Fourier method, Poisson's and Laplace's equations in the stator teeth/slots, tooth tips/slot openings, air gap, and PMs regions are solved. Consequently, the electromagnetic performance, including the magnetic field distribution in all regions, exciting force density, cogging torque, and electromagnetic torque, is calculated. The results of finite element analysis (FEA) show that the analytical model is highly accurate. Furthermore, the influences of the permeability of the STTT and the number of blocks per pole (NBPP) on the performance of the PMMSHA are studied.