Oscillating horizontal bar problem revisited

TL;DR

This paper revisits a classic mechanics problem involving a horizontal bar on rotating rollers, incorporating viscoelastic and bulk rolling friction effects to derive a linear relationship that allows full determination of the rolling friction coefficient.

Contribution

It introduces a novel analysis of the oscillation frequency considering viscoelastic rollers and bulk rolling friction, enabling complete determination of the rolling friction coefficient from observations.

Findings

Inverse square of oscillation frequency linearly relates to center distance

Gradient and intercept determine rolling friction coefficient

Method allows full characterization of viscoelastic roller materials

Abstract

A simple text book problem in mechanics\cite{klep}, describes a massive horizontal bar placed on two oppositely rotating rollers, kept at a fixed center to center distance. Subsequent motion is to be found out in presence of kinetic frictions at the point of contacts of the two rollers\cite{demo}. Introducing bulk rolling friction effects, through the contact planes and considering viscoelastic rollers, we find that the inverse of the square of the oscillation frequency of the bar has a linear relationship with the center to center distance. The gradient and intercept of the linear relation together with observations about two consecutive positions of the bar, determine the rolling friction coefficient of the viscoelastic materials of the two rollers fully.