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This paper deals with the temperature-dependent modelling of iron losses in the context of magnetic ageing of electricals steel used in high power electrical machines. First, two electrical steel sheet grades were heat treated at three temperatures in order to study the ageing effect evolution as a function of temperature. Results show a significant increase in iron losses for both steel grades. Then, considering the link between the macroscopic magnetic properties evolution (effect) and the microscopic precipitation (cause), the Johnson – Mehl – Avrami – Kolmogorov (JMAK) law describing the kinetics of precipitation was applied to model the time evolution of magnetic ageing. By coupling this model with the Arrhenius’ law, a model is developed to be able to predict the ageing for several temperature levels.

This article deals with the modelling of iron losses due to the magnetic ageing of electrical steels used in energy conversion devices. This phenomenon is the consequence of irreversible mechanisms in the material which can be triggered by the operating temperature of electrical devices. At first, an experimental study is carried out at 180◦ C in order to assess the effect of isothermal ageing on electromagnetic properties of a magnetic steel sample. The results show that, during the thermal ageing, the hysteresis losses and the coercive field increase. These experimental observations, mainly caused by the formation of precipitates at the material microstructural scale, are then discussed. Considering the link between the effect of magnetic ageing on macroscopic magnetic properties (effect) and the microscopic precipitation (cause), the Johnson – Mehl – Avrami – Kolmogorov (JMAK) law describing the kinetics of precipitation was applied to model the time evolution of magnetic ageing. Once this approach was validated, it is proposed to integrate the JMAK law in the Steinmetz iron loss model.

During electrical machine manufacturing, the process may induce plastic mechanical strains, especially in the magnetic core. However, magnetic properties are highly sensitive to the material mechanical state. Thus, the performances of electrical machines, which also rely on the magnetic material properties, are often deteriorated. This paper proposes an approach to reduce the impact of the forming process on the magnetic core performances by creating high localized heterogeneous deformations instead of having a low homogeneous deformation distributed on the whole structure. A NO (non-oriented) FeSi (1.3%) electrical steel (M330-35A) is characterized after uniaxial tensile test. Samples are deformed either in heterogeneous or in homogeneous ways while keeping the same global deformation. Experimental measurements show that, for the same displacement value, the heterogeneous configuration, with localized strain, deteriorates less the global magnetic properties than the homogeneous configuration. These results are supported by a magneto-mechanical modeling approach that predicts accurately the physical behavior of test samples.

In this paper, the magnetic ageing of a bulk forged non-annealed magnetic core, used in claw pole synchronous machine, is investigated. The study is carried out by characterizing the material properties of two groups of samples subjected to a thermal ageing at 180 °C that corresponds to the maximum operating temperature of the claw pole rotor. The investigated characteristics are the electrical conductivity, the magnetic properties, the material microstructure and the Vickers hardness. They were characterized along with the ageing time. The results show that, during the thermal ageing, the hysteresis losses and the Vickers hardness have been affected by the magnetic ageing, whereas the electric conductivity and the normal B-H curve have not been modified. The microstructure analyses showed that carbides precipitates were the main cause behind the magnetic ageing. Moreover, the comparison between the results of two groups of samples revealed the possibility that the magnetic ageing of the material could have started during the manufacturing process of the magnetic core.

16MnCr5 steel parts were additively manufactured by laser powder bed fusion in order to investigate the effect of microstructure on electromagnetic properties. As process parameters have a direct impact on the obtained microstructure, different conditions were used to manufacture samples on which magnetic and electrical tests were conducted. The obtained results were presented and discussed in terms of density, microstructure and electromagnetic properties. Finally, correlations have been demonstrated between the microstructure and the electromagnetic performances. Lower magnetic and electric properties were obtained with the higher porosity rates at low volume energy density. The microstructural effects were evidenced, through a decrease in magnetic properties with grain orientation, and an improvement with stress relief annealing.

When a finger touches an ultrasonic vibrating plate, a non-sinusoidal contact force is produced. This force is called acoustic finger force. In a setup where closed-loop control is performed on the vibration amplitude, a component of the acoustic finger force can be measured at the fundamental vibration frequency of the plate. This calculation is obtained from the measurement of the variation of the controller voltage between the no-load case and when a finger is present. This calculation is made for a group of twelve participants. From these results a PCA (Principal Component Analysis) model is created. This model permits estimation of the acoustic finger force response of a participant at any vibration amplitude, based on a one or two point measurement. Finally, a linear relation between the PCA coefficients and the friction reduction is proposed. The objective of this relation would be to ultimately provide the means to create an amplitude reference calibration based on the desired friction reduction level, and thus be able to produce a standardized tactile feedback for each user, despite the biomechanical differences in finger pad properties between subjects.

In order to have a better convergence and accuracy for solving the ion-flow field problem, a novel and general numerical approach is proposed. In the past, the framework of the traditional mesh based method has a dilemma that the Kapzov boundary condition can be imposed properly, and it must have two loops: the “well-posed” problem is solved in the inner loop and the secant based method is applied to impose the Kapzov assumption in the outer loop. In contrast, the proposed method solves the ion flow field problem from the perspective of the inverse problem. The original boundary value problem is transformed into a regularized optimization problem based on the priori information about the smooth ion distribution on the conductors. The objective function is separated into two parts and minimized by the alternating direction iterative method. In contrast to the traditional methods, the proposed method has removed the redundant iterations and the contentious simplifications. Numerical experiments show that the performance of the proposed method is superior to the traditional method and the results obtained by the proposed method agree better with the physical law than the traditional method.

Metamodels proved to be a very efficient strategy for optimizing expensive black-box models, e.g., Finite Element simulation for electromagnetic devices. It enables the reduction of the computational burden for optimization purposes. However, the conventional approach of using metamodels presents limitations such as the cost of metamodel fitting and infill criteria problem-solving. This paper proposes a new algorithm that combines metamodels with a branch and bound (B&B) strategy. However, the efficiency of the B&B algorithm relies on the estimation of the bounds; therefore, we investigated the prediction error given by metamodels to predict the bounds. This combination leads to high fidelity global solutions. We propose a comparison protocol to assess the approach’s performances with respect to those of other algorithms of different categories. Then, two electromagnetic optimization benchmarks are treated. This paper gives practical insights into algorithms that can be used when optimizing electromagnetic devices.

