PurposeThis 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/approachThe 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.FindingsConsequently, 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/valueThis 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.

Purpose -The purpose of this paper is to present the identification method of restriction parameter and deformation parameter for membrane-type restrictors. Design/methodology/approach -A worktable mounting on the open-type hydrostatic bearing is utilized to calibrate recess pressures for regulating outlet pressures of restrictors by changing the load and then both restrictor parameters can be identified from the measurements of the inlet pressure, the outlet pressure, and the flow rate of a restrictor by minimizing the difference between measured and identified flow rates. Furthermore, the influences of supply pressure and restrictor designs on both parameters are also studied. Findings -An identification method for single-action membrane-type (SAM) restrictors is obtained directly from experimental results. The measurements of inlet pressure, outlet pressure, and flow rate of the restrictor are substituted into the combined equations for minimization of error between measured and identified flow rates to be solved for restriction and deformation parameters. The identified results show that both parameters can be described by polynomial functions of supply pressure. Both polynomials are regressed by curve fitting from identified results. Originality/value -The paper shows how to calibrate inlet and outlet pressures of restrictors for designing a hydrostatic bearing system by changing supply pressure and load applied on worktable for the measurements of both pressure and the flow rate of restrictor. Nomenclature¼ sum of square errors between both identified and measured flow rates, E ¼ P e 2 i E d , E z ¼ regression errors for restriction, deformation parameter h 0 ¼ initial clearance between worktable and bearing P r ¼ recess pressure, outlet pressure of restrictor (N/m 2 ) P s ¼ supply pressure (N/m 2 ) P ¼ dimensionless recess pressure Q, Q,Q ¼ flow rate (m 3 /s), dimensionless flow rate, unit Q Q i ¼ measured flow rate Q 0 ¼ identified flow rate r 1 ¼ radius of restrictor outlet (mm) r 2 ¼ restriction radius of cylindrical sill (mm) r 3 ¼ membrane radius (mm) t m ¼ membrane thickness (mm) x ¼ increased opening due to outlet pressure of restrictor induced by working load x 0 , x 0 ¼ initial, assembled clearance between membrane and sill d ¼ restriction parameter (m 5 /N ·s) d ¼ dimensionless restriction parameter z ¼ proportional parameter of membrane deformation (m 2 /N) m ¼ dynamic viscosity (N ·s/m 2 )The current issue and full text archive of this journal is available at

Purpose -This paper aims to study the static characteristics of the hydrostatic conical journal bearings by utilizing single-action membrane restrictors to compensate the working pressures of recesses. Design/methodology/approach -The flow resistance network method is used to analyze the influences of load capacity and static stiffness of bearing with the design parameters, including the number of recesses, radial eccentricity ratio, axial displacement ratio, restriction constant, membrane compliance, length-diameter ratio, circumferential land width ratio, axial land width ratio and half of cone angle. Findings -This study shows the infinite stiffness of the oil produced in the first and second recesses while single-action membrane restriction constant of 2 and 3, respectively, as well as in the fourth recess while single-action membrane restriction constant of 0.01 and 0.1, respectively. Research limitations/implications -This article provides the hydrostatic conical bearings in static and unbiased states for analyses of design parameters. The analyses ignore dynamic pressure effect and do not use the Reynolds equation, and assuming that each oil recesses pressure is constant. Practical implications -The influences of the design parameters including the number of recesses, membrane restriction, membrane compliance, length-diameter ratio, half of con-angle, circumferential land width ratio, and axial land width ratio are discussed to the load capacity and static stiffness of conical bearing. Originality/value -Based on the characteristics of the conical bearing through analysis, this article suggests the front bearing with hard membrane restrictor (capillary) and the back bearing with soft membrane restrictor are the most appropriate for axial stiffness.

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