Train Track Interaction Research Articles

Subsurface rolling contact fatigue damage of railway wheels – A probabilistic analysis

A numerical model for predicting the probability of subsurface initiated rolling contact fatigue failure in railway wheels subjected to operational loading is presented. The loading is evaluated through simulations of dynamic train–track interaction incorporating the influence of, e.g., corrugation. Contact stresses are found from Hertzian theory and the resulting stress field from theory of elasticity. Fatigue damage is evaluated by use of a Wöhler curve where the fatigue strength is decreased due to the influence of material defects, which are presumed to be of random size and occurrence in the stressed volume of the wheel rim. Damage accumulation is performed using the Palmgren–Miner rule, extending the model to cases of variable loading. The results show how a combination of rail corrugation and high train speeds have a significant impact on the probability of fatigue failure. A sensitivity analysis reveals a strong influence of the fatigue strength and the material defect distribution on the probability of fatigue failure.

Effect on vehicle and track interaction of installation faults in the concrete bearing surface of a direct-fixation track

Various installation faults can occur in fasteners in the construction of a direct-fixation track using the top-down method. In extreme cases, these faults may cause excessive interaction between the train and track, compromise the running safety of the train, and cause damage to the track components. Therefore, these faults need to be kept within the allowable level through an investigation of their effects on the interactions between the train and track. In this study, the vertical dynamic stiffness of fasteners in installation faults was measured based on a dynamic stiffness test by means of an experimental apparatus that was devised to feasibly reproduce installation faults with an arbitrary shape. This study proposes an effective analytical model for a train–track interaction system in which most elements, except the nonlinear wheel–rail contact and some components that behave bilinearly, exhibit linear behavior. To investigate the effect of the behavior of fasteners in installation faults in a direct-fixation track on the vehicle and track, vehicle–track interaction analyses were carried out, targeting key review parameters such as the wheel load reduction factor, vertical rail displacement, wheel load, and mean stress of the elastomer. From the results, it was noted that it is more important for the installation faults in the concrete bearing surface of a direct-fixation track to be limited for the sake of the long-term durability of the elastomer rather than for the running safety of the train or the structural safety of the track.

Dynamic comparison of different types of slab track and ballasted track using a flexible track model

The dynamic performance of a ballasted track and three types of slab track is analysed and compared by means of a comprehensive dynamic model of the train–track system, generated using two commercial analysis software packages: the commercial multibody system (MBS) analysis software SIMPACK and the finite element method (FEM) analysis software NASTRAN. The use of a commercial MBS software makes it possible to include, in a reliable way, models of advanced non-linear wheel–rail contact as well as complex elements or joints in the vehicle model, while the FEM the flexibility of the rail and the slab to be taken into account. As a result, a combined MBS–FEM representation of the vehicle–track model is integrated into the MBS software, which allows for the study of dynamic phenomena in a wide frequency range. In this study, other simpler approaches for modelling the dynamic vehicle–track interaction are also considered, such as pure multibody or FE representations of the whole vehicle–track system. The quality of the results obtained with the different types of models used is analysed, and some conclusions are put forth regarding the possible validity of rather simple train–track interaction model types under certain conditions as well as the most suitable configuration of the most complex models.

Dynamic train–track interaction at high vehicle speeds—Modelling of wheelset dynamics and wheel rotation

Vertical dynamic train–track interaction at high vehicle speeds is investigated in a frequency range from about 20 Hz to 2.5 kHz. The inertial effects due to wheel rotation are accounted for in the vehicle model by implementing a structural dynamics model of a rotating wheelset. Calculated wheel–rail contact forces using the flexible, rotating wheelset model are compared with contact forces based on rigid, non-rotating models. For a validation of the train–track interaction model, calculated contact forces are compared with contact forces measured using an instrumented wheelset. When the system is excited at a frequency where two different wheelset mode shapes, due to the wheel rotation, have coinciding resonance frequencies, significant differences are found in the contact forces calculated with the rotating and non-rotating wheelset models. Further, the use of a flexible, rotating wheelset model is recommended for load cases leading to large magnitude contact force components in the high-frequency range (above 1.5 kHz). In particular, the influence of the radial wheel eigenmodes with two or three nodal diameters is significant.

Enhancement of the finite-element method for the analysis of vertical train—track interactions

The accuracy of the simulation of train—track interaction can be improved by adding a node at the point of loading, when a contact force exists within the beam element that models the rail. This causes difficulties in the formulation and entails large computational times since the node moves along with the point of contact. In this study, a more simplified method that can represent the discontinuities of slope deflection at the location of both the sleeper and of the moving contact force, while employing the customary finite-element method, has been presented. The simulation of the existence of such an added node without explicitly including it is realized by modifying the Hertzian spring coefficient and adding the additional mass matrix to the existing mass matrix. Also, to enhance the convergence and to overcome the computational burden of load vector calculations at all iterations, a modified Newmark-β integral scheme is proposed. The suggested model was validated by comparing the results with field-test data and other numerical models reported in the literature by other researchers.

