Calculation of operational parameter variation of infinitely long slider bearings with stochastic roughness

In the framework of stochastic representation of surface roughness, a novel Reynolds-type Equation has been derived recently by the authors and utilized to calculate the average values of a bearing’s operational parameters. To acquire an improved insight to the hydrodynamic lubrication phenomena in rough bearings, the stochasticity of the operational parameters should be described, by calculating their higher-order moments, such as the variation. The present work aims at deriving equations for calculation and quantification of these higher-order moments. More specifically, in the present paper equations for the variation of a slider bearing operational parameters (pressure, load carrying capacity, friction force and friction coefficient) are derived. The obtained results are validated against the deterministic Reynolds Equation solution, for a series of bearings with different random Gaussian surface roughness profiles, over a wide range of bearing design and operational parameters. •Stochastic implementation of the surface roughness profiles as Gaussian variables.•Hydrodynamically lubricated bearings with surface roughness on the bearing and slider.•Utilization of Stein’s Lemma, novel stochastic calculus theorem of probability theory.•Mathematical derivation of novel equations for calculating the variance of critical bearing’s operational parameters.•Validation of acquired equations via numerical simulations and with existing results found in literature.