Study on Electromagnetic Force Characteristics and Deformation Behavior of Plates Loaded via Eddy Current Attraction Effect
Liang Shuai1,2, Wang Yiyi1, Qiu Li1,2, Fang Chunhua1, Jiang Jinbo1
1. College of Electrical Engineering and New Energy China Three Gorges University Yichang 443002 China; 2. Hubei Provincial Key Laboratory for Operation and Control of Cascaded Hydropower Station Yichang 443002 China
Abstract：Conventional electromagnetic forming (EMF) of flat metal plates often yields highly nonuniform deformation and a small effective forming zone, as the unconstrained plate center tends to over-deform into a conical shape. To address this limitation, a sheet-forming approach based on the eddy-current attraction (ECA) effect is proposed. In this method, a solid conductor is placed coaxially inside the EMF drive coil, inducing eddy currents that generate an upward electromagnetic attraction on the plate. This upward force counteracts the excessive downward Lorentz force at the plate’s center, evening out the pressure distribution and suppressing the central “over-punch” deformation. A coupled electromagnetic-solid mechanics finite element model (implemented in COMSOL) is used to analyze the ECA-based loading scheme, enabling systematic variation of the conductor’s material properties and geometry. Simulation results show that a highly conductive insert (e.g. copper or aluminum) produces strong eddy currents and a large upward attraction force, dramatically reducing the net downward force at the plate center. This significantly lowers the peak axial deflection of the plate - in fact, with sufficiently high conductivity, the plate’s center experiences a slight inward collapse instead of bulging upward. In contrast, a less conductive insert (e.g. steel or titanium) yields a much weaker attraction, and the plate deforms in the usual bulging manner with greater central protrusion. These findings confirm that the conductor’s electrical conductivity (and thus the strength of induced eddy currents) strongly influences the deformation behavior. The geometry of the conductor insert is also crucial. Introducing a concave indentation on the conductor’s top face reduces the upward attraction; a deeper concavity further weakens the effect and allows more central bulging, which can improve uniformity by avoiding an overly flattened center. Conversely, giving the conductor a slight convex (bulged) top surface strengthens the attraction and flattens the plate center. Increasing the radial size of an indentation broadens the area of upward pull on the plate and raises the overall displacement, but provides only a limited additional improvement in deformation uniformity. Similarly, increasing the gap (distance) between the conductor and the plate mainly increases the total deformation achieved without significantly compromising deformation evenness. By appropriately tuning the conductor’s conductivity, shape and positioning, the electromagnetic force distribution can be controlled to obtain a much more uniform forming outcome. Overall, the ECA-based loading method greatly expands the uniformly deformed region of the plate. Under the same maximum axial displacement condition, the radial span over which the plate’s deflection stays within 95% of the peak value is about 79.5 mm with the ECA method, compared to only ~21.6 mm for the conventional method. This corresponds to roughly a 3.7-fold increase in the uniform deformation area. Consequently, the final plate shape is significantly flatter and more axisymmetric than that from a standard EMF process. Although the peak deformation is slightly lower due to the opposing attraction force, this trade-off yields a substantially larger area of uniform strain on the workpiece. In summary, inserting a coaxial conductor to harness the ECA effect provides a means to reshape the electromagnetic force field during plate forming. The proposed approach requires only the addition of a conductor inside the coil and can be readily adapted to different plate sizes. By significantly improving deformation uniformity and expanding the effective forming zone, this ECA-based method can enhance electromagnetic sheet forming for a wide range of applications.
梁帅, 王易弋, 邱立, 方春华, 江进波. 基于涡流吸引效应加载的板件电磁力特性及变形行为研究[J]. 电工技术学报, 2026, 41(19): 6449-6461.
Liang Shuai, Wang Yiyi, Qiu Li, Fang Chunhua, Jiang Jinbo. Study on Electromagnetic Force Characteristics and Deformation Behavior of Plates Loaded via Eddy Current Attraction Effect. Transactions of China Electrotechnical Society, 2026, 41(19): 6449-6461.
