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Selected Problems in Railway Vehicle Dynamics Related to Running Safety

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Selected Problems in Railway Vehicle Dynamics Related to Running Safety THE ARCHIVES OF TRANSPORT ISSN (print): 0866-9546 Volume 31, Issue 3, 2014 e-ISSN (online): 2300-8830 DOI: 10.5604/08669546.1146984 SELECTED PROBLEMS IN RAILWAY VEHICLE DYNAMICS RELATED TO RUNNING SAFETY Ewa Kardas-Cinal Warsaw University of Technology, Faculty of Transport, Warsaw, Poland e-mail: [email protected] Abstract: The paper includes a short review of selected problems in railway vehicle-track system dynamics which are related to the running safety. Different criteria used in assessment of the running safety are presented according to the standards which are in force in Europe and other countries. Investigations of relevant dynamic phenomena, including the mechanism of railway vehicle derailment, and the resulting modifications of the running safety criteria are also discussed. Key words: railway vehicle, dynamics, running safety, derailment 1. Introduction and a great development in the field of modeling of Among the first problems that have emerged in the the railway vehicle-track systems and simulations early development of the railways was guidance of of their motion, remain valid and are still used in the railway vehicle along the track and the the analysis of the dynamics of such systems. associated excessive wear of wheel flanges. Solution to both problems was achieved in the 2. Investigations of railway vehicle dynamics second and third decades of the nineteenth century The first realistic model of railway vehicle by the introduction of a conical wheel tread and a dynamics was proposed by Frederick W. Carter – a clearance between wheel flange and the rail head. British engineer who graduated in mathematics at This was primarily the result of empirical the University of Cambridge. In his model, he observations, supported by the intuition of the first established that the forces acting between the constructors of railway vehicles, starting from wheels and the rails are proportional to the slip at George Stephenson who built the steam locomotive the point of wheel-rail contact, which helped to for the first public inter-city railway, the Liverpool explain the mechanism of the wheelset hunting and Manchester Railway [11]. Already then, the within the theoretical description of the lateral designers were aware that the introduction of motion of the vehicle. Further understanding the wheels with conical profiles leads to the dynamics of railway vehicles, especially the appearance of lateral vehicle vibrations (hunting) stability of their motion, was significantly during the vehicle motion which are now known as contributed to by the studies of Tadashi Matsuidara kinematic oscillations. working at Railway Technical Research Institute of Before it was possible to solve numerically the Japanese National Railways (JNR). The aim of equations of motion of mechanical systems with these studies was to increase the vehicle speed and many degrees of freedom with the aid of their results, indicating an important role of the computers, investigations of the dynamics of vehicle suspension in ensuring the running safety, railway vehicles were mainly done in a theoretical have been applied in the technical solutions used in way and were focused on analytical relations the high-speed Shinkansen trains. Similar associated with the running safety and the stability conclusions have been obtained a result of the of the vehicle motion [52]. At this point one should investigations (largely independent of the Japanese mention the work by W. Klingel [30] on the studies) conducted by the group of A.H. Wickens at wheelset hunting and the investigations of J. Nadal the research center of the British Railways in Derby [35] aimed to determine the dynamic conditions in since the early sixties of the last century. Another which there is a danger of derailment due to the important, and, in fact, truly landmark step in the wheel climb on the rail. The results of these field of railway vehicle dynamics was the theory of studies, despite the passage of over a hundred years rolling contact developed by J.J. Kalker [25] which 37 Ewa Kardas-Cinal Selected problems in railway vehicle dynamics related to running safety has provided an effective way to determine characteristic equation with positive real parts. In tangential forces in the wheel-rail contact with high the case of nonlinear models, studies based on the accuracy. A simplified form of this theory, known bifurcation theory have shown that, the Hopf as the FASTSIM algorithm [24], is currently the bifurcation occurs in a railway vehicle-track most widely used method for determining contact system, which leads to the hunting of the wheelsets. forces in the simulation models of railway vehicle- At the same time, as it is underlined the author of track systems. the monograph [59], both sub-critical bifurcation, An important problem in the dynamics of railway with a stable limit cycle (attractor) in a certain vehicles is wheelset hunting which can strongly speed range, and supercritical bifurcation, with no affect the running safety. Hunting