Dynamic Vehicle Track Interaction Research Articles

The effect of fastener clip fatigue for high-speed railway on vehicle-track dynamic interaction: Numerical analysis and probabilistic evaluation

To investigate the vehicle-induced fatigue damage evolution of fastener clips and their impact on the vehicle-track (VT) system, a numerical dynamic model is established to achieve probabilistic evaluation. The “rain flow” counting method is adopted to describe the stress cycles of the hazard area of the clips, and the S-N curve is used to predict the fatigue life of the clips. The solution of the dynamic equation of motion is obtained by the time-domain Green's function method, which is an effective method to improve computational efficiency. A versatile iterative algorithm is adopted to solve the nonlinear system considering the damaged clips. In the probabilistic evaluation framework, a novel random field method is employed to depict the spatial variability of clips’ strength. The applicability of the model established in this work in aspects of expressing random damage of fasteners and evaluating the dynamic behavior of the system is demonstrated by different numerical examples. The results show that the dynamic responses of the train and track system significantly exacerbate as the number of train cycles increases, which is closely related to the variability and non-uniform damage of the fasteners. The probability of cumulative damage to the fasteners induced by the train follows a three-stage rule, and the fatigue damage of the non-uniform fastener system caused by the train is greater than that of the uniform situation. In addition, the short wave components of track irregularity will significantly exacerbate the damage to fasteners and therefore degrade the status of the railway line. As the driving speed increases, the damage to the fasteners also increases, but the impact of vehicle speed on the fastener damage is smaller than that of track irregularity, especially in the range of fatigue damage greater than 0.9. Therefore, maintaining the geometric smoothness of the track, controlling the uniformity of the mechanical properties of the fasteners, and reducing the driving speed are feasible measures to extend the service life of the fastener system, thereby ensuring the operation of high-speed trains.

Parametric investigation of railway fastenings into the formation and mitigation of short pitch corrugation

Short pitch corrugation has been a problem for railways worldwide over one century. In this paper, a parametric investigation of fastenings is conducted to understand the corrugation formation mechanism and gain insights into corrugation mitigation. A three-dimensional finite element vehicle–track dynamic interaction model is employed, which considers the coupling between the structural dynamics and the contact mechanics, while the damage mechanism is assumed to be differential wear. Various fastening models with different configurations, boundary conditions, and parameters of stiffness and damping are built up and analysed. These models may represent different service stages of fastenings in the field. Besides, the effect of train speeds on corrugation features is studied. The results indicate: (1) Fastening parameters and modelling play an important role in corrugation formation. (2) The fastening longitudinal constraint to the rail is the major factor that determines the corrugation formation. The fastening vertical and lateral constraints influence corrugation features in terms of spatial distribution and wavelength components. (3) The strengthening of fastening constraints in the longitudinal dimension helps to mitigate corrugation. Meanwhile, the inner fastening constraint in the lateral direction is necessary for corrugation alleviation. (4) The increase in fastening longitudinal stiffness and damping can reduce the vibration amplitudes of longitudinal compression modes and thus reduce the track corrugation propensity. The simulation in this work can well explain the field corrugation in terms of the occurrence possibility and major wavelength components. It can also explain the field data with respect to the small variation between the corrugation wavelength and train speed, which is caused by frequency selection and jump between rail longitudinal compression modes.

Dynamic vehicle–track interaction and structural loading in a crossing panel – calibration and assessment of a model with a 3D representation of the crossing rail

