Anisotropic model for the numerical computation of magnetostriction in grain-oriented electrical steel sheets

Abstract

Purpose

The modeling of magnetostrictive effects is a topic of intensive research. The authors' goal is the precise modeling and numerical simulation of the magnetic field and resulting mechanical vibrations caused by magnetostriction along the joint regions of electric transformers.

Design/methodology/approach

The authors apply the finite element (FE) method to efficiently solve the arising coupled system of partial differential equations describing magnetostriction. Hereby, they fully take the anisotropic behavior of the material into account, both in the computation of the nonlinear electromagnetic field as well as the induced magnetostrictive strains. To support their material models, the authors measure the magnetic as well as the mechanical hysteresis curves of the grain-oriented electrical steel sheets with different orientations (w.r.t the rolling direction). From these curves they then extract for each orientation the corresponding commutation curve, so that the hysteretic behavior is simplified to a nonlinear one.

Findings

The numerical simulations show strong differences both in the magnetic field as well as mechanical vibrations when comparing this newly developed anisotropic model to an isotropic one, which just uses measured curves in rolling direction of the steel sheets. Therefore, a realistic modeling of the magnetostrictive behavior, especially for grain-oriented electrical steel as used in transformers, needs to take into account the anisotropic material behavior.

Originality/value

The authors have developed an enhanced material model for describing magnetostrictive effects along the joint regions of electric transformers, which fully considers the anisotropic material behavior. This model has been integrated into a FE scheme to numerically simulate the mechanical vibrations in transformer cores caused by magnetostriction.

Citation

Kaltenbacher, M., Volk, A. and Ertl, M. (2013), "Anisotropic model for the numerical computation of magnetostriction in grain-oriented electrical steel sheets", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32 No. 5, pp. 1620-1630. https://doi.org/10.1108/COMPEL-04-2013-0116