基于能量法的高速铁路无砟轨道钢轨碎弯研究
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摘要
研究目的:在温度力作用下高速铁路无砟轨道钢轨产生碎弯变形,严重影响行车平稳性、舒适性和安全性。本文将扣件分别假定为连续弹性介质和等间距弹性支座,建立无砟轨道钢轨碎弯分析模型,采用能量法推导相关计算公式,研究扣件刚度与钢轨碎弯波形的关系、碎弯临界温度力、扣件刚度视为连续弹性介质的精度以及为最大限度提高长钢轨稳定性的扣件极限刚度等问题。研究结论:(1)随着钢轨碎弯波长的增加,其临界温度力基本不变,差值不超过1%,但碎弯半波数有了很大的增加,这从理论上解释了碎弯变化的过程,并且有碎弯的长钢轨始终处于不稳定平衡状态;(2)钢轨碎弯存在最不利半波数,并对应最低载荷,主波总波长取10倍扣件间距时,得到主波最不利半波数为5,最低临界温度力为1. 021 5×10~7N;(3)随着扣件刚度的增加,碎弯半波数有所增加,临界温度也升高;随着扣件间距的增加,碎弯半波数也增加,基础模量减小;(4)通过对比分析扣件假定为连续弹性介质和等间距弹性支座计算钢轨碎弯临界温度力,得出当每个半波内有不少于3个扣件时,扣件假定为连续弹性介质能够满足工程精度要求,并且随着半波中扣件数量的增加或者总波长的增加,两者数值更加接近;(5)当半波变形波长为支座间距时钢轨碎弯临界温度力可得最大值,并且随着主波扣件跨数的增加,扣件极限刚度收敛于确定值1. 010 2×10~6N/cm;(6)本研究成果可为高速铁路无砟轨道钢轨碎弯提供理论参考,并可为高速铁路扣件参数的检算及合理性提供计算依据。
Research purposes: The rails of ballastless track of high-speed railway will produce continuous bending deformation under temperature force,which seriously affects the running stability,comfort and safety. In this paper,the fasteners are assumed to be continuous elastic medium and equal interval elastic support respectively. The analysis model of the rail continuous bending of the ballastless track is established,and the relevant calculation formula is derived by energy method. Problems such as the relationship between the fastener stiffness and the bending curve of the rail,the critical temperature force of the continuous bending,the precision of the fastener stiffness when regarded as continuous elastic medium,and the ultimate fastener stiffness to furthest improve the stability of the long rail are studied.Research conclusions:(1) As the wavelength of the rail continuous bending increases,the critical temperature force is basically constant,and the difference does not exceed 1%,but the half-wave number of the continuous bending has greatly increased. This result theoretically explains the process of the continuous bending,and the long rails with them are always in an unstable equilibrium state.(2) The most unfavorable half-wave number exists in rail continuous bending,which corresponds to the lowest load. When the total wavelength of the main wave is 10 times the fastener spacing,the most unfavorable half-wave number of the main wave is 5,and the lowest critical temperature force is 1. 021 5 × 10~7 N.(3) With the increase of fastener stiffness,the half-wave number of continuous bending and the critical temperature increases. With the increase of the fastener spacing,the half-wave number of continuous bending also increases,and the foundation modulus decreases.(4) By calculating the critical temperature force of the rail continuous bending through the method comparing the fastener assumption of continuous elastic medium and equal interval elastic support,it is concluded that when there are no less than 3 fasteners in each half wave,the fastener which is assumed to continuous elastic medium can meet the engineering accuracy requirements,and the values are closer as the number of fasteners in the half wave or the total wavelength increases.(5) When the half-wave deformation wavelength is equal to the support spacing,the critical temperature force of the rail continuous bending can be maximized,and as the number of spans of the main wave fasteners increases,the ultimate fastener stiffness converges to the determined value 1. 010 2 × 10~6 N/cm.(6) The research results can provide theoretical reference for the rail continuous bending of ballastless track of high-speed railway,and provide calculation basis for the check-calculation and rationality of fastener parameters of high-speed railway.
Research purposes: The rails of ballastless track of high-speed railway will produce continuous bending deformation under temperature force,which seriously affects the running stability,comfort and safety. In this paper,the fasteners are assumed to be continuous elastic medium and equal interval elastic support respectively. The analysis model of the rail continuous bending of the ballastless track is established,and the relevant calculation formula is derived by energy method. Problems such as the relationship between the fastener stiffness and the bending curve of the rail,the critical temperature force of the continuous bending,the precision of the fastener stiffness when regarded as continuous elastic medium,and the ultimate fastener stiffness to furthest improve the stability of the long rail are studied.Research conclusions:(1) As the wavelength of the rail continuous bending increases,the critical temperature force is basically constant,and the difference does not exceed 1%,but the half-wave number of the continuous bending has greatly increased. This result theoretically explains the process of the continuous bending,and the long rails with them are always in an unstable equilibrium state.(2) The most unfavorable half-wave number exists in rail continuous bending,which corresponds to the lowest load. When the total wavelength of the main wave is 10 times the fastener spacing,the most unfavorable half-wave number of the main wave is 5,and the lowest critical temperature force is 1. 021 5 × 10~7 N.(3) With the increase of fastener stiffness,the half-wave number of continuous bending and the critical temperature increases. With the increase of the fastener spacing,the half-wave number of continuous bending also increases,and the foundation modulus decreases.(4) By calculating the critical temperature force of the rail continuous bending through the method comparing the fastener assumption of continuous elastic medium and equal interval elastic support,it is concluded that when there are no less than 3 fasteners in each half wave,the fastener which is assumed to continuous elastic medium can meet the engineering accuracy requirements,and the values are closer as the number of fasteners in the half wave or the total wavelength increases.(5) When the half-wave deformation wavelength is equal to the support spacing,the critical temperature force of the rail continuous bending can be maximized,and as the number of spans of the main wave fasteners increases,the ultimate fastener stiffness converges to the determined value 1. 010 2 × 10~6 N/cm.(6) The research results can provide theoretical reference for the rail continuous bending of ballastless track of high-speed railway,and provide calculation basis for the check-calculation and rationality of fastener parameters of high-speed railway.
