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This paper is the third part of a serial studies for constant and variable compensations of the closed-type hydrostatic thrust bearings which has face-to-face recesses couple. The static stiffness of closed-type hydrostatic thrust bearings can then be obtained from the differentiation of recess pressure with respect to worktable displacement. The paper aims to discuss these issues.

In this paper, the double-action restrictors of cylindrical-spool-type and tapered-spool-type are taken into consideration for variable compensation of hydrostatic bearings.

The static stiffness in thrust direction of hydrostatic bearing is determined by the flow continuity equations that are formulated by film flow and compensation flow for each recess, respectively. The type selection and parameter determination of the double-action spool-type restrictors can be obtained from finding results of this study for maximum stiffness in design of hydrostatic bearings.

This study reveals that the appropriate range of recess pressure ratio and design parameters of restrictors for the maximum stiffness can be obtained, the avoidance of negative stiffness is also provided.

The purpose of this paper is to study the dispersion and tribological properties of liquid paraffin with aluminum nanoparticles as additive, which are prepared by the surface‐modification method using oleic acid (OA).

The dispersion stability of aluminum nanoparticles in liquid paraffin is measured by spectrophotometry, which can be optimization by Taguchi method. The tribological properties are evaluated by using a ball‐on‐ring wear tester.

The results show that few concentrations of aluminum nanoparticles as additives in liquid paraffin have better antiwear and antifriction properties than the pure paraffin oil. Scanning electron microscopy and energy dispersive spectrometer analyses can show that the thin films on the rubbing surfaces can be formed by these aluminum nanoparticles, which not only bear the load but also separate the both interfaces, thus the wear and friction can be reduced.

Machine components and mechanism pairs rely on high‐quality lubricants to withstand high temperature and extreme pressure. Extreme pressure and antiwear additives are typically adopted to improve the tribological performance of a fluid lubricant in reducing friction and surface damage under severe conditions.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Constant flow valves have been presented in industrial applications or academic studies, which compensate pressures of bearing recesses as load fluctuates. The flow rate of constant-flow valves (CFVs) can be constant in spite of the pressure changes in recesses. However, specific condition of design parameters must be satisfied. The paper aims to discuss these issues.

This paper utilizes analytical method to study the static characteristics of CFVs, three types belong to traditional design of CFV are reviewed afresh. Moreover, an innovative design for constant flow is presented and studied.

The review and study results reveal that appropriate relationships among design parameters for these types of CFVs.

The numerical simulation is used to investigate the influence of design parameters on the change of flow rate when pressure ratio of recess is changed.

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.

This paper utilizes the equations of flow equilibrium to determine the film thickness or displacement of worktable with respect to the recess pressure.

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.

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.

The purpose of this paper is to discuss the dispersion capacity and tribological behavior of liquid paraffin added by diamond nanoparticles.

The structure of the modified diamond nanoparticles which are prepared by oleic acid (OA) is observed by scanning electron microscopy (SEM) and infrared spectroscopy (IR). The dispersivity of these nanoparticles in liquid paraffin is measured by nanoparticle analyzer. The tribological behavior of adding diamond nanoparticles in liquid paraffin is evaluated by using a ball‐on‐ring wear tester.

The measurement results reveal the dispersion capability of OA modified diamond nanoparticles and indicate the dispersing stability in liquid paraffin of the OA which is bonded to the surface of diamond nanoparticles through esterification. It is found from wear testing results that the diamond nanoparticle as additive in liquid paraffin at proper concentration shows better tribological properties for anti‐wear (AW) and antifriction than the pure paraffin oil and different AW ability depending on the particle size.

It is shown in the paper that by reducing friction and AW, the lubricant prepared by the methods described can prolong operating hours of machinery.

This 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.

The 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.

Consequently, 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.

This 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.

This 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.

According 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.

The 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.

This 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.

The present paper proposes a theoretical analysis of the stability characteristics of a rigid rotor‐hybrid bearing system. It is intended that on the basis of the numerical results drawn from this study, the optimal restriction parameter for stable operation can be determined for use in the bearing design process.

A rigid rotor supported by hybrid oil film bearings with six recesses and capillary‐compensated restrictors is studied. In order to facilitate the calculation of film dynamics, using the perturbation method, the Reynolds equation was linearized and subsequently solved using finite difference techniques, whilst the stability maps were determined by the Routh‐Hurwitz method.

The data reported here suggest that the stability characteristics of the rigid rotor‐bearing system could be improved by the use of shallow, dual‐recessed hybrid bearings with capillary compensation. For the same restriction parameter and the same land‐width ratio used in large eccentricity case the stability characteristics of a shallow‐recessed bearing is superior to that of a deep‐recessed bearing, however, a deep‐recessed bearing with a small land‐width ratio and a small restriction parameter can provide better stability than a shallow‐recessed bearing with a large land‐width ratio or with a large restriction parameter.

This study proposes an extensive database as a critical requirement in the design of hybrid bearings, in order to ensure that a rotor bearing system is operating stably.