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This paper presents three analytical techniques for 3D modeling and analysis of coreless stator axial flux permanent-magnet (CS-AFPM) machines under no-load condition. Quasi 3D analytical model based on Hague’s solution, magnetic equivalent circuit (MEC) model, and analytical model based on Fourier-Bessel series are used to calculate the components of air-gap magnetic flux density. In quasi 3D analytical model, the 3D geometry of CS-AFPM machine is transformed into the 2D geometries in different radii. Hague’s solution is used to calculate the tangential and axial components of air-gap flux density in corresponding radius. The law of superposition is then used to calculate the flux-linkage of stator phase. In the MEC model, the non-linear permeance network is used to calculate the axial component of air-gap flux density while considering the curvature effect, the fringing effect, and the leakage magnetic fluxes. In the proposed 3D analytical model, all components of air-gap flux density are calculated while considering the edge effect, the curvature effect, fringing and leakage fluxes, the magnetic saturation, and the skewed PMs. In final, the accuracy and capabilities of these techniques are verified through comparing with corresponding results obtained from 3D finite element method (FEM) and the experiment set-up.

This paper presents a new 3D analytical model based on the Fourier–Bessel series for electromagnetic modeling of the performance of slotless axial flux permanent magnet (AFPM) machines under no-load conditions. The machine geometry is divided into different domains including the permanent magnet (PM) domain, the air-gap domain, and so on. The Laplace equation in terms of scalar magnetic potential is solved in each domain, and their solutions are expressed based on the Fourier–Bessel series to accurately consider the radial variation of the air-gap magnetic field. A 2D geometry function based on the Fourier–Bessel series is introduced to accurately consider the different PM shaping in the magnet domain. The boundary condition is then used to determine the unknown constants in the general solutions. This 3D analytical model is prepared to calculate the no-load flux linkage of stator phases while considering different PM shapes and skewing effects. Two indexes including the amplitude of the fundamental component and the total harmonic distortion (THD) of no-load phase flux linkage are considered to investigate the effect of skewed PMs and other PM shapes. The capability of the proposed 3D analytical model is also presented to calculate the air-gap magnetic field due to the stator phases for determining the inductance matrix. Finally, the accuracy of the proposed 3D analytical model is verified by comparing it with the corresponding results obtained through the finite element method (FEM) and the experiment setup.

The Hybrid Excitation Flux Switching Permanent Magnet (HEFSPM) motor with magnetic bridge is a topology of hybrid excitation Flux-Switching Permanent Magnet (FSPM) machines. Despite its excellent performance such as high torque/power density, high flux enhancing/weakening capability and so on, it has received less attention due to its complicated structure. Therefore, its optimal design and performance all need to be further investigated. This paper presents a multi objective optimization design of a HEF SP M motor with magnetic bridge based on design sensitivity analysis. At first, the machine structure and basic working principle are discussed briefly. Then, a design sensitivity analysis for geometric optimization is carried out to improve the motor performance. This optimized motor is compared with initial design. Finally, a prototype of the optimized proposed motor is built and tested to validate the simulation results. KEYWORDS Cogging torque; Finite Element Method (FEM); Flux-switching; Hybrid excitation; Magnetic bridge; Permanent Magnet (PM).

The purpose of this paper is to present a new Hybrid Analytical Model (HAM) based on Winding Function Theory (WFT) for electromagnetic analysis of the performance of one typical Unbalanced Two-Phase Induction Motor (UTPIM). Different indexes of electromagnetic modeling, such as winding distribution, slotting effect, and magnetic saturation, can be accurately considered by using the proposed HAM. To obtain this new hybrid technique, WFT is reformulated to consider magnetic saturation in addition to the influence of slotting and winding distribution. The Conformal Mappings (CMs) are used to calculate the slotted air-gap length accurately. The Magnetic Equivalent Circuit (MFC) model is used to consider the Magneto-Motive Force (MMF) drop in stator and rotor cores due to the excitation of one phase-winding. The results obtained from CMs and MEC are then utilized in reformulated WFT to calculate the inductances of the respective phase-winding. Transient analysis is then done to calculate the indexes of performance, such as air-gap magnetic field, phase currents, electromagnetic torque, and rotor speed, by using the lookup table of inductances while considering different capacitors in the auxiliary phase. In each step, the accuracy of analytical results is confirmed by comparing with corresponding results obtained from the Finite Element Method (FEM).

