This paper reviews the progress that has been made in the analysis and design of axial-flux permanent-magnet machines over the past decade, with particular attention to aspects such as electromagnetic and thermal modeling, materials, manufacturing, pulsating torque, and extended speed range. Comparisons with other machine types and applications are also reviewed.

Recent Advances in Axial-Flux Permanent-Magnet Machine Technology

In this paper, a theoretical analysis of an axial magnetic coupling is presented, leading to new closed-form expressions for the magnetic axial force and torque. These expressions are obtained by using a 2-D approximation of the magnetic coupling geometry (mean radius model). The analytical method is based on the solution of Laplace's and Poisson's equations by the separation of variables method. The influence of geometrical parameters such as number of pole pairs and air-gap length is studied. Magnetic field distribution, axial force, and torque computed with the proposed 2-D analytical model are compared with those obtained from 3-D finite elements simulations and experimental results.

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Simple Analytical Expressions for the Force and Torque of Axial Magnetic Couplings

This paper presents a multi-slice analytical model for prediction of the open-circuit magnetic field in slotted semi-closed permanent-magnet axial flux synchronous machines. The technique is based on 2-D exact solution of the Maxwell's equations using the separation of variables method. The magnetic field expressions are developed in slots regions, slot opening regions, magnetic air gap regions, and permanent magnet regions leading to an exact calculation of the slot effects on the air gap magnetic field. The model is established considering that ferromagnetic parts are infinitely permeable, and end effects at inner and outer radii are neglected. The open circuit machine's global quantities (electromotive force and cogging torque) are then deduced from the local magnetic field expressions. Finally, the accuracy of the presented analytical model is validated by comparing its results to corresponding finite-element analyses for two different axial flux machines.

Analytical Modeling of the Open-Circuit Magnetic Field in Axial Flux Permanent-Magnet Machines With Semi-Closed Slots

Axial-flux permanent magnet (PM) synchronous machines are suitable for direct drive applications. Axial-flux PM synchronous machines with fractional windings provide high power density, low torque ripple, and sinusoidal phase voltages, but suffer from high rotor losses due to stator field harmonics and slotting. This paper formulates an electromagnetic model based on the polar coordinate representation of the air-gap magnetic field. No-load and load tests are carried out on a soft-magnetic-composite stator axial-flux machine to validate the model. Rotor losses represent the largest loss figure in this machine. Most rotor losses are due to slotting harmonics.

Electromagnetic Analysis of Axial-Flux Permanent Magnet Synchronous Machines With Fractional Windings With Experimental Validation

Magnetic-gearing effect has become increasingly attractive when designing direct-drive low-speed permanent-magnet machines. The machines derived from the magnetic-gearing effect can be termed as harmonic machines. Unlike the conventional types, harmonic machines rely on the field harmonics to achieve energy conversion and transmission. The detailed knowledge of the field distributions in the air gap is vitally important for predicting and optimizing its performance. In this paper, we present an analytical approach to calculate the magnetic field distribution in a low-speed permanent-magnet harmonic machine. A series-slot model which is composed of a group of partial differential equations concerning the scalar magnetic potential is built up. Then, the field solutions are obtained by using the method of separating variables and analyzing the field boundary conditions. Finally, the flux densities are derived from the scalar magnetic potentials. All the results agree well with those obtained from the finite element method.

Analytical Method for Magnetic Field Calculation in a Low-Speed Permanent-Magnet Harmonic Machine

A quasi-three-dimensional (3-D) analytical model of the magnetic field in an axial flux permanent-magnet synchronous machine is presented. This model is derived from an exact two-dimensional analytical solution of the magnetic field extended to the 3-D case by a simple and effective radial dependence modeling of the magnetic field. The obtained quasi-3-D solution allows rapid parametric studies of the air-gap magnetic field. Then, analytical modeling of the cogging torque is presented. It is based on the obtained quasi-3-D analytical solution. Results issued from the proposed model in the air gap are compared with those stemming from a 3-D finite-element method simulation as well as with prototype measured values.

Quasi-3-D analytical modeling of the magnetic field of an axial flux permanent-magnet synchronous machine

A quasi-three-dimensional (3D) analytical model of the magnetic field in an axial flux permanent magnet synchronous machine (AFPMSM) is presented. This model is derived from an exact 2D analytical solution of magnetic field extended to the 3D case by a simple and effective radial dependence modeling of the magnetic field. The obtained quasi-3D solution allows rapid parametric studies of airgap magnetic field. Then, an analytical modeling of the cogging torque is presented. It is based on the obtained quasi-3D analytical solution. Results issued from the proposed model in the airgap are compared with those stemming from a 3D finite elements method (FEM) simulation as well as with prototype measured values.

Quasi-3D analytical modeling of the magnetic field of an axial flux permanent magnet synchronous machine

In this paper, an analytical modeling of an axial flux permanent magnet synchronous generator (AFPMSG) is investigated. The proposed model is based on an exact two dimensional (2D) solution of the magnetic field in the generator. Then, the generator's quantities such as the phase electromotive force (EMF), the cogging torque and electromagnetic torque are written based on the developed exact 2D solution. To validate the proposed modeling, a 2D finite elements analysis (FEA) is performed, and results issued from the proposed model are compared with those stemming from a 2D FEA simulations. According to the simulation results, it is possible to evaluate the performance of the AFPMSG with reasonable accuracy via the developed analytical model

Analytical modeling of an axial flux permanent magnet synchronous generator for wind energy application

This paper describes the skewed analytical model of an axial flux permanent magnet synchronous machine (AFPMSM) for further optimization process of a 10 kW/130 rpm slotted axial flux machine dedicated to wind energy application. The proposed model is based on the exact 2D solution of the magnetic field in the generator by solving the Maxwell's equations. This approach is very helpful to calculate accurately the magnetic field distribution in the machine with a reasonable computation time. The global quantities of the machine (inductances, EMF) are then calculated by using the winding functions technique. The developed model is finally used to study the influence of skewing on the main quantities (EMF, cogging torque, main torque) of a 10 kW/130 rpm, 14 poles AFPMSM dedicated for wind energy applications.

Influence of skewing on the performances of an axial flux PM wind generator coupled to a diode rectifier

This paper presents a design optimization of an axial flux permanent magnet synchronous machine (AFPMSM). The design optimization is performed using separately two different algorithms: a deterministic algorithm and a stochastic algorithm. The used DIRECT algorithm and genetic algorithm (GA) are described and tested separately to optimize a 10kW / 130 rpm AFPMSM. The obtained results by the two algorithms are compared in terms of precision of the found global optimum, convergence speed and simplicity of implementation. In particular, optimal design results show the effectiveness of DIRECT algorithm.

J. Azzouzi

Papers

Quasi-3-D analytical modeling of the magnetic field of an axial flux permanent-magnet synchronous machine

Quasi-3D analytical modeling of the magnetic field of an axial flux permanent magnet synchronous machine

Analytical modeling of an axial flux permanent magnet synchronous generator for wind energy application

Influence of skewing on the performances of an axial flux PM wind generator coupled to a diode rectifier

Design Optimization of an Axial Flux PM Synchronous Machine: Comparison Between DIRECT Method and GAs Method