A New Method for Quantitative Evaluation of Mechanical Stress of Oriented Electrical Steel Sheets Using the Differential Susceptibility at the Coercive Point
Meng Xiaoge, Li Lin
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China
Abstract As a soft magnetic material with excellent electromagnetic properties, oriented electrical steel sheet is widely used in the manufacture of transformer cores. In the actual operation process, due to the bending effect inside the transformer and the overlaying of the silicon steel sheet, the iron core will be subjected to certain extrusion or tensile stress, and the magnetic characteristics of the silicon steel sheet under different stresses will be very different. Although tensile stress causes little change in magnetic properties, even a small compressive stress can cause serious deformation of the hysteresis loop and increase the hysteresis loss. Therefore, it is very important to determine the stress type of oriented silicon steel sheet and evaluate its magnitude to improve the operation efficiency of transformer. In this paper, a novel method for measuring the stress of electrical steel sheet is presented by using the differential susceptibility of the hysteresis loop at the coercive point. Firstly, based on the extended magnetomechanical magnetic hysteresis model and considering that the pinning coefficient of soft magnetic materials is approximately equal to the coercivity field, the linear expression of the relationship between the reciprocal of the differential magnetic susceptibility of the coercive point and the stress is derived, and the linear calibration curve is obtained. Then the hysteresis loops and magnetostrictive curves of B30P105 and 30QG120 silicon steel sheets under different stresses are measured by the BROCKHAUS-MPG200 soft magnetic material testing system. According to the hysteresis loops, the relationship between the differential magnetic susceptibility of the coercive point and the stress of the two silicon steel sheets is obtained. The magnetic susceptibility of the two kinds of silicon steel sheet increases with the increase of compressive stress and decreases with the increase of tensile stress, and the effect of compressive stress on the magnetic susceptibility of the coercive point is greater than that of tensile stress. Finally, according to the theoretical relation expression, the theoretical relation curves between the reciprocal of differential magnetic susceptibility and the stress of two kinds of silicon steel sheets are drawn. There is a good agreement between the theoretical curves and the experimental values of the two kinds of silicon steel sheets, which proves the correctness and universality of the theoretical derivation. Based on the extended magnetomechanical hysteresis model, a novel method for quantitative evaluation of mechanical stress of silicon steel sheet is presented. The reciprocal of the differential magnetic susceptibility of the coercive point varies linearly with the stress. By measuring the hysteresis loop of the silicon steel sheet, the stress of the silicon steel sheet can be calculated, which provides a linear calibration curve for stress detection. Different types, batches and manufacturers of silicon steel sheets will have different magnetostrictive characteristics, in other words, the slope of the calibration curve will also be different. However, in practical engineering applications, as long as the differential magnetic susceptibility of the coercive point is measured under zero stress and any two other stresses, the corresponding calibration curve can be drawn more accurately. This provides a convenient method for quantitative stress assessment of silicon steel sheet and a new idea for stress detection of other ferromagnetic materials.
Meng Xiaoge,Li Lin. A New Method for Quantitative Evaluation of Mechanical Stress of Oriented Electrical Steel Sheets Using the Differential Susceptibility at the Coercive Point[J]. Transactions of China Electrotechnical Society, 2023, 38(7): 1705-1712.
