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This paper describes a methodology for modelling a six-phase claw-pole alternator with its electrical environment. Magnetic nonlinearities, eddy currents and rectifiers are taken into account. To solve magnetodynamic problems, we use the modified magnetic vector potential formulation. The complex structure of the machine requires a 3D finite element analysis. To limit the mesh size, we introduced a refinement strategy based on the calculation of the time derivative of magnetic vector potential, solution of the magnetostatic case. In addition, we propose to reduce the transient state by improving the initial solution from the solution of a magnetostatic problem. These different numerical techniques reduce drastically the computational time and memory resources. To validate the proposed approach, some results are compared with experimental ones.

In this paper a guaranteed equilibrated error estimator is developed for the 3D harmonic magnetodynamic problem of Maxwell’s system. This system is recasted in the classical A-phi potential formulation and solved by the Finite Element method. The error estimator is built starting from the A-phi numerical solution by a local flux reconstruction technique. Its equivalence with the error in the energy norm is established. A comparison of this estimator with an equilibrated error estimator already developed through a complementary problem points out the advantages and drawbacks of these two estimators. In particular, an analytical benchmark test illustrates the obtained theoretical results and a physical benchmark test shows the efficiency of these two estimators.

In the domain of field computation with the finite element method, choosing the mesh refinement is an important step to obtain an accurate solution. In order to evaluate the quality of the mesh, a posteriori error estimators are frequently used. In this communication we propose to analyze and to compare residual and equilibrated error estimators for eddy current problems in the case of A-φ and TΩ formulations. The different properties of the estimators will be discussed.

To determine the steady state of an electromagnetic structure with the finite element method without calculation of the transient state. The proposed method permits to reduce the computation time if the transient state is important. In the case of coupling magnetic and electric circuit equations to obtain the steady state with periodic conditions, an approach can be to discretise the time with periodic conditions and to solve the equation system. Unfortunately, the computation time can be prohibitive. In this paper, the authors proposed to use the waveform relaxation method associated to Newton method to accelerate the convergence. The obtained results show that the proposed approach is efficient if the transient state is important. On the contrary, if the transient is very low it is preferable to use the classical approach namely the time stepping finite element method. The main limitation of the proposed approach is the necessity to evaluate or to know the time constant and consequently the duration of the transient state. Moreover the method requires some important memory resources. In the context of the use of the time stepping finite element method, one of the problems is the computation time which can be important to obtain the steady state. The proposed method permits avoidance of this difficulty and gives directly the steady state. The novelty is the proposal of the waveform relaxation Newton method to obtain directly the steady state in the case of the study of the three phases transformer

In numerical computation, the finite element (FE) method associated with external electric circuits is often used to evaluate electromagnetic devices with voltage sources. To study the solution of the steady state, the computation time can be prohibitive due to a large transient state compared to the time step used to discretize the time domain. In this paper, a method based on Waveform Relaxation Method is developed in order to impose the steady state of the solution in the case of a nonlinear magnetostatic problem coupled with electric circuit equations.

In the modeling of eddy current problems, potential formulations are widely used in recent days. In this paper, the results of residual-based a posteriori error estimators, which evaluate the discretization error in the finite-element computation, are extended to the case of several kinds of source terms for both A/φ and T/Ω harmonic formulations. The definitions of the estimators are given and some numerical examples are provided to show the behavior of the estimators.

A strategy of mesh adaptation in eddy current finite element modeling is developed from both residual and hierarchical error estimators. Wished distributions of element sizes of adapted meshes are determined from the element-wise local contributions to the estimators and define constraints for the mesh generator. Uniform distributions of the local error are searched.

In this work, an a posteriori residual error estimator is presented for the 3D eddy current problem modeled by the space-time A-phi potential formulation. It is solved by the finite element method in space and the backward Euler scheme in time. Once the reliability as well as the efficiency of the estimator are established, two numerical tests are proposed: an analytical one in order to validate the theoretical results and a physical one in order to illustrate the performance for a real eddy current problem.

