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。     

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.     

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.     

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。     

Preliminary Development of Characterization Methods for Compliant Air Bearings

Developing a system for dynamic stiffness and damping measurements for foil bearings is crucial for future advancements in the design and use of oil-free bearing technology. This paper addresses some of the preliminary issues involved in developing such a measurement system. Steady-state stiffness measurements are taken and used as a learning tool for the use and development of a fiber optic displacement probe system. The problems encountered with these probes and the problems expected in their use at high temperature are addressed. Some possible solutions for these issues are also discussed. From this effort it appears that it is feasible to experimentally characterize foil bearings at high speeds and temperatures.     

Effect of internal friction in the dynamic behavior of aerodynamic foil bearings

The development of aerodynamic foil bearings in the past decade is due, for a major part to environmental reasons because: first, air is a clean lubricant and second foil bearings can be used in very critical thermal environment: air has a poor sensitivity to high temperature changes. Foil bearings are often used for very high velocity turbines. Experimental studies have shown the capability of foil bearing to work under rather high load capacity with good dynamic behavior. Numerical simulations are now able to predict with a good accuracy foil bearing load capacity. They take into account foil deformation and dry friction between foils. For dynamic simulation, dry friction has been taken into account only through damping coefficient. As damping is not completely similar to dry friction, this paper is a first attempt in taking account its effect in the foil bearing dynamic behavior. A non-linear model, coupling a simplified equation for the rotor motion to both Reynolds equation and foil assembly model is described. Then the dynamic behavior, for a given unbalance is studied. For different values of friction coefficient, the rotor trajectory is studied when velocity increased. For low and high friction coefficient, the dynamic behavior shows critical speeds. For medium values (between 0.2 and 0.4), these critical speeds disappear. This work outlines that it is possible to optimize the friction between the foils in order to greatly improve the dynamic behavior of foil bearings. With a detailed analysis of these first results we propose primary physical explanation of this phenomena.     

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.     

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.     

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.     

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.     

无油涡轮增压器的设计及其试验研究

对采用空气箔片轴承支承的无油涡轮增压器进行了设计和试验性研究。详细阐述了无油涡轮增压器以及所采用的空气箔片轴承的设计过程。通过静态加载试验预估了空气箔片轴承的名义间隙,采用Link-Spring模型预测了空气箔片轴承支承结构的刚度,结合Link-Spring模型和雷诺方程,采用扰动法对轴承的动态刚度和阻尼系数进行了有效预测。线性转子动力学分析表明设计的无油涡轮增压器转子的前两阶刚体模态临界转速均在所用空气箔片轴承的起飞转速之下,转子的正常运行转速在一阶弯曲模态临界转速之下并具有足够的安全裕度。对整个转子系统进行了转子动力学分析与计算之后,在此基础上搭建了无油涡轮增压器试验台,初步的升降速试验结果表明：转子在20 kr/min~60 kr/min出现较大的次同步振动,但是转子在68 kr/min时次同步振动显著减小,转子在68 kr/min稳速时的轨迹以及FFT分析表明转子在该转速下的主要振动来自同步振动,这表明增压器可以在68 kr/min稳定运行。同时,实时测量了推力轴承和径向轴承的温度,在68 kr/min稳速期间,推力轴承和径向轴承温度分别在52℃和32℃处小幅波动,说明了该转子-轴承系统的相对稳定性。     

Unbalance Response of a Super-Critical Rotor Supported by Foil Bearings—Comparison with Test Results©

This article compares theoretical and experimental results on the unbalance response of a super-critical rotor supported by two kinds of gas foil bearings. Analysis of the super-critical rotor is performed with viscoelastic foil bearings (VEFB) and conventional bump foil bearings and compared with early published experimental data. The vibration orbits obtained by theoretical investigation on the viscoelastic foil bearings (VEFB) and the conventional bump foil bearings are compared with the experimental vibration orbits of the super-critical rotor supported by both foil bearings. A numerical analysis program can calculate the static and dynamic characteristics of the elastically supported gas foil bearing using the measured stiffness and damping of the elastic foundation. After the stiffness and damping of both foil bearings are calculated using the perturbation method, vibration orbits of the flexible rotor modeled by the finite element method are calculated. Vibration orbits calculated by numerical analysis agree well with experimental data when the vibration amplitude is small and the rotating speed is below the bending critical speed. The numerical results also show that the enhanced structural damping of the elastic foundation reduces vibration near the bending critical speed.     

