Effects of Stochastic Roughness on the Performance of Magnetic-Fluid-based Hydrodynamic Bearings

This paper presents a novel formulation of the Reynolds Equation for magnetohydrodynamical ferrofluid lubricated bearings with stochastic roughness. An advanced form of Reynolds-type Equation is derived on the basis of stochastic analysis. The proposed equation formulation, utilizing Stein's Lemma to calculate variational derivatives of the pressure and magnetic field with respect to roughness variables, differs from deterministic Reynolds Equations and other previously published approaches that consider surface roughness in a stochastic way. The proposed methodology is compared with and validated against relevant results found in the literature. It is applied to characterize the tribological performance of rough surface sliders and journal bearings, using ferrofluids as lubricants, over a wide range of bearing geometries, operational parameters, and magnetic properties.