ABSTRACT A three-dimensional (3D) finite element model of a railway crossing panel for use in multibody simulation (MBS) of dynamic vehicle–track interaction is presented. It is a two-layer track model with stock rails and sleepers represented by beam elements and a crossing rail represented by 3D solid elements. The track model uses linear bushings for the rail fastenings and bi-linear bushings for the ballast to allow for potentially voided sleepers. Based on the output from the MBS, the structural loading of the crossing in terms of strains, stresses and sleeper-ballast contact pressures is extracted in a post-processing step. The model is calibrated and validated to measurement data from a comprehensively instrumented switch & crossing (S&C) demonstrator installed in the Austrian railway network as a part of the European research programme Shift2Rail. The applied procedure for the calibration and critical assessment of the crossing model is described in detail. It is based on a model parameterisation with eight parameters relating to the rail fastening and foundation stiffnesses and to a distribution of the ballast voids. The calibration method uses Latin hypercube samples to explore the parameter space in a sensitivity analysis before a parameter optimisation is performed using a gradient-based method on a response surface built from a polyharmonic spline. In a comparative study it is shown that the 3D model and a more conventional beam model of the crossing rail show similar calibration results and good agreement with the measured data. The 3D model allows for the extraction of stress concentrations in the crossing rail but has an increased computational time of about 30% compared to the beam model.

Experimental and numerical investigation into the characteristics of continuously measured rail profiles and its influence on simulations of vehicle-track interaction

This study investigates the influence of variations in rail profiles along the operation direction on simulations of vehicle-track interaction by combining numerical and experimental approaches. For this purpose, a procedure for the evaluation of rail profile measurement data is proposed based on the GEKON 3D inspection instrument. By establishing a dynamic vehicle-track interaction model, a comparative evaluation is performed with the uniform rail profiles or variations in the rail profiles. The results indicate that the proposed procedure can process raw data from continuous measurements, and the indices in terms of rail section loss, curvature index, and wheel-rail contact geometry can be evaluated. Furthermore, the influence of the rail profile variations along the train operating direction should not be overlooked, especially in curved tracks where the symmetry of the left and right rail profiles is poor. By considering the influence of variations in rail profiles, the simulated results are more likely to reflect the actual situation of dynamic vehicle-track interaction. It is believed that the use of uniform rail profiles may result in accuracy loss when analyzing dynamic vehicle responses, especially under scenarios of long-distance wheel-rail contact status.

Dynamic vehicle–track interaction and loading in a railway crossing panel – calibration of a structural track model to comprehensive field measurements

This paper presents a finite element model of a railway crossing panel for use in multibody simulations (MBS). It is a two-layer track model with rails and sleepers represented by beam elements that use linear bushings for rail fastenings and non-linear bushings for ballast. The model is calibrated and validated to measurement data from a comprehensively instrumented switch and crossing demonstrator installed in the Austrian railway network as a part of the European research programme Shift2Rail. The validation concerns the capability of the model to capture the structural response of the crossing panel under traffic loading after calibration of physical track parameters to realistic values. The structural response is measured in the form of displacements, strains, and sleeper-ballast contact forces. It is shown that the developed model can represent the measured track responses well and that it was necessary to account for a varying sleeper-ballast gap distribution along the crossing transition sleeper to obtain good agreement. The calibration uses Latin hypercube samples to explore the parameter space in a sensitivity analysis before a parameter optimisation is performed using a gradient-based method on a response surface built from a polyharmonic spline.

Effect of polygonal wheel on the vehicle-track dynamic interaction in turnout and its transmission to the trailer bogie wheels

The dynamic interaction between the vehicle and track is strongly influenced by out-of-round wheels and turnout rail profile geometries, which result in high-magnitude contact forces and abnormal vibrations. This study presents the dynamic response of the tram-turnout interaction due to polygonal wheel wear and analyses its transmission between the wheelsets. A three-dimensional coupled tram-turnout dynamic model was formulated, taking into account the polygonal wear on the front bogie wheelsets. Through numerical simulations, the dynamic characteristics of a tram passing through the turnout switch and crossing panels under the influence of polygonal wear were simulated. Furthermore, the impact of polygonal wear amplitudes and tram speeds on the transmission of dynamic impact forces and vibrations from the front bogie wheelset to the trailer bogie wheels are described. According to the numerical findings, when the flexible wheelset experiences polygonal wear, it can lead to substantial impact forces and vibrations as the tram moves through the turnout switch and crossing zones. Moreover, the transmission of dynamic impact forces and vibrations from the front bogie wheelset to the trailer wheels increases as the wheel wear amplitude and the vehicle speed increase.

