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 destabilize 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 destabilizing random forcing is developed. An external force characterized 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. Y., Hibberd, S., Tretyakov, M. V., & Power, H. (2019). Effect of random forcing on fluid-lubricated bearing. IMA Journal of Applied Mathematics, 84(3), 632-649. [hxz007]. https://doi.org/10.1093/imamat/hxz007