Railway Curves Research Articles

Influence of coupling vertical and lateral loads on the centre negative flexural behaviour of prestressed monoblock concrete sleepers

At horizontal railway curves, the track is frequently subject to coinciding vertical and lateral wheel loads, which in some cases could be of high intensity. Currently, the influence of such loading pattern on the centre negative flexural response of prestressed monoblock concrete sleepers (PMCS) is not clearly analysed. As a result, the current codes of practice provide limited guidance pertinent to the design of PMCS under this loading condition. To address these issues, finite element models were accomplished and rigorously verified against analytical and experimental studies existing in the literature. The noteworthiness of the numerical findings, based on the considered loading scenarios, is that the presence of lateral load could increase the flexural stress at the top fibre of midspan sections by 223% compared to the influence of vertical load alone. Based on the numerical outputs, an equation has been proposed to quantify the increased flexural stress of PMCS due to lateral load, and further studies are recommended to complement the results expressed in this research.

Estimating railway resilience curves: recovery duration and train traffic response to floods and tree fall

An important aspect of transport infrastructure resilience is recovery, i.e. the process of returning to original service levels after a disruption. In this paper, we estimate recovery trajectories of the German rail network for two specific types of natural hazards: floods and tree fall. Extensive traffic data on track segments of the Deutsche Bahn are matched to geospatial information on disruptive flood and tree-fall events between 2018-2020. We quantify mean resilience curves for flood and tree-fall events by taking average train counts for each day within a (–7, +14)-day window. Results suggest that traffic takes about three days on average to return to normal operations after a tree-fall disruption lasting longer than one day, while it takes five days on average to recover from a flood. Trajectories vary according to route type and are influenced by seasonal weather conditions.

Maintenance Reliability of Railway Curves Using Their Design Parameters

Maintenance Reliability of Railway Curves Using Their Design Parameters

Modelling of the shape of railway transition curves from the point of view of passenger comfort

In the past, railway transition curves were not used. Instead of it, a simple connection of the straight track and circular arc was applied. Nowadays, such simplicity is not allowed due to the increasing vehicle operating velocities. It is mainly visible in the high-speed train lines, where long curves are used. The article aims to develop a new shape of railway transition curves for which passenger travel comfort will be as high as possible. Considerations in this paper concern the polynomials of 9th- and 11th-degrees, which were adopted to the mathematical model of the mentioned shape of curves. The study's authors applied a 2-axle rail vehicle model combined with mathematically understood optimisation methods. The advanced vehicle model can better assign the dynamical properties of railway transition curves to freight and passenger vehicles. The mentioned model was adopted to simulate rail vehicle movement in both cases of the shape of transition curves and the shape of circular arc (for comparison of the results). Passenger comfort, described by European Standard EN 12299, was used as the assessment criterion. The work showed that the method using the 2-axle railway vehicle model combined with mathematically understood optimisation works correctly, and the optimisation of the transition curve shape is possible. The current study showed that the 3rd-degree parabola (the shape of the curve traditionally used in railway engineering) is not always the optimum shape. In many cases (especially for the long curves), the optimum shape of curves is between the standard transition curves and the linear curvature of the 3rd-degree parabola. The new shapes of the railway transition curves obtained when the passenger comfort is taken into account result in new railway transition curves shapes. In the authors' opinion, the results presented in the current work are a novelty in optimisation and the properties assessment of railway transition curves.

Is the cubic parabola really the best railway transition curve?

Abstract In the current study, the authors tested two railway transition curves in terms of their usefulness for railway practice. The first curve was a cubic parabola – the curve most popular in railway engineering. The second curve was a polynomial of ninth degree, and this curve was chosen due to the fact that this curve satisfies advanced geometrical demands. In this study, the model of a two-axle vehicle was applied. The study relied on the passage of the vehicle model through the route consisted of straight track, railway transition, and circular arc. Three different circular arc radii were used. The value – 0.6 m/s2 – of maximum lateral acceleration in the circular arc was applied. Three different vehicle velocities were also used. In this study, the authors simulated vehicle dynamics for different curves and ten lengths of the curves. As the main criterion, lateral acceleration of the vehicle body was applied. The results for these two mentioned curves were compared.

