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Research Papers: Elastohydrodynamic Lubrication

An Exact and General Model Order Reduction Technique for the Finite Element Solution of Elastohydrodynamic Lubrication Problems

[+] Author and Article Information
W. Habchi

Lebanese American University,
Department of Industrial
and Mechanical Engineering,
Byblos, Lebanon
e-mail: wassim.habchi@lau.edu.lb

J. S. Issa

Lebanese American University,
Department of Industrial
and Mechanical Engineering,
Byblos, Lebanon

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 3, 2016; final manuscript received October 19, 2016; published online May 15, 2017. Assoc. Editor: Xiaolan Ai.

J. Tribol 139(5), 051501 (May 15, 2017) (19 pages) Paper No: TRIB-16-1206; doi: 10.1115/1.4035154 History: Received July 03, 2016; Revised October 19, 2016

This work presents an exact and general model order reduction (MOR) technique for a fast finite element resolution of elastohydrodynamic lubrication (EHL) problems. The reduction technique is based on the static condensation principle. As such, it is exact and it preserves the generality of the solution scheme while reducing the size of its corresponding model and, consequently, the associated computational overhead. The technique is complemented with a splitting algorithm to alleviate the hurdle of solving an arising semidense matrix system. The proposed reduced model offers computational time speed-ups compared to the full model ranging between a factor of at least three and at best 15 depending on operating conditions. The results also reveal the robustness of the proposed methodology which allows the resolution of very highly loaded contacts with Hertzian pressures reaching several GPa. Such cases are known to be a numerical challenge in the EHL literature.

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References

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Figures

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Fig. 1

Geometry of a line contact (left) and circular contact (right)

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Fig. 2

Computational domain of a line contact

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Fig. 3

Computational domain of a circular contact

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Fig. 4

Extra coarse (left), normal (center), and extra fine (right) mesh cases for line contacts

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Fig. 5

Extra coarse (left), normal (center), and extra fine (right) mesh cases for circular contacts

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Fig. 6

Dimensionless central and minimum film thickness mesh sensitivity analysis for typical heavily loaded line contact (left) and circular contact (right) cases

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Fig. 7

Line contact dimensionless pressure and film thickness profiles for a typical lightly loaded contact (left) and highly loaded contact (right)

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Fig. 8

Circular contact dimensionless pressure and film thickness profiles for a typical lightly loaded contact (top) and highly loaded contact (bottom)

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Fig. 10

Effect of subsurface inclusions on line contact dimensionless Von Mises stress distribution within the solid containing the inclusion, for the case M = 10 and L = 10

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Fig. 9

Effect of subsurface inclusions on line contact dimensionless pressure (left) and film thickness (right) profiles for the case M = 10 and L = 10

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Fig. 11

Decay of normalized K̂ee coefficients with distance for a considered node in the vicinity of the contact center: line contact (top) and circular contact (bottom)

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Fig. 12

Dimensionless elastic deformation of the equivalent solid for the line contact case under unusual loading patterns: triangular (left) and step (right)

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Fig. 13

Dimensionless elastic deformation of the equivalent solid along the central line of the contact in the X-direction for the circular contact case under unusual loading patterns: conical (left) and step (right)

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Fig. 14

Dimensionless pressure and film thickness profiles for the line contact case with surface features: indent (left), bump (center), and waviness (right) for the case M=10, L=10, and ph=0.84 GPa

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Fig. 15

Dimensionless pressure and film thickness profiles along the central line of the contact in the X-direction for the circular contact with surface features: indent (left), bump (center), and waviness (right) for the case M=20, L=10, and ph=0.66 GPa

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