Effect of track stiffness on vibration levels in railway tunnels

The paper discusses the difficulties in comparing and drawing conclusions from vibration measurements made in different railway tunnels. A number of new measurements are presented, which have been made and analyzed on a consistent basis. The track stiffness has been determined for each of the measurements. Graphs are presented which indicate the level of rail and tunnel floor vibration likely to occur for different track stiffnesses. The variance in the measurement results also indicates the potential error in using the data to predict vibration levels in new situations.     

Prediction of vibrations induced by underground railway traffic in Beijing

This paper examines the problem of subway induced vibrations on line 4 of Beijing metro, which is currently under construction and is planned to pass in close proximity of the Physics Laboratory of Beijing University. The laboratory has a lot of equipment that is very sensitive to traffic induced vibrations and future operation of metro line 4 is a matter of concern. Hence, it is important to study the influence of subway induced vibrations inside the laboratory and to propose a viable solution to mitigate the vibrations. In this paper, the tunnel north of Chengfulu station is modelled using a coupled periodic FE-BE model and the free-field response due to moving trains is predicted. In addition, vibration measurements have been performed on the site of the Physics Laboratory to estimate the existing vibration levels due to road traffic. The predicted and measured vibrations are superimposed to assess the vibrations due to the combined effect of road and railway traffic in the vicinity of the Physics Laboratory. Apart from the numerical investigations, vibration measurements have also been performed on a similar site at line 1 of Beijing metro to substantiate the estimated results on metro line 4. Finally, it is studied how the vibrations can be controlled using a floating slab track, which is widely used as an effective measure of vibration isolation in tunnels. The efficiency of a 7.9 Hz floating slab track as a vibration countermeasure is assessed in this paper. This study demonstrates the applicability of the numerical model for the relevant assessment of subway induced vibrations and its use to study the performance of different track structures in the tunnel.     

A Study of the Suitable Measurement Location and Metrics for Assessing the Vibration Source Strength Based on the Field-Testing Data of Nanchang Underground Railway

Underground railway vibration source strength is one of the key values used for environmental impact assessment and the evaluation of mitigation measure’s performance. However, currently there is no international standard of measuring the underground railway vibration source strength for such purposes. The available local standards and industrial guidelines do not agree on measurement locations as well as the metrics for presenting the source strength. This has caused many confusions. This paper aims to study the suitable measurement location and metrics using the data from a large scale field-testing carried out at the Nanchang underground railway (Metro Line 1, China) in 2017. 200 passing trains were recorded during the test at two different sections of the railway line, one with the spring floating slab installed and the other without. Three locations were chosen at each section, including one in the middle of the track and two on the tunnel wall at different heights. Based on the results of statistical analysis, the maximum of z-weighted vertical vibration level (VLzmax) obtained at a lower measurement location on the tunnel wall is the best for representing the underground railway vibration source strength, which is 76.66 dB obtained from this study.     

On the dynamics of interaction between a moving mass and an infinite one-dimensional elastic structure at the stability limit

The paper herein deals with the study of the dynamic behaviour generated by the instability of the vibration of a loaded mass, uniformly moving along an Euler-Bernoulli beam on a viscoelastic foundation, induced by the anomalous Doppler waves excited in the beam. This issue is relevant for the case of modern trains travelling along a track with soft soil when the trains speed exceeds the phase velocity of the waves induced in the track. The model corresponds to a railway vehicle reduced to a loaded wheel running along a (half) track. The beam takes account of the bending stiffness of the rail and the mass of the track, including the mass of the rail, semi-sleepers and half of the ballast layer, where the viscoelastic foundation represents the subgrade. The model includes the wheel/rail Hertzian contact and it allows the simulation of the possibility of contact loss. The nonlinear equations of motion are integrated using a numerical approach based on the Green’s function method. When the vibration becomes unstable, the system evolution is a limit cycle characterised by a succession of shocks, due to the action of two opposite factors: the anomalous Doppler waves that pump energy at the interface between the moving mass and the beam, thus forcing the mass to take off, and the static load that push the mass downwards. The frequency of the shocks increases at higher velocity and the magnitude of the impact force decreases; the most dangerous velocity is the critical one, which represents the stability limit of the linear approximation of the motion equations. The transient behaviour that precedes the limit cycle appearance is being analysed. The Hertzian contact influences the time history of the limit cycle and the magnitude of the impact force and, therefore, it is essential to be included in the model. To the authors’ knowledge, this problem has never been dealt with.     

