USE OF A MODEL-REDUCTION PROCEDURE TO SPEED-UP TIME-DOMAIN SIMULATIONS OF RAIL VEHICLES

The set of ordinary differential equations governing the motion of a r ail 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 ''sti ffness'' of the equations is traced to negative, real eigenvalues of l arge magnitude which are inherent to the modelling of wheel/rail force s. These eigenvalues appear even in the simplest dynamic model, that o f a single free wheelset. An attempt to develop an analytical method f or eliminating the contributions of these eigenvalues is described. Co mplex modal analysis is used to remove the extraneous solutions numeri cally from a linear model and there is a resultant increase in the eff iciency of the solution. The case of non-linear wheel/rail forces cann ot be handled by the modal reduction method and another transformation is being sought.