Equivalence between the method of magnetic images and the variable separation method in the study of some slotless surface permanent magnet synchronous machines

In the present paper, the equivalence between the magnetic images method and the classical variable separation method is set up. These methods are separately applied to calculate the magnetic scalar potentials and the magnetic vector potentials in the air-gap of some cylindrical synchronous machines, excited by surface permanent magnets with radial and/or azimuthal magnetisation, and without polar pieces. The rotor and the stator are assumed slotless, and the whole electric machine non saturated. The expressions of the magnetic scalar potentials of each method are interpreted, and their equivalence is established. The Mayn purpose of this paper is then the demonstration that the magnetic images method is applicable for the study of simplified synchronous machines. The interest of the magnetic images use in comparison with the variable separation method is shown.