Linear stability analysis of long journal bearings: couple stress fluid model

TLDR: In this article, the authors derived a dynamic Reynolds-type equation governing the film pressure to account for the couple stress effects resulting from the non-Newtonian behavior of complex fluids.

Abstract: Purpose – The purpose of the present study is to provide the dynamic characteristics of long journal bearings lubricated with couple stress fluids.Design/methodology/approach – Based upon the micro‐continuum theory generated by Stokes, the dynamic Reynolds‐type equation governing the film pressure is derived to account for the couple stress effects resulting from the non‐Newtonian behavior of complex fluids. By applying the linear stability theory to the non‐linear equations of motion the journal rotor, the equilibrium positions and dynamic characteristics of the system are evaluated.Findings – As compared to the classical Newtonian model, the effects of couple stresses signify enhanced stiffness and damping coefficients (including KXX, KXY , BXX and BXY) at moderate values of the steady eccentricity ratio. Totally, as the rotor center operates at an eccentricity ratio about es≤0.71, long bearings lubricated with couple stress fluids under small disturbance results in a higher stability threshold speed th...