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.     

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.     

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.     

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.     

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.      

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.     

钢轨横向不均匀支撑刚度对钢轨波磨的影响

建立了钢轨波浪形磨损计算模型,模型中考虑车辆轨道垂向横向耦合动力学行为、轮轨三 维滚动接触力学行为和轮轨材料摩擦磨损的循环相互作用关系. 发展了相应的计算程序,并 用1: 1试验装置验证了理论模型. 详细分析了实际线路上由轨枕离散支撑导致的钢轨横向不均匀刚度和不同行车速度对曲线钢轨接触表面不均匀磨损的影响. 通过数值分析可知： (1)列车通过曲线钢轨时,轨枕离散支撑导致的钢轨横向不均匀刚度易引发曲线钢轨波磨的形 成和发展;(2)这类钢轨波磨具有与轨枕间距几乎相等的波长和28~35mm的短波长,这个短波长不均匀磨损主要是由轮轨高频接触振动引起;(3)同一个转向 架4个车轮作用下形成的钢轨波磨最大深度波谷的分布是不同的;(4) 改变过车速度不能有效地抑制轨枕离散支撑导致的钢轨波磨形成和发展速度.     

研磨子抑制高速列车车轮多边形磨耗的机理研究

高速列车车轮多边形磨耗是我国高速列车自2008年开行以来出现的最严重的问题之一,直接影响到高速列车的运行安全.利用高速轮轨滚动试验机试验研究了研磨子的增黏作用和局部缺陷修复作用,探讨了其作用机制.建立了由轮对、钢轨和整体道床组成的轮轨系统滑动摩擦自激振动模型,研究了轮轨黏着和滑动工况下的轮轨系统摩擦自激振动发生趋势,指出研磨子抑制高速列车车轮多边形磨耗的主要机理在于以下两个方面:(1)研磨子的增黏作用,使轮轨系统制动和牵引时不容易发生滑动,消除了车轮多边形发生的条件;(2)研磨子中硬质颗粒能够有效地将车轮踏面的微观缺陷及时打磨清除,从而有效抑制车轮多边形、异常磨耗及接触疲劳裂纹的产生.     

基于优化多核极限学习机的车轮多边形磨耗识别

多边形车轮是铁路机车车辆中普遍存在的一种磨损现象, 随着列车运营里程的增加, 车轮磨耗程度显著提升, 严重影响着列车乘坐舒适性和运营安全性, 借助于列车运营监测大数据开展多边形车轮动态检测方法研究具有重要意义. 本研究基于列车轴箱垂向加速度建立了多边形车轮定量识别模型, 首先通过阶次分析识别出轴箱加速度中包含的多边形车轮主要阶次, 同时获取各阶次对应的加速度幅值信息, 在此基础上引入加速度信号熵特征共同构建多边形车轮磨耗幅值识别特征矩阵, 然后建立遗传变异粒子群优化多核极限学习机 (GMPSO-MKELM) 识别模型, 通过特征矩阵与磨耗幅值的映射关系, 进一步实现了车轮多边形磨耗幅值识别. 通过仿真与现场实测数据研究结果表明, 所提出的识别模型能有效地从轴箱加速度中提取多边形车轮主要阶次, 磨耗幅值的识别精度均优于对比模型且具有较高的检测效率, 可实现均方根误差为0.0010 (仿真结果) 与0.0134 (试验结果) 的精确识别, 本文提出的多边形车轮磨耗识别模型可为列车车轮检测与智能维护提供理论基础.      

