Influence of some vehicle and track parameters on the environmental vibrations induced by railway traffic

A study is performed on the influence of some typical railway vehicle and track parameters on the level of ground vibrations induced in the neighbourhood. The results are obtained from a previously validated simulation framework considering in a first step the vehicle/track subsystem and, in a second step, the response of the soil to the forces resulting from the first analysis. The vehicle is reduced to a simple vertical 3-dof model, corresponding to the superposition of the wheelset, the bogie and the car body. The rail is modelled as a succession of beam elements elastically supported by the sleepers, lying themselves on a flexible foundation representing the ballast and the subgrade. The connection between the wheels and the rails is realised through a non-linear Hertzian contact. The soil motion is obtained from a finite/infinite element model. The investigated vehicle parameters are its type (urban, high speed, freight, etc.) and its speed. For the track, the rail flexural stiffness, the railpad stiffness, the spacing between sleepers and the rail and sleeper masses are considered. In all cases, the parameter value range is defined from a bibliographic browsing. At the end, the paper proposes a table summarising the influence of each studied parameter on three indicators: the vehicle acceleration, the rail velocity and the soil velocity. It namely turns out that the vehicle has a serious influence on the vibration level and should be considered in prediction models.     

Train–track–bridge dynamic interaction: a state-of-the-art review

ABSTRACT

Train–track–bridge dynamic interaction is a fundamental concern in the field of railway engineering, which plays an extremely important role in the optimal design of railway bridges, especially in high-speed railways and heavy-haul railways. This paper systematically presents a state-of-the-art review of train–track–bridge dynamic interaction. The evolution process of train–bridge dynamic interaction model is described briefly, from the simplest moving constant force model to the sophisticated train–track–bridge dynamic interaction model (TTBDIM). The modelling methodology of the key elements in the TTBDIM is systematically reviewed, including the train, the track, the bridge, the wheel–rail contact, the track–bridge interaction, the system excitation and the solution algorithm. The significance of detailed track modelling in the whole system is highlighted. The experimental research and filed test focusing on modelling validation, safety assessment and long-term performance investigation of the train–track–bridge system are briefly presented. The practical applications of train–track–bridge dynamic interaction theory are comprehensively discussed in terms of the system dynamic performance evaluation, the system safety assessment and train-induced environmental vibration and noise prediction. The guidance is provided on further improvement of the train–track–bridge dynamic interaction model and the challenging research topics in the future.     

城市轨道交通桥梁墩台纵向线刚度限值问题的研究

本文首先阐述了轨道桥梁梁轨相互作用的一些概念、研究现状以及存在的问题,接着对城市轨道交通桥梁墩台最小纵向刚度的限值的制定的依据、演变以及和铁路桥梁一些区别做了分析比较,对公轨合建桥梁中公路车辆制动力对轨道结构的作用机理做了计算与分析,最后对地铁规范中的轨道交通桥梁墩台纵向刚度限值条文合理值提出了看法与建议。     

A structural articulation method for assessing railway bridges subject to dynamic impact loading from track irregularities

This paper discusses the importance of track irregularities in railway bridge design, and presents a new technique for calculating the dynamic impact load induced by such irregularities: the structural articulation method. The properties of the combined bridge-suspension system are coupled through global mass, stiffness, and damping matrices. Under the proposed method, the true suspension system over a particular point on the bridge girder at time t is divided into equivalent suspension systems attributed to adjacent finite-element nodes of the bridge. The time-dependent effects of a moving mass are thereby included in the equation of motion.     

空间缆索自锚式悬索桥动力特性及刚度影响规律

空间缆索自锚式悬索桥的主缆直接锚固在加劲梁上,同时由于主缆的空间特性,与地锚式悬索桥及传统平面索相比,其动力性能存在很大的差异.针对青岛海湾大桥大沽河航道桥建立非线性空间有限元模型,对其动力特性及结构刚度影响规律进行了分析.结果表明,该桥振型基本合理,具有密布的频谱;作为自锚式悬索桥其整体刚度较低,固有周期较长;单柱式桥塔的横向刚度较弱,横向振动出现较早;另外,由于缆索横向间距较小,刚度较小,前10阶振型中有5阶索振.各振型受结构刚度的影响不同,主缆刚度主要影响悬索桥的1阶竖弯及扭转,加劲梁竖向刚度对加劲梁1阶竖弯及加劲梁扭转振型影响较大,横向刚度主要影响悬索桥的加劲梁横向振型,扭转刚度主要影响悬索桥的1阶扭转振型;主塔纵向刚度主要影响悬索桥的纵飘振型;横向刚度主要影响索塔的1阶横向振型.     

