Numerical prediction of slip flow effect on gas-lubricated journal bearings for MEMS/MST-based micro-rotating machinery

The fluid dynamics of gas-lubricated journal bearings in micro-rotating machinery is different from those of larger size. One point to be considered is a slip flow effect. In this paper, the slip flow effect is considered in order to estimate load-carrying capacity and dynamic coefficients of micro gas-lubricated journal bearings. Based on a modified compressible Reynolds equation including slip flow effect, the first slip approximation was applied. To extract dynamic coefficients, the linearized dynamic equations were formulated by the perturbation method. Numerical predictions compared the static and dynamic characteristics considering slip flow at room-to-high temperature in a range of bearing numbers. The results including load-carrying capacity and dynamic coefficients demonstrate that the slip flow effect becomes significant with temperature increase as well as in the lower range of bearing numbers.     

Wave Journal Bearing with Compressible Lubricant—Part II: A Comparison of the Wave Bearing with a Wave-Groove Bearing and a Lobe Bearing

To identify the potential advantages of the wave journal bearing, a three-wave journal bearing was compared to both a three-wave-groove bearing (a wave bearing with axial grooves that isolate each wave) and a three-lobe bearing. The lobe bearing's profile was selected to approximate the wave journal bearing's profile. The lubricant was assumed to be compressible (gas). The bearing number, A, was parameterized from 0.01 to 100, and the eccentricity ratio, ε, was varied from 0 to 0.4. Data at bearing numbers 0.1, 1, and 50, and eccentricity ratios of 0.1 and 0.4, were selected as representative of the bearing performance. The calculated load capacity and the critical mass are presented for the three bearings. The wave bearing shows a better load capacity than the other bearings at any applied load and running regime. However, at high bearing numbers the lubricant compressibility effect is predominant and all three analyzed bearings show similar load capacity. The critical masses of the wave-groove and lobe bearing are greater than the critical mass of the wave bearing if the applied load is small. For low and intermediate bearing numbers the wave-groove bearing is more stable than the other bearings especially at low wave's amplitude ratio. The lobe bearing is more stable than the other analyzed bearings at high bearing numbers or at large preload ratios. If the applied load increases, the wave bearing dynamic performance is competitive with both wave-groove and lobe bearings. In addition, at high bearing numbers, the wave bearing could run stably for any allocated rotor mass over a wide range of wave position angle. Three wave bearings are more sensitive to the direction of the applied load than the other bearings especially at low and intermediate bearing numbers. Therefore, a careful selection of the waves position angle has to be done to maximize the wave bearing performance.     

Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications

This paper introduces a simple “Rule of Thumb” (ROT) method to estimate the load capacity of foil air journal bearings, which are self-acting compliant-surface hydrodynamic bearings being considered for Oil-Free turbomachinery applications such as gas turbine engines. The ROT is based on first principles and data available in the literature and it relates bearing load capacity to the bearing size and speed through an empirically based load capacity coefficient, D. It is shown that load capacity is a linear function of bearing surface velocity and bearing projected area. Furthermore, it was found that the load capacity coefficient, D, is related to the design features of the bearing compliant members and operating conditions (speed and ambient temperature). Early bearing designs with basic or “first generation” compliant support elements have relatively low load capacity. More advanced bearings, in which the compliance of the support structure is tailored, have load capacities up to five times those of simpler designs. The ROT enables simplified load capacity estimation for foil air journal bearings and can guide development of new Oil-Free turbomachinery systems.     

Numerical Analysis of a Slider Bearing with a Heterogeneous Slip/No-Slip Surface

The behavior of a fluid-film bearing depends on the boundary conditions at the interfaces between the liquid and the solid bearing surfaces. For almost all solid surfaces, the no-slip boundary condition applies. However, a number of researchers have recently found that slip can occur with specially engineered surfaces. These include molecularly smooth surfaces and surfaces with micron-scale patterns. By constructing an engineered heterogeneous surface on which slip occurs in certain regions and is absent in others, the flow in the liquid film of a bearing can be altered, and such characteristics as load support and friction can be improved. In the present study, a numerical analysis of a slider bearing with such an engineered slip/no-slip surface is analyzed. Slip is assumed to occur when a critical shear stress is exceeded and follows the Navier relation. The results show that with a critical shear stress of zero, a significant increase in load support and decrease in friction can be achieved with an appropriate surface pattern. With nonzero values of critical shear stress, an instability occurs over a range of speeds. At speeds above this range, the bearing behaves similar to the case with zero critical shear stress, while below this range it behaves like a conventional bearing.     

