Analytical and numerical techniques for solving Laplace and Poisson equations in a tubular permanent magnet actuator: Part I: Semi-analytical framework

We present analytical and numerical methods for determining the magnetic field distribution in a tubular permanent-magnet actuator (TPMA). In Part I, we present the semianalytical method. This method has the advantage of a relatively short computation time and it gives physical insight. We make an extension for skewed topologies, which offer the benefit of reducing the large force ripples of the TPMA. However, a lot of assumptions and simplifications with respect to the slotted structure have to be made in order to come to a relatively simple semianalytical description. To model the slotting effect and the related cogging force, we apply a Schwarz–Christoffel (SC) mapping for magnetic field and force calculations in Part II of the paper. Validation of the models is done with finite-element analysis. Index Terms—Analytical, permanent magnet, skewing, tubular actuator.