The Investigation of Locomotive Dynamics via A Large Degree of Freedom Modeling

Abstract

An analytical model of a locomotive due to S. Levy is modified to accept random track input and used as the basis of a locomotive study with 63 degrees of freedom. This model differs from precursors in that it is faster, it accepts nonlinear suspension components and wheel/rail interactions, it includes routines so that track irregulatiries may be incorporated by means of vertical and lateral PSD curves, it accounts for adhesion limits, checks derailment conditions, and provides time histories of generalized variables. With this code, a specific locomotive model, similar to the General Electric Company’s U33-C locomotive, is evaluated to ascertain what changes in either the model or the track parameters will permit higher safe speeds. This parametric study addresses speeds in the range of 70 to 280 ft/sec. (21.34 to 85.34 m/sec), three classes of track, 4, 5, and 6, primary suspension stiffnesses from 18 to 300 klbs/ft. (.263 to 4.38 MN/m), wheel flange clearances from .05 to .75 inches (1.27 to 19.1 mm) and the effect of vertical and lateral rail stiffnesses in the ranges of .5 to 8 and .25 to 4 Mlbs/ft. (7.3 to 117 and 3.65 to 58.4 MN/m), respectively. The results generally agree well with current standards governing safe running speeds on various class tracks. They indicate that at speeds equal to accepted safe operating speeds on class 4, 5, and 6 tracks, the rms values of the vertical forces at the contact of the first wheel and rail do not increase beyond 25% of the nominal vertical load at this point. Under these same conditions, maximum wheel-rail separations, if they occur, are for each case less than the wheel flange height assumed one inch (25.4 mm); for class 6 track, no separations larger than the flange height occur even at 280 ft/sec. (85.34 m/sec.).