On the railway track dynamics with rail vibration absorber for noise reduction

A promising means to increase the decay rate of vibration along the rail is using a rail absorber for noise reduction. Compound track models with the tuned rail absorber are developed for investigation of the performance of the absorber on vibration reduction. Through analysis of the track dynamics with the rail absorber some guidelines are given on selection of the types and parameters for the rail absorber. It is found that a large active mass used in the absorber is beneficial to increase the decay rate of rail vibration. The effectiveness of the piecewise continuous absorber is moderate compared with the discrete absorber installed in the middle of sleeper span or at a sleeper. The most effective installation position for the discrete absorber is in the middle of sleeper span. Over high or over low loss factor of the damping material used in the absorber may degrade the performance on vibration reduction.     

A rational fraction polynomials model to study vertical dynamic wheel–rail interaction

This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel–rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel–rail contact passing over a welding defect at different speeds.     

Measuring,modelling and optimising an embedded rail track

A finite element (FE) model and a boundary element (BE) model have been developed to predict the decay rate, vibration and noise responses of an embedded rail track. These models are validated using measured results. The optimisation of the embedded rail track is conducted using these calculated models. The results indicate that the optimised cross-section of the gutter for the embedding rail can significantly reduce the radiated noise of the embedded rail track. The embedded rail track using the I-shaped cross-section gutter reduces the radiated noise of the track by at least by 3 dB(A). Furthermore, combining the material parameter optimisation with the gutter cross-section optimisation can further reduce the radiated noise of the embedded rail track. Increasing the Young’s modulus of the rail pad in the embedded rail track with the I-shaped cross-section gutter can result in a radiated noise reduction of 4 dB(A).     

Application of MetaRail railway noise measurement methodology: comparison of three track systems

Within the fourth RTD Framework Programme, the European Union has supported a research project dealing with the improvement of railway noise (emission) measurement methodologies. This project was called MetaRail and proposed a number of procedures and methods to decrease systematic measurement errors and to increase reproducibility. In 1999 the Austrian Federal Railways installed 1000 m of test track to explore the long-term behaviour of three different ballast track systems. This test included track stability, rail forces and ballast forces, as well as vibration transmission and noise emission. The noise study was carried out using the experience and methods developed within MetaRail. This includes rail roughness measurements as well as measurements of vertical railhead, sleeper and ballast vibration in parallel with the noise emission measurement with a single microphone at a distance of 7.5 m from the track. Using a test train with block- and disc-braked vehicles helped to control operational conditions and indicated the influence of different wheel roughness.It has been shown that the parallel recording of several vibration signals together with the noise signal makes it possible to evaluate the contributions of car body, sleeper, track and wheel sources to the overall noise emission. It must be stressed that this method is not focused as is a microphone-array. However, this methodology is far easier to apply and thus cheaper. Within this study, noise emission was allocated to the different elements to answer questions such as whether the sleeper eigenfrequency is transmitted into the rail.     

Reducing slab track vibration into bridge using elastic materials in high speed railway

In this paper, the problem of vibration transmission from slab track structures into bridge is studied by theoretical analysis. A vehicle-track-bridge coupling system dynamics model is established based on a multibody dynamics theory and a finite element method. The system model consists of vehicle model, track-bridge model and wheel/rail interaction model. The vehicle model is established based on the multibody dynamics theory, and the tack-bridge model is established by the finite element method. The vehicle model and track-bridge model are coupled through wheel/rail interaction model, and the track irregularities are included. The system dynamic responses are calculated, and the effectiveness of elastic materials in vibration reducing is discussed. The results demonstrate that elastic materials like slab mat layer inserted between slab track and bridge can reduce vibration transmitted from track into the bridge. Some suggestions for the design and application of slab mat are provided in the end of the paper.     

