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In this article, a nonlinear semianalytical model (SAM) is presented to predict the magnetic field distribution (MFD) and electromagnetic performances (EPs) in the cubic spoke-type permanent magnet (PM) machine. To model the rectangular PMs, the rectangular PM is simplified as a combination of fan-shaped regions with different arc angles. Then, the MFD and EPs of the cubic spoke-type machines can be obtained by the harmonic modeling technique. Particularly, the saturation of the magnetic bridges is considered by the nonlinear iterative algorithm. The proposed nonlinear SAM is studied on a 12-slot/8-pole cubic PM prototype, and the nonlinear finite element model and experiment verify its correctness. The main contribution of this article is to present a general analytical modeling method for cubic spoke-type PM machines and consider the magnetic saturation of magnetic bridges.

In this article, a new analytical model for predicting the magnetic field of the U-shaped interior permanent magnet motor (IPMM) is proposed. In the polar coordinates, rectangular permanent magnets are equivalent to the combination of consistent fan-shaped subdomains, and after that, the Laplace or Poisson equation of each solution domain can be obtained. Furthermore, based on the harmonic modeling (HM) technique, the saturation characteristics of the magnetic bridge are accurately considered, and then its magnetic field distribution (MFD) and electromagnetic performances (EPs) can be obtained. The approach proposed in this article includes but is not limited to U-shaped IPMMs, and it can also be applied to spoke-type or V-shaped IPMMs with a minor modification.