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Surface roughness effects on squeeze film behavior in porous circular disks with couple stress fluid

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Abstract

The effect of surface roughness on squeeze film behavior between two circular disks with couple stress lubricant is analyzed when the upper disk has porous facing which approaches the lower disk with uniform velocity. The modified Stochastic Reynolds equation is derived on the basis of Stokes micro-continuum theory for couple stress fluid and Christensen Stochastic theory for the rough surface. Closed form solution of the Stochastic Reynolds equation is obtained in terms of Fourier–Bessel series. The importance of roughness and couple stress on bearing characteristics are presented in terms of load carrying capacity, squeeze time, and relative percentage of the load. It is observed that, effect of couple stress fluid, and surface roughness is more pronounced compared to classical case. These predictions enable design engineers to choose suitable parameters.

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Abbreviations

a :

Outer radius of the plate

c :

Maximum asperity deviation from the nominal film height

c′ n :

Fourier coefficient

C :

Non-dimensional roughness parameter \({(=\frac{c}{h_0})}\)

E :

Expectancy operator

f :

Probability density function

h :

Nominal film height

\({\bar{{h}}}\) :

Non-dimensional film height \({(=\frac{h}{h_0})}\)

h s :

Deviation of film height from nominal level

H :

Film thickness (= h + h s)

\({\bar{{h}}}\) :

Non-dimensional film thickness \({(=\bar{{h}}+\bar{{h}}_{\rm s})}\)

H * :

Film thickness of the porous layer

\({\bar{{H}}^{{\ast}}}\) :

Non-dimensional film thickness of the porous layer

J 0 :

Bessel function of first kind of zeroth order

l :

Couple stress parameter (= (μ /η)1/2)

p :

Pressure in the film region

\({\bar{{p}}}\) :

Non-dimensional pressure in the fluid region

p * :

Pressure in the porous region

r :

Radial co-ordinate

T :

Non-dimensional squeeze film time

u,w :

Velocity components in r and z-directions respectively

u *,w * :

Darcy’s velocity components in the porous region

\({\bar{{w}}_0}\) :

Modified form of the Darcy’s law

E(W):

Mean load carrying capacity

\({\bar{{W}}}\) :

Non-dimensional mean load carrying capacity

α n :

Nth eigenvalue

β:

Ratio of microstructure size of polar additives to the pore size

μ:

Viscosity of the lubricant

η:

Material constant

τ:

Non-dimensional couple stress parameter

ξ:

Random variable

θ:

Angular co-ordinate

ϕ:

Permeability parameter

ψ:

Non-dimensional permeability parameter

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Authors and Affiliations

  1. Department of Mathematics, Karnatak University, Dharwad, 580 003, India

    N. M. Bujurke

  2. Department of Mathematics, SDM College of Engineering & Technology, Dharwad, 580 002, India

    D. P. Basti

  3. Tata Institute of Fundamental Research, Indian Institute of Science campus, Bangalore, 560 012, India

    Ramesh B. Kudenatti

Authors
  1. N. M. Bujurke
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  2. D. P. Basti
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  3. Ramesh B. Kudenatti
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Correspondence to N. M. Bujurke.

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Bujurke, N.M., Basti, D.P. & Kudenatti, R.B. Surface roughness effects on squeeze film behavior in porous circular disks with couple stress fluid. Transp Porous Med 71, 185–197 (2008). https://doi.org/10.1007/s11242-007-9119-2

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  • DOI: https://doi.org/10.1007/s11242-007-9119-2

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