[1] 杨庆新, 李永建. 先进电工磁性材料特性与应用发展研究综述[J]. 电工技术学报, 2016, 31(20): 1-12. Yang Qingxin, Li Yongjian.Characteristics and developments of advanced magnetic materials in electrical engineering: a review[J]. Transactions of China Electrotechnical Society, 2016, 31(20): 1-12. [2] Singh D, Rasilo P, Martin F, et al.Effect of mechanical stress on excess loss of electrical steel sheets[J]. IEEE Transactions on Magnetics, 2015, 51(11): 1-4. [3] Kai Y, Tsuchida Y, Todaka T, et al.Influence of stress on vector magnetic property under alternating magnetic flux conditions[J]. IEEE Transactions on Magnetics, 2011, 47(10): 4344-4347. [4] Augustyniak B, Piotrowski L, Jasnoch P, et al.Impact of tensile and compressive stress on classical and acoustic barkhausen effects in grain-oriented electrical steel[J]. IEEE Transactions on Magnetics, 2014, 50(4): 1-4. [5] Anon.Measuring casting residual stress with X-ray diffraction[J].Modern Casting, 2005, 95(9): 48-49. [6] 李向东, 涂春磊, 伍昊, 等. 材料内应力的检测方法[J]. 理化检验(物理分册), 2020, 56(6): 15-20. Li Xiangdong, Tu Chunlei, Wu Hao, et al.Testing method for internal stress of materials[J]. Physical Testing and Chemical Analysis (Part A (Physical Testing)), 2020, 56(6): 15-20. [7] 张闯, 李雪霏, 刘素贞, 等. 单向载荷下铝板电磁超声兰姆波的波速响应特性[J]. 电工技术学报, 2021, 36(8): 1579-1586. Zhang Chuang, Li Xuefei, Liu Suzhen, et al.Wave velocity response characteristics of electromagnetic ultrasonic lamb wave of aluminum plate under unidirectional load[J]. Transactions of China Electrotechnical Society, 2021, 36(8): 1579-1586. [8] Yamazaki T, Furuya Y, Hata S, et al.Stress-driven magnetic barkhausen noise generation in FeCo magnetostrictive alloy[J]. IEEE Transactions on Magnetics, 2022, 58(1): 1-8. [9] Prabhu Gaunkar N.Magnetic hysteresis and barkhausen noise emission analysis of magnetic materials and composites[D]. Ames, IA, USA: Iowa State University, 2014. [10] Fagan P, Ducharne B, Daniel L, et al.Multiscale modelling of the magnetic Barkhausen noise energy cycles[J]. Journal of Magnetism and Magnetic Materials, 2021, 517: 167395. [11] Sablik M J, Jiles D C.Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis[J]. IEEE Transactions on Magnetics, 1993, 29(4): 2113-2123. [12] Jiles D C, Kiarie W.An integrated model of magnetic hysteresis, the magnetomechanical effect, and the barkhausen effect[J]. IEEE Transactions on Magnetics, 2021, 57(2): 1-11. [13] Jiles D C.Theory of the magnetomechanical effect[J]. Journal of Physics D: Applied Physics, 1995, 28(8): 1537-1546. [14] Sablik M J, Langman R A.Approach to the anhysteretic surface[J]. Journal of Applied Physics, 1996, 79(8): 6134-6136. [15] Sablik M J.A model for the Barkhausen noise power as a function of applied magnetic field and stress[J]. Journal of Applied Physics, 1993, 74(9): 5898-5900. [16] Garikepati P, Chang T T, Jiles D C.Theory of ferromagnetic hysteresis: evaluation of stress from hysteresis curves[J]. IEEE Transactions on Magnetics, 1988, 24(6): 2922-2924. [17] Mierczak L, Jiles D C, Fantoni G.A new method for evaluation of mechanical stress using the reciprocal amplitude of magnetic barkhausen noise[J]. IEEE Transactions on Magnetics, 2011, 47(2): 459-465. [18] Lo C C H, Lee S J, Li L, et al. Modeling stress effects on magnetic hysteresis and Barkhausen emission using a hysteretic-stochastic model[J]. IEEE Transactions on Magnetics, 2002, 38(5): 2418-2420. [19] Jiles D C.Dynamics of domain magnetization and the Barkhausen effect[J]. Czechoslovak Journal of Physics, 2000, 50(8): 893-924. [20] Jiles D C, Atherton D L.Theory of ferromagnetic hysteresis (invited)[J]. Journal of Applied Physics, 1984, 55(6): 2115-2120. [21] Zhu Lihua, Li Jingjing, Yang Qingxin, et al.An improved magnetostriction model for electrical steel sheet based on Jiles-Atherton model[J]. IEEE Transactions on Magnetics, 2020, 56(3): 1-4. [22] 祝丽花, 李晶晶, 朱建国. 服役条件下取向硅钢磁致伸缩模型的研究[J]. 电工技术学报, 2020, 35(19): 4131-4138. Zhu Lihua, Li Jingjing, Zhu Jianguo.Research on magnetostrictive model for oriented silicon steel under service conditions[J]. Transactions of China Electrotechnical Society, 2020, 35(19): 4131-4138. [23] Liu T, Kikuchi H, Ara K, et al.Magnetomechanical effect of low carbon steel studied by two kinds of magnetic minor hysteresis loops[J]. NDT & E International, 2006, 39(5): 408-413.
2023, Vol. 38 
