评价箔片径向空气轴承载荷性能的一种经验方法

介绍一种简单的“经验法则”来评价箔片空气轴承的载荷性能,它是一种可挠面的动压气体轴承,正在研究其在无油透平机械中的应用。经验法则是基于基本原理和文献中报道的可靠实验数据得出的,通过一个经验值——载荷系数D,将轴承的载荷性能和轴承的尺寸、速度联系起来。在经验法则中,轴承承载力是轴承转速和轴承设计面积的线性函数。轴承载荷系数D和轴承弹性支承结构的设计特点和轴承运行工况(温度、速度)有关。     

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.     

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.     

弹性箔片动压径向气体轴承起飞转速和承载能力的实验研究

在建立的气体轴承性能测试实验台上对新型弹性箔片气体动压径向轴承进行了起飞转速和承载能力的实验研究,并分别通过摩擦力矩和径向位移响应频谱两种方法分析了轴承的起飞转速。结果表明:轴承起飞后摩擦力矩逐渐减小并趋于稳定,且径向位移响应频谱图上只有较大的低倍频分量出现,高倍频分量和其它频率分量要小得多;两种分析方法得到的轴承起飞转速基本吻合;载荷越大,轴承和转子中心的偏心距越大;由于箔片弹性变形使卸载过程存在能量损失,同样载荷下卸载时的偏心距比加载时大。     

The Role of Radial Clearance on the Performance of Foil Air Bearings

Load capacity tests were conducted to determine how radial clearance variations affect the load capacity coefficient of foil air bearings. Two Generation III foil air bearings with the same design but possessing different initial radial clearances were tested at room temperature against an as-ground PS304 coated journal operating at 30000 rpm. Increases in radial clearance were accomplished by reducing the journal's outside diameter via an in-place grinding system. From each load capacity test the bearing load capacity coefficient was calculated from the rule-of-thumb (ROT) model developed for foil air bearings.

The test results indicate that, in terms of the load capacity coefficient, radial clearance has a direct impact on the performance of the foil air bearing. Each test bearing exhibited an optimum radial clearance that resulted in a maximum load capacity coefficient. Relative to this optimum value are two separate operating regimes that are governed by different modes of failure. Bearings operating with radial clearances less than the optimum exhibit load capacity coefficients that are a strong function of radial clearance and are prone to a thermal runaway failure mechanism and bearing seizure. Conversely, a bearing operating with a radial clearance twice the optimum suffered only a 20% decline in its maximum load capacity coefficient and did not experience any thermal management problems. However, it is unknown to what degree these changes in radial clearance had on other performance parameters, such as the stiffness and damping properties of the bearings.     

On the Fluid Flow and Thermal Analysis of a Compliant Surface Foil Bearing and Seal

Foil gas bearings have been applied successfully to a wide range of high-speed rotating machinery such as air cycle machines (ACMs) and auxiliary power units (APUs). The performance of these bearings are based on the high pressure gas in a very thin layer between the journal and the bearing governed by the Reynolds equations. Generation of heat in these bearings especially at high journal rotating speed and high loads or at high ambient temperature directly affect their performance. Thermal and fluid flow analysis of an advanced compliant foil journal bearing/seal are presented. The side flow (known as leakage) and the approximate temperatures are the results of this analysis. The result of preliminary analysis shows that the major portion of the heat is carried through conduction and using the modified Couette flow approximation for the present working fluid, air, helped in analysis of the temperature magnitude, which can be related to the gas viscosity behavior and thin gas film thicknesses.     

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.     

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.     

Stiffness and Damping Coefficient Estimation of Compliant Surface Gas Bearings for Oil-Free Turbomachinery

Gas foil bearings are a key technology in many commercial and emerging oil-free turbomachinery systems. These bearings are nonlinear and have been difficult to analytically model in terms of performance characteristics such as load capacity, power loss, stiffness, and damping. Previous investigations led to an empirically derived method, a rule-of-thumb, to estimate load capacity. This method has been a valuable tool in system development. The current article extends this concept to include rules for stiffness and damping coefficient estimation. It is expected that these rules will further accelerate the development and deployment of advanced oil-free machines operating on gas foil bearings.     

Journal Design Considerations for Turbomachine Shafts Supported on Foil Air Bearings

Foil air bearings can offer substantial improvements over traditional rolling element bearings in many applications and are attractive as a replacement to enable the development of advanced oil-free turbomachinery. In the course of rigorous testing of foil journal bearings at NASA Glenn Research Center, shaft failure was repeatedly encountered at high ambient temperature and rotational speed, with moderate radial load. The cause of failure is determined to be excessive non-uniform shaft growth, which increases localized viscous heating in the gas film and eventually leads to a high-speed rub and destruction of the bearing and journal. Centrifugal loading of imbalance correction weights and axial temperature gradients within the journal due to the hydrodynamic nature of the foil bearings, determined by experiment and finite element analysis, are shown to be responsible for the non-uniform growth. Qualitative journal design guidance is given to aid in failure prevention.     

