MODELISATION DU COUPLAGE MAGNETO-THERMIQUE APPLIQUÉE AUX RALENTISSEURS ÉLECTROMAGNÉTIQUES

La conception industrielle de systemes de freinage a courants induits passe par l'analyse des phenomenes mis en jeu lors de leur fonctionnement, et notamment les phenomenes couples magneto-thermiques. Une methode a base d'elements finis a ete developpee, qui consiste a coupler deux codes de calcul, l'un specialise en magnetisme, et l'autre en thermique. La partie electromagnetique du probleme a fait l'objet de developpements specifiques, tels : -la prise en compte de la dependance thermique des caracteristiques B(H) de l'acier, a l'aide d'un modele analytique : -la prise en compte d'ailettes de refroidissement pour le calcul du couple, a l'aide de techniques de pas-a-pas dans le temps avec mouvement, et, beaucoup plus rapides, d'homogeneisation ; -la prise en compte de deformations dues aux contraintes thermo-mecaniques, en utilisant des elements finis transformes plutot qu'un remaillage ; -un mode de calcul 3D des courants induits dus au mouvement, base sur la formulation T-Q., la methode de Petrov-Galerkine, une methode de Newton-Raphson relaxee de facon adaptative, et l'emploi d'elements de raccordement pyramidaux.

[1]  Ernst Rank,et al.  On the importance of the discrete maximum principle in transient analysis using finite element methods , 1983 .

[2]  T. Hsu,et al.  On the solution of diffusion—convection equations by the space—time finite element method , 1986 .

[3]  N. Takahashi,et al.  IMPROVEMENTS OF THE T-R METHOD FOR 3-D EDDY CURRENT ANALYSIS , 1988 .

[4]  Y. Marechal,et al.  Computation of 2D and 3D eddy currents in moving conductors of electromagnetic retarders , 1990, International Conference on Magnetics.

[6]  Kurt Preis,et al.  Some improvements in nonlinear 3D magnetostatics , 1990 .

[7]  J. Simkin,et al.  A General purpose 3-D formulation for eddy currents using the lorentz gauge , 1990, International Conference on Magnetics.

[8]  Christian Magele,et al.  Different finite element formulations of 3D magnetostatic fields , 1992 .

[9]  J. M. Thomas,et al.  Introduction à l'analyse numérique des équations aux dérivées partielles , 1983 .

[10]  A. J. Davies,et al.  On the use of the total scalar potential in the numerical solution of field problems in electromagnetics , 1988 .

[11]  Z. J. Cendes,et al.  Convergence of iterative methods for nonlinear magnetic field problems , 1988 .

[12]  N. Takahashi,et al.  Comparison of different finite elements for 3-D eddy current analysis , 1990 .

[13]  Takehisa Hara,et al.  Time-periodic finite element method for nonlinear diffusion equations , 1985 .

[14]  M. Morisup,et al.  A comparison of the Coulomb gauge and Lorentz gauge magnetic vector potential formulations for 3D eddy current calculations , 1992 .

[15]  W. J. Gordon,et al.  Transfinite element methods: Blending-function interpolation over arbitrary curved element domains , 1973 .

[16]  K. Preis,et al.  Calculation of 3D eddy current problems by finite element method using either an electric or a magnetic vector potential , 1988 .

[17]  A. Nicolas Application de la méthode des équations intégrales de frontière à la modélisation des phénomènes d'induction , 1983 .

[18]  Guglielmo Rubinacci,et al.  Formulation of eddy current problem , 1990 .

[19]  D. Rodger,et al.  Coupled elements for problems involving movement (switched reluctance motor) , 1990 .

[20]  Computation of 3D electromagnetic fields by finite elements , 1992 .

[21]  Koji Fujiwara,et al.  Method for determining relaxation factor for modified Newton-Raphson method , 1993 .

[22]  P. R. Kotiuga On making cuts for magnetic scalar potentials in multiply connected regions , 1987 .

[23]  René Tinawi,et al.  Une présentation de la méthode des éléments finis , 1983 .

[24]  G. Meunier,et al.  2D nonlinear finite element modelling of electromagnetic retarders using time-stepping algorithms, and the Petrov-Galerkin method with homogenization techniques , 1996 .

[25]  F. Piriou,et al.  Study of 3D formulations to model electromagnetic devices , 1994 .

[26]  D. Rodger,et al.  An optimal formulation for 3D moving conductor eddy current problems with smooth rotors , 1990, International Conference on Magnetics.

