The Dynamic Effects of Conventional Freight Car Running over a Dipped-joint

Available experimental data of the dynamic force at a rail joint are used to validate the Discrete Support (DS) model of vehicle-track system. The validated DS model is employed to investigate the characteristics of dynamic forces due to a dipped rail joint. The results show that increasing axle load and rail equivalent mass significantly increases the first peak load. The wheel (unsprung) mass, stiffness of bearing rubber pad, and ballast stiffness mainly affect the second peak load. Properly designing a profile near the rail joint may reduce the dynamic load at the joint. The results obtained also indicate that the dynamic load generated at one wheel partially transmits to a neighboring wheel.     

Impact Loads due to Wheel Flats and Shells

A Finite Element (FE) model of vehicle-track system is employed to duplicate the experiments carried out by British Rail and CP Rail System. The theoretical results of the wheel/rail contact forces, rail-pad forces and strains in the rail showed very good correlation to the experimental data. Extensive results are compared with experimental data in the time domain for through validation of the developed model. The characteristics of the impact loads due to wheel flats and shells are investigated based on the validated FE model. The study shows that the shape and size of flat or shell, axle load, vehicle speed and rail-pad stiffness mainly affect the impact loads. Adding elastomeric shear pads on the wheelset bearing does not reduce the wheel/rail dynamic contact force but it may reduce the dynamic force on the bearing. Reducing rail-pad stiffness to a certain level on a concrete-tie track may significantly reduce the dynamic load and the force transmitted to the concrete tie.     

Dynamic vehicle–track interaction in switches and crossings and the influence of rail pad stiffness – field measurements and validation of a simulation model

A model for simulation of dynamic interaction between a railway vehicle and a turnout (switch and crossing, S&C) is validated versus field measurements. In particular, the implementation and accuracy of viscously damped track models with different complexities are assessed. The validation data come from full-scale field measurements of dynamic track stiffness and wheel–rail contact forces in a demonstrator turnout that was installed as part of the INNOTRACK project with funding from the European Union Sixth Framework Programme. Vertical track stiffness at nominal wheel loads, in the frequency range up to 20?Hz, was measured using a rolling stiffness measurement vehicle (RSMV). Vertical and lateral wheel–rail contact forces were measured by an instrumented wheel set mounted in a freight car featuring Y25 bogies. The measurements were performed for traffic in both the through and diverging routes, and in the facing and trailing moves. The full set of test runs was repeated with different types of rail pad to investigate the influence of rail pad stiffness on track stiffness and contact forces. It is concluded that impact loads on the crossing can be reduced by using more resilient rail pads. To allow for vehicle dynamics simulations at low computational cost, the track models are discretised space-variant mass–spring–damper models that are moving with each wheel set of the vehicle model. Acceptable agreement between simulated and measured vertical contact forces at the crossing can be obtained when the standard GENSYS track model is extended with one ballast/subgrade mass under each rail. This model can be tuned to capture the large phase delay in dynamic track stiffness at low frequencies, as measured by the RSMV, while remaining sufficiently resilient at higher frequencies.     

On vehicle/track impact at connection between a floating slab and ballasted track and floating slab track's effectiveness of force isolation

When a vehicle runs over the connection between a floating slab track (FST) and ballasted track, wheel/rail impact may occur because of the stiffness difference in the two kinds of track, and thus a transition sector is usually included at the connection to smoothen the stiffness change. This phenomenon is studied by numerical simulation using a time-domain model for an idealised case without such a transition to determine whether it is actually necessary. Calculation results show that the wheel/rail impact load is moderate for a light FST and increases with the vehicle speed or decreasing the natural frequency of the FST. From simulation the wheel/rail parametric excitation is observed, as a result of variation in the stiffness of the FST with the period of the single slab length. The wheel/rail load due to the parametric excitation also increases with the vehicle speed. In addition, good performance of vibration isolation can be seen for the FST in terms of the force transmitted to the infrastructure.     

