A time‐domain finite element homogenization technique for lamination stacks using skin effect sub‐basis functions

Development of an homogenization technique to directly and efficiently take the eddy current effects in laminated magnetic cores within time domain finite element (FE) analyses. The technique is developed for being used within a 3D magnetodynamic b-conform FE formulation, e.g., using a magnetic vector potential. To avoid a fine FE discretization of all the laminations of a magnetic core, this one is considered as a source region that carries predefined current and magnetic flux density distributions describing the eddy currents and skin effect along each lamination thickness. Both these distributions are related and are first approximated with sub-basis functions. Through the homogenization or averaging of the sub-basis functions contributions in the FE formulation, the stacked laminations are then converted into continuums, thus implicitly considering the eddy current loops produced by parallel magnetic fluxes. The continuum is then approximated with classical FE basis functions and can be defined on a coarser discretization. The developed method appears attractive for directly and efficiently taking into account within finite element analyses the eddy current effects, i.e., the associated losses and magnetic flux reduction, that are particularly significant for high frequency excitations. The time domain analysis allows the consideration of both nonlinear and transient phenomena. The averaging of sub-basis functions contributions, describing fine distributions of fields in a FE formulation, leads to an original way to homogenize laminated regions. The proposed method is naturally adapted for time domain analyses and in some sense generalizes what can be done more easily in the frequency domain.