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Ultrasonic vibration-assisted grinding is a critical method for machining ultra-hard optical molds. However, current ultrasonic-assisted grinding spindles, as essential foundational equipment, face limitations in maintaining ultra-high rotational speed, high precision, and a compact structure during ultrasonic operation. This study presents a novel ultra-precision ultrasonic-assisted high-speed aerostatic spindle for grinding ultra-hard optical molds, developed through theoretical calculations, FEM, and CFD simulations. The spindle features a simple and compact design (φ60 mm outer diameter × 194 mm length), operates at an ultrasonic frequency of 41.23 kHz, and is driven by an impulse turbine providing torque up to 50.4 N•mm, achieving speeds exceeding 40,000 r/min. Aerostatic bearings provide axial and radial load capacities of 89 N and 220 N, respectively. The results demonstrate that the proposed high-speed precision ultrasonic spindle exhibits both feasibility and potential for practical application. [ABSTRACT FROM AUTHOR]

In this study, in order to reveal the influence mechanism of bearing parameters on pneumatic hammering, an aerostatic bearing with a multi-orifice-type restrictor is analyzed. Firstly, the flow field is investigated, and the vortex-induced excitation is discussed in both the frequency and time domains. Then, the frequency-related displacement impedance is analyzed, and the effects of vortex-induced excitation on pneumatic hammering are discussed. Experiments are also conducted for verification. Moreover, the influence of damping on pneumatic hammering is identified. The results show that with larger damping, the risk of pneumatic hammering can be reduced. Finally, the impacts of design parameters on the damping are discussed in detail using an approximate model. Design optimization is considered to achieve the maximum damping, i.e., the minimum risk of pneumatic hammering. The results show that both the air supply pressure and the pocket volume should be minimized. The analysis process provides a reference for the design of bearings to reduce pneumatic hammering. [ABSTRACT FROM AUTHOR]

Instruments with high levels of precision commonly use aerostatic bearings. Moreover, the use of porous (Al2O3 membrane) material validates that the pressure is spread uniformly throughout the air film region. The impression of applied load on the thickness of the air film of the aerostatic bearings was evaluated using a certain experimental technique. As the applied load rises, the thickness of the air film expands, and as the compressive stress rises, it contracts. The theoretical model parameters were set using the experimental stipulations. It was discovered that the theoretical model and the experimental data were consistent. The pressure gradient induced in the air film and the air bearings' capacity for carrying loads were calculated using a theoretical simulation. The results of theoretical modeling and experimental comparison of the different characteristics of porous (Al2O3 membrane) aerostatic bearings based on stiffness and load-carrying capacity are graphically illustrated in this study. Porous aerostatic bearings with Al2O3 membranes have a number of potential applications, including high-speed spindles, precision instruments, microelectromechanical systems, vacuum pumps, cryogenic applications, etc. [ABSTRACT FROM AUTHOR]

The performance of the porous gas bearing depends on the geometric characteristics, material, fluid properties, and the properties of the porous media, which is a restrictor that controls the gas flow. Its application in industrial environments must support higher loads, higher supply pressure, and, consequently, higher pressure in the lubricant fluid film. Because porous media has a relatively low elastic modulus, it is necessary to consider its deformation when designing porous gas bearings. The design of porous gas bearings is a multi-objective problem in engineering because the optimization objectives commonly are to maximize the load capacity or static stiffness coefficient and minimize the airflow; these objectives conflict. This work presents a multi-objective optimization algorithm based on the nature-inspired Flower Pollination Algorithm enhanced with Non-Dominated Sorting Genetic Algorithm II. The algorithm is applied to optimize the design of a porous gas bearing, maximizing the resultant force and the static stiffness coefficient and minimizing the airflow. The results indicate a better performance of the Multi-Objective Flower Pollination Algorithm than the Multi-Objective Cuckoo Search. The results show a relatively short running time of 6 min for iterations and a low number of iterations of 50.

