高速铁路三维线形参数及其对列车运动的影响
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摘要
研究目的:为避免传统二维设计方式出现的设计差错,明确线路的三维曲线线形对高速列车运动的影响,以微分几何不变量曲率、挠率为参数,并结合三维曲线的Frenet标架,建立线路三维线形设计指标以及列车三维运动学模型,然后分析三维线形参数对线路走向及对列车运动特性的影响。研究结论:(1)任何线路的走向及形状都可以通过曲率、挠率及Frenet标架进行表达,以此为参数建立的列车运动学模型可准确反映列车运动状态;(2)二维设计易产生设计差错,并不能准确评价列车的运动状态;(3)线形参数对列车加速度、急动度起主导作用,其中曲率决定了加速度的大小,但横、竖向加速度大小也受控于Frenet标架的侧倾;急动度由曲率变化率、挠率产生,其中曲率变化率是急动度是否超限的关键因素;(4)为避免设计差错,在高速、超高速铁路设计中应引入三维线形设计方式。
Research purposes:For the purpose that avoiding the design error caused by design method of traditional two-dimension(2D),and ascertaining the influence of the three-dimension railway alignment on the motion of high-speed train,the system of design parameters of three-dimension(3D) railway alignment and the 3D motion model of the train is established by the differential geometric invariants(curvature,torsion and Frenet frame) in this paper.And then,the influence of the parameters of 3D alignment on the trend of the railway alignment and the characteristics of the train motion is analyzed.Research conclusions:(1) The trend and shape of any railway alignment could be expressed by curvature,torsion and Frenet frame,the motion model of the train based on these parameters could accurately reflect the motion state of the train.(2) The method of 2D design is prone to design error and hard to accurately evaluate the motion state of the train.(3) The parameters of alignment play a dominant role in acceleration and jerk of the trains,in which curvature determines the value of acceleration,but the horizontal and vertical acceleration is controlled by roll angle of Frenet frame as well;the jerk is produced by the torsion and change rate of curvature,and change rate of curvature is the key factor whether the jerk exceeds the limit.(4) For the purpose that avoiding the design error,the 3D design method should be introduced to the design of the high speed railway and the super-high speed railway.
Research purposes:For the purpose that avoiding the design error caused by design method of traditional two-dimension(2D),and ascertaining the influence of the three-dimension railway alignment on the motion of high-speed train,the system of design parameters of three-dimension(3D) railway alignment and the 3D motion model of the train is established by the differential geometric invariants(curvature,torsion and Frenet frame) in this paper.And then,the influence of the parameters of 3D alignment on the trend of the railway alignment and the characteristics of the train motion is analyzed.Research conclusions:(1) The trend and shape of any railway alignment could be expressed by curvature,torsion and Frenet frame,the motion model of the train based on these parameters could accurately reflect the motion state of the train.(2) The method of 2D design is prone to design error and hard to accurately evaluate the motion state of the train.(3) The parameters of alignment play a dominant role in acceleration and jerk of the trains,in which curvature determines the value of acceleration,but the horizontal and vertical acceleration is controlled by roll angle of Frenet frame as well;the jerk is produced by the torsion and change rate of curvature,and change rate of curvature is the key factor whether the jerk exceeds the limit.(4) For the purpose that avoiding the design error,the 3D design method should be introduced to the design of the high speed railway and the super-high speed railway.
引文
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[6]练松良,陈松林,李向国.客运专线竖曲线与平面曲线重叠的试验验证[J].铁道学报,2005(2):75-79.Lian Songliang,Chen Songlin,Li Xiangguo.Test of Vertical Carve Overlapping Plane Curve for Dedicated Passenger Traffic Railway Line[J].Journal of the China Railway Society,2005(2):75-79.
[7]胡建平.300~350 km/h客运专线平竖曲线重叠设置对舒适度影响[J].高速铁路技术,2010(2):34-43.Hu Jianping.Vertical and Horizontal Curve Overlap Influence on Riding Comfort[J].High Speed Railway Technology,2010(2):34-43.
[8]魏庆朝.铁路线路设计[M].北京:中国铁道出版社,2016:257-258.Wei Qingchao.Railway Line Design[M].Beijing:China Railway Publishing House,2016:257-258.
[9]李运胜.高速环道几何线形的运动学评价[J].中国公路学报,2002(3):23-27,32.Li Yunsheng.Kinematics Appraisal on the Geometric Route of High-speed Loop[J].China Journal of Highway and Transport,2002(3):23-27,32.
[2]Kuhn W.Methodology for Checking Shortcomings in the Three-Dimensional Alignment[J].Transportation Research Record:Journal of the Transportation Research Board,2011(1):13-21.
[3]Jha M.K.,Kumar G.A.,Kuhn W.ThreeDimensional Highway Design Methodologies Based on Piecewise Polynomials and Integral Bezier Splines[C]//TRB 92nd Annual Meeting,Transportation Research Record,2013.
[4]葛婷,符锌砂,李海峰,等.公路空间几何特性对汽车运动影响[J].同济大学学报:自然科学版,2016(12):1867-1872.Ge Ting,Fu Xinsha,Li Haifeng,etc.Influence of Spatial Geometric Properties of Highway Alignments on Vehicle Kinematics[J].Joural of Tongji University:Natural Science,2016(12):1867-1872.
[5]Long X.Y.,Wei Q.C.,Jin S.,etc.Simulation and Analysis of High-Speed Train Running Quality Affected by Route Alignment Condition[C]//International Conference on Intelligent Computation Technology and Automation.IEEE Computer Society,2008:708-712.
[6]练松良,陈松林,李向国.客运专线竖曲线与平面曲线重叠的试验验证[J].铁道学报,2005(2):75-79.Lian Songliang,Chen Songlin,Li Xiangguo.Test of Vertical Carve Overlapping Plane Curve for Dedicated Passenger Traffic Railway Line[J].Journal of the China Railway Society,2005(2):75-79.
[7]胡建平.300~350 km/h客运专线平竖曲线重叠设置对舒适度影响[J].高速铁路技术,2010(2):34-43.Hu Jianping.Vertical and Horizontal Curve Overlap Influence on Riding Comfort[J].High Speed Railway Technology,2010(2):34-43.
[8]魏庆朝.铁路线路设计[M].北京:中国铁道出版社,2016:257-258.Wei Qingchao.Railway Line Design[M].Beijing:China Railway Publishing House,2016:257-258.
[9]李运胜.高速环道几何线形的运动学评价[J].中国公路学报,2002(3):23-27,32.Li Yunsheng.Kinematics Appraisal on the Geometric Route of High-speed Loop[J].China Journal of Highway and Transport,2002(3):23-27,32.