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 paper aims to determine whether the type selection and parameters determination of the compensation are most important for yielding the acceptable or optimized characteristics in design of hydrostatic bearings. Design/methodology/approach -This paper utilizes the equations of flow equilibrium to determine the film thickness or displacement of worktable with respect to the recess pressure. Findings -The stiffness due to compensation of constant-flow pump increases monotonically as recess pressure increases. Also, the paper considers which is larger than that due to orifice compensation and capillary compensation at the same recess pressure ratio. Originality/value -The findings show that the usage range of recess pressure and compensation parameters can be selected to correspond to the smallest gradient in variations of worktable displacement or film thickness.
PurposeThis paper seeks to modify the determinations of flow rate and fluid resistance, which can be realized and confident from the measurements of flow rates in experiments.Design/methodology/approachAccording to coupled physics of solid membrane and lubrication fluid, finite element method is used simultaneously to determine membrane deflection and film thickness. Several cases are simulated by traditional method, finite element method and compared with experimental method for the flow rates and fluid resistances to present the modification of determination results.FindingsThe FEM results for the fixed eight‐section are approximated to actual flow rate and are consistent with the modified determination of the flow rates, and so the modified determinations of the flow rates are verified. When a computer of P4 with 1.8 GHz CPU and 512 MB RAM is utilized, time needed for traditional method or modified formula is fewer than one second. However, more than 4 h is required for FEM by using the same computer.Originality/valueThis study provides the modified method for the determinations of flow rate and fluid resistance in membrane‐type restrictors by using FEM. The FEM results can increase the determination accuracy of the flow rate and restriction coefficient in the design of membrane‐type restrictors.
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