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Hydrodynamic lubrication of squeeze-film porous bearings

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Summary

Closed-form analytical solutions for three different types of squeeze-film porous bearing are introduced in this paper. The effects of the permeability parameter on the pressure profile, load-carrying capacity, and time required to squeeze the fluid out of the lubricated conjunction are presented. The results show that as the permeability parameter increases, both the pressure profiles and the load-carrying capacity of the bearing decrease in the case of pure squeeze motion. Furthermore, the results show that for dimensionless permeability parameters less than 0.001, the effect of the porous layer on the hydrodynamic lubrication of squeeze-film porous bearings can be neglected.

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Abbreviations

c :

Clearance, m

e :

Eccentricity, m

h :

Film thickness, m

h p :

Porous layer thickness, m

k x :

Permeability of the porous layer inx-direction, m2

k y :

Permeability of the porous layer iny-direction, m2

k z :

Permeability of the porous layer inz-direction, m2

k 1 :

Permeability ratio

p :

Pressure within film region, Pa

p * :

Pressure within porous layer, Pa

P :

Dimensionless pressure within film region

P * :

Dimensionless pressure within porous layer

r :

Radial coordinate

\(\bar r\) :

Dimensionless radial coordinate

u a :

Velocity of surfacea inx-direction, m/s

u b :

Velocity of surfaceb inx-direction, m/s

v a :

Velocity of surfacea iny-direction, m/s

v b :

Velocity of surfaceb iny-direction, m/s

w :

Squeeze velocity, −∂h/∂t, m/s (w a =−w,w b =0)

w 0 :

Flow velocity into porous layer inz-direction, m/s

w z :

Load-carrying capacity per unit width, N/m

W z :

Dimensionless load-carrying capacity

x :

Coordinate, m

X :

Dimensionlessx-coordinate

y :

Coordinate, m

z :

Coordinate, m

Z :

Dimensionlessz-coordinate

γ:

Dimensionless parameter,l/h p

η:

Lubricant viscosity within film region, Pa s

η * :

Lubricant viscosity within porous layer, Pa s

η 0 :

Lubricant viscosity at atmospheric pressure, Pa s

ϱ:

Lubricant density within film region, Kg/m3

ϱ * :

Lubricant density within porous layer, Kg/m3

ϕ:

Circumferential coordinate, rad

ψ:

Dimensionless permeability parameter,\(k_z h_p /h_{0^3 } \)

ɛ:

Eccentricity ratio

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Author notes

  1. A. A. Elsharkawy

    Present address: Department of Mechanical and Industrial Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, 13060, Safat, Kuwait

  2. M. M. Nassar

    Present address: Department of Mathematics, College of Technological Studies, Safat, Kuwait

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    1. A. A. Elsharkawy
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    2. M. M. Nassar
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    Elsharkawy, A.A., Nassar, M.M. Hydrodynamic lubrication of squeeze-film porous bearings. Acta Mechanica 118, 121–134 (1996). https://doi.org/10.1007/BF01410512

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