The linearized dynamic models for the conformal contact of a wheel and rail presented in reference (1) have been used to calculate the dynamic response to a prescribed sinusoidal ripple on the railhead. Three models have been developed: single-point contact with low or high conformity, and two-point contact. The input comprises a normal displacement Δeiwt together with a rotation Δeiwt applied to the railhead. The output comprises rail displacements and forces, contact creepages and forces, and frictional energy dissipation. According to the Frederick-Valdivia hypothesis, if this last quantity has a component in phase with the input ripple, the amplitude of the ripple will be attenuated, and vice versa. Over most of the frequency range, a pure displacement input (Ψ = 0) was found to give rise, predominantly, to a normal force at the railhead. A purely rotational input (Δ = 0) caused a single point of contact to oscillate across the railhead or, in the case of two-point contact, to give rise to fluctuating out-of-phase forces at the two points. The general tenor of behaviour revealed by the three models was similar: frictional energy dissipation, and hence wear, increases with conformity and is usually of such a phase as to suppress corrugation growth. Thus the association, found on the Vancouver mass transit system, of corrugations with the development of close conformity between wheel and rail profiles must arise from some feature of the system not included in the present models.
Frictional Energy Dissipation in a Contact of Elastic Bodies
Subjected to Superimposed Normal and Tangential Oscillations