Human reaction to vibrations from blasting activity – Norwegian exposure–effect relationships

Rock blasting may cause disturbances, fear, and annoyance in residential and community areas affected by such activities. These community reactions can be quite strong, even when the blasting activities and the resulting vibrations are unlikely to cause physical damage to building foundations or buildings. A socio-vibrational survey was undertaken to assess residential reactions to blasting activities. Vibration velocities were obtained for 520 respondent dwellings located in seven study areas, and compared to the residents’ assessments of environment quality. Even at low vibration values, many people report annoyance. Exposure–effect relationships with acceptable statistical error bands were obtained. The level of annoyance from long-term blasting activities (quarry blasting) was not higher than from finite periods of more intense blasting activities (road and rail tunnels). Providing information in advance of the blasting activities, can reduce community reactions. Self-reported sensitivity to vibrations was associated with significantly increased annoyance. Sensitivity to vibrations was uncorrelated with exposure to vibrations. Sensitivity to noise and sensitivity to vibration were moderately correlated.     

Ground-borne noise and vibration from underground rail systems

Ground-borne noise is one of the main causes of environmental impact from urban rail transit systems. The vibration resulting from track-train interaction is transmitted through the tunnel 3tructure and the surrounding ground to adjacent buildings. The resulting vibrations of the walls and floors of these buildings cause secondary radiation of noise. This paper presents a method for estimating A-weighted sound levels as well as noise and vibration spectra due to ground-transmitted vibration in buildings near subways.     

A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheelset-track system

The present work proposes friction coupling at the wheel-rail interface as the mechanism for formation of rail corrugation. Stability of a wheelset-track system is studied using the finite element complex eigenvalue method. Two models for a wheelset-track system on a tight curved track and on a straight track are established. In these two models, motion of the wheelset is coupled with that of the rail by friction. Creep force at the interface is assumed to become saturated and approximately equal to friction force, which is equal to the normal contact force multiplied by dynamic coefficient of friction. The rail is supported by vertical and lateral springs and dampers at the positions of sleepers. Numerical results show that there is a strong propensity of self-excited vibration of the wheelset-track system when the friction coefficient is larger than 0.21. Some unstable frequencies fall in the range 60-1200 Hz, which correspond to frequencies of rail corrugation. Parameter sensitivity analysis shows that the dynamic coefficient of friction, spring stiffness and damping of the sleeper supports all have important influences on the rail corrugation formation. Bringing the friction coefficient below a certain level can suppress or eliminate rail corrugation.     

基于视觉的车辆与轨道相对振动状态测量方法研究

车辆与轨道相对振动状态对轨道线形测量有重要影响;分析了传统检测车辆与轨道相对振动状态测量方法的缺陷,提出一种基于视觉的车轨相对振动状态测量方法,以轨道建立世界坐标系,以车体建立车体坐标系。考虑相机镜头畸变,建立相机非线性模型,基于机器人手眼方法标定相机与车体,求解相机内外参数。依据车体运动姿态特征,推导基于双目机器视觉的车辆运动姿态偏移补偿计算方法;运用实验平台设计验证实验,通过计算所得的车体振动位移与真实值高度吻合,随着车速增加振动位移误差也随之增大,验证了该方法的正确性和可行性;提供一种车辆与轨道相对振动状态测量方法。     

The effect of critically moving loads on the vibrations of soft soils and isolated railway tracks