The dynamic response of rail support

This research reviews principles behind the dynamic response of rail supports, and introduces a method of analysis to find the maximum response in a realistic setting. Assuming a time-dependent, moving mass with massive wheels is essential, because the ratio of the moving mass to the rail mass is significant. However, the dynamic response of the track is not affected by dynamic properties of the train other than its unsprung mass, because the natural frequencies of the train suspension and track are significantly different. A numerical method is developed to model the dynamic response based on these principles, and applied to the Korean urban transit. The dynamic response includes multiple peaks with a large amplitude range, creating noise while the wheel passes the support. The dynamic impact factor (DIF) for the rail support depends mainly on the stiffness and damping of the rail support. The DIF for the rail moment is below the code value, whether this value is based on numerical analysis or on-site measurements. However, our numerical analysis results in a DIF for support settlement that is greater than the code value, if the damping is less than 3%.     

A linear complementarity method for the solution of vertical vehicle–track interaction

A new method is proposed for the solution of the vertical vehicle–track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel–rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel–rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel–rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle–track interaction including a separation between wheel and rail.     

轴重和胎压对车轮动荷载的影响

为研究重型运输车辆对路面作用的动荷载,建立车辆动力学模型,模型中将簧上质量处理为空载簧上质量与装载质量,将轮胎刚度表示为轴重和胎压的函数。研究了轴重和胎压对车辆动荷载的影响。结果发现,车轮动荷载随着轴重和胎压的增加而增加;动载系数随着胎压的增加而增加,但随着轴重的增加而减小;胎压越高,车轮动载随轴重增加速度越快;仅仅采用轴重不足以评价重载高压车辆对路面的破坏作用,在治理超载的同时也应进一步治理超压：空载车辆对路面的冲击作用较大,不能忽视空载车辆对路面的破坏作用;实际高速运行车辆对路面施加较大的附加动荷载,现有《公路沥青路面设计规范》没有考虑附加动荷载是引起路面结构发生早期破坏的原因之一。     

Wheel/Rail Non-linear Interactions With Coupling Between Vertical and Lateral Directions

Summary A theoretical model is developed to explore the high frequency wheel/rail interaction with coupling between the vertical and lateral directions. This coupling is introduced through the track dynamics due to the offset of the wheel/rail contact point from the rail centre line. Equivalent models of the railway track in the time domain are developed according to the rail vibration receptances in the frequency domain. The wheel is represented by a mass in each direction with no vertical-lateral coupling. The vertical wheel/rail interaction is generated through a non-linear Hertzian contact stiffness, allowing for the possibility of loss of contact between the wheel and rail. The lateral interaction is represented by a contact spring and a creep force damper in series and their values depend on the vertical contact force. The vibration source is the roughness on the wheel and rail contact surfaces which forms a relative displacement excitation in the vertical direction. Using the combined interaction model with this relative displacement excitation, the wheel/rail interactions with coupling between the vertical and lateral vibrations are simulated. It is found that the lateral interaction force caused by the offset is usually less than thirty percent of the vertical dynamic force. The lateral vibration of the rail is significantly reduced due to the presence of the lateral coupling, whereas the vertical interaction is almost unaffected by the lateral force.     

用于公路车-桥系统振动分析的精细化轮胎模型

为了解决当前公路车桥耦合振动模型中轮胎模型过于简化、车轮-路面接触力与桥梁响应计算结果不够精确的问题,提出了一种精细化轮胎模型.首先基于车辆橡胶轮胎的几何、力学特征,建立了径向弹簧力学模型并进行了理论推导;然后考虑轮胎与路面接触面的刚度分布特征和高速状况下轮胎的惯性力,提出了轮胎接触面分布刚度的计算方法,保证了轮胎接触...     

