货物列车编组对列车-桥梁系统空间振动的影响
向 俊,孔凡兵,曾庆元
(中南大学 土木建筑学院,湖南 长沙,410075)
摘 要:基于列车、桥梁空间振动分析模型,利用弹性系统动力学总势能不变值原理及形成系统矩阵的“对号入座”法则,建立了列车-桥梁系统空间振动矩阵方程,采用Wilson-θ法求解。研究了5种不同货物列车编组对列车-桥梁系统空间振动响应的影响,得出了一些符合物理概念的桥梁振动响应时程曲线。研究结果表明:机车、车辆轴重是影响桥梁竖向振动位移的主因;空载货车作用下的车桥系统横向振动响应比重车的要大;全列空车编组及空重混编是影响列车-桥梁系统横向振动响应的不利编组,而全列空车编组更为不利;在进行桥上货物列车脱轨分析时,宜采用全列空车编组;通过改善列车编组的方法可以提高列车-桥梁系统振动性能。
关键词:桥梁;货物列车;全列空车编组;全列重车编组;空重车混编组;振动
中图分类号:U446 文献标识码:A 文章编号:1672-7207(2007)02-0345-06
Influence of freight train formation on spatial vibration of train-bridge system
XIANG Jun, KONG Fan-bing, ZENG Qing-yuan
(School of Civil and Architectural Engineering, Central South University, Changsha 410075, China)
Abstract: Based on the spatial vibration analysis models of train and bridge, the spatial vibration matrix equation of the train-bridge system was established by the principle of total potential energy stationary value in elastic system dynamics and the rule of “set-in-right-position” in formulating system matrix. The matrix equation of the system was solved by the Wilson-θ method. The influence of five different freight train formations on the spatial vibration responses of the train-bridge system was studied. Some history curves of the bridge vibration response were also obtained, which are agreement with the physics concepts. The results show that the axle load of locomotive and car is the primary matter affecting the vertical bridge displacement. The transverse vibration responses of the train-bridge system are larger under the action of empty cars than those of loaded cars. Both the full empty car formation and mixed empty and loaded car formation are the disadvantage formation, which affects the vibration responses of the train-bridge system, and the full empty car formation is the worst. When analysis of train derailment on bridge is made, the full empty car formation should be applied. The vibration performance of train-bridge system can be improved by reforming the train formation.
Key words: bridge; freight train; full empty car formation; full loaded car formation; mixed empty and loaded car formation; vibration
在通常情况下,货物列车过桥引起桥梁的振动要比客车过桥更加剧烈。列车提速以后,人们还注意到这样一种现象,即同样是货物列车过桥,全列空车及空重混编列车过桥引起桥梁振动往往比全部重车编组列车过桥引起的震动大;而且提速运营后,几次列车过桥脱轨事故,基本上都是在全列空车及空重混编列车中的空车上发生[1-4]。因此,对上述现象进行理论分析很有意义。
