Keywords: magnetic measurement, magnetic hysteresis, mechanical stress.

The application of a mechanical stress to a magnetic material changes its magnetic properties and results in different magnetic induction for a given magnetic field at different applied stresses. This phenomenon is known as the Villari effect or inverse magnetostriction. The magnetic behaviour of iron under applied mechanical stress is quite a complex phenomenon. In general, the effect of unidirectional stress on magnetization depends on the magnetostriction of the material [1].

The measurements have been realized with a grain-oriented GO Fe-(3.1 wt%)Si alloy. Transformers cores are built today with GO Fe-Si laminations, where the crystallites have their easy axis close to the rolling direction, and their plane is nearly parallel to the lamination surface. It is called as Goss texture [2]. The applied laminations have a 0.27 mm thickness, and the maximum specific total core loss W_15/50=0.89 W/kg at 1.5 T and 50 Hz.

The apparatus of the measurement contains two computers to measure the mechanical and the magnetic properties independently.

The mechanical stress has been varied from a value of 0 MPa to 136.66 MPa in five steps. At each step the magnetic measurement has been carried out with sinusoidal and triangular waves, first demagnetizing the sheet and then changing the primary current from the maximum to the minimum value with thirty different amplitudes through five periods at each amplitude to stabilize the hysteresis loop. It results in the major loop with twenty-nine minor loops, which is required to the installation of a stress-dependent model, to develope. At each steps, the measurement frequency has been selected 1 Hz, 2 Hz, 5 Hz, 10 Hz and 20 Hz [3].

The measurement proved, that the increase of the measurement frequency increases the energy loss per cycle. The increase of the tension resulted in increased permeability, magnetization, and magnetic flux density at the negative saturation magnetization, and decreased permeability, magnetization, and magnetic flux density at the positive saturation magnetization. By increasing the tension the coercive field H_c decreased and the slope of the hysteresis loop changed.

By increasing the tension, the energy loss decreased in exponential scale in all measurement frequencies. The rates of change of the energy losses are approximately 33-45% at the maximum applied stress of =136.66 MPa. The measurements proved, that the effect of the applied stress decreased with increasing measurement frequencies.

A measurement based stress dependent model has been developed and it has been realized in three steps. The simple Preisach-type models have been implemented by the results of the measurement with Everett-functions. It resulted 5x5 Everett-surfaces. The discrete values of the surfaces were stored in rectangular two-dimensional arrays. To simulate the magnetic behavior at arbitrary stress value, it has to be interpolate between the 5x5 arrays. It has been solved with a two-dimensional spline interpolation technique. The interpolation has been implemented between the cells in same position of the arrays. The interpolation can be solved between the minimum and the maximum value of the measured mechanical stresses at each value of the measurement frequency. The interpolation has been solved with a spline technique, although it is possible to use one of the other well known interpolation techniques as well. The interpolations have been resulted five Everett-surfaces at the optional stress value versus the measurement frequency. With the interpolation we obtain a new array to represent the Everett-surface of the stress and frequency dependent magnetic properties. With the new Everett surface we can install the Preisach model and the simulation results a magnetic characteristic by a required mechanical stress and measurement frequency value. The maximum value of the error, was about 9.0%. This value of the error is approximately equivalent with the installation error of the simple Preisach model.

This is a strongly measurement based model, but it represents the real stress dependent magnetic behaviour accurately for the measured interval.

1

R.M. Bozorth, "Ferromagnetism", Toronto: Van Nostrand, 1951.

2

F. Fiorillo, "Measurement and Characterization of Magnetic Materials", San Diego: Elsevier, 2004.

3

A. Sipeky, A. Ivanyi, "Magnetic hysteresis under applied stress", Physica B, Vol. 372, 177-180, 2006. doi:10.1016/j.physb.2005.10.042

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