Proposal for fast computational method for Hertzian contact theory

TL;DR

This paper introduces a rapid computational approach for Hertzian contact theory, utilizing an incremental formula to accurately determine contact ellipticity with minimal iterations, applicable across various contact geometries.

Contribution

A novel incremental method for efficiently calculating contact ellipticity in Hertzian contact problems is proposed, improving speed and accuracy over existing methods.

Findings

Accurately computes ellipticity with few iterations

Applicable to a wide range of contact geometries

Maintains good accuracy in diverse contact scenarios

Abstract

Fast computational method for Hertzian contact theory is proposed. An incremental formula is introduced to calculate the ellipticity of the contact disk when two elastic bodies are in contact. This method can determine the ellipticity with good accuracy in a small number of iterations is reported. This method is also shown to be applicable from the case of a near perfect circle to the case where the major diameter is sufficiently long compared to the minor diameter.