An Efficient 3-D FEM Model for Electromagnetic Force and Torque Calculation in Null-Flux Superconducting EDS Trains

This article presents an efficient 3-D finite element method (FEM) model for calculating dynamic electromagnetic forces and torques in a null-flux superconducting electrodynamic suspension (EDS) train. The model introduces two innovations to enhance efficiency: a static modeling method for simulating the moving magnets that incorporates magnetic potential boundary (MPB) conditions, and a method for minimizing the modeling unit of the suspension coils using the superposition principle. The model consists of two submodels. Submodel 1 performs a steady-state calculation of the magnetic vector potential for the superconducting magnets and suspension coils, represented as a time- and space-dependent interpolation function, which is then applied in submodel 2 to conduct a transient analysis of induced currents, dynamic forces, and torques on the suspension coils. These forces and torques are subsequently translated into their effects on the bogie. The model was validated using both our experimental data and the Yamanashi Maglev Test Line data. Moreover, it reduces computation time by over 98% compared to an existing 3-D FEM model that employs the moving mesh technique and periodic boundary conditions. Using this model, we investigated the dynamic forces and torques on the bogie, revealing how their averages and harmonics evolve with the bogie’s posture. The proposed modeling method is also well-suited for the precise and efficient simulation of electromagnetic coupling in other systems with infinitely long or moving components, offering significant potential for a wide range of applications.