A theory of static friction between homogeneous surfaces based on compressible elastic smooth microscopic inclines

TL;DR

This paper presents a novel theory of static friction based on microscopic inclines, showing how the static friction coefficient varies with normal force and other factors, supported by experimental validation with Teflon.

Contribution

It introduces a microscopic incline model for static friction that accounts for elastic compression and predicts variable friction coefficients, validated by experiments.

Findings

Friction coefficient decreases with increasing normal force.

Static friction depends on Young's modulus and contact area.

Experimental results with Teflon confirm the model's predictions.

Abstract

We develop a theory of static friction by modeling the homogeneous surfaces of contact as being composed of a regular array of compressible elastic smooth microscopic inclines. Static friction is thought of as the resistance due to having to push the load over these smooth microscopic inclines that share a common inclination angle. As the normal force between the surfaces increases, the microscopic inclines would be compressed elastically. Consequently, the coefficient of static friction does not remain constant but becomes smaller for a larger normal force, since the load would then only need to be pushed over smaller angles. However, a larger normal force would also increase the effective compressed area between the surfaces, as such the pressure is distributed over this larger effective compressed area. The relationship between the normal force and the common angle is therefore non-linear. Overall, static friction is shown to depend on the normal force, apparent contact area, Young's modulus, and the compressed efficiency ratio (effective compressed area per apparent contact area). Experimental measurements using teflon were carried out, and the results confirm predictions of this theory.