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.     

Aerostatic and Aerodynamic Performance of an In-Pump Spirally Grooved Thrust Bearing: Analysis and Comparisons to Static Load Experiments

The combined effects of external pressurization and in-pump spiral grooves are studied according to the incompressible Whipple analysis; the results are examined in terms of non-dimensional parameters that bring out the interaction between the action of the spiral groove self-pressurization and that of the external pressurization through orifices. It is found that the interaction is significant when the supply pressure level to the orifices is near the peak pressure that can be reached by the spiral grooves alone. An optimized interacting design can improve the bearing stiffness. Away from the optimized interacting design, one of the two actions would dominate and the other one would cause a detraction of the bearing performance. As speed is sufficiently high, the pressurization action of spiral grooves causes the reduction of orifice flow and even its reversal. At such a condition the orifices are merely leakage paths that detract from the self-pressurization action of the spiral grooves. These predicted trends are qualitatively substantiated by tests.     

Analysis,Design, and Comparison of Different Types of Pistons for Sealless Pneumatic Cylinders and Valves

This article presents a theoretical and experimental analysis of sealless pistons featuring a special geometry capable of eliminating friction in pneumatic cylinders and valves. Three different piston geometries were investigated: tapered, stepped, and slot-pocket. Performance was evaluated for each geometry in terms of pressure distribution, leakage flow rate, and the self-centering force on the piston. The piston configuration that provides the best tradeoff between self-centering thrust and leakage flow rate in the air gap was also determined. The theoretical and experimental results obtained with the different piston designs were then compared.     

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.     

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.     

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。     

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.     

An Application of Newton's Method to the Lubrication Analysis of Air-Lubricated Bearings

This study deals with the development of a computational procedure for solving the isothermal compressible Reynolds equation as the governing equation of air-bearing analysis. Newton's method is used to linearize Reynolds equation and an iterative successive relaxation process is adopted to solve for the air film pressure. The optimal value of relaxation factor for the cases studied is suggested in this report for numerical stability and computational efficiency. The model is verified numerically by examining the conservation of mass flow of the lubricant. The dimensional analysis of the governing equation permits the model to be readily applied to any given film geometry.

The computer model developed can evaluate the air film pressure distribution, load capacity, frictional force, and mass flow of an air bearing. The proposed computational scheme efficiently analyzes the performance of air-lubricated journal bearings at large eccentricity ratios. A similar procedure can be employed to investigate the performance of highspeed noncircular air bearing or gas-lubrication film under slip-flow conditions. This study gives an analytical basis for the design of orifice-compensated externally pressurized air-lubricated bearing.     

Load Capacity for Adiabatic Infinitely Wide Plane Slider Bearings in the Turbulent Thermohydrodynamic Regime

A two-dimensional Navier-Stokes-based model developed using the Legendre collocation method is used to analyze turbulent plane slider bearings with wide ranges of bearing configuration, 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.     

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.     

On the Steady Performance of Hydrostatic Thrust Bearing: Rabinowitsch Fluid Model

The present theoretical analysis is to investigate the effect of non-Newtonian pseudoplastic lubricant (lubricant blended with viscosity index improver and viscosity thickener)–Rabinowitsch fluid model on the performance of externally pressurized hydrostatic thrust bearing. The expression for pressure has been derived using an energy integral approach. The load capacity and frictional torque of the bearing have also been numerically calculated for various values of viscosity index improver along with the centrifugal effects. The results so obtained are compared and found to be in good agreement with the earlier theoretical and practical results of Dowson, and the effect of viscosity index improver is also analyzed.     

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.     

Influence of Wall Slip on the Dynamic Properties of a Rotor-Bearing System

Based on the limiting shear stress model, we used a multi-linearity finite element algorithm and quadratic programming technique to study the influence of wall slip (boundary slip) on the operation stability of a rigid rotor-bearing system. The shaft surface is designed as a no-slip surface. The bearing sleeve surface is designed as three types of surfaces: (a) no slip is allowed (traditional no-slip rotor-bearing system), (b) the entire sleeve surface has the same slip property (the homogeneous slip bearing), and (c) the sleeve surface is optimized to have an optimized slip zone (the optimized slip bearing). It is found that if the sleeve surface has a single slip property, the wall slip generally reduces the system operation stability, as well as the load-carrying capacity. However, if the sleeve surface is designed as the optimized slip surface, the wall slip enhances the system operation stability as well as the load-carrying capacity. Furthermore, the smaller the surface limiting shear stress, the better the dynamic stability and the higher the load-carrying capacity.     

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.     

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.     

Scuffing Tests on Gear Oils in the FZG Apparatus

The FZG test is a usual and standardized method in West Germany to evaluate the antiscuffing properties of oils for reduction gears, hypoid gears, automatic transmission gears, etc. The paper gives a brief survey of the test apparatus, the test gears, and the test procedure. It describes also the criteria of failure and the evaluation of the results, taking into account not only the load-carrying capacity but also the wear performance of an oil. The repeatability and the scattering range is discussed with respect to the test conditions. The field of application for standardized gear rigs is pointed out. This is followed by a discussion of results showing the effect of tooth profile, mineral and synthetic oils, pitch line velocity, temperature, and surface treatment on the load-carrying capacity.

Furthermore the paper presents a formula to transfer the obtained test results to other gears. Results of the FZG apparatus are compared with values obtained on Ryder and IAE machines.     

Incompressible and Analytical Study on Load-Carrying Capacity of a Complex Thrust Gas Bearing

ABSTRACT

A type of aerodynamic/aerostatic complex thrust gas bearing was presented in the investigation of the coupling between aerodynamics and aerostatics with the objective of further improving the performance of the thrust gas bearing. Its analytical model was also set up completely under incompressible conditions. Based on this model, the load-carrying capacity function apparently included pressure and structure coupling items. However, this structure cannot be used when the pressure ratio of the complex gas bearing is less than 1.

     

Incompressible and Analytical Study on a Basic Model of a Complex Journal Gas Bearing

ABSTRACT

A basic analytical model of a hybrid journal gas bearing was set up completely for investigating the coupling between aerodynamics and aerostatics in a hybrid gas bearing under incompressible conditions, and for further improving its performance, under incompressible conditions. In this analytical model, the load-carrying capacity function is composed of five items. Apparently, there are pressure coupling and structure coupling between aerodynamics and aerostatics and when the groove distribution coefficient is 0.36, it is approximately maximum. However, this type of hybrid gas bearing structure can not be used when the pressure ratio is less than 1.

     

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.     

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.