Mesh-to-mesh field transfer arises frequently in finite element computations. Typical applications may concern remeshing, multigrid methods, domain decomposition and multi-physics problems. For electromagnetic fields, one of the essential constraints in such transfers is to conserve energetic quantities such as the magnetic energy and the joule heating. Within the framework of Galerkin projection on overlapping domains, we introduce the definition of energetic norms for electromagnetic fields. The corresponding formulations we propose, provide energy-conserving projection of electromagnetic fields between different meshes.

The finite element computation of eddy current problems introduces numerical error. This error can only be estimated. Among all error estimators (EEs) already developed, two estimators, called residual and hierarchical EEs, proven to be reliable and efficient, are theoretically and numerically compared. Both estimators show similar behaviors and locations of the error.

In finite element computations, the choice of the mesh is crucial to obtain accurate solutions. In order to evaluate the quality of the mesh, a posteriori error estimators can be used. In this paper, we develop residual-based error estimators for magnetostatic problems with both classical formulations in term of potentials used, as well as the equilibrated error estimator. We compare their behaviors on some numerical applications, to understand the interest of each of them in the remeshing process.

To solve multi-physics problems, weak coupling of finite element calculations can be carried out: the subproblems of which the physical nature differs, are solved separately on their own meshes. In this case, Galerkin projection provides useful tool to ensure the transfer of physical fields between different meshes. In terms of implementation, the Galerkin projection system can be either accurately assembled over the intersection of two meshes or approximately integrated over the target mesh. This paper describes and compares these two implementation techniques for the Galerkin projection.

Purpose: In this paper, the aim is to propose a residual‐based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a finite element method in the case of the harmonic A‐φ formulation. Design/methodology/approach: The residual based error estimator used in this paper verifies the mathematical property of global and local error estimation (reliability and efficiency). Findings: This estimator used is based on the evaluation of quantities weakly verified in the case of harmonic A‐φ formulation. Originality/value: In this paper, it is shown that the proposed estimator, based on the mathematical developments, is hardness in the case of the typical applications.

For eddy current problems, potential formulations are widely used nowadays. In this paper, residual based a posteriori error estimators are introduced to evaluate the discretization error in the finite element calculation in both case of A /φ and T /Ω harmonic formulations. A device with eddy currents is studied in order to show the efficiency of the proposed estimators.

Coupled problems are made up of subproblems of which the physical nature differs. Using indirect coupling models, the subproblems are calculated separately on their own meshes to ensure precision. To obtain a precise solution for the total problem, it is important to ensure the transmission of information between the subproblems. In this paper, we present field projection methods on overlapping domains. In comparison to earlier works, the classical $L^{2}$ or $mathbf{L}^{2}$ projection theory is extended to $H(mathbf{grad})$, $mathbf{H}(mathbf{curl})$ and $mathbf{H}(div)$ to obtain increased projection accuracy for the distributional derivatives. A Petrov-Galerkin method is then presented to fill the test space using a bi-orthogonal basis, without losing the optimality of the result in comparison to the $L^{2}$ or $mathbf{L}^{2}$ Ritz-Galerkin method. Using the Petrov-Galerkin method and bi-orthogonal test functions, the projection is presented using a diagonal matrix. However, in the standard Ritz-Galerkin projections, a linear system must be solved.

In this paper, we focus on an a posteriori residual-based error estimator for the T/Omega magnetodynamic harmonic formulation of the Maxwell system. Similarly to the A/Phi formulation, the weak continuous and discrete formulations are established, and the well-posedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad-hoc Helmholtz decomposition for the T/Omega case is derived, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results.

Short circuits in turbo-generator stators can lead to a modification of the magnetic flux distribution that impacts the performances and, in some extreme cases, can lead to local damage of the iron core. This work presents the modeling of short circuited laminations in a stator yoke of a turbo-generator. A 3D finite element (FE) model, associated to a homogenization technique, is used to calculate the short circuit current. The results are compared with the experiment, especially for the electrical signature of the diagnosis test known as Electromagnetic Core imperfection detector (El Cid).

