为研究中低速磁浮最小曲线半径及缓和曲线长度，本文基于磁浮交通线路参数的计算方法、相关要素，以及线路自身的特点，推导出适用于中低速磁浮的曲线半径、缓和曲线长度计算公式，在参考相关标准的基础上，对中低速磁浮列车以20~160 km/h速度运行时的最小平、竖曲线半径及缓和曲线长度进行了理论分析，进一步给出其建议值，并建立了考虑主动反馈控制特性的车辆模型，通过动力学仿真对取值的可靠性进行了验证。研究结果表明：最小平曲线半径取值受指向外侧的最大侧向加速度控制，最小竖曲线半径取值受凹曲线上最大法向加速度控制，列车运行速度一定时，横坡角越大，最小平曲线半径取值越小，而纵坡对最小竖曲线半径取值几乎无影响；当横坡角为2°，列车在正常条件下运行时，最小缓和曲线长度主要受最大侧向冲击控制，在困难条件下运行时，最小缓和曲线长度主要受最大法向冲击控制，当横坡角为4°、6°，列车在正常/困难条件下运行时，最小缓和曲线长度主要受最大法向冲击控制；按横坡角最大值6°考虑，列车以160 km/h在正常条件下运行时，建议最小平曲线半径及缓和曲线长度分别取970 m、120 m。本文研究成果可为中低速磁浮交通的选线设计提供理论依据和数据参考。
Abstract
In order to study the minimum curve radius and transition curve length of medium and low speed maglev, this paper deduces the calculation formula of curve radius and transition curve length suitable for medium and low speed maglev based on the calculation method of maglev traffic line parameters, related factors, and the characteristics of the line itself. On the basis of referring to relevant standards, a theoretical analysis is carried out on the minimum horizontal and vertical curve radius and the length of the transition curve when the medium and low speed maglev trains run at a speed of 20~160 km/h, and their recommended values are further given. The reliability of the value is verified with the dynamic simulation of the vehicle model with feedback control characteristics. The research results show that the radius of the minimum horizontal curve is controlled with the maximum lateral acceleration pointing to the outside, and the radius of the minimum vertical curve is controlled with the maximum normal acceleration on the concave curve. When the train speed is fixed, the larger the horizontal slope angle, the smaller the minimum flat curve radius value, and the longitudinal slope has almost no effect on the minimum vertical curve radius value; When the cross slope angle is 2° and the train is running under normal conditions, the length of the minimum transition curve is mainly controlled with the maximum lateral impact, when running under difficult conditions, the length of the minimum transition curve is mainly controlled with the maximum normal impact. When the cross slope angle is 4° or 6° and the train is running under normal/difficult conditions, the minimum transition curve length is mainly controlled with the maximum normal shock; Considering the maximum cross-slope angle of 6°, when the train is operating at 160 km/h under normal conditions, it is suggested that the radius of the minimum horizontal curve and the length of the transition curve should be taken as 970 m and 120 m respectively. The research results of this paper can provide theoretical basis and data reference for the route selection design of medium and low speed maglev traffic.
关键词
中低速磁浮 /
曲线半径 /
缓和曲线 /
加速度 /
冲击
{{custom_keyword}} /
Key words
medium-low speed maglev /
curve radius /
transition curve /
acceleration /
impact
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 翟婉明, 赵春发. 现代轨道交通工程科技前沿与挑战[J]. 西南交通大学学报, 2016, 51(2): 209-226.
ZHAI Wanming, ZHAO Chunfa. Frontiers and challenges of sciences and technologies in modern railway engineering[J]. Journal of Southwest Jiaotong Universiy, 2016, 51(2): 209-226.
[2] 徐飞, 罗世辉, 邓自刚. 磁悬浮轨道交通关键技术及全速度域应用研究[J]. 铁道学报, 2019, 41(3): 40-49.
XU Fei, LUO Shihui, DENG Zigang. Study on key technologies and whole speed range application of maglev rail transport[J]. Journal of The China Railway Society, 2019, 41(3): 40-49.
[3] 马卫华, 罗世辉, 张敏, 等. 中低速磁浮车辆研究综述[J]. 交通运输工程学报, 2021, 21(1): 199-216.
MA Weihua, LUO Shihui, ZHANG Min, et al. Research review on medium and low speed maglev vehicle[J]. Journal of Traffic and Transportation Engineering, 2021, 21(1): 199-216.
[4] 王相平, 李国芳, 慕显龙, 等. 小半径曲线中低速磁浮车辆-轨道耦合系统动力响应分析[J]. 振动与冲击, 2022, 41(10): 81-89.
WANG Xiangping, LI Guofang, MU Xianlong, et al. Dynamic response analysis of a low-medium speed maglev vehicle-track coupled system on tight curve[J]. Journal of Vibration and Shock, 2022, 41(10): 81-89.
[5] 罗英昆, 赵春发, 梁鑫, 等. 小半径竖曲线上磁浮车辆空气弹簧动态响应分析[J]. 振动与冲击, 2020, 39(17): 99-105.
