Rolling of a cylinder with slip-dependent friction: The Carter solution revisited

The problem of a wheel under tractive rolling of Carter is revisited here by assuming a slip-dependent friction force. By assuming a change from static to dynamic friction coefficient occurs over a small distance, we develop effectively a fracture mechanics solution for the shear tractions, which describes some aspects of “falling friction” creepage forces which are commonly observed experimentally. Possible agreement with experiments is discussed, suggesting that friction may include also rate-dependent effects. A simple strip theory is used to estimate 3D effects, which reduce the strength of the singularity at the edges being the peak pressure lower there