The coefficient of friction (CoF) is one of the most important parameters for the contact between the wheel and the rail. Accurate estimation or measurement of the CoF has a very important role, both in terms of modeling the train dynamics and in terms of reducing operational costs in the long-term. For ease of implementation, since the nature of the wheel-rail contact dynamics is very complex, the assumption of a constant CoF is still used in most theoretical studies. Nevertheless, experimental work indicates that the CoF depends on dynamic changes in various wheel-rail conditions, like sliding velocity, contact patch shape and size for stick and sliding region, wheel and rail geometry, wheel vibration, rail surface roughness and/or lubrication, etc. In this paper we present the proposed equation to model the nonlinear dry friction coefficient at the wheel-rail contact. The friction coefficient is calculated at the three different values for change in the damping ratio while maintaining all the other conditions the same. As expected, the analysis performed to estimate the dry friction coefficient based on the proposed equation and using NUCARS® simulation results shows that the coefficient of friction has a highly nonlinear dependence on its parameters.

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