Influence of railway wheel tread damage on wheel–rail impact loads and the durability of wheelsets

Dynamic wheel–rail contact forces induced by a severe form of wheel tread damage have been measured by a wheel impact load detector during full-scale field tests at different vehicle speeds. Based on laser scanning, the measured three-dimensional damage geometry is employed in simulations of dynamic vehicle–track interaction to calibrate and verify a simulation model. The relation between the magnitude of the impact load and various operational parameters, such as vehicle speed, lateral position of wheel–rail contact, track stiffness and position of impact within a sleeper bay, is investigated. The calibrated model is later employed in simulations featuring other forms of tread damage; their effects on impact load and subsequent fatigue impact on bearings, wheel webs and subsurface initiated rolling contact fatigue of the wheel tread are assessed. The results quantify the effects of wheel tread defects and are valuable in a shift towards condition-based maintenance of running gear, and for general assessment of the severity of different types of railway wheel tread damage.

Probability of rail break caused by out-of-round wheel loads

A simulation procedure to predict the probability of rail break due to a measured wheel load spectrum is presented. The load distribution includes a representative proportion of high-magnitude dynamic loads generated by out-of-round wheels. Linear elastic fracture mechanics is applied to determine the stress intensities of pre-existing rail head cracks in a continuously welded rail subjected to combined bending and temperature loading. Rail bending moments are evaluated using a validated time-domain model of dynamic vehicle–track interaction. The considered multi-dimensional stochastic parameter space includes field test data of dynamic loads from a wheel impact load detector and crack depths from eddy current data. Meta-models based on poly-harmonic splines are applied to reduce the computational cost of the analysis. Supported by the extensive field test data, the simulation procedure is demonstrated by investigating the influences of freight traffic type, track support stiffness and rail temperature on the probability of a rail break initiated at a pre-existing rail head crack.

Comprehensive model of a rotating flexible wheelset for high-frequency railway dynamics

The development and application of wheelset models that realistically incorporate both flexibility and rotation, constitutes a topic that has recently been active in the literature regarding high-frequency railway dynamics. The main application of these models is the simulation of the railway vehicle-track dynamic interaction, which justifies the fact that most of them are formulated using coordinates that do not rotate with the solid (Euler coordinates). Wheelset models based on rotating coordinates are scarce, although they have some practical applications when the vibration response at points fixed in the material is required (e.g., to simulate the signal of a transducer that is fixed at a point on the wheelset). The present work provides a global method in the modelling of a flexible and rotating railway wheelset, independent of the coordinates used (fixed or rotating). To achieve this, a compact formulation is developed adopting axisymmetric coordinates through both Lagrangian and Eulerian approaches, which are related by means of a coordinate transformation. The equations of motion that are deduced for both reference frames are linear, which allows the natural frequencies to be obtained as seen from a fixed frame as well as the ones observed for a system that rotates with the wheelset. The relationship between the natural frequencies obtained from both equations of motion is expressed as a closed-form formula that depends on the angular velocity of the wheelset. The model is applied to simulate the response measured by the strain gauges used in load-measuring wheelsets, in which a vertical force is acting in the wheel-rail contact. The results can contribute to establish limits on the use of the instrumented wheelsets based on the angular velocity and the frequency of the force applied in the wheel-rail contact.