目前,有关不同列车编组对车-桥系统振动影响的研究很少。吴定俊[1]分析了轻重混编货物列车作用下的车桥动力响应;赵治冶等[2-3]从试验角度就列车编组对车桥系统振动的影响进行了分析;向俊等[5-8]在进行货物列车脱轨分析中,所采用的列车不利编组形式为全列空车编组,但其根据也只是来源于一些实验结果,缺乏理论依据;朱金龙等[9]认为轻重混编列车过桥引起桥梁有载频率变化与轮对蛇行运动频率吻合引起剧烈振动;向俊等[10]研究了轻重混编列车过桥的脱轨机理;肖艳平等[11]对不同客车编组作用下桥梁竖向振动和车体竖向加速度进行了研究。但目前人们对不同列车编组过桥时车桥系统振动响应的变化规律未完全了解,在此,本文作者以京山线(北京至山海关)下行线滦河老桥为例,研究货物列车编组对车-桥系统振动响应的影响规律,在此基础上,进一步得出进行桥上货物列车脱轨分析的最不利编组形式。
1 计算原理
1.1 列车空间振动模型
将货物列车中的机车及所有车辆统一表示成26个自由度位移模式的多刚体系统模型[12],并采用如下一些基本假定:
a. 车体、转向架和轮对被认为是绝对刚体。
b. 车体、转向架和轮对沿桥梁方向作匀速运动,即不考虑纵向振动的影响。
c. 车体、转向架和轮对前后、左右对称。
有了上述位移模式,就可以导出列车空间振动总势能式
。
1.2 桥梁空间振动模型
滦河老桥为上承式钢板梁桥[13],其主梁由两片工字型截面的板梁组成,主梁按空间梁段有限元计算,主梁单元横截面的空间振动位移模式为横向位移,左、右腹板竖向位移及绕扭心的转角位移。有了单元位移模式,就可推导桥梁结构空间振动总势能
。
1.3 车桥系统空间振动方程的建立及求解
列车过桥时,设在t时刻有n辆车在桥上,则桥上列车空间振动总势能为
![](/web/fileinfo/upload/magazine/82/2787/image003.jpg)
桥梁结构空间振动的势能为
,则在t时刻,车桥系统空间振动的总势能为
![](/web/fileinfo/upload/magazine/82/2787/image004.jpg)
由弹性系统动力学总势能不变值原理[14]及形成系统矩阵的“对号入座”法则[15],可直接形成t时刻车桥系统空间振动的总体质量矩阵[M]、总体阻尼矩阵[C]、总体刚度矩阵[K]及荷载列阵{P},从而,得出t时刻车桥系统空间振动的矩阵方程如下:
![](/web/fileinfo/upload/magazine/82/2787/image005.jpg)
2 计算结果及分析
2.1 货物列车编组工况
考虑如下5种主要编组工况的货物列车分别以60 km/h速度在滦河老桥上的走行情况。
工况一:全列空车(1台DF4型内燃机车+19辆空载货车);
工况二:全列重车(1台DF4型内燃机车+19辆重载货车);
工况三:空重混编(1台DF4型内燃机车+13辆空载货车+6辆重载货车);
工况四:空重混编(1台DF4型内燃机车+13辆重载货车+6辆空载货车);
工况五:空重混编(1台DF4型内燃机车+5辆重载货车+8辆空载货车+6辆重载货车)。
2.2 计算结果及其分析
分别计算了上述5种编组货物列车以60 km/h速度通过滦河老桥(考虑15跨)时的车桥系统空间振动响应。5种工况下的桥梁跨中竖向振动位移时程曲线分别如图1~5所示,桥梁跨中横向振动位移时程曲线分别如图6~10所示,桥梁跨中横向振动位移及加速度计算最大值如表1所示,机车及车辆振动响应计算最大值如表2所示。
表1 不同编组货物列车作用下桥梁振动响应计算最大值的比较
Table 1 Comparison of calculated maximum values of
bridge vibration response under action of freight trains with various formations
![](/web/fileinfo/upload/magazine/82/2787/image006.jpg)
表2 不同编组货物列车振动响应计算最大值的比较
Table 2 Comparison of the calculated maximum values of vibration response of freight train with various formation
![](/web/fileinfo/upload/magazine/82/2787/image008.jpg)
由图1~10可见,空车作用下的桥梁竖向振动位移比机车及重车的小得多,机车及重车作用下的桥梁竖向振动位移接近,这是因为空车轴重比机车及重车轴重小得多,而机车及重车的轴重比较接近。所以,机车、车辆轴重是影响桥梁竖向振动位移的主因。
![](/web/fileinfo/upload/magazine/82/2787/image010.jpg)
图1 桥梁第10跨跨中竖向位移时程曲线(工况一)
Fig.1 Time history curve of vertical displacement at middle point in 10th span of bridge under No.1 condition
![](/web/fileinfo/upload/magazine/82/2787/image012.jpg)
图2 桥梁第10跨跨中竖向位移时程曲线(工况二)
Fig. 2 Time history curve of vertical displacement at middle point in 10th span of bridge under No.2 condition
![](/web/fileinfo/upload/magazine/82/2787/image014.jpg)
图3 桥梁第10跨跨中竖向位移时程曲线(工况三)
Fig.3 Time history curve of vertical displacement at middle point in 10th span of bridge under No.3 condition