Thermal Structural Effects in a Gas-Lubricated Foil Journal Bearing

A theoretical model for gas-lubricated foil journal bearings that incorporates thermal structural effects is presented. Bending and membrane effects in the top foil resulting from temperature are included along with thermal expansion of the journal, subfoil, and bearing housing. The model includes thermal transport through the journal, foils, and bearing housing. Pressure in the gas film is predicted using the Reynolds equation, and a thermal bulk flow model is used to predict temperature. The results demonstrate that models will overpredict film thickness along the side edge of a bearing if thermal strain in the top foil is not included. In addition, the results show the need for a three-dimensional thermal flow model at the trailing edge of a bearing when backflow occurs.     

An Original Definition of the Profile of Compliant Foil Journal Gas Bearings: Static and Dynamic Analysis

This article deals with a numerical analysis of the static and dynamic performance of a compliant journal gas bearing. The common approach found in foil bearing literature consists in calculating the carrying capacity for a given shaft position. In this study the external load is fixed (magnitude and direction) and the related shaft position is investigated. Nevertheless, a rigid profile, able to support high imposed loads, is no longer valid if one considers that the bearing becomes compliant. An original calculation method of the initial profile considering rigid surfaces is proposed to overcome this problem. The prediction of nonlinear dynamic behavior, i.e., stability and response to external excitation, is investigated. Finally, a viscous damping model is introduced into the dynamic model in order to obtain the amount of structural damping necessary to increase the stability of the compliant journal gas bearing.     

Analysis of Foil Journal Bearings with Backing Springs

Gas-lubricated foil journal bearings are simple, in construction, lightweight and well suited for high-temperature applications in turbomachinery. Hearing stiffness is governed primarily by the foil flexural stiffness. The bearing consists essentially of thin overlapping circular metal foils, one end of which is cantilevered to the bearing housing and. the other end rests on an adjacent foil.

An analysis of gas-lubricated foil bearings is presented with a specific type of backing spring used under the foils to control bearing preload, and stiffness. The backing spring acts like, an elastic foundation tinder the foil and radically changes the hydrodynamic pressure distribution generated in the gas film. The pressure distribution is obtained by simultaneously solving the compressible Reynolds equation and. the elasticity equations governing the compliant bearing surface, consisting of foils and backing springs. An iterative scheme is used, to obtain pressure distributions for heavily loaded cases, involving extensive computation, because of the sensitivity of pressure solution to small changes in film thickness distributions attributable to the compliant bearing surface. Pressure distribution, film thickness, bearing load capacity, iterative solution convergence characteristics and bearing power dissipation are presented as a function of journal eccentricity.     

Minimum Film Thickness in a Gas Foil Journal Bearing with an Unbalanced Rotor

A gas-lubricated foil journal bearing consists of a compliant metal shell structure that supports a rigid journal or rotor by means of a gas film. The response of this system to the periodic forces of an unbalanced rotor supported by a single bearing is predicted using perturbation analysis. The foil structure and the gas film are modeled with an analytically perturbed finite element approach to predict the rotor dynamic coefficients. A dynamic model of the rotor is used to predict periodic journal motion. The perturbation analysis is then used with the periodic response of the rotor to calculate periodic changes in the gas film thickness. Other quantities such as the gas film pressure and the foil deflection can also be calculated. The model includes bending and membrane effects in the top foil, coupled radial and circumferential deflections in the corrugated sub-foil, and the equivalent viscous dissipation of Coulomb friction effects in the foil structure. The approach is used to investigate the effects of top-foil thickness on minimum film thickness in a bearing.     

