Experimental Investigation on Dynamic Railway Sleeper/Ballast Interaction

In ballasted railway tracks, one of the important components that supports the rails and distributes wheel/rail loading onto the ballast supporting formation is a railway sleeper (sometimes is also called a “railway tie”). This paper presents results of an experimental modal analysis of prestressed concrete sleepers in both free-free and in-situ conditions, incorporating the dynamic influence of sleeper/ballast interaction. Dynamic interaction between concrete sleepers and ballast support is crucial for the development of a dynamic model of railway track capable of predicting its responses to impact loads due to wheel flats, wheel burns, irregularities of the rail, etc. In this study, four types of prestressed concrete sleepers were in-kind provided by the Australian manufacturers. The concrete sleepers were tested using an impact hammer excitation technique over the frequency range of interest, 0–1600 Hz. Frequency response functions (FRFs) were measured using PULSE modal testing system. The FRFs were processed using STAR modal analysis package to identify natural frequencies and the corresponding mode shapes for the sleepers. The conclusions are presented about the effect of the sleeper/ballast interaction on the dynamic properties of prestressed concrete sleepers and their use for predicting railway track dynamic responses.     

Propagation of perturbances generated in classic track, and track with Y-type sleepers

Railway track with classic and Y-shaped sleepers or slab track is composed of two rails that are assumed to be infinitely long and joined with sleepers by viscoelastic pads. Numerous assumptions are used in railway-track modelling, leading to different simplifications. The two-dimensional periodic model of track consists of two parallel infinite Timoshenko beams (rails) coupled with equally spaced sleepers on a viscoelastic foundation. Nowadays the interest of engineers is focused on slab track and track with Y-shaped sleepers. The fundamental qualitative difference between the track with classic and Y-shaped sleepers is related to local longitudinal symmetric or antisymmetric features of the railway track. The sleeper spacing influences the periodicity of the foundation elasticity coefficient, mass density (rotational inertia) and the effective shear rigidity. Track with classic concrete sleepers is affected much more by rotational inertia and shear deflections than track with Y-shaped sleepers. The increase of the elastic-wave velocity in track with Y-shaped sleepers and more uniform load distribution will be proved by analysis and simulation. The analytical and numerical analyses allows us to evaluate the track properties in a range of moderate and high train speeds. However, the correct approach is not simple, since the structure of the track interacts with the wheels, wheelsets and vehicles, which constitute complex inertial loads. We note that the growth of amplitude in selected velocity ranges depends strongly on the track type.     

Interaction of railway vehicles with track in cross-winds

This paper presents a framework for simulating railway vehicle and track interaction in cross-wind. Each 4-axle vehicle in a train is modeled by a 27-degree-of-freedom dynamic system. Two parallel rails of a track are modeled as two continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The vehicle subsystem and the track subsystem are coupled through contacts between wheels and rails based on contact theory. Vertical and lateral rail irregularities simulated using an inverse Fourier transform are also taken into consideration. The simulation of steady and unsteady aerodynamic forces on a moving railway vehicle in cross-wind is then discussed in the time domain. The Hilber–Hughes–Taylor α-method is employed to solve the nonlinear equations of motion of coupled vehicle and track systems in cross-wind. The proposed framework is finally applied to a railway vehicle running on a straight track substructure in cross-wind. The safety and comfort performance of the moving vehicle in cross-wind are discussed. The results demonstrate that the proposed framework and the associated computer program can be used to investigate interaction problems of railway vehicles with track in cross-wind.     

Receptance behaviour of railway track and subgrade

Summary Vertical dynamic behaviour of a railway track on an elastic halfspace or on a layered halfspace is investigated by a frequency domain analysis. The results are compared with those for a simpler model, where ballast and subgrade are considered as a viscoelastic foundation. In the low- and medium-frequency range up to 250 Hz, great differences are observed between the results of the halfspace model and the results of the viscoelastic foundation model. This is because the damping due to wave propagation and coupling between sleepers cannot be modelled correctly by a viscoelastic foundation. Contradictions observed in the past between measured and calculated results can be explained with the new halfspace model. For frequencies higher than 250 Hz, the influence of the subgrade is negligible, so that here the simpler viscoelastic foundation model can be used. Received 5 January 1998; accepted for publication 7 April 1998     

