Improvements on winding flux models for a slotless self-bearing motor

For a large-scale slotless permanent-magnet self-bearing motor actuator, finite-element analysis (FEA) indicates a significant difference from the previous simple winding flux model. In this paper, we first derive a general winding current distribution. We use and compare three analytical methods to calculate the air gap field produced by the windings when only torque is required. Each of the first two solves one homogeneous Laplace's equation with the current source incorporated into a harmonic boundary condition, in polar and Cartesian coordinates, respectively. The good agreement between these two allows the third method to treat the current source separately and solve one nonhomogeneous and one homogeneous Laplace's equations simultaneously in two subregions, simply using the unwrapped geometry in Cartesian coordinates. The result from the two-layer model matches the FEA prediction for this particular actuator very well and it is thus more accurate to model the thick windings as a separate source layer. We propose a simple approach to include the interference of the magnetic fields due to the segment currents whenever a bearing force is required, which was completely neglected in all the previous models. The approach is quite accurate, as shown by the corresponding FEA result.