Effects of rail thermal stress on the dynamic response of vehicle and track

A new method is proposed to obtain the dynamic responses of the vehicle–track coupling system under the conditions of rail thermal stress changes in high-speed railways. Exact models are established with different rail longitudinal forces, in which multibody dynamic models are used for vehicles and the direct stiffness method for structures. In order to provide a general, simple and flexible formulation to express longitudinal stress distribution, the accurate model of long slab track consists of many small units with parameters which can be initialised separately. The exact analytical equation of track frequency and modal function was obtained by the transition matrix method, which can be used in calculating the dynamic response of wheel–rail coupling model. The proposed model is verified through comparisons with other classical solutions. Under the influence of train velocities and track irregularities, the specific vibration performances that frequency shifted and amplitude peak enhanced with thermal force are demonstrated through examples. The results show that the response analyses of vehicle and track have great application potentiality for fast estimation of the rail longitudinal stress.     

Modelling,validation and analysis of a three-dimensional railway vehicle–track system model with linear and nonlinear track properties in the presence of wheel flats

This paper presents dynamic contact loads at wheel–rail contact point in a three-dimensional railway vehicle–track model as well as dynamic response at vehicle–track component levels in the presence of wheel flats. The 17-degrees of freedom lumped mass vehicle is modelled as a full car body, two bogies and four wheelsets, whereas the railway track is modelled as two parallel Timoshenko beams periodically supported by lumped masses representing the sleepers. The rail beam is also supported by nonlinear spring and damper elements representing the railpad and ballast. In order to ensure the interactions between the railpads, a shear parameter beneath the rail beams has also been considered into the model. The wheel–rail contact is modelled using nonlinear Hertzian contact theory. In order to solve the coupled partial and ordinary differential equations of the vehicle–track system, modal analysis method is employed. Idealised Haversine wheel flats with the rounded corner are included in the wheel–rail contact model. The developed model is validated with the existing measured and analytical data available in the literature. The nonlinear model is then employed to investigate the wheel–rail impact forces that arise in the wheel–rail interface due to the presence of wheel flats. The validated model is further employed to investigate the dynamic responses of vehicle and track components in terms of displacement, velocity, and acceleration in the presence of single wheel flat.     

Inverse identification of wheel–rail contact forces based on observation of wheel disc strains: an evaluation of three numerical algorithms

In this paper, three numerical algorithms for the identification of wheel–rail contact forces based on measured wheel disc strains on an instrumented railway wheelset are discussed and compared. The three algorithms include one approach resting on static calibration, one that is applying a Kalman filter and the third is exploiting an inverse identification scheme. To demonstrate and evaluate the alternative methods, two load cases including periodic excitation by sinusoidal wheel–rail irregularities and transient excitation by an insulated rail joint are considered. Based on a previously presented vehicle–track interaction model in the time domain, load scenarios are defined by taking the calculated vertical wheel–rail contact forces as the reference force to be re-identified by the proposed algorithms. The reference contact forces are applied on a finite element model of the wheel to generate synthetic observation data, that is, radial strains at the positions of the strain gauges, serving as input to the identification procedures. It is concluded that the inverse identification scheme leads to superior accuracy at higher computational cost. If on-line implementation and evaluation is required, the Kalman filter generates better accuracy than the static calibration approach.     

Further study on the wheel–rail impact response induced by a single wheel flat: the coupling effect of strain rate and thermal stress

A comprehensive dynamic finite-element simulation method was proposed to study the wheel–rail impact response induced by a single wheel flat based on a 3-D rolling contact model, where the influences of the structural inertia, strain rate effect of wheel–rail materials and thermal stress due to the wheel–rail sliding friction were considered. Four different initial conditions (i.e. pure mechanical loading plus rate-independent, pure mechanical loading plus rate-dependent, thermo-mechanical loading plus rate-independent, and thermo-mechanical loading plus rate-dependent) were involved into explore the corresponding impact responses in term of the vertical impact force, von-Mises equivalent stress, equivalent plastic strain and shear stress. Influences of train speed, flat length and axle load on the flat-induced wheel–rail impact response were discussed, respectively. The results indicate that the maximum thermal stresses are occurred on the tread of the wheel and on the top surface of the middle rail; the strain rate hardening effect contributes to elevate the von-Mises equivalent stress and restrain the plastic deformation; and the initial thermal stress due to the sliding friction will aggravate the plastic deformation of wheel and rail. Besides, the wheel–rail impact responses (i.e. impact force, von-Mises equivalent stress, equivalent plastic strain, and XY shear stress) induced by a flat are sensitive to the train speed, flat length and axle load.     

