Influence of stator slot geometry and rotor eccentricity on field distribution in cylindrical magnetic actuators

The paper presents an analytical method for computing the instantaneous air-gap flux distribution in cylindrical magnetic actuators with slotted stators and rotor eccentricity. The method does not rely on permeance functions; therefore, the resulting flux distribution can be used to compute actuator properties such as negative stiffness, cogging torque, and back-emf. The method uses Fourier series expansions to model current distributions and permanent magnets as sources of magnetomotive force (MMF) on the air-gap boundary and then solves the Dirichlet boundary value problem in the eccentric annulus for the MMF within the permanent magnet and air gap regions. It accounts for the slotting effect by adding a boundary perturbation step to the solution that includes the decreased permeance of the slots. The method is applied to a sample problem that examines both the effects of slot length and slot width on negative stiffness coefficients. The method is benchmarked against finite-element solutions; the two models agree well up to a certain critical slot length. This critical slot length corresponds to the traditional infinite slot length (that slot length beyond which no appreciable change in flux distribution occurs). While the method is applied to a permanent magnet motor of internal rotor construction, it is generally applicable to many actuator topologies.