Willy Legros

Calculation of eddy currents and associated losses in electrical steel laminations

Starting from the well known analytical formula for the eddy current losses in electrical steel laminations, saturation and edge effects are studied by means of 1D and 2D finite element models of a single lamination. A novel method for directly including the laminated core energy dissipation in a time stepped 2D model of a complete (rotating) machine is proposed. By way of example the method is applied to a tooth model with enforced flux waveforms.

Coupling of local and global quantities in various finite element formulations and its application to electrostatics, magnetostatics and magnetodynamics

A method for defining global quantities related to fluxes and circulations is proposed in the frame of the finite element method. The definition is in perfect accordance with the discretized weak formulations of the problems. It therefore enables a natural coupling between local and global quantities in various formulations, while keeping a symmetrical matrix for the system, and then is open to the coupling of physical problems. Applications are given for electrostatics, magnetostatics and magnetodynamics.

Mixed finite elements associated with a collection of tetrahedra, hexahedra and prisms

A generalization of the Whitney complex is proposed, which is not now associated with simplices, i.e. tetrahedra in three dimensions, but with collections of three kinds of geometric elements: tetrahedra, hexahedra and prisms. Nodal, edge, facet and volume finite elements, i.e. mixed elements, associated with collections of those geometric elements, are defined. Base functions for approximation relative to these finite elements are defined and their properties are established. A geometric interpretation of these functions is given. >

A Galerkin projection method for mixed finite elements

The aim of the proposed method is the projection of an electromagnetic field belonging to a given function space (continuous or not) onto a discrete one spanned by finite element basis functions. This technique is useful for imposing inhomogeneous boundary conditions or volumic source fields, for calculating a dual field given the primal one or for mesh to mesh interpolation.

A general and natural method to define circuit relations associated with magnetic vector potential formulations

A procedure is proposed to deal with magnetic vector potential finite element magnetodynamic formulations and the definition of their associated circuit relations, involving voltages and currents, especially for massive inductors. It consists in solving two successive problems thanks to the use of edge elements, the first problem releasing the second one, which is especially useful for efficient nonlinear time stepping analyses.

Transformation methods in computational electromagnetism

The representation of electromagnetic quantities by differential forms allows the use of nonorthogonal coordinate systems. A judicious choice of coordinate system facilitates the finite element modeling of infinite or very thin domains.

Harmonic-balance finite-element modeling of electromagnetic devices: a novel approach

In this paper, a novel and easy-to-implement approach to the harmonic-balance finite-element modeling of electromagnetic devices is presented. The governing system of nonlinear algebraic equations is derived assuming an arbitrary (anisotropic) magnetic constitutive law. It is solved by means of the Newton-Raphson (NR) method, the elaboration of which is very simple thanks to the introduction of the differential reluctivity tensor. The method is validated by applying it to a three-dimensional and a two-dimensional voltage-driven model of a three-phase inductor. The convergence of the NR scheme and the accuracy of the obtained harmonic-balance current waveforms are studied.

50 Hz magnetic field exposure influence on human performance and psychophysiological parameters: Two double‐blind experimental studies

Two double-blind studies were performed to examine magnetic field (MF) exposure effects and to determine the impact of temporal variation (continuous vs. intermittent exposure) of 100 mu T(rms) 50 Hz MF diurnal exposure on psychological and psychophysiological parameters in healthy humans. Three cephalic exposure sessions of 30-min, i.e., sham, continuous, and intermittent (15 s ON/OFF cycles) MF conditions, were involved. Each subject participated in all sessions, which were spaced at 1-wk intervals. In each session, mood ratings and performance measures were obtained before, during, or after exposure and several electrophysiological data (event-related brain potentials [ERP]) were recorded after each exposure session. These criteria were chosen to evaluate sensory functions as well as automatic and voluntary attentional processes. In experiment 1, 21 healthy male volunteers (20 to 27 years of age) were studied. Ten subjects were exposed at 13:30 h, and 11 subjects were exposed at 16:30 h. Statistically significant changes in the amplitude of ERP were observed after MF exposure in the dichotic listening task, indexing selective attention processes. Eighteen of the 21 original male volunteers took part in experiment 2, undertaken to better understand the results related to information processing involved in selective attention and control for ultradian rhythmicity. Exposure time for all the subjects was at 13:30 h. The analysis of the data again revealed significant amplitude changes of the ERP recorded in the dichotic listening task. Moreover, they demonstrated ERP latency and reaction time slowing in the oddball paradigm, a visual discrimination task after real MF exposure. These results also indicate that a low level 50 Hz MF may have a slight influence on event-related potentials and reaction time under specific circumstances of sustained attention.

A generalized source magnetic field calculation method for inductors of any shape

A general method to compute source fields in magnetostatics or magnetodynamics is presented for inductors of any shape. That source field is not the physical one because the zero divergence condition is not satisfied. However, the freedom so obtained is exploited to minimize its support as well as to reduce the CPU time. The use of edge finite elements enables its rigorous construction. A test problem illustrates the method.

Finite element modelling with transformation techniques

Transformation methods are a very powerful tool in finite element modelling. In many cases, an adequate mapping transforms the problem into an easier one or allows advantage to be taken of the symmetries. This paper demonstrates that any mapping can be handled automatically provided the classical vector analysis approach is given up for the benefit of a differential geometry approach. As a first example, it is shown that axisymmetrical problems need no more a particular treatment provided the mapping of the cylindrical coordinates on the cartesian ones is considered as it is. Furthermore, a novel axisymmetrical formulation is proposed which relies on one further transformation and improves considerably the quality of the interpolated field. Transformation methods are also of great help to model the infinite space by means of finite elements. Many authors have presented such transformations which are often instances of the same general shell transformation that is presented here.