Dynamic model for the wheel–rail contact friction

Accurately estimating the coefficient of friction (CoF) is essential in modelling railroad dynamics, reducing maintenance costs, and increasing safety in rail operations. The typical assumption of a constant CoF is widely used in theoretical studies; however, it has been noticed that the CoF is not constant, but rather depends on various dynamic parameters and instantaneous conditions. In this paper, we present a newly developed three-dimensional nonlinear CoF model for the dry rail condition and test the CoF variation using this model with estimated dynamic parameters. The wheel–rail is modelled as a mass–spring–damper system to simulate the basic wheel–rail dynamics. Although relatively simple, this model is considered sufficient for the purpose of this study. Simulations are performed at a train speed of 20 m/s using rail roughness as an excitation source. The model captures the CoF extremes and illustrates its nonlinear behaviour and instantaneous dependence on several structural and dynamic parameters.     

A dynamic wheel–rail impact analysis of railway track under wheel flat by finite element analysis

Wheel–rail interaction is one of the most important research topics in railway engineering. It involves track impact response, track vibration and track safety. Track structure failures caused by wheel–rail impact forces can lead to significant economic loss for track owners through damage to rails and to the sleepers beneath. Wheel–rail impact forces occur because of imperfections in the wheels or rails such as wheel flats, irregular wheel profiles, rail corrugations and differences in the heights of rails connected at a welded joint. A wheel flat can cause a large dynamic impact force as well as a forced vibration with a high frequency, which can cause damage to the track structure. In the present work, a three-dimensional finite element (FE) model for the impact analysis induced by the wheel flat is developed by the use of the FE analysis (FEA) software package ANSYS and validated by another validated simulation. The effect of wheel flats on impact forces is thoroughly investigated. It is found that the presence of a wheel flat will significantly increase the dynamic impact force on both rail and sleeper. The impact force will monotonically increase with the size of wheel flats. The relationships between the impact force and the wheel flat size are explored from this FEA and they are important for track engineers to improve their understanding of the design and maintenance of the track system.     

Effect of temperature- and frequency-dependent dynamic properties of rail pads on high-speed vehicle–track coupled vibrations

The soft under baseplate pad of WJ-8 rail fastener frequently used in China’s high-speed railways was taken as the study subject, and a laboratory test was performed to measure its temperature and frequency-dependent dynamic performance at 0.3?Hz and at ?60°C to 20°C with intervals of 2.5°C. Its higher frequency-dependent results at different temperatures were then further predicted based on the time–temperature superposition (TTS) and Williams–Landel–Ferry (WLF) formula. The fractional derivative Kelvin–Voigt (FDKV) model was used to represent the temperature- and frequency-dependent dynamic properties of the tested rail pad. By means of the FDKV model for rail pads and vehicle–track coupled dynamic theory, high-speed vehicle–track coupled vibrations due to temperature- and frequency-dependent dynamic properties of rail pads was investigated. Finally, further combining with the measured frequency-dependent dynamic performance of vehicle’s rubber primary suspension, the high-speed vehicle–track coupled vibration responses were discussed. It is found that the storage stiffness and loss factor of the tested rail pad are sensitive to low temperatures or high frequencies. The proposed FDKV model for the frequency-dependent storage stiffness and loss factors of the tested rail pad can basically meet the fitting precision, especially at ordinary temperatures. The numerical simulation results indicate that the vertical vibration levels of high-speed vehicle–track coupled systems calculated with the FDKV model for rail pads in time domain are higher than those calculated with the ordinary Kelvin–Voigt (KV) model for rail pads. Additionally, the temperature- and frequency-dependent dynamic properties of the tested rail pads would alter the vertical vibration acceleration levels (VALs) of the car body and bogie in 1/3 octave frequencies above 31.5?Hz, especially enlarge the vertical VALs of the wheel set and rail in 1/3 octave frequencies of 31.5–100?Hz and above 315?Hz, which are the dominant frequencies of ground vibration acceleration and rolling noise (or bridge noise) caused by high-speed railways respectively. Since the fractional derivative value of the adopted rubber primary suspension, unlike the tested rail pad, is very close to 1, its frequency-dependent dynamic performance has little effect on high-speed vehicle–track coupled vibration responses.     

