Finite Element Numerical Simulation and Experimental Verification of Frequency Characteristics of Wind-Induced Vibration of Catenary
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摘要:
接触网风致振动是多风地区铁路供电系统的典型灾害，现有振动特性理论分析与有限元软件难以准确模拟现场条件，导致其计算结果难以使用现场测量数据进行验证，不利于后续非线性模型计算精度提高，为此搭建了小比例接触网模型. 首先在MATLAB中编写集成了接触网大变形几何非线性与吊弦伸缩刚度非线性的有限元数值计算程序，求解小比例接触网模型在不同频率横向激励作用下的振型，其次搭建横向激励频率可调的试验平台，采用激光位移传感器测量各个频率水平气流作用下的振型，最后对比研究两种方法所得振动波形. 计算结果表明，在一定频率范围内，模型振动频率与横向激励频率相同，且横向激励频率等于模型基频时，其水平最大位移距离达到最大；不同频率横向激励作用下测量点运动轨迹不同，频率小于基频时运动轨迹多为“8”字形，大于基频时主要为扁椭圆形，等于基频时则几乎为水平直线. 对比试验结果可知：有限元数值计算方法可准确计算模型的基频和激励下的响应频率、振型以及振幅随频率的变化趋势，但其振幅计算值与试验结果存在显著偏差. 因此，对关键振幅值的计算与预测还需结合试验修正.
Abstract:Wind-induced vibration of catenary is a typical disaster of railway power supply systems in windy areas. It is difficult for existing theoretical analyses of vibration characteristics and finite element software to accurately simulate field conditions, which makes it difficult to verify their calculation results with field measurement data, and is not conducive to improving the calculation accuracy of subsequent nonlinear models. Therefore, a small-scale catenary model was built. Firstly, a finite element numerical calculation program integrating the large-deformation geometric nonlinearity of catenary and the stretching-contracting stiffness nonlinearity of suspension string was written in MATLAB, and the vibration modes of the small-scale catenary model under lateral excitations of different frequencies were solved. Secondly, an experimental platform with adjustable lateral excitation frequency was built, and the vibration modes under horizontal airflows at various frequencies were measured by a laser displacement sensor. Finally, the vibration waveforms obtained by the two methods were comparatively studied. The calculation results indicate that in a certain frequency range, the vibration frequency of the model is the same as the lateral excitation frequency, and when the lateral excitation frequency is equal to the fundamental frequency of the model, the maximum horizontal displacement distance reaches the maximum. Under the lateral excitations of different frequencies, the trajectories of the measuring point are different: When the frequency is less than the fundamental frequency, the trajectory is mostly 8-shaped; when the frequency is greater than the fundamental frequency, it is mainly a flat oval; when the frequency is equal to the fundamental frequency, it is almost a horizontal straight line. By comparing the test results, it is revealed that the finite element numerical calculation method can accurately calculate the fundamental frequency of the model, as well as the response frequency, vibration mode, and variation trend of amplitude with frequency under excitation. However, there is a significant deviation between the calculated amplitude values and the test results. Therefore, the calculation and prediction of key amplitude values need to be corrected by combining with experiments.
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Key words:
- catenary /
- wind-induced vibration /
- finite element analysis /
- experimental verification /
- frequency
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图 4 不同张力下测量点水平位移
Figure 4. Horizontal displacement of measuring point under different tensions
图 9 不同张力下试验测量点水平位移图
Figure 9. Diagram of horizontal displacement of experimental measurement points under different tensions
图 10 试验模型测量点水平位移时程曲线（6.0 Hz）
Figure 10. Time-history curve of horizontal displacement of measuring point in experimental model （6.0 Hz）
图 11 试验模型测量点水平位移时程曲线（9.5 Hz）
Figure 11. Time-history curve of horizontal displacement of measuring point in experimental model （9.5 Hz）
图 12 试验模型测量点水平位移时程曲线（13.0 Hz）
Figure 12. Time-history curve of horizontal displacement of measuring point in experimental model （13.0 Hz）
图 13 不同频率激励对应的最大振幅
