不同压力腔的气体静压轴承静特性的数值模拟

气体静压轴承以其低摩擦、高精度成功应用于高精密回转运动台,其定位精度已达到纳米级水平,达到了物理极限,因此压力腔形状对气体静压轴承的影响无法忽略。通过CFD数值模拟,研究了不同压力腔形状对气体静压轴承静态性能的影响。针对矩形压力腔、圆形压力腔和锥形压力腔,研究分析了气膜内压力分布、气体质量流量和承载力等静态性能。结果表明:相同的条件下,锥形压力腔承载力较大,且压力腔内部气旋强度较弱,比较适合应用于高压重载的场合。     

An experimental investigation into the performance of externally pressurized rectangular air bearings

An experimental programme which was designed to investigate the performance characteristics of externally pressurized rectangular air bearings considering the effects of pad geometry and inlet gas conditions is presented. Three forms of rectangular bearings were considered: one arrangement consisted of continuous plane surfaces, the second had a recessed pad and a plane bed and the third had a plane bed and a recessed pad with a step in the bearing area following the recess.

The results revealed that the recess length has a dominant effect on the pressure distribution in the air film. The effect of pressure depression is obvious at extremely small clearances and supply pressures. Such an effect is exaggerated when a step is introduced in the pad surface. The introduction of the step improves the load-carrying capacity of the bearing as long as the bearing is free from shock-wave formation.     

Effects of operating conditions and supply hole diameter on the performance of a rectangular aerostatic bearing

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.     

Performance of membrane compensated multirecess hydrostatic/hybrid flexible journal bearing system considering various recess shapes

The paper describes a theoretical study concerning the performance of an externally pressurized multirecess hydrostatic/hybrid flexible journal bearing system by varying the geometric shape of recess and using the membrane flow valve restrictor as a compensating element. The four different recess geometries of the bearing studied in the present study are a square recessed bearing, a circular recessed bearing, an elliptical recessed bearing and a triangular recessed bearing. The equation governing the flow of lubricant in a journal bearing together with 3D elasticity equation and restrictor flow equation are solved by using the Finite Element Method. The study describes the effect of recess shape, bearing flexibility and a method of compensation on the performance characteristics of a hydrostatic/hybrid journal bearing system. A comparative performance of the membrane compensated hydrostatic/hybrid journal bearing system has also been studied vis-à-vis capillary, orifice and constant flow valve restrictors. The results presented in this study amply demonstrate that the shape of recess/pocket of a hydrostatic/hybrid flexible journal bearing system affects the performance of the bearing quite appreciably and a proper selection of recess shape along with a suitable compensating device is needed to get an improved performance from the bearing.     

The Performance of Externally Pressurized Bearings Using Simple Orifice Restrictors

The load capacity and vibration characteristics of externally pressurized thrust and journal bearings have been investigated. The bearings used orifices sufficiently recessed back from the bearing surface to ensure that the area of the orifice is the minimum presented to the gas flow. The journal bearings consist of plain cylinders with one or two rows of eight orifices, and the thrust plates of plain discs with six orifices drilled in equispaced circumferential grooves.

The load capacity of the thrust plates agrees with that calculated but the vibrations are greater than predicted. The load capacity of journal bearings is about half that calculated assuming axial flow conditions in the bearing, but circumferential flow can account for the difference. Synchronous and half-speed vibrations of a shaft rotating within these bearings have been measured and found to agree with those calculated on the assumption that the gas films behave as linear springs.     

Static characteristics of aerostatic porous rectangular thrust bearings

A theoretical analysis of the steady state performance of aerostatic rectangular thrust bearings with porous pads is presented. The equations governing the gas flow through the porous pad and the bearing clearance are solved simultaneously using a finite-difference method to obtain the pressure distribution in the bearing clearance. The load capacity, the mass rate of flow and the static stiffness are calculated numerically for different bearing dimensions and operating pressures and are presented in graphical form. The load capacity predicted for a square bearing correlates with previous results.     

Air Vortices and Nano-Vibration of Aerostatic Bearings

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.     