This paper is devoted to the derivation of an a posteriori residual-based error estimator for the A-Phi magnetodynamic harmonic formulation of the Maxwell system. The weak continuous and discrete formulations are established, and the well-posedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad hoc Helmholtz decomposition is proven, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results.

An approach based on the double Lagrange multipliers is developed in the finite element method in order to impose complex periodic or anti-periodic boundary conditions. The magnetostatic equations are solved using the vector or scalar potential formulations. In order to show the possibilities of the proposed approach, an example of application is studied and the results are discussed.

The presented work is about the implementation of a vector hysteresis model in a Finite Integration Technique (FIT) calculation code. This is achieved in the magnetostatic case using the vector potential formulation and with the external electric circuit coupling. The used behavior law model is the vectorized Jiles-Atherton model with the magnetic flux density as input variable. The proposed approach is illustrated by modeling a coil made of Soft Magnetic Composite (SMC) magnetic core. Comparison with measured global quantities is also performed.

In this paper, we propose to introduce the single and double Lagrange multipliers approaches in the case of the finite element method (FEM). These approaches allow non-conforming meshes to be linked together. The methods introduced are developed in the case of a magnetostatic problem solved by the scalar potential formulation. An application is studied and the results obtained by both approaches are compared.

Projecting discrete quantities from one mesh to another one is a critical operation which is usually required in multi-physical problems. The efficiency of a Galerkin projection method is studied for magneto-thermal and magneto-elasticity couplings. As examples of application, two electromagnetic devices are studied: a three-phase busbar system as a magneto-thermal problem and an electromagnet as a magneto-mechanical problem.

In term of magneto-thermal coupling, two different strategies � direct and indirect � can be used. One of the advantages of the indirect coupling strategy is its ability to solve each problem separately on dedicated meshes. However, such a technique requires a projection of each solution obtained on one mesh onto another one. In this paper a comparison of two projection methods � collocation and Galerkin projection method - is presented.

We describe in this paper the design of a permanent magnet actuator for linear and rotary movement. The actuator can make linear and rotary movements and special attention has been placed on the simplicity and the swiftness behavior. At first, we compare the different approaches to perform a linked movement and a structure is adopted. Then, we detail the adopted magnetic conversion through a rotary machine and a linear actuator. In a last part, the studied actuator is presented and results concerning the flux linkages and forces are given using 3D finite element simulations.

A paraître
Abstract - To solve the Maxwell’s equations in the magnetosatic case the formulations in terms of vector potential or scalar potential can be used. If to solve the equations we use the Finite Element Method on the primal mesh we obtain two complementary solutions. In this paper, both formulations in terms of potential and using the fields H and B are developed and solved with the help of the Finite Integration Technique. The solutions computed in the primal and dual meshes are analysed and discussed.

The accuracy of the magnetic field strength estimation in rotational single sheet tester is investigated with the finite element method and measurements. The incorporation of a vector hysteresis model, derived from the original scalar Jiles-Atherton model, in a finite element magnetic field code is performed. The application of this method leads to use the differential reluctivity tensor that arises naturally from the vector model. The effect of the shielding on a Rotational Single Sheet Tester is analyzed in order to improve the field homogeneity in the sample area.

For designers, calculation of local fluxes can be very useful. In the vector potential formulation, the local fluxes can be easily deduced. In the scalar potential formulation, the determination of these fluxes presents some difficulties. In this paper, we present three methods to compute a flux through any surface in the scalar potential formulation. These are compared with the one used in the vector potential formulation for two application examples.

Nowadays, the electromagnetic actuators for industrial processes have to present very specific features which can not always be obtained by classical machines. Hence, to reach the wanted features, one has to design the actuator and to quantify its performance with a good accuracy and reasonable computation time. The purpose of this paper is to present the design and the study of a linear actuator. First, we present the design of the chosen actuator structure. The second part is devoted to describe the approaches used (permeance network model and the 3D Finite element model) to study the behaviour of the actuator. Lastly, we give the results of the study, obtained by both models, and we compare them to experimental data obtained from the prototype build up.