以高压CO2为介质的推力箔片轴承静特性分析

针对超临界二氧化碳布雷顿循环用压缩机中的推力箔片轴承开展了数值研究,通过MATLAB编程数值计算求解变密度、变黏度湍流雷诺方程和耦合弹性箔片变形方程,得到楔形间隙内气膜压力分布及推力箔片轴承承载力和摩擦功耗,并与空气润滑介质对比;进一步分析推力箔片轴承节距比、瓦张角、楔形高度及最小气膜厚度对轴承承载力和摩擦功耗的影响。计算结果表明:高压CO₂下弹性箔片变形比常压空气时更大,轴承承载力远高于常压空气轴承;瓦张角为45°和节距比为0.5的推力箔片轴承具有较高的承载力和较低的摩擦功耗;楔形高度设计过大会降低承载力,增大摩擦功耗,使载荷集中在水平区域;增大最小气膜厚度设计值虽能减小摩擦功耗,但却引起承载力的显著降低。     

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。     

Performance and Durability of High Temperature Foil Air Bearings for Oil-Free Turbomachinery

The performance and durability of advanced, high temperature foil air bearings are evaluated under a wide range (10 to 50 kPa) of loads at temperatures from 25° to 650 °C. The bearings are made from uncoated nickel based superalloy foils. The foil surface experiences sliding contact with the shaft during initial start/stop operation. To reduce friction and wear, the solid lubricant coating, PS304, is applied to the shaft by plasma spraying. PS304 is a NiCr based Cr₂O₃ coating with silver and barium fluoride/calcium fluoride solid lubricant additions.

The results show that the bearings provide lives well in excess of 30,000 cycles under all of the conditions tested. Several bearings exhibited lives in excess of 100,000 cycles. Wear is a linear function of the bearing load. The excellent performance measured in this study suggests that these bearings and the PS304 coating are well suited for advanced high temperature, oil-free turbomachinery applications.     

Foil Bearing Technology for High Speed Single Stage Air Compressors for Fuel Cell Applications

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 ...     

Foil Bearing Technology for High Speed Single Stage Air Compressors for Fuel Cell Applications

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 ...     

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.     

基于弹性壳体模型的波箔型气体动压径向轴承静特性分析

采用有限单元法,对波箔型气体动压径向轴承的箔片建立了弹性壳体单元模型。该模型综合考虑了箔片膜效应与弯曲效应之间的耦合,更能真实地反映出波箔和平箔的变形。运用有限差分法及Newton-Raphson迭代法耦合求解Reynolds方程和气膜厚度方程,分析了轴承气膜厚度分布、压力分布、箔片变形量分布以及承载能力,并与实验结果进行了比较,证明了该方法的可行性和精确性。分析了转速、箔片厚度对轴承特性的影响,结果表明:转速上升,承载能力增大;箔片厚度小于0.2mm时,厚度的改变对轴承的影响较大。     

Analysis of gas foil bearings integrating FE top foil models

Gas foil bearings (GFBs) find widespread usage in oil-free turbo expanders, APUs, and micro gas turbines for distributed power due to their low drag friction and ability to tolerate high-level vibrations. The performance of GFBs depends largely on the support elastic structure, i.e. a smooth foil on top of bump strips. Conventional models include only the bumps as equivalent stiffnesses uniformly distributed around the bearing circumference. More complex finite element (FE) models couple the elastic deformations of the 2D shell or 1D beam-like top foil to the bump deflections as well as to the gas film hydrodynamics. Predictions of journal attitude angle and minimum film thickness for increasing static loads and two journal speeds are obtained for a GFB tested decades ago. For the GFB studied, 2D FE model predictions overestimate the minimum film thickness at the bearing centerline, while underestimating it at the bearing edges. Predictions from the 1D FE model compare best to the limited tests data, reproducing closely the experimental circumferential wavy-like film thickness profile. Predicted stiffness and damping coefficients versus excitation frequency show that the two FE models result in slightly lower direct stiffness and damping coefficients than those from the simple elastic foundation model.