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.     

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.     

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).     

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.     

Dynamic studies of railtrack sleepers in a track structure system

This paper discusses the dynamic response of a typical prestressed concrete railtrack sleeper due to wheel-track interaction dynamics, involving wheel and rail imperfections, under various parametric conditions. The interaction dynamics of the vehicle and track is first carried out in the time domain using MSC/NASTRAN. Using the resulting load time histories on an isolated sleeper, a detailed finite element model of the sleeper is used to analyze its dynamic behaviour. The dynamic amplification factors for deflection, ballast pressure and bending moments have been evaluated at the critical section (rail-seat and centre) for various exciting frequencies under different vehicle-track parametric conditions. The results provide a basis for improved and rational design of the sleeper.     

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.     

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 tuned damping device for reducing noise from railway track

A promising means to reduce the component of railway rolling noise radiated by the track is to increase the damping of the rail. This increases the attenuation with distance of vibrations transmitted along the rail and thereby reduces the noise radiated. To achieve this, a tuned, damped mass-spring absorber system has been designed. To cover a wide range of frequencies, multiple tuning frequencies are used along with a material with a high damping loss factor. Suitable materials have been found from extensive tests on samples and prototypes of the damper have been built and tested, both in the laboratory and in the field. Results are very promising with reductions of the track component of noise of around 6 dB being measured.     

Application of dynamic vibration absorbers in floating raft system

To improve the isolation performance of the traditional floating raft system, dynamic vibration absorber (DVA) is introduced into floating raft in this research. The mathematical models of floating raft system consisting of beams are implemented by assembling the mobility matrices of the subsystems. Then the power flow transmission characteristics of the coupled system with/without the DVAs are investigated to evaluate the vibration reduction performance of DVAs. Numerical simulations are performed to explore the influence of several parameters, such as the setting positions, damping and mass of the passive DVAs, on the vibration reduction effects of DVAs. Moreover the vibration reduction performance of the semi-active absorber adjusting its stiffness adaptively is analyzed for the case of time-varying frequency excitation. In addition, the vibration reduction effects of semi-active DVAs under multi-frequency excitation are investigated. The results show that DVAs can significantly improve the isolation performance of floating raft system.     

Ground vibrations from heavy freight trains

Ground vibration from heavy freight trains on good quality welded track are found to have only a weak dependence on train speed above 30 km/h. At the site on which these tests were carried out a critical speed was found at which the vibration reached a peak. The frequencies of vibration produced appear to be functions of track and vehicle dimensions and the critical speed occurs at the coincidence of sleeper passage frequency and the total vehicle on track resonance frequency.     

Attenuation of flexural vibration for floating floor and floating box induced by ground vibration

This paper investigates the vibration isolation performance of floating floor and floating box structures to control rail vibration transmission. Simple theoretical and experimental methods are developed to analyze the effects of stiffener beam, mass and arrangement of isolator on the fundamental natural frequency of the flexural vibration of floating floor and box structure.The vibration reduction performances of floating floor and box structure are found to be degraded by flexural vibration of the floor or supporting stiffener beam. From the results of vibration measurements; stiffener beams increase the fundamental natural frequency of flexural vibration of floating floor and enhance vibration isolation. Also they can further alleviate the effect of flexural vibration using optimum isolator arrangement effectively. The proposed floating box design achieved a vibration reduction of 15-30 dB in frequency region of critical rail vibration (30-200 Hz).     

Design optimization of a damped hybrid vibration absorber

In this article, the H_∞ optimization design of a hybrid vibration absorber (HVA), including both passive and active elements, for the minimization of the resonant vibration amplitude of a single degree-of-freedom (sdof) vibrating structure is derived by using the fixed-points theory. The optimum tuning parameters are the feedback gain, the tuning frequency, damping and mass ratios of the absorber. The effects of these parameters on the vibration reduction of the primary structure are revealed based on the analytical model. Design parameters of both passive and active elements of the HVA are optimized for the minimization of the resonant vibration amplitude of the primary system. One of the inherent limitations of the traditional passive vibration absorber is that its vibration absorption is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The proposed HVA overcomes this limitation and provides very good vibration reduction performance even at a low mass ratio. The proposed optimized HVA is compared to a recently published HVA designed for similar propose and it shows that the present design requires less energy for the active element of the HVA than the compared design.     

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。     

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.     

Amplitude reduction of parametric resonance by dynamic vibration absorber based on quadratic nonlinear coupling

The paper proposes an amplitude reduction method for parametric resonance with a new type of dynamic vibration absorber utilizing quadratic nonlinear coupling. A main system with asymmetric nonlinear restoring force and harmonic excitation causes parametric resonance in the system. In contrast with autoparametric vibration absorber, the natural frequency of the vibration absorber is tuned to be in the neighborhood of twice that of the main system. For such a vibration absorber, we investigate the effect on the amplitude reduction for a parametrically excited main system. Analytical results using the method of multiple scales show that the amplitude of parametric resonance is reduced by the effect of the vibration absorber. The experimental results by a simple apparatus indicate that the parametric resonance is stabilized by the effects of both vibration absorber and Coulomb friction of the main system. Moreover, numerical results considering the Coulomb friction of the main system show that the amplitude of parametric resonance becomes close to zero by the proposed vibration absorber.     

