Cusp Catastrophe Theory of Train Derailment Early Warning
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摘要: 为了能更好的预测车辆的运行安全性, 现基于突变理论讨论了列车在曲线处由稳定运行到完全脱轨的状态突变过程。考虑车轮抬升量和轮轨横向力对列车运行状态的影响, 建立了尖点突变模型, 通过分叉集给出了列车在曲线处发生脱轨的危险区域。应用SIMPACK软件建立车辆系统仿真模型, 通过改变曲线半径的大小, 分析车轮抬升量和轮轨横向力随时间的变化情况。将不同工况下获得的控制变量的值与尖点突变理论的分叉集进行对比分析, 结果表明, 曲线半径过小时, 车轮抬升量和轮轨横向力均会超出极限值, 此时, 列车就会脱离轨道。由此验证了突变理论模型在列车脱轨预警上应用的有效性。Abstract: In order to better predict the train operation safety, the sudden transition process of the train from stable operation to complete derailment at the curve is discussed based on the catastrophe theory. Considering the influence of wheel raise and wheel-rail lateral force on the train operation, a cusp catastrophe model is established, and the dangerous area of train derailment at the curve are given by the bifurcation set of the cusp catastrophe theory. By applying the SIMPACK software to establish a train system simulation model and by transforming the radius of the curve, the changes of wheel raise and wheel-rail lateral force with time are analyzed. The values of control variables obtained under different working conditions are compared with the bifurcation set. The results show that when the curve radius is too small, the wheel raise and wheel-rail lateral force may exceed the limit value, and then the train will be off track, thus verifying that the catastrophe theory is effective for train derailment early warning.
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Key words:
- cusp catastrophe theory /
- train derailment /
- wheel raise /
- wheel-rail lateral force /
- bifurcation set
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表 1 C64k型敞车的技术
参数名称 数值 参数名称 数值 自重 22.5 t 商业运行速度 120 km/h 载重 61 t 通过最小曲线半径 145 m 轴重 21 t 车辆定距 8 700 mm 轨距 1 435 mm 车轮踏面 磨耗型车轮踏面 表 2 线路条件的设置
工况种类 曲线半径/m 直线 缓和曲线 圆曲线 外轨超高/m 工况1 165 100 200 300 0.09 工况2 166 100 200 300 0.09 工况3 500 100 200 300 0.09 工况4 600 100 200 300 0.09 工况5 1200 100 200 300 0.09 -
[1] 王健, 王平, 马道林, 等. 准静态下轮对脱轨安全限值研究[J]. 铁道学报, 2019, 41(8): 123-130 doi: 10.3969/j.issn.1001-8360.2019.08.016WANG J, WANG P, MA D L, et al. Study on safety limit of wheelset derailment under quasi-static condition[J]. Journal of the China Railway Society, 2019, 41(8): 123-130 (in Chinese) doi: 10.3969/j.issn.1001-8360.2019.08.016 [2] 张茉颜, 肖宏, 赵越. 小半径曲线地段车轮多边形对地铁安全性影响[J]. 中国安全科学学报, 2019, 29(S1): 27-31 https://www.cnki.com.cn/Article/CJFDTOTAL-ZAQK2019S1007.htmZHANG M Y, XIAO H, ZHAO Y. Influence of polygonal wheel on safety of subway in curve with small radius[J]. China Safety Science Journal, 2019, 29(S1): 27-31 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZAQK2019S1007.htm [3] 李万磊, 陈天星, 胡瑞霞, 等. 磁悬浮列车运行平稳性研究[J]. 机械科学与技术, 2019, 38(5): 677-683 doi: 10.13433/j.cnki.1003-8728.20180238LI W L, CHEN T X, HU R X, et al. Study on running stability of maglev train[J]. Mechanical Science and Technology for Aerospace Engineering, 2019, 38(5): 677-683 (in Chinese) doi: 10.13433/j.cnki.1003-8728.20180238 [4] CHUNG M H, CHANG C H, CHANG K Y, et al. A framework for train derailment risk analysis[J]. Journal of Central South University, 2019, 26(7): 1874-1885 doi: 10.1007/s11771-019-4141-4 [5] YU X L, LIU G W, QIN Y, et al. The prediction of derailment coefficient based on neural networks[M]//JIA L M, LIU Z G, QIN Y, et al. Proceedings of the 2013 International Conference on Electrical and Information Technologies for Rail Transportation (EITRT2013)-Volume Ⅱ. Berlin: Springer, 2014: 267-274 [6] 曾庆元, 向俊, 周智辉, 等. 列车脱轨分析理论与应用[M]. 长沙: 中南大学出版社, 2006ZENG Q Y, XIANG J, ZHOU Z H, et al. Train derailment analysis theory and application[M]. Changsha: Central South University Press, 2006 (in Chinese) [7] 龚凯, 向俊, 毛建红, 等. 重载铁路桥上货物列车脱轨预防措施[J]. 中南大学学报(自然科学版), 2017, 48(12): 3406-3414 doi: 10.11817/j.issn.1672-7207.2017.12.035GONG K, XIANG J, MAO J H, et al. Derailment precautions of freight train on bridge in heavy haul railway[J]. Journal of Central South University (Science and Technology), 2017, 48(12): 3406-3414 (in Chinese) doi: 10.11817/j.issn.1672-7207.2017.12.035 [8] 曾庆元, 周智辉, 赫丹, 等. 