Oscillations and chaotic behaviour of unstable railway wagons over large distances

Abstract

Considering the physico-mathematical problem set at the title of this paper, knowing also that it covers actual circumstances of dynamical derailments of vehicles with large safety consequences, one has to face unusual modelling difficulties. Mainly two results are awaited: (1) the description of the mechanisms allowing derailment and (2) an evaluation of the risk. Obviously (and fortunately), dynamical derailments resulting of random association of track geometry with chaotic oscillations of the wagons are rare, almost impossible to produce experimentally on purpose and consequently difficult to describe. However, the available experimental field is not empty but presents lots of time histories of chaotic signals (forces) which cannot be studied on a deterministic basis. As these vehicles are quite non-linear mechanical systems, the only possibility of their modelling is numerical. Thus, there is only one chance to be effective, it is to develop numerical models using simplifying hypothesis in order to yield the shortest CPU times so as to be able to test and adjust the effects of modelling assumptions and to cover the largest possible field, including influence of wear modifications of the rolling profiles. This task has been done (the development lasted 10 years) and our method, which we do not pretend to be the only one, is explained in this paper focusing on physical assumptions rather than on already published mathematical developments. Among numerous difficulties, we had to face chaotic results of the computations. They appeared when vs/time numerical results of long computations were found depending, for instance, on the type of the micro-processor or on the way of factorising the Fortran statements. We are now convinced that there is no solution to this difficulty in the direction of increasing numerical precision because it comes from the nature of the physical problem itself. We could not prove it, but, as all experimental signals were different from each other, one has to admit that the physical reality that is to be modelled cannot be observed deterministically and, consequently, that, even if it would be possible to develop a deterministic model, it would be impossible to validate it.