The performance of the porous gas bearing depends on the geometric characteristics, material, fluid properties, and the properties of the porous media, which is a restrictor that controls the gas flow. Its application in industrial environments must support higher loads, higher supply pressure, and, consequently, higher pressure in the lubricant fluid film. Because porous media has a relatively low elastic modulus, it is necessary to consider its deformation when designing porous gas bearings. The design of porous gas bearings is a multi-objective problem in engineering because the optimization objectives commonly are to maximize the load capacity or static stiffness coefficient and minimize the airflow; these objectives conflict. This work presents a multi-objective optimization algorithm based on the nature-inspired Flower Pollination Algorithm enhanced with Non-Dominated Sorting Genetic Algorithm II. The algorithm is applied to optimize the design of a porous gas bearing, maximizing the resultant force and the static stiffness coefficient and minimizing the airflow. The results indicate a better performance of the Multi-Objective Flower Pollination Algorithm than the Multi-Objective Cuckoo Search. The results show a relatively short running time of 6 min for iterations and a low number of iterations of 50. [ABSTRACT FROM AUTHOR]

In this work, the numerical analysis of the modified Reynolds equation is compared. The difference between the two analyses is the porous media flow equation; the first considers the Darcy model, and the other the Darcy–Forchheimer model. The solution algorithms were developed using finite center differences for the geometric variable. This numerical scheme resulted in a non-linear set of equations solved with the Newton–Raphson method. Due to the nonlinearity of the problem, the relationship between the steps between axial and circumferential dimensions and the initial assumption is the main conditions for the solution to converge; the precision of the results obtained, in comparison with previous works, was acceptable; this contributes an additional effort in the development of the technology of the porous gas bearings. This work analyzed the differences in predicting the static behavior of a porous gas bearing using the Darcy model and the extended Darcy–Forchheimer model to determine the flow behavior through the porous medium. The solution algorithm of the modified Reynolds equation with the Darcy–Forchheimer model offers a broader range of solutions because it is capable of predicting both the linear and non-linear behavior of the flow through the porous medium and the influence in the lubricant film; this is essential for the design of porous gas bearings for industrial applications. The Finite Difference solutions are compared with a Finite Element and Finite Volume solution. The results show similar approximations with the advantage that the finite difference solution is more straightforward and can be coupled with a dynamic lump-mass model. [ABSTRACT FROM AUTHOR]

In order to improve the load carrying capacity and stiffness of the aerostatic bearings of the radial inflow turbogenerator for the organic Rankine cycle (ORC) system, the aerostatic bearings with R245fa as the lubricating medium was designed by gauge pressure ratio method, and the effects of rotor eccentricity, orifice size and inlet pressure on the load carrying capacity and stiffness of the aerostatic bearings were analyzed.The results show that the bearing load capacity and stiffness increase with the increase of speeds under the same air supply pressures. At the same speed,the load capacity and stiffness of the bearing at the air supply pressure of 0.7 MPa is slightly higher than those at other air supply pressures. The greater the eccentricity of the aerostatic bearings, the greater the load carrying capacity. The load carrying capacity and stiffness of the aerostatic bearings increases with the increase of rotational speeds under the same air supply hole diameter. The larger the air supply hole diameters, the greater the bearing capacity and stiffness of the aerostatic bearings. [ABSTRACT FROM AUTHOR]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Lubrication Engineering (0254-0150) is the property of Editorial Office of LUBRICATION ENGINEERING and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, in order to reveal the influence mechanism of bearing parameters on pneumatic hammering, an aerostatic bearing with a multi-orifice-type restrictor is analyzed. Firstly, the flow field is investigated, and the vortex-induced excitation is discussed in both the frequency and time domains. Then, the frequency-related displacement impedance is analyzed, and the effects of vortex-induced excitation on pneumatic hammering are discussed. Experiments are also conducted for verification. Moreover, the influence of damping on pneumatic hammering is identified. The results show that with larger damping, the risk of pneumatic hammering can be reduced. Finally, the impacts of design parameters on the damping are discussed in detail using an approximate model. Design optimization is considered to achieve the maximum damping, i.e., the minimum risk of pneumatic hammering. The results show that both the air supply pressure and the pocket volume should be minimized. The analysis process provides a reference for the design of bearings to reduce pneumatic hammering.

