Development of a Mixed Solution of Maxwell’s Equations and Magnetic Equivalent Circuit for Double-Sided Axial-Flux Permanent Magnet Machines

This article presents a quasi-3-D analytical model for double-sided axial-flux permanent magnet machines (AFPMMs) with coreless structures. A simple, fast, and accurate technique is developed to calculate flux densities in different parts of the AFPMM combining the solution of Maxwell's equations and the magnetic equivalent circuit (MEC). In this technique, Maxwell's equations are used to generate flux sources that are used in the reluctance network of the MEC. After calculating all the reluctances and flux sources, the magnetic flux densities are obtained. This method takes into account the effects of permanent magnet (PM) reluctance, leakage flux between PM-to-PM, PM-to-rotor leakage flux at different PM edges, and the fringing flux effect. By considering these leakage fluxes as a factor called variation function in the design procedure of the machine, the analysis time is dramatically reduced compared to numerical methods while maintained high reliability. It should be noted that since considering saturation phenomenon effects in coreless AFPMM analysis does not give rise to significantly different performances, they are not included in the proposed model. Furthermore, the machine's main features, such as the axial and tangential components of the no-load flux density in the air-gap and stator areas, as well as the back electromotive force (EMF), are derived by using magnetic field solutions and simple equivalent circuits. Finally, to validate the accuracy of the proposed method, the analytical results are compared to the case that no leakage fluxes are included in the analytical model and to the 3-D finite-element analysis (FEA) in terms of computation time and accuracy.