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H. Silm, M. Kaltenbacher, J. Schöberl, M. Schöbinger, K. Hollaus:
"Multiscale finite element methods for eddy current problems in laminated iron MSFEM4ECP";
International Compumag Society Newsletter, 23 (2016), 2; 3 - 13.

This article is about the ongoing research projekt "Multiscale Finite Element Methods for Eddy Current Problems" MSFEM4ECP in laminated iron.
The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical machines and transformers. In extrem cases the iron core is made of grain oriented ferromagnetic laminates, the material properties are anisotropic and exhibit a magnetic hysteresis. The scales vary from the meter range for the iron core to the thickness of single laminates (typically in the range of 0,2 - 0,3 mm). Clearly, modeling each laminate individually is not a feasible solution. Many finite elements (FEs) have to be used in such a model leading to extremely large nonlinear systems of equations. An accurate simulation fo eddy currents and iron lossis in laminated ferromagnetic cores with reasonable computer resources is not solved stisfacorily. It is still one of the major challenges in the computational electromagnetics. Laminated cores represent simple speaking a periodic microstructure and therefore are well suited for multiscale finite element methods (MSFEMs).
Simulatons with MSFEM show a boundary layer quite similar to that which occurs in corresponding brute force models of such cores with anistropic material properties. An accurate approximation of the boundary layer is essential for an exact evaluation of the iron losses. However, this requires many FE layers, which considerably increases the total number of FEs in the model. The periodic natrue of the lamination is interrupted by step lap joints, ventilation ducts or disturbed by skewing leading to complex geometries which are costly in FE modeling on its own.