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Lubricants 2015, 3(3), 493-521; doi:10.3390/lubricants3030493

Probability of Face Contact for a High-Speed Pressurised Liquid Film Bearing Including a Slip Boundary Condition

1
University Technology Centre in Gas Turbine Transmission Systems, Faculty of Engineering, University of Nottingham, Nottingham, NG7 2PB, UK
2
School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2PB, UK
3
Faculty of Engineering, University of Nottingham, Nottingham, NG7 2PB, UK
*
Author to whom correspondence should be addressed.
Academic Editors: Romeo P. Glovnea and Michel Fillon
Received: 29 January 2015 / Revised: 18 May 2015 / Accepted: 11 June 2015 / Published: 24 June 2015
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
View Full-Text   |   Download PDF [479 KB, uploaded 24 June 2015]   |  

Abstract

An initial deterministic mathematical model for the dynamic motion of a simple pressurised liquid film bearing is derived and utilised to evaluate the possibility of bearing contact for thin film operation. For a very thin film bearing the flow incorporates a Navier slip boundary condition as parametrised by a slip length that in general is subject to significant variability and is difficult to determine with precision. This work considers the formulation of a modified Reynolds equation for the pressurised liquid flow in a highly rotating coned bearing. Coupling of the axial motion of the stator is induced by prescribed axial oscillations of the rotor through the liquid film. The bearing gap is obtained from solving a nonlinear second-order non-autonomous ordinary differential equation, via a mapping solver. Variability in the value of the slip length parameter is addressed by considering it as a random variable with prescribed mean and standard deviation. The method of derived distributions is used to exactly quantify the impact of variability in the slip length with a parametric study investigating the effect of both the deterministic and distribution parameters on the probability of contact. Additionally, as the axial rotor oscillations also have a random aspect due to possible varying excitations of the system, the probability of contact is investigated for both random amplitude of the periodic rotor oscillations and random slip length, resulting in a two parameter random input problem. The probability of contact is examined to obtain exact solutions and evaluate a range of bearing configurations. View Full-Text
Keywords: Reynolds equation; slip condition; method of derived distribution; probability density function; face contact Reynolds equation; slip condition; method of derived distribution; probability density function; face contact
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Bailey, N.Y.; Cliffe, A.; Hibberd, S.; Power, H. Probability of Face Contact for a High-Speed Pressurised Liquid Film Bearing Including a Slip Boundary Condition. Lubricants 2015, 3, 493-521.

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