高速铁路碎石道砟振动的离散元模拟

道砟振动对其磨损、破碎和道床累积变形有显著影响,为揭示高速车辆移动荷载作用下道砟动态响应特性,建立有砟道床离散元模型,开展车辆-轨道耦合动力学计算得到离散元模型输入荷载,模拟分析高速车辆以不同速度通过时有砟道床的振动响应,并与车辆-轨道耦合动力学计算结果进行对比分析。结果表明,轨枕、道砟和道床块振动位移波形相似,位移幅值沿道床深度方向减小,道床块振动位移与轨枕底面以下0.3m处道砟的振动位移相当;轨枕、道床块振动速度与加速度随行车速度提高而增大;受道砟颗粒间复杂相互作用的影响,道砟振动加速度会出现突变。道床离散元模型能合理反映道砟颗粒的振动响应特性,道床块模型体现了道床层在有砟轨道结构中的动力传递与减振特性,两种道床模型的计算结果具有一定的相似性。     

Periodically supported beam on a visco-elastic layer as a model for dynamic analysis of a high-speed railway track

This paper presents a theoretical study of the steady state dynamic response of a railway track to a moving train. The model for the railway track consists of two beams on periodically positioned supports that are mounted on a visco-elastic 3D layer. The beams, supports, and layer are employed to model the rails, sleepers and soil, respectively. The axle loading of the train is modeled by point loads that move on the beams. A method is presented that allows to obtain an expression for the steady-state deflection of the rails in a closed form. On the basis of this expression, the vertical deflection of the rails and its dependence on the velocity of the train is analyzed. Critical velocities of the train are determined and the effect of the material damping in the sub-soil and in the pads on the track response at these critical velocities is studied. The effect of the periodic inhomogeneity of the track introduced by the sleepers is studied by comparing the dynamic response of the model at hand to that of a homogenized model, in which the supports are assumed to be not discrete but uniformly distributed along the track. It is shown that the vertical deflection of the rails predicted by these models resemble almost perfectly. The elastic drag experienced by a high-speed train due to excitation of track vibrations is studied. Considering a French TGV as an example, this drag is calculated using both the inhomogeneous and homogenized models of the track and then compared to the rolling and aerodynamic drag.     

Interaction of subway LIM vehicle with ballasted track in polygonal wheel wear development

This paper develops a coupled dynamics model for a linear induction motor (LIM) vehicle and a subway track to investigate the influence of polygonal wheels of the vehicle on the dynamic behavior of the system. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom. A Timoshenko beam is used to model the rails which are discretely supported by sleepers. The sleepers are modeled as rigid bodies with their vertical, lateral, and rolling motions being considered. In order to simulate the vehicle running along the track, a moving sleeper support model is introduced to simulate the excitation by the discrete sleeper supporters, in which the sleepers are assumed to move backward at a constant speed that is the same as the train speed. The Hertzian contact theory and the Shen- Hedrick-Elkins’ model are utilized to deal with the normal dynamic forces and the tangential forces between wheels and rails, respectively. In order to better characterize the linear metro system (LMS), Euler beam theory based on modal superposition method is used to model LIM and RP. The vertical electric magnetic force and the lateral restoring force between the LIM and RP are also taken into consideration. The former has gap-varying nonlinear characteristics, whilst the latter is considered as a constant restoring force of 1 kN. The numerical analysis considers the effect of the excitation due to polygonal wheels on the dynamic behavior of the system at different wear stages, in which the used data regarding the polygonal wear on the wheel tread are directly measured at the subway site.     

