Gerard Meunier, Quang-Anh Phan, Olivier Chadebec, Jean-Michel Guichon, Bertrand Bannwarth and Riccardo Torchio
This paper aims to study unstructured-partial element equivalent circuit (PEEC) method for modelling electromagnetic regions with surface impedance condition (SIBC) is proposed…
Abstract
Purpose
This paper aims to study unstructured-partial element equivalent circuit (PEEC) method for modelling electromagnetic regions with surface impedance condition (SIBC) is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The formulation is applied in the context of low frequency problems with volumic magnetic media and coils. Non simply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation.
Design/methodology/approach
Because of the use of Whitney face elements, two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The air is not meshed.
Findings
The new surface impedance formulation enables the modeling of volume conductive regions to efficiently simulate various devices with only a surface mesh.
Research limitations/implications
The propagation effects are not taken into account in the proposed formulation.
Originality/value
The formulation is original and is efficient for modeling non simply connected conductive regions with the use of SIBC. The unstructured PEEC SIBC formulation has been validated in presence of volume magnetic nonconductive region and compared with a SIBC FEM approach. The computational effort is considerably reduced in comparison with volume approaches.
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G. Meunier, Y. Le Floch and C. Guérin
To model magneto‐harmonic devices including solid conductors with holes when the skin depth is very small.
Abstract
Purpose
To model magneto‐harmonic devices including solid conductors with holes when the skin depth is very small.
Design/methodology/approach
The 3D finite element magnetic scalar potential formulation combined with the surface impedance condition approximation is used. It allows the modelling of thin skin depth effect at low cost.
Findings
The paper shows how to use surface impedance condition for solid conductors with holes, when using the magnetic scalar potential. Specific equations must be added to respect Ampere's theorem. The paper establishes these equations and the coupling with the finite element formulation. The final system of equations is symmetric.
Research limitations/implications
The formulation allows to treat linear material in the magneto‐harmonic assumption.
Originality/value
The use of surface impedance condition with the 3D finite element magnetic scalar potential formulation is well known. The originality is to take into account holes (multiply connected conductors).
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Andrzej Demenko and Dorota Stachowiak
The aim of the paper is to find the effective algorithms of electromagnetic torque calculation.
Abstract
Purpose
The aim of the paper is to find the effective algorithms of electromagnetic torque calculation.
Design/methodology/approach
The proposed algorithms are related to the analysis of electrical machines using the methods of equivalent magnetic networks. The presented permeance and reluctance networks are formulated using FE methods. Attention is paid to the algorithms of electromagnetic torque calculation for 3D models. The virtual work principle is applied. The principle is adapted to the discrete network models. The network representations of Maxwell's stress formula are given.
Findings
The proposed method of electromagnetic torque calculation can be successfully applied in the 3D calculations of rotating electrical machines. It can be used for scalar and vector potential formulations. The obtained results and their comparison with the measurements show that the method is sufficiently accurate.
Originality/value
The presented formulas of electromagnetic torque calculation are universal and can be successfully applied in the FE analysis of electrical machines using nodal and edge elements.
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O. Maloberti, V. Mazauric, G. Meunier and A. Kedous‐Lebouc
The purpose of this paper is to introduce the dynamic hysteresis and losses of soft magnetic materials in numerical computation of high‐sensitive devices.
Abstract
Purpose
The purpose of this paper is to introduce the dynamic hysteresis and losses of soft magnetic materials in numerical computation of high‐sensitive devices.
Design/methodology/approach
So as to do this, the authors propose to lump all the microscopic dynamic effects due to averaging and smoothing techniques that lead to the definition of a dynamic field as proposed by other contributions. In this paper, the method to implement the modified field diffusion process in finite element computations is investigated, explained, detailed and put to the test.
Findings
In order to take microscopic magnetization reversal processes and eddy currents that damp the field at the mesoscopic scale, the authors have been led to define a new dynamic property Λ representative of the magnetic structure and its easiness to change. It is involved in an additional term in both the magnetic behaviour law and the bulk and surface coupling formulations describing the physical problem in iron and at the borders.
Research limitations/implications
This model can only be used for macroscopic pieces for which each dimension is bigger than at least four times the characteristic length of magnetic domains.
Originality/value
The originality of the paper comes from the need to investigate the possibility to predict iron losses and the corresponding dynamic hysteresis during the processing computation of power electrical devices such as accurate sensors and high‐sensitive actuators of earth leakage circuit breaker for example.
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Yann Le Floch, Christophe Guérin, Dominique Boudaud, Gérard Meunier and Xavier Brunotte
This paper presents the modeling of a current transformer by various methods with the FLUX3D software. The technique used is based on the finite element method coupled with…
Abstract
This paper presents the modeling of a current transformer by various methods with the FLUX3D software. The technique used is based on the finite element method coupled with electric circuits. A magnetic scalar potential reduced versus T0 formulation (T0ϕ−ϕ) taking into account the electric circuits with an air‐gap is used for this purpose. The air‐gap is described either by a thin volume region or by a surface region.