In this article, an experimental procedure is presented to handle magnetic measurements under uniaxial tensile stress reaching the plastic domain. The main advantage of the proposed procedure is that it does not require an additional magnetic core to close the magnetic flux path through the studied sample. The flux flows only in the sample, and no parasitic air gaps are introduced, thus avoiding the use of the H-coil to evaluate the magnetic field, which is often very sensitive and not easy to calibrate. A specimen of nonoriented FeSi (1.3%) sheet (M330-35A) is characterized under uniaxial tensile stress. To validate the proposed procedure, a comparison with the single sheet tester procedure is carried out. The results obtained by the two procedures are in good agreement. Moreover, to illustrate the possibilities offered by the proposed procedure, we confirm some results obtained in the literature. We show that the positive plastic strain leads to a significant degradation of magnetic behavior. An applied tensile stress on a virgin (unstrained) sample leads to a degradation of the magnetic behavior. However, on a pre-strained sample, an applied tensile stress results in reducing the deterioration caused by the plastic strain until a stress value called optimum is attained. Above this threshold, the magnetic behavior re-deteriorates progressively.

During the operation of Claw Pole (CP) machines, and for some operating loads, the magnetic core temperature can reach 180°C in some hot spots. As a consequence, the core electromagnetic properties may considerably change, impacting the machine performances. In such a case, a deep knowledge of the electromagnetic behavior as a function of the temperature is required. In this paper, we present a dedicated study of the CP rotor made from a forged magnetic steel. In fact, the CP magnetic properties heterogeneity and the claw shape made it necessary to extract specific samples that are characterized with a miniaturized Single Sheet Tester (SST). To that end, this work proposes a specific methodology to characterize the electromagnetic properties of the CP rotor material as a function of the temperature in order to better predict the machine electrical performances, especially regarding the iron losses.

An experimental approach is proposed to study the influence of the punching on the magnetic behavior of a stator core strips. Specimens of a non-oriented M330-A35 punched lamination sheet are picked up from a real manufacturing process. The proposed approach is based on the use of two types of specimens; one is a closed magnetic circuit while the second one is split into two parts. Magnetic measurements are performed on both types and compared with those made on specimens cut by WEDM which has a lower impact on the magnetic behavior. The specific purpose of this paper is to investigate the impact of punching in presence of an air gap that exists in electrical machines between rotor and stator. Therefore a dedicated device, optimized by FEM simulations, is developed in order to account accurately the air gap.

Claw pole machine performances are strongly related to the electromagnetic properties of ferromagnetic materials. These properties are impacted by the manufacturing processes, in a heterogeneous way, as well as by the thermal behavior of the machine and the mechanical stress distribution. Due to the complexity of CP geometry, extracted samples cannot respect the dimensions prescribed in international standards of electric and magnetic measurements. This paper proposes a specific methodology to characterize the electrical conductivity and the magnetic behavior of massive parallelepiped specimens extracted from different locations of a CP rotor.

The calculation of the probability of detection in non-destructive eddy-current testing requires the solution of a stochastic model requiring numerous calls of a numerical model leading to a huge computation time. To reduce this computation time, we propose in this paper to combine either the use of a stochastic metamodel or a mapping which avoids the remeshing step. The stochastic metamodel is constructed using the least-angle regression method. This approach is tested on an axisymmetric problem with six random input paramters which shows its efficiency and its accuracy.

High operating temperatures modify the magnetic behavior of ferromagnetic cores which may affect the performance of electrical machines. Therefore, a temperature-dependent material model is necessary to model the electrical machine behavior more accurately during the design process. Physics-inspired hysteresis models, such as the Jiles-Atherton (JA) model, seem to be promising candidates to incorporate temperature effects and can be embedded in finite element simulations. In this paper, we have identified the JA model parameters from measurements for a temperature range experienced by non-oriented electrical steels in electrical machines during their operation. Based on the analysis, a parameter reduction has been performed. The proposed approach simplifies the identification procedures by reducing the number of model parameters and does not require any additional material information, such as the Curie temperature. The resulting temperature-dependent JA model is validated against measurements, and the results are in good agreement.

This paper presents a methodology that allows taking advantage of the geometrical periodicity of electrical machines together with the modeling of rotor motion. It enables by means of the discrete Fourier transform (DFT) to reduce the large-scale system obtained from the finite-element model to several smaller independent subsystems, allowing a shortening of the computational time. Due to DFT properties, the computational time can be more reduced especially when we consider the inter-dependence of the spectral components under either balanced or unbalanced supply condition. In addition, a further reduction is possible in the case of balanced regimes where the distribution of the eventual numerical solution is governed by a limited number of prevailing harmonics.

This paper compares different probabilistic optimization methods dealing with uncertainties. Reliability-Based Design Optimization is presented as well as various approaches to calculate the probability of failure. They are compared in terms of precision and number of evaluations on mathematical and electromagnetic design problems to highlight the most effective methods.

Meta-models proved to be a very efficient strategy for optimization of expensive black-box models, e.g. Finite Element simulation for electromagnetic devices. It enables to reduce the computational burden for optimization purposes. Kriging is a popular method to build meta-model. Its statistical properties were firstly used in efficient global optimization for unconstrained problems. Afterwards many extensions were introduced in the literature to deal with constrained optimization. This paper presents a comparative study of some infill criteria for constraints handling and a new strategy for parallelization of the expensive computations of models.

Reliability-Based Design Optimization (RBDO) in electromagnetic field problems requires the calculation of probability of failure leading to a huge computational cost in the case of expensive models. Three different RBDO approaches using kriging surrogate model are proposed to overcome this difficulty by introducing an approximation of the objective function and constraints. These methods use different infill sampling criteria (ISC) to add samples in the process of optimization or/and in the reliability analysis. Several enrichment criteria and strategies are compared in terms of number of evaluations and accuracy of the solution.

In the field of electrical machines, the finite element method provides accurate results but requires a high computational cost to perform, with sometimes weeks of computations. Therefore, model order reduction methods such as the proper orthogonal decomposition combined with the discrete empirical interpolation method are able to speed up the solution of the finite element problem. To use the obtained results for predictive computations, an error estimator is required. However, the different estimators found in the literature do not apply to our problem. Therefore, a simple error indicator that can be applied to a wide range of problems is proposed in this paper.

This paper shows the influence of the manufacturing process of a claw-pole alternator on its acoustic noise. First, the stator welds and the assembly of the stator in the brackets are linked to deformations of the inner diameter of the stator. Then, the influences of these deformations on the magnetic forces and the subsequent acoustic noise are investigated. Results show that the deformations caused by the manufacturing process significantly increase the sound power level of particular orders.

The Proper Orthogonal Decomposition (POD) combined with the (Discrete) Empirical Interpolation Method (DEIM) can be used to reduce the computation time of the solution of a FE model. However, it can lead to numerical instabilities. To increase the robustness, the POD_DEIM model must be constructed by preserving the structure of the full FE model. In this article, the structure preserving is applied for different potential formulations used to solve electromagnetic problems.

