rolling cylinder on an elastic half-plane with harmonic oscillations in normal force and rotational speed. part ii: energy dissipation receptances and example calculations of corrugation in the short-pitch range

in this paper, starting from results of part i, we develop a procedure to evaluate the frequency dependent receptances of the energy dissipation at the contact interface, which is the quantity of interest in corrugation studies as the most known wear laws assume the local wear proportional to the frictional dissipation. these results are applied to the calculation of the growth rate of corrugation in railway tracks with an initial sinusoidal undulation. in particular, the wheel inertia and the transient contact mechanics effects are considered using a continuum description of the rail (hence neglecting pinned–pinned resonance due to the beam bending between two successive supports) by the simplest model (the euler beam) which we can use to describe the normal receptance of the rail. the presence of a finite partial slip zone in the contact area can significantly modify the results, partially explaining the scatter of the experimental data collected in the literature. in particular, we found that partial slip affects the predicted apparent wavelength of highest growth of corrugation, and with respect to the full stick conditions, higher tractive ratio increases significantly the growth factors and non-linearity, showing an unexpected absolute maximum of growth at intermediate velocities, and the “resonance-free” regime becomes increasingly not a constant “frequency”, spanning a range of frequency between 700 and 1500 hz even for a given system and set of loads. only a full investigation involving all other resonances in the system may clarify further the correspondence with experimental values, since the corrugation “enigma” may be due to a combination of effects.