Ultrasonic vibration-assisted grinding is a critical method for machining ultra-hard optical molds. However, current ultrasonic-assisted grinding spindles, as essential foundational equipment, face limitations in maintaining ultra-high rotational speed, high precision, and a compact structure during ultrasonic operation. This study presents a novel ultra-precision ultrasonic-assisted high-speed aerostatic spindle for grinding ultra-hard optical molds, developed through theoretical calculations, FEM, and CFD simulations. The spindle features a simple and compact design (φ60 mm outer diameter × 194 mm length), operates at an ultrasonic frequency of 41.23 kHz, and is driven by an impulse turbine providing torque up to 50.4 N•mm, achieving speeds exceeding 40,000 r/min. Aerostatic bearings provide axial and radial load capacities of 89 N and 220 N, respectively. The results demonstrate that the proposed high-speed precision ultrasonic spindle exhibits both feasibility and potential for practical application.

The solution of equilibrium positions is a critical component in the calculation of the dynamic characteristic coefficients of aerostatic bearings. The movement of the rotor in one direction leads to bidirectional variations in the air film force, resulting in low efficiency when using conventional calculation methods. It can even lead to iterative divergence if the initial value is improperly selected. This study concentrates on the orifice throttling aerostatic bearings and proposes a novel method called the bivariate interpolation method (BIM) to calculate the equilibrium position. The equilibrium equation for the rotor under the combined influence of air film forces, gravity, and external loads is established. A calculation program based on the finite difference method is developed to determine the equilibrium position. The process of solving the equilibrium position and the convergence is compared with the secant method and the search method. Furthermore, the variation trend of the equilibrium position and stiffness when the external loads changes are studied based on the BIM. Finally, the correctness of the BIM to solve the equilibrium position is proved by comparing it with the experiment results. The calculation results indicate that the BIM successfully resolves the problem of initial value selection and exhibits superior computational efficiency and accuracy. The equilibrium position initially moves away from the direction of the external load as the load increases, and then this gradually approaches the load direction. The main stiffness increases with increases in the external load, while the variation in cross stiffness depends on the direction of the external load. [ABSTRACT FROM AUTHOR]

Due to the advantages of low friction, high accuracy, and pollution-free characteristics, aerostatic bearings are widely used in precision and ultra-precision equipment machines. In order to improve the stability, this paper proposes a novel aerostatic bearing with damper modules to suppress the vibration on the bearing surface. A hermetically squeeze film damper (HSFD) constructed by sheet damper module (SDM) is applied to aerostatic bearings for acquiring good stability. The appropriate stiffness range of HSFDs can be obtained for meeting different air film thicknesses and excitation frequencies by theoretical calculations. Various stiffness and damping characteristics can be acquired by adjusting the thickness of sheets in SDMs. In addition, an experimental device is established to identify the stiffness and damping behavior of dampers. In order to further gain insight to evaluate the performance of bearings, a simple test rig has also been set up to measure the vibration characteristics. Experimental results reveal that the damper concept yields high viscous damping characteristics an order of magnitude larger than aerostatic bearing without dampers, which leads to the vibration amplitude be obviously suppressed. The proposed aerostatic bearings with HSFDs can provide a better performance on damping and stability. • In order to improve the stability, this paper proposes a novel aerostatic bearing with damper modules to suppress the vibration of bearing surface. • A hermetically squeeze film damper (HSFD) constructed by sheet damper module (SDM) is applied to aerostatic bearings to acquire good stability. • Experimental results show that the damper concept yields high viscous damping characteristics an order of magnitude larger than aerostatic bearing without dampers, which leads to the vibration amplitude on bearing surface can obviously been decreased. [ABSTRACT FROM AUTHOR]

According to the common body of knowledge, aerostatic bearings invariably need narrow manufacturing tolerances to ensure maximal load capacity and high stiffness. This study experimentally investigates the manufacturing of porous material aerostatic bearings and the effect of manufacturing parameters on the performance properties of the bearings. During the study, samples were manufactured using different methods, and the geometrical and performance properties of each sample were inspected. The bearing performance measurement device developed during the study is introduced. The results present the dependence between manufacturing parameters and bearing properties under varying load and operating pressure conditions. The results clearly suggest that effect of bearing surface roughness on load capacity is small; meanwhile, surface planarity has a major impact on load capacity. [Display omitted] • Automated performance measurement setup for aerostatic bearings. • Porous aerostatic bearings are manufactured with variable manufacturing parameters. • Correlation between manufacturing methods and bearing performance. [ABSTRACT FROM AUTHOR]