An Alternative Rail Pad Tester for Measuring Dynamic Properties of Rail Pads Under Large Preloads

One of the main components in ballasted railway track systems is the rail pad. It is installed between the rail and the sleeper to attenuate wheel/rail interaction loads, preventing the underlying railway sleepers from excessive stress waves. Generally, the dynamic design of tracks relies on the available data, which are mostly focused on the structural condition at a specific toe load. Recent findings show that track irregularities could significantly amplify the loads on railway tracks. This phenomenon gives rise to a concern that the rail pads may experience higher effective preloading than anticipated in the past. On this ground, this paper highlights the significance of accounting for effects of preloading on dynamic properties of polymeric rail pads. An innovative test rig for controlling preloads on rail pads has been devised. A non-destructive methodology for evaluating and monitoring the dynamic properties of the rail pads has been developed based on an instrumented hammer impact technique and an equivalent single degree-of-freedom system approximation. Based on the impact-excitation responses, some of the selected rail pads have been tested to determine such modal parameters as dynamic stiffness and damping constants in the laboratory. The influence of large preloads on dynamic properties of both new and worn rail pads is demonstrated in this paper. Additionally, the design criteria, which has been used to take into account the influence of the level of preload on dynamic properties of generic rail pads, are discussed. Note: The authors’ work in the references can be found electronically via UoW Research Online at URL     

列车荷载作用下轨道和地基的动响应分析

分析了列车运动荷载引起的应力波在轨道结构和周围地基中的传播,用动力子结构方法求解了铁路轨道和多层地基的相互作用问题,特别是在模型中考虑了轨枕离散支撑的作用.研究的对象结构包括列车运动荷载和受轨枕支撑的钢轨,以及下面的无限分层黏弹性地基.通过傅里叶变换求解微分形式的支配方程,得到了在频域和波数领域中的钢轨以及周围地基的振动准解析解,而响应时程则通过傅里叶逆变换得到.利用结果可以评估高速铁路列车运行时产生的轨道与周围地基的振动强度;同时提出了一种直观的方法来确定轨道与地基中产生共振时列车运行的临界速度.     

Dynamic model of vertical vehicle-subgrade coupled system under secondary suspension

As it is known, track transportation can be divided into track system above and track system below. While the train is moving, the parts above and below are interacted and influenced. Therefore, in fact, the problem of track transportation is the match between the vehicle and the railway line system. In this paper, on a basis of dynamic analysis of the vehicle-subgrade model of vertical coupled system under primary suspension, utilizing track maintenance standard and simulating track irregularity excitation, the dynamic interaction of vehicle-track-subgrade system is researched in theory and dynamic model of the vertical vehicle-track-subgrade coupled system under secondary suspension is established by compatibility condition of deformation. Even this model considers the actual structure of a vehicle, also considers vibration characteristic of the substructure of track including subgrade and foundation. All these work want to be benefit for understanding and design about the dynamic characters of subgrade in high speed railway.     

Analytical study of the dynamic response of an embedded railway track to a moving load

Summary In this paper, the steady-state dynamic response of an embedded railway track to a moving train is investigated theoretically. The model for the track consists of a flexible plate performing vertical vibrations, two beams that are connected to the plate by continuous visco-elastic elements and an elastic foundation that supports the plate. Two harmonic loads that move uniformly along the beams describe the train load. The plate, the beams and the elastic foundation are employed to model a concrete slab of an embedded track, the rails and the ground reaction, respectively. The problem is studied by employing the Fourier integral transforms in the following way. Firstly, the dispersion analysis of waves that may propagate along the system is accomplished in the frequency-wavenumber domain. On the basis of this analysis, critical velocities of the loads are found both for the in-phase and anti-phase vibrations of the loads. Secondly, the vertical displacement of the rails and the slab, along with the stresses in the slab, are investigated as functions of the velocity and frequency of the loads. Finally, the response of the two-dimensional model is compared to that of a simplified one-dimensional model.     

风沙影响下铁路道碴变形模量的离散元数值分析

针对风沙区有碴铁路道床的结构特性,对其在细沙贯入下的有效变形模量研究有助于理解风沙影响下的道床动力特性。采用离散单元模型对道碴碎石和细沙颗粒进行数值建模,并对不同含沙率γ下的有效变形模量进行了数值分析。结果表明,在低含沙率下(γ<30%)沙石混合体的变形模量基本保持不变,在高含沙率下(γ>30%),变形模量随含沙率的增加呈线性降低,以上变形模量随含沙量的变化规律与试验结果相一致。基于离散单元模型的数值模拟,在细观尺度上对沙石混合体的力链强度、空间分布及配位数进行了分析,揭示了沙石混合体有效变形模量随含沙量变化的内在机理。本文工作对风沙区有碴铁路道床力学行为的研究具有一定的借鉴意义,有助于促进风沙影响下有碴铁路道床的结构设计和沙害治理。     