Proper Orthogonal Decomposition (POD) has been successfully used to reduce the size of the equation system and the computation time of linear Finite Element (FE) problems. With a nonlinear behavior law, the POD is not so efficient due to the computation cost of nonlinear entries of the full FE model. Then, the POD approach must be combined with an interpolation method of nonlinear terms to obtain an efficient reduced model. An interpolation method consists on the computation of a small number of nonlinear entries and on the interpolation of other terms. Different methods have been presented to select the set of nonlinear entries to be calculated. Then, the (Discrete) Empirical Interpolation method ((D)EIM) and the Best Points Interpolation Method (BPIM) have been developed. In this article, we propose to compare two reduced models based on the POD-(D)EIM and on the POD-BPIM in the case of nonlinear magnetostatics coupled with electric equation.

In the field of computational electromagnetics, taking into account the rotation of a sub-domain is required to simulate certain devices such as electrical machines. Several methods have been proposed in the literature, but they remain quite difficult to implement. In this paper, we propose a sliding surface method based on a spatial Fourier interpolation in order to take into account any rotation angle with a very simple numerical implementation.

The performances of electrical machines depend highly on the behavior of ferromagnetic materials. In some applications, these materials operate under DC polarization, i.e. when the magnetic field oscillates around a DC bias. In that condition, it is required to know the incremental permeability which characterizes the magnetic behavior of the material around the operating point. In this paper, a non-destructive approach, involving a combination of experiment and Finite Element (FE) technique, is presented in order to determine the incremental permeability. The proposed sensor is based on the four-needles method. With this sensor, Bowler et al. have proposed a method to determine the initial permeability of homogeneous metal plates based on an analytical model. Here we propose to use the same kind of sensor to determine the incremental permeability. The measurement process is analyzed using a FE model. It is shown that the analytical approach reaches its limits if the permeability of the plate and its thickness become too high. A combination between the measurements and a FE model is introduced to overcome this difficulty to determine the incremental permeability. The study of two magnetic steel samples illustrates the interest of this method.

Model order reduction (MOR) methods are more and more applied on many different fields of physics in order to reduce the number of unknowns and thus the computational time of large-scale systems. However, their application is quite recent in the field of computational electromagnetics. In the case of electrical machine, the numerical model has to take into account the nonlinear behaviour of ferromagnetic materials, motion of the rotor, circuit equations and mechanical coupling. In this context, we propose to apply the proper orthogonal decomposition combined with the (Discrete) empirical interpolation method in order to reduce the computation time required to study the start-up of an electrical machine until it reaches the steady state. An empirical offline/online approach based on electrical engineering is proposed in order to build an efficient reduced model accurate on the whole operating range. Finally, a 2D example of a synchronous machine is studied with a reduced model deduced from the proposed approach.

Model order reduction (MOR) methods are more and more applied on many different fields of physics in order to reduce the number of unknowns and thus the computational time of large-scale systems. However, their application is quite recent in the field of computational electromagnetics. In the case of electrical machine, the numerical model has to take into account the nonlinear behaviour of ferromagnetic materials, motion of the rotor, circuit equations and mechanical coupling. In this context, we propose to apply the proper orthogonal decomposition combined with the (Discrete) empirical interpolation method in order to reduce the computation time required to study the start-up of an electrical machine until it reaches the steady state. An empirical offline/online approach based on electrical engineering is proposed in order to build an efficient reduced model accurate on the whole operating range. Finally, a 2D example of a synchronous machine is studied with a reduced model deduced from the proposed approach.

In this paper, we propose an a posteriori error estimator for the numerical approximation of a stochastic magnetostatic problem, whose solution depends on the spatial variable but also on a stochastic one. The spatial discretization is performed with finite elements and the stochastic one with a polynomial chaos expansion. As a consequence, the numerical error results from these two levels of discretization. In this paper, we propose an error estimator that takes into account these two sources of error, and which is evaluated from the residuals.

We present an optimization problem that requires the modeling of a multirate system composed of subsystems with different time constants. We use waveform relaxation method (WRM) in order to simulate such a system, but computation time can be penalizing in an optimization context. Thus, we apply output space mapping (OSM) that uses several models of the system to accelerate optimization. WRM is one of the models used in OSM.

In this paper, we analyze the influence of the uncertainties on the behavior constitutive laws of ferromagnetic materials on the behavior of a turboalternator. A simple stochastic model of anhysteretic nonlinear B(H) curve is proposed for the ferromagnetic yokes of the stator and the rotor. The B(H) curve is defined by five random parameters. We quantify the influence of the variability of these five parameters on the flux linkage of one phase of the stator winding depending on the excitation current I. The influence of each parameter is analyzed via the Sobol indices. With this analysis, we can determine the most influential parameters for each state of magnetization (according to the level of I) and investigate where the characterization process of the B(H) curve should focus to improve the accuracy of the computed flux linkage.

Classically the magnetic material models are considered with a deterministic approach. Nevertheless, when submitted to the fabrication process, the magnetic core properties are negatively impacted and may be subject to variability during the process. This variability can be of such importance that the performances of the final device (electrical machine) will also present a noticeable variability. The aim of this research is to develop a stochastic model of the magnetic behaviour law of slinky stators used in claw pole generators. The proposed methodology is general and can be applied to other physical properties of electrical devices.

When modeling a system subject to uncertainties, a fundamental aspect is the stochastic modeling of the input parameters of the model. Several calculation and analysis steps have to be considered, and can be found in the literature. In this paper, after presenting such steps, these are applied for the modeling of the variability of the magnetic behavior law related to a set of slinky stator samples, issued from the same production chain. The probabilistic model of the parameters is therefore validated using a statistical test and a classical Monte Carlo simulation. The importance of taking account of the dependency structure between the parameters is then emphasized, as it may modify significantly the results related to the validation of the model.

To take account of the uncertainties introduced on the soft magnetic materials properties (magnetic behavior law, iron losses) during the manufacturing process, the present work deals with the stochastic modeling of the magnetic behavior law B-H and iron losses of claw pole stator generator. Twenty eight (28) samples of slinky stator (SS) coming from the same production chain have been investigated. The used approaches are similar to those used in mechanics. The accuracy of existing anhysteretic models has been tested first using cross validation techniques. The well known iron loss separation model has been implemented to take into account the variability of the losses. Then, the Multivariate Gaussian distribution is chosen to model the variability and dependencies between identified parameters, for both behavior law and iron loss models. The developed stochastic models allow predicting a 98% confidence interval for the considered samples.

