The authors present a novel nonlinear homogenization technique for laminated iron cores in 3D FE models of electromagnetic devices. It takes into account the eddy current effects in the stacked core without the need of modelling all laminations separately. A nonlinear constitutive magnetic law is considered. The system of nonlinear algebraic equations obtained after time discretisation is solved by means of the Newton-Raphson scheme. By way of validation the method is applied to a 3D FE model of a laminated ring core with toroidal coil.

International audienceModel refinements of magnetic circuits are performed via a subdomain finite element method based on a perturbation technique. A complete problem is split into subproblems, some of lower dimensions, to allow a progression from 1-D to 3-D models. Its solution is then expressed as the sum of the subproblem solutions supported by different meshes. A convenient and robust correction procedure is proposed allowing independent overlapping meshes for both source and reaction fields, the latter being free of cancellation error in magnetic materials. The procedure simplifies both meshing and solving processes, and quantifies the gain given by each model refinement on both local fields and global quantities

Abstract-A subproblem technique is applied on dual formulations to the solution of thin shell finite element models. Both the magnetic vector potential and magnetic field formulations are considered. The subproblem approach developed herein couples three problems: a simplified model with inductors alone, a thin region problem using approximate interface conditions, and a correction problem to improve the accuracy of the thin shell approximation, in particular near their edges and corners. Each problem is solved on its own independently defined geometry and finite element mesh. I. INTRODUCTIONThe solution by means of subproblems provides clear advantages in repetitive analyses and can also help in improving the overall accuracy of the solution [1], [2]. In the case of thin shell (TS) problems the method allows to benefit from previous computations instead of starting a new complete finite element (FE) solution for any variation of geometrical or physical characteristics. Furthermore, It allows separate meshes for each subproblem, which increases computational efficiency.In this paper, a problem (p = 1) involving massive or stranded inductors alone is first solved on a simplified mesh without thin regions. Its solution gives surface sources (SSs) for a TS problem (p = 2) through interface conditions (ICs), based on a 1-D approximation [3], [4]. The TS solution is then considered as a volume source (VSs) of a correction problem (p = 3) taking the actual field distribution of the field near edges and corners into account, which are poorly represented by the TS approximation. The method is validated on a practical test problem using a classical brute force volume formulation.

In this paper, we investigate the modeling of ferromagnetic multiscale materials. We propose a computational homogenization technique based on the heterogeneous multiscale method (HMM) that includes both eddy-current and hysteretic losses at the mesoscale. The HMM comprises: 1) a macroscale problem that captures the slow variations of the overall solution; 2) many mesoscale problems that allow to determine the constitutive law at the macroscale. As application example, a laminated iron core is considered.

Model refinements of magnetic circuits are performed via a subproblem finite element method based on a perturbation technique. An approximate problem considering ideal flux tubes and simplified air-gap models is first solved. It gives the sources for a finite element perturbation problem considering the actual air gaps and flux tubes geometries with the exterior regions. The procedure simplifies both meshing and solving processes, and allows to quantify the gain given by each model refinement.Index Terms-Finite-element method (FEM), magnetic circuits, perturbation method.

A method for solving eddy current problems in two separate steps is developed for global-local analyses with hconform finite element formulations. An unperturbed problem is first solved in a global mesh excluding additional conductive regions. Its solution gives the sources for a sequence of other problems, perturbed by adding conductive regions. Each problem only requires a new adapted mesh of a local region. The way the local problems and their sources are defined leads to a significant speed-up of parameterized analyses, e.g. in optimization and sensitivity analyses.

Analyses of magnetic circuits with position changes of both massive and stranded conductors are performed via a finite element subproblem method. A complete problem is split into subproblems associated with each conductor and the magnetic regions. Each complete solution is then expressed as the sum of subproblem solutions supported by different meshes. The subproblem procedure simplifies both meshing and solving processes, with no need of remeshing, and accurately quantifies the effect of the position changes of conductors on both local fields, e.g. skin and proximity effects, and global quantities, e.g. inductances and forces. Applications covering parameterized analyses on conductor positions to moving conductor systems benefit from the developed approach.Index Terms-Finite element method (FEM), subdomain method, conductor systems.

Abstract-In this paper the authors propose an original timedomain extension of the frequency-domain homogenization of multi-turn windings in FE models. For the winding type in hand (e.g. round conductor with hexagonal packing), an elementary FE model is used for determining dimensionless frequency and time domain coefficients regarding skin and proximity effect. These coefficients are readily utilized for homogenizing the winding in the FE model of the complete device. The method is successfully applied to an axisymmetric 103-turn inductor. The results agree very well with those obtained by an accurate but very expensive FE model in which all turns are finely discretised.