Vehicle-track Coupling Research Articles

Effect of Control Measures on Wheel/Rail Noise When the Vehicle Curves

This paper developed a time domain simplified model to study the effect of control measures on wheel/rail noise when the vehicle curves. The time domain model consists of two parts, one being a vehicle-track coupling dynamic model for wheel/rail interaction, the other being a transient finite element and boundary element domain model for vibration and sound radiation. Wheel/rail noise under wheel/rail lateral creep force is predicted for a narrowly curved section of a conventional underground railway, and compared with measurement. Based on the developed model, the effect of wheel/rail friction modification on squeal noise is investigated. In addition, effectiveness of resilient wheel and embedded track to control curve squeal noise are also assessed.

Time-domain model for wheel-rail noise analysis at high operation speed

This paper develops a numerical model for wheel-rail noise analysis in the time-domain. This model for wheel-rail noise is based on vehicle-track coupling dynamics considering the effect of flexible wheelsets and track, and a transient wheel-rail noise prediction method. This model can approximatively characterize the components of vibration and noise in the frequency range up to 3.5 kHz. The wheel-rail forces are calculated and shown in both time and frequency domains by using the vehicletrack coupling dynamic model. Then the vibration and sound of the flexible wheelset are calculated by the transient finite elementboundary element (FE-BE) prediction model at 300 km/h, in which the effects of random irregularity and discrete supporting excitation are considered. The numerical results calculated by using the present model are discussed. The present model is also used to calculate the effect of corrugation with wavelengths of 40 mm to 300 mm on wheel-rail noise. The numerical results can be useful for academic research and engineering application to railway noise and vibration.

Finite-infinite element coupled analysis on the influence of material parameters on the dynamic properties of transition zones

Based on the theory of vehicle-track coupling dynamics, a plane stress finite-infinite element model of a high-speed railway subgrade-bridge transition zone is proposed. With this model, the influence of 2 simultaneously varied subgrade material parameters on the dynamic response of the vehicle-track-subgrade system in a high speed railway transition zone with the slab track is investigated. The results indicate that the influence of the dynamic elastic modulus of the graded broken stone on the dynamic response of the vehicle system is larger than that of the dynamic elastic modulus of the subgrade bed surface layer. The recommended dynamic elastic moduli of the subgrade bed surface layer and the graded broken stone are chosen as 4000MPa and 2000MPa, respectively.

Extended applications of track irregularity probabilistic model and vehicle–slab track coupled model on dynamics of railway systems

ABSTRACTTrack irregularities are inevitably in a process of stochastic evolution due to the uncertainty and continuity of wheel–rail interactions. For depicting the dynamic behaviours of vehicle–track coupling system caused by track random irregularities thoroughly, it is a necessity to develop a track irregularity probabilistic model to simulate rail surface irregularities with ergodic properties on amplitudes, wavelengths and probabilities, and to build a three-dimensional vehicle–track coupled model by properly considering the wheel–rail nonlinear contact mechanisms. In the present study, the vehicle–track coupled model is programmed by combining finite element method with wheel–rail coupling model firstly. Then, in light of the capability of power spectral density (PSD) in characterising amplitudes and wavelengths of stationary random signals, a track irregularity probabilistic model is presented to reveal and simulate the whole characteristics of track irregularity PSD. Finally, extended applications from three aspects, that is, extreme analysis, reliability analysis and response relationships between dynamic indices, are conducted to the evaluation and application of the proposed models.