is an undulating stable periodic solution for any velocity, may occur motion along the track, during which oscillatory in nonlinear models. Investigations of the wheelset changes of the lateral wheelset displacement from hunting phenomenon and the stability of the the track centre line are coupled with its yaw railway vehicle motion using the bifurcation theory rotation which an oscillatory rotation of the have been the subject of many works, among others wheelset around the axis perpendicular to the track [39,49,53,58,60]. plane. In the simplest terms wheelset hunting is The rapid development of the information purely kinematic phenomenon associated with the technology and the increase in computing power of conicity of the wheels, whereas the wavelength of modern computers enables simulations of the the hunting determined with the Klingel formula is dynamics of multibody systems (MBS) using independent of the railway vehicle velocity [30,41]. increasingly accurate simulation models which The phenomenon of the wheelset swaying motion describe them. The results of simulations of railway while hunting along the track is very accurately vehicle motion can be used to understand the basic described by W. Gąsowski and R. Lang [20]. To phenomena which determine their dynamics quote these authors, "swaying of a wheelset occurs [10,13,18,23]. Simulation studies are also a widely when it moves without slip along the track used approach for evaluating the dynamic direction, and some random factor, for example, properties of railway vehicles related to the running local track irregularity knocks it out of the center safety and the ride comfort [3,6,43]. Simulations position on the track, or deviates its axis from the are used at the stage of designing railway vehicles, direction perpendicular to the track" ([20]-(7)). As in diagnosing problems occurring during vehicle the authors point out in the summary of the work operation, as well as in investigating the causes of [20] the analysis of the hunting phenomenon railway accidents and their reconstruction. extends the ability to understand manyphenomena Simulations are used even to predict the dynamics associated with the dynamics of railway vehicles. of the vehicle after its derailment [2]. The use of An example of this approach is the works of the simulations has many advantages compared to the present author [26-28], which have analysed the experimental studies of the real systems: in impact of geometrical irregularities of the track on addition to being much cheaper (by avoiding the the wheelset hunting and the derailment coefficient cost of access to railway infrastructure), they which determines the running safety. provide possibility to perform tests in a much wider In general, the wheelset hunting is related to the range of running conditions (even extreme ones stability of the railway vehicle motion and which lead to the vehicle derailment) and allow one corresponds to oscillations with a fixed amplitude to determine quantities whose direct measurement which occur at high vehicle velocities (above the is difficult or impossible (like creepages and forces critical speed). From a mathematical point of view, present in the wheel-rail contact). Simulation hunting is a kind of self-excited vibrations that after models are also used for diagnosis and monitoring a long time become periodic vibrations called limit the state of the railway vehicle-track system [7,8]. cycles. In linear models of railway vehiclestrack In the studies of railway vehicle dynamics with the systems such vibrations are represented by aid of simulations, though in many cases original asymptotically unstable solutions of the equations programmes are still used to target specific of motion, which, according to the Routh-Hurwitz problems, commercial software is increasingly criterion, correspond to the roots of the more frequently applied, since it allows not only to 38 AoT Vol. 31/Issue 3 2014 carry out the simulations, but it also provides a operation for various types of railway vehicles, convenient way to create a mathematical model including locomotives, passenger cars, freight using the graphical user interface and to wagons as well as special and auxiliary vehicles. automatically generate equations of motions. The The UIC 518 and EN 14363 standards include first such program was MEDYNA developed by permissible length of the track section, on which W. Kik [29]. A list of other currently available the condition specified in the criterion Nadal can be commercial packages includes ADAMS/Rail, violated without the risk of derailment. It should be NUCARS, SIMPACK Rail, VAMPIRE. Still, in noted, however, that despite the modifications many cases, due to the specific aspects of the taking into account, to a significant extent, the examined problems and the possibility of full dynamic aspect of the derailment phenomenon, the control over the applied simulation model and Nadal criterion is based mainly on quasi-static introduced modifications, original programmes are conditions of the vehicle motion that lead to the developed by the research groups working in the risk of derailment by the wheel flange climb on the field of the railway vehicle dynamics.
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