Efficient Modeling Approach for Motion-Induced Eddy Currents in Ferromagnetic Conductors With Magnetic Equivalent Circuits

Calculating electromagnetic fields, including moving ferromagnetic conductors, often requires a computationally expensive finite element analysis. As a result, coupled electromagnetic-mechanical simulations or optimisations of mechatronic devices may become impractical. Consequently, an efficient modelling approach based on magnetic equivalent circuits interacting with electric circuits of motion-induced eddy currents is presented. Based on the skin effect in moving conductors, the electromagnetic field is concentrated in the penetration depth, which is utilised during the discretisation and enables a significant reduction of the unknowns. The penetration depth is approximated by the magnetic diffusion equation and is assumed to be spatially constant. The provided approach applies to three-dimensional problems with linear high-permeability material behaviour if the geometry is invariant to the motion. To account for the geometry of the moving conductor and the boundary conditions of the magnetic field, an identified prefactor is introduced in the analytical estimation of the penetration depth. The presented modelling approach is applied to a generic geometry, and the results are compared to a finite element analysis for various constant velocities, geometric parameters, and magnetic permeabilities. The comparison shows good agreement across a wide range of parameters, with an accurate representation of the reluctance force, achieving a reduction in computation time of several orders of magnitude, once the prefactor in the estimation of the penetration depth is identified. Based on the presented discretisation, scalar values and the magnetic field distribution in the direction of motion are described accurately.