Dynamic Train-Track Interaction: Variability Attributable to Scatter in the Track Properties

A numerical method to simulate vertical dynamic interaction between a rolling train and a railway track has been used to investigate the influence of stochastic properties of the track structure. A perturbation technique has been used to investigate the influence of the scatter in selected track properties. The train-track interaction problem has been numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the whole track structure. All numerical simulations have been carried out in the time-domain with a moving mass model. Properties such as rail pad stiffness, ballast stiffness, dynamic ballast-subgrade mass and sleeper spacing have been studied. To obtain sufficient statistical information from track structures, full-scale measurements in the field and laboratory measurements have been carried out. The influence of scatter in the track properties on the maximum contact force between the rail and the wheel, the maximum magnitude of the vertical wheelset acceleration, and the maximum sleeper displacement have been studied. Mean values and standard deviations of these quantities have been calculated. The effects of the variation of the investigated track properties are discussed.     

Dynamic Train-Track Interaction: Variability Attributable to Scatter in the Track Properties

A numerical method to simulate vertical dynamic interaction between a rolling train and a railway track has been used to investigate the influence of stochastic properties of the track structure. A perturbation technique has been used to investigate the influence of the scatter in selected track properties. The train-track interaction problem has been numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the whole track structure. All numerical simulations have been carried out in the time-domain with a moving mass model. Properties such as rail pad stiffness, ballast stiffness, dynamic ballast-subgrade mass and sleeper spacing have been studied. To obtain sufficient statistical information from track structures, full-scale measurements in the field and laboratory measurements have been carried out. The influence of scatter in the track properties on the maximum contact force between the rail and the wheel, the maximum magnitude of the vertical wheelset acceleration, and the maximum sleeper displacement have been studied. Mean values and standard deviations of these quantities have been calculated. The effects of the variation of the investigated track properties are discussed.     

移动荷载作用下特大悬索桥的行车舒适性

为研究移动荷载作用下特大悬索桥的动力响应和行车舒适性问题,用正交异性矩形板单元弯曲形函数的6次Hermitian插值函数,通过Matlab编程把车辆移动过桥时的荷载转换成加劲梁各节点的荷载时程,用通用有限元程序ANSYS,对移动荷载作用下特大悬索桥动态响应进行了时程分析,给出了悬索桥在不同荷载作用下的数值分析结果。实例分析表明,该方法具有很好的适用性和很高的精度,加劲梁最大位移响应位于桥梁中跨的跨中位置,发生在移动荷载通过桥梁跨中位置前后。最后,通过对某悬索桥动力响应的时程结果进行小波变换,研究了该悬索桥的行车舒适性。     

Dynamic response of the train–track–bridge system subjected to derailment impacts

Derailments on bridges, although not frequent, when occurs due to a complex dynamic interaction of the train–track–bridge structural system, are very severe. Furthermore, the forced vibration induced by the post-derailment impacts can toss out the derailed wagons from the bridge deck with severe consequences to the traffic underneath and the safety of the occupants of the wagons. This paper presents a study of the train–track–bridge interaction during a heavy freight train crossing a concrete box girder bridge from a normal operation to a derailed state. A numerical model that considers the bridge vibration, train–track interaction and the train post-derailment behaviour is formulated based on a coupled finite-element – multi-body dynamics (FE-MBD) theory. The model is applied to predict the post-derailment behaviour of a freight train composed of one locomotive and several wagons, as well as the dynamic response of a straight single-span simply supported bridge containing ballast track subjected to derailment impacts. For this purpose, a typical derailment scenario of a heavy freight train passing over a severe track geometry defect is introduced. The dynamic derailment behaviour of the heavy freight train and the dynamic responses of the rail bridge are illustrated through numerical examples. The results exhibit the potential for tossing out of the derailed trains from the unstable increase in the yaw angle signature and a lower rate of increase of the bridge deck bending moment compared to the increase in the static axle load of the derailed wheelset.     

