Dynamic interaction between metro vehicle and steel spring floating slab track under emergency braking condition
-
摘要: 为了优化坡道上钢弹簧浮置板轨道的设计, 在考虑轮轨纵向作用关系与钢弹簧浮置板轨道特点的基础上, 运用多体动力学理论和有限元法建立了紧急制动条件下地铁车辆与钢弹簧浮置板轨道动力相互作用模型, 利用多体动力学软件UM验证了模型的有效性, 分析了车辆与轨道的动力响应。研究结果表明: UM软件与本文模型计算得到的车体纵向加速度和轮轨纵向力平均相对误差分别为1.3%、2.8%;在紧急制动过程中, 车体始终处于向前点头和纵向振动的状态, 导致前轮增载, 后轮减载; 由于板与板之间不连续, 钢轨和浮置板之间会产生纵向相对错动, 须注意钢轨与浮置板之间不协调的纵向变形; 间隔2组扣件布置一对隔振器方案(方案1) 所得板端钢轨垂向位移比板中大0.2 mm, 间隔2组扣件布置一对隔振器, 再间隔3组扣件布置一对隔振器方案(方案2) 所得板端钢轨垂向位移比板中小0.5 mm; 2种布置方案下, 轨道纵向变形相差不超过5%, 扣件和钢弹簧受到的纵向作用力相差不超过15%;短波轨道不平顺显著加剧了钢轨和浮置板的垂向振动效应, 不平顺状态下钢轨最大垂向加速度可达15g左右; 钢弹簧浮置板轨道可以降低传递到基础底部的垂向振动, 加速度降幅约为0.2 m·s-2, 但会显著放大低频段钢轨、浮置板的垂向振动, 振动量增幅约为15 dB。Abstract: To optimize the design of steel spring floating slab track on the grade, based on the consideration of longitudinal wheel-rail relationship and structure characteristics of steel spring floating slab track, the dynamic interaction model of metro vehicle and steel spring floating slab track under the emergency braking condition was established through the multi-body dynamics theory and finite element method. The validity of the model was verified through the multi-body dynamics software UM. The dynamic responses of vehicle and track under the emergency braking condition were analyzed. Research result shows that the average relative errors of longitudinal acceleration of car body and longitudinal wheel-rail force calculated by the UM and the model in this paper are 1.3% and 2.8%, respectively. During the emergency braking process, the car body is always in the state of forward pitching and longitudinal vibration, resulting in the increased load in the front wheel and the decreased load in the rear wheel. Owing to the discontinuities between the slabs, a longitudinal relative dislocation occurs between the track and floating slab. The special attentions should be paid to the longitudinal uncoordinated deformation between the rail and floating slab. For the scheme of arranging a pair of isolators at the intervals of two sets of fasteners (scheme 1), the vertical displacement of rail at the end of slab is 0.2 mm larger than that at the middle of slab. For the scheme of arranging a pair of isolators at the intervals of two sets of fasteners, then arranging a pair of isolators at the intervals of three sets of fasteners (scheme 2), the vertical displacement of rail at the end of slab is 0.5 mm smaller than that at the middle of slab. Under the two layout schemes, the difference of longitudinal deformation of track is no more than 5%, and the difference of longitudinal force acting on fastener and steel spring is no more than 15%. The short wave track irregularity significantly increases the vertical vibrations of rail and floating slab, and the maximum vertical acceleration of rail can reach up to approximately 15g in the presence of track irregularity. Steel spring floating slab can reduce the vertical vibration transmitted to the bottom of the foundation, and the acceleration decreases by approximately 0.2 m·s-2. However, the low-frequency vertical vibrations of rail and floating slab amplify significantly, and the vibration increases by approximately 15 dB.
