A Synthetic Frozen Permeability Method for Torque Separation in Hybrid PM Variable-Flux Machines

This paper proposes a synthetic frozen permeability method (SFPM) to separate torque components of a hybrid permanent magnet variable-flux machine (HPM-VFM). The machine in this study employs an Alnico magnet as a variable permanent magnet (VPM) to adjust flux linkage, and adopts Neodymium Iron Boron (NdFeB) magnet as a constant permanent magnet (CPM) to enhance torque density. The dimensions of the two types of PMs not only determine the output capacity, but also influence the magnetization performance of HPM-VFM. For the design and optimization, the total torque separation and PM torque segregation of the two kinds of PMs are needed to examine the actual contribution of them. Generally, frozen permeability method (FPM) can separate on-load field components produced by various excitation sources. However, in a variable-flux machine, due to the VPM's nonlinear magnetic property, the operating point of the VPM changes along with the variation of the load condition. As a result, conventional FPM will cause an obvious error in on-load PM field component. In the proposed method, the recoil line of VPM is considered and frozen in the finite-element analysis (FEA), then the total PM torque and individual PM torques produced by different magnets can be obtained considering cross coupling effect. Finally, the results based on the two methods are compared with the value calculated by direct nonlinear FEA. By comparison, it can be concluded that the SFPM is considerable reliable and accurate in torque components decomposition.