R. Bogacz

Computer simulation of the interaction between a wheel and a corrugated rail

The paper discusses the problems of modelling and simulation of the wheel/rail contact in the case when geometrical irregularities of the rail are taken into account. The iterative method for determining the geometrical relationship between the profile of a rigid rail and the trajectory of the centre of a rigid wheel is presented. The computer code that implements this method is a part of the computer model of the wheel/rail system. The model allows the case when the wheel loses contact with the rail and afterwards hits the rail. Simulation analysis is focused on the question as to whether the wheel bouncing off and on the rail may occur under normal operation conditions. The other question is how this bouncing influences the pressure forces between the wheel and the rail, and how it influences the stress distribution within the contact zone.

On dynamics and stability of continuous systems subjected to a distributed moving load

SummaryThe paper deals with an analysis of different models of continuous systems subjected to a load distributed over a given length and moving at a constant velocity.The general discussion concerns a beam resting on a viscoelastic semi-space. The motion of the body is described by polynomial differential operators. With body forces being disregarded, the motion of the beam lying on a viscoelastic foundation is discussed with either taking into account the effect of shear deflection and the inertia of rotation or with neglecting them. Consideration is also given to the cases of relative motion of two continuous systems and the stability of their interaction. The above cases represent the models of a number of mechanical systems applied in e.g. modern transportation facilities, technology of bonding of layer materials, etc.The analysis is substantially simplified because the equations of motion and the boundary conditions are written in a moving coordinate system related with the load and only stationary solutions are considered. With such an approach, the solutions depend only on the transformed space variable, while the velocity of the load appears as one of the parameters of the system. Interesting conclusions are drawn from the obtained solutions and numerical calculations.ÜbersichtDer vorliegende Beitrag behandelt die Analyse von kontinuierlichen Systemen, die verteilten bewegten Lasten ausgesetzt sind. Es wird zunächst ein Balken auf viskoelastischem Halbraum behandelt. Die Bewegung des Körpers wird beschrieben durch Differentialoperatoren in Polynomform, wobei der Einfluß von Schubverformung und Drehträgheit diskutiert wird. Der Fall der Relativbewegung von zwei kontinuierlichen Systemen und ihre Stabilität wird ebenfalls diskutiert. Die untersuchten Fälle stellen Modelle zahlreicher mechanischer Systeme dar, wie zum Beispiel moderne Schnelltransportsysteme, Fügevorrichtungen von Schichtmaterialien, usw.Die Analyse der Probleme wird wesentlich dadurch vereinfacht, daß die Bewegungsgleichungen und Randbedingungen in einem mitbewegten Koordinatensystem formuliert werden und nur stationäre Lösungen betrachtet werden. Auf diese Weise hängen die Lösungen nur von der transformierten Ortsvariablen ab; die Geschwindigkeit der Belastung tritt als ein Parameter des Systems auf.Aufschlußreiche Schlußfolgerungen werden anhand der erhaltenen Lösungen und numerischen Berechnungen dargestellt.

Adaptive space-time elements in the dynamic elastic-viscoplastic problem

Abstract An adaptive technique for the solution of the dynamic elastic-viscoplastic problem has been developed. The mesh modification is performed by the use of the space-time element method according to error estimation. The number of joints is preserved and the mesh is refined in regions of high stress gradients. This enables the size of the problem to be reduced and increases the speed of computations. The incremental procedure in the case of a small time step allows the nonlinear path iteration to be associated with the time marching scheme. The remesh and remap problems related to stresses are described. Numerical examples of a plane strain rolling contact problem and collision of the plane strain object prove the efficiency of the approach.

Optimal design of structures subjected to follower forces

SummaryThe optimal design of columns, consisting of segments with arbitrary thickness and length, subjected to follower forces is considered in this paper. The solution is presented for the case of cross modal interaction of a vibrating system. Since the resulting boundary value problem is nonselfadjoint only approximate solutions are generally possible. Herein, for the solution the method of the generalised functional and the transfer matrix technique have been used. As typical examples, the solutions of Becks, Reuts, Leipholzs and Hangers column are investigated.ÜbersichtBehandelt wird die optimale Auslegung von Stäben, die aus Abschnitten beliebiger Querschnittsfläche und Länge bestehen und durch Folgelasten beansprucht sind. Eine Lösung wird angegeben unter Berücksichtigung des Zusammenwirkens der Eigenformen des Systems. Da das zugehörige Randwertproblem nicht selbstadjungiert ist, sind im allgemeinen nur Näherungslösungen angebbar. Hier werden das Verfahren eines generalisierten Funktionais sowie das Übertragungsmatrizenverfahren verwendet. Als typisches Beispiel werden die Lösungen zu den Stäben von Beck, Reut, Leipholz und Hauger betrachtet.