An accurate thrust control of permanent magnet linear synchronous motors (PMLSM) is more efficient with a fine knowledge of the harmonics value of the electromotive force (EMF). This is often difficult to obtain experimentally for a PMLSM. As a consequence, this paper deals with the study of the non-sinusoidal EMF of a PMLSM using the 3D Finite-Element Method (FEM). Two potential formulations are used to consider several cases. Afterwards, for the same accuracy, the computation times are examined. The results of the FEM are compared to those given by the measurements from a test bench composed of a Siemens LIMES400/120 linear motor and a dSPACE DS1005 real-time controller board. Finally, the advantages and the limitations of the FE Analysis will be discussed.

In this paper, a 7-phase Axial-flux Double-rotor Permanent Magnet Synchronous Machine is studied using analytical and Finite Element methods. This type of machine shows a higher sensitivity to the inductance harmonics and electromotive force (emf) compared with the 3-phase machines. So, the conventional analytical modeling method, in which only the first harmonic is taken into account, leads to significant errors in the determination of the control parameters, e.g. the frequency of Pulse Width Modulation Voltage Source Inverter. A multi-machine model explains the reasons for this sensitivity and a more sophisticated analytical method is used. Results are compared with those obtained by the 3-D FEM.

In this paper the slip surface and the moving band techniques are used to model the rotation of electrical machines in 3D with FEM and the results are compared. For the slip surface technique, several method are explained; such as the locked-step approach and linear and quadratic interpolation. For this study, the proposed techniques are applied to a permanent magnet synchronous machine. The comparison is carried out at no-load for the electromotive force and the cogging torque. Furthermore, the torque is also compared for the short-circuit case.

In this paper, the Finite Integration Technique and an approach to solve simultaneously the magnetic and electric circuit equations is presented in magnetostatic case. The developments of the FIT will be compared with those used for the Finite Element Method. As example of application an iron core coil is studied and the results of both approaches are compared

Résumé - In this communication, the Preisach and Jiles-Atherton models are studied to take hysteresis phenomenon into account in finite element analysis. First, the models and their identification procedure are briefly developed. Then, their implementation in the finite element code is presented. Finally, their performances are compared with an electromagnetic system made of soft magnetic composite. Current and iron losses are calculated and compared with the experimental results.

Résumé - In this communication, we propose a dynamical model of hysteresis giving the magnetization M in function of the flux density B. The mathematical development is based on the Jiles approach for frequency dependent hysteresis. The obtained model is simple to carry out and fast. The model is tested through a comparison with experimental results on FeSi steel sheets. Then, the accuracy and the range of application of the model are discussed.

Résumé - In electrical engineering, study and design of electromagnetic systems require more and more accurate models. To improve the accuracy of field calculation code, hysteresis phenomenon has to be taken into account to model ferromagnetic material. This material model has to be accurate and fast. In that context, two macroscopic models are often used: the Preisach and the Jiles–Atherton (J–A) models.
In this paper, both models are presented. Field calculation requires a model giving the magnetization M versus either the magnetic field H or the magnetic flux density B. Consequently, from the classical Preisach and J–A, two sub-models M(H) and M(B) are deduced. Then, we aim at comparing these models in terms of identification procedure facilities, accuracy, numerical implementation and computational effort. This study is carried out for three kinds of materials, which have different magnetic features: ferrites, FeSi sheets and a soft magnetic composite material. Then, the implementation of these models in a finite element code is presented. As example of application, a high-frequency transformer supplied by a rectangular voltage is studied.

This communication presents a method to discretize electromagnetic source fields in the Whitney element spaces for static electromagnetic potential formulations. This method requires no finite element solution to calculate this source fields. It is based on the use of a facet or an edge tree. We will test it on electrokinetic, electrostatic and magnetostatic examples

In this paper, a claw pole permanent magnet machine is studied using a 3D scalar potential formulation. First, the discretization of Maxwell’s equations using Whitney’s elements is presented. Especially, the method to take the winding current distribution into account by means of source fields is detailed. Then, a numerical model of the studied machine is presented. Simulation results (inductance, EMF, torque) are discussed by comparison with experimental ones.

