Boundary-Free Analytic Magnetic Field Calculations Including Soft Iron and Permanent Magnets Using an Iterative Discretisation Technique

An extremely fast magnetostatic magnetic field modeling method is developed that includes nonlinear relative permeabilities (or “magnetic saturation”) of soft magnetic materials with nonuniform magnetization. The model assumes regions of linearity within the material in order to apply analytic equations and superposition. This article presents the general theory and method for 3-D geometries, along with a 2-D axisymmetric example case study that is of interest for tubular linear actuator (or motor) design. The case study maximizes the average air-gap flux of an axially magnetized pole piece and shows a close correlation of the internal and external magnetic flux densities with a finite element analysis. This demonstrates the method as suitable for large parametric searches of topologies, toward the optimization of electrical machines, linear actuators, transformers, or more general 3-D electromagnetic problems.