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Boundary slippage for generating hydrodynamic load-carrying capacity

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Abstract

Boundary slippage is used to generate the load-carrying capacity of the hydrodynamic contact between two parallel plane surfaces. In the fluid inlet zone, the fluid-contact interfacial shear strength on a stationary surface is set at low to generate boundary slippage there, while in the fluid outlet zone the fluid-contact interfacial shear strength on the stationary surface is set at high enough to prevent the occurrence of boundary slippage. The fluid-contact interfacial shear strength on the entire moving surface is set at high enough to prevent boundary slippage on the moving surface. These hydrodynamic contact configurations are analyzed to generate the pronounced load-carrying capacity. The optimum ratio of the outlet zone width to the inlet zone width for the maximum load-carrying capacity of the whole contact is found to be 0.5.

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Abbreviations

c 1 :

integral constant

c 2 :

integral constant

G :

3ψ/(1 + 4ψ)(1 + ψ)

h :

fluid film thickness

H :

dimensionless fluid film thickness

l 1 :

width of the “A” sub-zone

l 2 :

width of the “B” sub-zone

p :

fluid pressure

p max :

maximum fluid pressure

P max :

dimensionless maximum fluid pressure

q :

fluid mass flow through the contact per unit contact length

q v :

fluid volume flow through the contact per unit contact length

u :

sliding speed between two surfaces

U :

dimensionless sliding speed between two surfaces

ū a :

fluid film velocity at the top boundary

u a :

speed of the upper contact surface

ū b :

fluid film velocity at the bottom boundary

u b :

speed of the lower contact surface

w :

carried load per unit contact length

w max :

maximum carried load per unit contact length

W :

dimensionless load per unit contact length of the contact

x :

coordinate shown in Fig. 1

ρ :

fluid density

λ 1 :

3τ sa/2h − 3uη/h 2 − 3q v η/h 3

λ 2 :

−6uη/h 2 − 12q v η/h 3

ψ :

l1/l2

η :

fluid viscosity

τa, τb:

shear stresses at the top and bottom boundaries respectively

τ a,A :

shear stress at the top boundary in the “A” sub-zone

τ b,B :

shear stress at the bottom boundary in the “B” sub-zone

τ sa :

fluid-contact interfacial shear strength in the “B” sub-zone at the top boundary

τ sa,A :

fluid-contact interfacial shear strength at the upper plane surface in the “A” subzone

τ sb :

fluid-contact interfacial shear strength at the lower plane surface

Δu a :

fluid slipping velocity at the top boundary in the “B” sub-zone

\( \bar \tau \)a,A, \( \bar \tau \)b,B:

dimensionless fluid-contact interfacial shear stresses respectively

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Authors and Affiliations

  1. Huaihai Institute of Technology, Lianyungang, 222005, Jiangsu Province, P. R. China

    Yong-bin Zhang  (张勇斌)

Authors
  1. Yong-bin Zhang  (张勇斌)
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Corresponding author

Correspondence to Yong-bin Zhang  (张勇斌).

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Communicated by ZHOU Zhe-wei

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Zhang, Yb. Boundary slippage for generating hydrodynamic load-carrying capacity. Appl. Math. Mech.-Engl. Ed. 29, 1155–1164 (2008). https://doi.org/10.1007/s10483-008-0905-y

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  • DOI: https://doi.org/10.1007/s10483-008-0905-y

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

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