[1] Zhou Bo, Liu Bo, Zhang Shengen.The advancement of 7XXX series aluminum alloys for aircraft structures: a review[J]. Metals, 2021, 11(5): 718. [2] 邱立, 李彦涛, 苏攀, 等. 电磁成形中电磁技术问题研究进展[J]. 电工技术学报, 2019, 34(11): 2247-2259. Qiu Li, Li Yantao, Su Pan, et al.Research on electromagnetic problems in electromagnetic forming process[J]. Transactions of China Electrotechnical Society, 2019, 34(11): 2247-2259. [3] 邱立, 靳海若, 李梦瑶, 等. 基于同时加载的管-板电磁翻边能量利用率研究[J]. 塑性工程学报, 2025, 32(6): 33-45. Qiu Li, Jin Hairuo, Li Mengyao, et al.Study on energy efficiency of tube-plate electromagnetic flanging based on simultaneous loading[J]. Journal of Plasticity Engineering, 2025, 32(6): 33-45. [4] Psyk V, Risch D, Kinsey B L, et al.Electromagnetic forming: a review[J]. Journal of Materials Processing Technology, 2011, 211(5): 787-829. [5] 李亮. 我国多时空脉冲强磁场成形制造基础研究进展[J]. 中国基础科学, 2016, 18(4): 25-35. Li Liang.Progress of the basic research on the space-time-controlled multi-stage pulsed magnetic field forming and manufacturing technology[J]. China Basic Science, 2016, 18(4): 25-35. [6] 张锦荣, 邱立, 李梦瑶, 等. 基于T型线圈的双管件电磁翻边能量利用率研究[J]. 锻压技术, 2025, 50(2): 65-74. Zhang Jinrong, Qiu Li, Li Mengyao, et al.Research on energy utilization rate for dual tube fittings electromagnetic flanging based on T-coil[J]. Forging & Stamping Technology, 2025, 50(2): 65-74. [7] 邱立, 陈玉红, 张锦荣, 等. 基于离散屏蔽的管件电磁胀形电磁力分布与轴向均匀度研究[J]. 电工技术学报, 2025, 40(21): 6932-6944. Qiu Li, Chen Yuhong, Zhang Jinrong, et al.Research on electromagnetic force distribution and axial uniformity of tube electromagnetic bulging based on discrete shielding[J]. Transactions of China Electro-technical Society, 2025, 40(21): 6932-6944. [8] 熊奇, 路凯, 程辉, 等. 铝合金空心板件复合式电磁成形研究[J].电工技术学报, 2026, 41(6): 1828-1843. Xiong Qi, Lu Kai, Cheng Hui, et al.Research on composite electromagnetic forming of aluminum alloy hollow plate[J]. Transactions of China Electro-technical Society, 2026, 41(6): 1828-1843. [9] 徐巍, 赖智鹏, 李昌兴, 等. 局部脉冲强磁场驱动下的薄壁金属构件变形稳定性研究[J/OL]. 电工技术学报, 1-12[2026-05-18]. https://doi.org/10.19595/j.cnki.1000-6753.tces.251879. Xu Wei, Lai Zhipeng, Li Changxing, et al. Study on deformation stability of thin-walled metal components driven by local pulsed high magnetic field[J/OL]. Transactions of China Electrotechnical Society,1-12[2026-05-18]. https://doi.org/10.19595/j.cnki.1000-6753.tces.251879. [10] Zhang Zixuan, Lai Zhipeng, Li Changxing, et al.A novel actuator for precise design of the spatial-distributed Lorentz force in electromagnetic sheet metal forming: process principle, optimization methodology, and experimental validation[J]. The International Journal of Advanced Manufacturing Technology, 2024, 131(9): 4425-4445. [11] 唐天宇, 黄亮, 徐佳辉, 等. 跑道型线圈板料电磁成形磁场分布的调控[J]. 中国机械工程, 2024, 35(2): 337-346. Tang Tianyu, Huang Liang, Xu Jiahui, et al.Regulation for magnetic field distribution of sheet metal electromagnetic forming with track coil[J]. China Mechanical Engineering, 2024, 35(2): 337-346. [12] 程啸, 李瑞, 邹贵生, 等. 薄壁构件渐进式电磁成形技术研究进展[J]. 中国机械工程, 2024, 35(12): 2092-2105. Cheng Xiao, Li Rui, Zou Guisheng, et al.Research progresses on incremental EMF technology for thin-walled components[J]. China Mechanical Engineering, 2024, 35(12): 2092-2105. [13] 熊奇, 邱爽, 李彦昕, 等. 组合式电磁成形技术研究进展[J]. 