Theoretical analysis of two configurations of aerostatic flat pad bearings using pocketed orifice restrictors

Aerostatic flat pad bearings are finding increased applications in high-precision machine tools, high-performance measuring equipment and coordinate measuring machines. To date, much of the development of these bearings has been of an empirical nature since there are no detailed design procedures for assisting designers to optimize their designs^1,2. In the field of aerostatic journal bearing design, comprehensive procedures do exist. The object of this paper is to exploit the principles developed for the analysis of aerostatic journal bearings to the area of flat pad bearings, which are more widely used in industrial situations. In this paper, similar analysis tools are developed and are used to obtain design performance data for a number of flat pad bearing configurations. These data include load, flow and stiffness parameters, all of which are fundamental to design optimization.     

Design of aerostatic flat pad bearings using pocketed orifice restrictors

Design charts are presented to enable the design of aerostatic thrust bearings which use pocketed orifice restrictors. Attention has been paid to ensuring that pneumatic hammer instability is avoided by providing design information on the maximum depth and diameter of the orifice pocket. The design procedures presented are based upon analyses produced using finite difference equations to the compressible form of the Reynolds equation. The procedures presented provide the designer with a graphical technique that enables him to take into account stiffness, clearance, number of orifices and bearing dimensions when deriving a satisfactory solution to his problems.     

Design of aerostatic flat pad bearings using annular orifice restrictors

Design charts are presented for use in the design of aerostatic thrust bearings which use annular orifice restrictors. Annular orifices are preferred when pneumatic hammer instability is a potential problem. The design procedures presented are based upon analyses produced using finite difference equations to the compressible form of the Reynolds equation. The method provides the designer with a graphical technique that enables him to take into account bearing stiffness, clearance, number of orifices and bearing dimensions in obtaining a satisfactory solution to his problem.     

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.     

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。     

Static tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors

Aerostatic rectangular thrust bearings with compound restrictors have often been used in ultra-precision machine tools and precision measuring equipment because high bearing stiffness is easily achieved. Compound restrictors combine a feed-hole restrictor with a groove compensation restrictor. This paper investigates, theoretically and experimentally, the static tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors, when coupled loads or offset loads are applied. Furthermore, the usefulness of aerostatic thrust bearings with compound restrictors is clarified by comparison with the characteristics of conventional aerostatic thrust bearing with feedhole restrictors.     

Optimum design of hydrostatic journal bearings Part II. Minimum power

The optimization problem is formulated with a view to maximizing the load-carrying capacity of hydrostatic journal bearings. Equations governing the performance of multi-recess hydrostatic journal bearings are summarized. Practical design limits and operational constraints are also defined. The optimization process is based on the well known Rosenbrock method. Results illustrating the effect of area ratio, axial land width and circumferential land width on load capacity, flow rate and power ration are reported. In conclusion precision bearings with small clearances and low pressure ratios are recommended for applications involving low supply pressures, while bearings with large clearances and pressure ratios close to 0.5 are recommended for applications involving high supply pressures     

Optimum design of hydrostatic journal bearings Part I: Maximum load capacity

The optimization problem is formulated with a view to maximizing the load-carrying capacity of hydrostatic journal bearings. Equations governing the performance of multi-recess hydrostatic journal bearings are summarized. Practical design limits and operational constraints are also defined. The optimization process is based on the well known Rosenbrock method. Results illustrating the effect of area ratio, axial land width and circumferential land width on load capacity, flow rate and power ration are reported. In conclusion precision bearings with small clearances and low pressure ratios are recommended for applications involving low supply pressures, while bearings with large clearances and pressure ratios close to 0.5 are recommended for applications involving high supply pressures     

Improvement of static characteristics of an aerostatic journal bearing using the elastic deformation of an O-ring

A new type of aerostatic journal bearing in which the elastic deformation of an O-ring is used to improve its static characteristics is proposed. The static characteristics of this bearing are determined theoretically by both the finite difference method and the small perturbation method. Effects of parameters on the static characteristics are shown, and the optimum design method for the static characteristics is discussed. Further, theoretical results are compared with experimental results to confirm the validity of theoretical predictions. It is consequently found that the new type of bearing possesses higher static stiffness and greater load capacity than conventional point source bearings with inherently compensated feeding holes.     

