Track Model with Nonlinear Elastic Characteristic of the Rubber Rail Pad

This paper presents a new basic nonlinear track model consisting of an infinite Euler-Bernoulli beam (rail) resting on continuous foundation with two elastic layers (rail pad and ballast bed) and intermediate inertial layer (sleepers). The two elastic layers have bilinear elastic characteristic obtained from the load-displacement characteristic of the rail pad and ballast. A time-varying load with two components - time-constant one and harmonic other, representing the wheel/rail contact force is considered as the track model input. Rail deflection due to the time-constant component of the load is obtained solving the nonlinear equations of the balance position. Subsequently, the structure of the nonhomogeneous foundation is determined. Dynamic rail response in terms of receptance due to the harmonic component of the load is calculated using the linearised track model with nonhomogeneous elastic characteristic. Influence of the time-constant component and the reflected waves due to the nonhomogeneous foundation are presented.

Vibration source properties of cargo trains: free field vibration and trackside measurement analysis

Annoyance caused by railway operations has gained increasing attention in the Netherlands. This has led to a multimillion research project into different aspects of train passages as a source of vibration. The project is initiated by the Dutch railway operator ProRail. In advance of this project a study has been performed on vibration signals at free field caused by cargo train passages at four different sites. The signals have been compared to trackside measurements. The trackside measurements consist of fibre optic measurements of the rail deflection at pre-installed locations different from the free field vibration measurement sites. Different vibration level indicators have been studied like train speed, axle loads and wheel roughness indicators and their correlation with vibration levels. Vibration levels are defined in several ways, a frequency weighted running mean square value (so-called Veffmax), a 2-second RMS level (unweighted) and levels per frequency band. Special attention is given to the variation in time of the measured vibration signals during the train passage to see whether 'bad quality' wheel passages can be identified. The results give valuable input for a future case study in which wheel quality and its influence on vibration levels will be studied further.

Numerical Analysis of the Vertical Bogie Accelerations at Failure of the Damper in the Primary Suspension of the Railway Vehicle

Jointed track is still used to build the secondary lines where the maximum speed does not exceed 100-120 km/h. Jointed track construction is based by the fact that the rails are joined end-to-end via the rail joints in order to assure the continuity of the rolling surface of the rails. The rails are jointed using two metal joint bars (fishplates) bolted to the ends of adjoining rails. The rail joints are featured with small gaps to allow the thermic expansion of the rails when the environmental temperature is higher than that during the fitting. In this paper, an analytical model for the rail joint considering the influence of the joint gap is presented and analysed. The model consists of three Euler-Bernoulli beams, two for the rail ends of the rail joint and the third beam for the two joint bars, connected to the rail ends by a Winkler layer. The concept of weakness of the rail joint (rail joint deflection/continuous rail deflection) is introduced and used to analyse the static behaviour of three types of rail joints used at CFR (Romanian Railways). The influence of the joint bars length and bending stiffness, and the influence of the joint gap length upon the rail joint weakness is pointed out.

On the Modelling of Rail Joint

Jointed track is still used to build the secondary lines where the maximum speed does not exceed 100-120 km/h. Jointed track construction is based by the fact that the rails are joined end-to-end via the rail joints in order to assure the continuity of the rolling surface of the rails. The rails are jointed using two metal joint bars (fishplates) bolted to the ends of adjoining rails. The rail joints are featured with small gaps to allow the thermic expansion of the rails when the environmental temperature is higher than that during the fitting. In this paper, an analytical model for the rail joint considering the influence of the joint gap is presented and analysed. The model consists of three Euler-Bernoulli beams, two for the rail ends of the rail joint and the third beam for the two joint bars, connected to the rail ends by a Winkler layer. The concept of weakness of the rail joint (rail joint deflection/continuous rail deflection) is introduced and used to analyse the static behaviour of three types of rail joints used at CFR (Romanian Railways). The influence of the joint bars length and bending stiffness, and the influence of the joint gap length upon the rail joint weakness is pointed out.

