Improved finite difference method for pressure distribution of aerostatic bearing

An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.

Entrance Effect on Load Capacity of Orifice Compensated Aerostatic Bearing with Feeding Pocket

The current research of the aerostatic thrust bearing mainly focuses on the porous material bearing and inherent compensated air bearing, which aims at obtaining small physical dimension and large load capacity. Although porous material bearing appears larger load capacity, materials anisotropy itself and void content distortion caused in heat-treating, and machining processes add greater complexity to internal flow transfer process. Inherent compensated air bearing has the advantages of simple structure and good stability, but its load capacity and static stiffness is not worth somewhat. In this paper, based on hydrostatic lubrication theory, finite volume method is presented for taking entrance effects into account in computing pressure distribution, load capacity and mass flow rates of circular aerostatic thrust bearings. Technical analysis, numerical simulations and laboratory demonstration tests of influence of pocket diameter and pocket depth on loading capacity of aerostatic thrust bearing are carried out on simple orifice compensated air bearings with feeding pockets. The static parameters, such as air consumption and pressure distributions, are measured as a function of supply pressure and air gap height for several different orifices and pockets size. Entrance effects are described in term of typical throttling types, and the effect of pocket diameter and pocket depth on load capacity is systematically described respectively. The proposed research results uncover the causation of throttling action of the orifice compensated air bearing with feed pocket and further develop and improve the design theory of air bearing.

Numerical Simulation and Experimental Verification of the Stiffness and Stability of Thrust Pad Aerostatic Bearings

Many researchers concentrate on improving the stiffness and stability of aerostatic bearings, however the contradiction between stiffness and stability is still existed. Therefore, orifice, multiple, and porous restrictors are designed to illustrate the influence of restrictor characteristics on the stability and stiffness of the aerostatic circular pad bearings. Because both the stiffness and stability of aerostatic bearings are determined by the internal pressure distribution, the full Navier?Stokes(N?S) equations are applied to solve internal pressure distribution in bearing film by using computational fluid dynamics(CFD) method. Simulation results present that the stiffness and stability of aerostatic circular pad bearings are influenced significantly by geometrical and material parameters, such as film thickness, orifice diameters, and viscous resistance coe cient. Verified by the experimental data, the micro vibration of orifice restrictor is almost the same as multiple restrictors with amplitude of 0.02 m/s~2, but it is much stronger than the porous restrictors with acceleration of 0.006 m/s~2. The optimal stiffness of multiple restrictors increased by 46%, compared to only 30.2 N/μm of orifice restrictor, and the porous restrictors had obvious advantage in the small film thickness less than 6 μm where the optimal stiffness increased to 38.3 N/μm. The numerical and experimental results provide guidance for improving the stiffness and stability of aerostatic bearings.

Design of Microstructure Parameters on a Small Multi-Throttle Aerostatic Guideway in Photolithography

A compact multi-throttle aerostatic guideway is the preferred structure for high precision and acceleration motion in the variable-slit system(VS)of photolithography.The presence of microstructure,such as recesses and grooves,on the guideway working surface has been found to improve the loading performance.Nevertheless,the effects on the guideway performance of changing the microstructure on the micron level are not yet clear.The mesh adaptation method,which was proposed by the authors,is employed in this paper to quantitatively study the influences of four microstructure parameters.The effect of tuning these parameters on the loading performance is revealed.The level of impact determines the proposed design process of the parameters.The characteristic feature of the proposed design process is that the working points of carrying capacity,stiffness,and rotational stiffness are unified under twoway adjusting by means of recess parameters.According to the proposed design process and tuning method,the restriction of supply pressure is lifted to a certain extent and the mutual tradeoff among the loading performances is relieved.The experimental results show that the rotational stiffness of the designed guideway,based on the tuned parameters,reached 2.14×10^(4) Nmrad1 and increased by 69.8%.In a scanning test of the applied VS on argon fluoride laser(ArF)photolithography,the average scanning acceleration reached 67.5 m·s^(-2),meeting the design specification.

Study of the aerostatic and aerodynamic stability of super long-span cable-stayed bridges

With the increase of span length, the bridge tends to be more flexible, and the wind stability be- comes an important problem for the design and construction of super long-span cable-stayed bridges. By taking a super long-span cable-stayed bridge with a main span of 1 400 m as example, the aerostatic and aerodynamic stability of the bridge are investigated by three-dimensional nonlinear aerostatic and aerodynamic stability analy- sis, and the results are compared with those of a suspension bridge with a main span of 1 385 m, and from the aspect of wind stability, the feasibility of using cable-stayed bridge in super long-span bridge with a main span above l 000 m is discussed. In addition, the influences of design parameters including the depth and width of the girder, the tower structure, the tower height-to-span ratio, the side-to-main span ratio, the auxiliary piers in the side span and the anchorage system of stay cables, etc on the aerostatic and aerodynamic stability of su- per long-span cable-stayed bridges are investigated numerically; the key design parameters are pointed out, and also their reasonable values are proposed.

