A theoretical model for structure-borne excitation of a beam and a ring in rolling contact

Abstract

This paper presents a model which describes the structure-borne sound behaviour of a beam and a ring in rolling contact. By using point impedances the model is restricted to the area of the contact point. A further restriction is the consideration of the vertical direction of vibration only. In the model the main source of excitation is a force source. For the calculation of the force the original profile of the tread roughness, influenced- by the geometry of the rolling body as it picks up this roughness, is transformed into a so-called equivalent roughness with which the rolling body collides within a certain observation interval, producing a mean impulse. At the impact point the Hertzian elastic impact laws are applied so that the force-time history as well as the force spectrum can be calculated. Together with the theoretical transfer functions ( F/v ) of the model a precalculation of the structure-borne sound amplitudes excited during the rolling process becomes possible. Initial dimensions needed are the following: data on the point input impedances of the unloaded rolling body and track; data on the loss factor of the rolling process; data on the rolling body mass, contact geometry; material properties and rolling speed; data on the respective tread roughness. The method was validated by using an experimental combination of a hollow steel cylinder which rolls on two steel beams. The model also permits investigation of parameters which influence the noise behaviour during the rolling process. By means of an approximate representation of a wheel and rail as a ring and beam the model can also be applied to a wheel/rail system, and the results can be evaluated. The model is an approximation. It is not an exact realization of the actual physical process of rolling. Questions of radiation of airborne sound are not part of this study.