Use of a Model Reduction Procedure to Speed Up Time-Domain Simulations of Rail Vehicles

• Published in: Vehicle system dynamics 1994-01, Vol.23 (sup1), p.20-33
• Main Authors: Anderson, R.J., McPhee, J.J.
• Format: Article
• Language: English
• ISSN: 0042-3114; 1744-5159
• DOI: 10.1080/00423119308969502

The set of ordinary differential equations governing the motion of a rail vehicle are, in the terminology of numerical analysis, "stiff". That is, a numerical solution in the time-domain is constrained to use very small time steps even though the primary interest is in the low frequency oscillatory response of the vehicle. In this paper the "stiffness" of the equations is traced to negative, real eigenvalues of large magnitude which are inherent to the modelling of wheel/rail forces. These eigenvalues appear even in the simplest dynamic model, that of a single free wheelset. An attempt to develop an analytical method for eliminating the contributions of these eigenvalues is described. Complex modal analysis is used to remove the extraneous solutions numerically from a linear model and there is a resultant increase in the efficiency of the solution. The case of non-linear wheel/rail forces cannot be handled by the modal reduction method and another transformation is being sought.