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H. Szambolics, L.D. Buda‐Prejbeanu, J.C. Toussaint and O. Fruchart
The aim of this work is to present the details of the finite element approach that was developed for solving the Landau‐Lifschitz‐Gilbert (LLG) equations in order to be able to…
Abstract
Purpose
The aim of this work is to present the details of the finite element approach that was developed for solving the Landau‐Lifschitz‐Gilbert (LLG) equations in order to be able to treat problems involving complex geometries.
Design/methodology/approach
There are several possibilities to solve the complex LLG equations numerically. The method is based on a Galerkin‐type finite element approach. The authors start with the dynamic LLG equations, the associated boundary condition and the constraint on the magnetization norm. They derive the weak form required by the finite element method. This weak form is afterwards integrated on the domain of calculus.
Findings
The authors compared the results obtained with our finite element approach with the ones obtained by a finite difference method. The results being in very good agreement, it can be stated that the approach is well adapted for 2D micromagnetic systems.
Research limitations/implications
The future work implies the generalization of the method to 3D systems. To optimize the approach spatial transformations for the treatment of the magnetostatic problem will be implemented.
Originality/value
The paper presents a special way of solving the LLG equations. The time integration a backward Euler method has been used, the time derivative being calculated as a function of the solutions at times n and n+1. The presence of the constraint on the magnetization norm induced a special two‐step procedure for the calculation of the magnetization at instant n+1.
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Norio Takahashi, Koji Akiyama, Hirokazu Kato and Kanji Kishi
To provide an approach to design the optimal open type magnetic circuit of permanent magnet producing uniform field.
Abstract
Purpose
To provide an approach to design the optimal open type magnetic circuit of permanent magnet producing uniform field.
Design/methodology/approach
The Biot‐Savart's law and evolution strategy are used for the initial design of permanent magnet configuration. In order to improve the uniformity, the ON/OFF method, which is the topology optimization method, is used for determining the shape of magnetic material which is set around the permanent magnet.
Findings
The optimal topology of permanent magnet and shape of magnetic material around it, which can produce nearly uniform field of about 0.15T, is obtained. The obtained uniformity is 3,583 ppm. More work for improving the uniformity is necessary.
Originality/value
A new approach for obtaining the optimal shape of open type magnetic circuit which may be used for magnetic resonance imaging is carried out.
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O.J. Antunes, J.P.A. Bastos and N. Sadowski
The purpose of this paper is to compare torque calculation methods when a non‐conforming movement interface is implemented by means of Lagrange multipliers.
Abstract
Purpose
The purpose of this paper is to compare torque calculation methods when a non‐conforming movement interface is implemented by means of Lagrange multipliers.
Design/methodology/approach
The following methods are here used for computing the torque in a synchronous machine and in a switched reluctance motor: Arkkio's method (AM), local Jacobian matrix derivative (LJD) method, Maxwell stress tensor method (MST) and co‐energy variation method.
Findings
This paper shows that, the numerical stability produced by Lagrange multipliers yields a stable torque result, even in thin airgap machines if AM, LJD method or MST method are used.
Originality/value
This work presents a comparative study to indicate the performance of the most commonly used torque calculation methods, when a non‐conforming technique is used, considering a small displacement of the rotor, which is necessary for dynamic cases or coupling with circuit.
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Ruth V. Sabariego and Patrick Dular
The aim of the present paper is to compare the performances of a finite‐element perturbation technique applied either to the h‐ conform magnetodynamic formulation or to its b‐…
Abstract
Purpose
The aim of the present paper is to compare the performances of a finite‐element perturbation technique applied either to the h‐ conform magnetodynamic formulation or to its b‐ conform counterpart in the frame of nondestructive eddy‐current testing problems.
Design/methodology/approach
In both complementary perturbation techniques, the computation is split into a computation without defect (unperturbed problem) and a computation of the field distorsion due to its presence (perturbation problem). The unperturbed problem is conventionally solved in the complete domain. The source of the perturbation problem is then determined by the projection of the unperturbed solution in a relatively small region surrounding the defect. The discretisation of this reduced domain is chosen independently of the dimensions of the excitation probe and the specimen under study and is thus well adapted to the size of the defect.
Findings
The accuracy of the perturbation model is evidenced by comparing the results of the two counterpart formulations to those achieved in the conventional way for different dimensions of the reduced domain. The size of the reduced domain increases with the size of the defect at hand. This proposed sub‐domain approach eases considerably the meshing process and speeds‐up the computation for different probe positions.
Originality/value
At a discrete level, the impedance change due to the defect is efficiently and accurately computed by integrating only over the defect itself and a layer of elements in the reduced domain that touches its boundary. Therefore, no integration of any flux variation in the coils is required.