The effect of slot length on flux distribution and rotordynamic coefficients in magnetic actuators using a boundary perturbation method

In previous work (Stephens and Casemore, 1999), the authors presented an analytical method to compute the flux distribution and negative stiffness of magnetic actuators. 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 (BVP) in the eccentric annulus for the MMF within the permanent magnet and air gap regions. The method is applicable to many common magnetic actuator designs but is limited to those with MMF sources that are located opposite of a smooth (unslotted) boundary. In this paper, the method is extended to remove this limitation and include the effect of slot length on flux distribution and rotordynamic coefficients. This is accomplished by adding a boundary perturbation step to the solution that accounts for the additional reluctance of the slots. The method is applied to a sample problem and is benchmarked against a finite element model. The results show good agreement between the two models up to a certain critical slot length. This critical slot length is shown to correspond to the traditional infinite slot length (that slot length beyond which no appreciable change in flux distribution occurs). The results indicate that slots in the stator have a significant impact on the negative stiffness and that the infinite slot length assumption is valid even for shallow and wide slots.