Оптимизация возвышения наружного рельса в железнодорожных кривых на основе стоимости межремонтного цикла

Objective: To determine the optimal elevation of the outer rail in a curved track section based on technical and economic criteria, calculating the life cycle cost using the methods of life cycle re-source management, risks, and reliability analysis (URRAN methodology). Methods: The authors used multivariate analysis, point estimation, the probability theory and mathematical statistics, the theory of reliability of technical systems, the URRAN methodology, field observations of the condi-tion of the curved track sections and the scope of work during their maintenance. Results: A model of the overhaul cycle of a curved track section has been developed. The dependences of the change in the intensity of the accumulation of faults and the cost of track maintenance during the overhaul cycle on the average values of undamped train accelerations when moving along the sur-veyed sections are presented. The optimal values of undamped acceleration are determined for various operating conditions of railway curves, which provide the minimum track maintenance costs. The authors have found that the minimum cost of the overhaul cycle is the factor for choos-ing the optimal undamped acceleration during the overhaul cycle. The optimal elevation of the out-er rail has been calculated and the actual values in the investigated sections have been analyzed. The method’s economic efficiency is calculated in the form of the ratio of the difference between the costs of the overhaul cycle for the actual and optimal elevations of the outer rail. Practical im-portance: Optimization of the elevation of the outer rail will enable minimizing the intensity of the accumulation of faults and, therefore, reduce the cost of maintenance on the track. The total cost of routine track maintenance will be reduced by 5–10 %.

Study on a Heuristic Wheelset Structure without Rail Corrugation on Sharply Curved Tracks

Rail corrugation on low rails of sharp railway curves is still a difficult problem to solve worldwide. Nearly all low rails of the sharp railway curves incur rail corrugation. In the present study, an active method to remedy rail corrugation was studied. From the viewpoint of the frictional self-excited oscillation of a wheelset-track system causing rail corrugation, the effect of wheelset structures on rail corrugation was studied. Three frictional self-excited oscillation models of wheelset-track systems with different wheelset structures were established, which include a heuristic wheelset structure and two being used in the railway industry. The incidence trends of the self-excited oscillations of these three wheelset-track systems were studied. It was found that the wheelset structure has an important effect on rail corrugation, and that the heuristic wheelset structure can restrain or get rid of rail corrugation. With the parameter sensitivity analysis, it was found that when the friction coefficient between the wheel and rail, rail gauge, rail cant, and sleeper span changes to some extent, the heuristic wheelset structure is robust enough to prevent rail corrugation. The proposed heuristic wheelset structure can be used as a potential solution to rail corrugation on sharply curved tracks.

Optimum Railway Transition Curves—Method of the Assessment and Results

This article discusses the optimization of railway transition curves, through the application of polynomials of 9th and 11th degrees. In this work, the authors use a 2-axle rail vehicle model combined with mathematically understood optimization methods. This model is used to simulate rail vehicle movement negotiating both a transition curve and circular arc. Passenger comfort is applied as the criterion to assess which transition is actually is the best one. The 4-axle vehicle was also used to verify the results obtained using the 2-axle vehicle. Our results show that the traditionally used in a railway engineering transition—3rd degree parabola—which is not always the optimum curve. This fact is especially valid for the longest curves, with lengths greater than 150 m. For such cases, the transition curves similar to standard curves of 9th and 11th degrees is the optimum ones. This result is confirmed by the use of the 4-axle vehicle.

Analysis of the properties of new forms of transitional sections of railway and highway curves

The properties of new forms of transitional sections of curves of railways and highways are largely determined by the specific features of the design and functioning of the systems “railway line-rolling stock” and “driver-car-road”. Taking them into account had a significant impact on the formalization of targets and criteria for the quality of the functioning of these systems, as well as on the mathematical means and methods of their achievement. The results obtained in this case significantly differ from the traditional ones. The geometric differences between the transitional sections of railways are in the nonlinear regularities of strictly monotonic, G4 smooth changes in the curvature of their line axis and G3 smooth cross slope, which are described by non-identical functions with variable properties. At the same time, the quality of movement, assessed at the design level of the rolling stock, is ensured by the harmonization of the length of the transition section and the variable properties of its functions with the given characteristics of other properties of the system. The differences between the transitional sections of highways consist in the inclusion of the calculated speed and the speed of its change directly into the principle of the trajectory curvature of vehicles. This ensures the safety and convenience of curvilinear movement of cars on them both at constant and variable speeds. The theoretically substantiated potential for the improvement of the quality of functioning of these systems with the proposed solutions determines the reasonability of their comprehensive testing in practice and further improvement of the theory, norms and rules for the design of transitional sections of curved rail and highways.

