Vehicle-Track Dynamics in the Mid-Frequency Range

During the last years railway companies have observed increasing problems with track damage like rail corrugation, deterioration of ballast or unround wheels. Since the origin of these damages is suspected in the mid-frequency dynamics, research activities in the frequency range from 50 up to 500 Hz have been initiated. The article demonstrates that in comparison to the low and high frequency range the knowledge about physical effects in the mid-frequency range is poor. Apart from a historical literature review on vehicle and track modelling, recently published methods and models are collated and problems in their mathematical treatise are mentioned. Regarding the vehicle, the paper shows the development starting with Klingel's massless wheelset model and ending with sophisticated elastic multibody system models. Concerning the track, different mathematical approaches in frequency and time domain are compared. In the mid-frequency range the pad, ballast and subsoil properties play an important role. Hence, the missing of experimentally validated models of these components is crucial. First attempts have been performed, which take into account the subsoil as layered half-space and the ballast as an assembly of viscoelastic rods. Besides the short time dynamics the article gives also an overview of the modelling of the wear phenomena mentioned above. An investigation of such long-term effects requires complex models of the entire vehicle-track system. The few wear models found in literature are discussed and first results are mentioned.     

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.     

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

Abstract

A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.     

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.     

Dynamic vehicle–track interaction in switches and crossings and the influence of rail pad stiffness – field measurements and validation of a simulation model

A model for simulation of dynamic interaction between a railway vehicle and a turnout (switch and crossing, S&C) is validated versus field measurements. In particular, the implementation and accuracy of viscously damped track models with different complexities are assessed. The validation data come from full-scale field measurements of dynamic track stiffness and wheel–rail contact forces in a demonstrator turnout that was installed as part of the INNOTRACK project with funding from the European Union Sixth Framework Programme. Vertical track stiffness at nominal wheel loads, in the frequency range up to 20?Hz, was measured using a rolling stiffness measurement vehicle (RSMV). Vertical and lateral wheel–rail contact forces were measured by an instrumented wheel set mounted in a freight car featuring Y25 bogies. The measurements were performed for traffic in both the through and diverging routes, and in the facing and trailing moves. The full set of test runs was repeated with different types of rail pad to investigate the influence of rail pad stiffness on track stiffness and contact forces. It is concluded that impact loads on the crossing can be reduced by using more resilient rail pads. To allow for vehicle dynamics simulations at low computational cost, the track models are discretised space-variant mass–spring–damper models that are moving with each wheel set of the vehicle model. Acceptable agreement between simulated and measured vertical contact forces at the crossing can be obtained when the standard GENSYS track model is extended with one ballast/subgrade mass under each rail. This model can be tuned to capture the large phase delay in dynamic track stiffness at low frequencies, as measured by the RSMV, while remaining sufficiently resilient at higher frequencies.     

The effect of worn profile on wear progress of rail vehicle steel wheels over curved tracks

Dynamic performance, safety and maintenance costs of railway vehicles strongly depend on wheelset dynamics and particularly on the design of wheelset profile. This paper considers the effect of worn wheel profile on vehicle dynamics and the trend of wear in the wheels as a result of the vehicle movements. ADAMS/RAIL is used to build a multi-body system model of the vehicle. The track model is also configured as an elastic body. Measured new and worn wheel profiles are used to provide boundary conditions for the wheel/rail contacts. The fleet velocity profile taken during its normal braking is also used for the simulation. Wear numbers are calculated for different sets of wheels and the results compared with each other. Outcome of this research can be used for modifying dynamic performance of the vehicle, improving its suspension elements and increasing ride quality. It can also be further processed to reach to a modified wheel profile suitable for the fleet/track combination and for improved maintenance of the wheels. A major advantage of the computer models in this paper is the insertion of the wheel surface properties into the boundary conditions for dynamic modelling of the fleet. This is performed by regularly measuring the worn wheel profiles during their service life and by the calculation of the wear rate for individual wheels.     

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.     

Fundamentals of vehicle–track coupled dynamics

This paper presents a framework to investigate the dynamics of overall vehicle–track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A three-dimensional vehicle–track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel–rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time–frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle–track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing–Qinhuangdao line and the high-speed running test on the Qinhuangdao–Shenyang line. Differences in the dynamic responses analysed by the vehicle–track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.     

