Influence of the Lubricant Thermo-Piezo-Viscous Property on Hydrostatic Bearings in Oil Hydraulics

In fluid power machinery hydrostatic bearings are frequently used, and a first approximation approach to design is determination of a balance ratio by analytical calculation of the hydrostatic pressure force. Usually this is performed assuming that the thermo-piezo-viscous property can be neglected. However, in applications as piston machines, where pressure in many cases exceeds 200 Bar, such assumption leads to considerable error in the balance ratio prediction, due to the piezo-viscous property of the lubricant. Furthermore, the thermo-viscosity relation also has a significant influence, which adds to the discrepancy of such simple design approach. In this paper the hydrostatic pressure force calculation is reviewed in terms of thermohydrodynamic (THD) lubrication theory, and simple analytical approximations of the hydrostatic pressure force, incorporating the piezo-viscous and thermo-viscous property of the lubricant, are presented. In order to investigate validity of the approximations a numerical THD model is developed. A comparison study of the numerical and analytical predictions is performed in order to validate the simple design approach. In addition, the assumptions that form the basis of these analytical approximations are explored in order to clarify the limits of application. In conclusion, it is found that the spatial gradient of the thermal field on the bearing surface is the significant factor in the thermo-viscous effect on the hydrostatic pressure profile, which leads to the conclusion that design engineers need to understand the thermodynamics of hydrostatic bearings, when using the conventional simple analytical approach, neglecting thermo-piezo-viscosity, in hydrostatic pressure force calculations.