电工技术学报, 2024, 39(9): 2710-2729. Xiong Qi, Qiu Shuang, Li Yanxin, et al.Research progress of combined electromagnetic forming technology[J]. Transactions of China Electrotechnical Society, 2024, 39(9): 2710-2729. [14] Kamal M, Daehn G S.A uniform pressure electromagnetic actuator for forming flat sheets[J]. Journal of Manufacturing Science and Engineering, 2007, 129(2): 369-379. [15] Golowin S, Kamal M, Shang Jianhui, et al.Application of a uniform pressure actuator for electromagnetic processing of sheet metal[J]. Journal of Materials Engineering and Performance, 2007, 16(4): 455-460. [16] 尹朋磊, 邱立, 李玉田, 等. 基于双向电磁力加载的板件电磁胀形均匀性研究[J]. 塑性工程学报, 2024, 31(3): 33-40. Yin Penglei, Qiu Li, Li Yutian, et al.Study on uniformity of sheet electromagnetic bulging based on bidirectional electromagnetic force loading[J]. Journal of Plasticity Engineering, 2024, 31(3): 33-40. [17] Ouyang Shaowei, Wang Chen, Li Changxing, et al.Improving the uniformity and controllability of tube deformation via a three-coil forming system[J]. The International Journal of Advanced Manufacturing Technology, 2021, 114(5): 1533-1544. [18] Lai Zhipeng, Cao Quanliang, Han Xiaotao, et al.Investigation on plastic deformation behavior of sheet workpiece during radial Lorentz force augmented deep drawing process[J]. Journal of Materials Processing Technology, 2017, 245: 193-206. [19] Qiu Li, Wang Chenglin, Abu-Siada A, et al.Study of a topology for plate electromagnetic forming based on inner reverse and outer positive double coil loading[J]. IEEE Access, 2020, 8: 196920-196930. [20] Qiu Li, Wu Weiye, Abu-Siada A, et al.Simulation analysis of the electromagnetic force distribution and formability parameters for sheet metal electromagnetic bulging using a new magnetic field shaper[J]. IEEE Access, 2021, 9: 70014-70023. [21] Huang Yifan, Wu Zelin, Dong Pengxin, et al.Investigation of electromagnetic punching process with adjustable collision velocity for ultra-thin titanium sheet[J]. Archives of Civil and Mechanical Engineering, 2023, 23(4): 263. [22] Wu Zelin, Cao Quanliang, Fu Junyu, et al.An inner-field uniform pressure actuator with high performance and its application to titanium bipolar plate forming[J]. International Journal of Machine Tools and Manufacture, 2020, 155: 103570. [23] 张望, 朱鑫辉, 邱立, 等. 基于铜环驱动的TA2钛板电磁成形数值模拟与实验研究[J]. 电工技术学报, 2025, 40(11): 3339-3348. Zhang Wang, Zhu Xinhui, Qiu Li, et al.Numerical and experimental study of electromagnetic drive forming for TA2 titanium sheet based on a copper ring[J]. Transactions of China Electrotechnical Society, 2025, 40(11): 3339-3348. [24] 谢冰鑫, 黄亮, 黄攀, 等. 铝合金板料电磁翻边全流程工艺研究[J]. 中国机械工程, 2021, 32(2): 220-226. Xie Bingxin, Huang Liang, Huang Pan, et al.Research on whole process route of electromagnetic flanging of aluminum alloy sheets[J]. China Mechanical Engineering, 2021, 32(2): 220-226. [25] 严思梁, 胡磊, 张晓丽, 等. 电磁成形中材料本构模型研究进展[J]. 塑性工程学报, 2023, 30(6): 10-21. Yan Siliang, Hu Lei, Zhang Xiaoli, et al.Investigation progress of material constitutive model for electromagnetic forming[J]. Journal of Plasticity Engineering, 2023, 30(6): 10-21. [26] 李梦瑶, 邱立, 易宁轩, 等. 基于驱动导体环的板件电磁成形电磁力分布与成形效果研究[J]. 电工技术学报, 2025, 40(1): 13-24. Li Mengyao, Qiu Li, Yi Ningxuan, et al.Study on electromagnetic force distribution and forming effect of plate electromagnetic forming based on driving conductor ring[J]. Transactions of China Electro-technical Society, 2025, 40(1): 13-24.
2026, Vol. 41 