PERFORMANCE AND DYNAMIC STABILITY OF GENERAL-PATH CENTRIFUGAL PENDULUM VIBRATION ABSORBERS

Centrifugal pendulum vibration absorbers are a type of tuned dynamic absorber used for the attenuation of torsional vibrations in rotating and reciprocating machines. They consist of masses that are constrained to move along specific paths relative to the rotational axis of the machine. Previous analytical studies have considered the performance of single absorber systems with general paths and of multi-absorber systems with a specific path type. In this paper, we investigate the performance and dynamic stability of systems comprised of multiple, identical centrifugal pendulum vibration absorbers riding on quite general paths. The study is carried out by considering a scaling of the system parameters, based on physically realistic ranges of dimensionless parameters, which permits application of the method of averaging. It is found that the performance of these systems is limited by two distinct types of instabilities. In one type, the system of absorbers lose their synchronous character, while in the other a classical non-linear jump affects all absorbers identically, leading to highly undesirable system behavior. These results are used to evaluate two common types of absorber paths, namely circles and cycloids, including intentional mistuning of the absorber frequencies. The results are used to make some recommendations about the selection of paths to achieve design goals in terms of absorber performance and operating range. The analytical predictions are confirmed by numerical simulations.     

H2 optimization of a non-traditional dynamic vibration absorber for vibration control of structures under random force excitation

The H₂ optimum parameters of a dynamic vibration absorber of non-traditional form are derived to minimize the total vibration energy or the mean square motion of a single degree-of-freedom (sdof) system under random force excitations. The reduction of the mean square motion of the primary structure using the traditional vibration absorber is compared with the proposed dynamic absorber. Under optimum tuning condition, it is shown that the proposed absorber when compared with the traditional absorber, provides a larger suppression of the mean square vibrational motion of the primary system.     

ADAPTIVE-PASSIVE ABSORBERS USING SHAPE-MEMORY ALLOYS

The adaptive-passive vibration absorber shows promise for combining the stability and low complexity of passive tuned absorbers with the robust performance of active vibration control schemes. Previous adaptive tuned vibration absorbers (ATVA) had been complex and bulky. Shape memory alloys (SMA), with their variable material properties, offer an alternative adaptive mechanism. Heating an SMA causes a change in the elastic modulus of the material. An ATVA using spring elements composed of three pairs of SMA wires and one pair of steel wires was constructed and tested. On-off actuation of the SMA elements created an ATVA with four discrete tuned frequencies. Characterization testing of the absorber showed variation of the natural frequency of the ATVA of approximately 15%. The ATVA was applied to a primary system and the frequency response of the system at various states of ATVA actuation was determined. Manual tuning of the ATVA actuation during a stepped-sine base excitation of the primary system showed a wider notch of attenuation than was possible with a non-adaptive absorber. Results of the tests indicate that an adaptive absorber incorporating SMA as a tuning element has potential as a simple, high-performance adaptive-passive technique for vibration control.     

A railway track dynamics model based on modal substructuring and a cyclic boundary condition

This article presents a technique for modelling the coupled dynamics of a railway vehicle and the track. The method is especially useful for simulating the dynamics of high speed trains running on nonlinear tracks. The main hypothesis is a cyclic system: an infinite track on which there is an infinite set of identical vehicles spaced at a regular interval of distance. Thus the main problems of the finite-length track models (e.g. the waves that reflect at the end of the track and interact with the vehicle; and the time interval of integration must be shorter than the track length divided by the velocity) are avoided. The flexibility of the method can be observed from the case studies presented in the present work: a vehicle passing over a hanging sleeper, and the vehicle-track dynamics for different ballast compaction cases. The results show the influence of the hanging sleeper gap on the wheel-rail contact forces, and the bending moment at the sleeper for different ballast compaction cases.     

A precise integration method for solving coupled vehicle–track dynamics with nonlinear wheel–rail contact

A new method is proposed as a solution for the large-scale coupled vehicle–track dynamic model with nonlinear wheel–rail contact. The vehicle is simplified as a multi-rigid-body model, and the track is treated as a three-layer beam model. In the track model, the rail is assumed to be an Euler-Bernoulli beam supported by discrete sleepers. The vehicle model and the track model are coupled using Hertzian nonlinear contact theory, and the contact forces of the vehicle subsystem and the track subsystem are approximated by the Lagrange interpolation polynomial. The response of the large-scale coupled vehicle–track model is calculated using the precise integration method. A more efficient algorithm based on the periodic property of the track is applied to calculate the exponential matrix and certain matrices related to the solution of the track subsystem. Numerical examples demonstrate the computational accuracy and efficiency of the proposed method.