Train---Track Interaction. Coupling of Moving and Stationary Dynamic Systems: Theoretical and Experimental Analysis of Railway Structures Considering Wheel and Track Imperfections

A general and well-structured method is advanced for analysis of the vertical dynamic interaction between a train and its track. The trains studied are modelled as linear or non-linear discrete mass-spring-damper systems. For the track structure, a linear three- dimensional continuous model is established where the rails are discretely supported, via railpads, by flexible sleepers on an elastic foundation. The complex-valued modal parameters of the track structure are solved for. This means that this structure is described as a modal component governed by fully decoupled equations of motion. Imperfections on the running surfaces of wheels and rails are incorporated in the algebraic constraint equations matching the train and the track. Possible loss of contact and recovered contact between a vehicle and its track are considered. <p> The system of coupled first-order differential equations governing the motion of the train and the track and the set of algebraic constraint equations are together compactly expressed in one unified matrix format by use of an extended state-space vector. A time-variant initial-value problem is thereby formulated such that its solution can be determined in a straight-forward manner by use of any one of several existing time- stepping methods available in standard subroutine libraries. <p> A method for determining the eigenfrequencies of structures containing non-discretized beam members in plane bending-shearing vibration is developed. Each beam member may rest on a general Winkler-type elastic foundation. The method can preferably be implemented within the Wittrick-Williams bisection algorithm. <p> An investigation of the influence of a number of selected track parameters on the dynamic interaction is performed by use of a two-level fractional factorial design method. This technique allows for a rational parametric search towards a combination of numerical levels of these parameters which minimizes the bending stresses in the track. <p> Comprehensive full-scale field experiments on a portion of a recently built railway track for high-speed trains are reported. Different train speeds and axle loads were tested. Flexible and solid wheels without and with wheelflats were instrumented for measurement of transient vertical wheel/rail contact forces. Accelerations and strains in the track structure were measured in parallel. The location of the instrumented wheelset in relation to the instrumented portion of the track was determined at each instant of time. The track parameters used in the numerical simulations were determined at the test-site. <p> Numerical application examples are given in which the influences of three types of practically important imperfections in the compound vehicle/track system are investigated. Physical explanations of the calculated interaction behaviour are offered