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Research Papers: Hydrodynamic Lubrication

A Comparison of the Roughness Regimes in Hydrodynamic Lubrication

[+] Author and Article Information
John Fabricius, Afonso Tsandzana, Peter Wall

Department of Engineering Sciences
and Mathematics,
Luleå University of Technology,
Luleå SE-971 87, Sweden

Francesc Perez-Rafols

Department of Applied Physics and
Mechanical Engineering,
Luleå University of Technology,
Luleå SE-971 87, Sweden

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 15, 2016; final manuscript received January 26, 2017; published online May 17, 2017. Assoc. Editor: Mihai Arghir.

J. Tribol 139(5), 051702 (May 17, 2017) (10 pages) Paper No: TRIB-16-1087; doi: 10.1115/1.4035868 History: Received March 15, 2016; Revised January 26, 2017

This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, with small roughness wavelength μ, so that the film thickness h becomes rapidly oscillating. Depending on the limit of the ratio h/μ, denoted as λ, three different lubrication regimes exist: Reynolds roughness (λ = 0), Stokes roughness (0 < λ < ∞), and high-frequency roughness (λ = ∞). In each regime, the pressure field is governed by a generalized Reynolds equation, whose coefficients (so-called flow factors) depend on λ. To investigate the accuracy and applicability of the limit regimes, we compute the Stokes flow factors for various roughness patterns by varying the parameter λ. The results show that there are realistic surface textures for which the Reynolds roughness is not accurate and the Stokes roughness must be used instead.

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References

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Figures

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Fig. 1

Asymptotic lubrication regimes (μ → 0)

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Fig. 3

Geometries: (a) sawtooth groove, (b) cylindrical groove, (c) cosinusoidal groove, (d) cosinusoidal dimple, (e) conical dimple, and (f) bisinusoidal dimple

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Fig. 4

Stokes flow in sawtooth geometry (λ = 1): (a) velocity and (b) pressure

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Fig. 5

The flow factors a11λ,a110, and a11∞ (sawtooth groove)

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Fig. 6

Stokes flow in cylindrical geometry (λ = 1): (a) velocity and (b) pressure

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Fig. 7

The flow factors a11λ,a110, and a11∞ (cylindrical groove)

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Fig. 8

Stokes flow in cosinusoidal geometry (λ = 1): (a) velocity and (b) pressure

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Fig. 9

The flow factors a11λ,a110, and a11∞ (cosinusoidal groove)

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Fig. 10

Stokes flow in cosinusoidal dimple geometry (cut plane y2 = 0.5): (a) w1 (λ = 1) and (b) q1 (λ = 1)

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Fig. 11

Stokes flow in cosinusoidal dimple geometry (cut plane z = 0.5): (a) w1 (λ = 1) and (b) q1 (λ = 1)

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Fig. 12

q1 (λ = 0, cosinusoidal dimple)

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Fig. 13

The flow factors a11λ,a110, and a11∞ (cosinusoidal dimple)

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Fig. 14

Stokes flow in conical dimple geometry (cut plane y2 = 0.5): (a) w1 (λ = 1) and (b) q1 (λ = 1)

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Fig. 15

Stokes flow in conical dimple geometry (cut plane z = 0.5): (a) w1 (λ = 1) and (b) q1 (λ = 1)

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Fig. 16

q1 (λ = 0, conical dimple)

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Fig. 17

The flow factors a11λ,a110, and a11∞ (conical dimple)

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Fig. 18

Periodic flow in bisinusoidal dimple geometry (cut plane y2 = 0.5): (a) w1 (λ = 1) and (b) q1 (λ = 1)

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Fig. 19

Periodic flow in bisinusoidal dimple geometry (cut plane z = 0.5): (a) w1 (λ = 1) and (b) q1 (λ = 1)

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Fig. 20

q1 (λ = 0, bisinusoidal dimple)

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Fig. 21

The flow factors a11λ,a110, and a11∞ (bisinusoidal dimple)

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