The combined effects of the centripetal inertia and the surface roughness on the hydrostatic thrust spherical bearings performance

This paper deals with the surface roughness and the predominant centripetal inertia terms due to the shaft rotation of the externally pressurized thrust spherical bearings. The solutions are presented for the fitted type of bearings, un-recessed and recessed hemispherical and partial hemispherical seats, with capillary tube and orifice restrictors. On the basis of the stochastic theory, Reynolds equation is developed. The bearing surfaces are assumed to have randomly distributed roughness. Expressions for the pressure distribution, load carrying capacity, volume flow rate, frictional torque, friction factor, power factor, power losses and stiffness factor are obtained. The paper shows the combined effects of the centripetal inertia and the surface roughness on the bearing performance. An optimum design based on the minimum power losses, minimum flow rate and optimal restrictor dimensions is theoretically examined.     

Performance of an externally pressurized rectangular gas bearing under constant effective recess pressure

The present study predicts the performance of an externally pressurized rectangular recessed gas bearing under different operating conditions. The analysis makes use of simplifying assumptions and an empirical formula which relates the recess pressure to the bearing supply pressure. A comparison between the theoretical results obtained and available experimental data shows qualitative agreement. There are some deviations in pressure distribution and load-carrying capacity especially at greater film thickness and supply pressures. The reasons for these deviations are discussed.     

Stability of multilobe hybrid bearing with short sills—part II

A small amplitude perturbation analysis has been carried out to determine the rotordynamic characteristics of multilobe hybrid bearings with short axial and circumferential sills. Unsteady state recess flow continuity equation has been written for orifice compensated bearing in terms of dynamic recess pressures by perturbing steady state flow equation. Dynamic recess pressures are evaluated by solving unsteady recess flow continuity equations to determine the dynamic load capacity of the bearing. Stiffness and damping coefficients of the bearing are determined from the dynamic load capacity of the bearing. Results of dynamic characteristics of three lobe and four lobe hybrid bearings are presented for various offset factors, speed, concentric pressure and eccentricity ratios. Multilobe hybrid bearings with offset factors more than one are found to exhibit better dynamic behaviour than circular hybrid bearings.     

基于匀压和阻尼的空气静压轴承静态特性研究*

针对常规空气静压轴承设计时存在的承载能力、刚度与气动锤之间的矛盾,提出一种基于虚拟均压和被动阻尼设计方法。采用该方法设计一种含环布均压槽和阵列阻尼孔的矩形平面空气静压止推轴承,并研究其静态特性。研究结果表明：与常规空气静压轴承结构相比,设计的空气静压止推轴承在供气压力0.5 MPa下的最高承载力提高了43.4%,最高刚度提高了51.3%;减小阻尼孔数量、减小节流孔径、提高供气压力和增设均压槽可获得最佳刚度特性;增加阻尼孔数量、减小节流孔径、提高供气压力和增设均压槽可获得最佳静态特性和动态稳定特性的综合性能。     

Performance analysis of high-speed spindle aerostatic bearings

The methods adopted to derive the pressure distribution and precision of bearing rotation are fundamental issues in the arena of gas bearing design. The current study presents a detailed theoretical analysis of bearing performance, in which the gas flow within the bearing is initially expressed in the form of simplified dimensionless Navier Stokes equations. Adopting the assumption of mass flow continuity between the bearing clearance and the orifice, the nonlinear dimensionless Reynolds equation is then derived and subsequently discretized using the Newton method. Finally, the modified Reynolds equation is solved by means of the iterative rate cutting method. The current numerical models are valid for the analysis of the film pressure distribution, friction effects, loading capacity, rigidity, lubricating gas flow rate, and eccentricity ratios of a variety of static and dynamic pressure aerostatic bearings, including high-eccentricity ratio journals, high-speed non-circular journals, thrust bearings, and slider bearings, etc. The proposed analytical models provide a valuable means of analyzing the static and dynamic performance of a high-precision rotating gas bearing, and allow its design to be optimized accordingly.     

球面螺旋槽气体动压轴承静态特性分析

以球面螺旋槽气体动压轴承为研究对象,建立了球面螺旋槽气体动压轴承的润滑分析数学模型,基于CFD技术,采用流体动力学Fluent软件,对球面螺旋槽气体动压轴承的三维气膜压力场进行分析,揭示不同转速下,轴承槽宽比、槽深比、螺旋角、气膜间隙对稳态轴承气膜压力以及承载能力的影响规律,并在此基础上,对轴承的结构参数进行了优化。结果表明,应用Fluent软件进行数值分析可以精确地模拟区域内气膜的复杂流场特性,并且转速越高,气体轴承内部的动压效应就越明显,因此合理地选择轴承结构参数和运行参数有助于改善润滑性能,提高轴承的稳态承载特性。     