Optimization of curving performance of rail vehicles

The curving performance of a transit rail vehicle model with 21 degrees of freedom is optimized using a combination of multibody dynamics and a genetic algorithm (GA). The design optimization is to search for optimal design variables so that the noise or wear, arising from misalignment of the wheelsets with the track, is reduced to a minimum level during curve negotiations with flange contact forces guiding the rail vehicle. The objective function is a weighted combination of angle of attack on wheelsets and ratios of lateral to vertical forces on wheels. Using the combination of the GA and a multibody dynamics modelling program, A’GEM, the generation of governing equations of motion for complex nonlinear dynamic rail vehicle models and the search for global optimal design variables can be carried out automatically. To demonstrate the feasibility and efficacy of the proposed approach of using the combination of multibody dynamics and GAs, the numerical simulation results of the optimization are offered, the selected objective function is justified, and the sensitivity analysis of different design parameters and different design parameter sets on curving performance is performed. Numerical results show that compared with suspension and inertial parameter sets, the geometric parameter set has the most significant effect on curving performance.     

Optimization of curving performance of rail vehicles

The curving performance of a transit rail vehicle model with 21 degrees of freedom is optimized using a combination of multibody dynamics and a genetic algorithm (GA). The design optimization is to search for optimal design variables so that the noise or wear, arising from misalignment of the wheelsets with the track, is reduced to a minimum level during curve negotiations with flange contact forces guiding the rail vehicle. The objective function is a weighted combination of angle of attack on wheelsets and ratios of lateral to vertical forces on wheels. Using the combination of the GA and a multibody dynamics modelling program, A'GEM, the generation of governing equations of motion for complex nonlinear dynamic rail vehicle models and the search for global optimal design variables can be carried out automatically. To demonstrate the feasibility and efficacy of the proposed approach of using the combination of multibody dynamics and GAs, the numerical simulation results of the optimization are offered, the selected objective function is justified, and the sensitivity analysis of different design parameters and different design parameter sets on curving performance is performed. Numerical results show that compared with suspension and inertial parameter sets, the geometric parameter set has the most significant effect on curving performance.     

Driver models in automobile dynamics application

Understanding the driver of an automobile has been attractive to researchers from many different disciplines for more than half a century. On the basis of their acquirements, models of the (human) driver have been developed to better understand, analyse and improve the combined couple of driver and automobile. Due to distinctive demands on the models in accordance with different kinds of applications, a variety of driver models is available. An overview of driver models is given with respect to their application and different methodical modelling approaches. The emphasis is put on the interest of engineers, who generally focus on the automobile (like design and optimization of vehicle components and the overall vehicle dynamics behaviour) by applying their approved (mathematical) methods. Nonetheless, a brief look beyond is added to better complete the view on the involved task of driving and driver modelling for automobile dynamics application.     

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.     

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.     

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.     

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.     

Field measurements of the evolution of wheel wear and vehicle dynamics for high-speed trains

This investigation demonstrates the wheel wear evolution and related vehicle dynamics of high-speed trains with an operating distance (OD) of around two million kilometres. A long-term experimental test lasting two years was conducted to record the wheel profiles and structural vibrations of various trainsets. The wheel wear, namely the profile shape, worn distribution and wheelset conicity, is investigated for several continuous reprofiling cycles. Typical results are illustrated for the stability analysis, and the ride quality is examined with increasing OD. In addition, the vibration transition characteristics between suspensions are investigated in both the time and frequency domains. The experiments show that the dominant wear concentrates on the nominal rolling radius, and the wear rate increases with OD because of the surface softening resulting from the loss of wheel material. The vibration of structural components is aggravated by the increase of the equivalent conicity of the wheelset, which rises approximately linearly with the wheel wear and OD. High-frequency vibrations arise in the bogie and car body related to the track arrangement and wheel out-of-roundness, causing the ride comfort to worsen significantly. Additionally, the system vibration characteristics are strongly dependent on the atmospheric temperature. Summaries and conclusions are obtained regarding the wheel wear and related vehicle dynamics of high-speed trains over long operating times and distances.     

有砟轨道动刚度特性及影响因素分析

应用轨道结构的动力学频域分析方法,研究了有砟轨道的动刚度特性及轨道参数对它的影响。有砟轨道动刚度随频率变化幅度很大,在激振频率为72 Hz时达到最小值55 kN/mm,约为静刚度的60 %。扣件刚度、扣件阻尼、轨枕类型、道床弹性模量对有砟轨道动刚度都有影响。     

A Review of Modelling Methods for Railway Vehicle Suspension Components

The dynamic behaviour of railway vehicles has been the subject of study for over a century but the advances in computing technology in the last few years have led to a very rapid development in the use of numerical techniques for solving railway vehicle dynamics problems. As these techniques have developed, and have been applied to ever more complex problems, the modelling of the vehicle components has increased in importance. Mathematical models of railway vehicles may now include components such as swing links, air-springs, trailing arm suspensions, load sensitive friction dampers, rubber bushes with hysteresis etc, all of which require sophisticated modelling techniques to produce accurate results. This paper looks at the developments that have taken place in this area, the background to the need for sophisticated models, the improvements in accuracy that can result and some of the difficulties in applying these techniques to the modelling of real situations.