In this article, an improved conformal mapping (ICM) method based on a complex potential function is proposed. It can improve the calculation speed and accuracy of magnetic fields for surface-mounted permanent magnet synchronous motors (SPMSMs). The eccentric-shaped poles are replaced by equivalent currents, and the improved conformal mapping method is adopted to transform an actual slotted motor air gap to an equivalent rectangular regular slotless air gap. The ICM method improves the speed of calculation because its number of mapping times is less than the traditional conformal mapping (TCM) method. By solving the complex potential generated by the equivalent current in the rectangular regular air-gap region, the air-gap magnetic field of the SPMSM under no-load, armature reaction and loaded conditions can be solved. Then, the no-load back-EMF and loaded torque performance under different load conditions are calculated. The accuracy of the ICM method is verified by finite-element simulation. In addition, the fast speed and high accuracy of the proposed ICM method incorporating the complex potential function for solving the air-gap magnetic field has been demonstrated in comparison to the TCM method with the Hague equation. An eccentric-shaped-pole permanent magnet motor prototype is also built and tested in experiment and the results agree with those calculated by the proposed ICM method.

Surface-mounted permanent magnet (SPM) motors with shaped magnets and a quasi-regular polygon rotor core (QPRC) are challenging to analyze in terms of accuracy and speed because of the special structure. This article proposes a new technique for the subdomain method which can accurately predict the electromagnetic performance of this kind of motor. The proposed new technique deals with the shaped magnet based on the method of magnet symmetrical segmentation, and it can solve the magnetic field generated by a pair of symmetrical segments together at each time. Especially, for the QPRC, the idea of variable rotor core radius is used in the new technique to analyze different segments. Furthermore, the new technique adopts a periodic boundary condition, which can quickly predict the electromagnetic performance of the motor, such as air-gap flux density, cogging torque, no-load back-EMF, winding inductance, electromagnetic torque and unbalanced magnetic force (UMF). This proposed new technique is applied to a 12-pole/3-phase SPM motor with shaped magnets and a QPRC, and its correctness is verified by finite-element analysis and experiment. The new technique can analyze the motor accurately, and its calculation speed is two orders of magnitude faster than that of the finite-element method.

In the eddy current braking system of high-speed maglev, the peak braking force and the critical speed are key factors determining the performance of eddy current braking force. In this paper, the analytical formula of eddy current braking force is derived by a subdomain method considering the skin effect of the induction plate, and, subsequently, the characteristics of peak braking force and critical speed are analyzed. The analytical model is set up in a 2D Cartesian coordinate system. The Poisson equations in each subdomain are listed by treating the vector magnetic potential as a variable. By combining the boundary conditions between two adjacent subdomains, the expressions of eddy current density and magnetic density in the induction plate are obtained. Then, the analytical formula of the eddy current braking force is obtained by the Ampere force formula. The results of finite-element analysis confirm the validity of the analytical calculation. The methods of improving the performance of eddy current braking force under high speed are proposed by parametric analysis of peak braking force and critical speed, which provides guidance for the design of the eddy current braking system in high-speed maglev.

This work establishes an optimized third-harmonic shaping model in order to reach the goals of high power density and low torque ripple of the surface-mounted permanent magnet motor (SPMM) The establishment of the model takes the non-ideal factors into consideration, including PM relative permeability, stator slotting, pole leakage, pole edge effect and magnetic circuit saturation. The formula of third-harmonic shaping and the optimal third-harmonic injection factor am(m) are derived from the model. Then a finite-element(FE) model was established to compare the electromagnetic(EM) performance of different magnetic poles. It is found that the average torque of the modified third-harmonic motor is 3.5% higher than that of the simplified third-harmonic motor, and the torque ripple is 47% lower than that of the simplified third-harmonic motor. This proves the superiority of the modified model. And experiments demonstrate that the modified model is feasible and effective.

In this article, permanent magnet (PM) machines with irregular rotor cores, mainly including surface-mounted PM (SMPM) machines and surface-inset PM (SIPM) machines, are analyzed by an enhanced conformal mapping (CM) model. The three special issues have been addressed. The irregular boundary in the rotor core is divided into several segments, and the enhanced CM model can be used to deal with PM machines with irregular rotor cores conveniently. Then, the proposed equivalent-current model converts various shaped PMs into current sheets, and the actual permeability of PMs can be considered by constructing the model of modified equivalent currents to improve the accuracy of the PM equivalent-current method. Furthermore, the enhanced model can also consider the magnetic-saturation effect of machines. Finally, the electromagnetic performances of machines, such as air-gap magnetic density and back-EMF, can be predicted accurately. PM machines with various rotor core structures and PM shapes are modeled by the enhanced CM model, and the finite-element model and experiments are used to verify its universality and correctness. This model has high universality, accuracy and speed, which is of great help to the initial design and optimization of PM machines.

In this article, a hybrid analytical model for a quasi‐regular polygon rotor (QPR) is proposed. It mainly uses the subdomain method and conformal mapping to solve a non‐circular boundary in the QPR. Firstly, the subdomain method combined with an equivalent surface current method is used to calculate the air‐gap magnetic field considering a slotted stator with a circular rotor. Secondly, by segmenting the non‐circular boundary in the QPR, the complex relative air‐gap permeance of the QPR can be calculated using the conformal mapping. Thirdly, this complex relative air‐gap permeance modifies the air‐gap magnetic field calculated in the first step to obtain the actual magnetic field distributions. Consequently, no‐load and loaded air‐gap flux densities, back‐electromotive force and torque can be obtained. A 12‐pole/3‐phase permanent magnet motor is modelled using the proposed hybrid analytical model, which is validated by finite‐element analysis and experiment. This proposed hybrid analytical model presents a new way of processing the QPR. Its calculation speed is nearly 50 times faster than the finite‐element analysis, which is of great help to the initial design and optimisation of machines with QPRs.