Topological data analysis for friction modeling

¹ Mechanical Engineering, University of Wisconsin-Milwaukee - 3200 N Cramer St, Milwaukee, WI 53211, USA
² Infochemistry Centre, ITMO University - 9 Lomonosova St., St. Petersburg, 191002, Russia

^(a) nosonovs@uwm.edu (corresponding author)

Received: 5 March 2021
Accepted: 13 September 2021

Abstract

Dry sliding friction is a complex but ubiquitous phenomenon. Experimental studies of friction produce large amounts of data, while most models are phenomenological rather than deduced from fundamental principles. Proper identification of relevant degrees of freedom is crucial for the development of adequate frictional models, such as the state-and-rate models. Topological data analysis is a mathematical method for dimensionality reduction for datasets characterizing surface roughness, contact of rough surfaces, and frictional sliding. We study tribological systems including the surface roughness and multi-asperity contacts using 33, 44, and 55 pixel patches. Depending on whether the surface is isotropic or anisotropic with particular lay directions, the data tends to concentrate at certain “primary” and “secondary” circles yielding different values of the Betti numbers. Scale dependency of corresponding structures is analyzed with persistence diagrams. Moreover, statistics of stick-slip zones can provide insights into relevant internal degrees of friction.