Study on numerical simulation methods of the railway vehicle-track dynamic interaction

A very efficient numerical simulation method of the railway vehicle–track dynamic interaction is described. When a vehicle runs at high speed on the railway track, contact forces between a wheel and a rail vary dynamically due to the profile irregularities existing on the surface of the rail. A large variation of contact forces causes undesired deteriorations of a track and its substructures. Therefore these dynamic contact forces are of main concern of the railway engineers. However it is very difficult to measure such dynamic contact forces directly. So it is important to develop an appropriate numerical simulation model and identify structural factors having a large influence on the variation of contact forces. When a contact force is expressed by the linearized Hertzian contact spring model, the equation of motions of the system is expressed as a second–order linear time–variant differential equation which has a time–dependent stiffness coefficient. Applying a well–known Newmark direct integration method, a numerical simulation is reduced to solving iteratively a time–variant, large–scale sparse, symmetric positive–definite linear system. In this study, by defining a special vector named a contact point one, it is shown that this time–variant stiffness coefficient can be expressed simply as a product of the contact point vector and its transpose and so the Sherman–Morrison–Woodbury formula applied for updating the inverse of the coefficient matrix. As a result, the execution of numerical simulation can be carried out very efficiently. A comparison of the computational time is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rail-bridge coupling element of unequal lengths for analysing train-track-bridge interaction systems

This paper presents a rail-bridge coupling element of unequal lengths, in which the length of a bridge element is longer than that of a rail element, to investigate the dynamic problem of train-track-bridge interaction systems. The equation of motion in matrix form is given for a train-track-bridge interaction system with the proposed element. The first two numerical examples with two types of bridge models are chosen to illustrate the application of the proposed element. The results show that, for the same length of rail element, (1) the dynamic responses of train, track and bridge obtained by the proposed element are almost identical to those obtained by the rail-bridge coupling element of equal length, and (2) compared with the rail-bridge coupling element of equal length, the proposed element can help to save computer time. Furthermore, the influence of the length of rail element on the dynamic responses of rail is significant. However, the influence of the length of rail element on the dynamic responses of bridge is insignificant. Therefore, the proposed element with a shorter rail element and a longer bridge element may be adopted to study the dynamic responses of a train-track-bridge interaction system. The last numerical example is to investigate the effects of two types of track models on the dynamic responses of vehicle, rail and bridge. The results show that: (1) there are differences of the dynamic responses of vehicle, rail and bridge based on the single-layer and double-layer track models, (2) the maximum differences increase with the increase of the mass of sleeper, (3) the double-layer track model is more accurate.     

Track–Monitoring of Wheel–Rail–Systems

Inspection and maintenance of railway networks is a complex and expensive task. Special measurement vehicles are used to record the geometrical properties of railway lines within required time intervals. Due to the extent of measurement data the quality of railway track is evaluated considering only a few parameters. Although safety and comfort of wheel–rail–systems depend on the dynamical behavior, current inspection vehicles are not equipped to measure dynamic properties. In this paper, we will discuss a novel approach to evaluate the quality of railway tracks based on wheel–rail dynamics: Wheelset dynamics of subway trains are analyzed by Karhunen–Loève Transformation to extract the principal dynamics from the collected measurement data. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comportamiento dinámico de viaductos cortos considerando la interacción vehículo-vía-estructura-suelo

The dynamic vehicle-track-bridge-soil interaction is studied on high speed lines. The analysis is carried out using a general and fully three dimensional multi-body-finite element-boundary element model, formulated in the time domain to predict vibrations due to the train passage over the bridge. The vehicle is modelled as a multi-body system, the track and the bridge are modelled using finite elements and the soil is considered as a homogeneous half-space by the boundary element method. Usually, moving force model and moving mass model are employed to study the dynamic response of bridges. In this work, the multi-body system allows one to consider the quasi-static and dynamic excitation mechanisms. Soil-structure interaction is taken into account on the dynamic structure behaviour on simply-supported short span bridges. The influence of soil-structure interaction is analysed in both resonant and non-resonant regimes.     

