Algebraic Equations for the Pile-Up Geometry in Debris Particle Indentation of Rolling Elastohydrodynamic Contacts

Metallic microparticles of 5–100 μm in size often contaminate elastohydrodynamic (EHD) contacts and indent surfaces. The geometrical characteristics of dents by such solid particles are linked to the way surface damage may evolve and how it may affect the life of the damaged contacts. In many cases, debris dents appear with shoulders raised above the original surface. Material piling-up this way causes high-pressure spikes when dents are over-rolled by an element such as a ball in a rolling bearing. This study introduces an approximate analytical method based on the so-called expanding cavity model (ECM) to calculate pile-up geometry with simple algebraic equations in thermoviscoplastic indentation of rolling EHD contacts by ductile spherical microparticles. Based on an experimentally validated debris indentation model published by the author, the pile-up model is shown to give realistic predictions in a wide range of operating parameters. Upon experimental validation, the new model is used to study the effects of particle size and hardness, Coulomb friction coefficient (CFC), strain hardening, and rolling velocity of EHD contacts on pile-up geometrical parameters including length, height, volume, and curvature.