The present work is dedicated to investigating both characteristics of the vortex-induced excitation and the displacement impedance and also weakening the micro-vibration for the aerostatic bearing with orifice type restrictor. Firstly, the numerical simulation is conducted to study the characteristics of the vortex flow in the frequency domain. Further, the displacement impedance is investigated based on an approximate model; the effects of bearing parameters on displacement impedance are also discussed. It is found that the vortex-induced excitation is the dynamic load acting on the floating device, while the displacement impedance reflects the capability of the bearing to withstand the dynamic load. Hence, it is necessary to enhance the displacement impedance for micro-vibration reduction in the bearing. Moreover, the design problem corresponding to the micro-vibration reduction is formulated, and the design optimization is carried out under several given bearing loads. Optimization results show that the micro-vibration can be reduced by increasing the displacement impedance and decreasing the Reynolds number in the flow field. The optimization process can provide an efficient way for reducing the micro-vibration in engineering application. [ABSTRACT FROM AUTHOR]

Precision measurement technology and instruments are the basis for high-quality development in modern industry. With the specialization of supporting facilities, ultra-precision motion guidance has become a core technology to achieve ultra-precision measurement. Aerostatic bearings have the advantages of low friction and high precision, and are gradually playing an irreplaceable role in precision measurement and instruments. This paper summarizes and puts forward two contradictions for improving the loading capacity of aerostatic bearings, and investigates how to solve them via structural design. This paper analyzes the characteristics of the engineering calculation method, the gauge pressure ratio method, the gas resistance calculation method, and the AFVM (adaptive finite volume method) proposed. Finally, this paper summarizes the application scope of each method, gives solutions to the core problems, and outlines the developing trends. [ABSTRACT FROM AUTHOR]

Copyright of Lubrication Engineering (0254-0150) is the property of Editorial Office of LUBRICATION ENGINEERING and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Under support forces from static pressure bearings, the solid deformations of static pressure spindle or slide systems will affect their performance, especially for those with high load-carrying capacity and stiffness. This paper proposes a steady modeling method to study the effect of fluid–structure interaction (FSI) on the thrust stiffness of an H-shaped aerostatic spindle. The proposed method can be readily applied to different static pressure spindles or slides, and can save a lot of time compared with the transient method, which is generally used to consider the phenomenon of FSI. The method proposed in this study is more suitable for studying the performance of spindles and slides with high load-carrying capacity and stiffness, especially in the design phase. In this paper, solid deformations, pressure distributions and the thrust stiffness are all obtained based on this method. Moreover, the effects of the axial position of the spindle and the air film thickness on the thrust stiffness are studied. The proposed method is verified by experimental results. The calculation error of the proposed method is reduced by nearly 77% compared with the traditional method ignoring FSI.

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The displacement impedance performance directly reflects the capability of the aerostatic bearing to resist the external dynamic load, and it should be optimized in design of bearing dynamic performances to reduce the pneumatic hammering vibration. To improve the bearing dynamic performances and reduce the pneumatic hammering vibration, the displacement impedance of the air film--floating facility system was studied. Using numerical simulation method and applying the dynamic mesh technology to calculate the displacement impedance, the influence mechanisms of the structural and operating parameters on the displacement impedance were discussed for the aerostatic bearing with multi-orifice type restrictor. Based on the radial basis function neural network model, an approximate analysis model of displacement impedance expressed by bearing parameters was established, and the influence of bearing parameters on displacement impedance was compared and discussed using PARETO analysis. The optimization model was established, the frequency among the pneumatic hammering vibration range was considered, and the displacement impedance was optimized with the given bearing load to reduce the pneumatic hammering vibration. The results indicate that due to the squeeze film effect, the excitation frequency has the largest influence on the displacement impedance. The displacement impedance increases dramatically with the increase of excitation frequency. Therefore, the bearing can resist the dynamic load with high frequencies effectively, and it is important to improve the displacement impedance with low frequency excitation. The orifice diameter, air film thickness and the air supply pressure have larger influence on displacement impedance than the air pocket sizes and the orifice position. The analysis and optimization process can give a reference for the bearing design in engineering. [ABSTRACT FROM AUTHOR]