轨下支承失效对直线轨道动态响应的影响

建立了基于Timoshenko梁模型的车辆/轨道耦合动力学模型,分析轨下支承失效对直线轨道动态响应的影响. 钢轨被视为连续弹性离散点支承上的无限长Timoshenko梁,通过假设轨道系统刚度沿纵向分布发生突变来模拟轨下支承失效状态. 推导了考虑钢轨横向、垂向和扭转运动的轮轨滚动接触蠕滑率计算公式. 利用Hertz法向接触理论和沈氏蠕滑理论计算轮轨法向力及轮轨滚动接触蠕滑力. 采用移动轨下支承模型的车辆/轨道耦合系统激振模式,考虑轨枕离散支承对系统动力响应的影响. 通过新型显式积分法求解车辆/轨道耦合动力学系统运动方程,由数值分析计算得到不同轨下支承失效状态下直线轨道的动态响应. 结果表明,轨下支承失效对直线轨道变形及加速度有显著的影响,随着失效轨下支承个数的增加,轮轨相互作用力和轨道部件的位移、加速度将会急剧增大,将加速失效区段线路状况的恶化.      

铁路车辆/轨道耦合系统在竖向冲击载荷作用下动态响应的计算机模拟研究

车辆与轨道的动态相互作用,是铁路轮轨接触式运输系统中最基本的问题之一,它直接制约着铁路运营速度的提高和运载重量的增加,也影响着铁路安全运行。本文采用有限元方法,对我国C61型运煤货车,按照车辆/轨道系统的实际几何形状、材料性质和边界条件建立了包括车辆和轨道系统的有限元模型,应用大型非线性动力分析程序LS-DYNA3D来模拟车辆通过轨道错牙接头时的轮/轨动态响应过程。计算结果表明车轮和轨道之间的竖向动态接触力大约是静轮载的2倍,与已有的现场试验结果基本吻合。因此应用有限元方法研究车辆/轨道耦合系统是可行和可靠的。     

Track dynamic behavior at rail welds at high speed

As a vehicle passing through a track with different weld irregularities, the dynamic performance of track com- ponents is investigated in detail by using a coupled vehi- cle-track model. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom, and a Timoshenko beam is used to model the rails which are dis- cretely supported by sleepers. In the track model, the sleepers are modeled as rigid bodies accounting for their vertical, lat- eral and rolling motions and assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. In the study of the coupled vehicle and track dynamics, the Hertizian contact theory and the theory proposed by Shen-Hedrick-Elkins are, respectively, used to calculate normal and creep forces between the wheel and the rails. In the calculation of the normal forces, the coefficient of the normal contact stiffness is determined by transient contact condition of the wheel and rail surface. In the calcu- lation of the creepages, the lateral, roll-over motions of the rail and the fact that the relative velocity between the wheel and rail in their common normal direction is equal to zero are simultaneously taken into account. The motion equations of the vehicle and track are solved by means of an explicit integration method, in which the rail weld irregularities are modeled as local track vertical deviations described by some ideal cosine functions. The effects of the train speed, the axle load, the wavelength and depth of the irregularities, and the weld center position in a sleeper span on the wheel-rail impact loading are analyzed. The numerical results obtained are greatly useful in the tolerance design of welded rail pro- file irregularity caused by hand-grinding after rail welding and track maintenances.     

