English

运筹学学报 ›› 2020, Vol. 24 ›› Issue (2): 103-110.doi: 10.15960/j.cnki.issn.1007-6093.2020.02.008

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铁磁性设备补偿磁场的数学模型及其应用

丁玉洁1, 张杰2, 陆震2, 鲁习文1,*   

  1. 1. 华东理工大学理学院, 上海 200237;
    2. 中国船舶重工集团公司第七〇四研究所, 上海 200031
  • 收稿日期:2020-03-21 发布日期:2020-06-13
  • 通讯作者: 鲁习文 E-mail:xwlu@ecust.edu.cn
  • 基金资助:
    国家自然科学基金（Nos.11871213，71431004）

Mathematical model of compensating magnetic field for ferromagnetic equipment and its application

DING Yujie1, ZHANG Jie2, LU Zhen2, LU Xiwen1,*   

  1. 1. School of Science, East China University of Science and Technology, Shanghai 200237, China;
    2. No. 704 Institute of CSIC, Shanghai 200031, China
  • Received:2020-03-21 Published:2020-06-13

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摘要： 研究用永磁体对铁磁性设备进行磁场补偿的问题，建立了补偿磁场的数学模型.将设备划分成若干个小长方体后，基于磁矩量法建立了数学模型，并对补偿磁场进行拟合.在计算模型中的耦合系数矩阵时，用多个点的平均值作为耦合系数的有效值，提高了计算结果的可靠性和稳定性.并且，针对永磁体距离设备很近时，设备呈现出的非线性磁化特性，通过优化方法求解各个单元的等效磁化率，这种方法不需要知道铁磁材料的磁化曲线和设备结构，便于计算和实际应用.最后，通过实验设计与数值计算，得到了永磁体对设备进行补偿的磁场分布，模型计算结果与实际测量数据误差11%以内，这说明该模型能够满足工业要求，具有实际应用价值.

关键词: 设备磁场, 磁场补偿, 磁矩量法, 耦合系数矩阵, 等效磁化率

Abstract: In this paper, the problem of magnetic field compensation for ferromagnetic equipment with permanent magnets is studied, and a mathematical model of the compensation magnetic field is established. After dividing the device into several small cuboids, a mathematical model is established based on the magnetic moment method to simulate the compensation magnetic field. When calculating the coupling coefficient matrix in the model, we use the average of multiple points as the effective value of the coupling coefficient, which improves the reliability and stability of the calculation results. Moreover, for the nonlinear magnetization characteristics of the equipment when the permanent magnet is close to the equipment, the equivalent susceptibility of each unit is solved by optimization method. This method does not need to know the magnetization curve of the ferromagnetic material, which is convenient for calculation and practical application. Finally, through the experimental design and numerical calculation, the magnetic field distribution of the permanent magnet compensation device is obtained. The error between our model calculation result and the actual measurement data is within 11%, which shows that the model can satisfy the industrial requirements. Therefore, the models and calculation method have practical application value.

Key words: equipment magnetic field, magnetic field compensation, magnetic moment method, coupling coefficient matrix, equivalent magnetic susceptibility

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