Railway Transition Curves Research Articles

Optimum railway transition curves for different circular arc radii

Optimum railway transition curves for different circular arc radii

Railway transition curves – optimization and assessment

Railway transition curves – optimization and assessment

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.

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.

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.

Discussion: Prospects in elongation of railway transition curves

Discussion: Prospects in elongation of railway transition curves

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.

Optimisation of polynomial railway transition curves of even degrees

This paper represents new results obtained by its authors while searching for the proper shape of polynomial railway transition curves (TCs). The search for the proper shape means the evaluation of the curve properties based on chosen dynamical quantities and generation of such shape with use of mathematically understood optimisation methods. The studies presented now and in the past always had got a character of the numerical tests. For needs of this work advanced vehicle model, dynamical track-vehicle and vehicle-passenger interactions, and optimisation methods were exploited. In this software complete rail vehicle model of 2-axle freight car, the track discrete model, and non-linear description od wheel-rail contact are used. That part of the software, being vehicle simulation software, is combined with library optimisation procedures into the final computer programme. The main difference between this and previous papers by the authors are the degrees of examinated polynomials. Previously they tested polynomial curves of odd degrees, now they focus on TCs of 6th, 8th and 10th degrees with and without curvature and superelevation ramp tangence in the TC’s terminal points. Possibility to take account of fundamental demands (corresponding values of curvature in terminal points) concerning TC should be preserved. Results of optimisation are compared both among themselves and with 3rd degree parabola. The aim of present article is to find the polynomial TCs’ optimum shapes which are determined by the possible polynomial configurations. Only one dynamical quantities being the results of simulation of railway vehicle advanced model is exploited in the determination of quality function (QF1). This is: minimum of integral of vehicle body lateral acceleration.

A Numerical Study of Cubic Parabolas on Railway Transition Curves

This paper mainly focuses on the design of transition curves of the cubic parabola type in track alignment design. Equations for the transition curves are first derived from the theory of cubic parabolas using calculus techniques. They are then analyzed using numerical analysis methods. The proposed formulation is evaluated by comparison of its calculated results with data in 684 actual cases of transition curves. The accuracy of the proposed method is verified in this study by comparing the estimated results with collected data from actual engineering projects, and the applicability of the new method to the engineering practice of track alignment design is justified. The chainage and coordinates of the control points as well as other curve points and the tangential angle can be easily calculated using the transition curve equations.

Optimisation of the Railway Transition Curves' Shape with Use of Vehicle-track Dynamical Model

Optimisation of the Railway Transition Curves' Shape with Use of Vehicle-track Dynamical Model

Comparison of railway track transition curves

There are no design parameters related to speeds exceeding 160 km/h in the effective Hungarian railway design rules. In the relevant international standard (ENV 13803) a similar speed limit is 300 km/h. This paper deals with the comparative of these regulations. Parameters of two transition curves used in Hungary and other used in Austria are determined. The importance of the new design parameters provided by ENV 13803 is assessed. It is demonstrated that the usability of the clothoide transition curves is unnecessarily restricted for the speeds v ≤120 km/h in the Hungarian regulations.

Dynamic analysis of railway transition curves

Transition curves play an important role in riding quality, especially for high-speed railways. Accordingly, various curves have been proposed as transition forms. To evaluate the effects of the forms in transition curves, the basic requirements and forms of transition curves were first discussed, and then simulations were performed with several typical transition curves at various speeds, based on the dynamic model developed in this research. The results indicate that the dynamic effects of transition curves are determined by the curvature variation and the order of the curvature derivative that is equal to zero at the curve endpoints, while the expression mode (such as algebraic or trigonometric expression) does not make much difference. From a dynamic viewpoint, the ideal transition form requires that the second derivative of its curvature is equal to zero at the curve endpoints at least, such as the seventh parabola, ninth parabola, and sinusoid, with which the vibration accelerations of the vehicle vary smoothly and the jerk can be effectively eased. Then the appropriate transition forms are recommended for ordinary and high-speed railways, respectively.

New Form of Road/Railway Transition Curve

Road and railway transition curves have again become the subject of important scientific research and serious traffic engineering analyses because of high driving speeds and demands for automatic drive (i.e., car pilots). This article shows, in an original way, how to define or reconstruct the track of a vehicle when passing the elements of a continuous curve (straight lines, circles) so the track (curve) suits all requirements to which transition curves must be adapted. The praxis whereby a known mathematical curve (e.g., a cubic parabola, lemniscate, or chlotoid) was assumed as a transition curve and its suitability was analyzed has been passed over. On the basis of assumed kinematics models of the motion of a vehicle along joint alignment elements with a changing radius of curvature, the writers have analyzed different transition curves resulting in safe, comfortable, and economic driving. The curve resulting from a parabolic velocity chart of front wheel rotation during such movement which found the most suitable has been named POLUSA; a geometrical analysis of POLUSA has been performed and a manual for practical use completed.