Analytical Solution of Magnetic Field Distribution in Brushless Permanent Magnet Machines With Rotor Axis Deflection

An analytical technique is presented to predict the magnetic field distribution in the brushless permanent magnet machine with rotor axis deflection. Focusing on the no-load field due to the magnets, a perturbation method is employed to solve the governing equations and associated boundary conditions defined on the cross section along the flux paths. The derived results consisting of the zeroth-order and the first-order terms are validated by the finite-element analysis. According to the case study, the curves from the two calculations are consistent with each other. It also shows that the rotor axis deflection results in some distortion of the air-gap flux density waveform.