Vibrations in roller coaster systems. Part I: friction-induced self-excited oscillations

Abstract Vibrations occurring during a roller coaster ride are a recurrent issue that negatively impacts the ride experience, accelerates material wear, and can increase passenger discomfort. Despite their common occurrence, the underlying causes of these vibrations remain poorly understood, making it difficult to predict them during the design phase. This article analyzes the effects of friction forces at the wheel-rail interface, unveiling that they may play a key role in generating these vibrations. Initially, minimal models are employed to investigate friction-induced self-excited oscillations, highlighting unstable equilibria that result in limit cycles. A nonlinear model describing both normal and tangential contact forces is then introduced, exploring how different parameters affect the intensity of vibrations. Finally, the study presents the vibration response of a nonautonomous dynamic system of a full train traveling along spatial tracks. While the minimal models associate instabilities with a decreasing friction coefficient characteristic and require large cornering stiffness values and slip angles, the full model demonstrates that friction can cause transient vibrations under less stringent conditions. Specifically, inadequate wheel preload and low contact damping are identified as factors that exacerbate vibrations, even in the absence of rail irregularities. An analysis of the effects of irregularities on the nonlinear frequency response in combination with dynamic track deflections and friction, as well as the validation of the proposed vibration causes via empirical data, is developed in a companion paper (Part II).