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RESEARCH PAPERS

Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts

[+] Author and Article Information
Yuchuan Liu1

Center for Surface Engineering and Tribology, Northwestern University, Evanston, IL 60208ycliu@northwestern.edu

Q. Jane Wang

Center for Surface Engineering and Tribology, Northwestern University, Evanston, IL 60208

Wenzhong Wang, Yuanzhong Hu

State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China

Dong Zhu

Innovation Center, Eaton Corporation, Southfield, MI 48037

1

Corresponding author. MCC Mechanical Engineering, 2145 Sheridan Rd, Room B224, Evanston, IL 60208.

J. Tribol 128(3), 641-653 (Mar 02, 2006) (13 pages) doi:10.1115/1.2194916 History: Received June 02, 2005; Revised March 02, 2006

This paper investigates the effects of differential scheme and mesh density on elastohydrodynamic lubrication (EHL) film thickness based on a full numerical solution with a semi-system approach. The solution variation with different schemes and mesh sizes is revealed based on a set of numerical cases in a wide range of central film thickness from several hundred nanometers down to a few nanometers. It is observed that when the film is thick, the effects of differential schemes and mesh density are not significant. However, if the film becomes ultra-thin, e.g., below 10–20 nanometers, the influence of mesh density and differential schemes becomes more significant, and a proper dense mesh and differential scheme may be highly desirable. The present study also indicates that the solutions from the 1st-order backward scheme give the largest film thickness among all the solutions from different schemes at the same mesh size.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Profiles of dimensionless pressure, film thickness, and first-order film thickness derivative along the centerline in a Hertzian contact

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Figure 2

Present results obtained from the working conditions in (21)

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Figure 3

Comparison of coefficient contributions between the Couette flow and the Poiseuille flows for a smooth case: (a) distributions of pressure and film thickness, (b) distribution of coefficient α in Eq. 10, (c) distribution of coefficient β in Eq. 10, (d) distribution of coefficient γ in Eq. 10, and (e) distribution of coefficient δ in Eq. 10

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Figure 4

Comparison of coefficient contributions between the Couette flow and the Poiseuille flows for a case involving a sinusoidal rough surface: (a) distributions of pressure and film thickness, (b) distribution of coefficient α in Eq. 10, (c) distribution of coefficient β in Eq. 10, (d) distribution of coefficient γ in Eq. 10, and (e) distribution of coefficient δ in Eq. 10

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Figure 5

Effect of entrainment speed on the shapes of film thickness and pressure: film thickness and pressure profiles along the centerline (a) in X direction and (b) in Y direction

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Figure 6

Effect of differential scheme on the shapes of film thickness and pressure: film thickness and pressure profiles along the centerline (a) in X direction and (b) in Y direction

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Figure 7

Variation of film thickness as mesh number increases for U=1250mm∕s: (a) central film thickness and (b) minimum film thickness

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Figure 8

Variation of film thickness as mesh number increases for U=312.5mm∕s: (a) central film thickness and (b) minimum film thickness

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Figure 9

Variation of film thickness as mesh number increases for U=100mm∕s: (a) central film thickness and (b) minimum film thickness

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Figure 10

Variation of film thickness as mesh number increases for U=30mm∕s: (a) central film thickness and (b) minimum film thickness

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Figure 11

Variation of film thickness as mesh number increases for U=10mm∕s: (a) central film thickness and (b) minimum film thickness

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Figure 12

Variation of film thickness as mesh number increases for U=3mm∕s: (a) central film thickness and (b) minimum film thickness

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Figure 13

Variation of film thickness as mesh number increases for U=1mm∕s: (a) central film thickness and (b) minimum film thickness

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