Foresight in static stiffness of hydrostatic bearings with various compensations by film gradient versus recess pressure

Abstract

Purpose -The purpose of this paper is to investigate the static stiffness of hydrostatic bearings with three constant compensations in types of constant-flow pump, capillary and orifice, and both single-action and double-action variable restrictors with cylindrical-spool, tapered-spool, and membrane types by film gradient and recess pressure. Design/methodology/approach -This paper utilizes the equations of flow equilibrium to determine the variations of film thickness or displacement of loading table with respect to the varying of recess pressure. For a hydrostatic bearing whose recess pressures are controlled by compensations, the stiffness characteristics can be presented directly by these variations. Findings -The usage range of recess pressure and compensation parameters should be selected to correspond to a variation with smallest gradient. Originality/value -This paper proposes an extensive database as a critical requirement for the selection of types and parameters of the compensation as to yield the acceptable or optimized characteristics in design of hydrostatic bearings.

Design for static stiffness of hydrostatic bearings: double-action variable compensation of spool-type restrictors

“…where functions F 1 and F 2 defined in equations ( 2a) and ( 2b) are expressed in the right side of equal sign in above equations. Kang et al (2010) has used equation ( 13) to determine the variations of dimensionless film thickness with respect to the pressure ratios of recesses for various C l and revealed that the dimensionless film thickness is almost not changed as P 1 changes from 0.3 to 0.7 for C l ¼ 0:3 and from 0.2 to 0.8 for C l ¼ 0:4: Also, they revealed that very high or infinite stiffness can be foresighted from tiny or no change of film thickness as recess pressure is varying and negative stiffness can be foresighted from that the film thickness increases as pressure ratio increases when C l is larger than and equal to 0.375. Differentiating equations (13a) and (13b) with respect to 1 gives the form described by equations (4a) and (4b) with the coefficients as shown below:…”

“…Although many other articles have studied in the same topic, almost all their investigations in relationships between compensation and hydrostatic bearing are constrained on fixed design. Kang et al (2010) issued that static stiffness can be forecasted by using gradients of film thickness or worktable displacement with respect to recess pressure. This study revealed that positive stiffness can be forecasted by the positive slope in plotting the variation of displacement ratio with respect to pressure ratio of recess, negative stiffness and infinite stiffness can be forecasted by negative and zero slopes in the plots, respectively.…”

Design for static stiffness of hydrostatic bearings: double-action variable compensation of membrane-type restrictors and self-compensation

“…Alternatively, the variations of displacement ratio 1 with respect to P 2 for various P 1 as parameter have the same patterns but skew symmetrical about the vertical lines of 1 ¼ 0. The complemented description as shown by the variations of (h/h 0 ) 3 with respect to pressure ratios can be seen in Kang et al (2010).…”

“…Although many other articles have studied in the same topic, almost all their investigations in relationships between compensation and hydrostatic bearing are constrained on fixed design. Kang et al (2010) issued that static stiffness can be forecasted by using gradients of film thickness or worktable displacement with respect to recess pressure.…”

Design for static stiffness of hydrostatic plain bearings: constant compensations

“…Although many other articles have studied in the same topic, almost all their investigations in relationships between compensation and hydrostatic bearing are constrained on fixed design. Kang et al (2010) issued that static stiffness can be forecasted by using gradients of film thickness or worktable displacement with respect to recess pressure for bearing performance taken into consideration before design.…”