This paper presents a method of coupling magnetostatic potential formulations with electrical circuits for the 3D FEM. Allowing for the current density distribution in stranded conductors, two vectors N and K are introduced. A systematic method of decomposing both vectors in Whitney’s element spaces is suggested. This method can be used for coils with a complex shape. As an example of application a three-phase transformer is studied.

In this paper we propose, an approach for coupling magnetostatic and electric circuit equations applicable to the case of stranded conductors. The method based on the calculation of global quantities is presented and applied to the magnetic formulation Hs-Ă. The properties and calculation of source field Hs are also discussed. As an example we have studied a permanent magnet synchronous machine. At no load, the magnetomotive force is determined and compared with experimental results. A calculation when the generator has a resistance load is also presented

In this paper we study different approaches to introduce the source terms due to the inductors crossed by a uniform current density J 0 in 3D FEM. Two equivalent methods are developed to decompose the current density J in the facet element space with divergence free close to J0. This decomposition is used in the a-formulation without gauge condition. Moreover, from the flux facet the source field Hs can be calculated in the edge element space and introduced into the ö-formulation. As examples of applications we have studied a coil with a complex geometry and a iron core coil

Cette communication présente une approche permettant d’imposer le courant ou la différence de potentiel dans le cas d’un problème d’électrocinétique. Pour une formulation en potentiel vecteur, l’approche proposée a été implantée dans un code de calcul basé sur la Technique d’Intégration Finie et dans un code éléments finis. Des simulations sont réalisées pour des cas simples et les résultats sont comparés à ceux obtenus à l’aide de la méthode des éléments finis.

This paper presents a 3-D finite element method to determine the steady state operation for magnetostatic problems coupled with electrical circuit equations. For this purpose, the waveform relaxation method combined with the Newton method (WR-NM) is developed. This method is especially suitable to long transient problems. To show the efficiency of this approach a three-phase transformer is studied. The results show that the WR-NM becomes very efficiency when the transient state is more important than about 10 periods.

In numerical computation, the finite element (FE) method associated with external electric circuits is often used to evaluate electromagnetism devices with voltage sources. To study the solution of the steady state, the computation time can be prohibitive due to a large transient state compared with the time step used to discretize the time domain. In this communication, the Waveform Relaxation Method is developed to impose the steady state of the solution in the case of magnetostatic problem coupled with electric cricuit equation.

The Galerkin projection provides an useful tool to transfer electromagnetic fields between different meshes. Given an electromagnetic field calculated on the source mesh, the transfer to a different mesh can be employed for model-coupling, domain decomposition, remeshing, visualization and similar proposes. The Galerkin projection consists of calculating a target field which minimizes the interpolation error between two discretized fields. However, the $L^2$ Galerkin projection suffers from non-conservation of the electromagnetic energy. In this paper, we present an energetic approach for Galerkin projections.

The finite element computation of eddy current problems gives numerical error. This error cannot be calculated, but can only be estimated. Among all error estimators already developed, it is proposed to compare two proven estimators called residual and hierarchical error estimators.