Manufacturing processesmay introduce a significant variability on the magnetic properties of claw pole generator stators. The present work deals with the analysis of two groups of stator samples. The first group is composed of 28 slinky stators (SS) and the second group is composed of 5 stators, manufactured using laser cut stacked laminations (SL). Both groups are made from the same lamination grade and with the same geometrical dimensions. Characterization was carried out for several levels of excitation field at 50 Hz. A noticeable variability has been observed on the iron losses for SS samples, whereas it appears to be not significant for SL samples. The loss separation technique has then been investigated for the SS samples. Results show that the variability of static losses is more important than the one of dynamic losses.

The Non-Intrusive Spectral Projection (NISP) method is widely used for uncertainty quantification in stochastic models. The determination of the expansion of the solution on the polynomial chaos requires the computation of multidimensional integrals. An automatic adaptive algorithm based on nested sparse grids has been developed to evaluate those integrals. The adapted algorithm takes into account the weight of each random variable with respect to the output of the model. To achieve that it constructs anisotropic sparse grid of the mean, leading to a reduction of the number of numerical simulations. Furthermore, the spectral form of the solution is explicitly identified from the constructed quadrature scheme. Numerical results obtained on an industrial application in NDT demonstrate the efficiency of the proposed method.

In this paper, a spectral stochastic finite element method (SSFEM) is described and applied to quantify uncertainties in an industrial eddy current non destructive testing (NDT) problem. A new iterative solver based on the fixed-point method is proposed to solve the large scale linear system. The efficiency of the suggested iterative solver to tackle the SSFEM computational complexity is demonstrated. The SSFEM results and the computation times obtained with 2 and 4 random variables are compared to those given by the anisotropic adaptive sparse grid non intrusive spectral projection (NISP). On this application, the SSFEM dedicated solver is competitive with the adaptive sparse grids strategy.

Methods are now available to solve numerically electromagnetic problems with uncertain input data (behaviour law or geometry). The stochastic approach consists in modelling uncertain data using random variables. Discontinuities on the magnetic field distribution in the stochastic dimension can arise in a problem with uncertainties on the geometry. The basis functions (polynomial chaos) usually used to approximate the unknown fields in the random dimensions are no longer suited. One possibility proposed in the literature is to introduce additional functions (enrichment function) to tackle the problem of discontinuity. In this study, the authors focus on the method of random mappings they show that in this case the discontinuity are naturally taken into account that no enrichment function needs to be added

Stochastic spectral finite-element method can be used to take into account some random aspects in the input data (material characteristic, source terms) involved in static electromagnetism problems. Similarly to the deterministic case, two potential formulations can be used in the stochastic case. The vector potential formulation applied to static problems is developed and compared to the scalar potential one, previously developed.

Overlapping elements can be used to connect non-conforming meshes in the finite-element method. This approach has been developed with the scalar potential formulation and used to solve magnetostatic problems but not in the case of the vector potential formulation. In this paper, we propose to introduce the overlapping element method in this second formulation

The numerical solution of partial differential equations onto random domains can be done by using a mapping transforming this random domain into a deterministic domain. The issue is then to determine this one to one random mapping. In this paper, we present two methodsone based on the resolution of the Laplace equations, one based on a geometric transformationto determine the random mapping. A stochastic magnetostatic example is treated to compare these methods.

The torque developed by a magnetorheological brake can exhibit a hysteretic behaviour when experiencing a time varying magnetic field. In this work, we focus on the numerical study of such phenomenon using 2D Finite Element (FE) analysis. The torque evolution is investigated when considering successively nonlinear and hysteretic behaviour laws in the ferromagnetic parts.

Overlapping elements have previously been employed to connect two surfaces or subdomains meshed separately. This method has been developed in 2D and in 3D for plane surfaces. The paper extends the overlapping method to arbitrary non-planar surfaces; this is accomplished by introducing new shape functions. The proposed method can be applied to account for movement without any undesirable distortion of the mesh. Two examples are presented to show the effectiveness of the new method.

The solution of stochastic PDEs using the Spectral Stochastic Finite Element Method (SSFEM) can lead to a very large linear system of equations. If the random input data are independent, it can be shown that the initial linear system can be split into smaller independent linear systems by using double orthogonal polynomials. In this paper, we propose the use of this approach in the case of dual potential formulations in electrokinetics. The method is applied on an electrokinetic problem taking into account the uncertainties on contact resistances.

A method to solve stochastic partial differential equations on random domains consists in using a one to one random mapping function which transforms the random domain into a deterministic domain. With this method, the randomness is then born by the constitutive relationship of the material. In this paper, this method is applied in electrokinetics in the case of scalar potential and vector potential formulations. An example is treated and the proposed method is compared to a Non Intrusive Method based on the remeshing of the random domains.

Input data to a numerical model are not necessarily well known. Uncertainties may exist both in material properties and in the geometry of the device. They can be due, for instance, to ageing or imperfections in the manufacturing process. Input data can be modelled as random variables leading to a stochastic model. In electromagnetism, this leads to solution of a stochastic partial differential equation system. The solution can be approximated by a linear combination of basis functions rising from the tensorial product of the basis functions used to discretize the space (nodal shape function for example) and basis functions used to discretize the random dimension (a polynomial chaos expansion for example). Some methods (SSFEM, collocation) have been proposed in the literature to calculate such approximation. The issue is then how to compare the different approaches in an objective way. One solution is to use an appropriate a-posteriori numerical error estimator. In this paper, we present an error estimator based on the constitutive relation error in electrokinetics, which allows the calculation of the distance between an average solution and the unknown exact solution. The method of calculation of the error is detailed in this paper from two solutions that satisfy the two equilibrium equations. In an example, we compare two different approximations (Legendre and Hermite polynomial chaos expansions) for the random dimension using the proposed error estimator. In addition, we show how to choose the appropriate order for the polynomial chaos expansion for the proposed error estimator.

Abstract: When modelling electrical devices, one has to estimate quite accurately the iron losses for the sake of efficiency. The use of non-sinusoidal electrical sources increases the harmonic content in electrical systems and, consequently, increases significantly the magnetic losses in devices feed by these sources. The harmonic content adds non centred minor hysteresis loops over the classical major one. The numerical tool used for the material modelling must be able to represent the magnetic behaviour in such conditions. Then, the use of a hysteresis model is the more suited solution, but the chosen model has to take into account correctly the minor loops. The Jiles-Atherton hysteresis model is one of the most employed, due its well known properties, but it is not able to represent closed minor loops. In this work, we propose a simple approach based on experimental observations and empirical considerations, to improve the representation of minor loops in this model by keeping its simplicity of use and implementation in a FE calculation code. Differently to other approaches found in the literature, the previously knowledge of the magnetic field evolution is not needed. A comparison between measured and calculated curves, as well with the Preisach model, is performed to validate the model.

This work deals with the implementation of a vector hysteresis model in a 2D finite element code with vector potential formulation. The inverse Jiles-Atherton hysteresis model leads to obtain a differential reluctivity tensor which can be directly applied to the field calculation equations.