Rail wheel removal and its implication on track life: A fracture mechanics approach

Wheel/rail forces generated by wheel defects is known to be one of the contributing factors to track failure. Current strategy of removing wheels from service is dependent on the magnitude of the impact forces generated by these defects. These impact forces are estimated with wheel impact monitor established along a section of the railway track. This is also known as wayside monitoring. The impact load levels recorded by these monitors are recorded and the wheels that generate impact loads above a stated level (e.g. 400 kN) will be removed from service for maintenance. The question one poses is “What if the impact force generated by a given wheel is just below this level and stays at this level for extended period of time?” Will this, e.g. 380 kN, impact force do as much damage to the track as a 400 kN impact force if it is allowed in service? What are the implications of allowing a wheel that generate a seemingly acceptable level of 250 kN impact load to remain in service for extended period of time? In an attempt to answer these questions, a series of investigations were carried out to investigate the effect of impact loads on the propagation of a Vertical Split Head (VSH) defect found in the head of a 50 kg/m rail.     

列车通过道岔时转向架结构振动特性的研究

建立了考虑线路弹性并视转向架构架为柔体的三节车辆组成的列车通过道岔运行的列车/线 路模型. 分析了列车通过道岔时作用于转向架构架上的动载荷,将动载荷通过程序 FEMBS{-1}转化为适用于FE程序的文件并由ANSYS软件分析整个构架的应力分布及最大应力时间历程变化等. 分析对比了列车及单节车辆的仿真结果并与线路动应力试验结果进行了对比. 研究认为列车通过道岔时各构架的拉、压动应力幅值变化各异且在岔心处大于单辆车的相应值,表明单辆车模型适用于初步的计算分析,欲详细分析构架的结构性能应采用多车模型. 根据动应力频谱分析可知,构架的动应力可分为3个频域区,分别对应由直线驶入道岔的曲线上、岔心和岔尖处及构架固有振动频率附近的弹性振动区.     

Determining the contact force during the transverse impact of plates

The contact force during the transverse impact of a plate is determined from dynamic strain-gage measurements made on the plate. Experimental results for the impact of an aluminum plate are presented, and comparisons are made with finite-element predictions and measurements from a force transducer. Paper was presented at the 1986 Spring Conference on Experimental Mechanics held in New Orleans, LA on June 8–13.     

Preliminary development, simulation and validation of a weigh in motion system for railway vehicles

The development of efficient Weigh In Motion (WIM) systems with the aim of estimating the axle loads of railway vehicles in motion is quite interesting both from an industrial and an academic point of view. This kind of systems is very important for safety and maintenance purposes in order to verify the loading conditions of a wide population of vehicles using a limited number of WIM devices distributed on the railway network. The evaluation of the axle load conditions is fundamental especially for freight wagons, more subjected to the risk of unbalanced loads which may be extremely dangerous both for the vehicle safety and the infrastructure maintenance. In this work the authors present the development, the simulation and the validation of an innovative WIM algorithm with the aim of estimating the axle loads $\widehat{N}$ of railway vehicles (the axle loads include the wheelset weights). The new estimation algorithm is a general purpose one; theoretically it could be applied by considering as input different kinds of track measurements (rail shear, rail bending, sleepers with sensors, etc.) and could be easily customized for different kinds of signals. In the paper a benchmark case based on rail bending measurements is proposed in which the longitudinal deformations ε _xx measured on the rail foot through strain sensitive elements are used as input. The considered input is affected by noise and bandwidth limitations and, consequently, is a good benchmark to test the robustness of the new algorithm. To estimate the axle loads, the algorithm approximates the measured physical input through a set of elementary functions calculated by means of a single fictitious load moving on the track. Starting from the set of elementary functions, the measured signal is then reproduced through Least Square Optimization (LSO) techniques: in more detail, the measured signal is considered as a linear combination of the elementary functions, the coefficients of which are the axle loads to be estimated. Authors have also developed a physical model of the railway track. The model consists of the planar FEM (finite elements method) model of the infrastructure and of the two-dimensional (2D) multibody model of the vehicle (the effects of lateral dynamics are treated as disturbances) and takes into account both the coupling between adjacent loads moving on the track and the vehicle dynamics. The physical model of the track and the innovative WIM algorithm (both considering possible measurement errors) have been validated by means of the experimental data kindly provided by Ansaldo STS and have been implemented in the Matlab and Comsol Multiphysics environments. In particular the model of the railway track has been developed expressly to test the WIM algorithm with a suitable simulation campaign when experimental data are not available; in other words it provides simulated inputs to test the WIM algorithm when there are no experimental inputs.