Experimental investigation into the performance of an aerostatic industrial thrust bearing

Load and flow versus air-gap curves and stability maps have been obtained for an industrial externally-pressurized air-lubricated thrust bearing with a central restrictor. Supply pressure and pocket depth were treated as parameters. Bearing stiffness was estimated by using a computer to fit a polynomial type curve to the test data. The results show that whereas the effect of inserting a pocket into the bearing improves its load capacity, there is no significant improvement in film stiffness at design conditions. The suggestion is made that the diameter of the orifice in the restrictor should be increased. As pocket depth is increased beyond the design value the bearing becomes prone to pneumatic hammer.     

均压槽对空气静压轴承微振动的影响

由于空气静压轴承工作过程中的微振动制约了它在超精密设备中的应用,本文对空气静压轴承的动态特性进行了实验分析,并提出用带均压槽的结构设计来解决上述问题。运用有限元软件对空气静压轴承进行仿真,得到了空气静压轴承的各项性能参数。分析了微振动产生的原因并提出在空气静压轴承工作表面增加均压槽来有效抑制空气静压轴承的微振动的方法。通过实验对提出方法进行了验证,结果显示计算结果与实验具有较好的一致性。实验表明通过增加均压槽的方式可以将轴承微振动降低80%,有效地提高了空气轴承的稳定性和运行精度。本研究为抑制空气轴承微振动和提高整个机床设备精度做出了有益探索。     

变截面节流器对空气静压轴承承载性能的影响

为了分析可变截面节流器对空气静压轴承性能的影响,提出了变截面节流器的空气静压轴承模型,通过轴承承载表面弹性薄板的挠度变形实现节流器截面形状的动态变化。建立固体薄板变形和气体润滑的耦合偏微分方程,采用有限差分法和超松弛迭代法对耦合方程进行离散和数值求解。计算结果表明:节流器的截面形状直接决定了数值计算过程中喷嘴系数的大小,与刚性节流器的空气静压轴承相比,变截面节流器的空气静压轴承刚度提高了15%,在较高承载力的情况下能够获得更大的刚度。实验测试结果和理论分析基本一致,变截面节流器的设计方法能够有效提高空气静压轴承的静特性。     

Static tilt characteristics of aerostatic rectangular double-pad thrust bearings with double row admissions

Aerostatic thrust bearings have been used in linear guideway systems of various precision measuring apparatus by reasons of low friction, non-hysteresis and high accuracy of motion. In such a case that the measuring systems do not satisfy the Abbé principle, the accuracy of linear guideway systems is greatly influenced by the tilt characteristics in pitch, roll and yaw directions of aerostatic thrust bearings. This paper proposes the application of aerostatic rectangular double-pad thrust bearings with double row admissions of compound restrictors to the linear guideway systems subjected to tilt moments in both pitch and roll directions, and investigates, theoretically and experimentally, the static tilt characteristics of these aerostatic thrust bearings.     

Lubrication of orifice-compensated flexible thrust pad bearings

The effects of the interaction between the restrictor design parameter ($\text{C}{}_{\mathrm{S2}}$), the deformation coefficient ($\text{C}{}_{\mathrm{d}}$) and the Poissons ratio (ν), on the performance characteristics of an orifice-compensated hydrostatic circular thrust pad bearing have been studied. The results are presented for various values of $\text{C}{}_{\mathrm{S2}}\text{,}\text{C}{}_{\mathrm{d}}\text{,}\text{and}\text{ν}$ and are compared with those of capillary-compensated bearings     

A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearings

Inertia effects in porous material, as well as velocity slip at the porous bearing surface, have hindered the use of simple mathematical models for the analyses of porous aerostatic bearings. Experimental evidence indicated that velocity slip at the porous surface did not obey the Beavers model, but could be approximated by an added equivalent clearance. This experimentally determined clearance value did not bear any direct relationship with the surface roughness of the test specimen. Good agreement between theoretical and experimental results of static load capacity of a porous ceramic test bearing, however, demonstrated the use of this equivalent clearance method, in conjunction with a proposed approximation to correct for inertia effects, as an effective modification to the simple one-dimensional model by Sheinberg.     