Dynamic properties of an individual wheelset drive of a railway vehicle

Spatial vibrations of an individual wheelset drive supported by rubber silent blocks in a two–axle bogie's frame of a railway vehicle are studied. The method, used for a creation of a mathematical model, is based on a decomposition of the wheelset drive into subsystems — a drive assembled from an engine and a gear transmission, a flexible composite hollow shaft and a flexible wheelset. Subsystems are modeled in local configuration spaces and they are mutually connected by deformable couplings. An adhesive characteristic in a wheel–rail contact is described using the Kalker's theory. The nonlinear mathematical model respects spatial vibrations of the drive's components and the flexible wheelset, a deformable rail ballast and it is used for investigating transient dynamic responses on different types of excitations. Experimentally investigated spatial bogie's frame displacements or displacements derived from a total model of the bogie caused by spatial irregularities of the rail track are main sources of excitations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A dynamic programming method for matching rail-track monitoring data

A commonly used method of monitoring the condition of rail track is to run an inspection vehicle over the track at intervals of about 3 months. Measurements of several geometric properties of the track are automatically recorded about every 900 mm, resulting in long sequences of data (signals) arising from runs of up to 100 km. Condition monitoring is done by comparing the results of a current run with those of a previously recorded reference run. Before this can be done, the two signals need to be aligned so that corresponding distance measurements in each signal actually refer to the same point on the track. A procedure for matching the two signals is presented, which has at its heart a dynamic programming method. The procedure is demonstrated on data from rail tracks in Australia.     

二系悬挂条件下的车-路垂向耦合系统的动力模型

在车辆的走行过程中,上部与下部是相互作用和影响的．因此,轨道交通问题实际上就是线路下部结构和车辆系统的体系匹配问题．在一系悬挂条件下的车-路系统耦合动力分析模型基础上,考虑了包含转向架在内的车辆的实际构成和轨下基础包括路基和地基的参振特性,利用轨道维护标准模拟行走不平顺激励,通过位移相容条件,从理论上研究车辆-轨道-路基体系的动力相互作用,建立了二系悬挂条件下的车辆-轨道-路基系统的垂向动力分析模型．为高速铁路路基的动力特性分析和设计提供参考．     

A stochastic dynamic model of train-track-bridge coupled system based on probability density evolution method

An innovative stochastic dynamic model of a 3D train-track-bridge coupled system (TTBS) with refined wheel/rail interaction is established for a high-speed railway based on the random theory of probability density evolution method (PDEM). The multi-coupling effect of excitations can be simultaneously input into the new model, e.g. random track irregularity, random vehicle loads, stochastic system parameters, et al. Moreover, a new approach, named “Number theoretic method of multi-target probability functions” (NTM-mp), is developed to obtain the discrete point sets of multidimensional random parameters in hypercube space, aims to solve the point design of system uncertainty. The stochastic harmonic function (SHF) is applied to generate representative random track irregularity samples. The results of TTBS got by PDEM are verified with several typical case studies for its efficiency and reliability, which are the deterministic results in the representative publication, the Monte Carlo method (MCM) results, and the field testing results on the high-speed railway. At last, a typical case study of TTBS on a high-speed railway is presented for numerical analysis. Discussions and significant conclusions on the random dynamic responses are presented.     

Dynamic stability of a curved rail under a moving load

The stability of a curved rail under a constant moving load has been investigated using a linear theory; critical speeds of the moving load, and the dynamic rail deflections and rotation were calculated. The effect of the foundation was included through distributed linear springs. It was assumed that the moving load remains in constant contact with the rail and travels along a fixed path on the rail head.     

轨道结构随机场模型与车辆-轨道耦合随机动力分析

将轨道结构视为一个参数随机系统,提出并建立了轨道结构的随机场模型.利用车辆-轨道耦合动力学的基本方法,将轨道系统有限单元模型与多刚体车辆模型相结合,建立了考虑铁路线路参数空-时随机变化的车辆-轨道动力计算模型.算例表明:所提出的方法较为可靠且高效;线路参数随机性对车辆-轨道系统的动力响应有明显的影响,随线路参数离散程度的增加,可能造成行车不安全、轨道损伤加剧等一些问题.     

