Simulation of Magnetic Hysteresis Characteristics of Electrical Steel Sheet under Mechanical Stress Based on Energetic Model
Chen Hao1, Li Lin1, Liu Yang2
1. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China; 2. State Key Laboratory of Advanced Power Transmission Technology State Grid Smart Grid Research Institute Co. Ltd Beijing 102209 China
Abstract：The electric steel sheets are widely used in the iron cores of electrical equipment such as transformers, motors, and reactors. However, in the actual processing and operation, the iron cores will be subjected to varying degrees of tensile or compressive stress, which will cause significant changes in the magnetic hysteresis characteristics of electrical steel sheets and affect the operating performance of the iron cores. Therefore, it is necessary to accurately simulate the magnetic hysteresis characteristics of electrical steel sheet under mechanical stress for the iron cores optimization design. At present, the simulation methods of magnetic hysteresis characteristics under mechanical stress are mainly divided into three categories: the method based on Preisach model, the method based on multiscale model and the method based on Jiles-Atherton (J-A) model. Among them, the method based on Preisach model is a pure mathematical method, and cannot explain the mechanism of mechanical stress on magnetization characteristics of magnetic materials. The method based on multiscale model has a clear physical basis, but it can only simulate the anhysteretic curve. The method based on J-A model need to solve a nonlinear differential equation, and the calculation process is relatively complex. Therefore, a novel method is needed to accurately simulate the magnetic hysteresis characteristics of electrical steel sheets under mechanical stress. Compared with the above models, Energetic hysteresis model has the advantages of simple expression and high calculation efficiency, and it can also consider the influence of mechanical stress on magnetic hysteresis characteristics. Therefore, this paper based on the original Energetic hysteresis model, the energy density caused by mechanical stress as an additional term is introduced into the total energy density of electrical steel sheets. Then according to the principle of energy balance, the field separation technology is used to realize the conversion of the energy density components to magnetic field components. Finally, considering the dependence of each parameter in Energetic model on mechanical stress, the principle of field superposition is used to establish a magnetic hysteresis model of electrical steel sheets under mechanical stress. Taking the grain-oriented silicon steel sheet as an example, the results show that under tensile and small compressive stress (less than-7.09 MPa), the overall accuracy of simulated results is high, and the root mean square error is less than 5 A/m, which proves the accuracy of the proposed method. When the compressive stress is large (-8.86 MPa and-10.63 MPa), the root mean square error becomes larger and is close to 10 A/m, but the overall fitting is acceptable. The reason why the error increases with the increase of compressive stress is that the magnetic domain structure changes significantly when the compressive stress increases. The decrease of experimental measurement accuracy is also one of the reasons for the large simulation error. Although the tensile stress and compressive stress are measured separately and the measurement is carried out incrementally from small stress to large stress in order to reduce the experimental errors, the measurement errors would gradually accumulate during the process of increasing compressive stress. The results also show that each parameter in the model is significantly dependent on the mechanical stress, and different parameters has different dependence on the mechanical stress, and the same parameter has different dependence on compression and tensile stress. Therefore, it is necessary to consider the stress dependence of model parameters to simulate the hysteresis characteristics of electrical steel sheet under mechanical stress. In order to further clarify the influence law of mechanical stress on magnetic hysteresis characteristics, the coercivity, loss density and remanence under the action of mechanical stress are analyzed by simulation and experiment. And the average relative errors are 3.93%, 3.12% and 7.81%, respectively.
陈昊, 李琳, 刘洋. 基于Energetic模型的机械应力作用下电工钢片磁滞特性模拟[J]. 电工技术学报, 2023, 38(12): 3101-3111.
Chen Hao, Li Lin, Liu Yang. Simulation of Magnetic Hysteresis Characteristics of Electrical Steel Sheet under Mechanical Stress Based on Energetic Model. Transactions of China Electrotechnical Society, 2023, 38(12): 3101-3111.
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2023, Vol. 38 