Air Injection as a Thermal Management Technique for Radial Foil Air Bearings

A thermal management technique for radial foil air bearings was experimentally evaluated. The technique is based on injecting air directly into the internal circulating fluid-film to reduce bulk temperatures and axial thermal gradients. The tests were performed on a single top foil, Generation III, radial foil bearing instrumented with three thermocouples to monitor internal temperatures. A through hole in the bearing shell coincident with the gap between the top foil's fixed and free ends provided entry for the injection air. The tests were conducted at room temperature with the bearing operating at speeds from 20 to 40 krpm while supporting 222 N. Two different mass flow rates of injection air were evaluated for this method, 0.017 and 0.051 kg/min. Test results suggest that the air injection approach is a viable thermal management technique capable of controlling bulk temperatures and axial thermal gradients in radial foil air bearings.     

Experimental Determination of the Dynamic Characteristics of a Two-Axial Groove Journal Bearing

A hydrodynamic bearing test rig was used to experimentally study the steady operating characteristics and dynamic coefficient of a plain two-axial groove journal bearing. Using two electrodynamic shakers to generate synchronous sinusoidal excitations, two small independent elliptical displacement orbits were produced for different static equilibrium positions. Data was measured for two fixed shaft speeds, while the steady load was varied to achieve Sommerfeld numbers ranging from 0.063 to 0.344. The four linearized stiffness and four linearized damping coefficients were determined for each speed-load condition by reducing the orbital data using an average magnitude and phase method. The coefficients are presented in dimensionless form as functions of the Sommerfeld number. Typical average uncertainty was found to be 12 percent for the coefficients and 8 percent for the Sommelfeld number. For the speed, load, and temperature ranges tested herein, the dynamic coefficient results for each speed agreed within the uncertainty of the data, supporting the first order approximation that, for the operating range studied, a coefficient's magnitude is independent of the absolute speed, load, and viscosity so long as the Sommerfeld number is matched. The same conclusion was reached for the steady operating location within the bearing clearance space. The overall consistency of these results also lends confidence as to their reliability. Additional experimental results presented include three sets of continuous circumferential oil film thickness and pressure profiles, and discrete temperatures.     

A Three-Dimensional Foil Bearing Performance Map Applied to Oil-Free Turbomachinery

To effectively apply compliant foil gas bearings to increasingly larger and more challenging turbomachinery, a comprehensive method that compares a foil bearing's capabilities with the application's operating requirements is needed. Extensive laboratory and field experience suggests that foil bearing failure is generally due to thermal stress brought on by excessive viscous power loss; therefore, a map that graphically relates component- and system-level parameters (bearing size, applied loads, and shaft rotational speeds) directly to bearing power loss is more elucidating than a map based on a lumped speed/load parameter like the Sommerfeld number. In this article we describe a performance map featuring a three-dimensional contour plot that illustrates the expected power loss in a foil bearing as a function of applied load and shaft speed. Using this performance map, bearing capabilities can be examined at the anticipated system operating conditions and safety margins between an operating point and incipient bearing failure can be ascertained. To demonstrate the concept's features and usefulness, we present a performance map generated from foil bearing power loss test data. We expect that these maps, combined with other predictive tools, will help evaluate a foil bearing's general suitability for a candidate rotor system and will lead to more robust and successful oil-free turbomachinery designs.     

Effects of Excitation Frequency and Orbit Magnitude on the Dynamic Characteristics of a Highly Preloaded Three-Lobe Journal Bearing

The independent effects of excitation frequency and excitation magnitude on experimentally derived bearing coefficients for a highly preloaded three-lobe journal bearing were studied. The effect of excitation frequency was determined by applying external dynamic forces at half-synchronous, synchronous, and twice synchronous frequencies with respect to the operating speed. Effect of excitation magnitude was independently determined by applying either three or four different amplitudes of excitation force to the bearing resulting in orbit sizes ranging up to 30% of clearance. Applying static forces to the bearing housing controlled the Sommerfeld number, and thus, the static operating position. Data was reduced as linear dynamic coefficients, and presented relative to excitation frequency and excitation magnitude over a range of Sommerfeld numbers from 0.2 to 3.0 and operating eccentricities from 0.3 to 0.9. In general, neither excitation frequency nor excitation magnitude was shown to have a measurable effect over the ranges studied.     