Ultrasonic wave propagation in a polymerizing medium

It is shown that by monitoring the propagation velocities of longitudinal and shear ultrasonic waves in a polymerizing system it is possible to keep a continuous track on the conversion of the monomer, estimate the effect of various technological factors — sensitizing additives, dose rate, absorbed dose — and trace the behavior of the dynamic moduli of elasticity and the dynamic Poisson's ratio of the polymeric material. Relations between the wavelength and the transverse dimension of the polystyrene specimens that satisfy the conditions for determining the speed of ultrasound in an infinite medium and in a rod are obtained.     

Dynamic fractal unifying interaction confirmed with magnetospheric behavior and orbital data

The solar wind makes the magnetosphere to expand and contract as indicated by the expansions and contractions of the auroral oval due to balancing of the dynamic pressure of the ambient space plasma at inner and outer magnetic lines. This self‐similar magnetospheric behavior elucidates the controversial magnetic storm‐substorm relationship and reveals the 3D‐spiral structure of magnetic interaction. The found self‐similarly evolving structure of one seen as fundamental interaction suggests dynamic fractal unifying interaction that builds a firework universe having 3D‐spiral code. The unifying interaction is described with equation drawn in new fundamental dynamic fractal framework. The equation of unifying interaction converges to the inverse square laws and the principle of uncertainty at laboratory scales. The dynamic fractal fundamental framework is made of one 3D‐spirally‐faster‐inward contracting and expanding, oscillating, basic matter. It simply accounts for observed constant speed of light and for the creation of bright and dark bands on a screen behind a tiny slit. The dynamic fractal framework is quantitatively confirmed with the orbital data for the Milky Way Galaxy, the Sun, the Earth, and the triple asteroid system 87 Sylvia. Many testable predictions are also made. The presented new fundamental dynamic fractal framework allows qualitative and quantitative modeling and simplification. © 2007 Wiley Periodicals, Inc. Complexity 12: 61–76, 2007     

Influence of yaw stiffness on the nonlinear dynamics of railway wheelset

A numerical simulation of the dynamic behavior of a railway wheelset is presented. The contact forces between the wheel and the rail are estimated using Johnson and Vermeulen theory of creepages. Nonlinear governing equations of motion of wheelset on a straight track are solved using fourth-order Runge–Kutta method. Both symmetric and asymmetric oscillations and chaotic motion are observed. The influence of yaw stiffness and axial velocity on the response of wheelset is studied. Broadband chaotic motion is developed at various velocity levels. The results are presented in the form of time evolution, phase plots, Poincare maps and bifurcation diagrams. The Lyapunov exponent is calculated and its variation with time is presented. Intermittency is observed. There is a shift in the bifurcation diagram by increasing the yaw stiffness. It indicates that chaotic behavior could be delayed with increasing yaw stiffness.     

Modeling and control of a novel pressure regulation mechanism for common rail fuel injection systems

This paper presents the modeling and control of a novel pressure regulation mechanism for the common rail (CR) fuel injection system of internal combustion engines (ICE). The pressure pulsations inside the common rail caused by the incoming and outgoing flows negatively affect the accuracy of both injected fuel quantities and flow rates. The objective of this work is to design a new regulating mechanism to suppress the pressure pulsation in the rail. We first present the one-dimensional distributed model for the common rail developed by using fluid flow equations, which can capture the distributed dynamics of the pressure pulsations in the rail and validating it with a physics based model developed in AMESim®. We then propose the concept of an active fluid storage device like a piezoelectric actuator (PZT) to minimize the pressure fluctuations. The location of the actuator on the common rail has also been evaluated to maximize its effect. The periodic nature of the injection event due to the stroke by stroke engine operation generates pressure pulsations in the rail which are periodic when represented in the rotational angle domain. To leverage this unique dynamic phenomenon we design a time-varying internal model-based controller to compensate the pressure pulsations.     

