Rolling Resistance of a Hard Sphere on Rubber Sheets: Limitations of Linear Viscoelastic Modeling and Influence of Nonlinearities

Abstract

A growing body of evidence suggests that limited accuracy can be expected from analytical and computational tools relying on linear viscoelasticity for the prediction of rolling resistance in real systems presenting material and geometric nonlinearities. A set of experimental data for the viscoelastic resistance to motion incurred by a rigid sphere rolling between two parallel sheets of rubber, in realistic in-service conditions, was determined, in a previous work [Zéhil and Gavin, 2019]. The tests involved different elastomers (a Urethane rubber and a Neoprene rubber) and different sheet thicknesses, ball diameters, loading levels and rolling speeds. The accuracy of linear models in predicting such practical data is assessed in this work. To this aim, the elastomers are described by general linear viscoelastic models whose master-curves are characterized by: (i) High Frequency Thermo-Viscoelastic Spectroscopy, under very small strain amplitudes and (ii) Dynamic Mechanical Analysis under relatively larger deformations. In both cases, rolling resistance predictions are obtained using computational tools based on linear viscoelasticity [Zéhil and Gavin, 2013a, 2013b] and compared to the measurements. Conclusions are drawn regarding: (i) the practical limitations of linear rolling resistance models and (ii) influences of nonlinearities such as those due to large deformations, to the Mullins effect [Mullins, 1969] and to the Payne effect [Payne, 1962], on predictions.