Prediction of long-term differential track settlement in a transition zone using an iterative approach

A methodology for the simulation of long-term differential track settlement, the development of voided sleepers leading to a redistribution of rail seat loads, and the evolving irregularity in vertical track geometry at a transition between two track forms, is presented. For a prescribed traffic load, the accumulated settlement is predicted using an iterative approach. It is based on a time-domain model of vertical dynamic vehicle–track interaction to calculate the contact forces between sleepers and ballast in the short-term. These are used in an empirical model to determine the long-term settlement of the ballast/subgrade below each sleeper. Gravity loads and state-dependent track conditions are accounted for, including a prescribed variation of non-linear stiffness of the supporting foundation along the track model. In parallel, a two-dimensional (2D) non-linear finite element model of layered soil is verified versus field measurements and used to determine the support stiffness of each sleeper in the track model. The methodology is applied to a transition zone between a ballasted track and a slab track that is subjected to heavy haul traffic. Analyses of the influence of higher axle loads and the implementation of under sleeper pads on sleeper settlement are demonstrated.

Influence of vibration suppression device for ladder-type sleeper track on vehicle-track system dynamic interaction

The ladder-type sleeper track (LS track) is one of the traditional vibration-attenuating track systems. Based on engineering experience, a vibration suppression device (VSD) for the LS track has been developed to reduce LS track vibration caused by metro trains and improve train running stability. In this work, numerical simulation was used to investigate the effect of essential VSD parameters such as stiffness, damping, and preload on the dynamic responses of the vehicle-LS track system. Firstly, a refined vehicle-LS track coupled dynamics model involving an elaborated model of VSD was developed to investigate the action principle of VSD and the influence of various action methods on LS track vibration suppression. Then, the effects of VSD were thoroughly investigated using the proposed model from the perspectives of vehicle-track dynamic interaction, vehicle dynamics, and LS track’s stability and vibration attenuation capabilities. Finally, the influence tendency of major VSD parameters on vehicle and LS track dynamic performance, as well as the range of VSD parameters engineering feasibility, was explored. The results show that VSD features can affect the vehicle-LS track dynamics performance. VSD not only reduces LS track vibration, but also improves vehicle’s operating stability, and VSD’s influence becomes more substantial with the rise of crucial VSD parameter values.

Dynamic response of vehicle-track interaction at the bolted rail joint in the presence of the polygonal wheel

Rail joints are the weakest link in the railway track structure due to the presence of discontinuities in the track stiffness and wheel-rail contact geometry. This paper presents the dynamic response of vehicle-track interaction at the bolted rail joint (BRJ) in the presence of polygonal wheel wear. A three-dimensional coupled vehicle-track dynamic model was established using the finite element method (FEM) and the multi-body system (MBS) approach, in which the flexibilities of the wheelset and track are taken into account. The proposed dynamic model is validated by the comparisons of field measurement and calculated vertical axle-box acceleration in time and frequency domains. The effects of the flexible wheelset in the presence of polygonal wear on the vehicle-track dynamic interaction at the BRJs are illustrated through comparisons with those obtained using without polygonal wheel model. The results show that the polygonal wheel wear and the rail joint irregularities can induce high-magnitude vertical wheel-rail contact force, and exacerbate the vibration responses of the axle box, the wheelset, and the rails. The simulation results also indicate that the wheelset bending modes, the P2 resonance due to rail joint excitation, and the track vibration modes have significant effects on the vertical vehicle-track dynamic interaction at the supported and suspended BRJs.

Comparison of the dynamic response and environmental impact between traditional and innovative railway track systems

ABSTRACT Railways employ a range of different railway track forms. Here, a ballasted track design is compared to three different slab track solutions. The track designs are compared using both a life cycle analysis (LCA) and a methodology for simulation of three-dimensional vertical dynamic vehicle–track interaction, which has been verified versus field measurements. The interaction between vehicle and track is simulated in the time domain using an extended state-space vector approach. For the investigated load cases involving representative wheel and track irregularities, it is concluded that the maximum stress in the concrete parts is, for all designs, below the maximum flexural tensile strength. From the LCA, it is concluded that the production of steel and concrete cause most CO2 emissions, while the CO2 emissions due to maintenance activities such as tamping and rail grinding are only a small part of the overall emissions.