空气箔片轴承技术在高速单级燃料电池空压机上的应用（英文）

The motivation to use air foil bearings in fuel cell compressors is driven by the demand for oil-free and high-power density system to reduce system volume and weight. The characteristics of air foil bearings that realize this demand are its independency on auxiliary system and no scheduled maintenance as well as their superb performance at high speeds. However, integration of the foil bearings to the compressor needs rigorous developmental tests for the bearing to withstand high g-load during vehicle maneuver and to remain stable in rotordynamics under external destabilizing forces. This paper presents multi-pads foil bearing technology applicable to single stage high speed fuel cell air compressors.Two different multi-pad air foil bearing designs(two-pad vs three-pad) were tested using a high-speed spin test rig to identify the differences in rotordynamics responses. The two-pad bearing is superior in rotordynamics without any sub-synchronous vibration while three-pad bearing provides more uniform load capacity in all directions with less rotordynamics stability. Frequency-domain modal analyses verify the experimental observations. Axial foil bearings with38 mm outer diameter was designed and tested up to 140 krpm with load capacity of 90 N(1.4 bar specific load capacity).Finally, a platform design of single stage 15 k W fuel cell compressor with rated speed of 130 krpm is proposed using the multi-pad foil bearings and axial foil bearings developed through this paper.     

应用于燃料电池的高速单级空气压缩机波箔轴承技术（英文）

The motivation to use air foil bearings in fuel cell compressors is driven by the demand for oil-free and high-power density system to reduce system volume and weight. The characteristics of air foil bearings that realize this demand are its independency on auxiliary system and no scheduled maintenance as well as their superb performance at high speeds. However, integration of the foil bearings to the compressor needs rigorous developmental tests for the bearing to withstand high g-load during vehicle maneuver and to remain stable in rotordynamics under external destabilizing forces. This paper presents multi-pads foil bearing technology applicable to single stage high speed fuel cell air compressors.Two different multi-pad air foil bearing designs(two-pad vs three-pad) were tested using a high-speed spin test rig to identify the differences in rotordynamics responses. The two-pad bearing is superior in rotordynamics without any sub-synchronous vibration while three-pad bearing provides more uniform load capacity in all directions with less rotordynamics stability. Frequency-domain modal analyses verify the experimental observations. Axial foil bearings with 38 mm outer diameter was designed and tested up to 140 krpm with load capacity of 90 N(1.4 bar specific load capacity).Finally, a platform design of single stage 15 k W fuel cell compressor with rated speed of 130 krpm is proposed using the multi-pad foil bearings and axial foil bearings developed through this paper.     

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.     

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.     

Dynamic characteristics of a flexible rotor system supported by a viscoelastic foil bearing (VEFB)

Foil bearings have been considered as an alternative to traditional bearings with the increasing need for high-speed, high-temperature turbomachinery. However, the lack of adequate load capacity and sufficient damping capacity is a key technical hurdle to super-bending-critical operation as well as widespread use of foil bearings in turbomachinery such as turbopumps, turbocompressors and turbochargers. A new foil bearing, ViscoElastic Foil Bearing (VEFB) is suggested in this paper. The super-bending-critical operation of the conventional bump foil bearing and the VEFB is examined, as well as the structural dynamic characteristics. The structural dynamic test results show that the equivalent viscous damping of the VEFB is much larger than that of the bump bearing and that the structural dynamic stiffness of the VEFB is comparable or larger than that of the bump bearing. The results of super-bending-critical operation of the VEFB indicate that the enhanced structural damping of the viscoelastic foil dramatically reduces the vibration near the bending critical speed. With the help of increased damping resulting from the viscoelasticity, suppression of the nonsynchronous orbit is possible beyond the bending critical speed.     

A Fully Coupled Finite Element Formulation for Elastically Supported Foil Journal Bearings

Foil gas journal bearings consist of a compliant metal shell structure that supports a rigid journal by means of a gas film. The prediction of steady operating characteristics such as minimum film thickness, load capacity, and drag require the coupled solution of the shell structure and the gas flow. A general fully coupled finite element approach is presented. A single four noded finite element that incorporates the elastically supported shell structure of the foil and the gas film modeled by a compressible Reynolds equation is developed. The resulting system of nonlinear finite elements is solved by the Newton Raphson method.     

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.     

弹性箔片动压气体推力轴承承载性能研究

气弹耦合解是准确预测弹性箔片动压气体轴承承载性能的有效方法。通过引入箔片的弹性变形以及联立求解动压气体润滑Reynolds方程和弹性箔片的变形方程,给出了弹性箔片动压气体推力轴承的气弹耦合解。应用气弹耦合解理论,将顶层箔片的局部弹性变形纳入考虑范围,对弹性箔片动压气体推力轴承的承载性能进行了计算和分析。有限元数值仿真结果表明:顶层箔片在气膜压力作用下的局部弹性变形直接导致弹性箔片动压气体推力轴承承载能力的降低;根据轴承瓦块上气膜压力分布的特点合理设计支承拱箔的结构形式,可以减小顶层箔片的局部弹性变形,有效提高轴承的承载能力。得到了一种承载能力较高的弹性箔片动压气体推力轴承支承拱箔结构设计方案。     

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.     

Dynamic stability experiments of compliant foil thrust bearing with viscoelastic support

In order to reduce the complexity of machine construction and improve the mechanical efficiency, high speed rotation machineries usually implement self-acting gas bearings to substitute the traditional oil-lubricated bearings. This paper presents test results of a gas thrust bearing with viscoelastic support which is designed for high speed turbo-machinery. The gas bearing, which belongs to compliant foil bearings, consists of a top thin metal foil and a bottom thin rubber foil. Static and stability experiments are conducted on a high speed gas turbine test rig. The static results indicate that the structural stiffness of test bearing generally increases with the increase in axial load and the decrease in thickness of bottom foil. In the rotation tests, rotor runs stably with small vibration amplitude, which is dominant in waterfall plot during whole speed up procedure. It shows that test bearing has preferable stability characteristics for high speed gas turbines.