A three-dimensional finite element analysis of concrete sleepers and fastening systems subjected to coupling vertical and lateral loads

At horizontal railway curves, the rail is typically a subject to both vertical and lateral wheel loads. The underestimated influence of lateral load at such locations in the design process could compromise the structural integrity of the whole railway track system. Rail-seat deterioration and damage of fastening system components are two possible failure mechanisms associated with high lateral loadings that could lead to safety concerns and costly maintenance activities. It is, therefore, of high importance to analyse the track response including concrete sleepers and fastening systems to coupling vertical and lateral loadings. For such end, a three-dimensional finite element railway model was created and subjected to a variety of lateral to vertical loading ratios. Of other elastic fastening systems, the Skl-style (W14) fastening system, which is currently of high demand, was accounted for as a result of it has been barely researched. The finite element model was rigorously verified with the experimental works and classical theories found in the previous knowledge. The finite element outputs could investigate the complex structural behaviour of railway concrete sleepers and fastening systems and the transmission mechanism of the lateral loading through the track system. The findings indicated that the concrete-rail pad interface is significantly influenced by the high lateral to vertical loading ratio which produces localized contact area of high compressive stress; however, the influence of lateral load on the produced stresses of both tension clamps and angled guide plates is minimal. Further, lateral sliding at concrete-rail pad interface was apparent even at low lateral load, increasing the possibility of wear deterioration of the contacting surfaces. Lastly, the gap between the field angled guide plate and the rail base is a critical parameter that influences the lateral load path and failure mechanisms. The outcomes of this research would lead to better insight into the influences of lateral wheel load more clearly and thus contribute to improvements in the current design practices of concrete sleepers and fastening systems at demanding locations.

Prospects in elongation of railway transition curves

The paper presents an analysis of the elongation of transition curves in relation to railway track alignment correction and modernisation. The analysis is based on numerical computations for a wide range of parameters describing a typical railway geometrical layout with transition curves. The differences between the horizontal ordinates of the existing layout and the layout with the elongated transition curves are evaluated and assessed. The analytical model comprises formulated appropriate theoretical dependencies for each characteristic zone of the layout. The impacts of a circular arc radius and a route intersection angle on the elongation process are considered. Based on the theoretical assumptions, an effective numerical algorithm for comparative analysis of the transition curves’ elongation variants is developed. The value of a new circular arc radius is determined in an optimisation process. For this purpose, the indicators for process evaluation and the constraints determining the feasibility of the design variants are defined.

Railway Transition Curves: A Review of the State-of-the-Art and Future Research

Transition curves are a useful tool for lateral alignment of railway segments. Their design is important to ensure safe and comfortable travel for passengers and cargo. Well designed transition curves can lead to reduced wear of tracks and vehicles, which is beneficial from a maintenance point of view. Extensive studies have been performed through decades to find transition curves that can replace existing railway segments for the purpose of enhancing certain properties. Those studies seek to form curves that satisfy desired evaluation criteria, which are often connected to geometric continuity between the curve segments, and vehicle dynamics, to secure a smooth ride. This research topic is still ongoing and active at present. Recent results and findings are in line with the developments on the topic of vehicle dynamics and within the railway industry. For this reason it is appropriate to collect and discuss the latest work, since there are no up-to-date detailed literature reviews available. This paper explores the present state-of-the-art of railway transition curves, and identifies some of the research challenges and future research opportunities in the field.

