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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.

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.

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.

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.

The usage range of recess pressure and compensation parameters should be selected to correspond to a variation with smallest gradient.

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.

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.

The purpose of this paper is to improve static/dynamic characteristics of active-controlled hydrostatic journal bearing by using fractional order control techniques and optimizing algorithms.

Active lubrication has ability to overcome the unpredictable harsh environmental conditions which often lead to failure of capillary controlled traditional hydrostatic journal bearing. The research develops a mathematical model for a servo feedback-controlled hydrostatic journal bearing and dynamics of model is analyzed with different control techniques. The fractional-order PID control system is tuned by using particle swarm optimization and Nelder mead optimization techniques with the help of using multi-objective performance criteria.

The results of the current research are compared with previously published theoretical and experimental results. The proposed servo-controlled active bearing system is studied under a number of different dynamic situations and constraints of variable spindle speed, external load, temperature changes (viscosity) and variable bearing clearance (oil film thickness). The simulation results show that the proposed system has better performance in terms of controllability, faster response, stability, high stiffness and strong resistance.

This paper develops an accurate mathematical model for servo-controlled hydrostatic bearing with fractional order controller. The results are in excellent agreement with previously published literature.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2020-0272

The purpose of this paper is to present the identification method of restriction parameter and deformation parameter for membrane‐type restrictors.

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.

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.

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.

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.

Large scale is a trend of the ball mill, so the loads on their bearings become very large, bearing operating conditions turn into more severe. The moment of inertia to their pivot of the pad increase significantly, so it leads to the difficult of the pad attitude adjustment and makes the pad tilting angles time response slow, the key factor to effects attitude adjustment is the oil film moment to the pad pivot at unbalance position. the oil film moment and its effect factors must be studied in the design of the bearing used in ball mill.

Models about the lubrication of multi-pocket pivoted pad hydrostatic bearing is established, the complicated relationship of the oil flow rate between the oil pockets are taken into account. Finite differential method is used to solv the model, and theroy of finite element method is use to calculate the oil flow rate out of the pocket edges. Newton’s methods are used to determine the pressure of pockets.The pad tilting moment to its pivot is numerically analyzed.

The tilting moment to its pivot is set as an indicator of the ability for a pad to adjust its attitude. The effects of the diameter of throttling capillary and the pocket area on the attitude adjusting capacity is studied. Relations between the attitude adjustment capacity for a pad and there effects factors are presented.

The methods and results have the special reference to the design and operation of multiple pockets tilted pad hydrostatic journal bearing.

Methods to studied the pad attitude adjustment are given in the article for the multi-pocket pivot pad hydrostatic beairng.The influence factors on pad attitude adjusting capacity are discussed for a this specail kind hydrostatic bearing, the how the factors influence the pad tilting angle adjustment are presented.