车桥耦合振动系统中车辆的走行性分析
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摘要
近年来,随着铁路提速、客运专线、高速铁路的修建,列车运行安全性与舒适性问题日趋突出,也越来越受到人们的关注。列车的安全和旅客的舒适度都和桥上的车辆与轨道的相互作用有关。就轮轨系统运输而言,由于列车与轨道的相互作用,势必会引起轨道几何形位的不断变化。这种变化即轨道不平顺,反过来又会影响列车快速行驶的舒适性和安全性。所以,有必要对轨道不平顺作用下的桥上列车的走行性进行研究。
本文采用车桥大系统空间耦合模型,在此模型的基础上分别建立31自由度车辆运动方程和桥梁结构的有限元动力学方程,进而建立车桥耦合振动方程。系统激励采用轨道不平顺,可根据研究的具体情况输入轨道不平顺。
编制了轨道不平顺模拟计算程序和车辆运行安全和平稳性评价体系程序。轨道不平顺模拟计算程序考虑周期不平顺、随机不平顺和自定义不平顺三种类型,随机不平顺的模拟考虑到德国、美国和中国三国的轨道不平顺功率谱,其模拟方法考虑三角级数法和频域法两种,并能根据任意时间步长,用线性插值生成实际状态下的不平顺具体值。车辆运行安全性和平稳性评价体系程序中的安全性方面考虑脱轨系数、轮重减载率和横向力三个指标,平稳性方面考虑车体加速度指标和旅客乘坐舒适度指标,并且对同一指标的评价考虑到现行的几种规范。
利用编制的程序,以轨道高低不平顺为例,模拟方法采用频域法,模拟计算分析了几种典型不平顺功率谱的平顺性。计算结果表明,德国的低干扰轨道谱、我国三大干线轨道谱、德国高干扰轨道谱与美国6级轨道谱的轨道不平顺幅值依次增加。以中国高低不平顺为例比较了两种模拟方法,结果显示两种方法模拟得到的不平顺幅值范围基本一致。
以脱轨系数、轮重减载率、横向力、车体的振动加速度、Janeway平稳性等级和Sperling舒适度指标作为管理标准,分别评价了轨道不平顺和行车速度对车辆运行安全性和旅客乘坐舒适度的影响。研究结果表明,随着轨道不平顺性的增加和行车速度的提高,列车的运行安全性降低,旅客的乘坐舒适度变差,并且车速对脱轨系数和横向力的影响比较显著,而车速对车体的横向振动加速度的影响较竖向振动加速度大。
In recent years, with improving of the vehicle speed and the construction of high-speed railway and passenger-only lanes, the problems on safety and comfort of train are becoming more and more prominent, so there is a growing concern about this issue. The running security and comfort of all passengers have a lot to do with the interaction between vehicle and track on the bridge. In the wheel-rail system, because of the interaction between the train and the track the Geometric shape and position of track will change. The change is the track irregularity, which in turn would affect the train running safety and comfort. Therefore, it is necessary to study the dynamic response of the train which is running on the bridge with the track irregularity.
In this paper, the space vehicle-bridge coupled model system is used, and on the basis of this model the vehicle’s dynamic formula and bridge’s finite elemental dynamic formula are set up, the vehicle’s model has thirty-one DOFs, Then, we set up the coupling vibration equation of vehicle-bridge. Track irregularity as incentive of the system can be used based on the specific circumstances of each case.
Two computing programs have been developed, one can simulate and calculate track irregularity and another can calculate the dynamic response of the train and evaluate the security and comfort according to the standards. In the Track irregularity simulation procedures cycle irregularity, random irregularity and user-defined irregularity were considered. For the track irregularity spectrum of random irregularity, we take into account Germany, the United States and Chinese, the trigonometric series method and frequency-domain method were regarded as simulation methods. Based on arbitrary time step, the specific value of irregularity can be generated with linear interpolation method. In the evaluation process, the common evaluating parameters of security and comfort are derailment coefficient, the rate of wheel load reduction, horizontal force, vibrating acceleration, comfortable value and sperling value, and for the same indicators evaluation, several existing standards were taken into account.
