Modelling methodology for transformer core vibrations based on the magnetostrictive properties

A mathematical model for vibration analysis of the transformer core is developed in this study. Core vibration is principally caused by magnetostriction effect which is also a function of magnetisation. A simplified magnetisation model is introduced and compared with the J-A model in term of accuracy for the magnetic intensity within -2500-A/m. As the magnetic properties are normally coupled with mechanical dependencies, the magnetostrictive characteristics are analysed based on establishment of the relationship between the strain and the stress. According to macroscopic thermodynamics and the law of energy conservation, a new model for magnetostriction effect is presented by expanding the Gibbs-free energy density in a polynomial form. In the cases where the magnetic field does not reach saturation, the quartic term and its above are neglected. The accuracy of the proposed magnetostrictive model is verified by comparing with the Sablik model. A mathematical expression for the equivalent magnetostrictive force is then derived, which is further utilised to calculate the core vibrations in the sinusoidal magnetic field. With the measurements previously available various numerical cases for core vibrations are evaluated and compared.