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.

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%.

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.

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.

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.

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.

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.

大跨斜拉桥双层桁架主梁施工状态的阻力系数

针对规范中对大跨径桁架桥的双层主梁阻力系数在取值上的局限,提出一种主梁阻力系数计算方法,以施工阶段节段模型的风洞试验结果为基础,对双层桁架主梁进行模型简化后,使用CFD计算得出其三分力系数.采用不同迎风面特征尺寸,桁架片数以及桁架间距,分析了迎风面特征尺寸对主梁的阻力系数的影响.讨论了桁架间距以及片数不同对主梁的阻力系数的影响趋势.结果表明:迎风面特征高度与特征宽度对主梁阻力系数影响的变化规律并不相同,对此提出以桁架纵高比为变量的双层桁架桥梁主梁的阻力系数拟合公式;当桁架间距较小时,桁架片数对主梁阻力系数无影响,但当桁架间距与桁架高度比值达到3时,桁架片数的变化会对主梁的阻力系数产生较大的影响.

考虑温度因素对带有柔性结构的静压气体轴承稳定性影响研究

为了研究静压气体轴承在工作状态下,温度对带有柔性结构的静压气体轴承柔性结构挠度变形量、流场流态及稳定性的影响规律,本文建立了带有柔性结构的静压气体止推轴承三维(3D)模型。首先,采用流-固-热多物理场耦合的计算方法,分析了工作状态下温度变化对静压气体轴承柔性结构挠度变形量、气膜流场流态及气膜稳定性的影响。然后,通过设计静压气体轴承试验台,对轴承受到载荷冲击时的振动情况进行测试,将测试结果与仿真分析结果对比,验证了仿真计算的可靠性。计算结果表明,环形柔性薄板在节流孔处的挠度变形量随温度升高而增大,当气膜间隙h=12μm的情况下,工作温度T=100℃相较于工作温度T=-20℃的挠度变形量提升了43%;其他条件相同下,随着温度的升高,气膜内气旋的范围逐渐减小;工作温度越高,受到载荷后轴承振动幅度越小。实验测试结果表明,随着工作温度的升高,轴承稳定性越高,与仿真分析结果基本一致。该研究为此类轴承在超精密领域的应用提供了理论参考。

基于不同加工工艺的微孔节流空气静压轴承的特性研究

随着超精密加工技术和地面微低重力仿真的发展,相关产业对空气静压轴承的性能要求越来越高。由于传统的孔式节流器其结构特点不能完全满足实际使用的需要,节流孔直径与气膜间隙同一数量级的微孔节流空气静压轴承因其良好的刚度和承载特性,越来越受到关注。但在微孔节流器的发展过程中,微孔的加工工艺却限制了其推广应用。针对目前常用的三类微孔加工工艺,进行了理论仿真研究,通过建立不同加工工艺轴承仿真模型,运用双向流固耦合仿真方法,对比分析了基于不同加工工艺的微孔节流空气静压轴承的动静态特性。研究结果表明:锥孔类轴承承载性能优于其他两类,但耗气量大且在小间隙时刚度较差;薄壁直孔类轴承承载性能稍逊,但在大间隙下轴承刚度较佳;嵌套类轴承承载性能较差,但在小间隙下轴承刚度较大且耗气量较低。

基于MEA-BP神经网络的多孔质轴承参数优化

为了提高圆盘类多孔质静压止推轴承的静态特性,采用思维进化算法(MEA)优化反向传播(BP)神经网络,创建圆盘类多孔质静压止推轴承静态特性的预测模型,完成轴承静态承载力、静刚度以及耗气量的高精度预测,其预测误差分别低于2%、5%以及5%。基于此模型,以最大化静态承载力和静刚度、最小化耗气量为优化目标值,采用遗传算法对轴承的多孔质参数组合进行多目标优化,实现轴承参数的快速优化设计。优化结果表明:此轴承静态承载力提高了64.53%,静刚度提高了31.93%,耗气量降低了56.52%。

环形多孔气体静压止推轴承静态性能研究

为提升气体静压止推轴承的静态性能,设计一种新型环形多孔气体静压止推轴承。依据气体润滑原理、采用有限体积法对环形多孔气体静压止推轴承的三维物理模型进行数值模拟,研究节流器上节流孔数量、直径、分布方式和供气压力对气体静压止推轴承静态性能的影响。结果表明:节流孔数量对环形气体静压止推轴承的承载力影响显著,但孔数增加到一定程度后承载力增速放缓;节流孔直径对承载刚度影响较大,随着节流孔直径逐渐减小最佳刚度逐渐增大;节流孔排布方式和供气压力对气体静压止推轴承的静态性能均有明显影响。

基于浮空器照射源的双基弧形阵列SAR辅助降落模式成像算法

较之传统的单基线性阵列SAR,以浮空器为照射源平台的双基弧形阵列合成孔径雷达(Synthetic Aperture Radar,SAR)是一种全新高效、高分辨率的雷达成像系统;该成像模式继承了弧形阵列天线和浮空器的优点,在直升机辅助降落、应急救灾等领域具有重要的应用前景。在该成像模式中,由于浮空器平台平向移动、直升机平台向下运动以及弧形阵列天线特殊的圆弧型构造的影响,目标的回波信号很难直接处理,给成像带来了困难。针对这些问题,根据浮空器照射源双基弧形阵列SAR模式的成像几何模型以及回波特征,本文提出了一种基于两步运动补偿和Keystone变换的方法。其中第一步利用Taylor级数展开对双平台复杂斜距方程进行近似处理,对该成像模式下的距离分辨率和方位分辨率进行了简单分析,第二步根据浮空器平向运动产生的斜距误差,构造相应的运动补偿因子对浮空器平移引起的距离徙动项进行相位补偿;第三步根据直升机平台向下运动产生的斜距误差,构造相应的补偿因子对直升机下降引起的距离徙动项进行补偿;之后为了校正距离向与方位向之间耦合,根据Keystone变换思想引入新的角度变量对方位角进行变换从而补偿掉距离频率及方位向角度的耦合,接着在方位频域内进行方位向脉冲压缩。最后通过对不同点阵目标成像补偿前后的仿真结果对比分析、点阵目标成像性能指标分析以及场景分布目标的模拟验证了成像结果的准确性以及成像方法的有效性。