GEODESIC CONTROL OF THE PLANNED POSITION OF THE OUTSIDE CURVES

Rail curves are the most vulnerable places on the rail in terms of design parameters violations. Existing approaches to the geodetic maintenance of the planned position of railway curves do not ensure the preservation of their design indicators. The way that can solve this problem is to create special benchmark systems on the sections of the curves. The main points of this system should be the vertices of the track or the points that allow you to determine the position of the vertex angle. More rational to date and far less costly is to set up local benchmark systems that are created for a single curve or group near the curves located. Created benchmark system in the future allows you to virtually exclude geodetic works from the current retention of the rail curve, reducing the control of its planned position to the measurements of distances from the benchmarks. These measures should be included in railway track reconstruction and repair projects. The definition of indentation in the plan can be made with respect to the chord that connects the intermediate points of the curve with the accepted interval of the breakdown. Calculations are made to determine the magnitudes of measurements within the transition and circular curves and the sequence of fixation of the value of displacements at the points of the curve to move these points to the design position.The peculiarities of the use of electronic tacheometers in bringing the railway curves to the design position are highlighted. Taking a curve with an electronic tachometer can be done in detail at all points of the breakdown or in a combined way, when the tachometer determines the coordinates of a limited number of points between which the displacements are determined.

Magnetic-Measuring Square in the Measurement of the Circular Curve of Rail Transport Tracks.

In rail transport, measuring the actual condition of a circular curve of a railway track is a key element of track position monitoring not only during operation but also during final works. Predicting changes in its position in the horizontal plane is one of the most important related scientific issues. This paper presents the results of measurements performed with an innovative measuring device called the Magnetic-Measuring Square (MMS). The aim of the research was to demonstrate the acceptability of using the MMS. Horizontal versines of a rail track curve were measured as three neighboring points on a curve (using the method of lacing/stringlining, also called the three-point or the Hallade method), and the perpendicularity of rail joints and shortenings were measured. The MMS device presented in this article was used to measure versines and differences in rails lengths (rail shortenings in the curve) in the operating mode involving a laser distance meter with a laser beam (laser power P < 1 mW, laser wavelength λ = 635 nm) with a target cross, a camera, and a surveying measuring disk. The measurement results confirmed that it is possible to employ the MMS to monitor the geometry of railway track fragments such as track transition curves and railway track curves in rail transport.

Use of shakedown maps to assess plastic flow in railway curves

Plastic deformation of rails can occur on tight curves, which can significantly reduce the rail life. This paper investigated the phenomena of gross plastic deformation, or plastic flow, using multibody vehicle–track interaction and simplified finite element analysis. The focus is on understanding the contact conditions on the low rail of curves and how these differ from those in shakedown maps. To this end, two trial sites are simulated using multibody vehicle–track software. The contact conditions are then compared against several criteria assumed in the derivation of the shakedown maps. A further assumption implicit in the shakedown maps is also investigated by a non-linear finite element analysis. In this case, a more realistic Chaboche material model is used as opposed to the simple linear elastic–perfectly plastic model in the shakedown theory. The results of the finite element analysis are combined with a bespoke indicator of plastic flow to assess the influence of distance to shakedown limits on the likely plastic flow. Finally, a simple interpolation scheme is used to map the finite element results back to the trial sites. The interpolated results for the sites are used to evaluate the influence of running speed and different levels of wheel profile wear. Results suggest that the bespoke indicator defined in this work can be used as an effective measure of plastic flow; this measure is then used to quantify the influence of cant excess on the rates of plastic flow.

Identification of the railway reconstruction parameters at imposition of high speed traffic on the existing lines

The problems of railroad design technical reconstruction aimed at ensuring train protection in introduction of high-speed traffic on the rail lines have been addressed. The description of railroad technical system with certain specific features has been proposed. The pair of mutually dual problems regarding the optimal reconstruction of railway curves for raising train speeds at minimal capital investments has been addressed. The problem of determining the optimal speeds of trains of each category under optimum outer rail cant, increase of the unbalanced acceleration value, compliance with the condition of uniform load on rail tracks, comfortable carriage of passengers, in which reduced costs on increased speeds in curved tracks will be minimal has been formulated. To achieve the goals of the study, mathematical optimization techniques and algorithms of analysis of the rail lines of different nature are used. This, by finding and value engineering optimization, allows to minimize high-value and lengthy procedures of physical simulation. As a problem-solving technique, Lagrange multiplier method and its applicability have been proposed. Numeral solution to the problem of selection of certain stretches for increasing rolling stock speeds on operating lines without reconstruction or with minimum expenses on reconstruction of contour of track has been reviewed.