[27]  T. Hsu,et al.  Analysis of heat conduction in solids by space‐time finite element method , 1985 .

[28]  J.-L. Coulomb,et al.  Mathematical minimization of the time harmonics of the EMF of a DC-PM machine using a finite element method , 1993 .

[29]  C. Magele,et al.  Numerical analysis of 3D magnetostatic fields , 1991 .

[30]  M. Morisup A Comparison of the Coulomb Gauge and Lorentz Gauge Magnetic Vector Potential Formulations for 3D Eddy Current Calculations , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[31]  R. Dautray,et al.  Analyse mathématique et calcul numérique pour les sciences et les techniques , 1984 .

[32]  J. C. Sabonnadiere,et al.  Simulation of induction machine operation using a step-by-step finite-element method , 1990 .

[33]  G. Henneberger,et al.  Calculation of the 3D nonlinear eddy current field in moving conductors and its application to braking systems , 1996 .

[34]  B. Davat,et al.  The movement in field modeling , 1985 .

[35]  T. Sebastian,et al.  Nonlinear two-dimensional finite element modeling of permanent magnet eddy current couplings and brakes , 1994 .

[36]  Mouloud Feliachi,et al.  Conception of an air-gap element for the dynamic analysis of the electromagnetic field in electric machines , 1982 .

[37]  Igor Tsukerman,et al.  Accurate computation of 'ripple solutions' on moving finite element meshes , 1995 .

[38]  Gérard Meunier,et al.  Finite element modeling of unbounded problems using transformations: a rigorous, powerful and easy solution , 1992 .

[39]  O. C. Zienkiewicz,et al.  An ‘upwind’ finite element scheme for two‐dimensional convective transport equation , 1977 .

[40]  A. Razek,et al.  Hybrid numerical methods for movement consideration in electromagnetic systems , 1988 .

[41]  H. Yee Effects of finite length in solid-rotor induction machines , 1971 .

[42]  Koji Fujiwara,et al.  Improvements of convergence characteristics of Newton-Raphson method for nonlinear magnetic field analysis , 1992 .

[43]  Frank Claeyssen,et al.  A new family of finite elements: the pyramidal elements , 1996 .

[44]  C. W. Chen Temperature Dependence of Magnetic Properties of Silicon‐Iron , 1958 .

[45]  J. O'Dwyer,et al.  Choosing the relaxation parameter for the solution of nonlinear magnetic field problems by the Newton-Raphson method , 1995 .

[46]  Gérard Meunier,et al.  A general purpose tool for restoring inter-element continuity , 1992 .

[47]  D. Heim,et al.  Mathematical model of a magnetoresistive read head for a magnetic tape drive , 1985 .

[48]  J. P. Bastos,et al.  Modélisation magnétique et numérique par éléments finis de feuilletages ferromagnétiques , 1980 .

[49]  Paul-Louis George,et al.  Génération automatique de maillages : applications aux méthodes d'éléments finis , 1991 .

[50]  R. Perrin-Bit,et al.  A three dimensional finite element mesh connection for problems involving movement , 1995 .

[51]  Oszkar Biro,et al.  Performance of different vector potential formulations in solving multiply connected 3-D eddy current problems , 1990 .

[52]  R. Albanese,et al.  Periodic solutions of nonlinear eddy current problems in three-dimensional geometries , 1992 .

[53]  F. Ossart,et al.  Analysis of convergence in nonlinear magnetostatic finite elements problems , 1994 .

[54]  J. Coulomb,et al.  The calculation of electromagnetic torque in saturated electric machines within combined numerical and analytical solutions of the field equations , 1981 .

[55]  N. Demerdash,et al.  Theoretical and numerical difficulties in 3D-Vector potential methods in finite element magnetostatic computations , 1990, International Conference on Magnetics.

[56]  Thomas J. R. Hughes,et al.  A simple scheme for developing ‘upwind’ finite elements , 1978 .

[57]  Alain Bossavit,et al.  The "TRIFOU" Code: Solving the 3-D eddy-currents problem by using H as state variable , 1983 .

[58]  Jean-Louis Coulomb Analyse tridimensionnelle des champs électriques et magnétiques par la méthode des éléments finis‎ , 1981 .

[59]  T. Morisue Magnetic vector potential and electric scalar potential in three-dimensional eddy current problem , 1982 .

[60]  W. J. Gordon,et al.  Construction of curvilinear co-ordinate systems and applications to mesh generation , 1973 .