不确定车轨耦合系统辛随机振动分析

建立了轨道不平顺作用下具有不确定参数车轨耦合系统随机振动评估方法. 车辆系统采用物理坐标下多刚体系统模型,并应用高斯随机变量模拟车体、转向架和轮对一系、二系连接系统中动力学参数具有的不确定性. 采用无穷周期结构进行弹性轨道模拟,在哈密顿状态空间下建立了典型轨道子结构的状态运动方程,通过轮轨耦合关系建立了混合 物理坐标及辛模态坐标车轨耦合系统运动方程. 应用Hermite正交多项式展开得到了耦合系统动力响应相对于不确定性参数的控制方程. 由于利用轨道周期特性建模,所获得的控制方程有效地降低了方程维度. 轮轨接触处轨道不平顺载荷模拟为完全相干多分量平稳随机过程,推广和发展虚拟激励法建立了耦合系统随机振动受不确定动力学 参数影响的量化评估方法. 通过Monte Carlo数值模拟,验证了该方法在不确定参数变异很大时也能够保持较好的精度,具有一定的工程实用性.     

车轮多边形激励下高速列车制动界面摩擦学行为分析

高速列车车轮多边形磨耗是一种沿车轮周向的不均匀磨耗,是列车服役过程中常见的车轮失效现象,其产生的剧烈轮轨激励严重威胁车辆系统服役可靠性.制动系统作为保障高速列车服役安全的核心部件,其界面摩擦学行为直接受到轮轨激励的影响.为探究车轮多边形激励下的制动界面摩擦学行为,建立了刚柔耦合车辆动力学模型和制动系统热机耦合有限元模型,并分别通过线路试验和台架试验验证了模型的正确性.然后,提出一种考虑车轮多边形激励的制动界面摩擦学行为分析方法,能够真实地反映服役过程中制动界面摩擦学行为.基于此,研究了不同车辆运行速度下车轮多边形激励对制动系统动态接触、温度以及振动特性的影响规律.结果表明：车轮多边形磨耗导致系统接触面积、摩擦热、接触应力和振动等摩擦学行为更为复杂且剧烈.此外,系统接触面积标准差和振动加速度均方根值随速度的增加而增大.因此,车轮多边形磨耗对制动界面摩擦学行为具有不可忽略的影响.该研究成果可为制动系统界面摩擦学行为研究及结构优化设计提供有效方法与工程指导.     

基于有限元的高速列车车轮多边形磨耗成因分析

研究了中国高速列车车轮多边形磨耗的形成原因,考虑轮对的旋转惯量,建立了高速列车轮对-轨道-盘式制动系统有限元模型. 基于轮轨系统摩擦自激振动的理论,采用有限元复特征值分析法研究了高速列车制动时轮对-轨道-盘式制动系统的稳定性. 研究了饱和的轮轨蠕滑力和盘式制动系统摩擦力耦合作用对车轮多边形磨耗的影响,并调查了轮轨-轨道-盘式制动系统的参数敏感性. 数值模拟结果表明:在饱和的轮轨蠕滑力和盘式制动器摩擦力耦合作用下,轮轨系统的摩擦自激振动导致高速列车车轮多边形磨耗的产生,其导致的21~22阶和23~24阶车轮多边形磨耗占主导地位,这与中国高速列车高阶车轮多边形磨耗最为符合. 饱和的轮轨蠕滑力主要影响较低阶车轮多边形磨耗,盘式制动器摩擦力主要影响较高阶车轮多边形磨耗. 制动压力为13 kN时,车轮多边形磨耗形成的几率最小,发展速度最慢. 过高或者过低的垂向悬挂力均不利于抑制车轮多边形磨耗. 垂向悬挂力为75 kN时,车轮多边形磨耗形成的可能性最小,发展速度最慢.      

Medium frequency dynamic investigation of the railway wheelset-track system using a discrete-continuous model

Summary In the paper, dynamic interaction between elastic high-speed-train car wheelset and track is studied using a discrete-continuous mechanical model. The model enables to investigate the influence of the parametric excitation from the track as well as static and dynamic unbalances of wheels and brake disks on the dynamic response of the wheelset running at various speeds on the track of various average vertical stiffness. From the results of numerical simulation it follows that particularly severe periodic resonances occur for the track of large stiffness, yielding high vertical dynamic contact forces between the wheels and rails. The maximum dynamic response has been obtained for parameters corresponding to the conditions at which the phenomenon of grumbling noise generation is usually observed in reality. Received 21 January 1997; accepted for publication 29 February 1997     

