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On the basis of Stokes theory and the Christensen's stochastic model, the combined effects of couple stresses and surface roughness on the instability threshold of hydrodynamic rotor bearings are theoretically studied. The film pressure is solved from the generalized stochastic non-Newtonian Reynolds-type equation and applied to evaluate the equilibrium solution of a short journal bearing. By using the linear theory, the eight oil-film stiffness and damping coefficients as well as the vibrational stability boundary were determined. According to the results obtained, the presence of couple stresses accompanied with a longitudinal roughness provides an increase in the values of stiffness coefficients K XX , K XY and K YX as well as the damping coefficient C XX , and results in a higher stability threshold speed. Whereas, when compared to the smooth bearing lubricated with couple stress fluid, a decrease in the threshold speed is found in the case of transverse roughness.

Based upon the Shliomis ferromagnetic fluid model and the Stokes microcontinuum theory incorporating with the Christensen stochastic model, a modified Reynolds equation of centrosymmetric squeeze films has been derived in this paper. The Reynolds equation includes the combined effects of non-Newtonian rheology, magnetic fluids with applied magnetic fields, rotational inertia forces, and surface roughness. To guide the use of the derived equation, the squeeze film of rotational rough-surface circular disks lubricated with non-Newtonian magnetic fluids is illustrated. According to the results obtained, the effects of rotation inertia decrease the load capacity and the squeeze film time of smooth circular disks. By the use of non-Newtonian magnetic fluids with applied magnetic fields, the rotational circular disks predict better squeeze film performances. When the influences of circumferential roughness patterns are considered, the non-Newtonian magnetic-fluid lubricated rotational rough disks with applied magnetic fields provide further higher values of the load capacity and the squeeze film time as compared to those of the smooth case.