Copyright of Lubrication Engineering (0254-0150) is the property of Editorial Office of LUBRICATION ENGINEERING and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The solution of equilibrium positions is a critical component in the calculation of the dynamic characteristic coefficients of aerostatic bearings. The movement of the rotor in one direction leads to bidirectional variations in the air film force, resulting in low efficiency when using conventional calculation methods. It can even lead to iterative divergence if the initial value is improperly selected. This study concentrates on the orifice throttling aerostatic bearings and proposes a novel method called the bivariate interpolation method (BIM) to calculate the equilibrium position. The equilibrium equation for the rotor under the combined influence of air film forces, gravity, and external loads is established. A calculation program based on the finite difference method is developed to determine the equilibrium position. The process of solving the equilibrium position and the convergence is compared with the secant method and the search method. Furthermore, the variation trend of the equilibrium position and stiffness when the external loads changes are studied based on the BIM. Finally, the correctness of the BIM to solve the equilibrium position is proved by comparing it with the experiment results. The calculation results indicate that the BIM successfully resolves the problem of initial value selection and exhibits superior computational efficiency and accuracy. The equilibrium position initially moves away from the direction of the external load as the load increases, and then this gradually approaches the load direction. The main stiffness increases with increases in the external load, while the variation in cross stiffness depends on the direction of the external load.

Aerostatic bearings are considered crucial components that can improve the measurement accuracy of ground simulation tests of space equipment. A structural optimization design method is proposed to enhance the static performance of aerostatic bearings. A mathematical model which can quickly calculate the aerostatic bearing capacity and gas consumption is established, and the influence of structural parameters on bearing performance is analyzed using simulation software. By comparing the convergence time and convergence results of the algorithm using different initialization methods, the Latin hypercube initialization method is selected instead of the random initialization method. The multi-objective particle swarm optimization algorithm is used to obtain the optimal solution set distributed in the objective space. It is found that the optimized structural parameters meet the requirements of improving the capacity and reducing gas consumption, which verifies the method's effectiveness in designing the structural parameters of aerostatic bearings. [ABSTRACT FROM AUTHOR]

Aerostatic bearings have been widely applied to high-rotating speed machines due to their low friction and high rotational speed advantages. The geometry parameters, supply pressure and rotational speed play important roles in the static and dynamic performances of the aerostatic bearings. In this paper, the steady state and dynamic Reynolds equations are solved by the finite difference method (FDM) and used to study the static and dynamic performances of the aerostatic bearings. Then, combined with the motion equation of the rigid rotor-aerostatic bearing system, the linear stability of the aerostatic bearing is also studied. Moreover, based on the theory mentioned above, the influences of the geometry parameters (such as orifice diameter, radial clearance and eccentricity), rotational speed and supply pressure are investigated in detail. It was found that aerostatic bearing geometries, rotational speed and supply pressure had a significant effect on the steady and dynamic performances. Under the low-speed conditions and high supple pressure, the static pressure effect plays the main role in the performances of the aerostatic bearings, while on the contrary, the rotational effect plays the main role. Furthermore, a half-speed whirl may generate under certain conditions. The results also provide useful design guidelines for aerostatic bearings in high-speed machines. [ABSTRACT FROM AUTHOR]

Aerostatic bearings are the key component of ultra-precision machine tools, and the bearing performance is critical to the machining accuracy and reliability. The characteristics of the air film pressure field (AFPF) mainly determine the bearing performance and are closely related to parameters such as the air supply pressure, the number, and position distribution of orifices. However, the orifices of aerostatic bearing were usually assumed to be ideal for the available related research. The phenomenon of orifice blockage is common in the actual working conditions, which has great impact on the bearing performance. In this study, the AFPF characteristics of aerostatic thrust bearing was analyzed by the theoretical and experimental way with the commonly single-orifice blockage (SOB) or double-orifice blockage (DOB) cases. The air film pressure distribution, load capacity, and tilting moment are obtained for each case. The effectiveness of simulation results is verified by the experiments. The results indicates that the air film pressure decreases significantly in the area of about three orifices adjacent to the blocked orifice in the condition of SOB. Different cases of orifice blockage have different bearing tilting moment, and resulting in different bearing tilting angle. According to different bearing tilting direction and tilting angle, a preliminary prediction method of the orifice blockage is proposed to judge the different cases of orifice blockage. [ABSTRACT FROM AUTHOR]