Figure 13. Maximum amplitude corresponding to excitations of different frequencies
表 1 接触网主要参数
Table 1. Main parameters of catenary
结构 材质 杨氏模量/
Gpa质量密度/
kg•m−3张力/
kN接触线 CuMg 0.5 AC120 120 8900 27 承力索 BzII 120 120 8900 21 吊弦 Bz 10 120 8900 
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表 2 试验模型主要参数
Table 2. Main parameters of experimental model
结构 材料 杨氏模量/Gpa 质量密度/(kg•m−3) 张力/N 接触线 铜线 103 8516 8.3 承力索 铜线 103 8516 5.4 吊弦 铜线 103 8516
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表 3 模型承力索与接触线对应张力
Table 3. Corresponding tensions of carrier cable and contact line in model
参数 模型1 模型2 模型3 承力索张力/N 5.4 6.4 8.3 接触线张力/N 8.3 8.3 10.3
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[1] 刘志刚, 宋洋, 韩烨, 等. 高速铁路接触网研究进展[J]. 西南交通大学学报, 2016, 51(3): 495-518. doi: 10.11985/2025.04.030Liu Zhigang, Song Yang, Han Ye, et al. Advances of research on high-speed railway catenary[J]. Journal of Southwest Jiaotong University, 2016, 51(3): 495-518. doi: 10.11985/2025.04.030 [2] 陈果. 横风作用下的受电弓-覆冰接触网系统气动弹性问题研究[D]. 成都: 西南交通大学, 2018. [3] Stickland M T, Scanlon T J, Craighead I A, et al. An investigation into the mechanical damping characteristics of catenary contact wires and their effect on aerodynamic galloping instability[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2003, 217(2): 63-71. doi: 10.1243/095440903765762814 [4] Stickland M T, Scanlon T J. An investigation into the aerodynamic characteristics of catenary contact wires in a cross-wind[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2001, 215(4): 311-318. doi: 10.1243/0954409011531602 [5] Kim J W, Sohn J H. Galloping simulation of the power transmission line under the fluctuating wind[J]. International Journal of Precision Engineering and Manufacturing, 2018, 19(9): 1393-1398. doi: 10.1007/s12541-018-0164-2 [6] 谢强, 支希, 李海若, 等. 高速铁路接触网系统气动弹性模型风洞试验研究[J]. 中国铁道科学, 2015, 36(3): 73-80. doi: 10.3969/j.issn.1001-4632.2015.03.12Xie Qiang, Zhi Xi, Li Hairuo, et al. Wind tunnel test on aeroelastic model of catenary system for high speed railway[J]. China Railway Science, 2015, 36(3): 73-80. doi: 10.3969/j.issn.1001-4632.2015.03.12 [7] 李瑞平, 周宁, 吕青松, 等. 横风环境中弓网动力学性能分析[J]. 振动与冲击, 2014, 33(24): 39-44, 53. doi: 10.13465/j.cnki.jvs.2014.24.007Li Ruiping, Zhou Ning, Lü Qingsong, et al. Pantograph-catenary dynamic behavior under cross wind[J]. Journal of Vibration and Shock, 2014, 33(24): 39-44,53. doi: 10.13465/j.cnki.jvs.2014.24.007 [8] 宋洋, 刘志刚, 汪宏睿. 高速铁路覆冰接触线气动系数研究与风振响应分析[J]. 铁道学报, 2014, 36(9): 20-27.Song Yang, Liu Zhigang, Wang Hongrui. Study on aerodynamic parameters and wind vibration responses of iced contact wires of high-speed railways[J]. Journal of the China Railway Society, 2014, 36(9): 20-27. [9] 汪宏睿, 刘志刚, 宋洋, 等. 高速铁路接触线气动参数仿真及风振响应研究[J]. 振动与冲击, 2015, 34(6): 6-12.Wang Hongrui, Liu Zhigang, Song Yang, et al. Aerodynamic parameters simulation and wind-induced vibration responses of contact wire of high-speed railway[J]. Journal of Vibration and Shock, 2015, 34(6): 6-12. [10] 宋洋, 刘志刚, 鲁小兵, 等. 计及接触网空气动力的高速弓网动态受流特性研究[J]. 铁道学报, 2016, 38(3): 48-58. doi: 10.3969/j.issn.1001-8360.2016.03.007Song Yang, Liu Zhigang, Lu Xiaobing, et al. Study on characteristics of dynamic current collection of high-speed pantograph-catenary considering aerodynamics of catenary[J]. Journal of the China Railway Society, 2016, 38(3): 48-58. doi: 10.3969/j.issn.1001-8360.2016.03.007 [11] 宋洋, 刘志刚, 汪宏睿, 等. 随机风场下高速铁路接触线风振疲劳分析[J]. 铁道学报, 2015, 37(7): 20-26.Song Yang, Liu Zhigang, Wang Hongrui, et al. Analysis on influence of stochastic wind field on wind vibration fatigue of high-speed railway catenary[J]. Journal of the China Railway Society, 2015, 37(7): 20-26. [12] 赵珊鹏, 陈智涛, 张友鹏, 等. 大风区接触网线路参数对附加导线舞动的影响[J]. 哈尔滨工业大学学报, 2024, 56(5): 74-83.Zhao Shanpeng, Chen Zhitao, Zhang Youpeng, et al. Influence of overhead contact system line parameters on additional conductors galloping in strong wind region[J]. Journal of Harbin Institute of Technology, 2024, 56(5): 74-83. [13] 刘志刚, 宋洋, 刘煜铖. 