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This paper presents an analytical method for predicting the electromagnetic performance in permanent magnet (PM) machine with the spoke-type rotor (STR) and a proposed hybrid rotor structure (HRS), respectively. The key of this method is to combine magnetic field analysis model (MFAM) with the magnetic equivalent circuit model. The influence of the irregular PM shape is considered by the segmentation calculation. To obtain the boundary condition in the MFAM, respectively, two equivalent methods on the rotor side are proposed. In the STR, the average flux density of the rotor core outer-surface is calculated to solve the Laplace’s equation with considering for the rotor core outer-surface eccentric. In the HRS, based on the Thevenin’s theorem, the equivalent parameters of PM remanence  $B_{\text {reB}}$  and thickness  $h_{\text {pme}}$  are obtained as a given condition, which can be utilized to compute the air-gap flux density by conventional classic magnetic field analysis model of surface-mounted PMs with air-gap region. Finally, the proposed analytical models are verified by the finite element analysis (FEA) with comparisons of the air-gap flux density, flux linkage, back-EMF and electromagnetic torque, respectively. Furthermore, the performance that the machine with the proposed hybrid structure rotor can improve the torque density as explained.

Analytical Model of Torque-Prediction for a Novel Hybrid Rotor Permanent Magnet Machines