Investigating the influence of soil properties on railway traffic vibration using a numerical model

This paper presents the influence of dynamic and geometrical soil parameters on the propagation of ground vibrations induced by external loads. The proposed approach is based on a three-dimensional model, focusing on realistic excitation sources like impulse loads and moving railway vehicles. For the latter, a complete vehicle/track model is developed. The simulation is performed in time domain, offering an interesting approach, compared with classic cyclic analyses. The ground is modelled initially as an elastic homogeneous half-space and additionally as a layered half-space. First, the effect of homogeneous soil properties on ground vibration is analysed. Soil stratification is then taken into account, using various configurations. Analysis reveals that as receiver distance increases ground wave reflection in a layered ground plays an important role in the reduction of ground surface motion. This effect is magnified when the phase velocity wavelength becomes large compared with the depth of the surface layer.     

On the interest of integrating vehicle dynamics for the ground propagation of vibrations: the case of urban railway traffic

This paper presents a complete numerical model for studying the vertical dynamics of the vehicle/track interaction and its impact on the surrounding soil, with the emphasis on vehicle modelling. A decoupling between the track and the soil is proposed, due to the difficulty of considering all the subsystem components. The train/track model is based on a multibody model (for the vehicle) and a finite element model (for the track). The soil is modelled using an infinite/finite element approach. Simulations of both models are carried out in the time domain, which is better able to simulate the propagation of the vibration waves and to take into account the possible nonlinearity of a component. The methodology is applied in the case of an urban tram track and validated with the available experimental data. Models for the tram, the track and the soil are described. Results from the complete model of the vehicle and a simple model, based on an axle load, are compared with experimental results and the benefits of a complete model in the simulation of the ground vibration propagation induced by railway vehicles are demonstrated. Moreover, a parametric study of the vehicle wheel type is conducted, which shows the advantage of a resilient wheel, for various rail defects.     

Influences on nonlinear judder vibrations of railway brakes

The paper reports on a joined research project of Knorr-Bremse, Siemens Mobility and the Institute of Robotics and Mechatronics. The goal of the project was to analyse the dynamical behaviour of friction brakes for high-speed trains. It was intended to gain insight into possible vibration mechanisms and to assess the potential for lay-out and operation improvements for future light-weight designs. In particular, the frequency range up to 250 Hz has been addressed, since the corresponding excitation is unavoidable at least to some extent and has to be considered when the brake system is designed. The study includes a comprehensive multibody simulation study and its comparison to experimental results at the test rig of Knorr-Bremse in Munich. The simulation model is adapted step by step in order to clearly identify and separate the influences on the dynamical properties of the complete brake system including its mounting. Additionally a minimal model is introduced that demonstrates some characteristics of the brake system. It turned out that the underlying knowledge is essential for the mechanical lay-out, which could be demonstrated by solving a particular vibration problem in an actual high-speed project.     

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.     

Considerations on active control of crosswind stability of railway vehicles

The DLR research project Next Generation Train deals with concepts, methods and technologies for a very high-speed train in double-deck configuration and light-weight design. Due to these three key features, crosswind stability is a particular subject of study. It is shown that conventional approaches here fall short of guaranteeing safety in high-wind occurrences according to the given homologation standards. Therefore, this paper discusses the feasibility of different approaches to ensure crosswind stability by means of active control. Four different concepts are overviewed, the most promising one is then chosen und examined in detailed multibody simulations that are based on data from wind tunnel measurements of the Next Generation Train.     

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.     

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.     

Analysis of dynamic interaction between catenary and pantograph with experimental verification and performance evaluation in new high-speed line

Understanding the dynamic interaction between the catenary and pantograph of a high-speed train is the one of the most important technical issues in the railway industry. This is because the catenary–pantograph system plays a crucial role in providing electric power to the railway vehicle for stable operation. The aim of the present paper is to estimate the current-collection performance of this system by using numerical analysis, in particular, the flexible multibody dynamic analysis technique. To implement large deformable catenary wires, an absolute nodal coordinate formulation is used for the cable element. Additionally, an efficient contact element and an interactive model for the catenary–pantograph system are introduced. Each developed model is then used for analytical and experimental verification. Actual on-line test results of existing high-speed railway vehicles are presented and used to verify the analysis model. Finally, the performance characteristics of a new 400 km/h-class high-speed line are estimated and evaluated on the basis of international standards.     

Development and validation of a wear model for the analysis of the wheel profile evolution in railway vehicles

The numerical wheel wear prediction in railway applications is of great importance for different aspects, such as the safety against vehicle instability and derailment, the planning of wheelset maintenance interventions and the design of an optimal wheel profile from the wear point of view. For these reasons, this paper presents a complete model aimed at the evaluation of the wheel wear and the wheel profile evolution by means of dynamic simulations, organised in two parts which interact with each other mutually: a vehicle's dynamic model and a model for the wear estimation. The first is a 3D multibody model of a railway vehicle implemented in SIMPACK?, a commercial software for the analysis of mechanical systems, where the wheel–rail interaction is entrusted to a C/C++user routine external to SIMPACK, in which the global contact model is implemented. In this regard, the research on the contact points between the wheel and the rail is based on an innovative algorithm developed by the authors in previous works, while normal and tangential forces in the contact patches are calculated according to Hertz's theory and Kalker's global theory, respectively. Due to the numerical efficiency of the global contact model, the multibody vehicle and the contact model interact directly online during the dynamic simulations.

