Critical velocity of railway vehicles

Railway vehicles are among the most complex dynamical systems in engineering due to the large number of degrees of freedom and the non-linear interaction between wheel and rail. The purpose of this research is to analyse the dynamic stability of a railway vehicle travelling on a tangent track at constant speed. As instability index, the establishment of a self-sustained limit cycle is considered. In reality, a limit cycle is almost always present. What separates stability from instability is the amplitude of such cycle. In fact, cycles characterised by small amplitudes can't endanger the vehicle's behaviour. This paper discusses both numerical integration methods of the non-linear equations of motion of the railway vehicle and the linear methods based on the equivalent conicity concept to assess the vehicle's critical velocity limit.