A first analysis of possible elementary causes of self‐excited vibrations in roller coaster rides

Abstract

The emergence of vibrations during a roller coaster ride is a recurring phenomenon that can deteriorate the overall experience and accelerate material fatigue. Nevertheless, the causes of such vibrations are still not completely understood and are consequently not fully predictable during the design process. One possible source lies on the irregularities of the rails, acting as a forced external excitation. However, a spectral analysis shows deviations with respect to real measurements [1], as the frequencies are not synchronous with the car velocity divided by the spatial irregularity period. Therefore, there is an indication that the vibrations may be due to self‐excitation and/or that the developed models should consider other phenomena not yet contemplated. This investigation analyses –for the first time to the knowledge of the authors– the plausibility of various causes of self‐excited vibrations during a roller coaster car motion. Given the complex structure of a real roller coaster train and the intricate geometry of the track, the study considers as a first step minimal dynamical models running along a straight track. The cause analyzed in this paper is the contribution of the transversal friction force component that develops in the wheel‐rail contact interface to the destabilization of the longitudinal motion, as well as the effect of the various geometrical and inertial parameters. In this first analysis, no external excitation is considered. For a range of parameters, the minimal system presents a Hopf bifurcation. The results are plausible from the general behavior and thus this cause may be retained as a candidate for the real vibrations occurring in roller coasters. However, the applicability of these preliminary results to general roller coaster motions is not yet confirmed, but a superposition with other causalities may render effective. In further investigations, a complete train motion on curved tracks and external perturbations will be studied to determine the share of the different causes.