This paper presents a framework to investigate the dynamics of overall vehicle-track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A three-dimensional vehicle-track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel-rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time-frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle-track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing-Qinhuangdao line and the high-speed running test on the Qinhuangdao-Shenyang line. Differences in the dynamic responses analysed by the vehicle-track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.

https://www.tandfonline.com/doi/pdf/10.1080/00423110802621561

Fundamentals of vehicle–track coupled dynamics

A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

http://www.polach.ch/data/object_4/Wear_2005.pdf

Creep forces in simulations of traction vehicles running on adhesion limit

Corrugation is a phenomenon which has excited the interest of railwaymen for more than a century, but for which there often does not appear to be a cure. It has generally been realized that there a...

Rail corrugation: Characteristics, causes, and treatments

Physicists are very familiar with forced and parametric resonance, but usually not with self-oscillation, a property of certain dynamical systems that gives rise to a great variety of vibrations, both useful and destructive In a self-oscillator, the driving force is controlled by the oscillation itself so that it acts in phase with the velocity, causing a negative damping that feeds energy into the vibration: no external rate needs to be adjusted to the resonant frequency The famous collapse of the Tacoma Narrows bridge in 1940, often attributed by introductory physics texts to forced resonance, was actually a self-oscillation, as was the swaying of the London Millennium Footbridge in 2000 Clocks are self-oscillators, as are bowed and wind musical instruments The heart is a "relaxation oscillator," ie, a non-sinusoidal self-oscillator whose period is determined by sudden, nonlinear switching at thresholds We review the general criterion that determines whether a linear system can self-oscillate We then describe the limiting cycles of the simplest nonlinear self-oscillators, as well as the ability of two or more coupled self-oscillators to become spontaneously synchronized ("entrained") We characterize the operation of motors as self-oscillation and prove a theorem about their limit efficiency, of which Carnot's theorem for heat engines appears as a special case We briefly discuss how self-oscillation applies to servomechanisms, Cepheid variable stars, lasers, and the macroeconomic business cycle, among other applications Our emphasis throughout is on the energetics of self-oscillation, often neglected by the literature on nonlinear dynamical systems

Klaus Knothe

Papers

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

Review on rail corrugation studies

An extended linear model for the prediction of short pitch corrugation

Determination of temperatures for sliding contact with applications for wheel-rail systems

A comparison of analytical and numerical methods for the calculation of temperatures in wheel/rail contact