Distributed support modelling for vertical track dynamic analysis

The finite length nature of rail-pad supports is characterised by a Timoshenko beam element formulation over an elastic foundation, giving rise to the distributed support element. The new element is integrated into a vertical track model, which is solved in frequency and time domain. The developed formulation is obtained by solving the governing equations of a Timoshenko beam for this particular case. The interaction between sleeper and rail via the elastic connection is considered in an analytical, compact and efficient way. The modelling technique results in realistic amplitudes of the ‘pinned–pinned’ vibration mode and, additionally, it leads to a smooth evolution of the contact force temporal response and to reduced amplitudes of the rail vertical oscillation, as compared to the results from concentrated support models. Simulations are performed for both parametric and sinusoidal roughness excitation. The model of support proposed here is compared with a previous finite length model developed by other authors, coming to the conclusion that the proposed model gives accurate results at a reduced computational cost.     

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

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

Simulation of vertical dynamic vehicle–track interaction using a two-dimensional slab track model

The vertical dynamic interaction between a railway vehicle and a slab track is simulated in the time domain using an extended state-space vector approach in combination with a complex-valued modal superposition technique for the linear, time-invariant and two-dimensional track model. Wheel–rail contact forces, bending moments in the concrete panel and load distributions on the supporting foundation are evaluated. Two generic slab track models including one or two layers of concrete slabs are presented. The upper layer containing the discrete slab panels is described by decoupled beams of finite length, while the lower layer is a continuous beam. Both the rail and concrete layers are modelled using Rayleigh–Timoshenko beam theory. Rail receptances for the two slab track models are compared with the receptance of a traditional ballasted track. The described procedure is demonstrated by two application examples involving: (i) the periodic response due to the rail seat passing frequency as influenced by the vehicle speed and a foundation stiffness gradient and (ii) the transient response due to a local rail irregularity (dipped welded joint).     

Effect of curved track support failure on vehicle derailment

In order to investigate the effect of curved track support failure on railway vehicle derailment, a coupled vehicle–track dynamic model is put forward. In the model, the vehicle and the structure under rails are, respectively, modelled as a multi-body system, and the rail is modelled with a Timoshenko beam rested on the discrete sleepers. The lateral, vertical, and torsional deformations of the beam are taken into account. The model also considers the effect of the discrete support by sleepers on the coupling dynamics of the vehicle and track. The sleepers are assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. In the calculation of the coupled vehicle and track dynamics, the normal forces of the wheels/rails are calculated using the Hertzian contact theory and their creep forces are determined with the nonlinear creep theory by Shen et al [Z.Y. Shen, J.K. Hedrick, and J.A. Elkins, A comparison of alternative creep-force models for rail vehicle dynamic analysis, Proceedings of the 8th IAVSD Symposium, Cambridge, MA, 1984, pp. 591–605]. The motion equations of the vehicle/track are solved by means of an explicit integration method. The failure of the components of the curved track is simulated by changing the track stiffness and damping along the track. The cases where zero to six supports of the curved rails fail are considered. The transient derailment coefficients are calculated. They are, respectively, the ratio of the wheel/rail lateral force to the vertical force and the wheel load reduction. The contact points of the wheels/rails are in detail analysed and used to evaluate the risk of the vehicle derailment. Also, the present work investigates the effect of friction coefficient, axle load and vehicle speed on the derailments under the condition of track failure. The numerical results obtained indicate that the failure of track supports has a great influence on the whole vehicle running safety.     

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

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

Prediction of the interaction between a simple moving vehicle and an infinite periodically supported rail – Green's functions approach

This paper herein describes the interaction between a simple moving vehicle and an infinite periodically supported rail, in order to signalise the basic features of the vehicle/track vibration behaviour in general, and wheel/rail vibration, in particular. The rail is modelled as an infinite Timoshenko beam resting on semi-sleepers via three-directional rail pads and ballast. The time-domain analysis was performed applying Green's matrix of the track method. This method allows taking into account the nonlinearities of the wheel/rail contact and the Doppler effect. The numerical analysis is dedicated to the wheel/rail response due to two types of excitation: the steady-state interaction and rail irregularities. The study points out to certain aspects regarding the parametric resonance, the amplitude-modulated vibration due to corrugation and the Doppler effect.     

