An H-ψ formulation for the three-dimensional eddy current problem in laminated structures

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Li, Peijun¹  Zheng, Weiying² 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, NCMIS, Beijing 100190, Peoples R China

关键词: Eddy current problem;    H-psi formulation;    Nonlinear Maxwell's equations;    Silicon steel laminations;   

DOI  :  10.1016/j.jde.2013.01.028

来源: Elsevier

【 摘 要 】

It is a very challenging problem for the direct simulation of the three-dimensional eddy currents in grain-oriented (GO) silicon steel laminations since the coating film is only several microns thick over each lamination and the magnetic permeability is nonlinear and anisotropic. In addition, the system of GO silicon steel laminations has multiple scales and the ratio of the largest scale to the smallest scale can be up to 10(6). In this paper, we study an H-psi formulation for the nonlinear eddy current problem in laminated conductors. By omitting the insulating films between neighboring laminations, we propose an approximate but effective H-psi formulation for the nonlinear eddy current problem, which reduces the scale ratio by 2-3 orders of magnitude. The well-posedness of the original problem and the approximate problem are established by examining their weak formulations. The convergence is proved for the solution of the approximate problem to the solution of the original problem as the thickness of coating films approaches zero. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free