Efficient numerical models have been already developed in 2D to take into account the movement of electromagnetic devices with rotating parts in the framework of the Finite Element Method (FEM). When the movement becomes complex it leads to large mesh distortions.A remeshing step is then required which increases the computational complexity and can also lead,in some cases,to numerical ripples on forces and torques due to the field projections between old and new meshes.Moreover,remeshing procedures in 3D remain an open topic.Meshless methods seem an appealing choice for alleviating the mesh constraints.The Natural Element Method (NEM)which,has known a growing interest in the domain of mechanics,allows to proceed in the meshless framework,avoiding one of the main drawbacks related to the vast majority of meshless techniques,as is the imposition of essential boundary conditions.In this paper,a variant of the NEM,known as constrained natural element method (C-NEM)is applied for simulating electromagnetic machines involving rotating parts.A new mixed strategy combining the finite element and the constrained natural element methods is proposed and then tested by using an appropriate error estimator.

This communication deals with a comparison between two methods of discretisation: the well known Finite Element Method and the Natural Element Method that is a meshless method. An error estimator, based on the non-verification of the constitutive law, is used. This estimation has been applied to two examples: a device with permanent magnets and a variable reluctance machine.

Electrical engineering often deals with global quantities as current, magnetic flux, difference of potentials, power or torque. Previous works have shown that Spectral Stochastic Finite Element Method SSFEM makes it possible to spread input data uncertainties (material characteristics) to the local output which are now random. The next step consists in deriving the random global quantities from the random distribution of the fields. It has been implemented in the extended stochastic version of a 3D FEM software. The approach has been successfully validated on a 3D electrical current density problem by comparing with Monte Carlo Simulation Method. Finaly, this method has been applied to an industrial device.

Electrical engineering often deals with global quantities as current, magnetic flux, difference of potentials, power or torque. Previous works have shown that Spectral Stochastic Finite Element Method SSFEM makes it possible to spread input data uncertainties (material characteristics) to the local output which are now random. The next step consists in deriving the random global quantities from the random distribution of the fields. It has been implemented in the extended stochastic version of a 3D FEM software. The approach has been successfully validated on a 3D electrical current density problem by comparing with Monte Carlo Simulation Method. Finaly, this method has been applied to an industrial device.

In this paper, we present a mesh adaptation procedure where the error distribution is calculated using two fields distribution in the cases without and with defaults. Usually, one field distribution is studied. The first part of this paper will deal with two FEM complementary formulations. From this, we will describe the local error estimators based on the non verification of the behaviour laws. We will give also the procedure used with the mesh refinement software. In the last part, we will compare the results of the established methodology on an example.

Rare earth permanent magnets are very sensitive to temperature as an overheating can leads to a partial or a total demagnetisation. It is then necessary to determine the losses in the permanent magnets to design with accuracy an electromagnetic system. In fact, if the permanent magnet experiences a high frequency magnetic field, significant losses appear. In the literature, these losses are calculated assuming the permanent magnet to be a bulk conductive material. In this work, we aim at verifying this assumption and we give a method to determine the equivalent conductivity. Then, we present a comparison between calculated and measured characteristics of two permanent magnets samples.

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.

The Natural Element Method, which belongs to the family of meshless methods, is applied in the context of 2D magnetostatics with moving parts. The method is reviewed and its interest for handling discontinuities in electromagnet devices with moving parts is illustrated through a numerical example

Résumé - Mechanical stress can heavily affect the magnetic behaviour law in ferromagnetic materials. This paper, aims to take into account the effect of mechanical stress into a hystreresis model. This model is implemented in a finite element analysis code and tested in the case of a simple system.
A simple extension of the classical Preisach model is proposed, in which a function linked to the Preisach density is parameterized using the mechanical stress as a supplementary parameter. The methodology is based on experimental measurements for identifying the required function. As a first approach, a linear interpolation is used between the measurements in order to have a continuous evolution of the magneto-mechanical behaviour. This model has been tested in the case of a steel sheet in which width is not constant in order to obtain a non-uniform distribution of stress and magnetic flux density.

Résumé - In this paper, we present a model of a hysteresis motor based on Maxwell’s equations coupled with the Jiles-Atherton (J-A) hysteresis model solved by the finite element method. The aim of this work is to validate such a model by comparison with the experimental results (electromagnetic torque, voltage, current). We also present an analysis of this motor when imposing current or voltage in the 2D vector potential formulation.

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.

Multi-phase motors are widely used in marine propulsion. In this paper, a Multi-machine modeling of Surface Mounted PM motors is presented and applied to a 5-phase one. The latter is proved to be equivalent to a set of two-phase fictitious machines each ones being characterized by a set of specific harmonic rank. A simple control consists in supplying each fictitious machine by a current which contains only one harmonic. A five phase machine is then supplied by currents with only both first and third harmonics. Considering this kind of control, it is proved that for given stator resistance and average torque the Joule losses and the torque ripple are minimized if a simple criterion on the harmonics of electromotive force at constant speed is fullfilled. Different structures of rotor are then compared to examine numerically which improvements can be practically obtained.

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

This paper deals with the study of an unconventional design of marine tidal turbine where the electrical generator is located in the periphery of the blades and where the magnetic gap is underwater. This kind of solution called "RIM DRIVEN" structure allows increasing the compactness and the robustness of the system. Due to the strong interaction of the multi physical phenomena, an electromagnetic model and a thermal model of the PM generator are associated with a hydrodynamic model of the blades and of the water flow in the underwater air gap. These models are used in a global coupled design approach in order to optimize, under constraints, the global efficiency of the system. This approach is illustrated in a case study which deals with the design of a 10m diameter tidal turbine. Proposed coupled models are validated by comparison with experimental data from the tests of an academic low power demonstrator

During the operation of electrical machines, the increase in temperature up to about 200 °C promotes, in some electrical steels, basically Fe-Si alloys, the formation of precipitates (carbides, nitrides…). This precipitation causes a deterioration of the magnetic properties, in particular an increase in iron losses, a phenomenon known as magnetic ageing [1]. The aim of this study is to develop a preliminary multi-physical and multi-scale modelling approach coupling precipitation kinetics and the evolution of magnetic losses due to magnetic ageing.