![](/web/fileinfo/upload/magazine/82/2787/image016.jpg)
图4 桥梁第10跨跨中竖向位移时程曲线(工况四)
Fig. 4 Time history curve of vertical displacement at middle point in 10th span of bridge under No.4 condition
![](/web/fileinfo/upload/magazine/82/2787/image018.jpg)
图5 桥梁第10跨跨中竖向位移时程曲线(工况五)
Fig. 5 Time history curve of vertical displacement at middle point in 10th span of bridge under No.5 condition
![](/web/fileinfo/upload/magazine/82/2787/image020.jpg)
图6 桥梁第10跨跨中横向位移时程曲线(工况一)
Fig.6 Time history curve of transverse displacement at middle point in 10th span of bridge under No.1 condition
![](/web/fileinfo/upload/magazine/82/2787/image022.jpg)
图7 桥梁第10跨跨中横向位移时程曲线(工况二)
Fig.7 Time history curve of transverse displacement at middle point in 10th span of bridge under No.2 condition
![](/web/fileinfo/upload/magazine/82/2787/image024.jpg)
图8 桥梁第10跨跨中横向位移时程曲线(工况三)
Fig.8 Time history curve of transverse displacement at middle point in 10th span of bridge under No.3 condition
![](/web/fileinfo/upload/magazine/82/2787/image026.jpg)
图9 桥梁第10跨跨中横向位移时程曲线(工况四)
Fig.9 Time history curve of transverse displacement at middle point in 10th span of bridge under No.4 condition
![](/web/fileinfo/upload/magazine/82/2787/image028.jpg)
图10 桥梁第10跨跨中横向位移时程曲线(工况五)
Fig.10 Time history curve of transverse displacement at middle point in 10th span of bridge under No.5 condition
由表1可见,在全列空车(工况一)作用下,桥梁跨中横向位移及横向加速度都最大;在空重混编(工况三、工况四、工况五)作用下,桥梁跨中横向位移及横向加速度均次之;在全列重车(工况二)作用下,桥梁跨中横向位移及横向加速度均最小。
由表2可见,在全列空车(工况一)作用下,机车、车辆振动响应,如脱轨系数、轮重减载率、心盘横向加速度、机车横向舒适性指标、车辆横向平稳性指标等都最大;在空重混编(工况三、工况四、工况五)作用下,机车、车辆振动响应,如脱轨系数、轮重减载率、心盘横向加速度、机车横向舒适性指标、车辆横向平稳性指标等均次之;在全列重车(工况二)作用下,机车、车辆振动响应,如脱轨系数、轮重减载率、心盘横向加速度、机车横向舒适性指标、车辆横向平稳性指标等均最小。此外,从图6~10中可以看出,在3种空重混编(工况三、工况四、工况五)条件下,空车作用下的桥梁跨中横向振动位移比相同编组的机车及重车作用下的要大。
综上所述,机车、车辆轴重是影响桥梁竖向振动位移的主因。全列空车编组及空重混编是影响车-桥系统横向振动响应的不利编组,而全列空车编组更为不利。这就从理论上反映了列车提速以后出现的一种现象:即同样是货物列车过桥,全列空车及空重混编列车过桥引起的桥梁振动往往比全部重车编组列车过桥引起的桥梁振动要大。
3 结 论
a. 桥梁竖向振动位移主要由机车、车辆的轴重引起。
b. 全列空车编组及空重混编是影响列车-桥梁系统横向振动响应的不利编组,而全列空车编组更为不利;在进行桥上货物列车脱轨分析时,宜采用全列空车编组。
c. 同一空重混编货物列车中,空载货车作用下的车桥系统横向振动响应比重车的要大。
d.在提速状态下解决桥梁横向晃动急剧的主要方法是对桥梁进行加固,以提高桥梁横向刚度,但有时效果不甚明显。
e. 通过改善列车编组的方法可以提高列车-桥梁系统振动性能,达到减小桥梁横向振动的目的。
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收稿日期:2006-10-17
基金项目:国家自然科学基金资助项目(50678176,50078006);高等学校博士点科研基金资助项目(20010533004);铁道部科技研究开发计划项目(2001G029,2003G043)
作者简介:向 俊(1968-),男,湖南沅陵人,副教授,博士,从事车桥(轨)系统振动及列车脱轨研究
通讯作者:向 俊,男,副教授, 博士;电话:0731-2656645;E-mail:jxiang@mail.csu.edu.cn