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For an aerostatic bearing with a multi-hole integrated restrictor, which achieved superior precision lubrication-bearing performance, the fluctuations of the velocity and the pressure of the flow field were investigated. In this paper, the large-eddy simulation method was used to solve the three-dimensional Navier–Stokes equation in the calculation area of the gas film flow field at the orifice outlet of an aerostatic bearing, while the overrelaxation iteration method was used to solve the Reynolds equation in the remaining calculation areas. The influence factors of the flow field, such as the diameter of the orifice, the gas supply pressure and the gas film clearance, were derived and discussed. The results showed that the diameter of the orifice and the gas film clearance of aerostatic bearings with a multi-hole integrated restrictor strongly affected the film flow field near the outlet of the restrictor under a specified gas supply pressure. There was a critical ratio between the gas film clearance and the diameter of the orifice of aerostatic bearings with a multi-hole integrated restrictor, which may be an initial signal and an important parameter of the flow field transition from laminar flow to turbulent flow.

Under misalignment condition, the film thickness distribution of aerostatic journal bearings is changed comparing with condition without misalignment, which results in the change of performances of aerostatic journal bearings. In the paper, the effects of misalignment along two perpendicular directions (along the vertical direction θ y and along the horizontal direction θ x) on the dynamic coefficients and stability thresholds of both critical whirl ratio and critical inertial force calculated by the motion equation of rigid rotor-aerostatic journal bearing system are studied comparatively. The results indicate that the dynamic coefficients, critical whirl ratio, and critical inertial force are more sensitive to θ x compared with θ y. Moreover, the stability threshold of whirl ratio reduces with increasing the misalignment degree, while stability threshold of inertial force increases with increasing the misalignment degree.

Aerostatic bearing is an ultra-precision component that uses a spindle surrounded by a thin film of air. Due to the high accuracy of aerostatic bearing, the demand for these components is very high in electronic, instrumentation, healthcare, and other manufacturing or processing industries. In the present work, the main focused area is on the experimental determination of the effect of roughness parameter on the performance of the aerostatic journal and thrust bearings. To achieve the aim, the aerostatic bearing is designed based on theoretical analysis. The present design is numerically investigated by simulation of airflow in ANSYS Fluent with computational fluid dynamics module. The results from the simulation are validated by the results generated for pressure distribution in previous researches. After performing the finishing on the bearing and spindle surface, the manufactured components are assembled for analysing the variation in radial and axial loads acting on the spindle with the spindle displacement (1-5 μm) in the direction of the load at supply pressures (3-6 bar) in the clearance of 30 μm. For surface improvement of the air bearing, three different techniques are used namely machining, grinding, and magnetorheological finishing. For each roughness reduction technique, the variation in axial and radial loads acting on the spindle is determined with variation in spindle displacement. The experimental results showed the increase in load capacity due to improvement in the surface finish for journal bearing and thrust bearing at 5 µm displacement in the spindle is found to be 0.68 N for machining to grinding and 2.0 N from grinding to magnetorheological finishing respectively. The results determined for the surface finish parameter reveals the effect of surface roughness on the load-carrying capacity of the aerostatic journal and thrust bearing. The current study on the surface finishing of aerostatic bearing is found effective for the applications such as drives in production machines where good grade of surface finish are the major parameters for improving the overall functional efficiency.

The pneumatic hammer phenomenon and pneumatic stability of a single-pad aerostatic thrust bearing with pocked orifice were investigated numerically. A time-dependent dynamic model for pneumatic stability analysis of the bearing was established with taking the pocket volume and the mass flow difference between the pocket inlet and outlet into account. The numerical prediction indicates that the delay effect is an important reason for the pneumatic hammer phenomenon. With considering the delay effect, an in-depth explanation for the pneumatic hammer phenomenon is proposed in this paper. The air compressibility combined with the volume effect in the aerostatic bearing could lead to the delay of pocket pressure change, then resulting in the delay of bearing force change at larger film thickness region. The delay of the bearing force change at larger film thickness region causes the bearing damping to become negative at larger film thickness. The negative damping provides some energy into the aerostatic bearing system at larger film thickness and maintains vibration, which leads to the pneumatic hammer phenomenon.