2D and 3D soil finite/infinite element models: modelling, comparison and application in vehicle-track dynamic interaction

ABSTRACT In this work, 2D and 3D vehicle-track-soil (VTS) models are developed in a coupled manner. The VTS system is modelled as an integration of the multi-rigid-body vehicle sub-model, multi-scale finite element ballastless track sub-model and finite/infinite element (FE/IE) soil sub-model, where the IE method is introduced to deal with the boundary condition of the far-field soil. Particularly, the detailed approach for modelling the FE/IE soil sub-model is depicted in the 2D and 3D space domain, respectively. Through comparisons, it is proved that the IE method shows advantages in simulating the soil far-field region by meeting a soil boundary condition. Case studies are conducted to demonstrate the superiority and applicability of this model in improving the computational efficiency. Besides, the influence of vehicle speed on system dynamic performance is revealed, where the soil critical speed derived by the soil Rayleigh surface wave speed is explored by the vehicle-induced vibrations.

Optimisation of slab track design considering dynamic train–track interaction and environmental impact

Modern railway tracks for high-speed traffic are often built based on a slab track design. A major disadvantage of slab track compared to conventional ballasted track is that the environmental impact of the construction is higher due to the significant amount of concrete required. In this paper, the dimensions of the rectangular cross-sections and the types of concrete used in slab tracks are optimised with the objective to minimise greenhouse gas emissions, while considering the constraint that the design must pass the static dimensioning analysis described in the European standard 16432-2. The optimised track design is also analysed using a three-dimensional (3D) model of vertical dynamic vehicle–track interaction, where the rails are modelled as Rayleigh–Timoshenko beams and the concrete parts are represented by quadratic shell elements. Wheel–rail contact forces and the time-variant stress field of the concrete parts are calculated using a complex-valued modal superposition for the finite element model of the track. For the studied traffic scenario, it is concluded that the thickness of the panel can be reduced compared to the optimised design from the standard without the risk of crack initiation due to the dynamic vehicle load. In parallel, a model of reinforced concrete is developed to predict crack widths, the bending stiffness of a cracked panel section and to assess in which situations the amount of steel reinforcement can be reduced. To reduce the environmental impact even further, there is potential for an extended geometry optimisation by excluding much of the concrete between the rails.

Vehicle-track random vibrations considering spatial frequency coherence of track irregularitives

To disclose the possible dynamic behaviours of vehicle-track systems subject to an entire railway network, random vibration analysis is of great concern in railway engineering due to the system geometric and parametric uncertainties. In this work, an emphasis is therefore put on the highly efficient simulation and numerical analysis of track geometry excitation and its induced system uncertain behaviours. Considering the spatial variability, frequency coherence and constant evolution of track irregularities, the random analysis of track irregularities belongs to a big data analysis scope. By introducing practical tools of power spectral density (PSD), frequency coherence analysis and correlated variable random simulation method, a strategy for obtaining representative and realistic track irregularity PSD samples is proposed. Besides, the modelling method of vehicle-track interactions, where versatile programming tactics to couple the track slab and subgrade elements with incompatible elemental sizes, is introduced. By combining the simulation methods of track irregularities and vehicle-track dynamic interaction, the dynamic performance of vehicle-track systems can be evaluated efficiently, and the full view of system dynamics is revealed with probabilistic characteristics.

A comparison of track model formulations for simulation of dynamic vehicle–track interaction in switches and crossings

This paper compares different track model formulations for the simulation of dynamic vehicle–track interaction in switches and crossings (S&C, turnouts) in a multi-body simulation (MBS) environment. The investigations are an extension of the S&C simulation Benchmark with the addition of a finite element model of a 60E1-760-1:15 turnout. This model constitutes a common reference from which four different track formulations are derived: co-running, modal superposition, finite element incorporated into the MBS model and finite element coupled to MBS using a co-simulation approach. For the different track models, the difference in modelling technique, results, simulation time, and suitability for different simulation tasks is compared. A good agreement is found between the different track model formulations for wheel–rail contact forces and rail displacements. This study found a better agreement between co-running and structural track models compared to previous studies in the prediction of wheel–rail contact forces. This appears to be due to the increased complexity of co-running track model used in this study together with a tuning of the co-running track model to the reference model in a wider frequency range. For the reader interested to reproduce the results in this paper, the reference track model is available for download.