Taking the track vertical profile irregularity as an illustration with frequency-domain method, several typical power spectrums were simulated and calculated. The results show that the track irregularity amplitude of Germany's Low disturbance track spectrum, Chinese track spectrum of the three main railways, Germany's Low disturbance track spectrum and the United States’six track spectrum is increasing in turn. Taking Chinese track vertical profile irregularity as an illustration compared the two kinds of simulation. The results showed that two values are basically the same amplitude range.
The derailment coefficient, rate of wheel load reduction, horizontal force, vibrating acceleration, comfortable value and sperling value were considered as management standards, the impact of track irregularity and traveling speed on the security and comfort have been evaluated. The results show that, with the increasing of track irregularity and the improving of running speed, the vehicle’s security will become lower and the comfortable feeling will become worse. Traveling speed has a significant impact on the derailment coefficient and lateral force, and has greater impact on lateral vibration acceleration than vertical vibration acceleration of the body.
本文采用车桥大系统空间耦合模型,在此模型的基础上分别建立31自由度车辆运动方程和桥梁结构的有限元动力学方程,进而建立车桥耦合振动方程。系统激励采用轨道不平顺,可根据研究的具体情况输入轨道不平顺。
编制了轨道不平顺模拟计算程序和车辆运行安全和平稳性评价体系程序。轨道不平顺模拟计算程序考虑周期不平顺、随机不平顺和自定义不平顺三种类型,随机不平顺的模拟考虑到德国、美国和中国三国的轨道不平顺功率谱,其模拟方法考虑三角级数法和频域法两种,并能根据任意时间步长,用线性插值生成实际状态下的不平顺具体值。车辆运行安全性和平稳性评价体系程序中的安全性方面考虑脱轨系数、轮重减载率和横向力三个指标,平稳性方面考虑车体加速度指标和旅客乘坐舒适度指标,并且对同一指标的评价考虑到现行的几种规范。
利用编制的程序,以轨道高低不平顺为例,模拟方法采用频域法,模拟计算分析了几种典型不平顺功率谱的平顺性。计算结果表明,德国的低干扰轨道谱、我国三大干线轨道谱、德国高干扰轨道谱与美国6级轨道谱的轨道不平顺幅值依次增加。以中国高低不平顺为例比较了两种模拟方法,结果显示两种方法模拟得到的不平顺幅值范围基本一致。
以脱轨系数、轮重减载率、横向力、车体的振动加速度、Janeway平稳性等级和Sperling舒适度指标作为管理标准,分别评价了轨道不平顺和行车速度对车辆运行安全性和旅客乘坐舒适度的影响。研究结果表明,随着轨道不平顺性的增加和行车速度的提高,列车的运行安全性降低,旅客的乘坐舒适度变差,并且车速对脱轨系数和横向力的影响比较显著,而车速对车体的横向振动加速度的影响较竖向振动加速度大。
In recent years, with improving of the vehicle speed and the construction of high-speed railway and passenger-only lanes, the problems on safety and comfort of train are becoming more and more prominent, so there is a growing concern about this issue. The running security and comfort of all passengers have a lot to do with the interaction between vehicle and track on the bridge. In the wheel-rail system, because of the interaction between the train and the track the Geometric shape and position of track will change. The change is the track irregularity, which in turn would affect the train running safety and comfort. Therefore, it is necessary to study the dynamic response of the train which is running on the bridge with the track irregularity.
In this paper, the space vehicle-bridge coupled model system is used, and on the basis of this model the vehicle’s dynamic formula and bridge’s finite elemental dynamic formula are set up, the vehicle’s model has thirty-one DOFs, Then, we set up the coupling vibration equation of vehicle-bridge. Track irregularity as incentive of the system can be used based on the specific circumstances of each case.
Two computing programs have been developed, one can simulate and calculate track irregularity and another can calculate the dynamic response of the train and evaluate the security and comfort according to the standards. In the Track irregularity simulation procedures cycle irregularity, random irregularity and user-defined irregularity were considered. For the track irregularity spectrum of random irregularity, we take into account Germany, the United States and Chinese, the trigonometric series method and frequency-domain method were regarded as simulation methods. Based on arbitrary time step, the specific value of irregularity can be generated with linear interpolation method. In the evaluation process, the common evaluating parameters of security and comfort are derailment coefficient, the rate of wheel load reduction, horizontal force, vibrating acceleration, comfortable value and sperling value, and for the same indicators evaluation, several existing standards were taken into account.