Usually, coupled problems (e.g. magneto-mechanical or magneto-thermal problems) with weak interactions can be decomposed into several sub-problems and solved separately. However, in the area of finite element computation, depending on the nature of the sub-problem to solve, the used meshes generally differ. In this case, transfers of fields are required to take into account the interaction between the sub-problems. Given a previously-computed field, in order to obtain on the target mesh its approximate image, the Galerkin projection enjoys several advantages over interpolation, especially in terms of precision. This method consists of minimizing the norm of the interpolation error in the chosen target space. The accuracy of the solution is ensured by the quasi-best property of the Galerkin method. Nevertheless, in practice the general implementation of the Galerkin projection has been proved challenging. As the source and target fields are discretized on different meshes, the accurate assembly of the projection system necessitates the numeric integrating over an intermediate mesh. In practice, such an intermediate mesh can be calculated by means of intersecting the source and target meshes. However, the use of intersection requires heavy work on programming and high computation cost (P.E. Farrell and J.R. Maddison, ”Conservative interpolation between volume meshes by local Galerkin projection”, in Comput. Methods Appl. Mech Engrg, Vol. 200, pp 89-100, 2009). This proposed paper discusses the possibility to avoid mesh intersections, by using an approximate integrating algorithm. Instead of integrating over the lowest common mesh, the integrals are computed over the target mesh. Over the quadrature points of targets elements, the source solution is interpolated and approximately integrated. This is less accurate than integrating over intersections. However, the accuracy can be improved using high-oder quadrature rules. Through analytical field distributions such as skin effect current densities, we have compared this approximate method to the intersection method, on node, edge and facet Whitney elements. The robustness of the approximate method will also be studied using reciprocal projection between fine and coarse meshes. In our examples of projection on edge elements, the computation time can be reduced by a factor up to one hundred. Meanwhile, the lost accuracy is less than 0.6%. The integration of physical constraints in the projection formulation will be shown to improve coarse-to-fine-mesh projected solutions.

For the eddy current problem, the potential formulations are widely used today. In this communication, residual based a posteriori error estimators are introduced to evaluate the discretization error in the finite element calculation in both case of A-Phi and T-Omega harmonic formulations. An example is carried out to show the behavior of our estimators.

In this paper a residual-based error estimator is proposed to evaluate the numerical error induced by the computation of the electromagnetic systems using a Finite Element Method in the case of the harmonic A-Phi formulation. This estimator is based on the evaluation of quantities weakly verified by the formulation. Furthermore as this estimator verifies the notions of reliability and efficiency it allows to estimate the qualities of local and global solutions. Two examples of electromagnetic systems with current density induced are used to show the efficiency of the proposed estimator.

Short-circuits in turbo-generator stators can lead to a modification of the magnetic flux distribution that impact the performances and, in some extreme cases, to local damage of the iron core. This work presents the modeling of short-circuited laminations in a stator yoke of a turbo-generator. A 3D finite element (FE) model, associated to a homogenization technique, is used to calculate the short-circuit current. The results are compared with the experiment, especially for the electrical signature of the diagnosis test known as Electromagnetic Core imperfection detector (El Cid).

This paper deals with the modelling of a lamination stack, crossed by a conducting building bar, in the presence of an inter-lamination short-circuit. Under a timevarying magnetic flux, an induced current loop flows through both the building bar and the fault. To reduce computational times, a homogenization technique is used to model the lamination stack. Eddy current losses and total magnetic energy values are compared for cases with and without homogenization for 50 Hz and 100 Hz.

In finite element computations, the choice of the mesh is crucial to obtain an accurate solution. In order to evaluate the quality of the mesh, a posteriori error estimators can be used. In this paper, we analyze and compare the residual and equilibrated error estimators for magnetostatic problems.

In this paper, we propose to compare two types of approximation of the vector potential used to solve a magnetostatic problem in the case of the domain decompostion. The single and Lagrange multipliers approaches and the Mortar method are considered in this context.

In this paper we compare different approaches for the lamination stack homogenization with a short-circuit due to an electrical fault between several sheets. The presented techniques are based on the determination of a complex equivalent magnetic permeability for the homogenized domain. The eddy current losses are calculated in the homogenized lamination stack and in the fault. These losses are compared with those obtained from a reference system where the lamination is modeled with its real geometry.

The Finite Integration Technique is used in the different engineering domains as well as to computing the electromagnetic phenomena. This technique is efficient if the mesh is generated by hexahedron elements. Moreover the matrix system, obtains from a regular mesh, can be exploit to use the parallel direct solver. In fact, in reordering the unknowns by the nested dissection method, it is possible to construct directly the lower triangular matrix of the Cholesky factorization with many processors without assembling the matrix system. In this paper, the parallel direct solver is described and the efficiency is shown as function to the number of processors.