列车-轨道(桥梁)系统横向振动稳定性分析[J]. 铁道学报, 2012, 34(5): 86-90 doi: 10.3969/j.issn.1001-8360.2012.05.014ZENG Q Y, ZHOU Z H, HE D, et al. Study on stability of lateral vibration of train-track (bridge) system[J]. Journal of the China Railway Society, 2012, 34(5): 86-90 (in Chinese) doi: 10.3969/j.issn.1001-8360.2012.05.014 [9] ZHOU Z H, LIU G, QIAN Z D, et al. Study on critical speed of freight train derailment on bridges[J]. Advanced Materials Research, 2013, 639-640: 456-459 doi: 10.4028/www.scientific.net/AMR.639-640.456 [10] 翟婉明, 陈果. 根据车轮抬升量评判车辆脱轨的方法与准则[J]. 铁道学报, 2001, 23(2): 17-26 doi: 10.3321/j.issn:1001-8360.2001.02.004ZHAI W M, CHEN G. Method and criteria for evaluation of wheel derailment based on wheel vertical rise[J]. Journal of the China Railway Society, 2001, 23(2): 17-26 (in Chinese) doi: 10.3321/j.issn:1001-8360.2001.02.004 [11] 孙善超, 刘金朝. 基于载荷辨识技术的轨道-车辆系统状态安全综合评判[J]. 中国铁路, 2017(10): 11-15 https://www.cnki.com.cn/Article/CJFDTOTAL-TLZG201710003.htmSUN S C, LIU J Z. Comprehensive assessment on track-vehicle system safety status based on load identification technology[J]. Chinese Railways, 2017(10): 11-15 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TLZG201710003.htm [12] 雷虎军, 黄炳坤, 刘伟. 基于几何指标的高速铁路桥上列车地震安全性评判方法[J]. 振动与冲击, 2020, 39(17): 57-63 https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202017009.htmLEI H J, HUANG B K, LIU W. Evaluation method for running safety of train on a high-speed railway bridge based on geometric indexes[J]. Journal of Vibration and Shock, 2020, 39(17): 57-63 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202017009.htm [13] SUN Z, DAI H Y, HEMIDA H, et al. Safety of high-speed train passing by windbreak breach with different sizes[J]. Vehicle System Dynamics, 2020, 58(12): 1935-1952 doi: 10.1080/00423114.2019.1657909 [14] 李俊成. 大准铁路老牛湾站列车脱轨原因分析和防范措施研究[J]. 中小企业管理与科技(下旬刊), 2017(11): 190-193, 196 https://www.cnki.com.cn/Article/CJFDTOTAL-ZXQX201711087.htmLI J C. Cause analysis of train derailment in Laoniuwan station of Dazhun railway and the preventive measures[J]. Management & Technology of SME, 2017(11): 190-193, 196 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZXQX201711087.htm [15] ZHU T, YANG B Z, YANG C, et al. The mechanism for the coupler and draft gear and its influence on safety during a train collision[J]. Vehicle System Dynamics, 2018, 56(9): 1375-1393 [16] WANG Y P, WEIDMANN U A, WANG H S. Using catastrophe theory to describe railway system safety and discuss system risk concept[J]. Safety Science, 2017, 91: 269-285 [17] 王阳鹏, 王化深, 牛儒. 基于突变理论的ATS系统安全状态预警模型研究[J]. 铁道学报, 2013, 35(9): 79-85 https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201309017.htmWANG Y P, WANG H S, NIU R. Research on early warning model of ATS system safety states based on catastrophe theory[J]. Journal of the China Railway Society, 2013, 35(9): 79-85 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201309017.htm [18] 李竹文, 戴焕云. 基于突变理论的列车脱轨机理研究[J]. 铁道建筑, 2013(1): 91-95 https://www.cnki.com.cn/Article/CJFDTOTAL-TDJZ201301028.htmLI Z W, DAI H Y. Train derailment mechanism study based on catastrophe theory[J]. Railway Engineering, 2013(1): 91-95 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TDJZ201301028.htm [19] 刘文辉, 戴焕云. 基于燕尾突变的车辆脱轨机理研究[J]. 机械工程与自动化, 2015(1): 1-3, 6 https://www.cnki.com.cn/Article/CJFDTOTAL-SXJX201501001.htmLIU W H, DAI H Y. Vehicle derailment mechanism study based on swallowtail catastrophe theory[J]. Mechanical Engineering & Automation, 2015(1): 1-3, 6 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SXJX201501001.htm [20] 雷内·托姆. 结构稳定性与形态发生学[M]. 成都: 四川教育出版社, 1992THOM R. Structural stabibity and morphogenesis[M]. Chengdu: Sichuan Education Press, 1992 (in Chinese) [21] 国家标准局. GB 5599-85铁道车辆动力学性能评定和试验鉴定规范[S]. 北京: 中国计划出版社, 1985NBS. GB 5599-85 Railway vehicles-specification for evaluation the dynamic performance and accreditation test[S]. Beijing: China Planning Press, 1985 (in Chinese) [22] 凌复华. 突变理论及其应用[M]. 上海: 上海交通大学出版社, 1987LING F H. Catastrophe theory and its application[M]. Shanghai: Shanghai Jiaotong University Press, 1987 (in Chinese)