An increasing need for fast and reliable models has led to a continuous development of Fourier-based (FB) analytical modeling. This paper presents an overview of the techniques that are currently available in FB modeling for electric machines. By coupling that overview to the most relevant literature related to the subject, an interesting starting point is provided for anyone who wants to use or improve FB models. The following seven aspects of FB models are discussed in detail: 1) the magnetic potential (scalar or vector potential); 2) the coordinate system and the solution of the partial-differential equations for each magnetic potential and for each coordinate system; 3) the way in which time dependence is accounted for; 4) the implementation of the source terms; 5) the possibilities to account for slotted structures; 6) the modeling of eccentricity; and 7) the post-processing computation of physical quantities, such as flux density, electromotive force, torque, losses, and eddy currents in conductive objects. Furthermore, this paper gives the closed form solution of the Laplace, Poisson, and Helmholtz equations in each coordinate system. In addition, this paper tackles other important features of FB models such as computational time reduction and coupling the machine model to an electric circuit.

In terms of analytical models used in initial motor design, subdomain, complex permeance and relative permeance models are among the main ones. This paper presents an analysis and comparison of these three models for a wide family of PM machines. Finite element models are used as a reference for comparison. The fundamental harmonic of the flux-linkage generated by PMs is selected to evaluate the precision of the analytical model in the initial design step. The number of slots, PM pole-pairs and ratio of tooth are selected as the key parameters to generate 749 designs for the test. The error distributions and the relationships between error and key parameters in the different analytical models are illustrated in the paper. The subdomain and complex permeance model give the best and worst results, respectively. This paper also explains how to select analytical model for high-torque-density motors.

Accurate models and fast calculations are required for the design of permanent magnet machines. This article presents a 2-D hybrid model for the surface-mounted permanent-magnet synchronous machine (PMSM) combining the Fourier model and the finite element method (FEM). Both magnetic saturation and parallel teeth are taken into account. The model is validated by FEM. The results show that in structures that are saturated, the hybrid model performs much better than the linear Fourier model and simultaneously reduces a large amount of computation compared with FEM.

In low-speed high-torque applications, gearboxes are widely used to amplify the output torque of electrical machines, which inevitably introduce side effects caused by mechanical contact. Consequently, a gear-free system has become increasingly interesting. Although a Vernier permanent-magnet machine has good torque capability, the low power factor is its weakness. This paper proposes a novel topology called the Vernier pseudo-direct-drive (VPDD) machine. A two-stepped design methodology is adopted by combining the subdomain analytical method and finite-element method (FEM). According to the results, the exact subdomain analytical model allows a quick pre-optimization of the structure, and the FEM can be used for further adjustment, dealing with the saturation effect and demagnetization. The optimized VPDD is capable of reaching a very high torque density of 91.8 Nm/L, and the torque ripple is negligible. Its power factor is 0.94.

Magnetic gears, an alternative to conventional mechanical gearboxes, have been extensively studied in the last decade. By combining a magnetic gear and a conventional permanent‐magnet machine into one frame, different magnetic‐gear‐integrated permanent‐magnet machines with a high‐torque density are obtained, among which the pseudo‐direct‐drive permanent‐magnet machine features both a high‐torque capability and a good power factor with an acceptable structural complexity. However, the stator PM array in the conventional pseudo‐direct‐drive permanent‐magnet machine obstructs the magnetic path and reduces the excitation torque due to the coils. Another problem is the large permanent‐magnet amount which increases the overall cost. The authors propose a novel topology which has an improved torque capability under the same excitation current with a reduced permanent‐magnet amount. The working principles of the proposed machine are analysed theoretically using the linear‐material assumption to decouple the permanent‐magnet‐machine part and the magnetic‐gear part. Its performance is then validated by the finite‐element method. A comparison study with the conventional topology is conducted to show its merits.

The coaxial magnetic gear is considered as a promising alternative to mechanical gearboxes. This paper proposes a novel single-permanent-magnet-array coaxial magnetic gear with only one layer of permanent magnets, which is stationary. The flux-modulating teeth are made of high-temperature-superconducting (HTS) material. Working principles of the proposed single-permanent-magnet-array coaxial magnetic gear are introduced analytically. A geometric optimization based on the ideal diamagnetic assumption of the superconducting bulks using the finite-element method is conducted to improve its torque capability. The performance is then evaluated by using the nonlinear E-J power law and compared with a single-permanent-magnet-array coaxial magnetic gear using ferromagnetic teeth. The result shows that the proposed topology can successfully magnify the input torque by a given gear ratio. The designed HTS-toothed single-permanent-magnet-array coaxial magnetic gear has a maximal output torque 1.73 times higher than its ferromagnetic-toothed counterpart.