Modeling of disturbance torque in an aerostatic bearings-based nano-satellite simulator

The disturbance torque of aerostatic bearings is in the same order of the reaction wheel, which causes difficulty in evaluation of the designed attitude control strategy of a nano-satellite based on the aerostatic bearing. Two approaches are proposed to model the disturbance torque. Firstly, the gravity induced moment,the vortex torque, and the damping moment are modeled separately. However, the vortex torque and the damping moment are coupled with each other as both of them are caused by the viscosity. In the second approach, the coupling effect is considered. A nano-satellite is constructed based on aerostatic bearing. The time history of the free rotation rate from an initial speed is measured by the gyro, which is further used to calculate the rotation angle and acceleration. The static vortex torque is measured via the removable micro-torque measurement system. Based on these data, the model parameters are identified and modeling errors are presented. Results show that the second model is more precise.The root mean squire error is less than 0.5×10^（-4） N·m and the relative error of the static vortex torque is 0.16%.

Dynamics modeling and simulation of a saucer-shaped stratospheric aerostat with an under-slung nacelle

A new concept stratospheric aerostat is investigated which consists of a saucer-shaped hull, multi-vectored thrusters, and an under-slung nacelle. The design of this aerostat involves tradeoffs between conventional airship and high altitude balloon. The sling connection simplifies structure design significantly, but brings challenges for dynamics analysis. Dynamics modeling for this aerostat is a kind of double-body problem with geometric constraint. Nonlinear dynamics model is established by considering the effects of under-slung nacelle. Oscillation behavior of this double-body system is superposed by a long-period oscillation of the hull and a short-period oscillation of the nacelle. The length of sling only influences the short-period oscillation but the mass ratio of nacelle to main body determines the stability of system. Finally, an envelope about mass ratio and maximal open loop forward thrust as well as speed is presented, where the system is stable.

Numerical analysis of the static performance of an annular aerostatic gas thrust bearing applied in the cryogenic turbo-expander of the EAST subsystem

The EAST superconducting tokamak, an advanced steady-state plasma physics experimental device, has been built at the Institute of Plasma Physics, Chinese Academy of Sciences. All the toroidal field magnets and poloidal field magnets, made of NbTi/Cu cable-in-conduit conductor, are cooled with forced flow supercritical helium at 3.8 K. The cryogenic system of EAST consists of a 2 kW/4 K helium refrigerator and a helium distribution system for the cooling of coils, structures, thermal shields, bus-lines, etc. The high-speed turbo-expander is an important refrigerating component of the EAST cryogenic system. In the turbo-expander, the axial supporting technology is critical for the smooth operation of the rotor bearing system. In this paper, hydrostatic thrust bearings are designed based on the axial load of the turbo-expander. Thereafter, a computational fluid dynamics-based numerical model of the aerostatic thrust bearing is set up to evaluate the bearing performance. Tilting effect on the pressure distribution and bearing load is analyzed for the thrust beating. Bearing load and stiffness are compared with different static supply pressures. The net force from the thrust bearings can be calculated for different combinations of bearing clearance and supply pressure.

Advanced aerostatic analysis of long-span suspension bridges

As the span length of suspension bridges increases, the diameter of cables and thus the wind load acting on them, the nonlinear wind-structure interaction and the wind speed spatial non-uniformity all increase consequently, which may have unnegligible influence on the aerostatic behavior of long-span suspension bridges. In this work, a method of advanced aerostatic analysis is presented firstly by considering the geometric nonlinearity, the nonlinear wind-structures and wind speed spatial non-uniformity. By taking the Runyang Bridge over the Yangtze River as example, effects of the nonlinear wind-structttre interaction, wind speed spatial non-uniformity, and the cable＇s wind load on the aerostatic behavior of the bridge are investigated analytically. The results showed that these factors all have important influence on the aerostatic behavior, and should be considered in the aerostatic analysis of long and particularly super long-span suspension bridges.

An Analysis of Restricting Patterns of Aerostatic Guideways

The effects of restricting petterns of rectangular aerostatic guideway, restricitng orifce, spread of restricting orifices, size of air cavity and making tiny groove on the air foating surface etc, on the function of aerostatic guideway are analyzed by applying the method of finite element. This also provides a theoretical evidence for the design of rectangular guideways. The non-linear pressure equation set of finite element are sovled by using Newton metehod which guarantees quick and satisfactory convergence, high precision computation and wide range of applications.