Influence of the Seam between Slab and CA Mortar of CRTSII Ballastless Track on Vibration Characteristics of Vehicle-Track System

With a lot of application of CRTSII slab ballastless track in China, a series of problems have arises during the slab track service. One of the most typical problems is the seam between the track slab and CA mortar layer, namely CA mortar seam. This may influence the vibration characteristics of the vehicle and CRTSII slab ballastless track. In order to study this phenomenon, according to the actual engineering and based on the finite element, a new vertical vehicle-track coupling dynamic model is established. The model consists of two parts, vehicle element and CRTSII slab ballastless track element. The former is regarded as multi-rigid-body systems, while the latter is established by means of finite element method, in which rail, fastening system, track slab, CA mortar, concrete base and subgrade are considered as a whole body. The rail, slab and the concrete base are simplified as layered Euler beam model. The fastener and subgrade are simplified as the linear spring. In order to consider the characteristics of the CA mortar seam, the nonlinear spring is used to simulate the CA mortar layer. Based on vehicle-track coupling dynamic model, the influence law of CA mortar seam on the safety of vehicle operation, on the displacement and acceleration of each part of the track structures, is revealed, by comparing the dynamics properties of the CRTSII slab ballastless track of the conditions without CA mortar seam and those with CA mortar seam. The result shows that while there is seam between the track slab and the CA mortar layer, it has slight influence on the smooth of vehicle operation, but has significant impact on the mechanical properties of the CRTSII slab ballast-less track structure. The study is expected to provide theoretical guidance for remediation if there are similar problems in the slab track.

Dynamic Characteristics of Coupled Vehicle–Track–Tunnel Interaction System

Dynamic Characteristics of Coupled Vehicle–Track–Tunnel Interaction System

Investigation on the sensitive and insensitive zones of the rail support stiffness for the dynamic response of a vehicle system under low excitation frequencies

ABSTRACTThe variation of the rail support stiffness is an inherent issue of railway tracks. There is still no consensus on the influence of the rail support stiffness variation on the dynamic response of the vehicle–track system. One view indicates that changes of the support stiffness do not have considerable influence on the vehicle dynamic response. The main influence factor is the rail deflection. However, the opposite view presents that the influence of the support stiffness on the system dynamic response is obvious. Reasons that lead to the dispute of previous studies are the neglect of the influence of the excitation frequencies and a lack of understanding of stiffness sensitive zones. In this study a vehicle–track coupling model with equivalent overall support stiffness is employed to investigate the response of the vehicle to changes of the track stiffness and excitation frequencies. Results show that for each of frequencies (1–40 Hz) the dynamic response of the vehicle is only sensitive to a certain range of the support stiffness. A stiffness sensitive zone for each excitation frequency can be observed. In order to further study the influence of the subgrade on the vehicle system dynamic response a vehicle–track-subgrade model is utilised. The subgrade stiffness belonging to the stiffness sensitive zone has a significant influence on vehicle vibrations. For overall support stiffness of the rail higher than 20 kN/mm, the stiffness sensitive zones of low excitation frequencies can be avoided.

An investigation of subgrade differential settlement on the dynamic response of the vehicle–track system

The construction of non-ballasted slab railway track on existing subgrade soils, or on embankments, is at an early stage of development on Chinese railways. Developing appropriate standards for the allowable amount of subgrade differential settlement that takes into account the dynamic response of the train–track system is one of a number of issues that need to be addressed. To inform the development of such standards, a model based on the theory of vehicle–track coupling dynamics, which considers the weight of the track structure, was created to investigate how differential settlement, in terms of the amplitude, wavelength and position of the settlement along the track, can affect various railway performance-related criteria, including ride quality, stability, vehicle safety and potential damage to the wheel of the train and the rail (i.e. forces at the wheel–rail contact and in the fasteners). The performance of the model was favorably compared with other widely used models described in the literature. The analysis of the study to inform design standards using the developed model demonstrated that the magnitude of the differential settlement influences passenger comfort the most compared with other performance criteria. For the considered CRTS I track, there exists a particular wavelength (8 m for the specific conditions considered) that results in all measures of performance being at their maximum values. Furthermore, the longitudinal position of the settlement waveform in relation to the joints between two concrete slabs, a factor which is not considered in design standards, was shown to influence component deterioration, passenger comfort and safety. The greatest propensity to cause component damage occurs when the beginning or end of the differential settlement waveform corresponds with the inter-slab joint of a concrete base. Accordingly, it is recommended that current design standards should be modified to specify appropriate combinations of amplitude, wavelength and position of the differential settlement to give acceptable measures of performance.

