A MODEL-REDUCTION PROCEDURE FOR THE DYNAMIC ANALYSIS OF RAIL VEHICLESSUBJECTED TO LINEAR CREEP FORCES

The set of differential equations governing the motion of an unrestrai ned coned wheelset travelling on a tangent section of track and acted upon by creep forces arising from the contact between wheel and rail a re, in the terminology of numerical analysis, extremely ''stiff''. Thi s stiffness can be attributed to the existence of two negative real ei genvalues in the solution of the eigenproblem associated with the line arized equations of motion. Compared with the two complex conjugate ei genvalues that complete this solution, the real eigenvalues have large magnitudes and necessitate that relatively. small timesteps be used i n order to obtain an accurate numerical integration of the full set of equations of motion. However, by truncating the set of left and right eigenvectors to eliminate these real eigenvalues in a modal analysis of the wheelset, it was found that their contribution to the overall d ynamic response is negligible. This same modal truncation approach was then applied to the substructured equations of motion for a simple ra il vehicle system consisting of two wheelsets connected to a main body by linear springs and dampers. Essentially, the physical degrees of f reedom for each wheelset substructure were replaced by a single comple x coordinate obtained from the previous normal modes analysis. Using t his model reduction procedure, accurate numerical results for the moti on of the rail vehicle were generated several times faster than the re sults obtained by numerically integrating the full set of differential equations directly.