The dynamic response of the railway track is strongly influenced by the underlying soil. For a soft soil and very high train speeds or for a very soft soil and regular train speeds, the train speed can be close to the speed of elastic waves in the soil. This paper presents a detailed study of the so-called “moving-load effect”, i.e. an amplification of the dynamic response due to the load movement, for the tracks on soft soil. The analysis is carried out by evaluating the related integrals in the wavenumber domain. The influence of the load speed is quantified for a large set of parameters, showing that the effect on the soil vibration is reduced with increase of the frequency, track width and inverse wave velocity. Therefore, the moving-load effect associated with vibratory train loads is negligible whereas the amplification associated with the moving dead weight of the train can be significant. The strong moving-load effect on a perfectly homogeneous soil, however, can be strongly diminished by a layered or randomly varying soil situation. This theoretical result is affirmed by measurements at a test site in Germany where the trains run on a very soft soil at a near-critical speed. The results for soft soils are compared with experimental and theoretical results for a stiff soil. It is found that the influence of the stiffness of the soil is much stronger than the moving-load effect. This holds for the soil vibration as well as for the track vibration which both show a minor dependence on the load speed but a considerable dependence on the soil stiffness in theory and experiment.Railway tracks can include soft isolation elements such as rail pads, sleeper shoes and ballast mats. For these types of isolation elements and normal soil conditions, the influence of the load speed is usually negligible. There is only one isolation measure for which the moving load may be effective: a track which is constructed as a heavy mass-spring system. The resonance of this track system is shifted to lower frequencies and amplitudes for increasing train speed. A critical train speed can be reached if the mass-spring system has a marginal bending stiffness along the track.     

A double tuned rail damper—increased damping at the two first pinned-pinned frequencies

Railway-induced vibrations are a growing matter of environmental concern. The rapid development of transportation, the increase of vehicle speeds and vehicle weights have resulted in higher vibration levels. In the meantime vibrations that were tolerated in the past are now considered to be a nuisance. Numerous solutions have been proposed to remedy these problems. The majority only acts on a specific part of the dynamic behaviour of the track. This paper presents a possible solution to reduce the noise generated by the ‘pinned-pinned’ frequencies. Pinned-pinned frequencies correspond with standing waves whose nodes are positioned exactly at the sleeper supports. The two first pinned-pinned frequencies are situated approximately at 950 and 2200 Hz (UIC60-rail and sleeper spacing of 0.60 m). To attenuate these vibrations, the Department of MEMC at the VUB has developed a dynamic vibration absorber called the Double Tuned Rail Damper (DTRD). The DTRD is mounted between two sleepers on the rail and is powered by the motion of the rail. The DTRD consists of two major parts: a steel plate which is connected to the rail with an interface of an elastic layer, and a rubber mass. The two first resonance frequencies of the steel plate coincide with the targeted pinned-pinned frequencies of the rail. The rubber mass acts as a motion controller and energy absorber. Measurements at a test track of the French railway company (SNCF) have shown considerable attenuation of the envisaged pinned-pinned frequencies. The attenuation rate surpasses 5 dB/m at certain frequency bands.     

The noise behavior of the wheel/rail-system— some supplementary results

Acoustical measurements were carried out on railroad coaches, on standard tracks and in the free field during test runs. In particular the influences of noise parameters like train speed, track condition, wheel type or locomotive propulsion were examined. Among other things, it appeared that the track conditions can vary considerably, a fact that has a great influence on all measurement values. One obtains a kind of “track profile” relatively independent of the train speed. Measurements both on the parts of the rail and in the free field during the pass-by of a train wheel, just as do the measurements of the wheel levels at the same time, indicate that the rail in the frequency range between 500 and 1200 Hz is the most important factor with regard to sound radiation. Only above this range is the wheel the essential radiator, mainly in the range around 2000 Hz. Further it could be ascertained that the total acceleration levels of the wheel rim have a greater speed exponent than the total acceleration levels of the rail. This can be important if one makes an extrapolation for high train speeds. Additional damping of coach wheels results in a greater noise reduction not only for the radiated sound but also for the structure-borne sound at the rails. This fact indicates the relatively strong coupling between rail and wheel. Furthermore it was ascertained that the levels generated by a locomotive in the upper frequency range are similar to those produced by damped coach wheels. A propulsion influence of an electrical locomotive on the radiated total sound level could not be ascertained. In the last section possible noise generating mechanisms are pointed out with regard to their importance as indicated by our present state of knowledge.     

