运动磁体感应电场特性分析

doi:10.12382/bgxb.2024.0577

摘要/Abstract

摘要：

为分析运动磁性物体产生的感应电场,改进现有模型的不足,提出一种更适用于任意方向运动的目标感应电场计算模型。对比现有运动磁体感应电场模型的适用范围及局限性,以磁偶极子的矢量磁位模型为理论基础,推导出运动磁体感应电场的数学模型。通过理论分析和仿真计算验证该模型的适用性,并结合实船磁场特性进行实例计算。理论分析和仿真计算结果表明,该模型适用于沿任意方向运动的磁性物体感应电场计算,且其推导和计算过程较基于库伦定律和毕奥-萨伐定律的传统模型更为简洁。实例计算结果表明,磁性船舶运动产生的感应电场具有明显的区域特性,电场强度量级可达mV/m,是船舶静电场的重要组成部分。新提出的感应电场模型为运动磁性物体的电场探测提供了更准确的理论支持,可有效应用于船舶电场的探测与分析。

关键词: 运动磁性物体, 磁偶极子, 感应电场, 矢量磁位, 船舶, 静电场

Abstract:

To analyze the induced electric fields generated by moving magnetic objects and address the limitations of existing models, this paper proposes a novel model that is more suitable for calculating the induced electric fields by the objects moving in any direction. The applicabilities and limitations of current models for induced electric fields from moving magnetic objects are evaluated. On the basis of evaluation, a mathematical model for the induced electric fields from moving magnetic objects is derived by using a vector potential model of magnetic dipole as the theoretical foundation. The proposed model is verified through theoretical analysis and simulating calculations. And it is further demonstrated through the case studies involving the magnetic field characteristics of actual ships. The results show that the proposed model is suitable for calculating the electric fields induced by the magnetic objects moving in any direction and is more concise in derivation and calculation compared to the traditional models based on Coulomb’s law and the Biot-Savart law. Case study results indicate that the induced electric fields generated by the motion of magnetic ships have distinct regional characteristics, with the electric field strength reaching mV/m level, which constitutes a significant component of the ship’s static electric field. The induced electric field model proposed in this study provides a more accurate theoretical basis for the detection of electric fields from moving magnetic objects and can be effectively applied to the detection and analysis of ship electric fields.

Key words: moving magnetic object, magnetic dipole, induced electric field, magnetic vector potential, ship, static electric field

中图分类号:

TM151

刘瑞杰, 张伽伟, 谢涛涛. 运动磁体感应电场特性分析[J]. 兵工学报, 2025, 46(5): 240577-.

LIU Ruijie, ZHANG Jiawei, XIE Taotao. Characteristic Analysis of Electric Field Induced by Moving Magnetic Object[J]. Acta Armamentarii, 2025, 46(5): 240577-.

图/表 7

图1 矢量磁位法求得的感应电场三分量

Fig.1 Three components of induced electric field obtained by vector magnetic potential method

图2 矢量磁位法求得的感应电场三分量

Fig.2 Three components of induced electric field obtained by vector magnetic potential method

图3 条形磁铁

Fig.3 Bar magnet

图4 磁矩测量

Fig.4 Magnetic moment measurement

图5 实测值与理论值对比

Fig.5 Comparison among measured values and theoretical values

表1 实船磁偶极子阵列磁矩大小及坐标

Table 1 Magnetic moment size and coordinates of real ship magnetic dipole array

航次编号	坐标/m			磁矩/(A·m²)
航次编号	x	y	z	M_x	M_y	M_z
1	47.22	0	0	-317393.95	-133312	852000.18
2	41.67	0	0	-610181.75	0	-360485.9
3	36.11	0	0	452385.193	-123292	0
4	30.56	0	0	-158650.42	0	457812.38
5	25	0	0	-177443.44	-37373.6	-54462.82
6	8.33	0	0	77508.4573	0	0
7	-8.33	0	0	43233.6445	0	0
8	-13.89	0	0	0	61726.65	0
9	-25	0	0	219284.476	0	0
10	-30.56	0	0	-79797.901	0	-95773.87
11	-36.11	0	0	234504.464	-149759	-128524.8
12	-41.67	0	0	0	111095.7	436032.82
13	-47.22	0	0	-568070.15	-106073	-117531.2
14	0	0	0	-11469727	-1427045	2792398.9

