Analytic solutions of magnetic field problems in slotless permanent magnet machines

The Grinberg method is used to derive general 2D and 3D analytical solutions of the magnetic field problem in the slotless permanent magnet machines. The machines with the internal and external rotors are presented. The radial and unidirectional magnetisation of the poles is considered. The effect of magnetisation and shapes of the magnet poles on the field distribution is analyzed. The 2D and 3D analytic solutions of the problem are compared. As a result of comparison the effect of the finite axial length of the machine on the flux density in the air gap is evaluated.