Influence of longitudinal creepage and wheel inertia on short-pitch corrugation: A resonance-free mechanism to explain the roaring rail phenomenon
Authors: Ciavarella M , Barber J 
Published: May 2008

Short-pitch corrugation (30–80 mm in wavelength) in railways, despite being well known since the early days of the railways because of its criticality in producing damage, ‘roaring rail’ or ‘howling wheel’ noise, and indirectly rolling contact fatigue, is considered an enigmatic phenomenon. In fact, most available data seem to show a non-linearly increasing wavelength with speed, and an almost fixed wavelength, while most models based on system resonances predict a fixed frequency. More enigmatic still, many data points fall in a range of frequencies where there is no evident resonance in the wheel—railtrack system (the large gap between the low frequencies resonances from 50 to 300 Hz and the very high pinned—pinned mode resonant frequencies which correspond generally to 850–1100 Hz in railways. Yet the most common classifications of corrugation continue to associate corrugation to frequency-fixing mechanisms. Johnson's early studies on the Hertz normal spring resonance suggest that plasticity-based repeats impact mechanism, or differential wear mechanism both seemed to be not appropriate to explain short-pitch corrugation. In particular, longitudinal creepage (obviously associated with braking or acceleration very common on uphill grades, near stations, but also in curves where profiles provide insufficient steering capability) seemed to act to suppress corrugation, rather than promoting it, as suggested in the model of Grassie and Johnson. Only a few, very comprehensive models that include all the relevant receptances consider the effect of wheel inertia: indeed, these models indicate many possible corrugation regimes and, in particular, point at lateral creepage mechanisms at the pinned—pinned resonant frequency as giving much larger growth than longitudinal creepage, so the possibility of a corrugation regime independent of wheelset or railtrack resonances has largely remained hidden, despite it being present in some results. In this paper, a simple model that returns to a pure longitudinal creepage mechanism is suggested, showing that it is essential to include the rotational dynamics of the wheel in the system, similar to Grassie and Johnson's model. In particular, a simple full-stick Winkler-contact mechanics model can estimate the effect of transient contact mechanics. For typical inertias, the conditions are closer to the constant tangential load (which is the correct limit at zero speed anyway) and seem to explain the basic features of wear-induced instability in the existing experimental data. For larger inertias, which may also be possible for heavy wheelsets, the model predicts results closer to Grassie and Johnson's assumption of constant creepage, i.e. only a limited range of possible short-pitch corrugation. The model also suggests that although the growth of corrugation depends strongly on the amplification of the normal load, the wavelength of this mode of corrugation depends very little on the vertical resonances of the systems, so that it would persist even in a model with no resonance altogether. It is possible that the exact frequency of this regime depends on the details of the contact geometry, here simplified using the Winkler model. Finally, a reason why this mechanism of longitudinal creepage corrugation, despite perhaps giving 10–20 times apparently lower growth than lateral creepage, may indeed be the correct mechanism to interpret the classical data, is that longitudinal creepage can be 10 times higher than lateral (5 per cent instead of 0.5 per cent), and as corrugation growth is proportional to square of creepage, there is a factor 100 that largely compensates for this. There is still some progress to be made to obtain a reliable model to compare the various regimes, but clearly this regime should be considered when devising remedies to corrugation.