This study presents a device to handle magnetic measurements under uniaxial tensile stress reaching the plastic domain. The proposed device does not require external magnetic core to close the magnetic flux loop through the studied sample. The flux flows only in the sample and no parasitic gaps are introduced which avoids the use of H-coils to evaluate the magnetic field, often very sensitive and not easy to calibrate. Two geometries of a non-oriented (NO) FeSi (1.3%) sheet (M330-35A) are characterized under uniaxial tensile stress. The magnetic hysteresis loop was measured at 50Hz. Results show that positive plastic strain results in significant degradation of the magnetic behavior. An applied tensile stress on a virgin (un-strained) sample leads to magnetic behavior degradation. Whereas, on a pre-strained sample, an applied tensile stress, leads to reduce the deterioration performed by the plastic strain until a stress value called optimum. Above this optimum value, the magnetic behavior re-deteriorates progressively.

The motivation of this communication is to test a method for computing the gradient of a quantity of interest for an electromagnetic device modeled by finite elements method (FEM). The gradient is a key ingredient in many important tasks: sensitivity analysis, robust design, design optimization and reliability analysis. It can be computed efficiently using the adjoint method, its advantage is not only reducing the computational cost of computing the gradient compared to different methods (e.g. finite difference) but also handling the numerical noise that could appear when re-meshing in the case of finite elements analysis.

The motivation of this communication is to test a method for computing the gradient of a quantity of interest for an electromagnetic device modeled by finite elements method (FEM). The gradient is a key ingredient in many important tasks: sensitivity analysis, robust design, design optimization and reliability analysis. It can be computed efficiently using the adjoint method, its advantage is not only reducing the computational cost of computing the gradient compared to different methods (e.g. finite difference) but also handling the numerical noise that could appear when re-meshing in the case of finite elements analysis.

Meta-models proved to be a very efficient strategy for optimization of expensive black-box models, e.g. Finite Element simulation for electromagnetic devices. It enables to reduce the computational burden for optimization purposes. Kriging is a popular method to build meta-model. Its statistical properties were firstly used in efficient global optimization for unconstrained problems. Afterwards many extensions were introduced in the literature to deal with constrained optimization. This paper presents a comparative study of some infill criteria for constraints handling and a new strategy for parallelization of the expensive computations of models.

Reliability-Based Design Optimization (RBDO) in electromagnetic field problems requires the calculation of probability of failure leading to huge computational cost in the case of expensive models. Three different types of RBDO approaches using kriging surrogate model are proposed to overcome this difficulty by introducing an approximation of the objective and of the constraints. These methods use different infill searching criteria to add new samples in the process of optimization or/and in the reliability analysis. The enrichment criteria and the best suited enrichment strategies are discussed in this communication. These approaches are compared in terms of number of evaluations and accuracy of the solution.

The manufacturing of a slinky stator core is the result of a sequence of difference processes: straightening, punching, rolling It has been shown in the literature that manufacturing processes lead to a degradation of the magnetic properties. However, it is really difficult from the state of art to classify them a priori from the most influent to the less. In order to determine the most influent processes, it is necessary the evaluate quantitatively the impact of impact of each process. In this paper, a campaign of magnetic characterization is carried out on FeSi 1.3% specimens extracted after each process on the manufacturing line of a slinky stator. Samples have different shapes, so different characterization methods were used to determine the normal curves and total losses. Results show that the dispersion in raw material is quite important and depends on the level of induction. Straightening and training processes deteriorate the magnetic material properties and dispersion after both processes is higher than the raw material one. The effect of rolling and cutting are the most harmful compared to the other manufacturing processes, while the compacting process shows a benefic effect.

The Proper Orthogonal Decomposition combinedwith the (Discrete) Empirical Interpolation Method can be used to reduce the size of a numerical model. To conserve robustness, the reduced model must be constructed by preserving the structure of the full model. In this communication, an approach is proposed with potential formulations used to solve electromagnetic problems.

In the field of computational electromagnetics, taking into account the rotation of a sub-domain is required to simulate certain devices such as electrical machines. We propose a sliding surface method based on a spatial Fourier interpolation in order to take into account any rotation angle with a very simple numerical implementation.

The magnetic properties of ferromagnetic cores and the resistance of conductors are severely affected by the high operating temperatures in modern electrical machines. These temperature effects must be taken into account in the electrical machine design process to optimize their performance. In this work, we have proposed a simple material model to predict the change in the single-valued B-H relationship of non-oriented electrical steel with respect to the temperature. The temperature dependent power loss curves have also been measured and are fitted to a two term iron loss formula to compute the magnetic losses. The temperature dependent magnetic properties (B-H relationship and power loss formula) and the resistivity values of the conductors have then been incorporated into the Finite Element (FE) based computer simulations of a transformer core and an induction machine. The effects of temperature on different performance parameters, such as magnetic and copper losses and supply current have been studied.

This paper compare different probabilistic optimization methods dealing with uncertainties. Methods of Robust Design Optimization (RDO), Reliability-Based Design Optimization (RBDO) and Reliability-Based Robust Design Optimization (RBRDO) are presented and the approaches to calculate the moments and probability of failure are introduced. Then mathematical and electromagnetic design problems are tested to show the effectiveness of these methods.

High operating temperatures modify the magnetic behavior of ferromagnetic cores which may affect the performance of electrical machines. Conventionally, in CAD simulations, iron losses are computed using models in which the temperature dependency is completely neglected. Therefore, a temperature dependent material model is necessary to model more accurately the electrical machine behavior during the design process. In this communciation, an approach to include the temperature effect in the Jiles-Atherton hysteresis model is proposed.

In the domain of numerical computation, Model Order Reduction (MOR) methods are more and more applied in mechanics and have shown their efficiency in terms of computation time and memory requirements. In computational electromagnetics, research has started recently and the different methods available in the literature need to be compared in order to find the most efficient one. We propose to evaluate MOR approaches in order to solve linear magnetoquasistatic field problems. Therefore, the Proper Orthogonal Decomposition (POD), the Centroidal Voronoi Tessellation (CVT), the Proper Generalized Decomposition (PGD) and the Arnoldi-Krylov projection (AKP) are developed and compared.

Model Order Reduction (MOR) methods are an active research field in the numerical analysis domain. They are applied to many different areas in physics, especially in mechanics because they allow to dramatically reduce the computational time. MOR is quite recent in electromagnetics and needs still to be investigated. The Proper Orthogonal Decomposition (POD) is the most famous one and has already shown very promising results. However, the POD approach minimizes the error in the L2 sense on the whole domain and cannot be very accurate to calculate quantities of interest, like flux associated with a probe in region where the field is low. In this communication, we present the Balanced Proper Orthogonal Decomposition (BPOD) which extends the POD by taking account of probes in its model. The BPOD and POD approaches will be compared on a 3D linear magnetoquasistatic field problem.

Organizing international conferences leads to emission of greenhouse gases (GHG). Even though, some conferences are devoted to “greener” systems (e.g. IEEE VPPC), the transport of attendees and the local organization of the conference are not “carbon free”. Consequently, some experiences are reported in this paper in order to reduce the ecological footprint of the conference itself and also to mitigate the emitted GHG for international congresses.

