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.     

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.     

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.     

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.     

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。     

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.     

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.     

Surface Roughness Effects in Journal Bearings with Non-Newtonian Lubricants

The static performance of finite journal bearings lubricated with non-Newtonian power law fluids is analyzed by using a control volume method with an Elrod algorithm to solve the average Reynolds equation and determine the cavitation region accurately. The results show that the flow behavior index of power law fluids has an insignificant affect on the load ratios, side flow ratios and cavitation regions, while it significantly affects load capacities and side flow rates. Furthermore, the effects of film thickness ratios, pressure flow factors, shear flow factors, slenderness ratios, eccentricities and inlet pressures on the variations of cavitation regions are also discussed.     

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.     

On the Adjusting of the Dynamic Coefficients of Tilting-Pad Journal Bearings

This paper gives a theoretical and experimental contribution to the problem of active modification of the dynamic coefficients of tilting-pad journal bearings, aiming to increase the damping and stability of rotating systems. The theoretical studies for the calculation of the bearing coefficients are based on the fluid dynamics, specifically on the Reynolds equation, on the dynamics of multibody systems and on some concepts of the hydraulics. The experiments are carried out by means of a test rig specially designed for this investigation. The four pads of such a bearing are mounted on four flexible hydraulic chambers which are connected to a proportional valve. The chamber pressures are changed by means of the proportional valve, resulting in a displacement of the pads and a modification of the bearing gap. By changing the gap, one can adjust the dynamic coefficients of the bearing. With help of an experimental procedure for identifying the bearing coefficients, theoretical and experimental results are compared and discussed. The advantages and the limitation of such hydrodynamic bearings in their controllable form are evaluated with regard to application on the high-speed machines.     

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.     

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.     

轴颈质量对动载滑动轴承润滑状况影响的研究

本文采用动载滑动轴承轴心软迹的动力学计算方法，详细地讨论轴系惯性质量对动载滑动轴承轴心软迹和润滑状况的影响，以及转速对轴承润滑状况的影响。     

Pressure Distributions along Vertical Hydrodynamic Herringbone-Grooved Journal Bearings

The pressure distributions generated along vertical hydrodynamic herringbone-grooved journal bearings were experimentally and numerically investigated at rotational speeds ranging from 203 to 2110 rpm. A test rig was designed and constructed for this purpose and four journals (shafts) with different herringbone-grooved patterns and radial gaps were tested: Journal 1 (with symmetrical and discontinuous grooves and 0.25-mm clearance gap), Journal 2 (with symmetrical and discontinuous grooves and 0.35-mm clearance gap), Journal 3 (with symmetrical and four continuous grooves), and Journal 4 (with asymmetrical and three continuous grooves). The journals were made of aluminum with diameters of 46.00 mm, and the sleeve was made of a transparent Plexiglas pipe for visual observation of the lubricant in the gap between the journal and the sleeve. Pressure taps were installed along the sleeve to obtain the pressure distributions using a pressure transducer. Numerical simulations were performed for these four herringbone-grooved journal bearings using commercially available computational fluid dynamic software. The computational simulations agree in trends with the experimental results and theoretical expectations.     

Boundary Conditions of Cavitation Regions in Journal Bearings

The behavior of the oil in a cavitation region is studied. Boundary conditions of the pressure distribution at the inlet and at the outlet border of such a region are given. Calculation of the power loss in a cavitated zone is demonstrated.     

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.     

The Effect of Perturbation Amplitudes on Eight Force Coefficients of Journal Bearings

This paper investigates the relationship between eight linear oil-film force coefficients of circular journal bearings and the perturbation amplitudes. The force coefficients are calculated by the finite perturbation method and compared with those calculated by the infinitesimal perturbation method. Numerical experiments show that the calculated results from both finite perturbation and infinitesimal perturbation methods are very close (with a variation less than 0.1 %) when the perturbation amplitudes are less than 0.02c (displacement) or 0.02ωc (velocity) for normal bearing eccentricities. For eccentricities between 0.2 and 0.8, the calculated coefficients by the finite perturbation method will differ less than 2.5 % from the results by the infinitesimal perturbation method if the perturbation amplitude is less than 0.05c or 0.04ωc. The bearing coefficients calculated by the finite perturbation method under different perturbation amplitudes are presented graphically.     

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.     

TEHD Analysis for Tilting-Pad Journal Bearings Using Upwind Finite Element Method

A general approach for incorporating heat transfer and elastic deformation effects into a tilting-pad journal bearing simulation model is presented. A global analysis method is used, which includes variable viscosity and heat transfer effects in the fluid film, elastic deformation and heat conduction effects in the pads, and elastic deformation effect in the pivots. The two-dimensional variable viscosity. Reynolds equation produces pressure distributions in the axial and circumferential directions. The energy equation is two-dimensional, assuming that the temperature variation in the axial direction is negligible. The elasticity and heat conduction models are also two-dimensional, being in the midline cross-section of the bearing, including the circumferential and cross-film directions. An upwind technique is used in the finite element formulation of the energy equation to remove numerical instability due to the convective term. Simulation results are compared with the test and predicted values of previous researchers.