Problems Associated with Kinetics of Lubricant Degradation
by
Ilya I. Kudish
Department of Science and Mathematics, Kettering University, Flint, MI 48504
Coauthors: Ruben G. Hayrapetyan, Department of Science and Mathematics, Kettering University, Flint, MI 48504

The paper deals with modeling and analytical and numerical analysis of some problems associated with kinetics of degradation of polymer additives to lubricants. The additive is modeled by long polymer molecules with linear structure, dissolved in lubricant, that under action of shear stress may undergo scission. The first problem considered in the paper is a problem on degradation of polymer molecules in a fluid flow under action of a given shear stress. The problem is reduced to determining of a probabilistic distribution of polymer molecular weight as a function of time, spatial variables, and polymer molecule length from solution of an initial-value problem for a linear integro-differential kinetic equation. The probabilities involved in the kinetic equation are derived. An analytical analysis of the problem allowed for some general results such as solution existence and uniqueness and some of its properties including conservation of molecular weight to be obtained. A method of numerical solution of the kinetic equation is developed and realized. Based on the above analysis a second problem for a lubricated contact of moving elastic solids separated by degrading lubricant is formulated. The problem is reduced to a boundary-value problem for a system of ill-posed highly nonlinear integral and integro-differential equations. The problem is solved numerically. Different solution components depend on one to three variables. The lubricant degradation is determined along the lubricant flow streamlines. The solution possesses a remarkable topological structure that depends on the problem initial parameters. In most cases some components of the problem solution are discontinuous functions of spatial variables.

Date received: March 3, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caky-12.