A coupled model for investigating the interfacial and fatigue damage evolution of slab tracks in vehicle-track interaction

Modeling, evaluation and prediction of slab track damage and its evolution are nowadays challenge and hot topics, in which the computer modeling program lies a foundation for vehicle-track dynamic analysis subject to slab track damage except the experimental research. In this work, the finite element modeling methods and related computer modules are presented to compile a simulation program to evaluate the slab track damage evolution accompanied by vehicle-track dynamic interaction, where the moving vehicle is modeled as a multi-rigid-body system with the primary and secondary suspensions, and the Bernoulli-Euler beam, thin-plate and solid finite element and spring-dashpots are introduced to model the track system. The fatigue damage constitutive models of the concrete slabs and viscoelastic filling layers, and the interfacial cohesive zone model, are set as the criteria to control and characterize the damage evolution of slab tracks. Apart from model validations, numerical studies are conducted to quantitatively show influence of track irregularities on slab track damage evolution and the slab track damage on vehicle-track system response. It illustrates the necessity of considering the combined fatigue and interfacial damages of slab tracks instead of separately accounting for the fatigue or interfacial damage.

Multibody simulation benchmark for dynamic vehicle–track interaction in switches and crossings: results and method statements

A Benchmark of railway multibody dynamics software application to switches and crossings (S&C) is presented, comparing all major commercially available software and a few independent codes. Two different representative S&C have been implemented, using the Manchester Benchmark passenger vehicle. The final results show that all software offer a reliable and efficient way to understand the kinematic and dynamics forces between the wheels and the track elements. The highest challenges are found when modelling a combination of multiple rails in simultaneous contact with a wheel (check-stock or switch-stock), large longitudinal variations in rail shape (crossings) and high lateral steering forces (diverging cases in tight radius). In those cases, the codes able to account for the exact relative motion of each wheels with respect to each rails independently are the most apt. The most significant variations between software are found in the contact prediction with an influence on the detailed contact tangential and normal forces. The user variability is found to be very small, with the most time-consuming and error prone being the task of handling the input data for the variable rails definition. All software could benefit from improvements to assist the user and ensure higher reliability and efficiency generally.

Modelling of periodic slab track using time-frequency hybrid Green's function method and its application to vehicle-track dynamic interaction

Periodic slab tracks, as a type of non-ballasted track, are widely used in the high-speed railway and urban subway. Efficient and accurate dynamics modelling of the periodic slab track is a crucial issue for solving the vehicle-track dynamic interaction. In this paper, a time-frequency hybrid Green's function method (GFM) is first developed to model the dynamics of the periodic slab track, in light of the properties of the periodicity, symmetry and attenuation of the Green's functions. By combining with the classical vehicle-rail dynamics model, the simulation of the vehicle-track dynamic interaction is then performed. To improve the computational efficiency, the step-moving window strategy is introduced to characterize the vehicle moving on the infinite length track. The floating slab track, a representation of the periodic slab track, is adopted to reflect the time-spatial distribution of the Green's functions. The truncation errors caused by the presented GFM are analysed by calculating dynamic responses induced by a metro vehicle moving on the floating slab track to determine the truncation parameters. The proposed GFM-based vehicle-track dynamic interaction model is finally validated by comparing with the finite element method (FEM) and the basic dynamic characteristics of the periodic slab track are further investigated. Numerical studies show that the computational accuracy of the GFM-based model is nearly the same with the FEM-based model, but the efficiency can be greatly improved. Moreover, it is concluded that the longitudinal uneven stiffness of the periodic slab track shows a significant influence on the slab displacement and stress, while has a slight influence on the fastener force and slab acceleration.