Analytical and Numerical Techniques for Solving Laplace and Poisson Equations in a Tubular Permanent Magnet Actuator: Part II. Schwarz–Christoffel Mapping

In Part I of the paper, we derive a semianalytical framework for the magnetic field calculation in the air gap of a tubular permanent-magnet (PM) actuator. We also make an extension for skewed topologies. However, the slotting effect and its related cogging force cannot be determined in a straightforward way. Therefore, in Part II, we apply the Schwarz-Christoffel (SC) conformal mapping method to one pole-pair of the tubular PM actuator. This mapping allows for field calculation in a domain where standard field solutions can be used. In this way, slotting effects can be taken into account; however, skewing cannot be implemented directly. The SC-conformal mapping method is valid only for two-dimensional Cartesian domains. We therefore apply a special transformation from the cylindrical to the Cartesian coordinate system to describe the tubular actuator as a linear actuator.