Influence of polygonal wear of railway wheels on the wheel set axle stress

The coupled vehicle/track dynamic model with the flexible wheel set was developed to investigate the effects of polygonal wear on the dynamic stresses of the wheel set axle. In the model, the railway vehicle was modelled by the rigid multibody dynamics. The wheel set was established by the finite element method to analyse the high-frequency oscillation and dynamic stress of wheel set axle induced by the polygonal wear based on the modal stress recovery method. The slab track model was taken into account in which the rail was described by the Timoshenko beam and the three-dimensional solid finite element was employed to establish the concrete slab. Furthermore, the modal superposition method was adopted to calculate the dynamic response of the track. The wheel/rail normal forces and the tangent forces were, respectively, determined by the Hertz nonlinear contact theory and the Shen–Hedrick–Elkins model. Using the coupled vehicle/track dynamic model, the dynamic stresses of wheel set axle with consideration of the ideal polygonal wear and measured polygonal wear were investigated. The results show that the amplitude of wheel/rail normal forces and the dynamic stress of wheel set axle increase as the vehicle speeds rise. Moreover, the impact loads induced by the polygonal wear could excite the resonance of wheel set axle. In the resonance region, the amplitude of the dynamic stress for the wheel set axle would increase considerably comparing with the normal conditions.     

Train–track–bridge dynamic interaction: a state-of-the-art review

ABSTRACT

Train–track–bridge dynamic interaction is a fundamental concern in the field of railway engineering, which plays an extremely important role in the optimal design of railway bridges, especially in high-speed railways and heavy-haul railways. This paper systematically presents a state-of-the-art review of train–track–bridge dynamic interaction. The evolution process of train–bridge dynamic interaction model is described briefly, from the simplest moving constant force model to the sophisticated train–track–bridge dynamic interaction model (TTBDIM). The modelling methodology of the key elements in the TTBDIM is systematically reviewed, including the train, the track, the bridge, the wheel–rail contact, the track–bridge interaction, the system excitation and the solution algorithm. The significance of detailed track modelling in the whole system is highlighted. The experimental research and filed test focusing on modelling validation, safety assessment and long-term performance investigation of the train–track–bridge system are briefly presented. The practical applications of train–track–bridge dynamic interaction theory are comprehensively discussed in terms of the system dynamic performance evaluation, the system safety assessment and train-induced environmental vibration and noise prediction. The guidance is provided on further improvement of the train–track–bridge dynamic interaction model and the challenging research topics in the future.     

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.     

基于Timoshenko梁理论考虑阻尼的承台-桩-土耦合横向振动解

由于缺乏合适的激振和接收位置,传统竖向低应变反射波法在检测带承台或未凿桩头的桩基动力特性时存在明显不足.为进一步拓展低应变检测波法应用范围,基于Timoshenko梁理论,考虑桩身材料阻尼、附加轴力及桩顶等效质量作用,建立了一种横向激励条件下承台-桩-土耦合振动模型,并求解了该模型的频域内解析解及其时域半解析解.进一步...     

A Track-Wheel-Terrain Interaction Model for Dynamic Simulation of Tracked Vehicles

A mathematical model of track-wheel-terrain interaction is presented that supports the dynamic simulation of tracked vehicles. This model combines approximate and known constitutive laws for terrain response with a new representation for the track segment. The resulting track-wheel-terrain model allows the computation of the track tension and the normal and shear forces at the track-terrain interface as the track negotiates terrain of arbitrary profile. A key feature of this model is the uniform treatment of contact between the track and the roadwheels and the track and the terrain. Treating both contact problems in the same manner significantly simplifies the problem formulation and also reduces difficulties in computing points of track-wheel and track-terrain separation. The model takes the form of a two-point nonlinear boundary value problem that accounts for tension variations along the track (due to the non-uniformly distributed normal pressure and traction), track extensibility, and geometrically large (nonlinear) track deflections. Solutions are obtained using a finite element formulation. Both the model and the solution method are formulated for implementation within a multibody dynamics code for simulating full vehicles. Several examples illustrate the capabilities of the proposed model.     

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.     

