Stéphane Clenet

Determination and utilization of the source field in 3D magnetostatic problems

In this paper we study different approaches to introduce the source terms due to the inductors crossed by a uniform current density J/sub 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 J/sub 0/. This decomposition is used in the a-formulation without gauge condition. Moreover, from the flux facet the source field H/sub s/ can be calculated in the edge element space and introduced into the /spl phi/-formulation. As examples of applications we have studied a coil with a complex geometry and a iron core coil.

Model Order Reduction of Non-Linear Magnetostatic Problems Based on POD and DEI Methods

In the domain of numerical computation, model order reduction approaches are more and more frequently applied in mechanics and have shown their efficiency in terms of reduction of computation time and memory storage requirements. One of these approaches, the proper orthogonal decomposition (POD), can be very efficient in solving linear problems but encounters limitations in the non-linear (NL) case. In this paper, the discrete empirical interpolation method coupled with the POD method is presented. This is an interesting alternative to reduce large-scale systems deriving from the discretization of NL magnetostatic problems coupled with an external electrical circuit.

Stochastic Modeling of Soft Magnetic Properties of Electrical Steels: Application to Stators of Electrical Machines

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 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.

Numerical model to discretize source fields in the 3D finite element method

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.

3-D Stochastic Spectral Finite-Element Method in Static Electromagnetism Using Vector Potential Formulation

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.

Adaptive Method for Non-Intrusive Spectral Projection—Application on a Stochastic Eddy Current NDT Problem

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.

Source Field Computation in NDT Applications

Numerical modeling of nondestructive testing (NDT) by eddy currents has been applied for qualification of two monitoring devices. Experimental data have enabled us to validate reliable and relevant finite-element method models. The encountered difficulties due to geometry (size and topology), the nature of the control signal (weak flux differences), and the movement accounting have been successfully overcome by evaluating the A-phi and T-Omega dual formulations with appropriate source fields and applying classical method to suppress the mesh numerical error and choosing the well-known lock-step technique

Application of the natural-element method to model moving electromagnetic devices

The natural-element method, which belongs to the family of meshless methods, is applied in the context of two-dimensional 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

Methodology to Study the Influence of the Microscopic Structure of Soft Magnetic Composites on Their Global Magnetization Curve

The methodology presented in this paper is using a modeling approach based on the observation of the real microscopic material structure to predict the global macroscopic magnetization curve of the soft magnetic composites (SMCs) materials. It can be used to investigate the influence of the variability of all parameters of the microstructure on the global macroscopic magnetization curve of the equivalent homogenous material that is essential to the optimal design of SMC electromagnetic devices. The proposed method includes several steps: acquisition of the microscopic structure by image processing, simulation by FE analysis, and identification of the global macroscopic magnetization curve. The results are validated by a comparative analysis with experimental hysteresigraph measurements and analyzed in order to investigate the influence of the microscopic structure on the global magnetic properties of the SMC material.

Error estimation of finite element solution in nonlinear magnetostatic 2D problems

This paper presents an error estimator which enables control of the quality of finite element solutions in nonlinear magnetostatics. This method, based on the works of P. Ladeveze [1983, 1991] in mechanics, consists of constructing complementary admissible field from the one calculated by the finite element method. This method has been transposed in the cases of nonlinear vector and scalar potential 2D formulations. The results given by the proposed estimator are compared to the one based on two finite element solutions on two examples.