Dynamic Vehicle Track Interaction Research Articles

An iterative methodology for the prediction of dynamic vehicle–track interaction and long-term periodic rail wear

In this study, a versatile numerical method for the prediction of long-term growth of rail roughness is presented and its functionality is demonstrated for the development of rail corrugation on small radius curves. The procedure includes two sub-modules: (1) a time-domain model for the simulation of dynamic vehicle–track interaction in a wide range of frequencies by using a commercial software for multibody dynamics and (2) a post-calculation of sliding wear based on the Archard’s model in combination with a non-Hertzian and transient wheel–rail contact model. The structural flexibility of the wheelset is accounted for by using the finite element method. The rail wear generated by a large number of passing trains is assessed by recurrently updating the rail surface based on the wear depth calculated in each post-processing step. The current work sets out from a previous study in which a model for the prediction of long-term growth of rail roughness on small radius curves was developed in a general-purpose programming language. By transferring the model into a commercial software, the aim is to develop an engineering tool that is more applicable for different operational conditions, such as various vehicle and track designs and track alignments. The proposed method is verified by comparing the simulation results against those obtained with the pre-existing software. Conditions similar to a 120 m radius curve on the Stockholm metro exposed to corrugation growth on the low rail are considered. The corrugation is found to be generated by the leading wheelsets. The prevailing wavelength-fixing mechanisms are identified and discussed.

Investigations on Vehicle Interaction with CWR Tracks Considering Some Aspects of Rail Support Modulus

One of the important parameters for controlling the behavior of continuous welded rail (CWR) in railway tracks is rail support modulus. Reviewing the technical literature reveals some elapsed points in this regard such as continuous or discrete supports, V-shaped rail irregularity and geometrical stiffness which can considerably affect on the vehicle-track dynamic interaction. So, the present study was allocated to numerical investigating the effects of aforementioned parameters on the vehicle-track dynamic interaction. In this matter, the finite element model of ballasted railway track in conjunction with multi-body dynamics model of vehicle was developed and they simultaneously solved numerically. This preliminary model was verified through comparison of the results with published works in this area. Consequently the model was promoted considering continuous and discrete support condition, implementing the V-shaped irregularity and geometrical stiffness. In each step, the results of the extended models were completely presented in the form track structure response.

Modern methods of railway track safety inspection

Railway and transit tracks are designed and constructed as smooth segments of straight lines and circular curves linked by transitional spirals. Dynamic traffic loads, material wear and environmental cycles gradually produce deviations in the track from the original smooth geometry. Such deviations lead to rough ride in the vehicles and furthermore higher dynamic vehicle-track interaction forces which lead to faster deviation growth. To monitor the geometric condition of the track and to guide maintenance and repair, hand tools were used to take consecutive measurements by track walkers. Modern state-of-the-art technology has since replaced the traditional slow and painful measurement practice. Inspections are now done from a moving vehicle at hundreds of km per hour without contacting the track. All track geometry parameters are measured up four times per meter; data are analysed in real time by onboard software to identify the location and magnitudes of deviations which exceeds the acceptable tolerance. Historical measurements are stored in databases which are used to establish degradation trends and to guide the planning of maintenance. With the help of high-speed imaging technology, automated video inspection systems are installed on some vehicles to detect other faults in the track structure. Four types of such modern inspection tools are introduced in the paper presentation. These are: a single-car comprehensive inspection vehicle; a dedicated inspection train; a highway-railway dual usage truck and an unmanned inspection system. Actual operational systems are used as examples to illustrate the design and capabilities of each of these types of inspection tools.

Modern methods of railway track safety inspection

Railway and transit tracks are designed and constructed as smooth segments of straight lines and circular curves linked by transitional spirals. Dynamic traffic loads, material wear and environmental cycles gradually produce deviations in the track from the original smooth geometry. Such deviations lead to rough ride in the vehicles and furthermore higher dynamic vehicle-track interaction forces which lead to faster deviation growth. To monitor the geometric condition of the track and to guide maintenance and repair, hand tools were used to take consecutive measurements by track walkers. Modern state-of-the-art technology has since replaced the traditional slow and painful measurement practice. Inspections are now done from a moving vehicle at hundreds of km per hour without contacting the track. All track geometry parameters are measured up four times per meter; data are analysed in real time by onboard software to identify the location and magnitudes of deviations which exceeds the acceptable tolerance. Historical measurements are stored in databases which are used to establish degradation trends and to guide the planning of maintenance. With the help of high-speed imaging technology, automated video inspection systems are installed on some vehicles to detect other faults in the track structure. Four types of such modern inspection tools are introduced in the paper presentation. These are: a single-car comprehensive inspection vehicle; a dedicated inspection train; a highway-railway dual usage truck and an unmanned inspection system. Actual operational systems are used as examples to illustrate the design and capabilities of each of these types of inspection tools.

