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According to the Stokes microcontinuum theorem and Christensen's stochastic model, the main objective of this paper is to theoretically predict the combined influences of couple stresses and surface roughness on the lubrication performance of journal‐bearing systems. To take account of the presence of both the surface roughness of bearings and the couple stress effect due to the lubricant containing the polar suspensions, the generalized stochastic non‐Newtonian Reynolds‐type equation is derived. Compared to the Newtonian‐lubricant smooth‐bearing case, the couple stress effects and the longitudinal roughness improve the load carrying capacity, and thus decrease the attitude angle and friction parameter, while the effect of transverse roughness is opposite to that of the longitudinal one in the journal‐bearing system.

The purpose of this paper is to present a theoretical study of non-Newtonian effects in conical squeeze-film plates that is based on the Rabinowitsch fluid model.

A non-linear, modified Reynolds equation accounting for the non-Newtonian properties following the cubic stress law equation is derived. Through a small perturbation method, first-order closed-form solutions are obtained.

It is found that the non-Newtonian properties of dilatant fluids increase the load capacity and lengthen the response time as compared to the case using a Newtonian lubricant; however, the non-Newtonian behaviors of pseudoplastic lubricants result in reverse influences.

Numerical tables for squeeze-film loads of conical plates are also provided for engineering applications.