Stability analysis of hydrodynamic journal bearings with variable axial geometrical configuration using titanium dioxide nanoparticles as lubricant additives

The dynamic stability of high-speed rotor systems is highly dependent on the interaction between bearing geometry and lubricant rheology. The present work examines the stability of hydrodynamic journal bearings with four different axial configurations: conical (wedge), concave, convex, and wavy, lubricated with TiO₂ nanofluids. The integration of a modified Krieger-Dougherty viscosity model that takes into consideration packing fractions and nanoparticle aggregation, extending beyond conventional static volume-fraction assumptions, is an important advance of this work. The governing Reynolds-like equation is expressed in curvilinear coordinates and numerically solved to determine the transition between stable and unstable vibrations. The results show that nanoparticle aggregate size and packing percent strongly influence the critical stability number, with larger aggregation generally improving the stable working range. The stability limitations are studied using a numerical simulation of the journal's vibration behavior. Vibration data is collected to create a stability map, which represents the transition between stable and unstable vibrations as a function of eccentricity ratio and stability number. It is found that concave and wedge geometries outperform the other shapes investigated; but the concave geometry is recommended to attain the highest critical stability number for a given eccentricity ratio.