-
图 8 紧急制动过程车辆响应时程
Figure 8. Time histories of vehicle responses during emergency braking
图 11 不同位置的钢轨与浮置板纵向位移差
Figure 11. Longitudinal displacement differences between rail and floating slab at different positions
图 12 不同布置方案下浮置板隔振效果
Figure 12. Vibration isolation results of floating slab under different layout schemes
图 13 轨道结构垂向振动分析结果
Figure 13. Analysis results of vertical vibration of track structure
图 14 轮载点钢轨纵向位移
Figure 14. Longitudinal displacements of rail at wheel-rail contact points
表 1 车辆与轨道参数
Table 1. Parameters of vehicle and track
参数名称 参数值 车体质量mc/kg 2.04×104 车体转动惯量Jc/ (kg·m2) 6.60×105 二系垂向刚度ksz/ (N·m-1) 4.50×106 二系垂向阻尼csz/ (N·s·m-1) 1.20×105 二系纵向刚度ksx/ (N·m-1) 2.00×105 二系纵向阻尼csx/ (N·s·m-1) 2.50×106 1/2车辆定距lc/m 6.30 转向架质量mt/kg 7.95×102 转向架转动惯量Jt/ (kg·m2) 3.38×102 1/2车辆轴距lt/m 1.10 一系垂向刚度kpz/ (N·m-1) 2.08×105 一系垂向阻尼cpz/ (N·s·m-1) 1.00×105 一系纵向刚度kpx/ (N·m-1) 1.00×107 一系纵向阻尼cpx/ (N·s·m-1) 1.00×105 轮对质量mw/kg 5.53×102 扣件垂向刚度kz1/ (N·m-1) 3.43×107 扣件垂向阻尼cz1/ (N·s·m-1) 3.00×104 扣件纵向刚度kx1/ (N·m-1) 7.50×107 扣件纵向阻尼cx1/ (N·s·m-1) 6.00×104 钢弹簧垂向刚度kz2/ (N·m-1) 6.30×106 钢弹簧垂向阻尼cz2/ (N·s·m-1) 8.00×103 钢弹簧纵向刚度kx2/ (N·m-1) 7.56×106 钢弹簧纵向阻尼cx2/ (N·s·m-1) 6.00×104 
下载: 导出CSV
表 2 不同布置方案下轨道动力响应峰值
Table 2. Peak values of dynamic responses of track under different layout schemes
轨道动力响应指标 方案1 方案2 钢轨 板中垂向位移/mm 2.500 2.800 板端垂向位移/mm 2.700 2.300 板中纵向位移/mm 0.083 0.086 板端纵向位移/mm 0.079 0.080 浮置板 板中垂向位移/mm 2.200 2.500 板端垂向位移/mm 2.600 2.100 板中纵向位移/mm 0.064 0.066 板端纵向位移/mm 0.064 0.066 扣件 板中垂向力/kN 24.8 24.8 板端垂向力/kN 29.4 29.5 板中纵向力/N -456.0 -454.0 板端纵向力/N -688.0 -685.0 钢弹簧 板中垂向力/kN 24.7 30.0 板端垂向力/kN 27.6 25.4 板中纵向力/N -482.0 -549.0 板端纵向力/N -474.0 -544.0
下载: 导出CSV
-
[1] 王伟华, 刘克飞, 李培刚. 长大坡道桥上单元板式无砟轨道纵向力学特性分析[J]. 铁道工程学报, 2011 (2): 65-70. doi: 10.3969/j.issn.1006-2106.2011.02.013WANG Wei-hua, LIU Ke-fei, LI Pei-gang. Analysis of longitudinal mechanics behaviour of ballastless slab track on long grade bridge[J]. Journal of Railway Engineering Society, 2011 (2): 65-70. (in Chinese). doi: 10.3969/j.issn.1006-2106.2011.02.013 [2] 沈彬然, 王冠, 刘浩, 等. 桥上纵连板在制动力作用下梁轨相互作用影响分析[J]. 铁道建筑, 2016 (3): 127-130, 146. doi: 10.3969/j.issn.1003-1995.2016.03.31SHEN Bin-ran, WANG Guan, LIU Hao, et al. Analysis of girder-rail interaction under braking effect of longitudinal connected slab on bridge[J]. Railway Engineering, 2016 (3): 127-130, 146. (in Chinese). doi: 10.3969/j.issn.1003-1995.2016.03.31 [3] 徐庆元, 张旭久. 高速铁路博格纵连板桥上无砟轨道纵向力学特性[J]. 中南大学学报(自然科学版), 2009, 40 (2): 526-532. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD200902048.htmXU Qing-yuan, ZHANG Xu-jiu. Longitudinal forces characteristic of Bogl longitudinal connected ballastless track on high-speed railway bridge[J]. Journal of Central South University (Science and Technology), 2009, 40 (2): 526-532. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD200902048.htm [4] 闫斌, 戴公连. 考虑加载历史的高速铁路梁轨相互作用分析[J]. 铁道学报, 2014, 36 (6): 75-80. doi: 10.3969/j.issn.1001-8360.2014.06.012YAN Bin, DAI Gong-lian. Analysis of interaction between continuously-welded rail and high-speed railway bridges considering loading-history[J]. Journal of the China Railway Society, 2014, 36 (6): 75-80. (in Chinese). doi: 10.3969/j.issn.1001-8360.2014.06.012 [5] 蔡小培, 高亮, 孙汉武, 等. 桥上纵连板式无砟轨道无缝线路力学性能分析[J]. 中国铁道科学, 2011, 32 (6): 28-33. