Design of Dimensionless Parameters of a Parallel Combination of Capillary restrictor and Membrane type restrictor in single-pad hydrostatic bearing set-up to achieve high static stiffness

Abstract

Hydrostatic bearings have been frequently used in high-precision machine tools at the present time for their ability to perform accurately with durability. One of the key characteristic of hydrostatic system is the stiffness of the bearing and it is generally true to design a hydrostatic bearing with a higher stiffness, such that the variation of the deflection due to load variation is limited. For a single pad hydrostatic bearing set-up with membrane type restrictor, the bearing stiffness will tend to infinite at a dimensionless load capacity of 0.33. The corresponding design restriction ratio and dimensionless bearing stiffness are 0.25 and 1.33 respectively. The current research explains that with the use of a hybrid restrictor set-up i.e. parallel combination of a membrane type restrictor and fixed capillary restrictor, the bearing stiffness will tend to infinity at relatively higher dimensionless load capacity. A major finding of the research work is that a high static stiffness of the hydrostatic bearing can be obtained over a higher value of load capacity controlling three major design parameters and they are dimensionless capillary ratio(c), dimensionless membrane stiffness(Kr*) and the design restriction ratio() of the membrane restrictor system. Target of current research was to derive the relation between Kr*,  and c. It has been derived that Kr* and  are the function of c only. In the parallel combination of capillary restrictor and membrane type restrictor, capillary restrictor acts as a bypass restrictor and hence the above design may be adopted to delay the flow minimizing the clogging effect of membrane-type restrictor at starting.