Density and Viscosity Models for Two-Phase Homogeneous Hydrodynamic Damper Fluids

Theoretical cavitation models previously adopted in analyzing dynamically loaded hydrodynamic bearings or squeeze-film dampers are inconsistent with experimental observations in that bubbles, once formed, in many instances do not completely redissolve upon the reappearance of high pressure. A more representative approach could be to model the lubricant as a homogeneous two-phase gas-liquid mixture. The density and viscosity of such a homogeneous mixture are developed as functions of the pressure and the known mole fraction of the noncondensable gas to the liquid at supply entry. Omitting the possible effects of surface tension, it is shown that if the vapor pressure of the lubricant is of the order of 10−3 atm or less, it has only a minimal effect on the density of the mixture and may be ignored. On the other hand, solubility effects may be significant, though it is unknown to what extent gases, once drawn out of solution, will redissolve in the short time of the cycle period of the dynamic loading. Hence, the density and viscosity relationships assume the extreme cases of either (1) solubility equilibrium, the so-called full-collapse model or (2) no solubility over a cycle period, the so-called non-collapse model. Also, isothermal or adiabatic or, indeed, polytropic gas behavior may be specified. The final density and viscosity are of the form where they may be gainfully utilized in obtaining so-lutions to the compressible Reynolds equation for dynamically loaded bearings.