The effect of vertical-lateral coupling of rails including initial curvature

An understanding of the dynamic behaviour of railway tracks at high frequencies, in both vertical and lateral directions, is important for the assessment of rolling noise. Although many analytical models can be found in the literature, these mostly focus on the vertical vibration of the track. Studies of the lateral vibration are less common while the coupling between the vertical and lateral directions has received very little attention. In this paper, a model of a beam on an elastic foundation is introduced that accounts for the coupling of the vertical and lateral vibration behaviour. The model allows for the effects of beam curvature, asymmetry of the cross-section, shear deformation, rotary inertia and warping. Consideration is given to the fact that the loads at the rail head, as well as those exerted by the railpads at the rail foot, may not be applied through the centroid of the section. The track is subjected to a non-moving harmonic load and the solution is obtained in the wavenumber domain using the Fourier transform method. Results are presented as dispersion curves for the free rail and are validated with the aid of a Finite Element software. Closed form analytical expressions are derived, using contour integration, for the forced response. The track vibration decay rates are also presented and analysed as a means of assessing the noise performance of the rail and the influence of vertical-lateral coupling

Modelling options for ballast track dynamics

Accurate modelling of railway ballasted track dynamics is an important issue for a variety of applications such as the assessment of wheel/rail contact force and critical speed of the vehicle. Track design and assessment against safety and stability criteria can now rely on a number of advanced and validated dynamic models. However, there is a large range of different models that can be used to predict ballasted track dynamics. They vary from fast and simple rigid multi-body models as used in commercial Multibody System approach (MBS) vehicle dynamics calculations, to more complex and expensive three-dimensional (3D) Finite Element (FE) models. This paper investigatesthe influence of different modelling options up to 2000 Hz for characterising ballasted track dynamics with the aim of providing guidelines for simplifying the model and summarising the advantages and limitations of each option. Five different models, a two-degrees-of-freedom (2 dof) multi-body track model, 2D FE model, 3D FE models with/without consideration of sleeper flexibility, and a 3D FE track model with homogeneous ballast layer are used to represent the ballasted track as a two-layer support and compared against an analytical solution. Consideration is given to the flexibility of the sleepers, inclusion of ballast density and geometry, element discretization level and FE model length. Equivalent parameters to convert input data from one model to another are summarize

A comparison between the use of straight and curved beam elements for modelling curved railway tracks

A major environmental concern related to railway traffic is vibration. A lot of re- search has been carried out to understand vibration of straight tracks, with less attention been paid to curved tracks. Modelling the dynamic behaviour of a curved railway track is important to understand the physics of generation and propagation of vibration fromtrains at non-straight sections of tracks. Modelling is also important to assess the current and any alternative track designs from an environmental point of view. In this paper a curved track is modelled and the effect of curvature is investigated. Two models have been developed and their results have been compared. In the first, the curved track is modelled using straight beam elements. In the second curved beam elements are used. For both, the Euler-Bernoulli beam theory has been adopted to describe their bending behaviour. The elements have 12 degrees of freedom accounting for displacements and rotations in the lateral, transverse and longitudinal directions. The excitation comes from an axle traversing the rails with subcritical velocity, accounting for the wheel-rail contact forces. The describedmodels are solved using the Finite Element Method. The time domain response of the versine of the curved track due to the passage of the axle is computed. A comparison is made on the efficiency of the two models for different curve radii and frequencies. The two models provide very similar results showing that the piecewise straight beam approximation represents the behaviour of the curved track accurately. Also the curved beam model used in this study shows some limitations for the specific application and therefore the straight element method is recommende

A holistic approach for the design and assessment of railway tracks

In spite of the global financial crisis, considerable investments are being made in railway infrastructure in the UK and many countries around the world. Improvements in the quality and capacity of current services and the development of new railway infrastructure are needed to meet the increasing demand for transferring more people and goods in a more sustainable way. In particular, the performance of the track system is crucial to the successful and cost-effective operation of the railway. This has motivated much scientific research with the aim of better understanding the performance of the railway system, including both existing railway tracks and improved tracks for the future. Much current research on railway track focuses on individual aspects of the design and performance, e.g. track settlement, rail fatigue, ballast degradation, ride quality, maintenance, and noise and vibration. However to achieve substantial advances in railway track design, it is important to consider all these aspects in an integrated way. Changes that can benefit one aspect should not be allowed to have a negative impact on others. To facilitate this, a single tool should be developed or the computational tools that consider individual aspects of the design need to be integrated. The resulting tool can therefore be used to assess the behaviour of railway tracks in a holistic manner. A preliminary version of such a holistic tool is presented here. In this version, fast running models and empirical relationships are put together in order to calculate the performance of a railway track with regard to ride quality, ground-borne noise and vibration and rolling noise. Results for practical case studies are presented and discussed. The paper also highlights the limitations of the preliminary version and the future plans to achieve a reliable and comprehensive tool

Dynamic analysis and performance of a Repoint track switch

This paper is closed access until 09 May 2020.Repoint is an alternative concept for the design of track switches developed at Loughborough University. The concept, based around a stub switch, offers several improvements over current designs. Through a novel locking arrangement, it allows parallel, multi-channel actuation and passive locking functions, providing a high degree of fault tolerance. The aim of the work presented in this paper is to evaluate the dynamic interaction forces due to the passage of rolling stock over the switch and, particularly, the area of the stub rail ends, in comparison to a conventional switch. Specific behaviour and load transfer conditions from one rail to the other at the joint are analysed, as well as long term wear conditions of the rails. These evaluations are undertaken by means of multi-body dynamic simulations, leading to design refinement of the stub rail ends and the identification of further research and development requirements in their design

Analytical modelling of the vibration of railway track

The high frequency dynamic behaviour of railway track, in both vertical and lateral directions, strongly affects the generation of rolling noise as well as other phenomena such as rail corrugation. One aspect that has received little attention is the coupling between the vertical and lateral directions. This thesis sets out to build an analytical model of a railway track with three principal targets: to improve the modelling for lateral vibration compared with existing models, to identify the most important sources of coupling between the vertical and lateral directions and to quantify the implications for rolling noise phenomena.Simple models for the axial, torsional, vertical and lateral vibrations of beams are first introduced. The results from these models are analysed based on their dispersion curves and their characteristic behaviour is identified. Furthermore, effects of cross-section asymmetry, shear deformation, rotational inertia, restrained warping and curvature are considered, as well as the fact that the loads at the rail head do not always act through the centroid of the rail section. These beam models are then brought together to formulate a fully coupled beam model.An elastic foundation is then introduced to the beam model to represent the railpads and the dispersion characteristics of the whole track are discussed. Subsequently, the effect of the foundation location is investigated, as well as the inclusion of additional layers of masses and springs, representing the sleepers and ballast. Two different sleeper models are introduced. The first is that of a simple mass allowed to translate and rotate, representing a single block of a bibloc sleeper. The second is that of a flexible finite length beam accounting for vertical, lateral, axial and torsional vibration, representing a monobloc sleeper, which is more widely used in railway tracks. The response of the beam model is compared against measurements performed on sleepers in the laboratory. An average error of less that 1% is observed for the natural frequency of all modes, excluding the first mode. This mode is most influenced by the sleeper cross-section variation which is not directly accounted for in the model

Dataset for "Analytical modelling of the vibration of railway track"

This dataset supports the PhD thesis of the same name.</span