A linear non-Hertzian unsteady tangential wheel-rail contact model

The increase in computational capacity has considerably reduced the use of linear models for wheel/rail tangential contact, being currently replaced by theories that adopt non-linear formulations able to address the most complex conditions realistically. However, linear formulations are difficult to replace in certain applications such as acoustic problem modelling, in which case a linear formulation of the track-contact-vehicle system is needed. The vibration that appears in this type of problem covers a wide range of audible frequencies, so, in addition to linearity, these theories are required to be non-stationary. The literature in contact mechanics gives response to this problem through models that consider low creepage levels, but it remains to cover other conditions in which the mean creepage is not small, such as when a railway vehicle negotiates a curve. This work presents a new theory of unsteady linear tangential rolling contact for non-Hertzian areas that considers kinematics as the sum of a constant creepage resulting from large stationary forces (such as those that occur when the vehicle negotiates a curve with constant radius) and small variable creepage due to a high-frequency phenomenon (e.g. the dynamic interaction between the vehicle and the track). The model is based on the Variational Theory (i.e. the CONTACT method for tangential problems), from which a linear formulation with variable creepage is deduced. According to this formulation, the non-steady state contact problem can be solved for any shape of the wheel/rail contact region, requiring a much smaller computational effort than the general unsteady CONTACT approach. The results show a satisfactory agreement of the proposed model to the unsteady CONTACT version, hence confirming the soundness of the proposed contact model.