Mixed lubrication characteristics of water-lubricated stern bearings considering coupled shaft deflection and wear evolution

Water-lubricated stern bearings commonly operate in mixed lubrication because the low viscosity of water limits film formation and propeller-induced shaft deflection creates a nonuniform axial clearance, leading to asperity contact and wear. However, the feedback between shaft deflection and wear-induced clearance evolution remains unclear. A time-marching model combines the averaged Reynolds equation with formulations for asperity contact, bearing elastic deformation, shaft deflection, and wear. At each wear increment, shaft deflection is determined from load equilibrium, and local clearance is updated using the accumulated wear profile. Results show that shaft deflection reduces film thickness near the trailing end and concentrates hydrodynamic and asperity-contact loads, thereby accelerating wear. As wear progresses, clearance growth reduces asperity-contact pressure and shifts the hydrodynamic pressure peak toward the leading end. The resulting redistribution of the fluid-film support alters the force balance on the shaft and further increases deflection. Higher bearing-specific pressure and larger radial clearance strengthen this interaction, whereas the effect of journal speed is governed by competition between hydrodynamic film formation and accumulated sliding distance. These findings clarify how wear-induced clearance evolution mediates the feedback between shaft deflection and load redistribution, providing a physical basis for understanding time-dependent mixed lubrication in water-lubricated stern bearings.