The second is the wear model, written in the MATLAB® environment, mainly based on an experimental relationship between the frictional power developed at the wheel–rail interface and the amount of material removed by wear. Starting from a few outputs of the multibody simulations (position of contact points, contact forces and rigid creepages), it evaluates the local variables, such as the contact pressures and local creepages, using a local contact model (Kalker's FASTSIM algorithm). These data are then passed to another subsystem which evaluates, by means of the considered experimental relationship, both the material to be removed and its distribution along the wheel profile, obtaining the correspondent worn wheel geometry.

The wheel wear evolution is reproduced by dividing the overall chosen mileage to be simulated in discrete spatial steps: at each step, the dynamic simulations are performed by means of the 3D multibody model keeping the wheel profile constant, while the wheel geometry is updated through the wear model only at the end of the discrete step. Thus, the two parts of the whole model work alternately until the completion of the whole established mileage. Clearly, the choice of an appropriate step length is one of the most important aspects of the procedure and it directly affects the result accuracy and the required computational time to complete the analysis.

The whole model has been validated using experimental data relative to tests performed with the ALn 501 ‘Minuetto’ vehicle in service on the Aosta–Pre Saint Didier track; this work has been carried out thanks to a collaboration with Trenitalia S.p.A and Rete Ferroviaria Italiana, which have provided the necessary technical data and experimental results.     

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.     

An approach for the validation of railway vehicle models based on on-track measurements

This paper proposes an approach for the validation of railway vehicle models based on on-track measurements. The validation of simulation models has gained importance with the introduction of new applications of multi-body simulation in railway vehicle dynamics as the assessment of track geometry defects, the investigation of derailments and the analysis of gauging. These applications are not only interested in qualitative predictions of the vehicle behaviour but also in precise quantitative results of the safety and comfort relevant vehicle responses. The validation process aims at guaranteeing that the simulation model represents the dynamic behaviour of the real vehicle with a sufficient good precision. A misfit function is defined which quantifies the distance between the simulated and the measured vehicle response allowing to evaluate different models at different running conditions. The obtained modelling errors are compared to the measurement uncertainty estimated for one vehicle using repeatability analysis.     

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.     

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.     

Assessment of the influence of the elastic properties of rail vehicle suspensions on safety,ride quality and track fatigue

A sensitivity analysis has been performed to assess the influence of the elastic properties of railway vehicle suspensions on the vehicle dynamic behaviour. To do this, 144 dynamic simulations were performed modifying, one at a time, the stiffness and damping coefficients, of the primary and secondary suspensions. Three values were assigned to each parameter, corresponding to the percentiles 10, 50 and 90 of a data set stored in a database of railway vehicles. After processing the results of these simulations, the analysed parameters were sorted by increasing influence. It was also found which of these parameters could be estimated with a lesser degree of accuracy in future simulations without appreciably affecting the simulation results. In general terms, it was concluded that the highest influences were found for the longitudinal stiffness and the lateral stiffness of the primary suspension, and the lowest influences for the vertical stiffness and the vertical damping of the primary suspension, with the parameters of the secondary suspension showing intermediate influences between them.     

Sensitivity analysis to assess the influence of the inertial properties of railway vehicle bodies on the vehicle's dynamic behaviour

A sensitivity analysis has been performed to assess the influence of the inertial properties of railway vehicles on their dynamic behaviour. To do this, 216 dynamic simulations were performed modifying, one at a time, the masses, moments of inertia and heights of the centre of gravity of the carbody, the bogie and the wheelset. Three values were assigned to each parameter, corresponding to the percentiles 10, 50 and 90 of a data set stored in a database of railway vehicles. After processing the results of these simulations, the analysed parameters were sorted by increasing influence. It was also found which of these parameters could be estimated with a lesser degree of accuracy for future simulations without appreciably affecting the simulation results. In general terms, it was concluded that the most sensitive inertial properties are the mass and the vertical moment of inertia, and the least sensitive ones the longitudinal and lateral moments of inertia.     

An investigation into the mechanism of the polygonal wear of metro train wheels and its effect on the dynamic behaviour of a wheel/rail system

This paper presents a detailed investigation conducted into the mechanism of the polygonal wear of metro train wheels through extensive experiments conducted at the sites. The purpose of the experimental investigation is to determine from where the resonant frequency that causes the polygonal wear of the metro train wheels originates. The experiments include the model tests of a vehicle and its parts and the tracks, the dynamic behaviour test of the vehicle in operation and the observation test of the polygonal wear development of the wheels. The tracks tested include the viaducts and the tunnel tracks. The structure model tests show that the average passing frequency of a polygonal wheel is approximately close to the first bending resonant frequency of the wheelset that is found by the wheelset model test and verified by the finite element analysis of the wheelset. Also, the dynamic behaviour test of the vehicle in operation indicates the main frequencies of the vertical acceleration vibration of the axle boxes, which are dominant in the vertical acceleration vibration of the axle boxes and close to the passing frequency of a polygonal wheel, which shows that the first bending resonant frequency of the wheelset is very exciting in the wheelset operation. The observation test of the polygonal wear development of the wheels indicates an increase in the rate of the polygonal wear of the wheels after their re-profiling. This paper also describes the dynamic models used for the metro vehicle coupled with the ballasted track and the slab track to analyse the effect of the polygonal wear of the wheels on the wheel/rail normal forces.     

液压驱动工程车辆牵引性能参数在行走机构滑转曲线上的配置与控制方法研究

提出了一种利用液压无级变速传动,进行恒功率速度自适应控制,动态工况下的牵引性能参数按照静态匹配理论计算,但在行走机构全打滑前进行极限负荷控制的设计方法.实践表明这是一种提高车辆动力性、经济性和作业生产率综合性能以及实现自动化的有效途径.