Study on the numerical optimization of rail profiles for heavy haul railways

The aim of this paper is to study the optimization of the rail profile for heavy haul railways. A numerical model is developed, where the rail profile is parameterized as a generalized function for a series of independent variables. A well-designed formula, which characterizes the conformance between wheel and rail profiles around contact point for all possible wheel–rail contact situations, is considered as the objective function. During the construction of the objective function, a wheel–rail contact geometry algorithm is implemented to detect contact point positions quickly. Linear and nonlinear constraints are introduced in order to meet some necessary conditions. Then, the optimization of rail profile can be transformed into a typical mathematical nonlinear optimization problem with single objective, multivariables, and multiconstraints. In order to solve this problem effectively and efficiently, the sequential quadratic programming algorithm combined with Lagrange function, quasi-Newton method is employed. At each major iteration, a quasi-Newton approximation is made of the Hessian matrix of the Lagrangian function using BFGS updating method. This is then used to generate a quadratic programming subproblem whose solution is for forming the search direction for the iteration of independent variables. Finally, the R75 rail profile, prevalently used in China’s heavy haul railways, is optimized using the developed model to better match the LM wheel profile. A modified rail profile is put forward and compared with the original rail profile systematically in wheel–rail contact geometry relationship, vehicle–track dynamic behaviors, and wear developments. A vehicle–track coupling dynamics model and a wheel–rail wear prediction model are respectively established to conduct the comparative study. According to the calculation results, the optimized rail profile is proved to have superior performances and, thus, can be considered a better choice to match LM wheel for China’s heavy haul railways, which is of practical value for the design and preventive grinding of heavy haul rails. In addition, this application example validates the rationality of the developed numerical optimization model. It can also be used for the optimization of other rail profiles.

Dynamic Analysis of the High Speed Train and Slab Track Nonlinear Coupling System with the Cross Iteration Algorithm

A model for dynamic analysis of the vehicle-track nonlinear coupling system is established by the finite element method. The whole system is divided into two subsystems: the vehicle subsystem and the track subsystem. Coupling of the two subsystems is achieved by equilibrium conditions for wheel-to-rail nonlinear contact forces and geometrical compatibility conditions. To solve the nonlinear dynamics equations for the vehicle-track coupling system, a cross iteration algorithm and a relaxation technique are presented. Examples of vibration analysis of the vehicle and slab track coupling system induced by China’s high speed train CRH3 are given. In the computation, the influences of linear and nonlinear wheel-to-rail contact models and different train speeds are considered. It is found that the cross iteration algorithm and the relaxation technique have the following advantages: simple programming; fast convergence; shorter computation time; and greater accuracy. The analyzed dynamic responses for the vehicle and the track with the wheel-to-rail linear contact model are greater than those with the wheel-to-rail nonlinear contact model, where the increasing range of the displacement and the acceleration is about 10%, and the increasing range of the wheel-to-rail contact force is less than 5%.

Contact Loss beneath Track Slab Caused by Deteriorated Cement Emulsified Asphalt Mortar: Dynamic Characteristics of Vehicle-Slab Track System and Prototype Experiment

The contact loss beneath track slab caused by deteriorated cement emulsified asphalt mortar (CA mortar) has been one of the main diseases occurring in the CRTS- (China Railway Track System-) I Slab Track of high-speed railway in China. Based on the slab track design theory and the vehicle-track coupling vibration theory, a vehicle-track vertical coupling dynamic FEM model was established to analyze the influence of the contact loss length on the dynamic characteristics of vehicle and track subsystems at different train speeds. A prototype dynamic characteristic experimental test of CRTS-I Slab Track with CA mortar contact loss was conducted to verify the FEM model results. The train load was generated by the customized ZSS50 excitation car. The results showed that when the operation speed is less than 300 km/h, the contact loss with length smaller than 2.0 m barely affects the running smoothness ride safety of vehicle. The contact loss length effect on the dynamic characteristics of track subsystem is pronounced, especially on the track slab. Once the contact loss beneath the track slab occurs, the vibration displacement and the acceleration of the track slab increase rapidly, while it has little influence on the displacement and acceleration of the concrete roadbed.

