Establishment of Dynamic Equivalent Magnetic Network Model and Multi-Field Coupling Calculation Method for Magnetic Lift CRDM
Yang Yun1, Xu Qiwei1, Miao Yiru1, Yu Tianda1,2, Chen Xinan2
1. State Key Laboratory of Power Transmission Equipment Technology Chongqing University Chongqing 400044 China; 2. Science and Technology on Reactor System Design Technology Laboratory Nuclear Power Institute of China Chengdu 610213 China
Abstract：The magnetic lift control rod drive mechanism (CRDM) is a critical electromagnetic actuator for regulating nuclear reaction rates. Its dynamic process is complex to predict due to the cross-coupling among current response, magnetic circuit saturation, and motion state. The latest equivalent magnetic network (EMN) model exhibits inaccuracies and relies on flux distribution during modeling, lacking generality. In multi-field coupling analysis, researchers often employ multi-software collaborative or semi-simulation methods, which incur significant time and hardware costs. This paper proposes a dynamic equivalent magnetic network (DEMN) model and a multi-physics field coupling calculation method considering transient current changes and saturation. Firstly, the structure of the magnetic lift CRDM is introduced, and its lift solenoid valve is selected to analyze the electromagnetism-mechanics coupling during dynamic processes. Then, the mechanism is partitioned using orthogonal grid lines, and mesh units of multiple media are consolidated into a single medium to unify the reluctance calculation formula. During dynamic changes, only the grid size or position in the motion region is altered, thereby eliminating redundant modeling and reducing computational errors caused by mesh discrepancies. A connection relationship and calculation method for branch reluctance are established to address the misalignment between fixed and moving mesh units, facilitating continuous armature movement. A multi-physics field coupling calculation method is proposed by combining circuit models and kinematic formulas, which consider transient current changes and saturation. Finally, Compared with 3D finite element analysis (FEA) and experiments, the DEMN model and the proposed multi-field coupling calculation method are verified. 3D FEA results show that the magnetic density distribution, inductance, and electromagnetic force are highly consistent with the DEMN results, where the maximum error of inductance is 5.7%, and the maximum error of electromagnetic force is 3.4%. The experiments show that linear and saturated inductance variations are similar. The calculation accuracy of the release and suction currents under various loads exceeds 91%. Additionally, the dynamic results closely align with experimental results, with motion time calculation errors at 28 A and 40 A currents of 0.99% and 2.99%, respectively. The conclusion is as follows. (1) By using orthogonal grid lines, the unified calculation of reluctance is achieved, accelerating the modeling speed. (2) By changing the grid size or position of local areas, the dynamic changes of the EMN model are achieved, avoiding the problem of repeated modeling in the multi-field coupling calculation process and reducing the calculation errors caused by differences in mesh partitioning. (3) Compared with FEA, the proposed DEMN model requires less computational resources and shorter computation time while ensuring accuracy. Compared with the experimental results, the effectiveness and accuracy of the DEMN model and multi-field coupling calculation method are verified. It can be extended to EMN modeling, performance analysis, and rapid optimization design of the entire CRDM.
杨云, 徐奇伟, 苗轶如, 于天达, 陈西南. 磁力提升型CRDM的动态等效磁网络模型建立与多场耦合计算方法[J]. 电工技术学报, 2025, 40(10): 3030-3043.
Yang Yun, Xu Qiwei, Miao Yiru, Yu Tianda, Chen Xinan. Establishment of Dynamic Equivalent Magnetic Network Model and Multi-Field Coupling Calculation Method for Magnetic Lift CRDM. Transactions of China Electrotechnical Society, 2025, 40(10): 3030-3043.
