François Henrotte

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.

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.

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.

Modelling of electromechanical relays taking into account movement and electric circuits

This paper presents a numerical modelling of an electromechanical relay connected with an electric excitation circuit. This transient modelling not only takes into account the classical electromagnetic equations of the device but also the movement and circuit equations. The use of the finite element-boundary element coupling method facilitates the computation of the movement while the actual coupling with circuit equations is necessary for an accurate and reliable representation of transient phenomena. >

Modeling of ferromagnetic materials in 20 finite element problems using Preisach's model

A complete 2-D finite-element modeling for ferromagnetic materials is described. It is based on the definition of an adapted constitutive law which has to be completed by an hysteresis model like Preisachs one. A representation of the irreversible part of the ferromagnetic behavior by equivalent currents is given; a classical nonlinear system must be solved finally. Some numerical results are presented to underline the physical capacities of the method. Quantities like remanent induction and demagnetizing field can be calculated by this method. >

Magnetostatic and magnetodynamic mixed formulations compared with conventional formulations

Mixed formulations are characterized by the use, of not only one kind of unknown, but of two distinct kinds of unknowns. Some well-known mixed finite elements are well suited to the approximation of electromagnetic fields. Several characteristics of magnetostatic and magnetodynamic mixed formulations are presented and discussed. The use of nodal, edge, facet and volume mixed elements enables their natural and rigorous discretization. Their advantages compared with conventional formulations are pointed out.

Error estimation and mesh optimisation using error in constitutive relation for electromagnetic field computation

This paper presents a complete methodology to control the quality of electromagnetic field computation using the finite element method. An error estimate is built up using the error in the constitutive relation. Proof is made that this estimate relates to the exact error in some cases. Both problems of control of quality and mesh optimisation are then discussed.

Influence of hysteresis on the behaviour of coupled finite element-electric circuit models

This paper describes the computation of waveforms of electrical current and voltage in inductances, taking into account the hysteresis phenomenon and electric circuit equations. The non-linear transient magnetic field is computed with the finite element method. The classical nonlinear case is compared to the hysteretic one: it is shown that hysteresis has a crucial importance on the waveform by introducing asymmetry and damping, and by modifying the natural frequency of the oscillations. >

A New Method for Axisymmetrical Linear and Non-Linear Problems

The problem of unacceptable inaccuracies sometimes observed in the fields computed with the classical axisymmetrical model (i.e., first-order finite elements with auxiliary potential V=A/r) is solved. Two methods are proposed to improve the accuracy of the results: isoparametrical second-order elements and first-order elements with a suitable coordinate transformation. The second method, using first-order elements, gives the exact solution for piecewise linear materials; it has also been generalized for nonlinear systems by defining a quadrilateral axis-dedicated element. >