A simplified magnetostrictive model under rotational magnetization in an electrical steel sheet taking the pinning hysteresis effect into account

A large number of experimental observations show that under two-dimensional (2-D) rotational magnetization, there is a complicated relationship between the magnetostrictive strain and magnetic flux density. In this paper, the magnetostrictive characteristics in a non-oriented electrical steel sheet under 2-D magnetization are measured and modelled based on the experimental system developed by the laboratory. The in-plane magnetostrictive strain tensor under the 2-D magnetization is expressed as nonlinear superposition of dynamic magnetostrictive strain in the rolling direction (RD) and transverse direction (TD), respectively. The magnetostriction's first derivative with respect to magnetization depicts the pinning effect and the interaction among magnetic domains which result in the hysteresis behaviour. And based on the particle swarm optimization (PSO), the model parameters are identified. The validity of the proposed model is verified by comparing the calculation results with the experimental ones. Studies have shown that the magnetostrictive properties in an electrical steel sheet have strong hysteresis behaviour under the 2-D magnetization, and the model proposed here can well characterize these characteristics.