Gas film performance of double-row orifices of aerostatic guideways

In order to analyze the performance of aerostatic guidways,the stiffness calculation equation of the aerostatic guideway with two-row orifice has been derived by gas lubrication theory. For the complex structure of the motion guideway and unloading guideway,the frequency of the whole slides in machining direction with gas thickness has been derived. Wavelet transform as a means to process the measured signal of workpiece surface, the frequency characteristics of gas fluctuation of aerostatic guideways has been extracted out from the measured signal,and the errors of the guideway system have been identified according to the power spectral density (PSD) ,and this provide a basis for the identification of machine tool error.

Application of non-probabilistic reliability on aerostat capsule

Aerostat capsule is small sample data,so designing reliability is very difficult to be obtained accurately by conventional probabilistic reliability method. Based on the interval non-probabilistic reliability theory,an instability mathematics model of envelope structure is studied,and the calculation formula of interval reliability index is put forward. Through the mechanical experiments of three capsule structures,the experimental results of the interval reliability are obtained. By comparing the theoretical and measured values,it is found that the theoretical reliability index is more conservative. Non-probabilistic reliability method can reflect the reliability degree of the capsule body under different loading conditions,which can provide some guidance for engineering application.

Spectral properties and identification of aerostatic bearings

Modified rotor kit Bently Nevada was used for dynamic characteristics measurements of new developed aerostatic bearings.Mathematical model 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.

Design, Development and Geometric Error Analysis of an Aerostatic Rotary Table

Rotary tables are equipments in precision machinery applied in five-axis Machine Tools and CMM （Coordinate Measuring Machines）, offering rotational （C-axis） and tilting motion （A-axis）, allowing the obtaining of several configurations for manufacturing or inspection of parts with complex geometries. The demand for high accuracy, high efficiency and fewer errors in the positioning of the part in precision machines increases every day, thus ensuring their high confidence and the use of aerostatic bearings enable constructive innovations to the equipment. In this context, this work presents the mechanical design, the development and error analysis of a prototype of an aerostatic rotary table. This study emphasizes the analysis of a prototype that uses the air as a working principle for reducing friction between moving parts, increasing the mechanical efficiency, and its influence of motion error is also discussed based on the experimental results. For the geometrical errors analysis, experimental tests were realized in laboratory using a DBB （Double Ballbar）. The tests are performed with only one axis moving, observing the behavior of the system for different feedrate at the C-axis.

Dynamic characteristics of ultra-precision aerostatic bearings

With high acceleration and ultra-precision requirements, the design of aerostatic bearings has been gradually focused on their dynamic performances. In this paper, the dynamic stiffness and damping coefficients of aerostatic bearings are investigated. Due to compressibility of the gas, the dynamic characteristics of aerostatic bear- ings show nonlinear frequency dependence. Particularly, their nonlinear dynamic behaviors are quite remarkable for ultra-precision aerostatic bearings with small air gap heights and high supply pressure.

Relationship between dynamic characteristics of air film of aerostatic spindle and mid-frequency of surface topography

The dynamic characteristics of the gas film of an aerostatic spindle primary affect workpiece waviness in ultra-precision machining.To improve the machining accuracy of the machine tool and provide a firm theoretical basis for the design of an aerostatic spindle,a simulation model combining transient computational fluid dynamics(CFD)analysis and transient dynamic analysis is established in this study to investigate the dynamic characteristics of the spindle under unstable operating conditions.Based on a large eddy simulation,a three-dimensional flow model of an air film in an aerostatic spindle is established.The simulation results show that the gas flow in the throttle chamber is turbulent,and that complex vortices are formed.Using dynamic grid modeling technology,a CFD numerical model for the unsteady calculation of the spindle is established,and the dynamic characteristics of the gas film are obtained.A transient dynamic simulation model of an aerostatic spindle is established,and the effect of the nonlinear dynamic characteristics of the gas film on the spindle displacement response is investigated.Subsequently,a surface morphology prediction model is established.Results show that film fluctuation significantly affects the dynamic characteristics of the spindle and subsequently affects the generation of surface ripples on the workpiece.

Experimental study of aerodynamic interference effects on aerostatic coefficients of twin deck bridges

The aerodynamic interference effects on aero-static coefficients of twin deck bridges with large span were investigated in detail by means of wind tunnel test.The distances between the twin decks and wind attack angles were changed during the wind tunnel test to study the effects on aerodynamic interferences of aerostatic coefficients of twin decks.The research results have shown that the drag coefficients of the leeward deck are much smaller than that of a single leeward deck.The drag coefficients of a windward deck decrease slightly com-pared with that of a single deck.The lift and torque coefficients of windward and leeward decks are also affected slightly by the aerodynamic interference of twin decks.And the aerodynamic interference effects on lift and torque coefficients of twin decks can be neglected.