A numerical study of the rolling friction between a microsphere and a substrate considering the adhesive effect

A numerical model of the rolling friction between a microsphere and a substrate is established by introducing the adhesion hysteresis between the front and rear sides of the contact region into Zhang's adhesive contact model. Effects of the size ratio which is defined as the sphere radius divided by the equilibrium separation, relative amount of adhesion hysteresis and Tabor parameter on the dimensionless maximum rolling friction torque in the case of zero normal force are inspected, and the quantitative relationship between the maximum rolling friction torque and the normal force is achieved. Results indicate that due to adhesion hysteresis at microscale, the dimensionless maximum rolling friction torque at zero normal force is not zero, which not only increases with decreasing size ratio, showing clear size effects, but also increases with increasing relative amount of adhesion hysteresis and Tabor parameter. In addition, the maximum rolling friction torque at microscale presents a sublinear relationship with the normal force, and the exponent of the normal force is influenced by the size ratio, relative amount of adhesion hysteresis and Tabor parameter, which are remarkably different from the superlinear relationship at macroscale. (paper)