Rolling motion of a rigid sphere on a structured rubber substrate aided by a random noise and an external bias

TL;DR

This study investigates how a small sphere's rolling motion on a structured rubber surface is influenced by external forces, noise, and vibrations, revealing complex frictional behaviors and transitions between different friction regimes.

Contribution

It introduces a novel analysis of frictional motion under noise and external bias, demonstrating velocity-dependent friction regimes and flow reversal phenomena.

Findings

Rolling velocity increases non-linearly with noise strength

Friction transitions from Coulomb-like to linear with velocity

Flow reversal occurs with increasing asymmetric vibration amplitude

Abstract

We study the rolling motion of a small solid sphere on a surface patterned rubber substrate in an external field with and without a noise. In the absence of the noise, the ball does not move below a threshold force above which it accelerates sub-linearly with the applied field. In the presence of a random noise, the ball exhibits a stochastic rolling with a net drift, the velocity of which increases non-linearly with the strength of the noise (K). From the evolution of the displacement distribution, it is evident that the rolling is controlled by a Coulomb like friction at a very low velocity, a super-linear friction at an intermediate velocity and a linear kinematic friction at a large velocity. This transition from a non-linear to a linear friction control of motion can be discerned from another experiment in which the ball is subjected to a small amplitude periodic asymmetric vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases with the increase of the strength of the noise suggesting a progressive fluidization of the interface. Furthermore, the ball exhibits a flow reversal with the increase of the amplitude of the asymmetric vibration, which is indicative of a profile of friction that first descends and then ascends with velocity. An approximate non-linear friction model with the non-linearity decreasing with K is somewhat consistent with the evolution of the displacement fluctuation that also explains the sigmoidal variation of the drift velocity with the strength of the noise. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic response is studied using the tools of statistical mechanics.