Structural Stiffness and Coulomb Damping in Compliant Foil Journal Bearings: Theoretical Considerations

Compliant foil bearings operate on either gas or liquid, which makes them very attractive for use in extreme environments such as in high-temperature aircraft turbine engines and cryogenic turbopumps. However, a lack of analytical models to predict the dynamic characteristics of foil bearings forces the bearing designer to rely on prototype testing, which is time-consuming and expensive. In this paper, the authors present a theoretical model to predict the structural stiffness and damping coefficients of the bump foil strip in a journal bearing or damper. Stiffness is calculated based on the perturbation of the journal center with respect to its static equilibrium position. The equivalent viscous damping coefficients are determined based on the area of a closed hysteresis loop of the journal center motion. The authors found, theoretically, that the energy dissipated from this loop was mostly contributed by the frictional motion between contact surfaces. In addition, the source and mechanism of the nonlinear behavior of the bump foil strips were examined. With the introduction of this enhanced model, the analytical tools are now available for the design of compliant foil bearings.     

Theoretical considerations of static and dynamic characteristics of air foil thrust bearing with tilt and slip flow

The thrust pad of the rotor is used to sustain the axial force generated due to the pressure difference between the compressor and turbine sides of turbomachinery such as gas turbines, compressors, and turbochargers. Furthermore, this thrust pad has a role to maintain and determines the attitude of the rotor. In a real system, it also helps reinforce the stiffness and damping of the journal bearing. This study was performed for the purpose of analyzing the characteristics of the air foil thrust bearing. The model for the air foil thrust bearing used in this study is composed of two parts: one is an inclined plane, which plays a role in increasing the load carrying capacity using the physical wedge effect, and the other is a flat plane. This study mainly consists of three parts. First, the static characteristics were obtained over the region of the thin air film using the finite-difference method (FDM) and the bump foil characteristics using the finite-element method (FEM). Second, the analysis of the dynamic characteristics was conducted by perturbation method. For more exact calculation, the rarefaction gas coefficients perturbed about the pressure and film thickness were taken into consideration. At last, the static and dynamic characteristics of the tilting condition of the thrust pad were obtained. Furthermore, the load carrying capacity and torque were calculated for both tilting and nontilting conditions. From this study, several results were presented: (1) the stiffness and damping of the bump foil under the condition of the various bump parameters, (2) the load carrying capacity and bearing torque at the tilting state, (3) the bearing performance for various bearing parameters, and (4) the effects considering the rarefaction gas coefficients.     

基于波纹箔片刚度试验的气体箔片轴承动力学特性

为了研究波纹刚度特性以及其对箔片轴承动力学特性的影响,设计了波纹箔片刚度测试试验台。分别对两端固定和一端固定一端自由两种约束条件下的波纹箔片刚度进行了测试,并将试验结果与仿真结果进行了对比分析。最后基于轴承波纹结构刚度特性,利用小扰动法求解了轴承动力学特性系数,研究了波纹箔片刚度特性对轴承动力学特性系数的影响。结果表明：两端固定波纹箔片刚度较一端固定一端自由波纹箔片单位宽度刚度大5倍以上,并且随着波纹变形量的增加,两端固定约束使其波纹箔片刚度比一端固定一端自由波纹箔片更具有非线性,而刚度仿真结果并没有体现出非线性,只是模型中引入的结构摩擦因数使得刚度值随摩擦因数有所增大。最后轴承载荷增加会使得轴承刚度系数以及主阻尼增加,其他阻尼系数减小,并且鉴于波纹箔片刚度非线性的原因,采用刚度试验值计算得到的轴承动力学系数增加幅度要明显大于文献仿真模型。     