电气化高速铁路接触网微风振动特性[J]. 西南交通大学学报, 2015, 50(1): 1-6. doi: 10.3969/j.issn.0258-2724.2015.01.001Liu Zhigang, Song Yang, Liu Yucheng. Aeolian vibration characteristics of electrified high-speed railway catenary[J]. Journal of Southwest Jiaotong University, 2015, 50(1): 1-6. doi: 10.3969/j.issn.0258-2724.2015.01.001 [14] 赵珊鹏, 张永丰, 张友鹏, 等. 兰新高铁大风区低风压正馈线受力特性[J]. 西南交通大学学报, 2023, 58(5): 1154-1161. doi: 10.3969/j.issn.0258-2724.20220437Zhao Shanpeng, Zhang Yongfeng, Zhang Youpeng, et al. Mechanical characteristics of low-wind-pressure catenary positive feeder in gale area of Lanzhou-urumuqi high-speed railway[J]. Journal of Southwest Jiaotong University, 2023, 58(5): 1154-1161. doi: 10.3969/j.issn.0258-2724.20220437 [15] 宋洋, 刘志刚, 汪宏睿, 等. 接触网三维模型的建立与风偏的非线性求解[J]. 铁道学报, 2015, 37(4): 30-38.Song Yang, Liu Zhigang, Wang Hongrui, et al. Establishment of 3D model for catenary and nonlinear solution for its wind deflection[J]. Journal of the China Railway Society, 2015, 37(4): 30-38. [16] Song Y, Liu Z G, Duan F C, et al. Study on wind-induced vibration behavior of railway catenary in spatial stochastic wind field based on nonlinear finite element procedure[J]. Journal of Vibration and Acoustics, 2018, 140: 011010. doi: 10.1115/1.4037521 [17] 储文平. 基于非线性有限元的高速铁路接触网风偏计算[J]. 机车电传动, 2023(4): 117-123.Chu Wenping. Estimation of wind deflection of high-speed railway catenary based on nonlinear finite element method[J]. Electric Drive for Locomotives, 2023(4): 117-123. [18] 施海健, 陈果, 杨翊仁, 等. 高速铁路覆冰接触网舞动行为研究[J]. 动力学与控制学报, 2022, 20(2): 50-61. doi: 10.6052/1672-6553-2021-059Shi Haijian, Chen Guo, Yang Yiren, et al. Study on the galloping behavior of the iced catenary of the high-speed railway[J]. Journal of Dynamics and Control, 2022, 20(2): 50-61. doi: 10.6052/1672-6553-2021-059 [19] 关金发, 吴积钦. 预弛度接触网静态形状解析计算[J]. 电气化铁道, 2013, 24(5): 10-14.Guan Jinfa, Wu Jiqin. Analytical calculation of static shape of pre-sag catenary[J]. Electric Railway, 2013, 24(5): 10-14. [20] 谢献忠, 张淳淇, 林文欣, 等. 输电线路共振舞动机理试验研究[J]. 工程力学, 2023, 40(10): 71-80. doi: 10.6052/j.issn.1000-4750.2022.01.0059Xie Xianzhong, Zhang Chunqi, Lin Wenxin, et al. Experimental study on resonance galloping mechanism of transmission line[J]. Engineering Mechanics, 2023, 40(10): 71-80. doi: 10.6052/j.issn.1000-4750.2022.01.0059 [21] 徐斌, 高跃飞, 余龙. MATLAB有限元结构动力学分析与工程应用[M]. 北京: 清华大学出版社, 2009: 1-24. [22] 吴磊, 徐梦楠, 张华鹏, 等. 电气化铁路接触网冲击振动除冰仿真分析[J]. 铁道学报, 2025, 47(1): 47-53. doi: 10.3969/j.issn.1001-8360.2025.01.006Wu Lei, Xu Mengnan, Zhang Huapeng, et al. Simulation analysis of impact vibration de⁃icing for overhead catenary of electrified railway[J]. Journal of the China Railway Society, 2025, 47(1): 47-53. doi: 10.3969/j.issn.1001-8360.2025.01.006 [23] 曾攀. 有限元基础教程[M]. 北京: 高等教育出版社, 2009: 12-91. [24] 陈龙, 刘志刚, 段甫川, 等. 刚性接触网-受电弓系统快速仿真方法[J]. 西南交通大学学报, 2025, 60(2): 434-444.Chen Long, Liu Zhigang, Duan Fuchuan, et al. Fast simulation method for pantograph and overhead conductor rail system[J]. Journal of Southwest Jiaotong University, 2025, 60(2): 434-444. [25] 罗群, 梅桂明, 赵晨, 等. 基于非线性理论的接触网找形方法研究[J]. 铁道学报, 2022, 44(7): 27-35.Luo Qun, Mei Guiming, Zhao Chen, et al. Research on form-finding of railway overhead based on nonlinear theory[J]. Journal of the China Railway Society, 2022, 44(7): 27-35. [26] 刘继冬, 梁茹楠, 陈交, 等. 接触网承力索集中荷载测量方法[J]. 西南交通大学学报, 2024, 59(3): 510-518. doi: 10.3969/j.issn.0258-2724.20211092Liu Jidong, Liang Runan, Chen Jiao, et al. Measurement method for concentrated load on catenary messenger wires[J]. Journal of Southwest Jiaotong University, 2024, 59(3): 510-518. doi: 10.3969/j.issn.0258-2724.20211092 [27] 周宁, 李瑞平, 张卫华. 基于负弛度法的接触网建模与仿真[J]. 交通运输工程学报, 2009, 9(4): 28-32.Zhou Ning, Li Ruiping, Zhang Weihua. Modeling and simulation of catenary based on negative sag method[J]. Journal of Traffic and Transportation Engineering, 2009, 9(4): 28-32. -
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