Dynamic Response Analysis of an Asymmetric Coupled Vehicle-Track System Generated by Voided Elastic Two-Block Sleeper

Based on vehicle-track coupled dynamic theory, a three-dimensional asymmetric vehicle-track coupling vibration model is developed to investigate the effect of voided elastic two-block sleepers on vehicle and track system dynamic responses. For the vehicle system, one car body, two frames, and four wheel sets are assumed to be rigid, with 35 degrees of freedom (DOF). For the track system, the rails and the concrete two-block sleepers are the main vibration components. The rails are modelled as Timoshenko beams, and the concrete two-block sleepers are assumed to be rigid mass with vertical and lateral movement. The pads under the rails and the rubber boots under the sleepers provide greater vertical and lateral elasticity for the track. The Hertz nonlinear elastic contact theory is used to calculate the normal wheel/rail force. The wheel/rail tangent creep force is first calculated using Kalker’s linear creep theory and then modified by the Shen-Hedrick-Elkins theory. The results show that the asymmetric voided elastic two-block sleepers have greater effects on the dynamic responses for fasteners and sleepers than on the car body and the wheel/rail forces under measured geometric irregularity and random irregularity. Two or more voided sleepers will greatly affect the vehicle running safety.

Study on the subgrade deformation under high-speed train loading and water–soil interaction

It is important to study the subgrade characteristics of high-speed railways in consideration of the water–soil coupling dynamic problem, especially when high-speed trains operate in rainy regions. This study develops a nonlinear water–soil interaction dynamic model of slab track coupling with subgrade under high-speed train loading based on vehicle–track coupling dynamics. By using this model, the basic dynamic characteristics, including water–soil interaction and without water induced by the high-speed train loading, are studied. The main factors-the permeability coefficient and the porosity-influencing the subgrade deformation are investigated. The developed model can characterize the soil dynamic behaviour more realistically, especially when considering the influence of water-rich soil.

Effect of track irregularity on the dynamic response of a slab track under a high-speed train based on the composite track element method

Slab tracks are common track structures in high-speed railways. In this study, a vehicle/slab track interaction model is developed based on vehicle–track coupling dynamics theory, and composite track elements are used to rapidly model the finite element equations of the slab track based on the stationary value theory of total potential energy. In the model, the rail is represented as a discretely-supported infinite beam, the slab and the base are considered as continuously-supported free beams, and the connections of the track structure are modelled as viscoelastic spring–damping elements. The composite track element method effectively derives the equations of motion with high or low degrees of freedom by increasing or decreasing the number of track elements; therefore, it can be applied to the dynamic analysis of the track and to investigate the dynamic responses of the slab track system, including the rail, pad, slab, Cement asphalt mortar (CA mortar) and base. The equations of motion of the vehicle system are also proposed using the finite element method. The vehicle system and the slab track system interact through the vertical wheel/rail force, which is approximated using Hertz contact theory. The dynamic responses of a slab track subjected to moving vehicle loads are analysed using dynamic simulations and are compared with another classic simulation method. The effects of random track irregularity and vehicle velocity on the dynamic responses of the slab track system are discussed.

Analysis of Local Vibration for High-Speed Railway Bridge Based on Finite Element Method

Based on the theory of vehicle track coupling dynamics, the local vibration of the high-speed railway box girder is analyzed by the Finite Element Method and the model is simulated with the solid elements. Through the study of vibration characteristics of the selected 6 sensitive points, the local vibrations in different parts of the box girder are figured out. It is compared the response of the time domain and frequency domain in different parts of the cross section on different train speeds. Furthermore, the influence of track irregularity of local vibration response is analyzed. The results show that the track irregularity is the main factor causing local vibration. At last, the effects of local vibration on the boundary conditions are discussed. The response of top panel, floor panel and web panel were different and the flange panel was similar between the simple supported beam and the fixed beam.

