Surface-Roughness Effects in Rolling Contact

A theory of rolling contact is presented which deviates from past theories in two respects: (a) the contacting surfaces are not assumed to be topographically smooth, and (b) Coulomb’s law of friction is replaced by a law describing the behavior of interfacial friction junctions. Numerical results for the slip as a function of the normal and tangential loads are shown to depend on a roughness parameter D, which, in turn, depends on surface topography, the gross geometry of the contacting bodies and on the normal load. It is found that when D is large (i.e., the surfaces are very rough, or the normal load is small), the slip-force relationship differs considerably from that predicted by the smooth-surface (or classical) theory. When D tends to zero, the two theories coincide. The dependence of D on topographical parameters is shown explicitly. Numerical examples indicate that for cylinders of small radius, surface-roughness effects may be important. Their importance decreases as the cylinder radius or the maximum contact pressure is increased, or the surface is made smoother.