Mechanics of Track Structure with Y-Shaped Steel Sleepers in Sharp Curves

Certain analytical elastic solution for curvilinear track section under uniform thermal loading has been proposed. Track section is composed of circular arc, transition curves and straight lines. Next step is the analysis of two-dimensional model of the track structure (stress plane, without vertical direction). The rails and the sleepers are assumed as elastic bodies. The fasteners and ballast are modeled as elastic-plastic elements. Non-linear properties of these elements are determined by comparison of numerical data with experimental results. Cyclic uniform thermal field is applied as the load of the system. Pre-buckling analysis is the basic part of the considerations. Certain remarks on the track stability, based on the previous author analyses, are also presented. It is shown that track structure with Y-shaped steel sleepers gives the possibility to use of continuous welded rail (CWR) track practically in any radius of curvature.

An application of torsional wave analysis to turbogenerator rotor shaft response

In this paper transient torsional vibrations of a steam turbogenerator rotor shaft system due to high speed reclosing of the electric network are investigated. The analysis is performed using torsional elastic wave theory applied to a continuous model in the form of a stepped shaft. Wave solutions of the equations of motion are used in order to determine dynamic torsional elastic moments and vibratory angular velocities in cross-sections of the turbine shafts. The results are illustrated in the form of graphs.

Condition monitoring of railway track systems by using acceleration signals on wheelset axle-boxes

The aim of this paper is to demonstrate the possibilities of estimating the track condition using axle-boxes and car-bodies motions described by acceleration signals. In the paper, the results presented indicate the condition of tracks obtained from the preliminary investigation on the test track. Furthermore, the results from the supervised runs (on Polish Railway Lines) of Electric Multiple Unit (EMU-ED74) with the prototype of track quality monitoring system installed on-board are described. As Track Quality Indicator (TQI) algorithm, used in the mentioned prototype, a modified Karhunen–Loeve transformation is used in preliminary preparation of acceleration signals. The transformation is used to extract the principal dynamics from measurement data. Obtained results are compared to other methods of evaluating the geometrical track quality, namely methods, which apply the synthetic coefficient Jsynth and five parameters of defectiveness W5. The results from the investigation showed that track condition estimation is possible with acceptable accuracy for in-service use and for defining cost-effective maintenance strategies. First published online 04 September 2017

Influence of Sleepers Shape and Configuration on Track-Train Dynamics

The paper is devoted to the study of dynamical behaviour of railway tracks as continuous systems (rails) supported by periodically spaced sleepers and subjected to moving concentrated loads. Several cases of dynamical problems, where elastically supported beams are excited by a moving concentrated force, are considered. In particular, the study is focused on interactions with structure periodic in the space. Results on one-dimensional structures are extended to the case of a two-dimensional system. The problems of stopping bands, passing bands, and mistuning are also mentioned.

Interface Conditions and Loss of Stability for Stepped Columns

We discuss the dynamic behavior of stepped columns subjected to follower forces. In particular, limit cases which correspond to columns with hinges or cracks and concentrated lateral supports are studied for the stability limit. Typically, solutions suffer jumps in certain derivatives, which have to satisfy compatibility conditions. The influence of these interface conditions on the critical force is investigated. The aim is to optimize the location of such singularities and thus to obtain maximum critical loads, respectively worst case estimates for the loss of stability.

On the shape of characteristic curves for optimal structures under non-conservative loads

SummaryIn numerous cases of optimal design of structures under non-conservative loads, it is essential to choose the most suitable stability constraint conditions. Some authors have investigated the optimal shape of structures (columns) subjected to follower loads assuming that the critical load is given by the horizontal tangent to the first branch of the characteristic curve in the force-frequency plane. However, maximization of such a critical load as well as minimization of the volume does not always lead to an optimal solution.The optimal design of structures consisting of stepped columns with arbitrary thickness and length, interacting with spring-mass systems and subjected to follower loads is considered in this paper. After solving the non-self-adjoint boundary value problem, various shapes of characteristic curves are found showing that other stability constraints should be taken into account to reach an optimal solution. Some numerical results are also presented.ÜbersichtBei der optimalen Auslegung von Strukturen unter nicht-konservativen Kräften ist es in vielen Fällen wesentlich, passende Stabilitätsbedingungen zu formulieren. Mehrere Autoren haben die optimale Form von Strukturen (Stäben) unter Folgelast mit der Annahme untersucht, daß die kritische Last durch die horizontale Tangente an den ersten Ast der charakteristischen Kurve in der Last-Frequenz-Ebene gegeben ist. Sowohl die Maximierung einer so gefundenen kritischen Last als auch die Minimierung des Stabvolumens führen nicht in allen Fällen zur optimalen Lösung.In dieser Arbeit wird die optimale Auslegung von Strukturen betrachtet, die aus Stäben mit Abschnitten beliebiger Dicke und Länge bestehen, mit Feder-Masse-Systemen zusammenwirken und durch Folgelasten beansprucht sind. Nach der Lösung des nicht selbstadjungierten Randwertproblems werden verschiedene Typen von charakteristischen Kurven dargestellt, die zeigen, daß andere als die oben erwähnten Stabilitätsbedingungen zu berücksichtigen sind, um eine optimale Lösung zu finden. Numerische Ergebnisse werden vorgestellt.