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

Abstract

Purpose -This article is the fourth part of a serial studies about constant and variable compensations of the closed-type hydrostatic plane-pad bearing, which is presented for the double-action membrane-type restrictor and self-type compensation. The paper aims to discuss these issues. Design/methodology/approach -The load capacity and static stiffness in thrust direction of the planar bearing is determined by the flow continuity equation which belongs to the same approaches as shown in previous parts of this serial studies. Findings -The results reveal that the appropriate range of recess pressure ratio and design parameters of bearing and restrictor for the infinite or maximum stiffness can be obtained. Also, the influence of design parameters on negative stiffness that should be avoided in bearing design is revealed in detail. Originality/value -The determination of design parameters of a double-action membrane-type restrictor can be yielded from finding results of this study for maximum stiffness in design of hydrostatic bearings. Nomenclature A; A eff ;A ¼ practical area of hydrostatic pad, effective area for loading, dimensionless effective areato the elastic restoring of membrane, dimensionless deformation coefficient (ddc) e, 1 ¼ displacement, displacement ratio of worktable h r ¼ film thickness of hydrostatic pad, r ¼ 1, 2 for number of bearing pads h 0 ¼ design film thickness of open-type bearing, bearing clearance or initial film thickness of closed-type bearing K; K ¼ static stiffness, dimensionless stiffness K ¼ Kh 0 ðP s AÞ 21 k p , k s ¼ dimensionless stiffness parameter (dsp) for membrane-type compensation (subscribed by p) and for self-compensation (subscribed by s) P r ; P r ¼ recess pressure, pressure ratio P r ¼ P r P 21 s , r ¼ 1, 2 for number of bearing pads P s ¼ supply pressure or limited pressure of pumping line P 1 ¼ occurring pressure ratio that corresponds to infinite stiffness Q; Q ¼ flow rate, dimensionless flow rate Q ¼ 12mQ ðP s h 3 0 Þ 21 r m1 , r m2 , r m ¼ inner, outer radius of restriction circular sill in membrane-type restrictor, membrane radius u ¼ equivalent additional opening due to membrane deformation W; W ¼ load capacity, dimensionless load capacity (dlc) W ¼ W ðP s AÞ 21The current issue and full text archive of this journal is available at ¼ dimensionless load parameter (dlp) x 0 ¼ initial gap between membrane and sill z r ¼ restriction ratio of bearing to restrictor (rrbr) a ¼ effective area ratio of both pads (ear) b ¼ cubic root of ratio for restriction ratios of both bearing pads relative to their restrictors (crr-rrbr) g ¼ geometric constant of film flow due to geometric design parameter of bearing pad Subscript r ¼ the number for bearing pads, r ¼ 1, 2

Identification of Characteristic Parameters for Hydrostatic Bearings

“…Kang et al [5][6][7][8] investigated the static characteristics of open-type and closed-type planar bearings compensated by the constant compensations and variable restrictors to give that the bearing characteristics is determined by bearing design and the match of bearing and compensation.…”

Fluid-structure coupling model and output characteristics of a diaphragm-type restrictor

“…10,11 Many scholars have conducted a lot of research on diaphragm-type restrictor. Kang et al 9,12 analyzed the static stiffness of hydrostatic bearing with two typical variable throttle devices: diaphragm-type and spooltype restrictor, and discussed the influence rule of throttle structure parameters on its performance. In addition, by changing the outlet pressure of loadregulated throttle, Kang et al 13 proposed a method to identify the restrictive and deformation parameters of diaphragm-type restrictor by replacing the measured values of inlet pressure, outlet pressure and flow with the combined equation.…”

Model-Based Design Approach to Improve Performance Characteristics of Hydrostatic Bearing Using Multivariable Optimization

“…Several authors have tried to improve the static/dynamic characteristics of hydrostatic bearings using different techniques and methods, and an overview of their achievement can be found in this paragraph. The dynamic characteristics are improved with the help of variable compensation, which is provided by using a double-action restrictor of the tapered spool type and the cylindrical spool type [2,3] but the deficiency of this approach is the slow response time of the spool type restrictor as compared to the servo valve. A numerical study is carried out to find the appropriate value of the recess shape, the strength of the magnetic field and the restrictor for the optimal performance of hydrostatic bearings [4].…”