[1] Chen Ronghua, Su G H, Zhang Kui.Analysis on the high-quality development of nuclear energy under the goal of peaking carbon emissions and achieving carbon neutrality[J]. Carbon Neutrality, 2022, 1(1): 33. [2] 吴宜灿, 李静云, 李研, 等. 中国核安全监管体制现状与发展建议[J]. 中国科学: 技术科学, 2020, 50(8): 1009-1018. Wu Yican, Li Jingyun, Li Yan, et al.Investigation and proposals for China’s nuclear safety regulations[J]. Scientia Sinica (Technologica), 2020, 50(8): 1009-1018. [3] Yu Tianda, Wu Hao, Chen Xinan, et al.Degradation- based reliability analysis of magnetic jack type control rod drive mechanism[J]. Quality and Reliability Engineering International, 2023, 39(8): 3369-3384. [4] Yang Yun, Xu Qiwei, Chen Yangming, et al.A fast nonlinear equivalent magnetic network model for magnetic jack type control rod drive mechanism in reactor[J]. Progress in Nuclear Energy, 2024, 169: 105058. [5] Oluwasegun A, Jung J C.The application of machine learning for the prognostics and health management of control element drive system[J]. Nuclear Engin- eering and Technology, 2020, 52(10): 2262-2273. [6] 许艳涛, 祖洪彪. 控制棒驱动机构步跃动作运动分析[J]. 核技术, 2013, 36(4): 347-351. Xu Yantao, Zu Hongbiao.Stepping movement analysis of control rod drive mechanism[J]. Nuclear Techniques, 2013, 36(4): 347-351. [7] 杨云, 于天达, 陈杨明, 等. 控制棒驱动机构磁路饱和特性分析[J]. 核动力工程, 2023, 44(3): 138-143. Yang Yun, Yu Tianda, Chen Yangming, et al.Analysis of magnetic saturation characteristics of control rod drive mechanism[J]. Nuclear Power Engineering, 2023, 44(3): 138-143. [8] 朱齐荣, 朱京昌. 控制棒驱动机构的电磁设计计算[J]. 核动力工程, 1991, 12(3): 35-40. Zhu Qirong, Zhu Jingchang.Electromagnetic design calculation of the control rod drive mechanism[J]. Nuclear Power Engineering, 1991, 12(3): 35-40. [9] Park B J, Pham P T, Hong K S.Model reference robust adaptive control of control element drive mechanism in a nuclear power plant[J]. International Journal of Control, Automation and Systems, 2020, 18(7): 1651-1661. [10] Yang Yun, Xu Qiwei, Chen Yangming, et al.An improved calculational model for inductance of CRDM based on equivalent magnetic circuit[J]. IEEE Transactions on Nuclear Science, 2022, 69(11): 2205-2213. [11] 佟文明, 姚颖聪, 李世奇, 等. 考虑磁桥不均匀饱和的内置式永磁同步电机等效磁网络模型[J]. 电工技术学报, 2022, 37(12): 2961-2970. Tong Wenming, Yao Yingcong, Li Shiqi, et al.Equivalent magnetic network model for interior permanent magnet machines considering non-uniform saturation of magnetic bridges[J]. Transactions of China Electrotechnical Society, 2022, 37(12): 2961-2970. [12] 佟文明, 王萍, 吴胜男, 等. 基于三维等效磁网络模型的混合励磁同步电机电磁特性分析[J]. 电工技术学报, 2023, 38(3): 692-702. Tong Wenming, Wang Ping, Wu Shengnan, et al.Electromagnetic performance analysis of a hybrid excitation synchronous machine based on 3D equi- valent magnetic network[J]. Transactions of China Electrotechnical Society, 2023, 38(3): 692-702. [13] 夏云彦, 周洲, 邵远亮, 等. 基于动态磁网络法大型感应电机阻抗参数及起动特性计算[J]. 电工技术学报, 2024, 39(14): 4341-4352. Xia Yunyan, Zhou Zhou, Shao Yuanliang, et al.Calculation of impedance parameters and starting characteristics of large induction motor based on dynamic magnetic network[J]. Transactions of China Electrotechnical Society, 2024, 39(14): 4341-4352. [14] 沈小要. 控制棒驱动机构的分段非线性动态特性[J]. 中国工程机械学报, 2011, 9(4): 410-415. Shen Xiaoyao.Study on segmental nonlinear dynamic properties for control rod drive mechanism[J]. Chinese Journal of Construction Machinery, 2011, 9(4): 410-415. [15] Ling Sitong, Li Wenqiang, Li Chuanxiao, et al.Flow field fusion simulation method based on model features and its application in CRDM[J]. Nuclear Science and Techniques, 2022, 33(3): 32. [16] 邓强, 陈西南, 刘佳, 等. 