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Effect of random forcing on fluid lubricated bearing

Bailey, N.Y.; Hibberd, S.; Tretyakov, M.; Power, H.


N.Y. Bailey

S. Hibberd

H. Power


A model for a fluid lubricated bearing is derived for operation under conditions where external forces are subject to random fluctuations that may act to destabilise the bearing. The fluid flow through the bearing is described by a Reynolds equation for incompressible flow and is coupled to the axial displacement of the bearing faces as modelled by spring-mass-damper systems. Representative dynamics of a highly rotating bearing subject to external potentially destabilising random forcing is developed. An external force characterised by a noise term is imposed on the rotor, where both white noise and coloured noise are considered. For industrial applications it is important to evaluate potential bearing failure that can arise when the face clearance becomes sufficiently small. Therefore, a quantity of interest is the average time for the face clearance to reach a prescribed tolerance. A computational technique to evaluate the bearing characteristics is implemented based on a simple random walk for a Dirichlet problem for a linear parabolic partial differential equation combined with a Monte Carlo technique. Results of numerical experiments are presented, to give indicative predictions of possible face contact, which has the potential to result in bearing failure.


Bailey, N., Hibberd, S., Tretyakov, M., & Power, H. (2019). Effect of random forcing on fluid lubricated bearing. IMA Journal of Applied Mathematics, 84(3), 632–649.

Journal Article Type Article
Acceptance Date Mar 26, 2019
Online Publication Date May 2, 2019
Publication Date Jun 1, 2019
Deposit Date Apr 1, 2019
Publicly Available Date May 3, 2020
Journal IMA Journal of Applied Mathematics
Print ISSN 0272-4960
Electronic ISSN 1464-3634
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 84
Issue 3
Pages 632–649
Keywords Reynolds equation; Fluid lubricated bearing; Random forcing; Random walk; Monte Carlo technique
Public URL
Publisher URL
Additional Information This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record Nicola Y Bailey, Stephen Hibberd, Michael V Tretyakov, Henry Power, Effect of random forcing on fluid-lubricated bearing, IMA Journal of Applied Mathematics, , hxz007 is available online at


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