气体静压轴承相位致振气锤失稳机理与试验

针对气体静压轴承在结构不合理或者工作参数选择不恰当时容易产生气锤失稳的问题,开展基于相位致振的气体静压轴承气锤失稳机理研究。从气体静压轴承的工作气压与气膜间隙随时间变化的相位关系出发,建立基于相位致振的气体静压止推轴承自激失稳理论模型,分析气体静压止推轴承在发生气锤失稳过程中,工作气压与气膜厚度的相位变化对应情况。理论分析和实验研究结果表明,在气体静压止推轴承发生气锤失稳过程中,工作气压与气膜厚度的相位不断变化,并在相位差为180°时发生气锤失稳,进而说明可以从相位角度解释气体静压轴承发生气锤失稳的原因。该研究进一步完善了气体静压止推轴承的自激失稳作用机理分析,为气体静压轴承的气锤失稳的机理分析及其抑制提供了一种新的方法。     

A study of optimum load-bearing capacity for slider bearings lubricated with couple stress fluids in magnetic field

A theoretical study of slider bearings in general form is presented, considering the lubricant to be an isothermal, incompressible electrically conducting couple stress fluid in the presence of a uniform magnetic field. An expression for a modified Reynolds equation is derived in order to obtain pressure gradient in terms of inlet–outlet (IO) film height ratio (simply IO film ratio) of slider bearings. As a special case, a study of the IO film ratio of four particular types of slider bearings is analysed. For the study of optimum load capacity, three-dimensional geometry has been assumed in order to consider side flow. Values of maximum load capacity for various values of couple stress and magnetic parameters, and the corresponding IO film ratio of the four bearings are obtained numerically, and a comparative study of these values has been presented. A comparative study of optimum load-carrying capacity for finite and infinite slider bearings has also been made. It is observed that both the values of maximum load capacity and the corresponding IO film ratio depend on couple stress and magnetic parameters and the shape of bearings conjointly. The present results are also compared with the similar available data in Newtonian cases.     

Optimal design of one-dimensional porous slider bearings using the Brinkman model

On the basis of the Brinkman model, a theoretical study of the optimal load-carrying capacity and friction coefficient for one-dimensional curved porous slider bearings with the gap width varying slowly is presented. The modified Reynolds equation is obtained by applying Brinkman equations to guide oil motion through the porous matrix. By using the technique of calculus of variations, the optimization is performed over a class of step profiles. According to the analysis, the step height ratio and riser location of the optimal geometry are found to depend upon the permeability parameter of the porous matrix. Compared with the inclined-plane bearing case, the stepped porous slider bearing provides an enhancement in the load-carrying capacity as well as a reduction in the friction parameter. An illustrative design example is also included for engineering and industrial applications.     

Orifice-compensated flexible thrust pad bearings of different configurations

Performance characteristics of capillary and orifice-compensated flexible thrust bearings are presented for various values of the restrictor design parameter, C_s2, and the deformation coefficient, C_d. Interactions between C_s2 and C_d are studied for various bearing configurations.     

Static characteristics of externally pressurized gas journal bearings with circular slot restrictors

The static characteristics of an externally pressurized gas journal bearing with a circular slot restrictor are described. The slot configuration is circumferentially continuous and is simpler than that of the journal bearing with discrete slots proposed by Dee and Shires¹. Here, the optimum design conditions for the load capacity are theoretically determined and it is shown that gas journal bearings with a circular slot restrictor possess a load capacity comparable to designs which have discrete slots.