Research on rolling friction's dependence on ball bearings' radius

TL;DR

This study experimentally compares Coulomb and Dupuit laws of rolling resistance for ball bearings, finding Coulomb's law more accurate and introducing a model to explain deviations based on surface roughness.

Contribution

The paper provides experimental validation favoring Coulomb's law for rolling friction and introduces the 'Cobblestones model' to explain deviations, along with a theoretical distinction between dynamical and kinematical friction.

Findings

Coulomb's law better fits experimental data

Deviations explained by the 'Cobblestones model'

Surface roughness measurements support the model

Abstract

There are two alternative historical laws of rolling resistance formulated by French scientist Coulomb and Dupuit. It has been decided to verify experimentally again, which of these laws describes freely rolling ball bearings on a hard surface better. An inducement to carrying out the measurements was the idea of the constant thickness of roadbed, which is consistent with Dupuit's theory. Measurements have been done using the damped oscillations in the pendulum bearings. Results have shown better consistency with the Coulomb's theory with small, but measurable deviations. These deviations were successfully explained by the so called "Cobblestones model". Parameters designated by this model have been successfully verified by the surface roughness's profile measurement. An additional theoretical aspect of this work is distinguishing two types of rolling friction force: dynamical and kinematical in an analogy to two types of specific heat capacity in the thermodynamics of gases.