Rail Vehicle Dynamics | springerprofessional.de

Springer Professional

Top

2017 | Book

Read chapter Read first chapter

Rail Vehicle Dynamics

Authors: Klaus Knothe, Sebastian Stichel

Publisher: Springer International Publishing

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Login to get access

About this book

This book on the dynamics of rail vehicles is developed from the manuscripts for a class with the same name at TU Berlin. It is directed mainly to master students with pre-knowledge in mathematics and mechanics and engineers that want to learn more. The important phenomena of the running behaviour of rail vehicles are derived and explained. Also recent research results and experience from the operation of rail vehicles are included. One focus is the description of the complex wheel-rail contact phenomena that are essential to understand the concept of running stability and curving. A reader should in the end be able to understand the background of simulation tools that are used by the railway industry and universities today.

Advertisement

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract

The transfer of all forces required for these functions occurs in the contact patch between wheel and rail, which has the approximate size of a circle with a 16.5 mm diameter. Naturally, the loads that occur in this contact are extremely high. The contact between wheel and rail also has great influence on the overall behavior of the railway vehicle on straight track as well as in curves.

Klaus Knothe, Sebastian Stichel

Chapter 2. Modeling of Vehicle, Track, and Excitation

Abstract

In order to be able to examine the dynamics of a vehicle, the vehicle must first be transformed into a mechanical model.

Klaus Knothe, Sebastian Stichel

Chapter 3. Modeling of Wheel/Rail Contact

Abstract

All forces between wheel and rail (Fig. 3.1) act on a contact patch of a size of about 1.5 \(\mathrm{cm}^2\). The weight of the vehicle is translated through normal forces; the guidance through large-radius curves is provided by tangential forces; and during acceleration and braking, additional tangential forces in the circumferential direction of the wheel arise.

Klaus Knothe, Sebastian Stichel

Chapter 4. Vertical Dynamics, Equations of Motion, and Free Vibrations

Abstract

In the present chapter, the differential equations for the motion of a rail vehicle with two axles will be examined in detail, first for longitudinal and lateral motion with the principle of linear and angular momentum. The reader who is familiar with these concepts can skip Sect. 4.2. Then the possibility to formulate the equations of motion by means of virtual displacements is discussed (Sects. 4.3 and 4.4). In this manner, it is also possible to derive the equations of motion for a vehicle with elastic carbody (Sect. 4.5). Finally, in Sect. 4.6, the solution of a two-axle vehicle (free vibration case) is discussed.

Klaus Knothe, Sebastian Stichel

Chapter 5. Forced Vertical Vibrations for Excitation with Harmonic and Periodic Track Irregularities (Frequency Domain Solution)

Abstract

On the basis of the equations of motion for the two-axle vehicle with its five degrees of freedom, Eq. (4.28), it can be shown that for the carbody, the degree of freedom of the vertical motion is not coupled with the other four degrees of freedom (pitching and longitudinal vibration of the carbody and wheelsets). The main features for the calculation of forced vibration can therefore be illustrated on a system of one degree of freedom that, excited by track irregularities, performs vertical motions; Fig. 5.1.

Klaus Knothe, Sebastian Stichel

Chapter 6. Random Vibrations due to Stochastic Track Irregularities

Abstract

To characterize stochastic track irregularities and the resulting random vibrations, different methods have to be used from those used for harmonic or general periodic vibrations.

Klaus Knothe, Sebastian Stichel

Chapter 7. Human Perception of Vibrations - Ride Comfort

Abstract

To assess the ride comfort of a road or rail vehicle, first the vibration response has to be measured or calculated. The assumption is that the comfort felt is determined by acceleration. It is not only the acceleration amplitudes that are important, however, but also the frequencies, since a human being can be regarded as a vibration system with resonances at certain frequencies; cf. Fig. 7.1.

Klaus Knothe, Sebastian Stichel

Chapter 8. Introduction to Lateral Dynamics of Railway Vehicles

Abstract

The vibration behavior of rail vehicles in the lateral direction is to a great extent determined by the behavior of the wheelset and thus by the processes in the contact between wheel and rail.