Taking the track vertical profile irregularity as an illustration with frequency-domain method, several typical power spectrums were simulated and calculated. The results show that the track irregularity amplitude of Germany's Low disturbance track spectrum, Chinese track spectrum of the three main railways, Germany's Low disturbance track spectrum and the United States’six track spectrum is increasing in turn. Taking Chinese track vertical profile irregularity as an illustration compared the two kinds of simulation. The results showed that two values are basically the same amplitude range.
The derailment coefficient, rate of wheel load reduction, horizontal force, vibrating acceleration, comfortable value and sperling value were considered as management standards, the impact of track irregularity and traveling speed on the security and comfort have been evaluated. The results show that, with the increasing of track irregularity and the improving of running speed, the vehicle’s security will become lower and the comfortable feeling will become worse. Traveling speed has a significant impact on the derailment coefficient and lateral force, and has greater impact on lateral vibration acceleration than vertical vibration acceleration of the body.
引文
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[2]铁木辛柯,工程中的振动问题(胡人礼译),北京:人民铁道出版社,1987
[3]Stokes G.. G..,Discussion of a differential equation relating to the breaking of railway bridge,Transactions of the Cambridge Philosophical Society,Part 5(85),1849
[4]Inglis G E,A Mathematical Treatise on Vibrations in Railway Bridge,London:Cambridge,1934
[5]夏禾,张楠,车辆与结构动力相互作用(第二版),北京:科学出版社,2005
[6]李国豪,桥梁结构稳定与与振动,北京:中国铁道出版社,1996
[7]曹雪琴,列车通过时桥梁结构竖向振动分析,上海铁道学院学报,1981,2(3):1～15
[8]曹雪琴,钢桁梁桥横向振动,北京:中国铁道出版社,1991
[9]曹雪琴,陈晓,轮轨蛇行引起桥梁横向振动随机分析,铁道学报,1986,8(1):89～97
[10]曹雪琴,刘必胜,吴鹏贤,桥梁结构动力分析,北京:中国铁道出版社,1987
[11]曹雪琴,顾萍,沪宁线限速钢梁桥提速试验与分析,上海铁道科技,2000,3:14～16
[12]曹雪琴等,列车过桥箱型钢梁空间振动分析,上海铁道学院学报,1982,3(3):17~35
[13]李小珍,高速铁路列车-桥梁系统耦合振动理论及应用研究,博士学位论文,成都:西南交通大学,2000
[14]沈锐利,高速铁路桥梁与车辆耦合振动研究,成都:西南交通大学,1998
[15]夏禾、陈英俊,车梁墩体系相互作用分析,土木工程学报,1992,25(2):3~12
[16]夏禾等,铁路斜拉桥的地震响应分析,北方交通大学学报,1995,19(2):137~142
[17]程庆国,许慰平,大跨度铁路斜拉桥列车走行性探讨,全国桥梁结构学术大会论文集,武汉,1992,41~51
[18]程庆国,潘家英,大跨度铁路斜拉桥刚度分析,全国桥梁结构学术大会论文集,武汉,1992,1163~1168
[19]曾庆元,弹性系统动力学总势能不变值原理,华中理工大学学报,1991,9(3):1~15
[20]曾庆元,郭向荣,列车桥梁时变系统振动分析理论及应用,北京:中国铁道出版社,1999
[21]曾庆元等,列车-桥梁时变系统横向振动分析,铁道学报,1991,13(2):38~46
[22]罗林等,我国干线轨道不平顺功率谱的研究.北京:铁科院研究报告,2000,
[23]胡津亚,曾三元编著.现代随机振动.北京:中国铁道出版社,1989
[25]王天胜.林红移动荷载作用下的轨道-地基系统的动力响应,武汉理工大学学报,2001
[26]夏禾,张楠,车辆与结构动力相互作用(第二版),北京:科学出版社,2005,18~20
[27]松本阳,车辆脱轨、颠覆的机理及其安全性研究,国外铁道车辆,2006,43(5):6～9
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