磁力提升型控制棒驱动机构提升动作过程动力学分析[J]. 机械设计与制造工程, 2017, 46(4): 106-110. Deng Qiang, Chen Xinan, Liu Jia, et al.Dynamic analysis of the lifting process for the magnetic lifting CRDM[J]. Machine Design and Manufacturing Engineering, 2017, 46(4): 106-110. [17] 邓强, 彭航, 谢细明, 等. 基于多学科协同仿真的控制棒驱动机构动力学分析研究[J]. 核动力工程, 2019, 40(增刊2): 78-81. Deng Qiang, Peng Hang, Xie Ximing, et al.Dynamic analysis and study for CRDM based on multi- disciplinary cooperative simulation[J]. Nuclear Power Engineering, 2019, 40(S2): 78-81. [18] 魏乔苑, 张飞, 吴和北, 等. 控制棒驱动机构运动过程的联合数值仿真研究[J]. 核动力工程, 2018, 39(5): 137-141. Wei Qiaoyuan, Zhang Fei, Wu Hebei, et al.Study on united numerical simulation for stepping motion of control rod drive mechanism[J]. Nuclear Power Engineering, 2018, 39(5): 137-141. [19] Sun Hongbiao, Li Wenqiang, Yu Tianda, et al.Research on associated motion simulation method and platform of control rod driving mechanism[J]. Advances in Mechanical Engineering, 2021, 13(9): 1-16. [20] Sun Hongbiao, Li Wenqiang, Zheng Lanjiang, et al.Adaptive co-simulation method and platform appli- cation of drive mechanism based on fruit fly optimization algorithm[J]. Progress in Nuclear Energy, 2022, 153: 104397. [21] 赵靖英, 李宁, 张雪辉, 等. 多簧片结构的磁保持继电器多物理场刚柔耦合仿真模型建立和实验分析[J]. 电工技术学报, 2024, 39(10): 3192-3205. Zhao Jingying, Li Ning, Zhang Xuehui, et al.Establishment and experimental analysis of rigid flexible coupling simulation model for multiphysics of magnetic latching relay with multi-reed structure[J]. Transactions of China Electrotechnical Society, 2024, 39(10): 3192-3205. [22] 张知竹, 刘志明, 李海博, 等. 磁力提升型控制棒驱动机构电磁场仿真分析[J]. 机械设计与制造工程, 2019, 48(12): 33-37. Zhang Zhizhu, Liu Zhiming, Li Haibo, et al.The simulation of electromagnetic lifting control rod drive mechanism[J]. Machine Design and Manufacturing Engineering, 2019, 48(12): 33-37. [23] 朱旭光, 刘正蒙, 刘国海, 等. 基于混合介质网格的表贴式永磁游标电机通用等效磁网络模型[J]. 中国电机工程学报, 2024, 44(5): 2009-2019. Zhu Xuguang, Liu Zhengmeng, Liu Guohai, et al.General equivalent magnetic network model of surface permanent magnet vernier machine based on hybrid medium mesh[J]. Proceedings of the CSEE, 2024, 44(5): 2009-2019. [24] Cao Donghui, Zhao Wenxiang, Ji Jinghua, et al.A generalized equivalent magnetic network modeling method for vehicular dual-permanent-magnet vernier machines[J]. IEEE Transactions on Energy Con- version, 2019, 34(4): 1950-1962. [25] Ghods M, Gorginpour H, Bazrafshan M A, et al.Equivalent magnetic network modeling of dual- winding outer-rotor vernier permanent magnet machine considering pentagonal meshing in the air-gap[J]. IEEE Transactions on Industrial Elec- tronics, 2022, 69(12): 12587-12599. [26] Liu Guohai, Jiang Shan, Zhao Wenxiang, et al.Modular reluctance network simulation of a linear permanent-magnet vernier machine using new mesh generation methods[J]. IEEE Transactions on Indu- strial Electronics, 2017, 64(7): 5323-5332. [27] 鲍光海, 王金鹏, 王毅龙. 磁保持继电器多物理场耦合模型设计与触头弹跳影响因素分析[J]. 电工技术学报, 2023, 38(3): 828-840. Bao Guanghai, Wang Jinpeng, Wang Yilong.Design of multi-physical field coupling model of magnetic- latching relay and analysis of influencing factors of contact bounce[J]. Transactions of China Electro- technical Society, 2023, 38(3): 828-840. [28] Hurley W G, Wolfle W H.应用于电力电子技术的变压器和电感: 理论、设计与应用[M]. 朱春波, 徐德鸿, 张龙龙, 译. 北京: 机械工业出版社, 2014.
2025, Vol. 40 
