Parameter identification for single‐action membrane‐type restrictors of hydrostatic bearings

Abstract

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

Identification of design parameters for spool-type restrictors

“…By using the same manner as references, 7,8 the pressurized lubricant which is measured as Psk for the k th supply pressure passes through each restrictors and flows into the j th recess with outlet pressure Prj and flow rate Q j , and finally flow out from the clearance and return to oil reservoir. The measurement range and sensitivity of pressure meters used to measure the pressures of upstream and downstream of restrictors are 0–50 bar and 0.15682 V (kg/cm), respectively, and the output is electric current which is necessarily transformed from 4 to 20 mA by resistance 250 Ω to voltage 1 V–5 V for computer input.…”

“…Kang et al. 7 presented an approach to identify the restriction parameter and membrane deformation coefficient of single-action membrane-type restrictor by experimental results. Using the same manner, Kang et al.…”

“…However, large differences between determined and real characteristics are induced by manufacturing errors and disregard in design. Kang et al 7 presented an approach to identify the restriction parameter and membrane deformation coefficient of single-action membrane-type restrictor by experimental results. Using the same manner, Kang et al 8 presented the identification of parameters for hydrostatic bearing.…”

Identification of Characteristic Parameters for Hydrostatic Bearings

“…Kang et al [18] presented an approach to identify the restriction parameter and membrane deformation coefficient of single-action membrane-type restrictor by experimental results which are measurements of the inlet pressure, the outlet pressure and the flow rate of restrictor.…”

Static analysis of hydrostatic conical bearings using flow resistance network method

“…In this paper, based on aforementioned methods, the fluid equilibrium equation of each recess is established from the resistance of network method. Furthermore, Kang et al (2012) used the identification method of restriction parameter, and deformation parameter for membrane-type restrictors is obtained directly from experimental results. To study the static characteristic of conical bearings which is influenced by the capillary method, a single-action membrane restriction, the radial and axial load capacity and the static stiffness of the bearings are obtained by vector computation from simultaneously solving the derivatives of various oil recess pressures and the pressure vs eccentricity ratio.…”