Analytical Calculation of Magnetic Field for Permanent Magnet Synchronous Machine with Hybrid Magnets

The hybrid permanent magnet (PM) machine with rare earth and non-rare earth materials has become a substitute for rare earth PM machine because of its low cost and relatively good torque performance. In this paper, an analytical approach is proposed to calculate the magnetic field of surface-mounted permanent magnet synchronous machine (SPMSM) with hybrid PMs. Based on the principle analysis and 2-D modeling of the hybrid-PM SPMSM with a given size, the analytical machine model is derived by Laplace and quasi-Poisson equations, and the exact expression of the flux density of the air gap is obtained. On this basis, the analytical model is improved for the influence of different thicknesses of PM materials and magnetic barriers on the air gap flux density. The results of the field distribution are compared with those obtained through the finite element method, and the accuracy of the proposed calculation is verified.