Mathematical Analysis of the Entrapment of Solid Spherical Particles in Non-Conformal Contacts

The process of entrapment of small spherical particles in both lubricated and dry, line, and point contacts, is mathematically analyzed and a criterion is postulated in order to evaluate the possibility of entrapment. The analysis is generalized for non-conformal contacts, operating under mixed rolling-sliding conditions with emphasis given to elastohydrodynamic contacts. This study aims to provide the methods, suitable for easy computer programming, to evaluate the risks of surface damage from small debris particles in machine element applications and to make the selection of proper filtration more confined.