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     

非球面超精密机床静压轴承温度场的分布

利用ANSYS CFX流体力学分析软件建立了不同油膜厚度下的液体静压轴承流体模型,研究了非球面超精密加工机床液体静压推力轴承的温度场分布。对静压推力轴承进行了试验研究,获得了工作台上不加负载、加300kg负载、加500kg负载3种情况下主轴性能各参数。仿真结果表明:油腔区域初始温度为20℃,从封油边开始温度逐渐升高,其中外侧的温度要比内侧温度稍高;当油膜厚度为33μm时,最高温度为20.29℃,当油膜厚度为23μm时,最高温度为21.72℃,油膜厚度越薄,温度越高。试验计算值与仿真值分别相差3.33%、8.33%、1.32%,证实了液体静压推力轴承设计和数值计算的正确性。     

A tolerancing procedure for inherently compensated, rectangular aerostatic thrust bearings

Manufacturing errors on aerostatic bearing surfaces and orifice geometry are known to impair performance. Theoretical analyses were carried out on a rectangular thrust bearing for the most common form of gap non-uniformities — tilt, concavity, convexity and waviness at various spatial wavelengths, as well as changes in orifice diameter and position from the bearing edge. The results illustrate the sensitivity of both static load and stiffness to various forms of manufacturing error. A tolerancing procedure is recommended to limit changes in static load and stiffness to 10%.     

端面型槽广义对数螺旋线的通用模型与应用

为解决流体润滑端面型槽设计中经典型线形状优化受限的问题,提出一种广义对数螺旋线模型,获得了斜直线、圆弧线、抛物线和椭圆曲线等经典几何型线的广义螺旋线表达式,掌握了不同参数条件下广义对数螺旋线的几何共性及演变规律。以气体推力轴承为例,对比分析了高速条件下广义螺旋角的分布规律和变化幅值对推力轴承承载性能的影响规律,结果表明:广义对数螺旋线具有很强的几何表征能力,从外径至内径侧流道渐扩的广义对数螺旋槽端面具有最大的气膜承载力。     

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.     

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     

CFD based investigation on influence of orifice chamber shapes for the design of aerostatic thrust bearings at ultra-high speed spindles

The influences of six orifice chamber configurations on performance characteristics of aerostatic thrust bearings under various operating conditions are thoroughly studied using the computational fluid dynamics approach. Experiments are carried out to further verify the simulations. The obtained results show that there are many differences in performance behaviors of the aerostatic thrust bearing caused by different orifice chamber shapes. Further analysis represents that the pressure depression, gas vortices, and the turbulent intensity which are all weakened with decreasing air film thickness. The load capacity of the aerostatic thrust bearing slightly decreases with increasing rotational speeds of the spindle.     

Static and dynamic characteristics of externally pressurized circular step thrust bearings lubricated with couple stress fluids

The combined effects of couple stresses, fluid inertia and recess volume fluid compressibility on the steady-state performance and the dynamic stiffness and damping characteristics of hydrostatic circular step thrust bearings are presented theoretically. Based on the micro-continuum theory, the modified Reynolds equation and the recess flow continuity equation are derived by using the Stokes constitutive equations to account for the couple stress effect resulting from a lubricant blended with various additives. Using a perturbation technique, results in terms of steady-state load-carrying capacity, oil flow rate, stiffness and damping coefficients are presented. A design example is also illustrated for engineering and industrial applications.     

滚动轴承承载能力及静力学计算软件设计与实现

在齿轮承载能力分析理论和滚动轴承寿命计算理论的基础上，以某轧机设备改进传动装置中的螺旋锥齿轮副和滚动轴承为例，采用VC＋＋6．0编制了螺旋锥齿轮副负载和滚动轴承承载能力及静力学计算可视化用户软件。     

Design of externally pressurized gas bearings for stiffness and damping

A design method for flat, circular thrust bearings is presented in this paper. The design method is based upon a new dynamic model of the bearing and permits the selection of stiffness and damping for applications of bearings in vibrating environments. Application of the design method to the tuning of bearing dynamics is emphasized here, while the development of the dynamic model is discussed in other references. Design constraints are considered in the iterative design procedure and are illustrated in a bearing design example.     

Considerations in the design of partially hydrostatic slipper bearings

The purpose of this study is to examine the design of hydrostatically balanced bearings as used in the slippers of high pressure axial piston pumps, and to outline a design procedure whereby the slipper behaviour, minimum film thickness and loss of high pressure fluid can be estimated. It is shown that for successful operation the slippers need to have small amounts of non-flatness on the running surfaces. In addition, good agreement between the measured and calculated film thickness is demonstrated.     

