Extended study of railway vehicle lateral stability in a curved track

This article presents results of the studies aimed at more accurate stability analysis of railway vehicles in a curved track. More accurate analysis means extended study of the stability as compared with the method used by the authors so far. New measures undertaken by the authors in order to achieve the goal are explained. Besides, differences between results obtained with the earlier and extended approaches are presented and discussed. Results that are expected on the basis of the theory are confronted with practical capabilities to generate them through simulations at the same time. The issues of interest are precise determination of nonlinear critical velocity, determination of linear system critical velocity, determination of unstable periodic and unstable stationary solutions, existence of multiple solutions and correct determination of velocity at which unbounded growth of the solutions (lateral dynamics coordinates) happens during calculations resulting in their stop.     

Influence of uneven rail irregularities on the dynamic response of the railway track using a three-dimensional model of the vehicle–track system

A mathematical model of the vehicle–track interaction is developed to investigate the coupled behaviour of vehicle–track system, in the presence of uneven irregularities at left/right rails. The railway vehicle is simplified as a 3D multi-rigid-body model, and the track is treated as the two parallel beams on a layered discrete support system. Besides the car-body, the bogies and the wheel sets, the sleepers are assumed to have roll degree of freedom, in order to simulate the in-plane rotation of the components. The wheel–rail interface is treated using a nonlinear Hertzian contact model, coupling the mathematical equations of the vehicle–track systems. The dynamic interaction of the entire system is numerically studied in time domain, employing Newmark's integration method. The track irregularity spectra of both the left/right rails are taken into account, as the inputs of dynamic excitations. The dynamic responses of the track system induced by such irregularities are obtained, particularly in terms of the vertical (bounce) and roll displacements. The numerical model of the present research is validated using several benchmark models reported in the literature, for both the smooth and unsmooth track conditions. Four sample profiles of the measured rail irregularities are considered as the case studies of excitation sources, examining their influences on the dynamic behaviour of the coupled system. The results of numerical simulations demonstrate that the motion of track system is significantly influenced by the presence of uneven irregularities in left/right rails. Dynamic response of the sleepers in the roll direction becomes more sensitive to the rail irregularities, as the unevenness severity of the parallel profiles (quantitative difference between left and right rail spectra) is increased. The severe geometric deformation of the track in the bounce–pitch–roll directions is mainly related to such profile unevenness (cross-level) in left/right rails.     

Probabilistic assessment of railway vehicle-curved track systems considering track random irregularities

The randomness of track irregularities directly leads to the random vibration of the vehicle–track systems. To assess the dynamic performance of a railway system in more comprehensive and practical ways, a framework for probabilistic assessment of vehicle-curved track systems is developed by effectively integrating a vehicle–track coupled model (VTCM), a track irregularity probabilistic model (TIPM) with a probability density evolution method (PDEM). In VTCM, the railway vehicle and the curved track are coupled by the nonlinear wheel–rail interaction forces, and through TIPM, the ergodic properties of random track irregularities on amplitudes, wavelengths and probabilities can be properly considered in the dynamic calculations. Lastly, PDEM, a newly developed method for solving probabilistic transmissions between stochastic excitations and deterministic dynamic responses, is introduced to this probabilistic assessment model. Numerical examples validate the correctness and practicability of the proposed models. In this paper, the results of probabilistic assessment are presented to illustrate the dynamic behaviours of a high-speed railway vehicle subject to curved tracks with various radii, and to demonstrate the importance of considering the actual status of wheel–rail contacts and curve negotiation effects in vehicle-curved track interactions.     

Sensitivity of train stochastic dynamics to long-term evolution of track irregularities

The influence of the track geometry on the dynamic response of the train is of great concern for the railway companies, because they have to guarantee the safety of the train passengers in ensuring the stability of the train. In this paper, the long-term evolution of the dynamic response of the train on a stretch of the railway track is studied with respect to the long-term evolution of the track geometry. The characterisation of the long-term evolution of the train response allows the railway companies to start off maintenance operations of the track at the best moment. The study is performed using measurements of the track geometry, which are carried out very regularly by a measuring train. A stochastic model of the studied stretch of track is created in order to take into account the measurement uncertainties in the track geometry. The dynamic response of the train is simulated with a multibody software. A noise is added in output of the simulation to consider the uncertainties in the computational model of the train dynamics. Indicators on the dynamic response of the train are defined, allowing to visualize the long-term evolution of the stability and the comfort of the train, when the track geometry deteriorates.     