Analysis of advanced gas foil bearings with piecewise linear elastic supports

Gas foil bearings (GFBs) rely on their underlying elastic foundation to support radial loads at high rotor speeds. The bump foil strip compliance determines the maximum load capacity with large rotor excursions, well in excess of the bearing nominal clearance. GFBs must be designed properly to permit their reliable (predictable) usage in aircraft engines and other heavy load applications since a too soft elastic foundation results in a bearing with limited load capacity. Configurations in practical use include a second bump strip layer or stop pins underneath the original bumps which become active above a certain load threshold. In these last configurations, the overall stiffness of the support structure has piecewise load versus deflection characteristics. Presently, a simple physical model for GFBs with a double bump strip layer follows. The analysis couples the Reynolds equation for the thin film flow of an ideal gas to the elastic supports deflections. An exact flow advection model is adopted to solve the partial differential equations for the zeroth- and first-order pressure fields, thus rendering the GFB load capacity and frequency-dependent rotordynamic force coefficients. Predictions show that heavily loaded GFBs comprising two bump layers in series and including stop pins prevent too large bump deflections which may induce permanent plastic deformations. The structural damping in a GFB with a two bump strip layer enhances the bearing direct damping force coefficients.     

Design,Fabrication, and Performance of Open Source Generation I and II Compliant Hydrodynamic Gas Foil Bearings

Foil gas bearings are self-acting hydrodynamic bearings made from sheet metal foils comprised of at least two layers. The innermost “top foil” layer traps a gas pressure film that supports a load while a layer or layers underneath provide an elastic foundation. Foil bearings are used in many lightly loaded, high-speed turbomachines such as compressors used for aircraft pressurization and small microturbines. Foil gas bearings provide a means to eliminate the oil system leading to reduced weight and enhanced temperature capability. The general lack of familiarity of the foil bearing design and manufacturing process has hindered their widespread dissemination. This paper reviews the publicly available literature to demonstrate the design, fabrication, and performance testing of both first- and second-generation bump-style foil bearings. It is anticipated that this paper may serve as an effective starting point for new development activities employing foil bearing technology.     

Experimental Study of a New Compliant Foil Air Bearing with Elastic Support

A new air-lubricated compliant foil journal bearing with elastic support, which has uniform surface stiffness and is much simpler in structure than previous compliant foil bearings (CFBs), is introduced in this article. Experiments have been conducted on the application of this type of CFB to a high-speed test rig, and this CFB can operate stably at 151,000 rpm. From the tests it is clear that the radial clearance C has a direct impact on the performance of this CFB, so the numerical relationship of structural parameters is listed in this article. Experimental results indicate that the CFB presented here offers preferable system dynamic and stability performance and has adequate damping to effectively reduce the possibility of self-excited and fractional frequency whirl.     

影响箔片结构阻尼的因素及箔片径向轴承结构形式的进展

稳定性是影响箔片轴承应用的一个关键问题，它与轴承弹性支承结构的阻尼特性密不可分。影响箔片阻尼的因素很多，内部因素如材料本身结构和性能，外部因素有温度、承载力和滑流等。本文介绍了箔片支承结构形式的进展，分析了影响箔片结构阻尼的几个外部因素，并结合实践提出改善箔片支承结构阻尼的几个途径。     

界面滑移对动压气体轴承间隙流动特性的影响*

为揭示转子静子表面流固界面非一致滑移状态下动压气体轴承转静子间隙流动机制以及对轴承性能的影响,建立界面非一致滑移修正雷诺方程,并耦合气膜厚度方程进行超松弛迭代求解,数值分析研究转静侧滑移状态、偏心率、间隙尺寸和耦合弹性箔片对间隙气膜流动特性的影响。结果表明：流固界面滑移状态对转静子间隙流动及其轴承性能具有显著的影响;转子侧滑移发生在压力上升区,这使得高压区压力减小;而静子侧滑移发生在压力下降区,使得高压区压力增大;与无滑移情形相比,局部滑移时间隙气膜压力峰值变化增幅达12%。在研究的参数范围内,随着偏心率减小和间隙高度增大,间隙界面滑移状态逐渐由转子侧滑移占主导向静子侧滑移占主导转变;耦合弹性箔片时,滑移区域增大1~4倍,滑移速度增大2~8倍,间隙气膜压力呈现双峰值分布。