In this paper, movement strategy, using the overlapping method, is studied. Non-conforming tetrahedral meshes and planar displacements are considered. The first part of this paper is devoted to the presentation of the FEM formulation. In the second part, the overlapping method is described in the case of planar movements. At last, results are given and discussed.

This paper presents a method allowing to impose global electrics quantities, in a time step magnetodynamic case, simulated with the Finite Integration Technique. The A- and T-Ω formulations are developed and two vectors fields are associated in order to impose and compute global quantities, such as currents and voltages. Several simulations, applied to a system with two conductors, were carried out and the results were compared to those obtained with the finite element method.

Application of different iterative methods (CG,MRTR, SQMR, MINRES) are proposed to solve linear systems from Finite Element Method (FEM) in 3-D electromagnetic field analysis, and their convergences are compared.

In this paper, the overlapping method is applied to connect non-conforming tetrahedral meshes. At first the FEM formulation is described. The overlapping method is presented as well as its implementation in a FEM calculation code. At last, applications will be studied and discussed.

Due to industrial needs, small stroke actuators present a growing interest. Generally, high acceleration, robustness and low manufacturing costs are frequently required. Today, improvements in the magnetic material as rare earth magnets or iron powder permit to design very compact actuators. To reach high performances, the actuator has to be controlled. This can be achieved using the last control capabilities (dsp, fpga...).However, this often needs sensors which increase the costs. In this paper, we deal with the simulation of the control of a PM linear small stroke actuator with non mechanical sensors. First, we present the actuator features. Then we introduce the simulation model based on the reluctance network model. To reach the information related to the position of the moving part, we use Hall effect sensors. In a third part, we show the placements of the sensors. Lastly, we introduce the control strategy and give some simulation results.

A fault-tolerant seven-phase axial-flux permanent magnet (AFPM) machine with a soft magnetic composite (SMC) stator has been designed thanks to analytical and 3D finite element method. In this paper, we present its characteristics and show that a high number of phases allows to get a good quality of the torque with a design simpler than this one of the three-phase AFPM machines. Experimental back-electromotive forces (back-EMF) and the cogging torque are then compared with predeterminations. Finally, experimental torque of a drive composed of a seven-leg Voltage Source Inverter (VSI) supplying the machine in a vector control is presented.

Permanent magnet actuators, widely used, often suffer from torque or force ripples. In this paper, we intend to reduce the cogging force of a PM linear actuator using two approaches. The first one consists on an optimisation of the teeth and magnet sizes. The second deals with the use of a supplementary steel piece in order create an opposite cogging force. The first calculations are achieved using 2D-FEM. Then 3D-FEM is used to validate the results.

For the experimental seven-phase machine studied in this paper, parameters necessary for the control such as inductances and electromotive force (EMF) are sensitive to harmonics. A conventional analytical method in which only the first harmonic is taken into account does not give good results. Besides, the machine is an axial-flux one and has two asymmetrical rotors: a 3D-FEM is then necessary. Comparisons between predeterminations and experimental results show sufficient accuracy to achieve a control model.

In this paper, a hybrid method is proposed for the simulation of rotating electrical machines taking into account the end winding effect. The method is based on the sliding surface that is decomposed on two parts. In the air gap we use the interpolation method at the second order and in the area of the end winding the Surface Interpolation Method (first order). As application a turbo-generator is studied.

The electromagnetic actuators for industrial processes have nowadays to present very specific features. To lead to a prototype and to study it with high accuracy, we use today partially or completely numerical methods. The purpose of this paper is to present the design and the study of a linear actuator. First, we present the structure of the actuator and its characteristics. The second part is devoted to describe the numerical approach. Lastly, we give the main results of the study and compare them to experimental data obtained from a prototype.

In the field of numerical modeling, applications with complex displacements are more and more met. The present paper deals with a procedure which permits to take into account two movements in the finite element method. Using the locked step method, it is possible perform both X-Y and X-q displacements. The procedure developed is explained and a 3D simple example is studied, both in magnetostatic and magnetodynamic, to show the validity of the proposed method.