Cementitious composites reinforced with silica, silicon carbide or carbon microfibres are designed, manufactured, characterised and tested as porous restrictor for aerostatic bearings. Carbon microfibres are residues obtained from the cutting process of carbon fibre-reinforced polymers. Porosity, permeability, flexural strength and stiffness are quite relevant in the design of aerostatic porous bearings. A 3141 full factorial design is carried out to identify the effects of particle inclusion and water-to-cement ratio(w/c) factors on the physical and mechanical properties of cementitious composites. Higher density material is achieved by adding silicon carbide. Higher porosity is obtained at 0.28 w/c level when silica and silicon carbide are used. Carbon microfibres are not effective under bending loads. Higher compressive strength is reached especially when silica particles are combined with 0.33 or 0.35 w/c. According to the permeability coefficient values the cementitious composites consisted of CMF (0.28 w/c), silica (0.30 w/c) or silicon carbide (0.30 w/c) inclusions are promising as porous restrictor; however, carbon microfibre porous bearings achieved the lowest air gap variation under the tested working conditions.

Aerostatic bearings are widely employed in precision machines due to their properties of low friction, low heat conduction, and long-life operation. In this work, static performance of the journal bearing with rectangular grooves is investigated numerically. The effect of geometrical parameters such as axial groove length [Formula: see text], circumferential groove length [Formula: see text], orifice diameter df, groove depth gh, misalignment angles [Formula: see text] and [Formula: see text] on the load capacity [Formula: see text], stiffness [Formula: see text], and gas flow rate [Formula: see text] are analyzed systematically. The resistance network method (RNM) is utilized to solve the Reynolds equation required in the analysis. Performance parameters including pressure distribution P, load force [Formula: see text], stiffness [Formula: see text], and gas flow rate [Formula: see text] are examined in the simulations. It is revealed from the simulations that the proper value of axial groove length [Formula: see text] to obtain a better static performance varies from 1/8 to 1/2 when df varies between 0.11 and 0.29 mm, respectively. Therefore, a larger load force and stiffness can be obtained if [Formula: see text] is chosen to be 1/4, when diameter of the bearing orifice df equals 0.17 mm. It is also suggested that [Formula: see text] be chosen from the range of 1/6 and 1/3 to obtain a better static performance and a smaller gas flow rate. [Formula: see text] decreases with an increase in df when [Formula: see text] is set to be 1/8. However, the load force [Formula: see text] increases with an increase in df when [Formula: see text] varies from 3/8 to 1/2. [Formula: see text] has a significant influence on the changes of [Formula: see text] with df when [Formula: see text] is set to be constant. Therefore, df should be selected according to [Formula: see text] for an optimal design. The increase of misalignment angle [Formula: see text] leads to an increase in the load force [Formula: see text]. [Formula: see text] has little influence on the load force [Formula: see text]. Misalignment angles [Formula: see text] and [Formula: see text] have little influence on stiffness [Formula: see text] and gas flow rate [Formula: see text]. Therefore, it is preferable if [Formula: see text] is larger than 0 rad.

The performance of aerostatic bearing mainly depends on the throttling effect of its restrictor. The orifice and porous material are the most common restrictors, which have their own advantages and...