Dynamics of the railway track and the underlying soil: the boundary-element solution,theoretical results and their experimental verification

A combined finite-element boundary-element method is presented in detail to calculate the dynamic interaction of the railway track and the underlying soil. A number of results are shown for ballasted and slab track, demonstrating the influence of the stiffness of the soil and the rail pads on the vertical compliance of the track. The compliance of the track is combined with a simple model of the vehicle giving the transfer function of vehicle–track interaction. An experimental verification of the theoretical results is achieved by harmonic and impulse excitation with and without static (train-) load and by combined measurements of train–track–soil interaction. A clear vehicle–track resonance is found for the slab track with elastic rail pads and for higher frequencies at highspeed traffic, the dynamic axle loads due to sleeper passage are reduced.     

A structural articulation method for assessing railway bridges subject to dynamic impact loading from track irregularities

This paper discusses the importance of track irregularities in railway bridge design, and presents a new technique for calculating the dynamic impact load induced by such irregularities: the structural articulation method. The properties of the combined bridge-suspension system are coupled through global mass, stiffness, and damping matrices. Under the proposed method, the true suspension system over a particular point on the bridge girder at time t is divided into equivalent suspension systems attributed to adjacent finite-element nodes of the bridge. The time-dependent effects of a moving mass are thereby included in the equation of motion.     

Effects of rail thermal stress on the dynamic response of vehicle and track

A new method is proposed to obtain the dynamic responses of the vehicle–track coupling system under the conditions of rail thermal stress changes in high-speed railways. Exact models are established with different rail longitudinal forces, in which multibody dynamic models are used for vehicles and the direct stiffness method for structures. In order to provide a general, simple and flexible formulation to express longitudinal stress distribution, the accurate model of long slab track consists of many small units with parameters which can be initialised separately. The exact analytical equation of track frequency and modal function was obtained by the transition matrix method, which can be used in calculating the dynamic response of wheel–rail coupling model. The proposed model is verified through comparisons with other classical solutions. Under the influence of train velocities and track irregularities, the specific vibration performances that frequency shifted and amplitude peak enhanced with thermal force are demonstrated through examples. The results show that the response analyses of vehicle and track have great application potentiality for fast estimation of the rail longitudinal stress.     

Influence of some vehicle and track parameters on the environmental vibrations induced by railway traffic

A study is performed on the influence of some typical railway vehicle and track parameters on the level of ground vibrations induced in the neighbourhood. The results are obtained from a previously validated simulation framework considering in a first step the vehicle/track subsystem and, in a second step, the response of the soil to the forces resulting from the first analysis. The vehicle is reduced to a simple vertical 3-dof model, corresponding to the superposition of the wheelset, the bogie and the car body. The rail is modelled as a succession of beam elements elastically supported by the sleepers, lying themselves on a flexible foundation representing the ballast and the subgrade. The connection between the wheels and the rails is realised through a non-linear Hertzian contact. The soil motion is obtained from a finite/infinite element model. The investigated vehicle parameters are its type (urban, high speed, freight, etc.) and its speed. For the track, the rail flexural stiffness, the railpad stiffness, the spacing between sleepers and the rail and sleeper masses are considered. In all cases, the parameter value range is defined from a bibliographic browsing. At the end, the paper proposes a table summarising the influence of each studied parameter on three indicators: the vehicle acceleration, the rail velocity and the soil velocity. It namely turns out that the vehicle has a serious influence on the vibration level and should be considered in prediction models.     

