Multigrid method for the solution of thermal elastohydrodynamic lubrication point contact problem with surface asperities

Vishwanath B. Awati; Parashuram M. Obannavar; Mahesh Kumar Nanjaiah

doi:10.59400/mea.v1i1.94

Vishwanath B. Awati Department of Mathematics, Rani Channamma University, Belagavi 591156, India
Parashuram M. Obannavar Department of Mathematics, Rani Channamma University, Belagavi 591156, India
Mahesh Kumar Nanjaiah Department of Mathematics, Rani Channamma University, Belagavi 591156, India

Article ID: 94

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DOI: https://doi.org/10.59400/mea.v1i1.94

Keywords: thermal; EHL; multigrid method; FAS; slide to roll ratio; MLMI

Abstract

The paper presents the numerical investigation of point contact thermal elasto-hydrodynamic lubrication (EHL) with surface asperities analyzed. The effect of temperature and surface roughness on fluid film thickness is studied in detail. The governing equations comprise Reynolds, film thickness, load balance, and energy equations with appropriate boundary conditions. The second-order finite difference approximation is used to discretize the governing equations, and the resultant nonlinear system of algebraic equations is solved using the Multigrid V-cycle with full approximation scheme (FAS) technique. The multi-level multi-integration (MLMI) technique is employed to solve the film thickness equation. The obtained results are illustrated in the form of graphs and tables that are comparable with earlier findings. The film thickness profiles show dimples near the outlet region due to the temperature-viscosity wedge mechanism. Isothermal minimum film thickness is higher than the thermal minimum film thickness. Minimum film thickness is much smaller due to the slide-to-roll ratio being positive as compared to negative, whereas the behavior of central film thickness is in contrast to that of minimum film thickness.

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