Aerostatic bearings are the core parts of ultra-high-speed spindles with maximum running speed greater than 100,000 r/min. In this paper, the influences of herringbone grooves on the performance of aerostatic journal bearings are studied to design spindles with the features of higher precision and higher speed. Parametric studies and sensitivity analyses are executed in terms of the improved finite element method, which is specially developed to solve the compressible Reynolds equation for herringbone grooved air bearings. The calculated results indicate that herringbone grooves significantly improve the performance of aerostatic journal bearings under the conditions of ultra-high speeds and low supply pressures. Groove parameters are nonlinear dependent, and groove depth and length are the dominant influential factors for the load capacity at speed of 200,000 r/min. Experiments are designed and conducted to verify the improved finite element method, which show that the improved finite element method can be used to analyze the influences of herringbone grooves on aerostatic journal bearings and also manifest that suitable herringbone groove geometrical parameters can obviously decrease spindle radial runouts at ultra-high speeds.

In order to further study the performance of aerostatic bearing, an aerostatic bearing with a multihole integrated restrictor was proposed in this paper. Based on the physical model of aerostatic bearings, the governing equation was established, deduced discretely, and solved numerically by the finite-difference method and flow balance principle in Cartesian coordinates. The bearing capacity and stiffness of aerostatic bearings have been analyzed, and the relevant experimental research has been carried out in this paper. The results showed that the number of orifices in the integrated restrictor had a significant effect on the bearing capacity, and the maximum bearing capacity of a nine-hole integrated throttling bearing was approximately 1.9 times greater than that of a single-hole bearing. The bearing stiffness was greatly affected by the diameter of the orifices, and the optimum bearing stiffness was determined. The corresponding gas film clearance also changed accordingly.

In this paper, the steady-state characteristics, including film pressure, load capacity, stiffness, misalignment moment of aerostatic bearings considering two types of misalignment (along vertical direction [Formula: see text] and along horizontal direction [Formula: see text]) are studied under pure-static and hybrid condition. The journal misalignment effects on the steady-state characteristics under pure-static condition and hybrid condition are studied comparatively. The results show that the load capacity and stiffness increase with the increase in the degree of journal misalignment under hybrid condition, while they decrease with the increase in the degree of journal misalignment under pure-static condition. Moreover, the journal misalignment along two perpendicular direction effects on the performances of aerostatic bearings are also investigated comparatively and the performances of bearing are found to be more sensitive to the misalignment along horizontal direction.

Friction and wear are tribological phenomena that have produced significant economic damage and environmental issues throughout our history. Different kinds of lubricants and coatings have been employed in the attempt of reducing friction losses. Because of their remarkable performance, gas lubricated systems are characterized by almost zero friction and wear. For this reason, they can be utilized in applications where rolling and fluid bearings cannot, e.g., metrology, medical equipment and tool machine. This paper reviews the evolution of gas lubrication through history. The topography of the subject is described from its origins to how it was shaped over the centuries, trying to preserve the logical cause and effect relationship of the events. For the sake of consistency, the review considers only the key past contributions which are strictly related to gas lubrication.

The objective of this work is to study the influence of error induced by gas film in micro-scale on the static and dynamic behavior of a shaft supported by the aerostatic bearings. The static and dynamic balance models of the aerostatic bearing are presented by the calculated stiffness and damping in micro scale. The static simulation shows that the deformation of aerostatic spindle system in micro scale is decreased. For the dynamic behavior, both the stiffness and damping in axial and radial directions are increased in micro scale. The experiments of the stiffness and rotation error of the spindle show that the deflection of the shaft resulting from the calculating parameters in the micro scale is very close to the deviation of the spindle system. The frequency information in transient analysis is similar to the actual test, and they are also higher than the results from the traditional case without considering micro factor. Therefore, it can be concluded that the value considering micro factor is closer to the actual work case of the aerostatic spindle system. These can provide theoretical basis for the design and machining process of machine tools.

