Analytical Calculation of No-load Magnetic Field Distribution in the Slotted Airgap of a Permanent Magnet Synchronous Motor

An analytical method for calculation of no-load magnetic field distribution in the slotted airgap of a surface permanent magnet synchronous motor has been presented. The method involves the solution of the governing field equations in polar coordinates in the annular airgap region of a slotless motor in which the magnets are assumed to have uniform radial magnetization and constant relative recoil permeability. Then it introduces the notion of complex relative airgap permeance calculated from the conformal transformation to account the effect of slotting. As a result, an accurate solution of both radial and tangential components of the flux density can be obtained.