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201106006.htmCAI Xiao-pei, GAO Liang, SUN Han-wu, et al. Analysis on the mechanical properties of longitudinally connected ballastless track continuously welded rail on bridge[J]. China Railway Science, 2011, 32 (6): 28-33. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201106006.htm [6] 方利, 王志强, 李成辉. 简支梁桥上CRTSⅡ型板式无砟轨道制动力影响因素分析[J]. 铁道学报, 2012, 34 (1): 72-76. doi: 10.3969/j.issn.1001-8360.2012.01.013FANG Li, WANG Zhi-qiang, LI Cheng-hui. Analysis on influencing factors of braking force of CRTS Ⅱ ballastless track slab on simply-supported beam bridges[J]. Journal of the China Railway Society, 2012, 34 (1): 72-76. (in Chinese). doi: 10.3969/j.issn.1001-8360.2012.01.013 [7] 徐庆元, 陈秀方, 李树德. 高速铁路桥上无缝线路纵向附加力研究[J]. 中国铁道科学, 2006, 27 (3): 8-12. doi: 10.3321/j.issn:1001-4632.2006.03.002XU Qing-yuan, CHEN Xiu-fang, LI Shu-de. Study on the additional longitudinal forces transmission between continuously welded rails and high-speed railway bridges[J]. China Railway Science, 2006, 27 (3): 8-12. (in Chinese). doi: 10.3321/j.issn:1001-4632.2006.03.002 [8] YAN Bin, DAI Gong-lian, GUO Wen-hua, et al. Longitudinal force in continuously welded rail on long-span tied arch continuous bridge carrying multiple tracks[J]. Journal of Central South University, 2015, 22 (5): 2001-2006. doi: 10.1007/s11771-015-2721-5 [9] 木东升, 周宇, 韩延彬, 等. 轨道综合作业对高速铁路有砟轨道几何不平顺改善效果[J]. 交通运输工程学报, 2018, 18 (5): 90-99. http://transport.chd.edu.cn/article/id/201805009MU Dong-sheng, ZHOU Yu, HAN Yan-bin, et al. Effect of track comprehensive maintenance on geometry irregularity improvement of ballast track in high-speed railway[J]. Journal of Traffic and Transportation Engineering, 2018, 18 (5): 90-99. (in Chinese). http://transport.chd.edu.cn/article/id/201805009 [10] RUGE P, BIRK C. Longitudinal forces in continuously welded rails on bridgedecks due to nonlinear track-bridge interaction[J]. Computers and Structures, 2007, 85 (7/8): 458-475. [11] DAI Gong-lian, LIU Wen-shuo. Applicability of small resistance fastener on long-span continuous bridges of high-speed railway[J]. Journal of Central South University, 2013, 20 (5): 1426-1433. doi: 10.1007/s11771-013-1631-7 [12] 吴定俊, 石龙, 李奇. 梁轨纵向位移阻力系数双弹簧模型研究[J]. 工程力学, 2015, 32 (10): 75-81. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201510012.htmWU Ding-jun, SHI Long, LI Qi. A double-spring model for longitudinal displacement-resistance relationship of fasteners in rail-bridge interaction analysis[J]. Engineering Mechanics, 2015, 32 (10): 75-81. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201510012.htm [13] 周宇, 木东升, 邝迪峰, 等. 城市轨道交通钢轨磨耗和裂纹萌生分析与选型建议[J]. 交通运输工程学报, 2018, 18 (4): 82-89. http://transport.chd.edu.cn/article/id/201805009ZHOU Yu, MU Dong-sheng, KUANG Di-feng, et al. Analysis on rail wear and crack initiation and recommendation on rail selection in urban rail transit[J]. Journal of Traffic and Transportation Engineering, 2018, 18 (4): 82-89. (in Chinese). http://transport.chd.edu.cn/article/id/201805009 [14] 吴亮秦, 吴定俊, 李奇. 城市轨道交通桥梁列车制动力试验研究[J]. 铁道学报, 2012, 34 (3): 88-93. https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201203021.htmWU Liang-qin, WU Ding-jun, LI Qi. Experiment study on braking force for urban rail transit bridge[J]. Journal of the China Railway Society, 2012, 34 (3): 88-93. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201203021.htm [15] TOTH J, RUGE P. Spectral assessment of mesh adaptations for the analysis of the dynamical longitudinal behavior of railway bridges[J]. Archive of Applied Mechanics, 2001, 71 (6/7): 453-462. [16] 李宏年, 朱晞, 季文玉. PC简支梁铁路桥承受制动力的动力分析[J]. 