For an aerostatic circular thrust bearing with a single pocketed orifice-type restrictor, the flow field in the bearing clearance is analyzed numerically, and the formation mechanism of the bearing micro-vibration is investigated. Through flow field analysis, the flow structures in the bearing clearance are discussed and classified. The formed vortex flow in flow field is analyzed, and the influence of the vortex flow on bearing dynamic stability related to micro-vibration is discussed. For each flow structure, the vortex flow always exists and induces the bearing micro-vibration. The Reynolds number is used to represent the degree of bearing micro-vibration and the rationality is verified. Based on the flow analysis results, the maximum Reynolds number in the bearing clearance flow field is taken as the optimization objective to reduce the micro-vibration amplitude, the approximate model for design optimization is established by using the radial basis functions method and the optimization methodology is illustrated. Several cases of optimization are carried out with different given bearing loads. Through optimization, the maximum Reynolds number is reduced greatly, which means the enhancement of the bearing dynamic stability. The optimization results show that in order to suppress the micro-vibration, the air supply pressure should be kept as small as possible, the small air pocket diameter and orifice diameter are also needed.

Porous aerostatic bearings as a new type of supporting component used in ultraprecision equipment. The study of porous models is essential as they are a basis for porous aerostatic bearings. However, the effects of micropore structure and flow state inside a material have not been addressed in previous studies. Herein, we propose a high-accuracy and low-cost method using deep learning to reconstruct a three-dimensional (3D) porous model and obtain the 3D flow state inside a porous material. It can reveal richer flow states such as the flow track and movement in three directions, which have not been revealed previously. This new method is effective for studying the properties of porous materials, micro-flow state, and simulation of parameters in detail.

The performance of potassium dihydrogen phosphate optics in inertial confinement fusion devices is highly affected by its surface topography. This paper theoretically investigates the relationship between the air-induced vibration of aerostatic bearing and high-frequency ripples (amplitudes of around 12 nm, spatial periods in the range of 8–30 mm) on machined surface of potassium dihydrogen phosphate optics. A simulation model, which combines transient computational fluid dynamic analysis and transient dynamic analysis, is proposed to simulate the vibration of tool tip. The three-dimensional flow status of air film is studied based on large eddy simulation method, and air vortex shedding phenomenon is observed, which results in the dynamical change of air film force. The simulated vibration amplitudes of tool tip is 8 nm, and its spatial periods are in the range of 10–24 mm, which agree well with the measured data.

Aerostatic pads are successfully employed in linear systems where very accurate and precise positioning is required, e.g. machine tools and measuring equipment. Both the static and dynamic performance of many different types of aerostatic pads have been already numerically and experimentally investigated. However, literature does not present so many works that investigate the performance of rectangular aerostatic pads with multiple restrictors, especially as regards their dynamic features. This paper shows an experimental and a numerical study of the static and dynamic performance of a rectangular aerostatic pad with multiple orifices distributed on a supply rectangle. The paper investigates the effect of the orifices diameter, of their position and of the supply pressure on the pad performance.

Microvibration has an important influence on the dynamic performance of aerostatic bearings. Dynamic stiffness and equivalent damping coefficient are the main indexes to evaluate the dynamic characteristics of the aerostatic bearing. In order to study the dynamic characteristics of a new type of aerostatic bearing with the elastic equalizing pressure groove (EEPG), the dynamic characteristics of the new type of bearing are studied by theoretical calculation and experiment. First, the dynamic gas-solid coupling control equation is established. Then, the steady term and the perturbation term are decomposed by the perturbation method. By solving the coupling model, the dynamic characteristics of the bearing are calculated and analyzed. The calculation results show that the perturbation frequency has a significant effect on the dynamic stiffness and equivalent damping coefficient of the aerostatic bearing with EEPG. The dynamic stiffness increases with the increase of frequency, and the equivalent damping coefficient decreases with the increase of frequency. The experimental results are basically the same with the theoretical results, which effectively verify the correctness of the theoretical analysis.

