Abstract：The magnetostrictive effect of silicon steel sheets is a major causes of vibration and noise in electrical equipment. Silicon steel sheets inevitably experience mechanical stress during stacking and operation. Magnetostriction arises from the rotation of magnetic domains within silicon steel sheets, and mechanical stress alters the material's original internal crystal structure and magnetic domain arrangement, thereby changing its magnetostrictive properties and potentially leading to more severe vibration and noise. Therefore, establishing a magnetostrictive model of silicon steel sheets that accounts for stress effects is significant for research on vibration and noise reduction in electrical equipment. In this paper, from a thermodynamic point of view, the strain is expressed as a differential of the Gibbs free energy with respect to the stress. The Gibbs free energy is expanded in a Taylor series and then simplified to account for magnetostriction. As a result, the general expression of magnetostriction considering mechanical stress is obtained. Subsequently, the magnetostriction considering stress is expressed as the sum of the magnetostriction under zero stress and the stress-induced additional magnetostriction. The magnetostriction under zero stress can be represented as a superposition of even-order terms concerning the magnetization strength M. The calculation of stress-induced additional magnetostriction comprehensively accounts for the nonlinear effects of the same stress on magnetostriction at different magnetization intensities and of different stresses on magnetostriction at the same magnetization intensity.Finally, the magnetostriction model incorporating stress has been established. The effectiveness of the model for grain-oriented (GO) and non-oriented (NO) silicon steel sheetsis verified by comparing model calculations with experimental measurements. The parameters to be identified depend on whether the stress is tensile or compressive and are independent of its magnitude. Moreover, the proposed model accurately simulates the magnetostrictive properties of GO and NO silicon steel sheets across different stress levels. The root-mean-square error of the proposed model for GO silicon steel sheets is below 0.28 μm/m and, under most stresses, below 0.1 μm/m. The root-mean-square error for NO silicon steel sheets is all below 0.4 μm/m. Compressive stress greatly enhances the material's original magnetostrictive properties. However, it is difficult to precisely control the stress magnitude during the stacking process, and the iron core, subjected to uneven stress, does not fully eliminate the material's magnetostrictive effect. Thus, compressive stress should be avoided when stacking iron cores in electrical equipment. Instead, the iron core can be subjected to tensile stress to reduce magnetostriction-induced vibrations. However, excessive tensile stress should be avoided because it can exacerbate iron-core vibration.
付裕恒, 李琳. 考虑磁-应力耦合效应的硅钢片磁致伸缩模型[J]. 电工技术学报, 2026, 41(12): 3937-3950.
Fu Yuheng, Li Lin. Magnetostriction Model of Silicon Steel Sheets Considering Magneto-Stress Coupling Effect. Transactions of China Electrotechnical Society, 2026, 41(12): 3937-3950.
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2026, Vol. 41 