Thermohydrodynamic Analysis and Thermal Management of Spherical Spiral Groove Gas Bearings

A thermohydrodynamic model of spherical spiral groove bearings is presented by considering the effect of bearing temperature change on the material property of lubricant, gas flow characteristics in the grooves, and thermal energy transported in the entire bearing system. A gas mixing model in the grooves is introduced as the boundary condition to solve the bearing temperature distribution simultaneously with the heat conduction at the shaft and the housing. The bearing and rotor expansion caused by temperature increases, which is considerable compared to bearing clearance, is also examined. Prediction results show that the thermal expansion determined by actual bearing clearance has a crucial influence on the bearing load capacity. Manufacturing bearings with proper materials has significant effects on controlling thermal expansion effects on the bearing performance. The load capacity, which corresponds to the lubricant gas pressure, and gas suck flow rate have the same variation tendencies as the variation in groove depth and spiral angle. These similar tendencies have an opposite influence on the temperature and result in the temperature increase not being affected by the variation in grooves. However, varying the groove characteristics has a similar effect in carrying away the thermal energy as the variation in heat transfer coefficient, which could significantly control the temperature increase at the same time.     

环形节流孔径向静压气体轴承的数值仿真

以环形节流孔径向静压气体轴承为研究对象,介绍了静压气体轴承的结构形式和工作原理,对气体润滑理论基础Reynolds方程进行了分析,利用计算流体动力学软件FLUENT对气体轴承的流场进行仿真分析,求解出了轴承气膜的压力分布.在轴承几何参数不变的情况下,分析了承载力与空气质量流量随不同供气压力和偏心率变化关系,并研究了静压气体轴承在高速工作下,动压效应对承载力的影响.     

Design of annular recess hydrostatic thrust bearing under dynamic loading

Design charts are presented of a dynamically loaded thrust bearing with as annular recess. The effect of non-parallelism between the bearing and the runner surfaces is also considered, since this is a common problem in hydrostatic thrust bearings. Based on pre-assigned dynamic excitations the pressure equation is solved numerically by finite difference methods to render the bearing performance characteristics namely: load capacity; bearing stiffness; damping coefficient; and lubricant flow rate. Results concluded that the bearing performance chareacteristics are dependent on the bearing radii ratios, the squeeze number, the bearing number and the tilt parameter.     

Performance of spherical thrust bearings

Spherical thrust bearings, generally operate with a non-uniform film thickness. The varying shape of the film thickness influences the resulting pressure gradient and distribution, and consequently affects the lubricant flow rate and the load carrying capacity of the bearing.A generalized analytical solution is presented for the performance of the spherical thrust bearing. The performance of the fitted type and that of the concentric position of the clearance type are obtained as special cases.     

The influence of the molecular mean free path on spherical thrust gas bearing performance

The performance of a spherical thrust gas bearing under slip flow conditions was investigated and it was shown that as the ratio of the mean free path to the minimum film thickness increased the bearing load-carrying capacity and the lubricant mass flow rate increased while the frictional torque decreased. The effect is more pronounced at lower values of inlet pressure and film thickness.     

The Design of Externally Pressurized Gas Lubricated Bearings by the Method of Bearing Equivalence

This paper presents the theoretical development and experimental verification of a simplified technique for the design of externally pressurized gas lubricated bearings. The general procedure is to establish an equivalent rectangular bearing which is the performance replica of an arbitrary gas bearing configuration. The resulting equivalent bearing has the same load support, clearance, area, source pressure, entrance losses, and mass flow as the arbitrary bearing which is analyzed. In accomplishing this end, the general rectangular bearing is analyzed, a consistent criterion of equivalence is defined, and theoretical analyses are compared to experimental data.     

Effects of velocity slip,anisotropy and tilt on the steady state performance of aerostatic porous annular thrust bearings

The analysis predicts the steady state performance characteristics of externally pressurized annular porous gas thrust bearings of finite pad thickness. The modified Reynolds equation, governing the flow in the bearing clearance, is derived from the Navier-Stokes equations using the Beavers-Joseph slip velocity condition at the porous interface. The anisotropy of the porous matrix and the tilt of the bearing are also taken into account. The dimensionless load capacity, the mass rate of flow and the static stiffness are computed numerically and presented in the form of charts for various operating parameters and bearing dimensions. The effect of slip is to reduce the load capacity and to increase the mass rate of flow for all values of the feeding parameter.