Usually the Finite Element Method (F.E.M) is used to model the electromagnetic devices for low frequency. But other methods can be used as the Cell-Method and the Finite Integration Technique (F.I.T.). The presented work is a comparative study about these methods. Their theories are reminded to show that the same source field can be used for all methods. The properties of the mass matrices generated though the three different methods are also discussed. Finally, as an example of application an iron core coil supplied by a voltage source is modelled.

In the case of permanent magnet linear synchronous motors (PMLSM), knowledge of the electromotive force (emf) is necessary to achieve accurate control. However, it is often difficult to obtain it experimentally. As a consequence, this paper deals with the study of the non-sinusoidal emf of a PMLSM using the Finite-Element Method (FEM). Two potential formulations are used to consider several cases. Then, for the same accuracy, the computation times are compared. The results of the FEM are compared to those given by the measurements from a test bench composed of a Siemens LIMES400/120 linear motor and of a dSPACE DS1005 real-time controller board. Finally, the effectiveness and the limits of the FE Analysis will be discussed.

In this paper three techniques ( the locked-step approach, the overlapping method and the nodal interpolation method) are compared to model the rotation of electrical machines in 3D using FEM. These methods are associated with a formulation expressed in terms of scalar potential. To extend the possibilities of the interpolation method we propose the Surface Interpolation Method, which allows us to use non-conform meshes in the air gap of the studied machine. These different techniques are used to model a permanent magnet machine and a turbo-generator. The results obtained are compared by calculating the electromotive force and the torque.

In this paper we compare three techniques to model the movement in 3D FEM using both classical formulations to solve the magnetic equations. To compare the methods a permanent magnet synchronous machine is modelled. The comparison is done at no load on the electromotive force and the cogging torque.

Une méthode de projection de champs entre deux maillages non coïncidents basée sur une approche énergétique est développée. Cette approche est proposée en magnétostatique pour les deux formulations en potentiel classiquement utilisées. Un exemple académique permet de montrer les possibilités.

B. AHMADA, F. ALVES, B. BEN ABDALLAH, Abdelkader BENABOU, Y. BERNARD, F. BOUILLAULT, J.P. CHABRERIE, S. CLENET, M. FELIACHI, A. LEBOUC, J.P. MASSON, E. MENDES, G. MEUNIER, A. NOURDINE, Y. OULED AMOR, F. PIRIOU, Y. SEGUI.

Numerical modeling now plays a central role in the design and study of electromagnetic systems. In the field of devices operating in low frequency, it is the finite element method that has come to the fore in recent decades. Today, it is widely used by engineers and researchers in industry, as well as in research centers. This book describes in detail all the steps required to discretize Maxwell’s equations using the finite element method. This involves progressing from the basic equations in the continuous domain to equations in the discrete domain that are solved by a computer. This approach is carried out with a constant focus on maintaining a link between physics, i.e. the properties of electromagnetic fields, and numerical analysis. Numerous academic examples, which are used throughout the various stages of model construction, help to clarify the developments

La modélisation numérique tient maintenant une place centrale dans la conception et l’étude des systèmes électromagnétiques. Dans le domaine des dispositifs fonctionnant en basse fréquence, c’est la méthode des éléments finis qui s’est imposée au cours de ces dernières décennies. Aujourd’hui, elle est couramment utilisée par les ingénieurs et les chercheurs dans l’industrie, ainsi que les centres de recherche. Cet ouvrage présente en détail toutes les étapes permettant, à partir des équations de Maxwell, d’aboutir aux équations à résoudre à l’aide d’un calculateur via la méthode des éléments finis. On passe ainsi des équations de base dans le domaine continu aux équations dans le domaine discret propre aux éléments finis. Cette démarche est menée avec un souci permanent de maintenir un lien entre la physique, c’est-à-dire les propriétés des champs électromagnétiques, et l’analyse numérique. De nombreux exemples académiques, que l’on retrouve lors des différentes étapes de la construction du modèle, permettent d’éclairer la compréhension des développements.