图6 磁性船舶运动感应电场空间分布

Fig.6 Spatial distribution of induced electric field in magnetic ship motion

参考文献 22

[1]	SCHAEFER D, THIEL C, DOOSE J. Above water electric potential signatures of submerged naval vessels[J]. Journal of Marine Science and Engineering, 2019, 7(2):1-12.
[2]	李松, 石敏, 栾经德, 等. 舰船轴频电场信号特征提取与检测方法[J]. 兵工学报, 2015, 36(增刊2):220-224.
	LI S, SHI M, LUAN J D, et al. The feature extraction and detection for shaft-rate electric field of a ship[J]. Acta Armamentarii, 2015, 36(S2):220-224. (in Chinese)
[3]	程锐, 姜润翔, 龚沈光, 等. 基于EMD和4阶累积量的船舶轴频电场线谱提取[J]. 舰船科学技术, 2016, 38(1):94-98.
	CHENG R, JIANG R X, GONG S G, et al. Extraction of line spectrum of the ship shaft-rate electric field based on EMD and fourth-order cumulant[J]. Ship Science and Technology, 2016, 38(1):94-98. (in Chinese)
[4]	程锐, 陈聪, 张伽伟. 基于EEMD和改进功率谱熵的船舶轴频电场检测[J]. 华中科技大学学报(自然科学版), 2017, 45(5):11-16.
	CHENG R, CHEN C, ZHANG J W. Detection of ship shaft-rate electric field based on EEMD and modified power spectral entropy[J]. Journal of Huazhong University of Science and Technology(Natural Science Edition), 2017, 45(5):11-16. (in Chinese)
[5]	张伽伟, 喻鹏, 姜润翔, 等. 基于舰船电场的目标跟踪方法研究[J]. 兵工学报, 2020, 41(3):559-566. doi: 10.3969/j.issn.1000-1093.2020.03.017
	ZHANG J W, YU P, JIANG R X, et al. Research on target tracking method based on ship electric field[J]. Acta Armamentarii, 2020, 41(3):559-566. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.03.017
[6]	姜润翔, 龚沈光. 基于AR模型参数的船舶轴频电场实时检测方法[J]. 哈尔滨工程大学学报, 2013, 34(8):952-956.
	JIANG R X, GONG S G. Vessel’s shaft-related electric field signal detection based on the AR model parameter[J]. Journal of Harbin Engineering University, 2013, 34(8):952-956. (in Chinese)
[7]	张伽伟, 姜润翔, 肖大为, 等. 基于静态电位差的船舶跟踪算法[J]. 哈尔滨工程大学学报, 2020, 41(6):812-816.
	ZHANG J W, JIANG R X, XIAO D W, et al. Ship tracking based on the difference of electric potential[J]. Journal of Harbin Engineering University, 2020, 41(6):812-816. (in Chinese)
[8]	陈聪, 蒋治国, 姚陆锋, 等. 浅海中潜艇腐蚀相关静态电磁信号特征[J]. 海军工程大学学报, 2014, 26(3):1-6.
	CHEN C, JIANG Z G, YAO L F, et al. Characteristics analysis of corrosion-related static electromagnetic produce by a submarine in shallow sea[J]. Journal of Naval University of Engineering, 2014, 26(3):1-6. (in Chinese)
[9]	WANG X J, WANG S C, HU Y P, et al. Mixed electric field of multi-shaft ship based on oxygen mass transfer process under turbulent conditions[J]. Electronics, 2022, 11(22):3684.
[10]	SUN J Z, JIANG H L, XIA Z S, et al. Real-time suppression technology research on shaft-rate electric field[J]. Applied Mechanics and Materials, 2014, 602-605: 2649-2653.
[11]	JIANG H L, ZHANG H P, XIA Z S, et al. Research on the ship electrical properties of shaft-rate electric field[J]. Applied Mechanics and Materials, 2014, 563:333-337.
[12]	ZHANG H P, CHENG X G, AO C Y, et al. Experimental verification of the suppression effect of ship shaft-rate electric field[J]. Applied Mechanics and Materials, 2014, 3025(527): 172-175.
[13]	张伽伟, 熊露, 龚沈光. 金属体在海水中运动产生的感应电场建模[J]. 国防科技大学学报, 2013, 35(6):147-151.
	ZHANG J W, XIONG L, GONG S G. Modeling of the electric field generated by metal body moving under seawater[J]. Jorunal of National University of Defence Technology, 2013, 35(6):147-151. (in Chinese)
[14]	张伽伟, 龚沈光, 姜润翔, 等. 旋转磁偶极子产生的感应电场研究[J]. 兵工学报, 2014, 35(2):285-288. doi: 10.3969/j.issn.1000-1093.2014.02.023
	ZHANG J W, GONG S G, JIANG R X, et al. Study of electric field induced by rotating magnetic dipole[J]. Acta Armamentarii, 2014, 35(2):285-288. (in Chinese)
[15]	陈聪, 李定国. 运动磁偶极子感应电场的理论和实验研究[J]. 华中科技大学学报(自然科学版), 2010, 38(10):116-118.
	CHEN C, LI D G. The experimental and theoretical research on the induce electric field by moving magnetic dipole[J]. Journal of Huazhong University of Science and Technology(Natural Science Edition), 2010, 38(10):116-118. (in Chinese)
[16]	YAAKOBI O, ZILMAN G. Detection of the electromagnetic field induced by the wake of a ship moving in a moderate sea state of finite depth[J]. Journal of Engineering Mathematics, 2010, 70:17-27.
[17]	林春生, 龚沈光. 舰船物理场[M]. 北京: 兵器工业出版社,2007:233-249.
	LIN C S, GONG S G. Ship physics field[M]. Beijing: Publishing House of Ordnance Industry, 2007:233-249. (in Chinese)
[18]	SUN Q, JIANG R X, YU P. Inversion of the equivalent electric dipole moment of ship’s corrosion-related static electric field in frequency domain[J]. Mathematical Problems in Engineering, 2020(9):1-6.
[19]	WOLOSZYN M, TARNAWSKI J. Minimization of a ship’s magnetic signature under external field conditions using a multi-dipole model[J]. Scientific Reports, 2024, 14(1): 7864.
[20]	LU B J, ZHANG X B. An improved composite ship magnetic field model with ellipsoid and magnetic dipole arrays[J]. Scientific Reports, 2024, 14(1):4070. doi: 10.1038/s41598-024-54848-6 pmid: 38374350
[21]	GIWOO J, CHANG S Y, HYUM J C, et al. Magnetic dipole modeling combined with material sensitivity analysis for solving an inverse problem of thin ferromagnetic sheet[J]. IEEE Transactions on Magnetics, 2009, 45(10): 4169-4172.
[22]	张伽伟, 熊露, 龚沈光. 运动船舶磁性船体产生的感应电场[J]. 国防科技大学学报, 2015, 37(2):86-91.
	ZHANG J W, XIONG L, GONG S G. Electric field induced by magnetic hull of moving ship[J]. Jorunal of National University of Defence Technology, 2015, 37(2):86-91.