Corrugation Models and the Roaring Rails Enigma: a Simple Analytical Contact Mechanics Model Based on a Perturbation of Carter's Solution

Corrugation in railways, and especially short pitch corrugation (30-80 mm), is still considered something of an enigma, despite extensive research. Models based on repeated impacts or differential wear, such as Grassie and Johnson's (1985) and Bhaskar et al.'s (1997), seem not to be conclusive, or not to suggest the correct wavelength. Further models have been suggested, either linear (Frederick, Valdivia, Hempelmann, Vassilly and Vincent) or nonlinear (Mueller), but most suggest a constant frequency mechanism invariably connected to vertical resonances of the system either in the low frequency range (50-100 Hz, the resonance of the vehicle's unsprung mass on the track stiffness referred to here as the "P2 resonance", close to the Hertz contact resonance), or at about 1000 Hz (pinned-pinned resonance, in which the rail vibrates almost as if it were a beam pinned at sleepers), or even higher frequencies still (1700-1800 Hz). The experimental data available, by contrast, do not fit these frequency ranges. The discrepancy is tentatively explained with "contact filtering" and varied traffic ideas, but do not convince completely. In this paper, we stress the importance of wheel inertia in coupling the oscillations of normal load, with the variations of tangential load and longitudinal creepage. A simple zeroth order perturbation of the classical rolling contact solutions is suggested, which obtains good qualitative agreement with experimental evidence. The model also leads to the recognition that vertical resonances are not crucial in explaining corrugation, as believed in previous models, since we use an extremely simple model of an Euler beam with no elastic support, having no resonances. Important factors for the growth of corrugation are the friction coefficient and the tractive ratio. High longitudinal creepage is needed to promote rapid development, and this can arise from curving, hunting motion or misaligned axles, and is probably exacerbated by high contact conformity, since this increases the fluctuating component of longitudinal creepage due to the movement of the contact point. With discrete supports, we expect a modulation of corrugation wavelength and amplitude, but this requires a separate investigation, not just the inclusion of pinned-pinned resonance.