A mechanistic model of spherical particle entrapment in elliptical contacts

Abstract

The dynamic interaction of solid, spherical particles with the counterfaces of concentrated, dry or lubricated, conforming or non-conforming, rolling -sliding elliptical contacts is mathematically analysed. Criteria for the entrapment or rejection of particles are postulated on the basis of the resolution of mechanical and fluid forces on a particle for given contact geometry and operating conditions. Three-dimensional maps of the various force components on a particle are presented for a typical application, together with the maps of the zones where a particle would be 'conditionally' entrapped, 'weakly' rejected, or 'unconditionally' rejected, where the previous terms are defined in a comprehensive evaluation system in the model to assess the risk of damage of the contact from the presence of contaminants. This study is concerned with the process of particle entrapment, meaning that a particle must be in contact with both the counterfaces of a concentrated contact, and not entrainment (particle wandering in the lubricant, which has been studied by the author (Nikas, 2002)). To the best of the author's knowledge, this is the first study explicitly dealing with the general case of elliptical contacts. Elliptical contacts cover circular contacts and, taken to the limit, can also simulate line contacts; thus, the model's applicability and validity as a design tool are generalized. In summary, the purpose of the article is to expand previous models developed for simpler geometries and to present an effective computational tool for the simulation of particle entry into elliptical contacts and the resulting risks of contact damage.

An experimentally validated numerical model of indentation and abrasion by debris particles in machine-element contacts considering micro-hardness effects

“…Obviously, the analysis of particle elastoplastic deformation is not performed unless the entrapment criteria are satisfied. [113][114][115] The second part is about modelling how a ductile particle passes through a concentrated contact. 59,62,99 This involves resolution of mechanical contact forces on the particle and fluid forces in the presence of a lubricant, the outcome being the evaluation of particle's motion.…”

A Recursive Wheel Wear and Vehicle Dynamic Performance Evolution Computational Model for Rail Vehicles with Tread Brakes

“…Note that the presence of hard particulate matter in the contact patch increases the rail and wheel wear through various modes such as abrasion, indentation and scuffing [47]. In the real track scenario considered here, there can be some variation in the friction coefficient over the length of the track due to various reasons.…”

Particle extrusion in elastohydrodynamic line contacts: Dynamic forces and energy consumption

“…51 Given the complexity of the contact mechanics to analyse the passage of even a single particle through a contact, it comes as no surprise that numerical models are rare and variable in their features and limitations. According to the author's own research, [51][52][53][54][55][56][57][58][59][60][61][62][63] the model of the passage of a single particle through a concentrated contact with clearance smaller than the particle's minimum dimension includes the following elements: (a) particle entrainment via the lubricating medium prior to reaching the contact; 53 (b) particle entrapment based on force-equilibrium criteria once the particle is pinched; [57][58][59] (c) stress, strain and damage analysis during particle compression, including thermoelastic effects, [54][55][56] elastoplastic effects, 60 thermoelastoplastic effects 51 or thermoviscoplastic effects, 61 depending on the operating conditions, as well as geometrical effects in case of surface pile-up around dents 63 and tribochemical effects in cases of high frictional heating. 62 With a numerical model as the one just described, calculating contact forces on a squashing particle is part of the stress analysis.…”

“…In the author's latest ductile debris model, 51,60-62 recapitulated in Nikas 62 and with sub-models on particle entrapment in non-conformal line contacts 57 and both conformal and nonconformal elliptical contacts, 58,59 the previously stated shortcomings and simplifying assumptions are all eliminated. The model was gradually constructed with rigorous experimental validation in each of five successive development stages, adding micro-hardness modelling, 60 thermoelastoplasticity, 51 thermoviscoplasticity, 61 tribochemistry 62 and geometrical (surface pile-up) effects, 63 although the last two are not of concern in the present study.…”