Theory of viscoelastic lubrication

•Rolling and sliding friction calculation for wet rough viscoelastic contacts.•The rubber rheology can be described by an arbitrary number of relaxation times.•The friction curves exibit new structures depending on the rolling number.•Rolling friction can originate from both asperity- and fluid–asperity interactions.•The rubbery-to-glassy transition attenuates the fluid-induced asperity flattening.

We study the lubricated (wet) contact mechanics of a smooth hard cylinder sliding on a randomly rough nominally flat surface of a linear viscoelastic solid. We calculate the rolling and sliding friction, and study the transition from the boundary lubrication to the elasto-hydrodynamic lubrication regime. For the viscoelastic contact the minimum (average) separation does not monotonically increase with the sliding velocity, and the Stribeck curve exhibits new structures not shown for elastic solids.