Simultaneous monitoring of oil film thickness and temperature in fluid film bearings

This paper reports on the application of an eddy current sensor with an active compensation for changes in sensor temperature to simultaneous monitoring oil film thickness and temperature in a tilting pad thrust bearing. Sensor design, calibration procedure, sensitivity and accuracy are described. Test equipment along with sensor mounting is also presented. Tests were run at different rotational speeds and bearing loads as well as different supplied oil flow rates to evaluate sensor performance in various operating conditions. During the tests film thickness and temperature were simultaneously measured. Temperatures were compared with data from thermocouples installed in the pads and thermistors mounted in the collar. Tests have shown that the sensor can successfully be used to reliably monitor the conditions within the bearing.     

CFD investigation of pressure depressions in aerostatic circular thrust bearings

Under certain operating conditions, the pressure distributions of aerostatic thrust bearings experience an undesirable pressure depression which decreases their load carrying capacity. Many investigators reasoned this phenomenon to the occurrence of shock waves in the bearing clearance. Recently, some investigators reasoned this phenomenon to the transition from laminar to turbulent flow and claimed that no shock wave is generated at the boundary between supersonic and subsonic flows. As such, there is a contradiction between these two opinions. In this paper, the rationale of the pressure depression phenomenon in aerostatic thrust bearings is investigated using computational fluid dynamics (CFD) simulations. The turbulent full Navier-Stokes equations for steady, three-dimensional, compressible flows are numerically solved in this study. Two circular bearing configurations are analyzed. The obtained results showed that the predicted pressure distributions along the fluid film compare well with the corresponding experimental data of other investigators. The present computational methodology allowed a clear capturing of the coherent structures of the flowfield in the bearing inlet region which include the coalescing of compression waves into shock waves and the region of shock/boundary layer interaction (pseudo-shock). The thorough understanding of this phenomenon is the first step towards the development of its appropriate control methods.     

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.     

Static performance of hydrostatic air bump foil bearing

A few years ago, a hydrostatic air foil bearing using compression springs as elastic foundation was firstly introduced by Kim and Park [1]. This paper presents recent experimental results on load capacity of a new hydrostatic air foil bearing made of corrugated bump foils. The new hydrostatic air foil bearing was designed with higher structural stiffness than the first design by Kim and Park [1]. A new test rig was also designed and constructed to measure load capacity of the bearing at higher speeds. The new test results indicate the hybrid operation has similar load capacity to that of hydrodynamic operation at high speeds due to dominance of hydrodynamic pressure. However, comparative tests at low speed (10,000 rpm) showed noticeable increase of load capacity in hydrostatic air foil bearing, manifesting effective hydrostatic levitation feature at low speeds.     

阶跃载荷扰动条件下推力轴承热瞬态过程研究

用一维绝热模型研究了滑动推力轴承在阶跃载荷冲击下的热瞬态行为.通过对轴承油膜压力、温度和推力盘的动力学参数进行建模,应用有限差分以及Runge-Kutta法等对模型求解,获得了大载荷阶跃冲击条件下推力轴承热瞬态过程中性能参数的非线性响应曲线,给出了瞬态过程中轴承最高温度、最小膜厚等参数的变化规律.结论认为如果轴承设计和运行不当,轴承有可能因为瞬态过程中温升过高或膜厚的突然减小而失效.     

关于滚动轴承选型设计问题的研究

介绍了滚动轴承选型设计方法的发展，提出了根据滚动轴承系统可靠性与寿命要求和实际工况来完成组成系统各单元滚动轴承的选型设计的方法，使所选择的滚动轴承组成的系统在使用中满足系统的设计要求。     

Analyses of thrust bearings in scroll compressors considering keyways

This work is an attempt to calculate the lubricating characteristics of thrust bearings in scroll compressors, which have non-circular shapes due to the keyways cut for the Oldham's coupling. The outer shapes of these bearings are not circular because the keyways intrude the bearing boundaries. A boundary fitted coordinate technique for hydrodynamic lubrication is modified to handle this non-circularity. The pressure distributions, resultant forces and moments are calculated, which are in equilibrium to the typical conditions generated in the compressing processes. The changes of nominal clearance and tilting angles are obtained during one cycle under the assumption of rigid-body motions.     

Development of an experimental rig with hydrostatic bearings for testing the EHD traction force of high-speed lubricants

A test rig for the EHD traction force of lubricants is essential equipment for the study of the non-Newtonian properties of lubricants operating at high pressure. In this paper is described the development of test equipment with hydrostatic bearings, on the basis of analysis of EHD traction and other test rigs. Hydrostatic bearings allow the rig to pick up the signals of the EHD traction force more precisely. Thus, good test results for an aviation lubricant have been obtained.     

Numerical and experimental analysis of aerostatic thrust bearings with porous restrictors

The finite element method is used to predict the performance of aerostatic thrust bearings with a complete porous surface. Results obtained by a 1D and 3D source flow model derived from D’Arcy’s law are compared for rectangular porous bearings having an infinite width. It turns out that the 1D source flow model is adequate for practical design parameters. For a circular aerostatic porous thrust bearing results calculated with several mathematical models for the source flow and slip flow are compared with experimental results. A relatively simple model incorporating unflatness and deformation of the bearing surface correlates well with the experimentally determined bearing performance.