Asymptotic Solution of the Contact Problem on the Stationary Rolling of a Rigid Cylinder with a Viscoelastic Surface Layer

An analytical method of calculating contact parameters during rolling of a cylindrical body, having a thin viscoelastic surface layer, over a rigid sideway was developed. The technique is based on elastic-viscoelastic analogy and asymptotic approximation of the exact solution of the elasticity theory problem for a thin strip. The mode of steady rolling at given normal force and speed of motion of the center of the rolling body is considered. In the example of calculation the initial parameters corresponded to rolling support of a mine skip with rolling elements in form of steel rollers with a polyurethane rim. The dependences of rolling resistance force (which is parallel to the supporting surface) on speed, friction coefficient during sliding, and Poisson’s ratio of the rim material were obtained. The dependence of rolling resistance force on speed has a maximum, which corresponds to a speed of 8 m/s in the example considered. The rolling resistance decreases as Poisson’s ratio of the rim material increases. The calculated values are compared with assessments of contact parameters obtained within the framework of a simplified Winkler’s base model. It is shown that the discrepancy of results does not exceed 5%. The developed technique can be used for designing and predicting the durability of metal-polymer rolling bearings.