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.