Longitudinal Displacement Behavior and Girder End Reliability of a Jointless Steel-Truss Arch Railway Bridge during Operation

The long length and complex service load form conflicts with the low limits of longitudinal and transverse displacements of jointless bridge design. The longitudinal displacements of the Nanjing Dashengguan Yangtze River Bridge, a jointless steel-truss arch railway bridge, and its girder end reliability are investigated in this article. The time–frequency characteristics of the longitudinal displacements of bearings and expansion joints are analyzed using the empirical wavelet transform. The long-term characteristics of the longitudinal displacements of bearings and expansion joints in the operation period are explored. Furthermore, the relative transverse displacements of the bridge girder end are calculated using longitudinal displacement monitoring data. The mechanical behaviors of the expansion device under relative transverse displacements are studied. The reliability of expansion devices and crossing trains under the effects of relative transverse displacements is studied using kernel density estimation. The main results demonstrate that: (1) The longitudinal displacements of bearings and expansion joints are mainly influenced by environmental temperature. (2) The maximum relative transverse displacement of the expansion joint is close to 1 mm in long-term bridge operation, with the transverse rail deflection at the expansion device approaching 1 mm, which reduces the stability of cross high-speed trains.

Use of fiber optic sensing to measure distributed rail strains and determine rail seat forces under a moving train

Rayleigh backscatter fiber optic sensing permits dynamic strains to be measured along an optical fiber with a gauge spacing and temporal resolution sufficient for rail applications. However, this sensing technology is highly sensitive to vibration. A 7.5 m long section of rail was instrumented with optical fiber and strain measurements were recorded during passage of a freight train slowed to 8–11 km/h. This strategy to minimize rail vibration was successful in permitting distributed dynamic rail strains to be measured under freight car loading. The measured rail strains were used to determine the rail shear forces, which were then used with the static wheel loads to determine the rail seat load for 14 consecutive sleepers as the train passed over the field monitoring site. These data were then combined with measurements of dynamic rail displacement captured using digital image correlation to infer the rail seat load–deflection relationships for individual sleepers. These relationships were observed to provide significantly more detailed information about unsupported voids and the sleeper contact stiffnesses than the traditional consideration of the relationship between applied load and rail deflection and highlights how track behavior at a monitored location can be dependent on the conditions and behavior of neighbouring sleeper.

Dynamics of a beam on elastic foundation - impact of the bilinear characteristic of the foundation upon the propagation of the bending wave

Rail is an important source of noise in the railway traffic and its acoustic power is depending on the rate of decay of vibration. The main characteristic of the track in terms of the vertical elasticity is the so-called track modulus which results from the load-rail deflection curve. In general, this curve is nonlinear and it can be approximated using piecewise linear function with bilinear characteristic. In this paper, the response of a beam on elastic foundation with bilinear characteristic due to constant and harmonic loads is investigated, pointing out the impact of the foundation characteristic on the rail response and the propagation of the bending waves along the track.

Iterative Method for Predicting Uneven Settlement Caused by High-Speed Train Loads in Transition-Zone Subgrade

Uneven subgrade settlement associated with rail deflection occurs mainly in the bridge–embankment transition zones of high-speed railways. An iterative method of computation is proposed for studying such uneven settlement in these zones. A vehicle–track–subgrade model is used to investigate the vehicle–track interactions and the deviator stress field of the transition zone, and a soil cumulative plastic strain model is used to obtain the deterioration process of uneven settlement in the transition zone. Results indicate that uneven settlement caused by train loads in the transition zone tends to plateau at 40,000 repeated load applications. Sub-grade settlement changes abruptly in the first measured 5 m, as well as from 25 to 30 m from the abutment; these two regions should be adequately strengthened and should receive more attention for track maintenance.

Static analysis of chosen imperfections of rail subgrade on additional rail deflection of contactless track

In the paper, the chosen imperfections of railway subgrade causing additional rail deflections in contactless tracks were analysed. For such imperfections the following problems were selected: contactless work of railway track resting on the local uneven subgrade; loss of contact between track and subgrade; influence of variable compressive force on the length of contactless track; change in support stiffness on the deflection of contactless rail track. The presented static analysis has shown the importance of unfavourable influence of selected factors on work of contactless rail track (e.g. increase in the length of contact loss between track and subgrade or arising an additional deflections and stresses). A special attention was paid on such imperfections, apart from deflections and stresses cause among other things a disturbance of translational motion of rolling stock due to these imperfections. In the paper, a special accent was laid on visualization the influence of selected factors on work of contactless rail track, giving in many places in the paper the proper publications, in which the complete procedures of theoretical analysis of the considered problems are shown in the comprehensive way.