Improving real-time train dispatching performance: optimization models and algorithms for re-timing, re-ordering and local re-routing

This is a summary of the author’s PhD thesis supervised by Ingo A. Hansen and defended on 7 April 2008 at the Delft University of Technology. The thesis is written in English and is available from http://www.darenet.nl. This work deals with the development of an innovative decision support system for railway traffic control in order to cope with real-time timetable disturbances (i.e., multiple train delays and blocked tracks) more effectively. This dynamic traffic control system co-ordinates the speed of successive trains on open track (re-timing), solves expected route conflicts (re-ordering) and provides dynamic use of platform tracks in a station or alternative paths in a corridor between stations (local re-routing). We adopt blocking time theory for a microscopic modeling track occupation and signaling constraints and alternative graphs for optimal solving dynamic traffic control problems with the aim of increasing the punctuality by a more intelligent use of infrastructure capacity at a network scale.     

Object-oriented modelling and simulation of a motorcycle

The design of a control oriented motorcycle model for the simulation of two-wheeled vehicles is widely recognized to be a very challenging task, as a complete analytical model is not directly available, due to its complexity and its high sensitivity to parameters' variations. Accordingly, a reliable model should be based on multibody modelling tools endowed with automated symbolic manipulation capabilities. This paper presents a simulation model for the dynamic behaviour of a motorcycle based on the object-oriented modelling paradigm developed in Modelica, within the Dymola environment. Specifically, we illustrate the modular approach to motorcycle modelling and discuss the tire-road interaction model, which is the crucial part of the proposed model. The validity of the proposed simulation model is assessed on real data, measured on an instrumented test vehicle. Further, to perform the verification phase a virtual driver model has been implemented, which allows to track both a roll angle and a target speed profile during different maneuvers. In particular, the behaviour of the driver is modelled as an inverse pendulum, with a rotational degree of freedom along the forward axis. This allows accounting for the driver lean angle, which is necessary to fully capture the real driving behaviour and its effects on the overall vehicle dynamics.     

Longitudinal track-bridge interaction due to loading sequences

For continuously welded rails the longitudinal track–bridge interaction plays an important role. The coupling between track and bridge consists of a ballasted interface or a slab track with rail–pads. European codes describe this coupling by means of a bilinear force–displacement relation with making a difference wether the track is loaded or not. This contribution is focussed on an incremental treatment of the long–term loading from seasonal temperature–change followed by several cycles unloaded–loaded–unloaded due to passing trains. As one cycle happens in a rather short time, the mass accelerations are involved, too. The load–character of the coupling–variation will be explained and a comparison between a statical and a dynamical treatment will be presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Friction and rheological properties of resin-impregnated glass tape

The dependence of the dynamic coefficient of friction of resin-impregnated glass tape on the sliding speed over the mandrel surface and the viscosity of the resin is derived. The formulas obtained are confirmed by the results of experiments which indicate a linear dependence of the coefficient of friction on the sliding speed of the tape over a metal mandrel. Graphically, this dependence is expressed by straight lines with a common origin and a slope that increases with the viscosity of the resin. The coefficient of friction of glass tape sliding over a prewound layer at low speeds also has a linear dependence. At high speeds the dependence takes the form of a damped curve.Translated from Mekhanika Polimoerov, No. 1, pp. 166–170, January–February, 1976.     

Dynamics of an Overhead Line and Pantograph System

The dynamic interaction between pantograph and catenary is studied. The overhead electrification system for high speed trains is modelled by visco‐elastically connected double homogeneous strings system, one finite suspended on rigid concentrated supports and the second of infinite length. The pantograph is represented by one degree of freedom oscillator moving along the string at a constant speed. The model is new in that it gives possibility to consider the influence of the locomotive transverse vibrations on railway overhead contact system. The dynamic state of the investigated system is described by a nonlinear set of coupled partial differential equations with complicated boundary conditions. Dynamic transverse displacements of the connected strings are determined. General results are illustrated by numerical examples.