Investigation of the Convergence of a Multi-Grid Algorithm for Solving the Task of Pressure in the Thin Lubricating Film of the Non-Newtonian Fluid

Abstract

The article describes a multi-grid algorithm for integrating the Reynolds equation for hydrodynamic pressures in the lubricating film of a heavy-loaded journal bearing. This equation is the basic one in solving the tasks of designing friction units of piston- and rotary machines. Lubrication sources of various configurations in the form of grooves and holes located on the friction surfaces were taken into account. The version of the multi-grid algorithm developed by the authors is based on Brandt’s work. At each level of grids, not only the convergence of the solution is controlled, but also the rate of convergence. The pressure equation was approximated by finite differences using the control volume method and passed to a system of algebraic equations, which were solved by the Seidel method. Bessel formulas were used as the interpolation operator. The function for taking into account the non-Newtonian properties of the lubricant is based on the power law. Comparison of the developed algorithm with other versions showed high efficiency. The use of multi-grid algorithms makes it possible to perform multi-variant calculations of the dynamics of heavily loaded bearings. As a result of the calculations, the characteristics of the connecting rod bearing of the heat engine, as well as the multilayer bearing of the turbocharger, are presented.

On the Difference in the Action of Anti-Wear Additives in Hydrocarbon Oils and Vegetable Triglycerides

“…Several prior studies by the authors [28][29][30][31] support the concept of the adsorption mechanism of anti-wear additives in hydrocarbon oils. The models developed are based on the physico-chemical principles of secondary polymolecular adsorption of hydrocarbon liquid on metal surfaces that have been modified by surfactants, specifically AW additives.…”

“…This representation was chosen for the sole purpose of convenience in hydrodynamic calculations for sliding bearings with liquid lubrication. The calculations based on the aforementioned model are presented in [31] and reveal the coincidence of both calculated and experimental dependencies of force and friction coefficient on contact pressure.…”