• The driving mechanism of aerostatic bearing vibrations was revealed through the POD method, identifying vortices and shear flow characteristics under different supply pressures and film thicknesses. • At a supply pressure of 3atm, low-frequency large-scale vortices within the recess dominate the flow field, while at 4atm and 5atm, high-frequency convection and shear processes become predominant. • Increasing the film thickness to 20 μm enhances the vortices at the recess inlet and leads to the emergence of new vortex structures at the recess outlet. • Four main flow features were identified, depending on supply pressure and film thickness. The driving mechanism of the vibration of aerostatic bearings is still unclear. Although there are several interpretations, none of them is conclusive. The difficulty lies in the complicated information concealed beneath the turbulence flow. To this end, the proper orthogonal decomposition (POD) method was systematically implemented in the aerostatic bearing flow field analysis in the present study, and some new findings have been proposed. First, the accuracy of our large eddy simulation (LES) has been validated through quantitative comparisons with the experimental references in terms of pressure distribution. Then, the mode decomposition has been conducted at a circumferential symmetry plane and bottom surface and the influence of supply pressure has been uncovered. It turns out that the vortices within the recess dominate the flowfield when the supply energy Ps=3atm, which could be recognized as the driving mechanisms of vibrations. The convection and shearing process in the vicinity of the recess inlet becomes intense and corresponding vortices become predominant in the cases of Ps=4atm and 5atm. Eventually, the influences of film thickness have also been discussed when Ps=4atm. Different from the case of h = 10 μm, the low-frequency vortices near the recess outlet could be detected when the film thickness is increased to 20 µm. The control of corresponding flow structures might be helpful for the vibration suppression. [ABSTRACT FROM AUTHOR]

Under support forces from static pressure bearings, the solid deformations of static pressure spindle or slide systems will affect their performance, especially for those with high load-carrying capacity and stiffness. This paper proposes a steady modeling method to study the effect of fluid–structure interaction (FSI) on the thrust stiffness of an H-shaped aerostatic spindle. The proposed method can be readily applied to different static pressure spindles or slides, and can save a lot of time compared with the transient method, which is generally used to consider the phenomenon of FSI. The method proposed in this study is more suitable for studying the performance of spindles and slides with high load-carrying capacity and stiffness, especially in the design phase. In this paper, solid deformations, pressure distributions and the thrust stiffness are all obtained based on this method. Moreover, the effects of the axial position of the spindle and the air film thickness on the thrust stiffness are studied. The proposed method is verified by experimental results. The calculation error of the proposed method is reduced by nearly 77% compared with the traditional method ignoring FSI. [ABSTRACT FROM AUTHOR]

All the static performance, dynamic characteristics, and stability are strongly associated with the flow field inside the aerostatic bearings. Therefore, a high-precision numerical method is beneficial for the detailed description of the bearing flow field. To this end, a modified interior penalty discontinuous Galerkin method was introduced here. Actually, a lift operator was included to eliminate the so-called homogeneity tensor connecting the viscous term and variable gradient, which could improve the numerical feasibility. The accuracy of the above numerical method has been comprehensively validated through viscous cases, including Couette flow and shear-driven cavity flow. Then, the flow fields of three aerostatic bearings were simulated with different orifice geometries. As a result, the Mach number distributions and static pressure could be estimated together with the integration of the pressure acting upon the thrust surface. The acceleration within the orifice and air film could be detected, and the influence of the orifice geometry has been systematically discussed. [ABSTRACT FROM AUTHOR]

Aerostatic bearings are widely used for spindles in ultra-precision machining tools. These spindles consist of a pair of aerostatic thrust bearings and several aerostatic journal bearings. The rotational accuracy of aerostatic spindles depends largely on the arrangement and performance of the individual bearings, but the evaluation of the rotational accuracy is mainly carried out experimentally using a prototype machine, which poses challenges in terms of the time and cost of building a prototype. Therefore, a real need exists to evaluate the spindle characteristics by numerical calculation. In this study, we developed a method to numerically calculate the trajectory of the spindle rotator which is supported by aerostatic bearings. The method was developed to numerically investigate and determine the effects on the rotational accuracy of the spindle during end milling when the cutting force is applied to the rotating rotor. A comparison was made regarding the amount of runout of the rotating shaft when side milling was performed using a spindle with a shaft diameter of 22 mm and a small end mill with a diameter of 1 mm, concerning three different spindles with different arrangements of thrust and journal bearings. The effects of rotational speed, radial depth of cut, and the number of tool teeth on the runout of the rotating shaft were numerically verified. As a result, it was found that a spindle structure in which the thrust bearing is placed on the tool side and the journal bearing span is lengthened is desirable. [ABSTRACT FROM AUTHOR]

