Ruth V. Sabariego

A nonlinear time-domain homogenization technique for laminated iron cores in three-dimensional finite-element models

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

Time-Domain Homogenization of Windings in 2-D Finite Element Models

In this paper, the authors propose an original time-domain extension of the frequency-domain homogenization of multiturn windings in finite element (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 discretized

A Perturbation Method for Computing Field Distortions Due to Conductive Regions With

A method for solving eddy current problems in two separate steps is developed for global-local analyses with h-conform 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 speedup of parameterized analyses, e.g., in optimization and sensitivity analyses

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This paper deals with the acceleration of the hybrid finite-element/boundary-element analysis of three-dimensional (3-D) eddy-current problems by means of the fast multipole method. An adaptive truncation scheme for the multipole expansion of the 3-D Laplace Green function is proposed. As an application example, the TEAM workshop problem 28 is considered. The computational cost without and with fast multipole acceleration is discussed.

-Conform Magnetodynamic Finite Element Formulations

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.

Fast multipole acceleration of the hybrid finite-element/boundary-element analysis of 3-D eddy-current problems

In this paper, the authors deal with the finite-element (FE) modeling of eddy-current effects in form-wound windings of electrical machines using a previously proposed general frequency- and time-domain homogenization method. By way of demonstration and validation, a real-life 1250-kW induction machine with double-layer stator winding is considered. The skin and proximity effects in one stator conductor (copper bar) are first quantified by means of a simple low-cost FE model, leading to complex and frequency-dependent coefficients for the homogenized winding (reluctivity for proximity effect and conductivity or resistance for skin effect). These complex coefficients are subsequently translated into real-valued and constant coefficients that allow for time-domain homogenization when introducing a limited number of additional degrees of freedom in the FE model. All results obtained with the homogenized model (considering one conductor or a complete slot) agree well with those produced by a brute-force approach (modeling and finely discretizing each conductor).

Computational Homogenization for Laminated Ferromagnetic Cores in Magnetodynamics

A perturbation technique applied to the finite element modelling of eddy-current nondestructive testing (ECNDT) problems is developed for taking into account differential probes and multiply connected domains. It concerns a h-conform formulation. The source term of the formulation is directly determined from the unperturbed field and the voltage change due to the presence of the flaw is calculated by performing an integral over the defect and a layer of elements in the exterior domain that touch its boundary

Homogenization of Form-Wound Windings in Frequency and Time Domain Finite-Element Modeling of Electrical Machines

The increasing use of composite materials in the technological industry (automotive, aerospace, ... ) requires the development of effective models that account for the complexity of the microstructure of these materials and the nonlinear behaviour they can exhibit. In this paper we develop a multiscale computational homogenization method for modelling nonlinear multiscale materials in magnetostatics based on the finite element method. The method solves the macroscale problem by getting data from certain microscale problems around some points of interest. The missing nonlinear constitutive law at the macroscale level is derived through an upscaling from the microscale solutions. The downscaling step consists in imposing a source term and determining proper boundary conditions for microscale problems from the macroscale solution. For a two-dimensional geometry, results are validated by comparison with those obtained with a classical brute force finite element approach and a classical homogenization technique. The method provides a good overall macroscale response and more accurate local data around points of interest.

A perturbation approach for the modelling of eddy current nondestructive testing problems with differential probes

Model 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.

Finite Element Computational Homogenization of Nonlinear Multiscale Materials in Magnetostatics

Purpose – This paper seeks to develop a sub‐domain perturbation technique to efficiently calculate strong skin and proximity effects in conductors within frequency and time domain finite element (FE) analyses.Design/methodology/approach – A reference eddy current FE problem is first solved by considering perfect conductors. This is done via appropriate boundary conditions (BCs) on the conductors. Next the solution of the reference problem gives the source for eddy current FE perturbation sub‐problems in each conductor then considered with a finite conductivity. Each of these problems requires an appropriate volume mesh of the associated conductor and its surrounding region.Findings – The skin and proximity effects in both active and passive conductors can be accurately determined in a wide frequency range, allowing for precise losses calculations in inductors as well as in external conducting pieces.Originality/value – The developed method allows one to accurately determine the current density distributio...