Kinematic oscillations of railway wheelsets

We show that Klingel’s classical formula for the frequency of the small kinematic oscillations of railway wheelsets results in a significant error even in the simplest physically relevant cases. The exact 3D nonlinear equations are derived for single-contact-point models of conical wheels and cylindrical rails. We prove that the resulting nonlinear system exhibits periodic motions around steady rolling, which consequently is neutrally stable. The linearised equations provide the proper extension of Klingel’s formula. Our results serve as an essential basis for checking multibody dynamics models and codes used in railway dynamics.