Dynamic Train-Track Interaction: Variability Attributable to Scatter in the Track Properties

A numerical method to simulate vertical dynamic interaction between a rolling train and a railway track has been used to investigate the influence of stochastic properties of the track structure. A perturbation technique has been used to investigate the influence of the scatter in selected track properties. The train-track interaction problem has been numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the whole track structure. All numerical simulations have been carried out in the time-domain with a moving mass model. Properties such as rail pad stiffness, ballast stiffness, dynamic ballast-subgrade mass and sleeper spacing have been studied. To obtain sufficient statistical information from track structures, full-scale measurements in the field and laboratory measurements have been carried out. The influence of scatter in the track properties on the maximum contact force between the rail and the wheel, the maximum magnitude of the vertical wheelset acceleration, and the maximum sleeper displacement have been studied. Mean values and standard deviations of these quantities have been calculated. The effects of the variation of the investigated track properties are discussed.     

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.     

Tangential force variation due to the bogie direction reversal procedure

A range of tangential forces is generated within the contact patch when a wheelset moves on the rail. These forces are intensified when incorporating curved tracks and motored axle rail vehicles [Arrus, P., de Pater, A.D. and Meyers, P., 2002, The stationary motion of a one-axle vehicle along a circular curve with real rail and wheel profiles. Vehicle System Dynamics, 37(1), 29–58]. The wheelset is subject to flange contact if an unbalanced force remains in a curve towards the high rail gauge face. The resultant force in the transverse direction includes the lateral force, the radial force, and the creep forces in addition to the effect of the frequent wheelset displacement due to the kinematic oscillation [Iwnicki, S., 2003, Simulation of wheel–rail contact forces. Fatigue Fracture Engineering Material Structure, 26, 887–900]. This article has focused on a potential variation in some of the forces cited when the wheelset is subject to backward and forward movements. A severe wear rate observed within the wheel flange region in Iranian Railways was investigated by operating a test bogie on a curvaceous track. An obvious improvement in the wear rate and wear pattern of the wheels was attained when the second test bogie encountered a bogie direction reversal procedure. This enhancement is considered in this article from the force analysis standpoint.     

Mathematical modelling of train–turnout interaction

The paper proposes a mathematical model of train–turnout interaction in the mid-frequency range (0–500 Hz). The model accounts for the effects of rail profile variation along the track and of local variation of track flexibility. The proposed approach is able to represent the condition of one wheel being simultaneously in contact with more than one rail, allowing the accurate prediction of the effect of wheels being transferred from one rail to another when passing over the switch toe and the crossing nose. Comprehensive results of train–turnout interaction during the negotiation of the main and the branch lines are presented, including the effect of wear of wheel/rail profiles and presence of track misalignment. In the final part of the paper, comparisons are performed between the results of numerical simulations and line measurements performed on two different turnouts for urban railway lines, showing a good agreement between experimental and numerical results.     

Theoretical and experimental excitation force spectra for railway-induced ground vibration: vehicle–track–soil interaction,irregularities and soil measurements

Excitation force spectra are necessary for a realistic prediction of railway-induced ground vibration. The excitation forces cause the ground vibration and they are themselves a result of irregularities passed by the train. The methods of the related analyses – the wavenumber integration for the wave propagation in homogeneous or layered soils, the combined finite-element boundary-element method for the vehicle–track–soil interaction – have already been presented and are the base for the advanced topic of this contribution. This contribution determines excitation force spectra of railway traffic by two completely different methods. The forward analysis starts with vehicle, track and soil irregularities, which are taken from literature and axle-box measurements, calculates the vehicle–track interaction and gets theoretical force spectra as the result. The second method is a backward analysis from the measured ground vibration of railway traffic. A calculated or measured transfer function of the soil is used to determine the excitation force spectrum of the train. A number of measurements of different soils and different trains with different speeds are analysed in that way. Forward and backward analysis yield the same approximate force spectra with values around 1 kN for each axle and third of octave.     

Structural safety of trams in case of misguidance in a switch

Tram vehicles mainly operate on street tracks where sometimes misguidance in switches occurs due to unfavourable conditions. Generally, in this situation, the first running gear of the vehicle follows the bend track while the next running gears continue straight ahead. This leads to a constraint that can only be solved if the vehicle's articulation is damaged or the wheel derails. The last-mentioned situation is less critical in terms of safety and costs. Five different tram types, one of them high floor, the rest low floor, were examined analytically. Numerical simulation was used to determine which wheel would be the first to derail and what level of force is needed in the articulation area between two carbodies to make a tram derail. It was shown that with pure analytical simulation, only an idea of which tram type behaves better or worse in such a situation can be gained, while a three-dimensional computational simulation gives more realistic values for the forces that arise. Three of the four low-floor tram types need much higher articulation forces to make a wheel derail in a switch misguidance situation. One particular three-car type with two single-axle running gears underneath the centre car must be designed to withstand nearly three times higher articulation forces than a conventional high-floor articulated tram. Tram designers must be aware of that and should design the carbody accordingly.     

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.     

Adhesion estimation at the wheel–rail interface using advanced model-based filtering

The railway industry in the UK is currently expanding the use of condition monitoring of railway vehicles. These systems can be used to improve maintenance procedures or could potentially be used to monitor current vehicle running conditions without the use of cost prohibitive sensors. This paper looks at a novel method for the online detection of areas of low adhesion in the wheel/rail contact that cause significant disruption to the running of a network, particularly in the autumn season. The proposed method uses a Kalman–Bucy filter to estimate the creep forces in the wheel–rail contact area; post-processing is then applied to provide information indicative of the actual adhesion level. The algorithm uses data that, in practice, would be available from a set of modest cost inertial sensors mounted on the vehicle bogie and wheel-sets. The efficacy of the approach is demonstrated using simulation data from a nonlinear dynamic model of the vehicle and its track interface.     

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%.     

Vertical random vibration analysis of vehicle–track coupled system using Green's function method

A vertical vehicle–track coupled dynamic model, consisting of a high-speed train on a continuously supported rail, is established in the frequency-domain. The solution is obtained efficiently by use of the Green's function method, which can determine the vibration response over a wide range of frequency without any limitations due to modal truncation. Moreover, real track irregularity spectra can be used conveniently as input. The effect of the flexibility of both track and car body on the entire vehicle–track coupled dynamic response is investigated. A multi-body model of a vehicle with either rigid or flexible car body is defined running on three kinds of track: a rigid rail, a track stiffness model and a Timoshenko beam model. The results show that neglecting the track flexibility leads to an overestimation of both the contact force and the whole vehicle vibration response. The car body flexibility affects the ride quality of the vehicle and the coupling through the track and can be significant in certain frequency ranges. Finally, the effect of railpad and ballast stiffness on the vehicle–track coupled vibration is analysed, indicating that the stiffness of the railpad has an influence on the system in a higher frequency range than the ballast.