Quasi-static analysis of two-dimensional rolling contact with slip-velocity dependent friction

In this paper the influence of a velocity-dependent friction law on the interactions inside the contact patch between a rolling wheel and a rail is presented, assuming that the quasi-static approach is still applicable. In the model, traction builds up until a critical configuration is reached, after which an instantaneous reset occurs. The system jumps from one state to another in a discontinuous way. This suggests that the true elastic field, including dynamical effects, is adjusted in a very short time span, which is not resolved in the quasi-static approach. Inside the contact patch much higher and swiftly changing micro-slip velocities may occur than were anticipated previously, which are not well-described by friction laws that use an instantaneous relation between sliding velocity v(t) and coefficient of friction μ ( t ) .