Two model order reduction approaches are applied to reduce the computational time of a quasistatic finite element problem. Both methods are compared on an academic example.

The modeling of a multirate system -formed by components with heteroge- neous time constants- can be done using fixed-point method. This method allows a time- discretization of each subsystem with respect to its own time constant. In an optimization process, executing the loop of the fixed-point at each model evaluation can be time consum- ing. By adding one of the searched waveform of the system to the optimization variables, the loop can be avoided. This strategy is applied to the optimization of a transformer.

For the optimization of a component from a multirate system, the article presents benefits of the joint use of several models for the optimization and of fixed-point strategy for the modeling. Thus, space mapping allows reducing time computation of an optimization process by limiting the number of evaluations of time consuming models. In the case of multirate problems, these models can be modeled by Waveform Relaxation Method to provide an additional time saving.

In the communication, the WRM and the POD techniques are applied to study a transformer supplied by a power converter. The transformer is modeled by Finite Element Method. A reduced model of the transformer provided by the POD tech- nique is used to couple the power converter and the transformer using the WRM technique.

This communication addresses the modelling of the parameter known as the pull-in voltage in electrostatic MEMS (Micro Electro Mechanical System). As this parameter is sensitive to the physical parameters of the MEMS device, a stochastic modelling approach may be required. Two non-intrusive stochastic techniques are used: a sampling method based on Monte-Carlo simulations and a Polynomial Chaos Expansion (PCE) approach. The electro-mechanical problem is solved using the coupling between a 2D Finite Element (2D-FE) electrostatic model and the Euler-Bernoulli beam equation for the mechanical model. The influence on the pull-in voltage of three parameters subjected to uncertainty (material property and geometry) is investigated.

When modeling a system subject to uncertainties, a fundamental aspect is the stochastic modeling of the input parameters of the model. In this work, this aspect is emphasized by modeling the variability of the magnetic behavior law related to a set of stator samples. The identified probabilistic model of the parameters is tested using a Monte Carlo simulation. The importance of taking account of the dependency structure between the parameters is also emphasized

Industrial processing (cutting, assembly…) of steel laminations can lead to significant modifications in the magnetic properties. Moreover, the repeatability of these modifications is not always verified because of the tool wear or, more intrinsically, to the manufacturing process itself. When investigating the iron losses, it is generally shown that the hysteresis loss contribution is more likely to be affected. In the present work, twenty eight (28) samples of slinky stator (SS) are investigated, at a frequency of 5Hz. A stochastic model is then developed, using the Jiles-Atherton model together with a statistical approach to account for the variability of the hysteresis loops

Development of new ways to provide clean onboard electric energy is a key feature for the sailing boat industry and sail race teams. This is why marine turbines (MT), are considered to provide onboard energy. These turbines can be used to harness kinetic energy of the water flow related to the ship motion. In this paper we propose to study an unconventional design of such a turbine where the electrical generator is located in the periphery of the blades and where the magnetic gap is water filled. This kind of solution called “RIM DRIVEN” structure allows to increase the compactness and the robustness of the system. Due to the strong interaction of the multi physical phenomena, an electromagnetic model and a thermal model of the PM generator are associated with a hydrodynamic model of the blades and of the water flow in the underwater air gap. These models are used in a global coupled design approach in order to optimize, under constraints, the global efficiency of the system. This solution allows to optimize the system design.

This paper investigates the stochastic post-processing calculation of iron losses. Twenty eight slinky stator samples are investigated in term of iron losses variability, and stochastic model is then developed to take account of this variability. The Multivariate Gaussian distribution (MG) of the iron losses parameters is thereafter used for stochastic post-processing calculation of the density of iron losses of a PMSM, with Monte Carlo simulation method. This approach allows one to take in consideration the magnetic core variability from the iron loss point of view, for the design of electrical machine.

Discontinuities on the magnetic field distribution in the stochastic dimension can arise in a problem with geometric uncertainties. The classical polynomial chaos that is often used to approximate the random variable is no longer suited. One possibility is to use some additional approximation functions to tackle the problem of discontinuity. In this paper, we focus on the method of random mappings and we show that in that case the discontinuity are naturally taken into account and that no additional approximation function needs to be added

The aim of this work is to study, using a statistical approach, the macroscopic behavior of a given number of anisotropic laminations, stacked randomly.

Stochastic Spectral Finite Element Method (SSFEM) can be used to take into account some random aspects in the input data (material characteristic, source terms) involved in static electromagnetism problems. Similarly to the deterministic case, two potential formulations can be used in the stochastic case. The vector potential formulation applied to static problems is developed and compared to the scalar potential one, previously developed.

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 an analytical multi-physic modeling tool for the design optimization of a new kind of naval propulsion system. This innovative technology consists in an electrical permanent magnet motor that is integrated into a duct and surrounds a propeller. Compared with more conventional systems such as pods, the electrical machine and the propeller have the same diameter. Thus, their geometries, in addition to speed and torque, are closely related and a multidisciplinary design approach is relevant. Two disciplines are considered in this analytical model: electromagnetism and hydrodynamics. An example of systematic design for a typical application (a rim-driven thruster for a patrol boat) is then presented for a set of different design objectives (efficiency, mass, etc). The effects of each model are commented.

In previous communications, we presented an adaptive mesh refinement strategy in eddy current non-destructive testing. Using the 3D FEM, the proposed approach does not require expertise from the user about the mesh construction. Furthermore, only the area under interest is refined. In this paper we study different kind of error estimators and refinement adapted to the studied refinement strategy.

In this paper we present the comparison of error estimators using in 3D magneto harmonic FEM. First estimator is based on the non verification of the behaviour law. This estimator is very accurate but requires the solution of both complementary formulations. The second is based on an energetic approach. Both estimators are coupled with an adaptative meshing software. The results will be compared with experimental tests.

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.

This paper is included into the theme “challenges for marine renewable energy”. It discusses an innovative concept of electrical machine that should be particularly fitted to marine current turbine generators. Our investigations focus on permanent magnet direct-driven synchronous generators connected to a variable speed power electronic drive. Original and conventional solutions are compared in terms of mass and cost for a common set of specifications of a realistic application.

This communication deals with a comparison between two methods of discretisation: the well known Finite Element Method and the Natural Element Method that is a meshless method. An error estimator, based on the non-verification of the constitutive law, is used. This estimation has been applied to two examples: a device with permanent magnets and a variable reluctance machine.

In this paper we present an experimental and numerical study rotational single sheet tester. We focus on the effect of the shielding sheet distance which influences the measured magnetic field by H-coil.

