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Abstract
A classification of wheel flats according to the different stages of their growth is given, along with the characteristic features of the dynamic wheel–rail interaction for each category. Mathematical expressions and frequency spectra of the corresponding wheel mass trajectories are derived. Difference is made between the subcritical and the transcritical speed regime. A criterion is derived for contact loss for worn flats. Simulations show that the dynamic wheel–rail interaction is governed by the track stiffness for low train speeds or long flat lengths; for high speeds and/or short flat lengths the interaction is governed by the inertial properties of the wheel and the rail. For a given flat geometry, nonlinearities in the relationship between the impact magnitude and the train speed occur in the stiffness-dominated speed domain, whereas this relationship is approximately linear in the inertia-governed domain. In the latter domain, the impact magnitude is found to be linearly dependent upon the maximum trajectorial curvature or inversely linearly dependent on the minimum circumferential wheel tread curvature. The above relationships are valid for the subcritical speed regime, in which no contact loss occurs. Different contributions from the literature are compared with respect to the established relationship between impact magnitude and speed. Significant differences are found, due to insufficiently defined parameters and conditions. Conditions are derived for a consistent application of the so-called equivalent rail indentation in experiments with wheel flats, and the indirect strain registration method for measuring dynamic wheel–rail contact forces is reviewed.