Railway track geometry degradation due to differential settlement of ballast/subgrade – Numerical prediction by an iterative procedure

An iterative procedure for numerical prediction of long-term degradation of railway track geometry (longitudinal level) due to accumulated differential settlement of ballast/subgrade is presented. The procedure is based on a time-domain model of dynamic vehicle–track interaction to calculate the contact loads between sleepers and ballast in the short-term, which are then used in an empirical model to determine the settlement of ballast/subgrade below each sleeper in the long-term. The number of load cycles (wheel passages) accounted for in each iteration step is determined by an adaptive step length given by a maximum settlement increment. To reduce the computational effort for the simulations of dynamic vehicle–track interaction, complex-valued modal synthesis with a truncated modal set is applied for the linear subset of the discretely supported track model with non-proportional spatial distribution of viscous damping. Gravity loads and state-dependent vehicle, track and wheel–rail contact conditions are accounted for as external loads on the modal model, including situations involving loss of (and recovered) wheel–rail contact, impact between hanging sleeper and ballast, and/or a prescribed variation of non-linear track support stiffness properties along the track model. The procedure is demonstrated by calculating the degradation of longitudinal level over time as initiated by a prescribed initial local rail irregularity (dipped welded rail joint).

Simulation of vertical dynamic vehicle–track interaction in a railway crossing using Green's functions

Vertical dynamic vehicle–track interaction in the through route of a railway crossing is simulated in the time domain based on a Green's function approach for the track in combination with an implementation of Kalker's variational method to solve the non-Hertzian, and potentially multiple, wheel–rail contact. The track is described by a linear, three-dimensional and non-periodic finite element model of a railway turnout accounting for the variations in rail cross-sections and sleeper lengths, and including baseplates and resilient elements. To reduce calculation time due to the complexity of the track model, involving a large number of elements and degrees-of-freedom, a complex-valued modal superposition with a truncated mode set is applied before the impulse response functions are calculated at various positions along the crossing panel. The variation in three-dimensional contact geometry of the crossing and wheel is described by linear surface elements. In each time step of the contact detection algorithm, the lateral position of the wheelset centre is prescribed but the contact positions on wheel and rail are not, allowing for an accurate prediction of the wheel transition between wing rail and crossing rail. The method is demonstrated by calculating the wheel–rail impact load and contact stress distribution for a nominal S1002 wheel profile passing over a nominal crossing geometry. A parameter study is performed to determine the influence of vehicle speed, rail pad stiffness, lateral wheelset position and wheel profile on the impact load generated at the crossing. It is shown that the magnitude of the impact load is more influenced the wheel–rail contact geometry than by the selection of rail pad stiffness.

Study of the dynamic vehicle-track interaction in a railway turnout

This paper analyzes the vertical dynamic response of a railway track subjected to traffic loads in a turnout, especially around the switch blades and the crossing nose. In order to study the influence of vehicle and track parameters on the vehicle-track dynamics, a numerical feedback interaction between a multi-body model of the vehicle and a 3D finite elements model of the track is carried out. For this purpose, two different models are developed. In the first one, the track is modeled by means of a FE model in the time domain through ANSYS software; while in the second one, the vehicle is simulated as a multi-body model by means of VAMPIRE PRO software. The influence of different parameters (e.g., speed, sprung masses, track stiffness and vehicle eigenfrequencies) on the generation of dynamic loads in a turnout, especially in the switch blades and the crossing nose, is studied. Finally, the vibrations induced by the passing of the vehicle are calculated for different scenarios.

