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, an efficient multi-objective optimization strategy for the Halbach array permanent magnet synchronous machine (PMSM) is developed by taking into consideration the nonlinear B-H behavior of soft magnetic materials. Based on the harmonic modeling (HM) technology, the electromagnetic performances (EPs) of the Halbach array PMSM can be computed. To specifically model the local magnetic saturation, the stator teeth are separated into several annular layers, and each tooth is further divided into several regions along the tangential direction. Then, the parameters of the Halbach array PMSM are optimized utilizing combined nonlinear semi-analytical model (SAM) and non-dominated sorting genetic algorithm II (NSGA-II). To validate the effectiveness and accuracy of the developed optimization scheme, a Halbach array prototype is then manufactured in accordance with the optimization results. The multi-objective rapid optimization strategy developed in this article, which includes but is not limited to Halbach array permanent magnet (PM) machines, serves as a reference for the design and optimization of various PM machines.

This article proposes a nonlinear semianalytical model (SAM) of the multiphase Halbach array axial flux permanent-magnet motor (AFPMM) to speed up the computation of its magnetic field. Compared to the existing analytical models, the proposed nonlinear SAM can directly consider magnetic saturation to obtain more accurate results. To this end, the multiphase Halbach array AFPMM is equivalent to several 2-D models by the quasi-3-D method under the Cartesian coordinate system. Then, the nonlinear SAM is developed by using the convolution theorem and the fast Fourier factorization. The proposed nonlinear SAM is studied on a five-phase Halbach array AFPMM with different rotors, and the nonlinear finite element (FE) model and experiment verify its effectiveness. The proposed SAM is computationally efficient and accurate, and it is also applicable to other types of multiphase Halbach array permanent magnet (PM) electrical motors in Cartesian coordinates.

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.

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.

This article proposes a hybrid analytical model (HAM) for predicting ac copper losses in hairpin windings. The HAM combines the nonlinear semi-analytical model (SAM) and the 1-D ac copper loss computation model to solve the inaccurate boundary solutions of the 1-D ac copper loss computation model when magnetic saturation occurs in the stator teeth. The HAM is used to study the ac losses of the hairpin windings with four different conductor arrangements under different current excitation conditions, and the versatility of the HAM is verified. The HAM has high calculation accuracy, and the calculation speed is 66% faster than the finite element (FE) model. The primary contribution of this research is to present a quick and simple approach for accurately predicting ac copper losses in hairpin windings with arbitrary conductor arrangements.

In this article, we propose a novel nonlinear semianalytical model (AM) for the magnetic field calculation of electric machines. The nonlinear properties and local saturation effect of the iron part are taken into consideration in Cartesian coordinates, which is the main contribution of the proposed model. Thus, high accuracy of electromagnetic field results can be obtained with the low computational time cost. The model is developed based on the harmonic modeling technique by solving Maxwell's equations. The detailed theoretical derivations, which use the complex Fourier series and the Cauchy product, are presented. To verify the proposed model, an axial flux permanent-magnet (PM) machine is selected to be investigated. Both finite-element model and experimental results agree well with that of the proposed model. Moreover, the nonlinear AM has potential application for other types of PM electrical motor in Cartesian coordinates, such as flat PM linear machines.