A model for magnetostriction in coupled nonlinear finite element magneto-elastic problems in electrical machines

A model has been developed for magnetostriction in coupled nonlinear finite element magneto-elastic problems in electrical devices. The formulation for this numerical model has been detailed and the all force components including those due to magnetostriction were developed. An expansion of the field and force formulation, for direct implementation in a finite element program, was also developed. This expansion was shown for both first order and second order triangular elements. The force formulation utilized the virtual work technique. Due to the lack of experimental data of the magnetostrictive phenomenon for electrical steels (used in the manufacture of electrical machines and transformers), an analytical model was also developed. This analytical model directly creates the magnetostriction curve λ(H) utilizing the magnetization curve data. The analytical model provided the expected behavior of ferrous substances as published in the literature. The curves created by this analytical model can be used as needed in numerical computation of fields and forces