Mathematical model of a micropolar lubricating stuff

Abstract

The article is devoted to the mathematical analysis model of the radial bearing of infinite length, lubricated with lubricating stuff and molten low-melting metal coating on the surface of the bearing bush, having the general rheological properties in the laminar condition of micro-polar lubrication properties, taking into account the dependence of viscosity rheological properties of micro-polar lubricating stuff, and the permeability of the porous coating from the pressure. The authors on the basis of the motion equations of a viscous incompressible fluid having micro-polar properties, and for “lamina”, of the continuity equation, Darcy equation and determining from the expression for the dissipation rate of mechanical energy, the profile of molten contour of the bearing bush, while taking account of the dependence of the overall rheological properties of the lubricating stuff and melt the low-melting metal coating having the micro-polar properties and the permeability of the porous coating of the pressure found the asymptotic and exact self-similar solution of the differential equation system on the parameter, due to the melt and the dissipation rate of mechanical energy to zero (without melt) and first (including melt) approximation.