Design for static stiffness of hydrostatic bearings: single-action variable compensations

Purpose - This study aims to utilize the equations of flow equilibrium to determine the variations of film thickness or worktable displacement with respect to the recess pressure for both open- and closed-type hydrostatic flat bearings. The static stiffness can be not only presented directly by these variations but also determined by the differentiation of flow equilibrium equations. Design/methodology/approach - The single-action variable compensations of three types including cylindrical-spool, conical-spool and membrane restrictors are taken into consideration in this study. Specifically, this study presents that membrane restrictor and both spool restrictors with or without preload whilst considering initial opening. Findings - Consequently, the usage range of recess pressure and optimal parameters of appropriate compensation type can be obtained from maximum stiffness and also according to smallest gradient in variations of worktable displacement or film thickness. Originality/value - This article studies the influences of single-action variable compensations for its design varieties. The determination of stiffness comes from the differentiating recess pressure with respect to worktable displacement. The large and small positive stiffness correspond to a negative slope in steep and plain gradient, respectively; the negative stiffness and infinite stiffness are obtained by positive gradient and zero gradient, respectively, in the variations of film thickness. The finding results can be expressed further in the relationship between the static stiffness and the static load.