Research Papers: Hydrodynamic Lubrication

Homogenization of the Reynolds Equation Governing Hydrodynamic Flow in a Rotating Device

[+] Author and Article Information
Andreas Almqvist

Division of Machine Elements, Luleå University of Technology, Luleå 97187, Swedenandreas.almqvist@ltu.se

Since the problem is stated in cylindrical coordinates.

J. Tribol 133(2), 021705 (Mar 23, 2011) (8 pages) doi:10.1115/1.4003650 History: Received August 25, 2010; Revised December 18, 2010; Published March 23, 2011; Online March 23, 2011

In this paper, a method facilitating the analysis of the effects of surface roughness on the lubrication of a rotating device is presented. The analysis utilizes homogenization—a suitable technique for averaging the effects of roughness as modeled by the Reynolds equation. The originality of this work lies in a novel way of deriving the so called local problems, also known as microbearing problems. It is clearly shown how this increases the computational efficiency by eliminating the dependence of the global coordinates on the formulation of these local problems. This does not only speed up the computation, it also means that the derived flow factors or flow tensors require less storage space. To provide for good usability, alongside the flow factors for the averaged Reynolds equation, the correction factors for the averaged friction torque (and force) and the expression for averaged load carrying capacity are presented here.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Illustration of the artificial scaling effect that arises due to modeling in cylindrical coordinates

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Figure 2

Illustrating the Cartesian approach of repeating the surface roughness pattern a

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Figure 3

Pressure solutions. Cylindrical ε=2−2 (left), Cartesian ε=2−2 (middle), and homogenized (right).

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Figure 4

The difference between the Cartesian and cylindrical pressure solutions for ε=2−2, 2−3, and 2−4

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Figure 5

The difference between the Cartesian and cylindrical homogenized pressure solutions

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Figure 6

An illustration of the type of structured mesh employed in the computations of the global problems



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