Robustness analysis of bogie suspension components Pareto optimised values

Bogie suspension system of high speed trains can significantly affect vehicle performance. Multiobjective optimisation problems are often formulated and solved to find the Pareto optimised values of the suspension components and improve cost efficiency in railway operations from different perspectives. Uncertainties in the design parameters of suspension system can negatively influence the dynamics behaviour of railway vehicles. In this regard, robustness analysis of a bogie dynamics response with respect to uncertainties in the suspension design parameters is considered. A one-car railway vehicle model with 50 degrees of freedom and wear/comfort Pareto optimised values of bogie suspension components is chosen for the analysis. Longitudinal and lateral primary stiffnesses, longitudinal and vertical secondary stiffnesses, as well as yaw damping are considered as five design parameters. The effects of parameter uncertainties on wear, ride comfort, track shift force, stability, and risk of derailment are studied by varying the design parameters around their respective Pareto optimised values according to a lognormal distribution with different coefficient of variations (COVs). The robustness analysis is carried out based on the maximum entropy concept. The multiplicative dimensional reduction method is utilised to simplify the calculation of fractional moments and improve the computational efficiency. The results showed that the dynamics response of the vehicle with wear/comfort Pareto optimised values of bogie suspension is robust against uncertainties in the design parameters and the probability of failure is small for parameter uncertainties with COV up to 0.1.     

应用CFRP索的缆索承重桥梁抗风稳定性研究

为了探讨CFRP索在缆索承重桥梁中应用的可能性,以缆索等轴向刚度为原则,基于润扬长江大桥和1400 m主跨斜拉桥设计方案,分别拟定了同跨径应用CFRP索的悬索桥和斜拉桥,并运用三维非线性空气动力稳定性分析方法进行了抗风稳定性分析。分析结果表明:缆索承重桥梁采用CFRP索后,由于结构自振频率特别是扭转频率的显著提高,其空气动力稳定性要好于钢索的缆索承重桥梁。因此从抗风稳定性角度而言,缆索承重桥梁采用CFRP索是可行的,缆索截面尺寸应采用等轴向刚度原则来确定。     

Thermal buckling and post-buckling behaviour of continuous welded rail track

Because thermal expansions are constrained within continuous welded rail track, the track can buckle, and does so mainly in the horizontal plane. In this paper, a parametric finite element model of railway track is presented, and its sensitivity to the variations of the main parameters that characterise the scenario has been investigated and discussed. Comparison with existing literature shows good agreement. It is found that curved tracks suffer from thermal buckling more than tangent tracks do. To simulate a track misalignment defect, a new methodology has been utilised that does not introduce, as is usual, geometrical discontinuities near the same defect, because it takes into account – in a natural way – the bending stiffness of the whole railway track in the horizontal plane. To contribute to a better understanding of the safe utilisation of raw experimental data obtained from in situ tests, a deep analysis of the effects on the thermal track buckling response produced by each parameter characterising the sleeper–ballast lateral resistance curve is presented and discussed. It is found that for current ballasted railway tracks, the minimum buckling temperature depends only on the limit lateral resistance, whereas a high value of the initial stiffness can lead to overestimation of the maximum buckling temperature, also taking into account the ‘natural’ decrease in the maximum buckling temperature due to an increase in the railway-traffic-induced defect amplitude.     

Vertical random vibration analysis of vehicle–track coupled system using Green's function method

A vertical vehicle–track coupled dynamic model, consisting of a high-speed train on a continuously supported rail, is established in the frequency-domain. The solution is obtained efficiently by use of the Green's function method, which can determine the vibration response over a wide range of frequency without any limitations due to modal truncation. Moreover, real track irregularity spectra can be used conveniently as input. The effect of the flexibility of both track and car body on the entire vehicle–track coupled dynamic response is investigated. A multi-body model of a vehicle with either rigid or flexible car body is defined running on three kinds of track: a rigid rail, a track stiffness model and a Timoshenko beam model. The results show that neglecting the track flexibility leads to an overestimation of both the contact force and the whole vehicle vibration response. The car body flexibility affects the ride quality of the vehicle and the coupling through the track and can be significant in certain frequency ranges. Finally, the effect of railpad and ballast stiffness on the vehicle–track coupled vibration is analysed, indicating that the stiffness of the railpad has an influence on the system in a higher frequency range than the ballast.     

Vehicle-Track Dynamics in the Mid-Frequency Range

During the last years railway companies have observed increasing problems with track damage like rail corrugation, deterioration of ballast or unround wheels. Since the origin of these damages is suspected in the mid-frequency dynamics, research activities in the frequency range from 50 up to 500 Hz have been initiated. The article demonstrates that in comparison to the low and high frequency range the knowledge about physical effects in the mid-frequency range is poor. Apart from a historical literature review on vehicle and track modelling, recently published methods and models are collated and problems in their mathematical treatise are mentioned. Regarding the vehicle, the paper shows the development starting with Klingel's massless wheelset model and ending with sophisticated elastic multibody system models. Concerning the track, different mathematical approaches in frequency and time domain are compared. In the mid-frequency range the pad, ballast and subsoil properties play an important role. Hence, the missing of experimentally validated models of these components is crucial. First attempts have been performed, which take into account the subsoil as layered half-space and the ballast as an assembly of viscoelastic rods. Besides the short time dynamics the article gives also an overview of the modelling of the wear phenomena mentioned above. An investigation of such long-term effects requires complex models of the entire vehicle-track system. The few wear models found in literature are discussed and first results are mentioned.     