Switch panel design based on simulation of accumulated rail damage in a railway turnout

A methodology for numerical prediction of accumulated rail damage in railway turnouts is presented. Based on simulation of dynamic vehicle-track interaction followed by a discretisation of the conditions in each wheel-rail contact, distributions of rail wear are calculated by the Archard model of sliding wear, while surface initiated rolling contact fatigue (RCF) damage is evaluated by the Palmgren–Miner rule and an index building on shakedown theory. Partial slip in the wheel-rail contacts and variable amplitude loading are considered. For freight traffic in the diverging route, the influence of rail inclination and switch rail elevation on damage in the switch panel is investigated in a demonstration example. Two-point contact situations with one contact on the switch rail and one on top of the stock rail induce relative motion and slip between wheel and rail leading to high energy dissipation. In agreement with field observations, it is concluded that wear is the dominating damage mechanism on the gauge side of the switch rail while the risk for RCF is higher on the crowns of the switch and stock rails. For accurate prediction of rail life for given combinations of wheel/rail materials and traffic conditions, the methodology needs to be calibrated by field measurements.

Integrated analysis of dynamic vehicle–track interaction and plasticity induced damage in the presence of squat defects

Despite significant efforts, the mechanisms behind the formation of squats – a form of rolling contact fatigue (RCF) damage – are not fully understood. This study employs numerical simulations to investigate the propensity of squat initiation in the vicinity of small, isolated rail surface irregularities. Time-domain dynamic vehicle–track interaction analysis is used to obtain wheel–rail contact stress distributions, which are mapped onto a continuum finite element model that accounts for plastic deformation of the rail material. The evaluated stress and strain fields are quantified using two RCF impact measures: accumulated effective strain and the Jiang–Sehitoglu multiaxial low cycle fatigue parameter. It is shown that the RCF impact increases with increasing size of the surface irregularity and that clustering of irregularities might strongly promote RCF. The friction coefficient is identified as a very influential parameter and also the effect of variations in friction along the rail is evaluated.

Drive-by detection of railway track stiffness variation using in-service vehicles

Railway track stiffness is an important track property which can help with the identification of maintenance related problems. Railway track stiffness can currently be measured using stationary equipment or specialised low-speed vehicles. The concept of using trains in regular service to measure track stiffness has the potential to provide inexpensive daily ‘drive-by’ track monitoring to complement data collected by less-frequent monitoring techniques. A method is proposed in this paper for the detection of track stiffness variation through an analysis of vehicle accelerations resulting from the vehicle–track dynamic interaction. The cross-entropy optimisation technique is applied to determine the track stiffness profile, which generates a vehicle response that best fits the measured vertical accelerations of a railway carriage bogie. Numerical validation of the concept is achieved by using a two-dimensional half-bogie dynamic model, representing a railway vehicle, to infer a global track stiffness profile along a track. The track stiffness measurement algorithm is implemented in Matlab. This paper reports the results of the numerical simulations. The proposed method gives good estimates of the track stiffness. To the authors’ knowledge, this is the first time an optimisation technique has been applied to the determination of railway track stiffness.

An efficient approach to the analysis of rail surface irregularities accounting for dynamic train–track interaction and inelastic deformations

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle–track interaction accounting for transient non-Hertzian wheel–rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang–Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.

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.

The influence of rail surface irregularities on contact forces and local stresses

The effect of initial rail surface irregularities on promoting further surface degradation is investigated. The study concerns rolling contact fatigue formation, in particular in the form of the so-called squats. The impact of surface irregularities in the form of dimples is quantified by peak magnitudes of dynamic contact stresses and contact forces. To this end simulations of two-dimensional (later extended to three-dimensional) vertical dynamic vehicle–track interaction are employed. The most influencing parameters are identified. It is shown that even very shallow dimples might have a large impact on local contact stresses. Peak magnitudes of contact forces and stresses due to the influence of rail dimples are shown to exceed those due to rail corrugation.

