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1

Pseudo-Gaussian Density Functions for Gap Height Between Two Surfaces

Wierzcholski K. Ch., Nowakowska K.

Journal of Applied Computer Science

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2010

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Vol. 18, nr 2

79-90

EN

The presented paper formulates the sequence of pseudo-Gaussian distributions where are presented the mathematical results of standard deviation and probability density function derivations for bio-and micro-bearing gap height on the basis of Mow, Dowson, Cwanek, Wierzcholski experimental results. The mathematical derivation of the optimum probability density functions and least standard deviation are illustrated in two cases. The first case relates to the height of the gap if vibration and unsteady load causes the random changes. The second case relates to the height of the gap if the asperities of the cartilage surface roughness cause the random changes. Author formulates one Theorem and some Corollaries where the sequence of pseudo-Gaussian-distributions are derived. The presented proof shows, that such sequence is convergent to the Gaussian distribution in infinity.

2

Magnetic fluid based squeze film behaviour between rotating porous circular plates with a concentric circular pocket and surface roughness effects

Patel R. M., Deheri G. M.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 2

271-277

EN

Efforts have been made to analyze the magnetic fluid based squeeze film between rotating porous circular plates with a concentric pocket. The porous housing is considered to be elastically negligibly deformable with its contact surface rough. The stochastic film thickness characterizing the roughness is considered to be asymmetric with zero mean and non-zero variance. The modified Reynolds' equation is solved in order to get pressure distribution which in turn, is used to obtain the expression for load carrying capacity. Then by making use of this expression we find the response time. These expressions are numerically computed and the results are presented graphically as well as in a tabular form. It is observed that the presence of pocket and the roughness of the surfaces affect the performance of the bearing adversely. However, the performance of the bearing gets enhanced due to negatively skewed roughness and the magnetic fluid.

3

Effect of transverse surface roughness on the behaviour of squeeze film in a spherical bearing

Andharia P. I., Gupta J. L., Deheri G. M.

Applied Mechanics and Engineering

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1999

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Vol. 4, no spec.

19-24

EN

Effect of transverse roughness on the behaviour of a hydrodynamic squeeze film between a non-rotating spherical surface and a hemispherical bearing under a steady load is discussed. It is assumed that the bearing surface as well as the surface of the approaching sphere have random roughness which is distributed throughout the surfaces. The stochastic film thickness characterizing the roughness is assumed to be symmetric with non-zero mean (a) and variance (s2). The modified Reynolds equation is solved and then the expressions for pressure, load carrying capacity and the response time are obtained and numerically computed. The results are presented both in graphical as well as tabular form. It is observed that the composite roughness of the surfaces affects the performance of the bearing adversely.