Vehicle-Track Dynamics in the Mid-Frequency Range

During the last years railway companies have observed increasing problems with track damage like rail corrugation, deterioration of ballast or unround wheels. Since the origin of these damages is suspected in the mid-frequency dynamics, research activities in the frequency range from 50 up to 500 Hz have been initiated. The article demonstrates that in comparison to the low and high frequency range the knowledge about physical effects in the mid-frequency range is poor. Apart from a historical literature review on vehicle and track modelling, recently published methods and models are collated and problems in their mathematical treatise are mentioned. Regarding the vehicle, the paper shows the development starting with Klingel's massless wheelset model and ending with sophisticated elastic multibody system models. Concerning the track, different mathematical approaches in frequency and time domain are compared. In the mid-frequency range the pad, ballast and subsoil properties play an important role. Hence, the missing of experimentally validated models of these components is crucial. First attempts have been performed, which take into account the subsoil as layered half-space and the ballast as an assembly of viscoelastic rods. Besides the short time dynamics the article gives also an overview of the modelling of the wear phenomena mentioned above. An investigation of such long-term effects requires complex models of the entire vehicle-track system. The few wear models found in literature are discussed and first results are mentioned.     

非线性随机车流-自锚式悬索桥耦合振动分析系统

自锚式悬索桥独特的锚固形式使其主梁承受主缆传递的巨大轴向压力,为了研究主梁刚度在初内力及活载作用下的弱化问题对自锚式悬索桥结构静动力响应的影响,首先,结合自锚式悬索桥的非线性特点引入初应力刚度矩阵,考虑随机车流过桥时几何非线性的时变性,采用分离迭代法建立非线性随机车流-自锚式悬索桥耦合振动分析系统,并编制相应的非线性分析模块。其次,以某三跨混凝土自锚式悬索桥为例,选取集中力匀速过桥工况,利用ANSYS软件对非线性分析模块的可靠性进行验证。最后,分别设置2种极端工况：第1种是单车工况,近似认为只有恒载作用下产生的几何非线性;第2种是密集交通流工况,认为是恒载和最不利活载共同作用产生的几何非线性,并采用元胞自动机模型对密集车流进行模拟,研究自锚式悬索桥恒载和活载初内力引起的几何非线性对桥梁响应的影响程度。研究结果表明：单车工况下,梁塔恒载初内力对自锚式悬索桥的车辆过桥结构响应影响显著,主梁和主塔初内力贡献程度明显不同,主梁初内力对结构刚度矩阵变化的影响贡献较大而主塔贡献微小;相对于恒载,密集车流作用下初内力效应引起的几何非线性对自锚式悬索桥结构刚度影响微小,对结构响应的非线性影响也不明显。     

天兴洲大桥斜拉桥铁路结合桥面系模型试验研究

武汉天兴洲公铁两用长江大桥斜拉桥铁路桥面采用纵横梁体系的混凝土结合桥面板、有碴桥面、结合桥面板处于空间受力状态.针对铁路纵横梁体系的静活载效应、混凝土道碴槽板的弯曲应力及局部关键区域的受力行为进行专项模型试验,研究结合桥面系的力学行为、应力分布规律及应力传递路径等关键问题.试验结果表明:该桥铁路桥面采用的纵横梁体系混凝土板结合桥面系受力合理、响应明确,结构应力及刚度满足规范要求;卸载后残余应变、位移很小,结构处于弹性工作状态,混凝土道碴板未发现可见裂缝;结合桥面系的受力性能良好,设计合理可行.     

Multiphysic modelling of railway vehicles equipped with pneumatic suspensions

This article presents a multidisciplinary approach of railway pneumatic suspension modelling: both multibody and pneumatic aspects are taken into account. The work aims at obtaining a realistic model of the secondary suspension and coupling it with a multibody model of a train. Various components of the pneumatic circuit such as bellows, tanks, pipes and valves are taken into account. The article focuses on the bellow–pipe–tank subsystem for which several modelling approaches are presented and compared. Differences between differential and algebraic models are highlighted, and an application-dependent choice between them is suggested. A complete model of the pneumatic circuit is then obtained and coupled with a multibody model of the train. As a result, the behaviour of a suburban train equipped with a pneumatic secondary suspension is analysed, in particular undesired oscillating motions which affect the comfort. Topological modifications and improvements of the suspension are also investigated and discussed.