# Numerical simulation of piston ring lubrication

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## Abstract

This paper describes a numerical method that can be used to model the lubrication of piston rings. Classical lubrication theory is based on the Reynolds equation which is applicable to confined geometries and open geometries where the flooding conditions are known. Lubrication of piston rings, however, fall outside this category of problems since the piston rings might suffer from starved running conditions. This means that the computational domain where the Reynolds equation is applicable (including a cavitation criteria) is unknown. In order to overcome this problem the computational domain is extended to include also the oil film outside the piston rings.The numerical model consists of a 2D free surface code that solves the time dependent compressible Navier-Stokes equations. The equations are cast in Lagrangian form and discretized by a meshfree moving least squares method using the primitive variables u, v, p for the velocity components and density, respectively. Time integration is performed by a third order Runge-Kutta method. The set of equations is closed by the Dowson-Higginson equation for the relation between density and pressure. Boundary conditions are the nonslip condition on solids and the equilibrium of stresses on the free surface. It is assumed that the surrounding gas phase has zero viscosity. Surface tension can be included in the model if necessary. The contact point where the three phases solid, liquid, and gas intersect is updated based on the velocity of the solid and the angle between the normals of the solid and the free surface.The numerical model is compared with the results from an analytical solution of the Reynolds equation for a fixed incline slider bearing. Then results from a more complicated simulation of piston ring lubrication are given and discussed. (C) 2007 Elsevier Ltd. All rights reserved.
Original language English Tribology International 41 9-10 914-919 0301-679X https://doi.org/10.1016/j.triboint.2007.11.018 Published - 2008 Yes

## Keywords

• Piston ring
• Reynolds equation
• Navier–Stokes equations
• Free surface
• Moving least squares