Behavior of the Lubricating Film between Sinusoidal Roughened Surfaces: Theoretical and Numerical Approaches with MATLAB Applications

Behavior of the Lubricating Film between Sinusoidal Roughened Surfaces: Theoretical and Numerical Approaches with MATLAB Applications

Leonid Burstein (Kinneret Academic College, Jourdan Valley, Israel)
DOI: 10.4018/IJSEIMS.2015010102
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Abstract

A theoretical model of roughened sliding surfaces with a sinusoidal profile is applied in the context of determining the pressure distribution, positive load support, and maximal hydrodynamic pressure in the lubricating film. Considered are surfaces with identical asperity heights and wave number characteristics. The obtained relations are verified numerically with the aid of the bvp4c solver and other functions for numeric calculations of the MATLAB® program. The influence of the wave number and asperity heights on the load support and maximal positive pressure is investigated parametrically over the wide range of gap-to-asperity-height ratios and wave number roughness characteristics. In addition, the cavitation and maximal pressures are compared. Specially developed MATLAB® programs permit to calculate pressure distribution, positive load support, and maximal hydrodynamic pressure in the lubricating film by the derived expressions.
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Roughness Model

The analysis is carried out for mechanical parts with roughened surfaces having an identical integer number of sinusoidal waves, k, and identical asperity heights, Ra, on each surface.

The profile geometry of two surfaces with equal roughness parameters, the upper moving at constant velocity and the lower fixed, is shown in Fig.1.

Figure 1.

Schematic of Roughened Surface Geometry at Wave Number k= 5, Clearance-Asperity Height Number A=/(h+2)=0.25 (dimensionless), and Phase Displacement φ=1/ (4k)

The analysis comprises the following phases: coordinate-time-dependent solution of the Reynolds equation for the hydrodynamic pressure in the lubricating film, deriving load support and maximal pressure expressions; numerical verifications of derived expressions by the comparison of the theoretical and numerical solutions – all this for a variety of wave numbers and asperity heights.

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