Vertical dynamic response of non-uniform motion of high-speed rails

In this paper, a computational study using the moving element method (MEM) is carried out to investigate the dynamic response of a high-speed rail (HSR) traveling at non-uniform speeds. A new and exact formulation for calculating the generalized mass, damping and stiffness matrices of the moving element is proposed. Two wheel–rail contact models are examined. One is linear and the other nonlinear. A parametric study is carried out to understand the effects of various factors on the dynamic amplification factor (DAF) in contact force between the wheel and rail such as the amplitude of acceleration/deceleration of the train, the severity of railhead roughness and the wheel load. Resonance in the vibration response can possibly occur at various stages of the journey of the HSR when the speed of the train matches the resonance speed. As to be expected, the DAF in contact force peaks when resonance occurs. The effects of the severity of railhead roughness and the wheel load on the occurrence of the jumping wheel phenomenon, which occurs when there is a momentary loss of contact between the wheel and track, are investigated.     

Investigation of rail noise and bridge noise using a combined 3D dynamic model and 2.5D acoustic model

Bridge noise and rail noise are two major sources of an elevated rail transit bridge in the low and medium frequency range (20–1000 Hz). However, in most of the existing literature, the noise radiated from the bridge and rail was investigated separately or using a simplified source model. In this study, an accurate method is proposed to simulate both the rail noise and bridge noise simultaneously. First, the dynamic responses of the rail and multi-span bridge are obtained using a three-dimensional (3D) vehicle-track-bridge interaction analysis model. Then, the two-dimensional (2D) infinite element model is used to calculate 3D modal acoustic transfer vectors of the rail and bridge based on the wavenumber transformation, in order to overcome the singularity and non-uniqueness of the conventional boundary element method and reduce the computation cost. Third, a field test is conducted, and the accuracy of the proposed simulation procedure is verified. Finally, the contribution of the rail and bridge noise to the total noise level is investigated in the whole space near the bridge. Generally the bridge noise occupies a higher contribution in the space beneath the girder due to the shielding effect of the bridge shape on the rail noise, while the rail noise is dominant in the upper space above the bridge. It is found the presence of the vehicle bodies has considerable effect on the rail noise but little influence on the bridge noise. The slope of the roughness level spectrum has significant influence on the dominant field of bridge noise and rail noise. For the excitation of the assumed ISO roughness level used in this study, the difference between the rail noise and bridge noise is only about 3 dB at field points 15–30 m away from the track center, which indicates both the bridge and rail noise should be included in the noise prediction for an elevated rail transit bridge.     

A HYBRID MODEL FOR THE NOISE GENERATION DUE TO RAILWAY WHEEL FLATS

A numerical model is developed to predict the wheel/rail dynamic interaction occurring due to excitation by wheel flats. A relative displacement excitation is introduced between the wheel and rail that differs from the geometric form of the wheel flat due to the finite curvature of the wheel. To allow for the non-linearity of the contact spring and the possibility of loss of contact between the wheel and the rail, a time-domain model is used to calculate the interaction force. This includes simplified dynamic models of the wheel and the track. In order to predict the consequent noise radiation, the wheel/rail interaction force is transformed into the frequency domain and then converted back to an equivalent roughness spectrum. This spectrum is used as the input to a linear, frequency-domain model of wheel/rail interaction to predict the noise. The noise level due to wheel flat excitation is found to increase with the train speed V at a rate of about 20 log₀V whereas rolling noise due to roughness excitation generally increases at about 30 log₀V. For all speeds up to at least 200 km/h the noise from typical flats exceeds that due to normal levels of roughness. When the wheel load is doubled the predicted impact noise increases by about 3 dB.