The effect of the frequency-dependent stiffness of rail pad on the environment vibrations induced by subway train running in tunnel

The influence of the frequency-dependent stiffness of rail pad on the frequency distribution of vibrations created by a subway train running in tunnel is investigated using a frequency-domain algorithm. The theoretical approach combines vehicle–track coupling dynamics and spectrum analysis using the finite element method. The proposed approach is validated by a comparison with measured data. The comparison further shows that the theoretical approach and the selection of calculation parameters are reasonable and they create high calculation accuracies in the considered frequency range. Compared with a constant stiffness pad, the frequency-dependent stiffness of rail pad has little effect on vibrations below the one-third octave center frequency of 25 Hz; however, it significantly changes the vibrations observed above that center frequency. It is also found that simply increasing the constant stiffness of rail pad can lead to predictions of the vibration that have only a small error in either the low-frequency or high-frequency domains.

Multiobjective Optimization of CRH3 EMU Wheel Profile

The wheel-rail wear problems inherent to railway operation have become increasingly prominent and serious, as they have been proven to be the main factors which affect safety, stability of electric multiple units (EMUs), and wheel-rail maintenance cost. The multiobjective optimization model of CN wheel profile proposed in this study was constructed in effort to reduce the wheel wear of CRH3. Reconstruction of the CN profile based on the nonuniform rational B spline (NURBS) curve theory was designed. Twenty vertical coordinates of the CN profile were selected as design variables, the first wheelset mean wear workand the wheel-rail lateral force were employed as the objective functions, and the wheel geometry, maximal contact pressure, and the derailment coefficient were chosen as the constraint conditions. Particle swarm optimization (PSO) was applied to complete the optimization model combined with the vehicle track coupling dynamics model. Analysis results indicated that the optimized CN-Opti profile possesses more favorable, comprehensive, dynamic, and effective characteristics than the traditional CN profile.

Time-frequency analysis of wheel-rail shock in the presence of wheel flat

Abstract: Against the deficiencies of traditional time domain and frequency domain analysis in detecting wheel-rail (W-R) system hidden risks which wheel flats generate, the time-frequency characteristics of W-R shock caused by wheel flat are analyzed and the vehicle-rail dynamic model with wheel flat is investigated. The 10 degrees of freedom (DOF) vehicle model is built up. 90-DOF rail model is constructed. The wheel flat excitation model is built up. The vehicle-track coupling dynamic model including wheel flat excitation is set up through nonlinear Hertzian contact theory. The vertical accelerations of axle box are calculated at different speeds and flat sizes based on the vehicle-track coupling dynamic model with wheel flat. Frequency slice wavelet transform (FSWT) is employed to analyze time-frequency characteristics of axle box accelerations to detect the W-R noncontact risks s which the traditional time domain or frequency domain method does not analyze. The results show that the small flat size and high running speed lead to high frequency W-R impact. Large flat size and high running speed result in momentary loss of W-R contact, and there exist security risks between wheel and rail. The conclusion that the phase of axle box accelerations is same to W-R forces lays a theoretical foundation of monitoring W-R contact safety from axle box acceleration instead of traditional W-R force detection.

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.

Dynamics of a vehicle–track coupling system at a rail joint

The dynamic behaviour at a rail joint is examined using a two-dimensional vehicle–track coupling model. The track system is described as a finite-length beam resting on a double-layer discrete viscous-elastic foundation. The vehicle is represented by a half car body and a single bogie. The influence of the number of layers considered, the number of elements between two sleepers, and the beam model is investigated. Parametric studies, both of the coupling model and the analytic formulae, are carried out in order to understand the influence of the main track and vehicle parameters on the P1 and P2 peak forces. Finally, the results in terms of P2 force from the proposed model are compared, not only with measured values but also with other simulated and analytical solutions. An excellent agreement between these values is found.