Vossloh300扣件阻尼频变对高铁高频振动的影响研究

以Vossloh300扣件胶垫为研究对象，利用配备温度箱的万能试验机测得其在-60℃~20℃的耗能刚度。在试验基础上结合温频等效原理及车辆-轨道垂向耦合Timoshenko梁模型，在频域内探究该型扣件频变阻尼对高铁轮轨系统动力特性的影响。结果表明:Vossloh300扣件胶垫在20℃，4 Hz激振频率下阻尼系数约152.2 kN/（m·s-1）。Vossloh300扣件频变阻尼主要影响车辆-轨道垂向耦合系统1/3倍频中心频率22 Hz以上的振动响应，即:①增大车辆和轨道系统22~56 Hz的中高频振动，同时减小其60~256 Hz的高频振动；②在512~1 500 Hz范围内，钢轨垂向1/3倍频加速度振级最大值增大了5 dB，同时，扣件力1/3倍频幅值最大值减小了92%。因此，为精确预测高速铁路车辆及轮下结构随机振动响应，需考虑扣件胶垫的阻尼频变特性。     

Impact Loads due to Wheel Flats and Shells

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

Ride Dynamics of High-Speed Tracked Vehicles: Simulation with Field Validation

SUMMARY

Ride dynamic behaviour of a typical high-speed tracked vehicle, such as a conventional military armoured personnel carrier (APC) negotiating rough off-road terrains, is studied through computer simulations and field tests. A comprehensive ride dynamic simulation model is developed, assuming constant forward vehicle speed and non-deformable terrain profile. The ride model includes dynamic track load and wheel/track-terrain interaction. Dynamic track load is modeled in view of track belt stretching and initial track tension, whereas an equivalent damper and continuous radial spring formulation is employed to model wheel/track-terrain interaction. Field testing of a APC subjected to discrete half round obstacles of various radii, a sinusoidal course, a random course, and a Belgian Pave\ is carried out for various vehicle configurations and speeds. Computer simulation results are validated against field measured results. The comparison of measured and predicted results shows generally good agreement.     

Dynamic Response of a Six-axle Locomotive to Random Track Inputs

SUMMARY

Spectral analysis techniques are employed to analyze the dynamic response of a six-axle locomotive on tangent track to vertical and lateral random track irregularities. The locomotive is represented by a thirty-nine (39) degrees of freedom model. A linear model is employed by considering small displacements, linear suspension elements and a linear theory for the wheel-rail interaction. Power spectral densities of displacements, velocities and accelerations and the statistical average frequencies of the system are obtained for each degree of freedom. Comparison of the calculated dominating frequencies with existing experimental values shows good agreement. The technique of spectral analysis is an effective tool for model validation, and for the determination of rail vehicle response to track irregularities. The probability functions for the response can be used as a measure for the ride quality of rail vehicles and for the study of fatigue damage of components.

     

High Speed Railway: Collecting Pantographs Active Control and Overhead Lines Diagnostic Solutions

SUMMARY

The catenary-pantograph system and its dynamic behaviour play a decisive role for high speed trains from the power collecting point of view. The decisive criterion for assessing the contact quality is to reduce the contact force variability as far as possible. In this paper active pantograph elements are introduced in order to improve the system performance. The control strategy is based on Extended Kalman Filter technique, used to get a contact force estimation available for control feedback. The same estimation procedure based on the Extended Kalman Filter is also used to obtain some information useful to overhead line diagnostic purposes.     

Vertical Vibration Analysis of Vehicle/Imperfect Track Systems

Summary This paper studies the vertical vibration of a vehicle traveling on an imperfect track system. The car body and sleepers are modeled as Timoshenko beams with finite length, and the rail is assumed as an infinite Timoshenko beam with discrete supports. Imperfection of the track system comes from a sleeper lost partial support by the ballast. Since deflection of the rail is limited within a certain interval where the vehicle is passing over, the infinite domain problem can be transformed into a finite domain problem with moving boundary. In this work, the equations of motion of the car body, rail and sleepers are discretized first by the finite element method. The discretized equations of motion for the vehicle and track systems are then assembled, respectively. Finally, the Newmark method is applied to obtain the response of the vehicle and track systems at each time step. The effect of the vehicle speed on the response of the vehicle and track systems is investigated.     

箱梁横梁的计算剖析

箱梁横梁起到连接腹板和支撑箱梁的作用。箱梁通过与其接触面上的剪应力来传递荷载,同时箱梁也是其边界的一部分。箱梁在横梁受弯上是否提供抗力以及其接触面上的剪应力如何分布?该文就这些问题来讨论箱梁横梁最佳的计算方法,同时给出空间的有限元解答。