An error‐based approach to complementary formulations of static field solutions

Rikabi, J.; Bryant, C.F.; Freeman, E.M.

doi:10.1002/nme.1620260906

Cited by 88 publications

(55 citation statements)

References 4 publications

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“…The results obtained from the calculations with both formulations are compared in Table 1. Classicaly, the a-formulation always gives greater values than the ϕ-formulation for the magnetic energy and the flux (16) . This is not always true in the case of the emf, because it is a derivative variable.…”

Section: Fem Resultsmentioning

confidence: 99%

Application of Finite-Element Method to a PMLSM with Non-Sinusoidal Electromotive Force

Remy

Tounzi²,

Barre

et al. 2006

IEEJ Trans. IA

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Remy Ghislain Non-member (L2EP, ENSAM Lille, ghislain.remy@lille.ensam.fr) Tounzi Abdelmounaïm Non-member (USTL, ENSAM Lille, mounaim.tounzi@univ-lille1.fr) Barre Pierre-Jean Non-member (L2EP, ENSAM Lille, barre@lille.ensam.fr) Piriou Francis Non-member (USTL, ENSAM Lille, francis.piriou@univ-lille1.fr) Hautier Jean-Paul Non-member (L2EP, ENSAM Lille, hautier@lille.ensam.fr) Keywords: PMLSM, non-sinusoidal electromotive force, finite-element analysis Nowadays industrial applications such as machine-tools applications require high speed and high precision. Fig.1 shows a prototype designed for high speed laser cutting. To improve the performances of linear motion systems, classical solutions used are to adapt more powerful linear motors, or to reduce the moving weight. But in the meantime, ripple forces induced by harmonics of Back-EMF are amplified as the power of the linear motor increases; consequently, the mechanical system is more and more perturbed by the force ripple and a high precision positioning becomes more difficult to reach. One solution is to improve the control strategy of such systems: to control permanent magnet linear synchronous motors (PMLSM) in an optimal way, the knowledge of the real waveform of different electrical characteristics is required. Thus, control strategies can be built on accurate values and yield reliable processes, notably on the thrust control. One of the electrical characteristics needed is the electromotive force (emf). This can be sinusoidal or not, which implies different control approaches. Furthermore, it is generally difficult to obtain this emf from measurements. Nowadays, the threedimensionnal finite-element method (3D-FEM) is widely used to model PMLSMs. Then, it can be helpful to determine the electrical characteristics of a PMLSM when it is difficult to measure them. It can also be used, in virtual prototypes, to quantify their electromagnetic variables in order to foresee the machine control or to modify the geometrical characteristics of the prototype to yield the desired results. The PMLSM studied is a LIMES400/120 from Siemens (Fig. 1). Measures and estimations of Back-EMF are made in realtime with a dSPACE 1005 card. Fig. 1. PMLSM PrototypeWe used the finite-element method to study the non-sinusoidal EMF of a PMLSM. Firstly, the finite-element method is introduced; as there are severals solutions to solve the Maxwell equations, two classical potential formulations are presented to express and solve the electromagnetic problem. Results presented give some advice to make the choice between the two formulations regarding to the studied system.Previous studies have shown that the high number of poles decreases the end effects and the dissymetry of the inductances. Consequently, it is possible to use the geometric periodicity to model only a part of the machine and then to limit the computation time without any effect on the accuracy of the results. We presented the elementary part modelled and the geometrical characteristics. Then, the several cases have been in...

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Section: Fem Resultsmentioning

confidence: 99%

Application of Finite-Element Method to a PMLSM with Non-Sinusoidal Electromotive Force

Remy

Tounzi²,

Barre

et al. 2006

IEEJ Trans. IA

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“…• in [3], a local error criterion based on the precision on the computation of the energy stored in each element; • for magnetostatics cases with movement [4], focusing on the maximization of the co-energy functional; • [5] proposes to evaluate the error on the behavior law, from the complementary variational principle, using the Ligurian. Some papers have presented adaptive meshing techniques dedicated to eddy-current problems:…”

Section: B Adaptive Meshing and Energy-based Approachesmentioning

confidence: 99%

“…• [6] is an extension of [5] to eddy-current problems, still using complementary formulations; • [7] proposes two error estimators, one based on the principle of the Ligurian and the other based on the numerical discontinuity of the field; • [8] uses a local solution in the conducting region; • [9] uses an error estimator based on the precision on the Mawxell-Ampère equation. However, adaptive meshing is not widely spread for timevarying cases.…”

Section: B Adaptive Meshing and Energy-based Approachesmentioning

confidence: 99%

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An Energy Based Approach of Electromagnetism Applied to Adaptive Meshing and Error Criteria

Ladas¹,

Mazauric²,

Meunier³

et al. 2008

IEEE Trans. Magn.

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In order to improve the finite-element modeling of macroscopic eddy currents (associated with motion and/or a time-varying electrical excitation), an original error criterion for adaptive meshing, based on a local power conservation, is proposed. Then, the importance of the order element in the error computation is investigated. Finally, the criterion is coupled to a "bubble" mesh generator, and an adaptive meshing of a 2-D induction heating case is performed.

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“…We will not consider in detail this subject here, assuming this function as given. For this important topic the reader is referred to the literature, in particular to that dealing with complementary variational techniques, which appear especially suited to the determination of physically significant local error functions linked to local and global energy estimates (Albanese and Rubinacci, 1998;Golias er al., 1994;Marmin et al, 1998;Oden, 1973;Penman, 1988;Remacle et al, 1998;Rikabi et al, 1988). Substituting the reconstruction operators [Eqs.…”

Section: Discretization Strategy 3: Error-based Discretizationmentioning

confidence: 99%

A reference discretization strategy for the numerical solution of physical field problems

Mattiussi

2002

Electron Microscopy and Holography

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An error‐based approach to complementary formulations of static field solutions

Cited by 88 publications

References 4 publications

Application of Finite-Element Method to a PMLSM with Non-Sinusoidal Electromotive Force

Application of Finite-Element Method to a PMLSM with Non-Sinusoidal Electromotive Force

An Energy Based Approach of Electromagnetism Applied to Adaptive Meshing and Error Criteria

A reference discretization strategy for the numerical solution of physical field problems

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