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Thermal and Roughness Effects in a Tilted Pad Slider Bearing Considering Heat Conduction Through the Pad and Slider

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Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

This paper analyses the thermal and roughness effects on different characteristics of an infinitely long tilted pad slider bearing considering heat conduction through both the pad and slider. The roughness is assumed to be stochastic, Gaussian randomly distributed. Density and viscosity are assumed to be temperature dependent. The irregular domain of the fluid due to roughness is mapped to a regular domain so that the numerical method can be easily applied. The modified Reynolds equation, momentum equation, continuity equation, energy equation and the heat conduction equations on the pad and slider are solved simultaneously using finite difference method to yield various bearing characteristics. The solutions with respect to different pad and slider boundary conditions are elaborated through tables and figures.

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Abbreviations

B :

Bearing width

c :

Specific heat of lubricant

E c :

Eckert number

E :

Expected value operator

F :

Frictional drag force

h :

Nominal film thickness

h i :

Nominal film thickness at the leading edge

h o :

Nominal film thickness at the trailing edge

h 1 :

Heat transfer coefficient

H :

The height of the film for rough surface

k 0 :

Thermal conductivity of the lubricant

k p :

Thermal conductivity of the stationary solid

k s :

Thermal conductivity of the moving solid

m :

ho/hi

p :

Film pressure

P e :

Peclet number

p i :

Inlet pressure

P r :

Prandtl number

T :

Lubricant temperature

T 1 :

Pad temperature

T 2 :

Slider temperature

T a :

Ambient temperature

T i :

Inlet temperature

T avg :

Average temperature across the film

t p :

Nominal pad thickness

t s :

Nominal slider thickness

u :

Fluid velocity in the direction of sliding

U:

Velocity of the moving surface

v :

Velocity in the direction of y coordinate

x :

Coordinate in the direction of sliding

y :

Coordinate in the direction of film thickness

x 1, y 1 :

Coordinate system for the pad

x 2, y 2 :

Coordinate system for the slider

x ′ , y ′ :

Transformed coordinate system for the fluid film

x ′1 , y ′1 :

Transformed coordinate system for the pad

x ′2 , y ′2 :

Transformed coordinate system for the slider

W :

Load carrying capacity of the bearing

β:

Temperature coefficient in viscosity formula

δ:

Random distributions of roughness

ε:

Random variable

λ :

Temperature coefficient in density formula

μ:

Viscosity of the lubricant

μa :

Ambient viscosity

μ avg :

Average viscosity across the film

ρ:

Density of the lubricant

ρa :

Ambient density

ρ avg :

Average density across the film

σ2 :

Variation of roughness

Super script *:

Depicts a corresponding non dimensional quantity and bar above a variable depicts the corresponding expected value

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Acknowledgments

The authors would like to thank CV Raman International Fellowship for African Researchers for its financial support for the first author in the form of Visiting Fellowship at IIT Kanpur, India.

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Authors and Affiliations

  1. Department of Mathematics, Bahir Dar University, Bahir Dar, P.O. Box 79, Ethiopia

    Getachew Adamu

  2. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, 208016, India

    Prawal Sinha

Authors
  1. Getachew Adamu
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  2. Prawal Sinha
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Correspondence to Prawal Sinha.

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Adamu, G., Sinha, P. Thermal and Roughness Effects in a Tilted Pad Slider Bearing Considering Heat Conduction Through the Pad and Slider. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 82, 323–333 (2012). https://doi.org/10.1007/s40010-012-0046-4

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  • DOI: https://doi.org/10.1007/s40010-012-0046-4

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