Excitation of ground vibration due to the passage of trains over a track with trackbed irregularities and a varying support stiffness

Train-induced ground vibration can be excited by wheel and track irregularities and by two kinds of irregularities of the soil, by geometric irregularities or by the spatially varying soil stiffness. For both types of irregularities, the effective track irregularity on top of the track is calculated in wavenumber domain and with wavenumber integrals. For a general multi-beam track model, the wavenumber integrals are solved numerically. The irregularities of the soil are filtered by the track when transferred from the bottom to the top of the track. The high-wavenumber irregularities are strongly reduced due to the bending stiffness of the track and the compliance of the support. In addition, soft track elements reduce directly the stiffness variation of the support. Therefore, the mitigation effect of elastic track elements for these excitation components seems to be important. For under-sleeper pads and slab tracks, calculation and measurements are presented including additional excitation components and the dynamic vehicle–track interaction, and the relevance of the excitation mechanisms is discussed based on the dynamic forces which are acting on the ground. Due to the restricted amplitudes, the parametric excitation by the stiffness variation seems to be less important than the geometric irregularities. The calculations yield the correct trends of the measurements and many details of the measured ballast, slab, and under-sleeper-pad tracks.

Rail corrugation growth accounting for the flexibility and rotation of the wheel set and the non-Hertzian and non-steady-state effects at contact patch

In this work, a simulation tool is developed to analyse the growth of rail corrugation consisting of several models connected in a feedback loop in order to account for both the short-term dynamic vehicle–track interaction and the long-term damage. The time-domain vehicle–track interaction model comprises a flexible rotating wheel set model, a cyclic track model based on a substructuring technique and a non-Hertzian and non-steady-state three-dimensional wheel–rail contact model, based on the variational theory by Kalker. Wear calculation is performed with Archard's wear model by using the contact parameters obtained with the non-Hertzian and non-steady-state three-dimensional contact model. The aim of this paper is to analyse the influence of the excitation of two coinciding resonances of the flexible rotating wheel set on the rail corrugation growth in the frequency range from 20 to 1500 Hz, when contact conditions similar to those that can arise while a wheel set is negotiating a gentle curve are simulated. Numerical results show that rail corrugation grows only on the low rail for two cases in which two different modes of the rotating wheel set coincide in frequency. In the first case, identified by using the Campbell diagram, the excitation of both the backward wheel mode and the forward third bending mode of the wheel set model (B-F modes) promotes the growth of rail corrugation with a wavelength of 110 mm for a vehicle velocity of 142 km/h. In the second case, the excitation of both the backward wheel mode and the backward third bending mode (B-B modes) gives rise to rail corrugation growth at a wavelength of 156 mm when the vehicle velocity is 198 km/h.

A Dynamic Vehicle-Track Interaction Model for Predicting the Track Degradation Process

Due to the repeated passage of trains, differential settlements are observed in the vertical direction of the railway tracks. These settlements depend on the platform quality, on the train speed, on the dynamic load, and on the track structural behavior. In recent years, several authors have defined laws and models for the prediction of settlement. The majority of those settlement models only consider the vertical degradation of the track, disregarding this phenomena in the lateral direction, since the vertical track geometry deteriorates faster than the horizontal one. In these models also the dynamic nature of the vehicle load is not considered accordingly. This paper presents a vehicle-track dynamic-interaction model for predicting the evolution of the vertical track profile and assessing the track response along the degradation process. The model is one-dimensional (1D) and it estimates the track degradation from a settlement law that uses deformation under instantaneous wheel passage as input. Although track degradation is a three-dimensional (3D) process, a 1D model is considered because the vertical component of the track settlement is the largest one. In order to predict the evolution of the track settlement due to the passage of the dynamic loads on the track, an iterative procedure is proposed. One cycle of this methodology is composed by three phases: numerical calculation of the train-track dynamic-interaction loads along the track, calculation of the track settlement, and definition of the track profile after settlement. Then, a new cycle begins. The proposed methodology is applied to a real track profile, measured in a Portuguese railway line, in order to understand the influence of the dynamic nature of the load on the track, the influence of the settlement rate and the influence of the type of vehicle on the evolution of the vertical track profile. The dynamic response of the track over time due to the evolution of the real vertical profile is evaluated through a vehicle-track dynamic-interaction approach. The attained results reveal the importance not only of the track irregularities, but also of the vehicle speed and characteristics on the evolution of the track profile. The numerical simulations presented in this paper evidence the potential of the proposed methodology, which can be used as a tool to forecast track settlement and to estimate the dynamic response of the track along the degradation process.