Application of 2D-infinite beam elements in dynamic analysis of train-track interaction

Railway structure is a structure with an infinite length for which its modeling is usually carried out by accepting some assumptions for boundary conditions. In practice, there are various methods of modeling by forming equations of motions and dynamic analysis. One of these methods is modeling the railway track by finite element method. Generally in such modeling, a limited length of a track is modeled and executed by implementing some boundary conditions. Assortment of boundary conditions has an effect on dynamic responses. To reduce such effects, usually the length of the track is chosen to such a measure to minimize the dynamic responses of the end points of the track elements to zero. Doing so would cause an increase in the length of the track and hence add to an equation’s degrees of freedom, volume of output and prolongation of analysis time. For this reason, a combination of finite elements and infinite beam elements (two end elements) has been proposed for railway track modeling. Also, matrices of mass, damping and stiffness of one infinite element which has been laid on a visco-elastic bed, have been calculated by implementing selected shape functions. Therefore, by applying two infinite beam elements on either side of the model, a railway track is formed like a beam on an elastic bed which creates the possibility of eliminating the boundary condition effects.

Effects of train impacts on urban turnouts: Modelling and validation through measurements

Train–track interaction at turnouts is a main issue in the design and maintenance of railway systems. Due to the particular geometry of wheel–rail contact and to the sudden variation of track flexibility, severe impact loads may occur during train passage over the turnout. In this paper, two different modelling approaches to reproduce train–turnout interaction are proposed and compared. A first technique, developed by Politecnico di Milano, is based on a detailed multi-body model of the trainset and of wheel–rail contact, whereas for the turnout structure a simplified finite element model is used. The second modelling technique, developed by the National Technical University of Athens, relies on a detailed finite element model of the turnout, while a simplified model is used to compute impact loading due to wheel passage. In this paper the two methods are validated trough comparison with line measurements performed on turnout systems from three different urban railway networks.

Numerical and experimental evaluation of extreme wheel–rail loads for improved wheelset design

The knowledge of extreme loads is of fundamental importance for the fatigue design of railway wheelsets. In the present research, attention is focused on the effect of impulsive loads produced by the negotiation of turnouts and other singularities in the line and by wheelflats. Numerical investigations were performed using a train/track interaction mathematical model accounting for different types of impulsive loads, and the results were compared with measurements performed by an instrumented test train on a railway line and on a test circuit. The results show that singularities in the line and wheelflats actually produce extremely high train–track interaction effects, although the stresses in the axle seem to be only marginally affected.

Ground-borne vibration due to static and dynamic axle loads of InterCity and high-speed trains

In predictions of railway-induced vibrations, a distinction is generally made between the quasi-static and dynamic excitation. The quasi-static excitation is related to the static component of the axle loads. The dynamic excitation is due to dynamic train–track interaction, which is generated by a large number of excitation mechanisms, such as the spatial variation of the support stiffness and the wheel and track unevenness. In the present paper, the quasi-static excitation and the dynamic excitation due to random track unevenness are evaluated by means of numerical predictions. A solution strategy is presented that allows for the evaluation of the second-order statistics of the response due to dynamic excitation based on the power spectral density function of the track unevenness. Due to the motion of the train, the second-order statistics of the response at a fixed point in the free field are non-stationary and an appropriate solution procedure is required. The quasi-static and dynamic contribution to the track and free-field response are analysed for the case of InterCity and high-speed trains running at a subcritical train speed. It is shown how the train speed affects the quasi-static and dynamic contribution. Finally, results of numerical predictions for different train speeds are compared with field measurements that have been performed at a site along the high-speed line L2 Brussels–Köln within the frame of homologation tests.

Under sleeper pads—Influence on dynamic train–track interaction

The influence of under sleeper pads (USP) on dynamic train–track interaction is investigated in a parameter study. Two numerical models that are valid in different frequency intervals are used. The time-domain model DIFF is used to study wheel–rail contact forces, rail bending moments, rail vibrations (displacements, velocities and accelerations), sleeper vibrations and loads on sleepers at high frequencies, here 50–3000 Hz. The frequency-domain model GroundVib is adopted to calculate sleeper vibrations at low frequencies. Frequency-dependent material properties of rail pads, USP and ballast/subgrade are accounted for by viscoelastic spring–damper models that are calibrated with respect to measured data. It is found that USP influence dynamic train–track interaction mainly in the frequency range 0–250 Hz. Similar sleeper responses are calculated by the two models, although some differences in magnitudes are present.