A high-speed precision air-bearing tool spindle with active aerodynamic bearing is proposed for improving the quality of machining using small-diameter cutting and grinding tools. The spindle is basically supported by aerostatic radial and thrust bearings. According to the spindle vibration detected by capacitance sensors, the wedge angle of the active aerodynamic bearing was controlled using piezoelectric actuators, thereby suppressing the spindle vibration. In the present paper, the performances of a prototype air-bearing spindle with single-row active aerodynamic bearing and an improved air-bearing spindle with double-row bearings are reported. Through experiments, it was demonstrated that the maximum rotational speed controlled by the active aerodynamic bearing is 800 Hz (48,000 min-1), and that the amplitude of spindle vibration can be suppressed to -1).

In this study, effects of surface roughness on the load carrying capacity of the rotor-bearing system supported by externally pressurized air bearing are theoretically investigated. Air flow between rotor and bearing surfaces, is modeled using Reynold's equation. In this model, film thickness function which is defined gap between rotor and bearing, is described with surface roughness. In order to obtained pressure distribution between rotor and bearing surface, Reynold's equation is solved with Differential Transform & Finite Difference hybrid numerical solution method and load carrying capacities is calculated. In order to analyze effect of the surface roughness on the load carrying capacity of rotor-bearing system supported by externally pressurized air bearing, an algorithm is developed in Matlab environment and it is simulated for different bearing geometric parameters and rotor angular velocities.

Advantages of aerostatic bearing are clean, no pollution and very low friction force. Therefore, it can easily be found in many high-precision machine tools and measurement equipments. However, owing to the compressibility of air, the stiffness of aerostatic bearing is relatively low compared to traditional ball bearing or hydrostatic bearing. In order to improve this fault, an active closed-loop gap control for aerostatic bearing with higher stiffness is proposed. First of all, an aerostatic bearing is designed and manufactured according to a previous report. Next, an experimental test rig based on LabVIEW software for the proposed active closed-loop gap control is constructed. Finally, it is proved that the gap between the aerostatic bearing and workpiece can be held at a stable and constant value even when the bearing is subjected to variable external disturbances.

With the objective of experimentally correlating several wear-process parameters, accurately and continuously over the duration of a sliding test, this paper presents a novel test rig as well as experimental results obtained by it. The developed test rig is a rotational one with axes supported on aerostatic bearings. It enables online measurement of normal load, friction force, angular position and normal displacement with high accuracy. These measurements are supplemented by ante- and postmortem optical and tactile inspection of the wear samples to determine their geometrical evolution. A set of ball-on-disc experiments is performed, with ball materials being nylon, steel and ceramic, on hard steel disc material. The performed experiments correlate three process variables and parameters: normal load, wear volume and dissipated energy. The basic trends observed show that the relationship between those three variable are quasi linear, but generally with nonzero intercepts, corresponding to energy thresholds; except that of wear of alumina on steel.

Small vibration on the order of nanometers poses challenges for the application of aerostatic bearings in ultra-precision machine tools and metrology equipments. In this article, the flow field in aerostatic bearings is numerically investigated and air vortices in the recess are analyzed. Vibration of the aerostatic bearing is also experimentally measured. Design and functioning parameters are varied to study their effects on the air vortices and nano-vibration of aerostatic bearings, and a direct relationship is established between the gas vortices and nano-vibration in aerostatic bearings. It is demonstrated that vibration energy of the aerostatic bearing increases with the strength of air vortices.

Modified rotor kit Bently Nevada was used for dynamic characteristics measurements of new developed aerostatic bearings. Mathematicalmodel of these bearings is considered as linear. Model was identified with the help of harmonic force excitation independently from the speed of journal rotation. The stiffness and damping matrices were identified for different air inlet pressures. The calculated spectral properties allow to determine the stability boundary for suitable variation of model parameters.

The ‘pneumatic servo bearing actuator (PSBA)’ that consists of an aerostatic bearing and a servo valve was proposed and developed for ultraprecise positioning. In the actuator, pressurized air controlled by the servo valve moves an actuated spool ultra-precisely. Even under open-loop control, the PSBA provided accurate replication and positioning resolution on a nanometer order. Applying simple positioning feedback and parallel observation that estimates the disturbance into the system increased the actuator stiffness to be almost infinite and promoted a sharp step response without drift and hysteresis, and thus the minimum positioning resolution of prototype PSBA was about 1 nm.

