Two-Dimensional Magnetostatic Finite-Element Simulation for Devices With a Radial Symmetry

This paper proposes a 2-D magnetostatic finite-element solver for radially symmetric devices, complementary to the standard Cartesian and axisymmetric solvers, which are typically used for translatory and cylindrically symmetric configurations. In contrast to the Cartesian and axisymmetric cases, a specific difficulty is encountered due to the particular dependence of the magnetic vector potential on the radial coordinate caused by the requirement for radial symmetry. Dedicated finite-element shape functions are developed such that the partition-of-unity property, consistency, and convergence of the formulation are guaranteed. Implementation aspects and modeling peculiarities are discussed. The new solver is validated for models in which analytical solutions exist. The modeling accuracy of the new 2-D solver is compared with a 3-D model for the calculation of the electromotive force and the electromagnetic torque of a twin-rotor axial-flux permanent magnet synchronous machine.