A Three Dimensional Analytical Study of the Excitation Field in a Permanent Magnet Synchronous Motor

In this paper, a three dimensional analytical study of some slot less synchronous permanent magnet machines is set up taking into account the real geometry of the machine. The rotor of the machine has surface sector-shaped permanent magnets, with rigid radial magnetisation, and without polar pieces. Two media are considered : the air gap of the machine and its magnets with empty space magnetic permeabilities on one hand, the stator and the rotor with infinite magnetic permeabilities on the other hand. Sources which are here permanent magnets, are modelled owing to Coulomb's model. The magnetic scalar potential is calculated in the air gap from which the flux density is deduced. This paper shows that a semi-analytical study of a surface permanent magnet machines can be done, leading to the possibilities of using many types of permanent magnets, and quantifying ends effects. This approach can hence contribute to the predetermination of some electric quantities like the counter E.M.F.