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The micro vibration of the aerostatic thrust bearing with shallow recess seriously restricts the improvement of the bearing working accuracy.The gas vortex inside the recess is the main reason of the micro vibration.An aerostatic thrust bearing with minor-hole compound restrictor was proposed to suppress the gas vortex.The influence of minor-hole compound restrictor parameters ( diameter and position of minor holes) on vortex suppression and static characteristics of the aerostatic bearing was investigated numerically. It is found that the bearing capacity and outlet flow rate decrease slightly by using the compound throttling method of main inlet hole and minor-hole, but using minor-hole compound restrictor can suppress the gas vortex in the shallow recess.With the increase of the minor-hole diameter and the distance between the minor hole and the main hole when other conditions remain unchanged, the bearing capacity and outlet flow generally show a downward and then upward trend.With the increase of the minor-hole diameter,the suppression effect on the gas vortex increases firstly and then weakens. With the increase of the distance between the minor hole and the main hole, the suppression effect on gas vortex continually weakens. [ABSTRACT FROM AUTHOR]

Precision measurement technology and instruments are the basis for high-quality development in modern industry. With the specialization of supporting facilities, ultra-precision motion guidance has become a core technology to achieve ultra-precision measurement. Aerostatic bearings have the advantages of low friction and high precision, and are gradually playing an irreplaceable role in precision measurement and instruments. This paper summarizes and puts forward two contradictions for improving the loading capacity of aerostatic bearings, and investigates how to solve them via structural design. This paper analyzes the characteristics of the engineering calculation method, the gauge pressure ratio method, the gas resistance calculation method, and the AFVM (adaptive finite volume method) proposed. Finally, this paper summarizes the application scope of each method, gives solutions to the core problems, and outlines the developing trends.

Copyright of Lubrication Engineering (0254-0150) is the property of Editorial Office of LUBRICATION ENGINEERING and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Lubrication Engineering (0254-0150) is the property of Editorial Office of LUBRICATION ENGINEERING and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Air turbine spindles with aerostatic bearings are widely used in ultraprecision machining equipment. Ultraprecision grinding processes using air turbine spindles with aerostatic bearings include constantpressure dry lapping of nano-polycrystalline diamond (NPD) tools and ultraviolet irradiation polishing of chemical vapor deposition diamond films. In the dry lapping of NPD tools, it is necessary to achieve constant-pressure grinding while flexibly adjusting the contact force between the NPD tool and the truer fixed on the end face of the aerostatic spindle to form a nose bite with a cutting-edge rounding radius, R, of 0.1 nm. However, it is common for operators to manually adjust the cut depth and the air pressure supplied to the aerostatic bearing by relying on the noise and rotation speed during machining. Moreover, aerostatic spindles without a control mechanism, such as active bearings, are widely used because of their low costs and versatility. For several years, the authors have been developing a method to control air bearing stiffness by controlling the bearing supply pressure with high speeds and precision using a high-precision quick response regulator for aerostatic spindles without a control mechanism, such as active bearings. In this study, the compliance control (control of spindle position and stiffness) of aerostatic bearings was investigated using the proposed method, and the effectiveness of the method to ultraprecision grinding applications was demonstrated. [ABSTRACT FROM AUTHOR]

Copyright of Lubrication Engineering (0254-0150) is the property of Editorial Office of LUBRICATION ENGINEERING and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Aerostatic bearings are considered crucial components that can improve the measurement accuracy of ground simulation tests of space equipment. A structural optimization design method is proposed to enhance the static performance of aerostatic bearings. A mathematical model which can quickly calculate the aerostatic bearing capacity and gas consumption is established, and the influence of structural parameters on bearing performance is analyzed using simulation software. By comparing the convergence time and convergence results of the algorithm using different initialization methods, the Latin hypercube initialization method is selected instead of the random initialization method. The multi-objective particle swarm optimization algorithm is used to obtain the optimal solution set distributed in the objective space. It is found that the optimized structural parameters meet the requirements of improving the capacity and reducing gas consumption, which verifies the method’s effectiveness in designing the structural parameters of aerostatic bearings.