A new approach to the analysis and presentation of vertical track geometry quality and rail roughness

A new approach on enhancing the assessment of track geometry quality and rail roughness by means of train–track interaction simulation and wavelength content analysis is presented. The dynamic model includes vehicle, track and linearized wheel–rail contact with moving irregularities and can be simulated either in the frequency domain by using FFT or in the time domain by constructing a filter function based on system identification technique. The system is suitable to calculate wheel–rail forces for very long track sections and for several vehicle types under a wide range of travelling speeds since the computational scheme is very efficient (300 km/s on a standard computer). With numerical results we demonstrate the potential benefits of improving conventional track geometry inspection methods and highlight short defects (0.5–2 m) as a cause of high dynamic wheel–rail interaction forces. By using a wavelength weighting of measured rail roughness a new improved way of analyzing rail roughness data is also presented. This improves condition assessment of tracks and rails and will enable the track engineer to monitor the track in a better way.

Safety assessment of underground vehicles passing over highly resilient straight track in the presence of a broken rail

The current article presents the results of a research study that dealt with the simulation of vehicle—track interaction for a new slab track design, conceived to reduce noise and vibration levels transmitted to the neighbouring buildings. This design is mainly distinguished by its high elasticity and damping. A more elastic track, however, leads to greater rail deflections, which could affect the train's overall running safety. In this study, the derailment risk for trains running on slab track when encountering a broken rail has been evaluated. Two different types of rail fastening system with different elasticities have been analysed and compared. The results of this study will be considered in future track work projects. Up to now, the study has only been applied to straight track, even though the model is currently being extended to also study curved tracks. Numerical methods were used in order to simulate the dynamic behaviour of the train—track interaction. For that purpose, multi-body system (MBS) modelling techniques were combined with the techniques based on the finite-element method (FEM). MBS modelling was used for modelling the vehicle and FEM for simulating the elastic track. The simulation model was validated by comparing simulated results with experimental data obtained in field testing. During the simulations, various safety indices, characteristic of derailment risk, were analysed. The simulations realized at the maximum running velocity of 110 km/h showed a similar behaviour for several track types. When reducing the running speed, the safety indices worsened for both cases. Although the worst behaviour was observed for the track with a greater elasticity, in none of the simulations did a derailment occur when running over the broken rail.

Dynamic Properties of the Railway Track

The paper is focused on different aspects of track dynamics and train-track interaction. The dynamic modeling of railway track response and of the interaction of vehicle and track at low and mid frequencies, that are significant for the track deterioration, is presented. Dynamic properties of the track structure as a whole is described and evaluated including the dynamics of compound train-track system. The dynamic amplification resulting from the simulated passage of the locomotive of the type E 499.0 (85t) is presented.

Subsurface initiated rolling contact fatigue of railway wheels as generated by rail corrugation

A fracture mechanics based fatigue index for rolling contact fatigue (RCF) initiated at deep (10–25 mm) defects is derived and employed together with a fatigue index for more shallow (4–10 mm) subsurface RCF initiation. Integrated simulations of high-frequency dynamic train–track interaction and prediction of RCF impact are then carried out to evaluate the influence of short-pitch rail corrugation on RCF of railway wheels. Parametric studies are carried out to identify operational conditions likely to generate high RCF impact. Simulation results show how rail corrugation causes a major increase in RCF impact at high-speed operations and that corrugation magnitudes measured in-field are sufficient to generate subsurface initiated RCF. At high speeds the main cause for increased fatigue impact is the increase in dynamic load magnitudes. At lower speeds and higher axle loads also the effect of poor contact geometry will have an influence.

NUMERICAL ANALYSIS OF VIBRATION EFFECTS OF METRO TRAINS ON SURROUNDING ENVIRONMENT

A finite element approach is extended to study the ground vibrations induced by metro trains and their propagation properties. Two dynamic interaction models are established: the two-dimensional train-track interaction model, which provides the excitation loads of moving trains onto the tunnel structure, and the three-dimensional track-tunnel-ground interaction model, by which the propagation properties of ground accelerations and velocities are analyzed. The results show that there exists a vibration amplifying area in certain distance away from the tunnel center, and the dominant frequencies of the ground vibration concentrate in a certain range. Buildings located in that area with their natural frequencies falling in the specific frequency range will be sensitive to the ground vibrations induced by metro trains.

