# Magnetostriction modelling

Magnetostriction is the effect that ferromagnetic materials deform when magnetised. The deformation differs from material to material and is dependent on the waveform, the frequency and the amplitude of the magnetic induction or the magnetic field. Other factors, such as applied mechanical stress on the material, also have an effect on the magnetostriction of the material.

On the one hand, the magnetostriction effect is a detrimental effect, because it is (partly) responsible for the generation of noise in the magnetic cores of transformers and electrical machines. This is an increasingly important criterion in the design of these devices. On the other hand, magnetostriction can also be used to our advantage in applications such as miniature actuators. For these applications, materials are designed to have an exceptionally large magnetostriction. Examples of these materials are Terfenol and Galfenol.

## Applications

**Calculation of vibrations and noise in electromechanical devices**

The magnetic cores of transformers and electrical machines are made from stacks of thin sheets of electrical steel. Electrical steel is an alloy of iron and silicon (3% - 5%). When a magnetic core is magnetised with an AC magnetic field, the deformations of the core will lead to vibrations and ensuing noise. In order to minimize these vibrations and noise, a numerical method is used to calculate the vibrations and noise of a device under design.

To determine the magnetostrictive behaviour of a ferromagnetic material, magnetostriction measurements are made on a PC-based measuring set-up. The main component of the measurement set-up is a small Single Sheet Tester (SST) with strain gauges applied on the sample sheet.

The measurement results are used to make a numerical magnetostriction model. This model is used in the numerical method that calculates the vibrations of the core under design. The specific numerical procedure consists of several steps.

A dynamical magnetic finite elements calculation of the core is the first step.

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Next, the magnetic force distribution and the force distribution due to the magnetostriction are calculated from the results of the previous step. These force distributions will then be used to calculate the vibrations of the core. Here, a finite element method, combined with a structural modal analysis is used. The resulting data can be used to alter to design of the core towards lower vibrations and noise production.

## Relevant publications

T. Hilgert, L. Vandevelde, J. Melkebeek, 'Numerical Analysis of the Contribution of Magnetic Forces and Magnetostriction to the Vibrations in Induction Machines', IET Science, Measurement and Technology, Vol. 1, No. 1, January 2007, pp. 21-24.

T. Hilgert, L. Vandevelde, J. Melkebeek, 'Application of Magnetostriction Measurements for the Computation of Deformation in Electrical Steel', Journal of Applied Physics 97 (10): Art. No. 10E101 Part 2 May 15 2005.

L. Vandevelde, T. Hilgert, J. Melkebeek, 'Magnetostriction and Magnetic Forces in Electrical Steel: Finite Element Computations and Measurements', IEE Proceedings - Science, Measurement and Technology, Vol. 151, No. 6, November 2004, pp. 456-459.

L. Vandevelde, J. Melkebeek, 'Magnetic Forces and Magnetostriction in Electrical Machines and Transformer Cores', IEEE Transactions on Magnetics, Vol. 39, No. 3, May 2003, pp. 1618-1621.

L. Vandevelde, J. Melkebeek, 'Modeling of Magnetoelastic Material', IEEE Transactions on Magnetics, Vol. 38, No. 2, March 2002, pp. 993-996.