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Surface roughness effects in dynamically loaded short bearings

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Summary

In this paper, the stochastic theory developed by Christensen is applied to the analysis of dynamically loaded short rough bearings. Approximate polynomial in place of Gaussian is used to represent the roughness height. To make the analysis applicable in real lubrication situations, it is assumed that the surface roughness and the minimum film thickness are of the same order. Attention is focussed on cyclic squeeze films under sinusoidal loading. It is concluded that the load is increased in the longitudinal case as compared with the transverse case. This happens due to excessive side leakage in the latter case. The effect of roughness is much more pronounced at the time when the load reverses its direction in both longitudinal and transverse cases.

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Abbreviations

c :

radial clearance

D :

diameter of the journal

e :

eccentricity

E():

expectation of ()

f(h s ):

probability density function

h :

film thickness

h n :

nominal film thickness

h s :

asperity height

H n :

dimensionless nominal film thickness

L 0 :

bearing length in the axial direction

n :

revolutions per unit time

p :

hydrodynamic pressure

P 0 :

unit loading

R :

radius of journal

S:

Sommerfeld number

t :

time

T :

dimensionless time

U :

tangential velocity of the journal

V 0 :

normal velocity of the journal centre

ω:

angular velocity of the journal

ω L :

frequency of applied load

ω p :

frequency of oscillation

W :

load capacity

W a :

mean amplitude of the load

W 0,W π/2 :

load components along and perpendicular to the line of centres

ε:

eccentricity ratio (=e/c)

μ:

Newtonian viscosity

σ:

standard deviation of the asperity height distribution

\(\bar \sigma \) :

dimensionless quantity (=σ/c)

Φ:

attitude angle

Ψ:

angle between vertical line and load line

ξ:

random variable

References

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Author notes

  1. A. Raj

    Present address: Department of Mathematics, Voorhees College, 632001, Vellore, India

  2. P. Sinha

    Present address: Department of Mathematics, Indian Institute of Technology Kanpur, 208016, Kanpur, India

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    1. A. Raj
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    2. P. Sinha
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    Raj, A., Sinha, P. Surface roughness effects in dynamically loaded short bearings. Acta Mechanica 101, 199–213 (1993). https://doi.org/10.1007/BF01175606

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