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

Elena Zadorozhnaya (), Igor Levanov, Igor Mukhortov and Vlad Hudyakov
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Elena Zadorozhnaya: Department of Motor Transport, Institute of Engineering and Technology, South Ural State University, 76 Prospekt Lenina, 454080 Chelyabinsk, Russia
Igor Levanov: Department of Motor Transport, Institute of Engineering and Technology, South Ural State University, 76 Prospekt Lenina, 454080 Chelyabinsk, Russia
Igor Mukhortov: Department of Motor Transport, Institute of Engineering and Technology, South Ural State University, 76 Prospekt Lenina, 454080 Chelyabinsk, Russia
Vlad Hudyakov: Department of Motor Transport, Institute of Engineering and Technology, South Ural State University, 76 Prospekt Lenina, 454080 Chelyabinsk, Russia

Mathematics, 2022, vol. 11, issue 1, 1-18

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.

Keywords: multi-grid algorithm; hydrodynamic pressures; journal bearing; non-Newtonian fluids; highly viscous boundary layer (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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