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.     

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.     

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.     

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。     

Thermal Management Techniques for Oil-Free Turbomachinery Systems

Tests were performed to evaluate three different methods of utilizing air to provide thermal management control for compliant journal foil air bearings. The effectiveness of the methods was based on bearing bulk temperature and axial thermal gradient reductions during air delivery. The first method utilized direct impingement of air on the inner surface of a hollow test journal during operation. The second, less indirect method achieved heat removal by blowing air inside the test journal parallel to the shaft axis to simulate air flowing axially through a hollow shaft. The third method emulated the most common approach to removing heat by forcing air axially through the bearing's support structure. Internal bearing temperatures were measured with three type K thermocouples embedded in the bearing that measured general internal temperatures and axial thermal gradients. Testing was performed in a 1 atm, 260°C ambient environment with the bearing operating at 60 krpm, and supporting a load of 222 N. Air volumetric flows of 0.06, 0.11, and 0.17 m³/min at approximately 150 to 200°C were used.

The tests indicate that all three methods provide thermal management but at different levels of effectiveness. Axial cooling of the bearing support structure had a greater effect on the bulk temperature for each air flow and demonstrated that the thermal gradients could be influenced by the directionality of the air flow. Direct air impingement on the journal's inside surface provided uniform reductions in both bulk temperature and thermal gradients. Similar to the direct method, indirect journal cooling had a uniform cooling effect on both bulk temperatures and thermal gradients but was the least effective of the three methods.     

Dynamic Stiffness and Damping Characteristics of a High-Temperature Air Foil Journal Bearing

Using a high-temperature optically based displacement measurement system, a foil air bearing s stiffness and damping characteristics were experimentally determined. Results were obtained over a range of modified Sommerfeld Number from 1.5E6 to 1.5E7, and at temperatures from 25° to 538°C.

An Experimental procedure was developed comparing the error in two curve fitting functions to reveal different modes of physical behavior throughout the operating domain. The maximum change in dimensionless stiffness was 3.0E-2 to 6.5E-2 over the Sommerfeld Number range tested. Stiffness decreased with temperature by as much as a factor of two from 25° to 538°C. Dimensionless damping was a stronger function of Sommerfeld Number ranging from 20 to 300. As the temperature is increased, the damping shifts from a viscous type to a frictional type.     

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.     

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.     

Subfoil Stiffness Effects in Gas-Lubricated Foil Journal Bearings

A gas-lubricated foil journal bearing consists of a compliant foil structure that supports a rigid journal by means of a gas film. The foil structure consists of a top foil and a subfoil. The subfoil, which is constructed of one or more corrugated strips of sheet metal, supports the top foil and provides the primary resistance to radial deflection. As such, the radial stiffness of the subfoil has a direct influence on the gas film thickness and pressure distributions in the bearing. A finite element model incorporating the gas film and the foil structure will be used to investigate the effects of axial variations in the stiffness of the subfoil.     

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.     

平箔式箔片止推气体轴承静特性的理论研究

根据平箔式箔片止推轴承的结构。导出了求解箔片止推气体轴承特性的方程。利用有限元法进行了数值求解。比较了箔片止推轴承与刚性轴承的不同之处，并讨论了影响箔片止推轴承特性的因素。     

Thrust Bump Air Foil Bearings with Variable Axial Load: Theoretical Predictions and Experiments

Thrust air foil bearings are critical components in high-efficiency turbomachinery, such as two-stage compressors subjected to large and irregular axial forces. In this article, a model of thrust bump foil bearings that predicts deflection with variable axial load is developed assuming no tilting effect of the thrust collar. To predict the air clearance, deflection of the elastic foundation was used in the air film height equation. Combined Dirichlet and Neumann-type boundary conditions were used for static load performance predictions.

To verify the theoretical model, tests were performed with three different thrust air foil bearings with outer radii of 45, 50, and 55 mm. The rotating speed ranged from 10,000 to 25,000 rpm. From the test results, the model using nonlinear stiffness was in better agreement with the experimental results than the model using linear stiffness.     

An Experimental Investigation into the Temperature Profile of a Compliant Foil Air Bearing

A series of tests was performed to determine the internal temperature profile in a compliant bump-type foil journal air bearing operating at room temperature under various speed and load conditions. The temperature profile was collected by instrumenting a foil bearing with nine type-K thermocouples arranged in the center and along the bearing's edges in order to measure local temperatures and estimate thermal gradients in the axial and circumferential directions. To facilitate the measurement of maximum temperatures from viscous shearing in the air film, the thermocouples were tack-welded to the backside of the bumps that were in direct contact with the top foil. The mating journal was coated with a high-temperature solid lubricant that, together with the bearing, underwent high-temperature start-stop cycles to produce a smooth, steady-state run-in surface. Tests were conducted at speeds from 20 to 50 krpm and loads ranged from 9 to 222 N.

The results indicate that, over the conditions tested, both journal rotational speed and radial load are responsible for heat generation with speed playing a more significant role in the magnitude of the temperatures. The temperature distribution was nearly symmetric about the bearing center at 20 and 30 krpm but became slightly skewed toward one side at 40 and 50 krpm. Surprisingly, the maximum temperatures did not occur at the bearing edge, where the minimum film thickness is expected, but rather in the middle of the bearing, where analytical investigations have predicted the air film to be much thicker. Thermal gradients were common during testing and were strongest in the axial direction from the middle of the bearing to its edges, reaching 3.78° C/mm. The temperature profile indicated the circumferential thermal gradients were negligible.     

A Method for Measuring the Intensity of a Line Load Around a Shaft or Tube

The slip flow effect is considered to estimate the load capacity and the dynamic coefficients of an elastically-supported gas foil hearing when the local Knudsen number for the minimum film thickness is greater than 0.01. The compressible Reynolds equation with slip flow conditions is used to evaluate the load capacity. The linearized dynamic coefficient equations are obtained by the perturbation method. Numerical predictions compare the static and dynamic force performances considering slip flow at room-to-high temperate with the performance of elastically-supported foil bearing without slip flow for a range of bearing compliances and bearing numbers. It has been shown that the slip flow effect on the load capacity and the dynamic coefficients at high temperature is significant in the region of low bearing numbers.     

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.     

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.     

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.     

Load Capacity for Adiabatic Finite-Width Plane Slider Bearings in the Turbulent Thermohydrodynamic Regime

A Navier-Stokes based model developed using the Legendre collocation method is used to analyze turbulent plane slider bearings with wide ranges of convergence ratio, slenderness ratio, mean Reynolds number, and a parameter characterizing the viscosity variation. The load-capacity formulations are established for turbulent isothermal and turbulent thermohydrodynamic bearings. With the equations provided in this study, designers can quickly determine the load capacity without extensive computation.     

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.