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 -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.
All deep‐groove ball bearings have similar features in geometry, mechanism, and structure. Stiffness of this type of bearings is related to geometry, dimensions, and operating conditions by a very complex, high‐order and coupled‐variable function. This paper has verified that the stiffness function for all deep‐groove ball bearings can be replaced by a back‐propagation neural network (BPNN) which is trained by using some (not all) samples.
Comparisons of CIE-Lab histograms of tested images on FPDs were performed by measurements with a 2D-colorimeter. The images were generated by manipulating original images according to FPD characteristics, correlated color temperature, lightness, and saturation. Experiments show that this method provides quantitative and intuitional data for assessments of the manipulating algorithms. IntroductionColor correction and manipulation (e.g., correlated color temperature (CCT), saturation, and lightness) of FPD are the important processes for the manufacturers to fit both accuracy and favor of consumers. There are many standards and algorithms for achieving this purpose [1-3], while evaluations on the results are essential for proofs of algorithms and further revisions. It was often done by single-point colorimetric measurements or by subjective observations [4,5]. The former method provides quantitative and content-independent results, but lacks of whole information of a tested image on FPD. While the latter will give more perceptual and qualitative rules for adjustments, but may lead to opinions differ and time consuming. To fill the gap between these two methods, this study provides an evaluation method by systematic analyses on the measurements with a 2D-colorimeter. ExperimentsSchematic process for the objective evaluations is shown in Fig. 1. The images for testing the manipulating algorithms were created by a PC controller, and then output to the FPD. The distributions and histograms of colorimetric parameters L*, a*, and b* were calculated from the X, Y, and Z distributions [6]. The original images used in this study are shown in Fig. 2, where the #1 and #2 images were chosen from ISO 12640-2 [7], and #3 is a photograph of a color-checker under a D65 illuminant.Controller FPD Calibrated 2D-Colorimeter
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