Full Two-Dimensional Model for Rolling Resistance: Hard Cylinder on Viscoelastic Foundation of Finite Thickness

Abstract

A new full two-dimensional semianalytical method is developed to rigorously and efficiently solve the problem of a rigid cylinder rolling with any given constant speed over a viscoelastic foundation of finite thickness. In this new method, the solution is expanded into a set of Fourier series, the master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special boundary element based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. A verification example is given to validate the methodology. Several numerical examples are given to study the influences of various factors on rolling resistance. The method as well as the conclusions drawn from the examples may be of interest to roller and belt-conveyor designers. This approach can be easily generalized to solve the general rolling contact problems of two viscoelastic bodies.