Optimal Axle Distance of a Railway Bogie

Abstract

The dynamics of a railway bogie are investigated by utilizing methods of nonlinear dynamic as system theory. The railway bogie model is that introduced by Cooperrider and further developed by Kaas-Petersen. "Principal" and "secondary" attractors are defined and periodic and chaotic attractors are described. A "qualitative" distinction of secondary attractors is introduced according to the robustness of the attractors with respect to random perturbations. The results suggest the possible existence of an optimal axle distance between two wheel sets.

An Unusual Hopf Bifurcation: The Railway Bogie

“…These critical velocities are all somewhat larger than those reported in [Galvanetto et al, 1997], but agree in the sense that larger inter-axle distances give rise to larger critical velocities.…”

“…To decide how to proceed, we first noted that [Galvanetto et al, 1997] used Runge-KuttaFehlberg integration to verify their results. For purposes of numerical experimentation we wished to maintain direct control over all parameters in the numerics, including the step size, so we chose classical Runge-Kutta integration.…”

“…We wish to thank Rüdiger Seydel for pointing out that the points of Hopf bifurcation reported in [Galvanetto et al, 1997] appeared to be low, and for being such a marvellous host during our visits to Ulm.…”

“…In [Kaas-Petersen, 1986] and [Galvanetto et al, 1997], the semiaxes of the contact ellipse are ambiguously denoted a and b and the value given for G, the shear modulus of steel, is too small by a factor of 100. Nevertheless, the value given for the compound constant Gπa e b e appears correct.…”

“…Galvanetto et al [1997] performed an expensive simulation of the dynamics of the railway bogie according to the model of Cooperrider [1972] and developed by KaasPetersen [1986]. It was brought to our attention by R. Seydel, that the values of the critical speeds reported in [Galvanetto et al, 1997] seemed to be low: His own computations gave somewhat higher values. To check, we performed two independent computations, one using a high-precision Maple program, the other using the general code BIFOR2 [Hassard et al, 1981].…”