On se propose ici d’utiliser l’estimateur basé sur la non-vérification de la loi de comportement pour évaluer l’erreur numérique lorsque la Méthode des Eléments Naturels (MEN) est utilisée pour résoudre un problème magnétostatique. La MEN est une méthode dite « sans maillage ». Cet estimateur est testé sur un exemple de deux aimants en mouvement.

Chania (Crete Island, Greece)

We present a method used to solve random problems, socalled Spectral Stochastic Finite Element Method (SSFEM ) developed by R. Ghanem. It allows to broadcast random properties from input data (sources, behaviour laws...) to output data. To reach this goal, we could discretize by using polynomial chaos expansion. In this paper, we point out the influence of expansion order on the model accuracy.

A global design methodology for AC inductors made of Soft Magnetic Composites (SMC) is presented. The optimal inductor dimensions and the optimal magnetic material characteristics that maximize the energy to weight ratio are determined. Several inductor modeling tools and a SMC material modeling tool are coupled together, furthermore controlled by a non-linear optimization routine. The material magnetization model is based on a physical representation at the millimetric scale.

La réduction des pertes fer dues au vieillissement magnétique des aciers doux est une voie d’optimisation de l’efficacité énergétique des machines électriques telle que recommandée par l’union européenne. Le vieillissement magnétique se traduit par une détérioration des propriétés magnétiques lors du fonctionnement de la machine électrique, ce vieillissement est lié à la formation de précipités de carbures ou nitrures à la température de fonctionnement (inférieure à 180°C). Cette étude propose un travail préliminaire dans le développement d’un modèle multi-physique et multi-échelles afin d’évaluer l’évolution des pertes fer pendant les cycles d’utilisation des machines électriques.

Une méthode de mesure combinant une démarche opératoire et la simulation par éléments finis est développée afin de caractériser la conductivité électrique locale de pièces massives. A l’aide d’un diagramme 5M (ou diagramme d’Ishikawa), une démarche d’optimisation de la méthode a été entreprise.

Dans un contexte particulièrement favorable au développement des énergies renouvelables, les travaux présentés concernent la conception d’une génératrice hydrolienne innovante pour la récupération de l’énergie des courants de marée. La génératrice, couplée à une hélice à axe horizontal conçue pour la récupération de l’énergie des courants, est une machine synchrone à aimants permanents et à entraînement direct. L’originalité réside dans la structure même de l’hydrolienne, inspirée directement de nouveaux systèmes de propulsion navale, où le rotor et le stator sont placés en périphérie de l’hélice et protégés par une tuyère. De fait, le diamètre de la machine, ainsi que son couple et sa vitesse de rotation, sont essentiellement dictés par des considérations hydrodynamiques. Il en résulte des machines électriques originales de forme annulaire: grand diamètre, grand nombre de pôles et très courtes axialement. Leur forme est assez proche de celles des machines dites « roue », bien que ces dernières soient plus longues et leur dimensionnement plutôt dicté par des considérations mécaniques. Ainsi, leur dimensionnement doit prendre en compte certaines spécificités dont l’une d’entre elles est la proportion des fuites magnétiques dans le sens axial. Généralement négligées, à juste titre, pour des machines ayant des proportions classiques, il devient important de prendre en compte leurs effets pour des machines ayant un ratio entrefer / longueur axiale anormalement élevé. Cet article propose des modèles analytiques simples, appuyés par des simulations par éléments finis 3D, permettant un calcul plus réaliste de la force électromotrice à vide et de l’inductance synchrone de ces machines particulières. Ils seront particulièrement adaptés à des travaux de pré dimensionnement systématique (optimisation) nécessitant un ensemble d’outils simples, robustes et de bonne précision.

Les machines synchrones à aimants permanents de grand diamètre et basse vitesse sont utilisées dans un nombre croissant d’applications. On les retrouve dans le domaine éolien de forte puissance, mais également dans la propulsion navale, où se développent des solutions à entraînement circonférentiel, ou encore la récupération d’énergie hydrocinétique (hydroliennes). Afin d’évaluer les performances de ces machines, il est souvent intéressant de disposer d’outils analytiques simples qui permettent des calculs rapides mais satisfaisants dans une approche de dimensionnement du premier ordre. Ces formulations simplifiées sont généralement suffisantes lorsqu’elles sont bien adaptées à la structure étudiée. Par contre, elles tendent à perdre en précision lorsque les dimensions deviennent inhabituelles, par exemple pour des nombre élevés de pôles. Cet article propose des formulations adaptées à ces structures particulières en prenant en compte, notamment, les fuites inter-aimant habituellement négligées. Les modèles proposés sont validés par des calculs numériques par différences finies 2D sur des applications concrètes.

Cet article s’intéresse à la conception des machines synchrones polyphasées à aimants déposés alimentées par onduleur de tension à Modulation de Largeurs d’Implusions (MLI). Ce type de machine permet de répondre à des cahiers des charges exigeants en terme de compacité, de comportement vibratoire et de tolérance aux pannes. En utilisant la décomposition multimachine, la conception d’une machine polyphasée peut s’aborder comme la conception de plusieurs machines fictives composant la machine polyphasée. L’adaptation de la machine polyphasée à son onduleur et l’amélioration de ses performances en terme de couple se traduit par la recherche de bobinage spécifiques. Ces bobinages doivent orienter le contenu de la force magnétomotrice statorique pour égaliser les constantes de temps des différentes machines fictives et filtrer correctement l’induction rotorique. L’intérêt de cette démarche de conception est illustrée par l’étude d’un petit propulseur en nacelle. On considère la structure initiale triphasée comportant 60 encoches et 14 pôles et on s’autorise uniquement une modification du bobinage. Un bobinage pentaphasé est déterminé : il permet de réduire les pertes Joule de 4% et d’atténuer les pulsations de couple de 94%. Si la stratégie de commande multimachine est mise en oeuvre, alors le couple moyen peut être augmenté de 11% à pertes Joule données par rapport à la solution triphasée.

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.

L'invention concerne un procédé de détermination des propriétés électromagnétiques d'un matériau magnétique, au moyen d'un dispositif comportant deux pointes de mesure et deux pointes excitatrices, et un capteur de champ placé à proximité dudit matériau, caractérisé en ce qu'il comporte les étapes suivantes : - l'application d'une polarisation magnétique H1 au matériau par un moyen de polarisation, - une imposition d'un signal d'excitation de courant i sur le matériau par l'intermédiaire des deux pointes excitatrices, - une mesure du champ H par le capteur de champ, - une mesure de la différence de potentiel U par les deux pointes de mesure, - une détermination de la perméabilité µ pour une zone de polarisation centrée autour de ladite polarisation magnétique H1 et - une modification de la polarisation H1 appliquée et une répétition des étapes 2 à 5.

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.