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THD analysis for slider bearing with roughness: special reference to load generation in parallel sliders

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Abstract

This paper analyzes the thermal and roughness effects on different characteristics of an infinite tilted pad slider bearing. The roughness is assumed to be stochastic, Gaussian randomly distributed. Density and viscosity are assumed to be temperature-dependent. In this study, two models of one-dimensional roughness, longitudinal and transverse, are considered. The irregular domain 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 and energy equation are coupled and solved using the finite difference method to yield various bearing characteristics. It is observed that for a non-parallel slider bearing, the load carrying capacity due to the combined effect is less than the load capacity due to the roughness effect for both models. However, in the case of a parallel pad slider bearing the reverse is true, though the load capacity is not significant. It is also observed that the load carrying capacity due to the combined effect is less than the load carrying capacity due to the thermal effect for the longitudinal roughness model, and it is the opposite for the transverse roughness model.

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Abbreviations

B:

bearing width

c:

specific heat of lubricant

E c :

Eckert number

E:

expected value operator

F :

friction force

h :

nominal film thickness

h i :

nominal film thickness at the leading edge

h o :

nominal film thickness at the trailing edge

H :

the height of the film for rough surface

k:

thermal conductivity of the lubricant

m :

ho/hi

P :

lubricant pressure

P e :

Peclet number

P i :

inlet pressure

P r :

Prandtl number

T :

lubricant temperature

T a :

ambient temperature

T i :

inlet temperature

T s :

temperature of the moving surface

T u :

temperature of the pad

T avg :

average temperature across the film

u :

fluid velocity in the direction of sliding

U :

velocity of the moving surface

v :

velocity in the direction of the y-coordinate

x :

coordinate in the direction of sliding

y :

coordinate in the direction of film thickness

x′, y′:

transformed coordinate system

W :

load carrying capacity of the bearing

β :

temperature coefficient in viscosity formula

δ :

random distribution of roughness

λ :

temperature coefficient in density formula

μ :

viscosity of the lubricant

μ a :

ambient viscosity

μ avg :

average viscosity across the film

ρ :

density of the lubricant

ρ a :

ambient density

ρ avg :

average density across the film

σ 2 :

variation of roughness

Superscript “*”:

denotes a corresponding non-dimensional quantity and a bar above a variable denotes the corresponding expected value

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Authors and Affiliations

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

    Prawal Sinha & Getachew Adamu

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

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Sinha, P., Adamu, G. THD analysis for slider bearing with roughness: special reference to load generation in parallel sliders. Acta Mech 207, 11–27 (2009). https://doi.org/10.1007/s00707-008-0094-7

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  • DOI: https://doi.org/10.1007/s00707-008-0094-7

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