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

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.