基于仿形门台架试验的滑移门动力学分析方法

准确分析滑移门系统的动力学特性,对车用滑移门的工程开发具有重要意义。文章基于仿形门试验台进行滚轮力试验测量,采用联合仿真的DOE方法,对滑移门动力学模型中的滚轮导轨接触模型进行两因素、多水平组合寻优,获取满足滚轮力误差要求的最优接触力参数组合,并对滑移门动力学模型进行开启、关闭的仿真分析。研究表明,基于此方法建立的滑移门动力学模型具有较高的分析精度,中导轨前导向轮峰值力最大误差为7.52%,能够准确地模拟滑移门的滑动过程;0 °导轨滚轮力比带倾角的滚轮力显著增大,与试验现象完全一致。文章所建立的仿形门试验、动力学建模、参数识别以及动力学分析等流程,可支持滑移门多参数影响分析和平顺性评估,为滑移门正向开发提供有效的理论分析依据。     

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification

Based on the theory of vehicle-track coupling dynamics, a new wheel/rail spatially dynamic coupling model is established in this paper. In consideration of rail lateral, vertical and torsion vibrations and track irregularities, the wheel/rail contact geometry, the wheel/rail normal contact force and the wheel/rail tangential creep force are solved in detail. In the new wheel/rail model, the assumption that wheel contacts rail rigidly and wheel always contacts rail is eliminated. Finally, by numeric simulation comparison with international well-known software NUCARS, comparison with vehicle-track vertical coupling model, and comparison with running test results by China Academy of Railway Sciences, the new wheel/rail spatially dynamic coupling model is shown to be correct and effective.     

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification

Based on the theory of vehicle-track coupling dynamics, a new wheel/rail spatially dynamic coupling model is established in this paper. In consideration of rail lateral, vertical and torsion vibrations and track irregularities, the wheel/rail contact geometry, the wheel/rail normal contact force and the wheel/rail tangential creep force are solved in detail. In the new wheel/rail model, the assumption that wheel contacts rail rigidly and wheel always contacts rail is eliminated. Finally, by numeric simulation comparison with international well-known software NUCARS, comparison with vehicle-track vertical coupling model, and comparison with running test results by China Academy of Railway Sciences, the new wheel/rail spatially dynamic coupling model is shown to be correct and effective.     

Effect of System Nonlinearities on Locomotive Bogie Hunting Stability

This paper presents the effect of system parameters on hunting of a rail vehicle with nonlinear yaw dampers and wheel-rail interface. This study is intended to complement earlier studies by True et al. where they investigated the effect of nonlinearities stemming from creep-creep force saturation and wheel/rail contact forces. The rail vehicle is represented by a two-axle truck (bogie) that includes the dynamics of the wheelsets and the truck frame. The numerical simulation results show that yaw damping can have a mixed effect on the hunting critical speed. In some ranges, increasing damping can actually lower the critical speed, unlike the results commonly obtained from a linear model. Flange contact nonlinearities can also have a significant effect on the hunting behavior. Large lateral stiffness of the rail can increase lateral force to vertical force (L/V) ratio during hunting. Increasing the gauge clearance, however, can have an opposite effect. The effect of a variety of other parameters, such as the primary suspension yaw and lateral stiffness, primary suspension lateral damping, wheelset mass, and truck frame mass, are summarized in a table.