铁道学报, 2000, 22 (4): 64-67. https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB200004016.htmLI Hong-nian, ZHU Xi, JI Wen-yu. Dynamic analysis of simply supported PC beam railway bridges under braking force[J]. Journal of the China Railway Society, 2000, 22 (4): 64-67. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB200004016.htm [17] 潘鹏, 雷晓燕, 张鹏飞, 等. 制动荷载作用下桥上无砟轨道动力响应分析[J]. 铁道科学与工程学报, 2017, 14 (11): 2309-2322. https://www.cnki.com.cn/Article/CJFDTOTAL-CSTD201711006.htmPAN Peng, LEI Xiao-yan, ZHANG Peng-fei, et al. Dynamic response analysis of ballastless track on bridge under braking load[J]. Journal of Railway Science and Engineering, 2017, 14 (11): 2309-2322. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CSTD201711006.htm [18] 朱志辉, 闫铭铭, 徐智伟, 等. 制动工况下高墩铁路桥梁纵向动力响应研究[J]. 铁道工程学报, 2017 (5): 52-58. https://www.cnki.com.cn/Article/CJFDTOTAL-TDGC201705010.htmZHU Zhi-hui, YAN Ming-ming, XU Zhi-wei, et al. Response analysis of railway bridge with high piers due to vehicle braking[J]. Journal of Railway Engineering Society, 2017 (5): 52-58. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TDGC201705010.htm [19] JU S H, LIN H T. A finite element model of vehicle-bridge interaction considering braking and acceleration[J]. Journal of Sound and Vibration, 2007, 303 (1/2): 46-57. [20] 程潜, 张楠, 夏禾, 等. 考虑制动条件的高速列车-轨道-桥梁系统动力响应分析[J]. 中国铁道科学, 2013, 34 (1): 8-14. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201301001.htmCHENG Qian, ZHANG Nan, XIA He, et al. Dynamic response analysis of vehicle-track-bridge system considering braking conditions for high-speed railway[J]. China Railway Science, 2013, 34 (1): 8-14. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201301001.htm [21] 沈锐利, 王江浩. 铁路悬索桥在制动力作用下的动力响应分析[J]. 桥梁建设, 2016, 46 (6): 24-28. https://www.cnki.com.cn/Article/CJFDTOTAL-QLJS201606005.htmSHEN Rui-li, WANG Jiang-hao. Analysis of dynamic responses of railway suspension bridge under action of train braking force[J]. Bridge Construction, 2016, 46 (6): 24-28. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-QLJS201606005.htm [22] YANG Y B, WU Y S. A versatile element for analyzing vehicle-bridge interaction response[J]. Engineering Structures, 2001, 23 (5): 452-469. [23] 吕龙, 李建中. 列车制动和运行下大跨度公铁两用斜拉桥纵向振动分析[J]. 铁道学报, 2017, 39 (3): 90-95. https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201703015.htmLYU Long, LI Jian-zhong. Study on longitudinal vibration of long-span rail-cum-road cable-stayed bridge induced by train braking and running[J]. Journal of the China Railway Society, 2017, 39 (3): 90-95. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201703015.htm [24] 陈士安, 杨鑫, 姚明, 等. 紧急制动工况下电磁式磁轨制动器极靴磨损计算方法[J]. 交通运输工程学报, 2017, 17 (1): 82-92. http://transport.chd.edu.cn/article/id/201701010CHEN Shi-an, YANG Xin, YAO Ming, et al. Pole shoe abrasion calculation method of electromagnetic track brake under emergency braking condition[J]. Journal of Traffic and Transportation Engineering, 2017, 17 (1): 82-92. (in Chinese). http://transport.chd.edu.cn/article/id/201701010 [25] 蒋吉清, 王永安, 魏纲, 等. 基于剪力铰的浮置板轨道减振性能优化分析[J]. 中国铁道科学, 2017, 38 (4): 15-23. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201704003.htmJIANG Ji-qing, WANG Yong-an, WEI Gang, et al. Optimum analysis of vibration reduction performance for floating slab track based on shear hinge[J]. China Railway Science, 2017, 38 (4): 15-23. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201704003.htm [26] ZHAI Wan-ming, SUN Xiang. A detailed model for investigating vertical interaction between railway vehicle and track[J]. Vehicle System Dynamics, 1994, 23 (S1): 603-615. [27] 杨静静, 张楠, 夏禾. 车轨耦合振动中4种轮轨竖向接触模型的适用性比较分析[J]. 中国铁道科学, 2016, 37 (6): 11-20. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201606002.htmYANG Jing-jing, ZHANG Nan, XIA He. Comparative analysis on applicability of four wheel-rail vertical contact models for coupling vibration of vehicle-track system[J]. China Railway Science, 2016, 37 (6): 11-20. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGTK201606002.htm [28] 朱志辉, 王力东, 龚威, 等. 多种垂向轮轨关系的对比及改进的车-线-桥系统迭代模型的建立[J]. 中南大学学报(自然科学版), 2017, 48 (6): 1585-1593. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201706023.htmZHU Zhi-hui, WANG Li-dong, GONG Wei, et al. Comparative analysis of several types of vertical wheel/rail relationship and construction of an improved iteration model for train-track-bridge system[J]. Journal of Central South University (Science and Technology), 2017, 48 (6): 1585-1593. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201706023.htm [29] 张楠, 夏禾, 程潜, 等. 制动力作用下车辆-车站结构耦合系统分析[J]. 振动与冲击, 2011, 30 (2): 138-143. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201102029.htmZHANG Nan, XIA He, CHENG Qian, et al. Analysis method for a vehicle structure coupled system under braking force[J]. Journal of Vibration and Shock, 2011, 30 (2): 138-143. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201102029.htm [30] 何越磊, 李再帏, 盛春玲, 等. 不同地铁线路条件下轨道谱的特性分析[J]. 铁道工程学报, 2014 (8): 99-104. https://www.cnki.com.cn/Article/CJFDTOTAL-TDGC201407019.htmHE Yue-lei, LI Zai-wei, SHENG Chun-ling, et al. Characteristic analysis of track spectrums of different subway line conditions[J]. Journal of Railway Engineering Society, 2014 (8): 99-104. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TDGC201407019.htm [31] 李再帏, 练松良, 李秋玲, 等. 城市轨道交通轨道不平顺谱分析[J]. 华东交通大学学报, 2011, 28 (5): 83-87. https://www.cnki.com.cn/Article/CJFDTOTAL-HDJT201105019.htmLI Zai-wei, LIAN Song-liang, LI Qiu-ling, et al. Characteristic analysis of track irregularity spectrum of urban rail transit[J]. Journal of East China Jiaotong University, 2011, 28 (5): 83-87. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HDJT201105019.htm [32] 徐庆元. 短波随机不平顺对列车-板式无砟轨道-桥梁系统动力特性影响[J]. 土木工程学报, 2011, 44 (10): 132-137. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201110022.htmXU Qing-yuan. Influence of short-wave random irregularity on the dynamic characteristics of train-slab track-bridge system[J]. China Civil Engineering Journal, 2011, 44 (10): 132-137. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201110022.htm [33] 李斌, 刘学毅. 基于随机振动理论的我国中高速铁路有砟轨道设计轮载研究[J]. 铁道学报, 2010, 32 (5): 114-118. https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201005027.htmLI Bin, LIU Xue-yi. Study on designed dynamic wheel loads of middle-speed and high-speed railways in China based on theory of random vibration[J]. Journal of the China Railway Society, 2010, 32 (5): 114-118. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201005027.htm -
点击查看大图
图(15) / 表(2)
计量
- 文章访问数: 1340
- HTML全文浏览量: 255
- PDF下载量: 1036
- 被引次数: 0