Discussion: Prospects in elongation of railway transition curves

Discussion: Prospects in elongation of railway transition curves

RESEARCH OF RAILWAY TRACK PARAMETERS IN THE PLAN BASED ON THE DIFFERENT METHODS OF SURVEY

Purpose. The main purpose of this paper is to analyze the existing methods for surveying curves in a plan, to study the influence of the errors in measuring plan parameters on the permitted speeds of motion, to develop re-commendations for reducing road disturbances by bringing the parameters of curves to the standards that operate in Ukraine in the directions of accelerated and high-speed train traffic. The problem of restructuring the curves was not so acute until there was a need to increase the speed of motion and technical condition monitoring of the track plan. Unreliable determination of the curves parameters leads to unjustified restrictions in the speed of motion or to large volumes of straightening operations. Methodology. The methodology used in the paper provides for a comprehensive and detailed study of different ways of railway curves survey, aimed at developing and obtaining the optimal solutions for the railway track plan. To date, there are different methods of survey the actual geometry of the railway track. To carry out research in various sections of complexity and for a long time of the railway track operation, the most convenient, first of all, considering the regularity of arrivals, there is a tape of the track-measuring car. However, this method is used to assess the state of the railway track, and not to determine the exact geometric position. Thus, when trying to determine the actual outline of the track unevenness using a track-measuring tape, a number of difficulties arise. When forming a mathematical model of the existing plan, the assumption is used: it is considered that three adjacent points on the curve are located along the circumference. The work of track renewal trains is based on this principle. As a result of track renewal operations with the aim of reducing the volume of flattening, the curve does not correspond to the initial passport data. Findings. The results of the work come out of the analysis of different approaches and methods of surveying the plan of the line, the parameters influence of the curves on establishing the permissible speed of motion. The recommendations received in the work will help to increase the efficiency of design decisions and the quality of railway track reconstruction as a whole. Originality. Scientific approaches to assessing the state of curves, studying the influence of their parameters on the permissible speed of trains, have been further developed. The system of criteria for assessing the state of curves that affect the accumulation of track disturbances in the plan is supplemented. Practical value. The results obtained will be useful for carrying out measures to improve speed, improve the smoothness of train traffic and the level of travel comfort on curved track sections, especially in the areas of accelerated and high-speed train traffic.

Combined use of dynamical simulation and optimisation to form railway transition curves

ABSTRACTThis paper describes the original method of searching for a proper shape of railway transition curves (TCs). The relevant literature survey, including some earlier results by present authors, provides a background for this description. In the concept and method, the complete dynamical model of vehicle–track system, capable of simulation, and optimisation methods are exploited. The principles and key details of the method are represented in the paper. They are supplemented with description of the software built to optimise (form) TCs’ shape effectively. Next, results generated with this software and aimed at its testing are presented comprehensively. At the end, selected example of practical optimisation and conclusions are included.

Exploring the relationship between vertical and lateral forces, speed and superelevation in railway curves

The research described in this paper is based on an experiment which involved running a test train through a curve at various speeds, changing the cant of the curve by tamping and repeating the train runs. The cant was changed due to high wheel wear rates. The curve already had a cant deficiency, and this cant deficiency was subsequently increased by reducing the curve's cant. Assessing the before and after tamping test data validated the existence of the expected relationships between the vertical and lateral rail forces, the speed and the cant. The change in cant had a minimal effect on the magnitude of the vertical forces, although a transfer of loading between the high and low legs did occur. The theory indicates that the 14% reduction in cant in this curve, given all of the other curve characteristics, should have resulted in an increase in the lateral forces. There was, however, a roughly 50% reduction in the maximum lateral forces, after the cant had been reduced, which can be explained from a train dynamics point of view. In addition, there was an increase in safety, due to a reduced derailment ratio at this curve's normal operating speed of 85 km/h. It is not unreasonable to presume that a 50% reduction in the maximum lateral forces could lead to a halving of the wear rate of the rail and wheels in this curve, with similar results to be expected in other curves on the rail network.