Purpose The purpose of this paper is to present an improved winding function theory (IWFT) for performance analysis of surface mounted permanent magnet (SMPM) motors, which can precisely and simultaneously consider the impacts of stator slotting, the winding distribution, the magnetic flux density within PMs because of the armature reaction, the PM magnetization angle and the magnetic saturation,. Design/methodology/approach To obtain this improved analytical model, the conformal mappings (CMs) are introduced to calculate the relative complex permeance of slotted air-gap, which is used to obtain the function of slotted air-gap length. The equivalent magnetizing current model is used to extract the equivalent winding function for each PM pole. For retaining the basic assumption of WFT, the magnetic saturation is also considered by a proper increase in the air-gap length in the front of the stator teeth. Findings A new hybrid analytical model (HAM) based on WFT is presented in this paper, which can simultaneously and accurately consider the effects of slotting, the magnetic saturation, the variation of PM operating point and the winding distribution. In fact, IWFT removes all the drawbacks of the conventional WFT. Moreover, IWFT is more user-friendly and faster than other analytical and numerical techniques. Practical implications The obtained HAM can be used for design, optimization and fault diagnosis in electric machines. Originality/value This paper presents a new HAM for accurate modeling the SMPM motors, which includes different considerations of electromagnetic modeling. This new HAM can also be used for modeling the other electric motors.

Purpose The purpose of this paper is to present a new optimal design for integral slot permanent magnet synchronous motors (PMSMs) to shape the air-gap magnetic field in sinusoidal and to reduce the cogging torque, simultaneously. Design/methodology/approach For obtaining this new optimal design, the influence of different magnetizations of permanent magnets (PMs), including radial, parallel and halbach magnetization is investigated on the performance of one typical PMSM by using the conformal mapping (CM) method. To reduce the cogging torque even more, the technique of slot opening shift is also implemented on the stator slots of analyzed PMSM without reduction in the main performance, including the air-gap magnetic field, the average torque and back-electromotive force (back-EMF). Findings Finally, an optimal configuration including the Hat-type magnet poles with halbach magnetization on the rotor and shifted slot openings on the stator is obtained through the CM method, which shows the main reduction in cogging torque and the harmonic content of air-gap magnetic field. Practical implications The obtained optimal design is completely practical and is validated by comparing with the corresponding results obtained through finite element method. Originality/value This paper presents a new optimal design for integral slot PMSMs, which can include different design considerations, such as the reduction of cogging torque and the total harmonic distortion of air-gap magnetic field by using the CM method.

An optimal permanent magnet synchronous motor (PMSM) should be a low cogging torque and a sinusoidal back-EMF. In this paper, different magnetizations and shaping models of permanent magnets (PMs) are investigated for achieving an optimal performance. The technique of slot opening shift is simultaneously implemented on the stator slots for more reducing of the cogging torque. To this end, the conformal mapping (CM) method as an accurate and fast technique is used to calculate the motor performance under each condition. In final, the optimal results obtained through the CM method are verified by comparing with the corresponding results obtained from the finite element method (FEM).

Purpose The purpose of this paper is to present an improved conformal mapping (ICM) method that simultaneously considers the influence of relative recoil permeability of PMs, the armature reaction, the stator slotting, and the magnetic saturation on determination of the PM operating point in its different parts. Design/methodology/approach The ICM method is a time-effective method that considers the magnetic saturation by suitable increments in air-gap length under each tooth and also the width of slot openings. In this paper, the analytical and numerical conformal mappings such as the Schwarz-Christoffel (SC) mapping are used for magnetic field analysis due to the permanent magnets and the armature reaction in one slotted air gap. The field solution in the slotted air gap is obtained through the modulation of field solution in one slotless air-gap using the complex air-gap permeance. Findings The ICM method can consider the magnetic saturation in different electric loadings, and also the variation of PM operating points in its different parts. Practical implications The ICM method is applied to one surface mounted permanent magnet (SMPM) motor and is verified by comparing with the corresponding results obtained through finite element method (FEM), and frozen permeability finite element method (FP-FEM). Originality/value This paper presents an ICM method with a new technique for saturation effect modeling, which can be used to separate and calculate the on-load components of air-gap field and torque.