LUO Yingkun, ZHAO Chunfa, LIANG Xin, et al. Dynamic responses of air-spring suspension of a maglev vehicle negotiating a small-radius vertical curved track[J]. Journal of Vibration and Shock, 2020, 39(17): 99-105.
[6] 姚金斌. 中低速磁浮交通线路最小平曲线半径的合理取值[J]. 都市快轨交通, 2007, 20(3): 17-20.
YAO Jinbin. Rational minimum plane curve radius on medium and low speed maglev lines[J]. Urban Rapid Rail Transit, 2007, 20(3): 17-20.
[7] 代一帆, 刘万明, 安超帅. 中低速磁浮交通线路最大横坡角的合理取值[J]. 铁道标准设计, 2018, 62(8): 29-33.
DAI Yifan, LIU Wanming, AN Chaoshuai. Reasonable value of maximum transverse gradient of medium and low-speed maglev[J]. Railway Standard Design, 2018, 62(8): 29-33.
[8] 时瑾, 魏庆朝, 鲍凤麒. 中低速磁浮交通圆曲线参数影响因素分析[J]. 铁道学报, 2019, 41(3): 40-49.
SHI Jin, WEI Qingchao, BAO Fengqi. Influence factors of circular curve parameters on medium and low speed maglev system[J]. Urban Rapid Rail Transit, 2019, 41(3): 40-49.
[9] Jiang F J, Sun X D, Li H B, et al. Optimization Analysis of Minimum Flat Curve Radius of High Speed Maglev Line with Design Speed of 500 km/h[J]. IOP Conference Series: Materials Science and Engineering, 2019, 12(8): 637-643.
[10] 武巍. 基于动力学分析中低速磁浮平面缓和曲线参数标准研究[D]. 成都: 西南交通大学, 2015.
WU Wei. Study on transition curve parameter standard of medium and low speed maglev traffic based on dynamics analysis[D]. Chengdu: Southwest Jiaotong University, 2015.
[11] 米隆, 招阳, 魏庆朝, 等. 磁浮交通系统线路缓和曲线参数取值方法研究[J]. 北京交通大学学报, 2007, 31(4): 92-95.
MI Long, ZHAO Yang, WEI Qingchao, et al. Research on alignment parameters of high-speed maglev railway transaction curve[J]. Journal of Beijing Jiaotong Universiy, 2007, 31(4): 92-95.
[12] 谢毅, 寇峻瑜, 余浩伟. 高速磁浮最小曲线半径及缓和曲线长度研究[J]. 铁道工程学报, 2020, 37(4): 43-48.
XIE Yi, KOU Junyu, YU Haowei. Research on the minimum plane curve radius and transition curve length of high-speed maglev[J]. Journal of Railway Engineering Society, 2020, 37(4): 43-48.
[13] 苟智平. 高速磁浮线路平纵面设计参数的建议[J]. 交通运输工程与信息学报, 2007, 5(4): 99-104.
GOU Zhiping. Parameters of the line plane and profile design for the high-speed maglev-train[J]. Journal of Transportation Engineering and Information, 2007, 5(4): 99-104.
[14] Han J B, Kin K J, Han S H, et al. Parametric study of curved guideways for urban maglev vehicle[J]. Transactions of the Korean Society of Mechanical Engineers A, 2014, 38(3): 329-335.
[15] CJJ/T 262-2017. 中低速磁浮交通设计规范[S]. 北京: 中国建筑工业出版社, 2017.
[16] TB 10630-2019. 磁浮铁路技术标准（试行）[S]. 北京: 中国铁道出版社, 2019.
[17] Shen T I, Chang C H, Chang K Y, et al. A numerical study of cubic parabolas on railway transition curves[J]. Journal of Marine Science and Technology(Taiwan): 2013, 21(2): 191-197.
[18] Martin L. New form of road/railway transition curve [J]. Journal of Transportation Engineering: 1998, 124(6): 546-556.
[19] Pogorelov D. Differential–algebraic equations in multibody system modeling[J]. Numerical Algorithms, 1998, 19(1): 183-194.
[20] CHEN X H, MA W H, LUO S H. Study on stability and bifurcation of electromagnet-track beam coupling system for EMS maglev vehicle[J]. Nonlinear Dynamics, 2020, 101(4): 2181-2193.
[21] BREZINA W, LANGERHOLC J. Lift and side force on rectangular pole pieces in two dimensions[J]. Journal of Applied Physics, 1974, 45(4): 1869-1872.
[22] WANG D X, LI X Z, LIANG L, et al. Influence of the track structure on the vertical dynamic interaction analysis of the low-to-medium-speed maglev train-bridge system[J]. Advances in Structural Engineering, 2019, 22(14): 2937-2950.
[23] 张耿, 李杰, 杨子敬. 低速磁浮轨道不平顺功率谱研究[J]. 铁道学报, 2011, 33(10): 73-78.
ZHANG Geng, LI Jie, YANG Zijing. Estimation of power spectrum density track irregularities of low-speed maglev railway lines[J]. Journal of the China Railway Society, 2011, 33(10): 73-78.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(2352 KB)