A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 2. A research on the motion resistance of road wheels

In spite of an increasing number of rubber-tracked crawlers, the literature provides few guidelines and calculation models suitable for minimizing their internal motion resistance. This article presents a model where the internal resistance of double-flanged road wheels for rubber-tracked vehicles is calculated as a sum of the losses resulting from the indentation of the wheels into the track surface and friction of the wheels against the track guide lugs. The model allows for vertical and lateral load of the wheels, the non-uniform distribution of the wheel pressure on the track, and the relationship between the friction coefficient and normal reaction force in the interface between the wheel and track guide lugs. The model has been verified by experiments. According to the results of model computations and experiments discussed in the article, the internal losses of a given rubber-tracked undercarriage might be reduced if: the road wheels are covered with a material that exhibits low friction coefficient and mechanical hysteresis, the vehicle suspension system features oscillating bogie wheels, the undercarriage is fitted with the largest possible number of road wheels, and the vehicle weight is evenly distributed to all of the road wheels.     

Finite element analysis for train–track–bridge interaction system

This article deals with the dynamic analysis of train–track–bridge interaction system using the finite element method. In this interaction system, each four-wheelset vehicle in the train is modeled by a mass–spring–damper system with 10 degrees of freedom; the rails and the bridge decks are modeled as a number of Bernoulli–Euler beam elements, while the elasticity and damping properties of the rail bed are represented by continuous springs and dampers. The equation of motion for the interaction system is presented in matrix form with time-dependent coefficients. The correctness of the proposed procedure is illustrated by a comparison with the numerical result from the existing literature. Several numerical examples are chosen to investigate the effect of two types of vehicle models, two types of bridge models and three damping values of bridge on the maximum dynamic responses of train, track and bridges.     

车致桥梁支座动反力频谱特性及影响因素研究

建立频域内的车辆-轨道-桥梁垂向耦合动力学模型,包括1/8车辆模型和CRTS-Ⅱ型板式无砟轨道-桥梁-支座模型两部分,以快速求解100Hz以内的桥梁支座动反力。将CRTS-Ⅱ型板式无砟轨道-桥梁-支座模型简化为4层叠合梁,采用Euler梁模拟钢轨、轨道板、底座板和箱梁,采用具有复刚度的弹簧模拟扣件、CA砂浆层、滑动层和桥梁支座。以32m简支桥梁为研究对象,分析了支座动反力的频谱特性,并讨论了轨道不平顺、扣件刚度和支座刚度对支座动反力的影响规律。结果表明:支座动反力在车轮-轨道系统的固有频率附近出现峰值;轨道不平顺幅值在很大程度上决定了支座动反力幅值,其峰值频率点在支座动反力曲线上得以体现;扣件刚度降低可一定程度上减小轮轨力及支座反力峰值、频段幅值及峰值频率;支座刚度降低可以减小支座反力幅值,同时降低峰值频率,其主要通过改变轨道-桥梁耦合系统的频响特性实现,而轮轨力基本不受其影响。     

A modular algorithm for linear, periodic train-track models

Summary  An algorithm is presented which can be used for the investigation of a large variety of train-track models. These models only have to fulfil the requirements of linearity and periodicity with respect to the track length direction. A steady-state solution is obtained for a vehicle moving on a tangent track with constant velocity. The algorithm itself can be split into three modules: one for the whole train-track system, one for the track, and one for a single rail support. These modules and their interfaces are described in detail. The article demonstrates the applicability of the algorithm by means of four examples. The first example shows the influence of the sleeper elasticity on the sleeper motion. The second one illustrates the effect of an advanced subsoil model on the wheel/rail contact force. Subsequently, as a further example, the compliance frequency-response functions of a ballasted track and a rigid track are compared. The last example deals with the sleeper passing excitation. Here, it is shown that even in the case of resonance, the wheel/rail contact-force fluctuations remain below ten percent of the static value. Received 17 January 2000; accepted for publication 18 August 2000