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Prediction of the film thickness for the normal approach of a rigid sphere towards a thin soft layer

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Abstract

A semi-analytical solution to the problem of the squeeze film between a rigid sphere and a thin soft layer attached firmly to rigid foundation is presented. It is assumed that the shapes of the solids are the same as the elastically deformed shapes under the unlubricated conditions (the Grubin’s approximation). Formulae for the variation of the film thickness with time are presented in the full range of Poisson’s ratio \(0\leq\nu\leq 0.5\) using two different pressure boundary conditions. It was found that only the magnitude of the film thickness predicted for an incompressible layer (ν=0.5), is influenced by the type of the pressure condition considered in the analysis.

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Abbreviations

a :

contact radius

d :

layer thickness

D :

dimensionless layer thickness, (\(\frac{a}{d}\))

E :

Young’s modulus of elasticity

h :

film thickness

H :

dimensionless film thickness (\(\frac{h}{R}\))

p :

pressure

p 0 :

pressure at r=0

R :

spherical punch radius

t :

time

T :

dimensionless time, (\(\frac{\alpha t}{\eta}\))

w :

applied load

W :

dimensionless load, ( \(\frac{w}{\alpha R^2}\))

α:

elastic constant, ( \(\frac{2E}{(1-\nu^2)}\))

β:

elastic constant, ( \(\frac{(1-\nu)^2}{(1-2\nu)}\))

η:

fluid viscosity

ν:

Poisson’s ratio

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Authors and Affiliations

  1. School of Engineering and Technology, De Montfort University, The Gateway, Leicester, LE1 9BH, UK

    M.J. Jaffar

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  1. M.J. Jaffar
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Jaffar, M. Prediction of the film thickness for the normal approach of a rigid sphere towards a thin soft layer. Tribol Lett 22, 247–251 (2006). https://doi.org/10.1007/s11249-006-9077-9

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  • DOI: https://doi.org/10.1007/s11249-006-9077-9

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