Klaus Knothe, Sebastian Stichel

Chapter 9. Derivation of Equations of Motion for Lateral Dynamics

Abstract

In deriving the equations of motion for vertical dynamics, we have seen that either the principle of impulse and momentum (Sect. 4.2) or the principle of virtual displacements, or in other words, the principle of d’Alembert in the version of Lagrange (Sect. 4.2) can be used. For general problems with constraints and preloads, it is often more convenient to use the principle of virtual displacements, even though the choice is also a matter of personal preference.

Klaus Knothe, Sebastian Stichel

Chapter 10. Lateral Eigenbehavior and Stability of a Wheelset on Straight Track

Abstract

With Eqs. (9.12) and (9.13), we have a general system of equations of motion of the form

$$\begin{aligned} {\varvec{M}}\ddot{\varvec{u}}+{\varvec{D}}\dot{\varvec{u}}+{\varvec{S}}{\varvec{u}}=\mathbf{0}. \end{aligned}$$

.

Klaus Knothe, Sebastian Stichel

Chapter 11. Lateral Eigenbehaviour and Stability of Bogies

Abstract

Up to now, we have looked at the natural vibration behavior of one wheelset. In this chapter, bogies will be investigated. It can be expected that it will be even more difficult to find general conclusions in this case. In Sect. 11.1, we will perform a numerical investigation and plot the eigenvalues derived as a function of vehicle speed v in root loci curves in the complex plane.

Klaus Knothe, Sebastian Stichel

Chapter 12. Lateral Eigenbehavior and Stability of Bogie Vehicles

Abstract

The investigation of the eigenbehavior and the stability of bogie vehicles, taking into account all degrees of freedom, is performed with the same numerical procedures as for a wheelset or a bogie. For presentation of the results, root loci curves and stability cards are used, which are derived from the root loci curves. In the following, first a characteristic result for a real vehicle is given. Thereafter, more general conclusions based on the literature are discussed.

Klaus Knothe, Sebastian Stichel

Chapter 13. Introduction to Non-linear Stability Investigations

Abstract

The stability investigations for the wheelset in Chap. 10, the bogie in Chap. 11, and for a bogie vehicle in Chap. 12 assume that the system can be described by linear equations.

Klaus Knothe, Sebastian Stichel

Chapter 14. Quasistatic Curving Behavior

Abstract

Interest in curving behavior of rail vehicles began earlier than interest in stability. In Germany, Redtenbacher is probably the first to have dealt intensely with curving behavior (Redtenbacher, Die Gesetze des Locomotiv–Baues, (The Laws of Design of Locomotives), 1855, [1]). In the monograph by Boedecker (Die Wirkungen zwischen Rad und Schiene und ihre Einflüsse auf den Lauf und den Bewegungswiderstand der Fahrzeuge in den Eisenbahnzügen (The effects between wheel and rail and their influences on the running behavior and the resistance of vehicles in railway trains), 1887, [2]), curving behavior is also the focus. Although the question of running on a straight line (and so the question of stability) is mentioned as a problem, the issue is, however, regarded as secondary in Boedecker’s work.

Klaus Knothe, Sebastian Stichel

Chapter 15. Determination of Load Collectives for Vehicle Components

Abstract

For most components of rail vehicles, including bogie frames and wheelsets, dynamic loads are dimensioning loads. The dynamic loads are superimposed on static loads from the weight. This is especially true for high-speed vehicles. For trams, metros, and freight wagons, the maximum static load can be decisive for dimensioning components. For optimal dimensioning of a component, it is therefore important to know the dynamic loads exerted on a vehicle throughout its lifetime as exactly as possible.

Klaus Knothe, Sebastian Stichel

Chapter 16. Appendix

Abstract

During the development of multibody system tools, the introduction of different coordinate systems is necessary, especially if large displacements and rotations are taken into account.

Klaus Knothe, Sebastian Stichel

Backmatter

Title: Rail Vehicle Dynamics
Authors: Klaus Knothe
Sebastian Stichel
Copyright Year: 2017
Publisher: Springer International Publishing
Electronic ISBN: 978-3-319-45376-7
Print ISBN: 978-3-319-45374-3
DOI: https://doi.org/10.1007/978-3-319-45376-7

Premium Partners