Contact Problem of Viscoelastic Cylinder Rolling along a Viscoelastic Base with a Viscous Lubricant Layer

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Based on the Kelvin model of a viscoelastic medium, the steady-state motion of a viscous lubricant thin layer between a viscoelastic cylinder and a viscoelastic base is considered. The effect of a dimensionless parameter proportional to the relaxation time of viscoelastic bodies exerted on the characteristics of the lubricant layer is studied. It is shown that for a high value of the mentioned parameter, the solution of the problem concerning the contact between viscoelastic bodies separated by a thin layer of lubricant is close to the solution of the elastohydrodynamic problem in the case of the elastic modulus equal to the instantaneous elasticity modulus inherent in viscoelastic bodies. As the value of the parameter decreases, the high-pressure area exhibits an expansion, whereas the maximum pressure exhibits a decrease, and the second pressure maximum decreases faster than the first one and then disappears. It is shown that the coefficient of rolling friction as a function of the relaxation time has a maximum. At small relaxation time values, the gap at the entry takes such a shape wherethrough the mode of abundant lubrication is impossible. As a result, the thickness of the lubricant layer rapidly decreases with decreasing relaxation time.