On the use of second-order derivatives of track irregularity for assessing vertical track geometry quality

This paper studies the use of second-order derivatives of track irregularities (longitudinal level, LL) for assessing vertical track geometry quality. Both a single-degree-of-freedom and a three-DOF vehicle–track model are investigated in order to explain theoretically why from the aspect of vehicle–track dynamic interaction it is relevant to consider not only the amplitudes of LL but also their second-order derivatives (LL2). Simulation results are then presented to demonstrate that dynamic vertical track forces are more correlated with the second-order derivatives (LL2) than to the amplitudes (LL) themselves. A comparison of the power spectral density (PSD) spectra for typical track reveals that it is more convenient to use the PSD spectra for the second-order derivatives than for the amplitudes, as the curves for the second-order derivatives are flat within the short wavelength range. Finally, the practical use of derivatives within the maintenance management system in order to achieve improved assessment of track geometry quality is also discussed.

Analysis of the influence of under sleeper pads on the railway vehicle/track dynamic interaction in transition zones

Sharp changes in the vertical stiffness levels of a track can increase train and infrastructure deterioration to the point where there is a serious risk of a derailment. Major overloading and unloading forces are created between the different track and vehicle components. This phenomenon has grown in importance as the operational speeds of trains have increased with the expansion of high-speed lines. In order to solve this problem a method has to be found to smooth the changes in vertical stiffness levels along the track. In the present paper, the combination of transition regions and under- sleeper pads (USPs) has been studied. The research has been performed by means of a dynamic vehicle–track interaction model created by synthesizing a series of sub-models of individual effects. The analysed variables allow various track configurations, train travelling speeds and the stiffness of the USPs to be investigated. The obtained results show that combining transition zones with USPs pads allows more homogeneous vertical stiffness levels to be achieved along the tracks which results in improved dynamic behaviour of the vehicle–track system.

Simulation of dynamic vehicle–track interaction on small radius curves

A time-domain method for the simulation of general three-dimensional dynamic interaction between a vehicle and a curved railway track, accounting for a prescribed relative wheel–rail displacement excitation in a wide frequency range (up to several hundred Hz), is presented. The simulation model is able to capture the low-frequency vehicle dynamics simultaneously due to curving and the high-frequency track dynamics due to the excitation by, for example, the short-pitch corrugation on the low rail. The adopted multibody dynamics formulation considers inertia forces, such as centrifugal and Coriolis forces, as well as the structural flexibility of vehicle and track components. To represent a wheel/rail surface irregularity, isoparametric two-dimensional elements able to describe generally curved surface shapes are used. The computational effort is reduced by including only one bogie in the vehicle model. The influence of the low-frequency vehicle dynamics of the remaining parts of the vehicle is considered by pre-calculated look-up tables of forces and moments acting in the secondary suspension. For a track model taken as rigid, good agreement is observed between the results calculated with the presented model and a commercial software. The features of the model are demonstrated by a number of numerical examples. The influence of the structural flexibility of the wheelset and track on wheel–rail contact forces is investigated. For a discrete rail irregularity excitation, it is shown that the longitudinal creep force is significantly influenced by the wheelset eigenmodes. The introduction of a velocity-dependent friction law is found to induce an oscillation in the tangential contact force on the low rail with a frequency corresponding to the first anti-symmetric torsional mode of the wheelset. Further, under the application of driving moments on the two wheelsets and excitation by a discrete irregularity on the high rail, the frequency content of the tangential contact forces on the low rail is significantly influenced by the P2 resonance as well as by several wheelset eigenmodes.

On the effect of unsupported sleepers on the dynamic behaviour of a railway track

The effect of unsupported sleepers on the dynamic behaviour of a railway track is studied based on vehicle–track dynamic interaction theory, using a model of the track as a Timoshenko beam supported on a periodic elastic foundation. Considering the vehicle's running speed and the number of unsupported sleepers, the track dynamic characteristics are investigated and verified in the time and frequency domains by experiments on a 1:5 scale model wheel–rail test rig. The results show that when hanging sleepers are present, leading to a discontinuous and irregular track support, additional wheel–rail interaction forces are generated. These forces increase as further sleepers become unsupported and as the vehicle's running speed increases. The adjacent supports experience increased dynamic forces which will lead to further deterioration of track quality and the formation of long wavelength track irregularities, which worsen the vehicles’ running stability and riding comfort. Stationary transfer functions measurements of the dynamic behaviour of the track are also presented to support the findings.