Homogenized Magnetoelastic Behavior Model for the Computation of Strain Due to Magnetostriction in Transformers

Abstract

This paper deals with the prediction of the deformation of a multi-layer transformer core made of an assembly of anisotropic 'E-shaped' and 'I-shaped' sheets. This magneto-mechanical coupled problem is solved by a stepping finite element method sequential approach: magnetic resolution is followed by mechanical resolution. A 3D Simplified Multi-Scale Model (SMSM) describing both magnetic and magnetostrictive anisotropies is used as the constitutive law of the material. The transformer core structure is modeled in 2D and an homogenization technique is implemented to take the anisotropic behavior of each layer into consideration and define an average behavior at each element of the finite element mesh. A three-layers transformer prototype is fabricated with Hi-B grain-oriented iron-silicon alloy. Experimental measurements are carried out and compared to the modeling results. Small discrepancies are observed and discussed.

Reduction of Power Transformer Core Noise Generation Due to Magnetostriction-Induced Deformations Using Fully Coupled Finite-Element Modeling Optimization Procedures

“…In terms of experimentation, vibration and deformation of a test transformer core are measured by means of accelerometers which give the acceleration of certain points [17], or by means of a laser scanning vibrometer, giving a 3D field of surface speed [22], [23]. Both need to consider the suspension of the core and post-processing of the measurement to correct the rigid body movement [9]. Direct measurement of noise is also carried out, allowing the comparison of different transformer cores [24] and the study of the physical parameters' influences, leading to an experience deduced noise computation equation [25].…”

“…This article is based on our previous work [9], briefly recalled hereafter. It dealt with the prediction of the deformation of a multilayer transformer stacked 'E-I' core.…”

“…For the application of small transformers in the aircraft considered in this paper, core sheets are preferred in the form of 'E' and 'I', or ideally noncut in the form of '8'. Since there is only little air-gap between each electrical sheet of the transformer core, magnetic forces are negligible [9]. Core deformation due to magnetostriction is then considered as the main source of noise emission.…”

Magnetostrictive and magnetic effects in Fe-27%Co laminations

“…The magnetostriction is linked to the presence of a magnetic domain structure 6 which tends to minimize the total local free energy (1). At the domain scale, the magnetic equilibrium results from a Contact author: hubert@lmt.ens-cachan.fr the competition between the different energetic terms:…”

“…However, such structures are well known to emit vibrations and noise. 1 This phenomenon has two possible origins: usual magnetic forces and associated elastic deformations (that induces the socalled form effect 2 ), and magnetostriction strain strongly correlated to the crystallographic texture and orientation of the magnetic field with respect to RD. Magnetostriction in a crystalline material is a spontaneous change of material shape depending of the local magnetic state.…”