This paper presents a report on the first stage of a research on the thermal analysis of spindle units with aerostatic bearings and an experimental investigation of temperature distributions. The objective of the present paper is to provide background information for further analysis. A test machine was used running to a maximum rotational speed of 20000 min −1 with a 60 mm diameter spindle supported by aerostatic journal bearings of 20 μm radial clearance, and the temperatures of the housing, bush and the interface between the bush and air film were measured. In addition, the inlet and outlet air temperatures, the air film pressures and the deformations of the housing and spindle were measured. The experimental results show that the heat flow pattern is essentially radial flow, although axial heat flow was observed. The circumferential temperature distribution can be considered to be uniform, and the temperatures are proportional to the square of the spindle speed.

Demand continues for the supply of machine tools with improved accuracy and productivity. This necessitates machine structures and spindle assemblies with much higher static and dynamic stiffness than are currently available, together with very low levels of thermal drift. The medium term accuracy of oil hydrostatic bearings has traditionally been limited by the thermal effects and although aerostatic bearings have relatively good thermal characteristics they suffer from a low relative stiffness and load capacity. New concepts are therefore required, and the authors describe a programme which is using fundamental principles to develop a new improved generation of porous bearings.

The present study is an experimental investigation of the performance characteristics of an externally pressurized rectangular recessed gas bearing operating under different working conditions. It includes the measurements of pressure, load carrying capacity, and mass flow rate. The experiments covered a wide range of film thicknesses and supply pressures. In addition, pads of different supply hole diameters were used. The results obtained from the present investigation show that the effect of varying the supply hole diameter on bearing performance is significant. Increasing the supply hole diameter to bearing length ratio has the effect of increasing the recess pressure and load carrying capacity. Further, as the supply pressure and/or film thickness increases the dimensionless load carrying capacity decreases and the lubricant mass flow rate increases.

The performance of an aerostatic bearing with a pocketed orifice-type restrictor is affected by the bearing size, pocket size, orifice design, supply pressure, and bearing load. This study proposes a modified particle swarm optimization (MPSO) algorithm to optimize a double-pad aerostatic bearing. In bearing optimization, the upper and lower bearing designs are independent and several design variables that affect bearing performance must be considered. This study also applies the concept of mutation from a genetic algorithm. The results show that the MPSO algorithm has a global search capability and high efficiency to optimize a problem with several design variables and that the mutation can provide an avenue for particles to escape from a local optimal value.

Influence of atmospheric pressure supplied on permittivity of the air-film is researched based on the capacitive testing method of the air film thickness of aerostatic bearing. An experiment platform is designed. The experimental results illustrate that permittivity has significant negative correlation with atmospheric pressure which varies from 0.1MPa to 0.48MPa when other environmental conditions remain unchanged. The curves conform to the fourth-order polynomial approximately. All of the values of R 2 are beyond 0.944 which means that trend lines fit the data curves well. Relative permittivity of the air film is between 0.996 and 1.324. This interval shows that weak current exists between restrictor and flat of the experiment which are not absolutely insulating and atmosphere of the air film is not pure. This result provides a basis both for establishing accurate mathematical model of air film thickness and capacitance value of the aerostatic bearing and for other exploratory experiments later.

This paper proposes a new type of aerostatic thrust bearing in order to achieve 10 times larger bearing stiffness compared with that of conventional aerostatic bearings. In this bearing, a porous restrictor with 1 - 3 mm diameter is employed instead of a conventional feed-hole restrictor to restrain gas flow entering the bearing clearance to a very small amount and the proposed bearing can operate in a bearing clearance of less than . The static characteristics of the proposed bearing are investigated theoretically and experimentally. It is consequently found that the proposed bearing can achieve a very high bearing stiffness of .