引文
[1]中国铁道科学研究院.遂渝线无砟轨道试验段钢轨碎弯现象及对策[R].北京:中国铁道科学研究院,2007.China Academy of Railway Sciences. The Phenomenon and Countermeasure of Rail Continuous Bending on the Suizhou-Chongqing Railway Ballastless Track Test Section[R]. Beijing:China Academy of Railway Sciences,2007.
[2]饶惠明.高速铁路桥隧过渡段钢轨温度和横向变形试验[J].铁道科学与工程学报,2017(9):1838-1844.Rao Huiming. Experiment on Temperature and Lateral Deformation of Rail at the Transition between Bridges and Tunnels for High-speed Railway[J]. Journal of Railway Science and Engineering,2017(9):1838-1844.
[3]卢耀荣.无缝线路研究与应用[M].北京:中国铁道出版社,2010.Lu Yaorong. Research and Application of Continuous Welded Rail[M]. Beijing:China Railway Publishing House,2010.
[4]肖杰灵,郭利康,刘学毅.无砟轨道钢轨碎弯成因分析[J].铁道建筑,2009(2):93-96.Xiao Jieling, Guo Likang, Liu Xueyi. Analysis on Causes of Rail Continuous Bending Deformation on Ballastless Track[J]. Railway Engineering,2009(2):93-96.
[5]赵国堂.高速铁路无碴轨道结构[M].北京:中国铁道出版社,2006.Zhao Guotang. Ballastless Track Structure of Highspeed Railway[M]. Beijing:China Railway Publishing House,2006.
[6]张向民.青藏铁路多年冻土区无缝线路稳定性理论及其试验研究[D].北京:北京交通大学,2016.Zhang Xiangmin. Theoretical and Experimental Research on the Stability CWR in Permafrost Area of Qinghai-Tibet Railway[D]. Beijing:Beijing Jiaotong University,2016.
[7]张向民,赵磊.高速铁路CRTSⅡ型板式无砟轨道稳定性理论研究[J].铁道工程学报,2018(1):49-55.Zhang Xiangmin,Zhao Lei. Research on the Stability Theory of CRTSⅡSlab Ballastless Track on Highspeed Railway[J]. Journal of Railway Engineering Society,2018(1):49-55.
[8] S. P.铁摩辛柯,J. M.盖莱.弹性稳定理论[M].张福范,译.北京:科学出版社,1965.S. P. Timoshenko,J. M. Gere. Theory of Elastic Stability[M]. Trans. Zhang Fufan. Beijing:Science Press,1965.
[2]饶惠明.高速铁路桥隧过渡段钢轨温度和横向变形试验[J].铁道科学与工程学报,2017(9):1838-1844.Rao Huiming. Experiment on Temperature and Lateral Deformation of Rail at the Transition between Bridges and Tunnels for High-speed Railway[J]. Journal of Railway Science and Engineering,2017(9):1838-1844.
[3]卢耀荣.无缝线路研究与应用[M].北京:中国铁道出版社,2010.Lu Yaorong. Research and Application of Continuous Welded Rail[M]. Beijing:China Railway Publishing House,2010.
[4]肖杰灵,郭利康,刘学毅.无砟轨道钢轨碎弯成因分析[J].铁道建筑,2009(2):93-96.Xiao Jieling, Guo Likang, Liu Xueyi. Analysis on Causes of Rail Continuous Bending Deformation on Ballastless Track[J]. Railway Engineering,2009(2):93-96.
[5]赵国堂.高速铁路无碴轨道结构[M].北京:中国铁道出版社,2006.Zhao Guotang. Ballastless Track Structure of Highspeed Railway[M]. Beijing:China Railway Publishing House,2006.
[6]张向民.青藏铁路多年冻土区无缝线路稳定性理论及其试验研究[D].北京:北京交通大学,2016.Zhang Xiangmin. Theoretical and Experimental Research on the Stability CWR in Permafrost Area of Qinghai-Tibet Railway[D]. Beijing:Beijing Jiaotong University,2016.
[7]张向民,赵磊.高速铁路CRTSⅡ型板式无砟轨道稳定性理论研究[J].铁道工程学报,2018(1):49-55.Zhang Xiangmin,Zhao Lei. Research on the Stability Theory of CRTSⅡSlab Ballastless Track on Highspeed Railway[J]. Journal of Railway Engineering Society,2018(1):49-55.
[8] S. P.铁摩辛柯,J. M.盖莱.弹性稳定理论[M].张福范,译.北京:科学出版社,1965.S. P. Timoshenko,J. M. Gere. Theory of Elastic Stability[M]. Trans. Zhang Fufan. Beijing:Science Press,1965.