Effect of vehicle vibration environment of high-speed train on dynamic performance of axle box bearing

In this study, we developed a comprehensive three-dimensional vehicle–track coupled dynamics model considering the traction drive system and axle box bearing. In this model, dynamic interactions between the axle box bearing and other components, such as the wheelset and bogie frame, are considered based on a detailed analysis of the structural properties and working mechanism of the axle box bearing. A few complicated dynamic excitations, such as the time-varying mesh stiffness of gears, time-varying stiffness of bearing, bearing gaps and track irregularities, are considered. Then, the dynamic responses of the vehicle–track system are demonstrated via numerical simulations based on the established dynamics model. The results indicate that the traction drive system and track irregularities can significantly influence the dynamic interactions of the axle box bearing. The necessity of considering the excitation caused by gear meshing and track irregularities when assessing the dynamic performance of the axle box bearing is demonstrated.     

A model for vehicle–track random interactions on effects of crosswinds and track irregularities

A stochastic mathematical model is developed to evaluate the dynamic behaviours and statistical responses of vehicle–track systems when random system excitations including crosswinds and track irregularities are imposed. In this model, the railway vehicle is regarded as a multi-rigid-body system, the track system is modelled by finite element theory. These two systems are spatially coupled by the nonlinear wheel–rail contact forces and unsteady aerodynamic forces. The high efficiency and accuracy of this stochastic model are validated by comparing to the robust Monte-Carlo method. Numerical studies show that crosswinds have a great influence on the dynamic performance of vehicle–track systems, especially on transverse vibrations. When the railway vehicle initially runs into the wind field, it will experience a severe vibration stage, and then stepping into a relatively steady state where the fluctuating winds and track irregularities will play deterministic roles in the deviations of system responses. Moreover, it is found that track irregularities should be properly considered in the safety assessment of the vehicle even in strong crosswinds.     

Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part I: system integration and modelling

In this paper, it is aimed to investigate semi-active suspension systems using magnetorheological (MR) fluid dampers for improving the ride quality of railway vehicles. A 17-degree-of-freedom (DOF) model of a full-scale railway vehicle integrated with the semi-active controlled MR fluid dampers in its secondary suspension system is proposed to cope with the lateral, yaw, and roll motions of the car body, trucks, and wheelsets. The governing equations combining the dynamics of the railway vehicle integrated with MR dampers in the suspension system and the dynamics of the rail track irregularities are developed and a linear quadratic Gaussian (LQG) control law using the acceleration feedback is adopted, in which the state variables are estimated from the measurable accelerations with a Kalman estimator. In order to evaluate the performances of the semi-active suspension systems based on MR dampers for railway vehicles, the random and periodical track irregularities are modelled with a uniform state-space formulation according to the testing data and incorporated into the governing equation of the railway vehicle integrated with the semi-active suspension system. Utilising the governing equations and the semi-active controller developed in this paper, the simulation and analysis are presented in Part II of this paper.     

Perspectives on railway track geometry condition monitoring from in-service railway vehicles

This paper presents a view of the current state of monitoring track geometry condition from in-service vehicles. It considers technology used to provide condition monitoring; some issues of processing and the determination of location; how things have evolved over the past decade; and what is being, or could/should be done in future research. Monitoring railway track geometry from an in-service vehicle is an attractive proposition that has become a reality in the past decade. However, this is only the beginning. Seeing the same track over and over again provides an opportunity for observing track geometry degradation that can potentially be used to inform maintenance decisions. Furthermore, it is possible to extend the use of track condition information to identify if maintenance is effective, and to monitor the degradation of individual faults such as dipped joints. There are full unattended track geometry measurement systems running on in-service vehicles in the UK and elsewhere around the world, feeding their geometry measurements into large databases. These data can be retrieved, but little is currently done with the data other than the generation of reports of track geometry that exceeds predefined thresholds. There are examples of simpler systems that measure some track geometry parameters more or less directly and accurately, but forego parameters such as gauge. Additionally, there are experimental systems that use mathematics and models to infer track geometry using data from sensors placed on an in-service vehicle. Finally, there are systems that do not claim to measure track geometry, but monitor some other quantity such as ride quality or bogie acceleration to infer poor track geometry without explicitly measuring it.     

Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part II: simulation and analysis

In this paper, the semi-active suspension system for railway vehicles based on the controlled (MR) fluid dampers is investigated, and compared with the passive on and passive off suspension systems. The lateral, yaw, and roll accelerations of the car body, trucks, and wheelsets of a full-scale railway vehicle integrated with four MR dampers in the secondary suspension systems, which are in the closed and open loops respectively, are simulated under the random and periodical track irregularities using the established governing equations of the railway vehicle and the modelled track irregularities in Part I of this paper. The simulation results indicate that (1) the semi-active controlled MR damper-based suspension system for railway vehicles is effective and beneficial as compared with the passive on and passive off modes, and (2) while the car body accelerations of the railway vehicle integrated with semi-active controlled MR dampers can be significantly reduced relative to the passive on and passive off ones, the accelerations of the trucks and wheelsets could be increased to some extent. However, the increase in the accelerations of the trucks and wheelsets is insignificant.     

Dynamics of the railway track and the underlying soil: the boundary-element solution, theoretical results and their experimental verification

A combined finite-element boundary-element method is presented in detail to calculate the dynamic interaction of the railway track and the underlying soil. A number of results are shown for ballasted and slab track, demonstrating the influence of the stiffness of the soil and the rail pads on the vertical compliance of the track. The compliance of the track is combined with a simple model of the vehicle giving the transfer function of vehicle-track interaction. An experimental verification of the theoretical results is achieved by harmonic and impulse excitation with and without static (train-) load and by combined measurements of train-track-soil interaction. A clear vehicle-track resonance is found for the slab track with elastic rail pads and for higher frequencies at highspeed traffic, the dynamic axle loads due to sleeper passage are reduced.     

Black-box modelling of nonlinear railway vehicle dynamics for track geometry assessment using neural networks

ABSTRACT

The use of vehicle dynamics simulation for the track geometry assessment gives rise to new demands. In order to analyse the responses of the vehicles to the measured track geometry defects, the integration of the simulation process in the measurement chain of the track geometry recording car is envisaged. Fast and reliable simulation results are required. This work studies the use of black-box modelling approaches as an alternative to multi-body simulation. The performances of different linear and nonlinear black-box models for the simulation of the vertical and lateral bogie accelerations are compared. While linear transfer function models give good results for the simulation of the vertical responses, their use is not suitable for the highly nonlinear lateral vehicle dynamics. The lateral accelerations are best represented by recurrent neural networks. For the training and validation on high-speed lines using measured vehicle responses, the performance of the black-box simulation outperforms the multi-body simulation. Due to the larger variability of track design and track quality conditions on conventional lines, the model performance degrades and depends significantly on the analysed vehicle type and the track characteristics.     

Construction of a stochastic model of track geometry irregularities and validation through experimental measurements of dynamic loading

This paper describes the construction of a stochastic model of urban railway track geometry irregularities, based on experimental data. The considered irregularities are track gauge, superelevation, horizontal and vertical curvatures. They are modelled as random fields whose statistical properties are extracted from a large set of on-track measurements of the geometry of an urban railway network. About 300–1000 terms are used in the Karhunen–Loève/Polynomial Chaos expansions to represent the random fields with appropriate accuracy. The construction of the random fields is then validated by comparing on-track measurements of the contact forces and numerical dynamics simulations for different operational conditions (train velocity and car load) and horizontal layouts (alignment, curve). The dynamics simulations are performed both with and without randomly generated geometrical irregularities for the track. The power spectrum densities obtained from the dynamics simulations with the model of geometrical irregularities compare extremely well with those obtained from the experimental contact forces. Without irregularities, the spectrum is 10–50?dB too low.     

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.     

On vehicle/track impact at connection between a floating slab and ballasted track and floating slab track's effectiveness of force isolation

When a vehicle runs over the connection between a floating slab track (FST) and ballasted track, wheel/rail impact may occur because of the stiffness difference in the two kinds of track, and thus a transition sector is usually included at the connection to smoothen the stiffness change. This phenomenon is studied by numerical simulation using a time-domain model for an idealised case without such a transition to determine whether it is actually necessary. Calculation results show that the wheel/rail impact load is moderate for a light FST and increases with the vehicle speed or decreasing the natural frequency of the FST. From simulation the wheel/rail parametric excitation is observed, as a result of variation in the stiffness of the FST with the period of the single slab length. The wheel/rail load due to the parametric excitation also increases with the vehicle speed. In addition, good performance of vibration isolation can be seen for the FST in terms of the force transmitted to the infrastructure.