Aerostatic bearings have been widely applied to high-rotating speed machines due to their low friction and high rotational speed advantages. The geometry parameters, supply pressure and rotational speed play important roles in the static and dynamic performances of the aerostatic bearings. In this paper, the steady state and dynamic Reynolds equations are solved by the finite difference method (FDM) and used to study the static and dynamic performances of the aerostatic bearings. Then, combined with the motion equation of the rigid rotor-aerostatic bearing system, the linear stability of the aerostatic bearing is also studied. Moreover, based on the theory mentioned above, the influences of the geometry parameters (such as orifice diameter, radial clearance and eccentricity), rotational speed and supply pressure are investigated in detail. It was found that aerostatic bearing geometries, rotational speed and supply pressure had a significant effect on the steady and dynamic performances. Under the low-speed conditions and high supple pressure, the static pressure effect plays the main role in the performances of the aerostatic bearings, while on the contrary, the rotational effect plays the main role. Furthermore, a half-speed whirl may generate under certain conditions. The results also provide useful design guidelines for aerostatic bearings in high-speed machines.

This article contains theoretical analysis and experimental study of the original mechatronics system with flexible characteristics which we can adapt to changing needs and external interference. The main purpose of our research is to find a solution that allows tailoring the desired characteristics of systems regardless of changing conditions without their mechanical interference. The system consists of the guide endowed with mass suspended in the air by the linear aerostatic bearing. Linear mechanical spring is attached to the one side of the guide whereas the neodymium magnet is fixed to the other side. Magnet-magnet and magnet-coil interactions have been investigated. The magnet-magnet interaction plays the role of the nonlinear magnetic spring while the magnet-coil interaction plays the role of the electromagnetic spring or electromagnetic damper in terms of the coil current signal. Static and dynamic characteristics of mechanical, magnetic and electromagnetic springs have been analyzed. A new physical model of the magnet-magnet interaction has been presented, the validity of which is confirmed experimentally. In addition, modern IT (information technology) techniques have been used to control the system behavior. The reliable results of the entire system and its springs are obtained by conducting tests on specially constructed laboratory setup. The main benefit of the fabricated setup concerns an elimination of dry friction effects though the frictions is viscous with identifiable movement resistance. [ABSTRACT FROM AUTHOR]

In order to improve the calculation efficiency of the aerostatic bearing, an impedance model for calculating the loading capacity of the aerostatic bearing with the radial pressure groove arranged on the surface was presented, and the feasibility of the impedance model was verified by CFD numerical simulation, and the influence of the depth, radius and angle of the pressure groove on the impedance model was analyzed. The results show that the impedance model can be used to calculate the loading capacity of radial pressure groove and non-pressure groove with different section shapes, and the results of CFD numerical simulation are in good agreement with those of the impedance model. When the air film is small, the system impedance coefficient and bearing capacity of the air aerostatic bearing can be improved by arranging the pressure groove on the surface of the aerostatic bearing. The depth and radius of the pressure groove have great influence on the impedance coefficient of the system while the angle of the pressure groove has little influence on the impedance coefficient of the system. [ABSTRACT FROM AUTHOR]

In aerostatic journal bearing, load capacity and bearing stiffness can be improved through asymmetric air supply. In order to explore the influence of asymmetric air supply conditions on pressure distribution and static characteristics of aerostatic bearings, the double row air supply aerostatic journal bearing was taken as the research object, and the static characteristics of the bearing under different air supply types (variable pressure air supply hole position and area) and air supply pressure were studied by numerical calculation. The numerical results indicate that the position of variable air supply pressure has a great influence on the static characteristics of the journal bearing. When increasing the air supply pressure in the main bearing area, the aerodynamic and aerostatic effect of the bearing can be significantly enhanced. The bearing load capacity can be elevated with increasing variable pressure area, but the pressurized gas consumption is also increased correspondingly. The bearing capacity can be improved effectively by either increasing the air supply pressure on the loading side or reducing the gas supply pressure on the counter--loading side. The latter method can also reduce the total mass flow rate of pressurized gas. The greater air supply pressure difference between the loading side and the counter--loading side is more conducive to the improvement of bearing capacity. [ABSTRACT FROM AUTHOR]

Copyright of Lubrication Engineering (0254-0150) is the property of Editorial Office of LUBRICATION ENGINEERING and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)