Rail corrugation growth—Influence of powered wheelsets with wheel tread irregularities

A multibody system model for simulation of general three-dimensional train-track interaction (accounting for frequencies up to several kHz) is used to investigate the hypothesis that rail corrugation is generated by powered wheelsets on the Swedish high-speed train X2. Part of the braking effort on the powered wheelsets is accomplished by tread braking with cast iron brake blocks. In particular, the influence of wheel corrugation, which is present because of such braking, on rail corrugation growth is studied. The numerical model uses an iteration scheme including simulation of dynamic train-track interaction in the time domain coupled with a long-term wear model. Measured wheel–rail contact forces and measured rail roughness are compared to the simulated results. Wheel–rail contact forces are considerably higher when wheel irregularities are present. However, the averaging effect from several passing wheelsets with different sets of wheel irregularities is found to give a rate of rail corrugation growth similar to the one obtained if the wheels had been completely round. The rail corrugation wavelengths are found to be explained by irregular wear due to high wheel–rail contact forces and slip caused by local rail bending modes between the two wheelsets in a bogie.

Comparison of Two Types of Deflection Functions for Analysing the Responses of the Rail and the Bridge under Static or Moving Vehicles

The interaction model consisting of a train, a two-layer railway track, and a railway bridge is presented for an analysis of the responses of the rail and the bridge, and two types of deflection functions are compared. One type is the shape functions of a beam element described by the cubic Hermitian interpolation functions in the finite-element method (FEM), and the other is the deflection of a beam described by the superimposing modes in the modal analysis method (MAM). In the present model, each vehicle is modelled as a two-wheel mass-spring-damping system with four degrees of freedom (DOFs); the track is modelled as a discrete supported undamped uniform Bernoulli-Euler beam with hinged-hinged ends representing rails, discrete lumped masses representing sleepers, and discrete massless springs and dashpots representing the characteristics of pads and ballasts; and the bridge deck is modelled as a simply supported uniform Bernoulli-Euler beam. Two different equations of motion for the present model with two types of deflection functions for the rail and the bridge deck are derived from the energy principle. These equations can be easily degenerated into the equations of either a train-track or train-bridge interaction system. Numerical results show that the difference between the two types of deflection functions to analyse the responses of the bridge is very small; and FEM can, yet MAM cannot, give an acceptable result if the bending moment of the rail is taken into account.

Simulation of dynamic interaction between train and railway turnout

Dynamic train–track interaction is more complex in railway turnouts (switches and crossings) than that in ordinary tangent or curved tracks. Multiple contacts between wheel and rail are common, and severe impact loads with broad frequency contents are induced, when nominal wheel–rail contact conditions are disturbed because of the continuous variation in rail profiles and the discontinuities in the crossing panel. The absence of transition curves at the entry and exit of the turnout, and the cant deficiency, leads to large wheel–rail contact forces and passenger discomfort when the train is switching into the turnout track. Two alternative multibody system (MBS) models of dynamic interaction between train and a standard turnout design are developed. The first model is derived using a commercial MBS software. The second model is based on a multibody dynamics formulation, which may account for the structural flexibility of train and track components (based on finite element models and coordinate reduction methods). The variation in rail profile is accounted for by sampling the cross-section of each rail at several positions along the turnout. Contact between the back of the wheel flange and the check rail, when the wheelset is steered through the crossing, is considered. Good agreement in results from the two models is observed when the track model is taken as rigid.

Prediction of dynamic train–track interaction and subsequent material deterioration in the presence of insulated rail joints

Numerical analysis of high-frequency dynamic train–track interaction is combined with the analysis of material deterioration in terms of rolling contact fatigue (RCF) and plastic deformations to analyze the influence of insulated rail joints. These joints form local rail irregularities and lead to a local change of dynamic track stiffness. Dynamic responses at wheel passes are evaluated. Further, related plastic deformations at the joint and increased RCF impact along a stretch of the track adjacent to the joint are predicted.

Out-of-round railway wheels—a study of wheel polygonalization through simulation of three-dimensional wheel–rail interaction and wear

The objective of this study is to develop a tool for investigation of wheel tread polygonalization with radial irregularities including 1 to 20 wavelengths around the circumference of the wheel. Therefore, an existing multibody system model for simulation of general three-dimensional train–track interaction (accounting for frequencies up to several kHz) is extended with rolling contact mechanics according to FASTSIM. Furthermore, the model is also modified to allow for general wheel–rail profiles. The numerical model uses the concept of an iteration scheme including simulation of dynamic train–track interaction in the time domain coupled with a long-term wear model. A demonstration example including a bogie of a subway train travelling on a straight track is presented. In the example, an initial wheel out-of-roundness (OOR) is applied to the wheels. This irregularity is based on an amplitude spectrum derived from measurements on new wheels. Simulation results show that the most important wavelength-fixing mechanisms of the wheel OOR are (i) the vertical resonance of the coupled train–track system at approximately 40 Hz (the P2 resonance) and (ii) the frequency region including the lowest vertical track antiresonance at 165 Hz, where the dynamic track stiffness is high. Only a straight track is studied, but the model allows for asymmetric train motion on such a track.