Gas-lubricated Bearings Research Articles

Analysis of Gas-Lubricated Bearings with a Coupled Boundary Effect for Micro Gas Turbine

Due to the limitation of micro-machining technology, the bearing aspect ratio for a micro gas turbine is limited to a small value. Therefore, the load-carrying capacity of such bearing is inherently small. Thus, it is desirable to predict the load-carrying capacity as accurately as possible without being unnecessarily conservative. The direct numerical analysis of bearing characteristics was performed by mass conservation at coupled boundary. Journal bearing was numerically simulated for two cases −1) an externally pressurized bearing with four feeding holes and 2) a hydrodynamic bearing. Characteristics such as pressure distribution at the bearing surface, load-carrying capacity as a function of aspect ratio with a coupled boundary effects are investigated for micro gas turbine bearings. It is shown that a model of thrust and journal bearings coupled at boundary generally predicts a greater load-carrying capacity than uncoupled models. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Triboiogy Conference in San Francisco, CA October 21–24, 2001

K-1233 気体軸受の動的挙動の数値シミュレーション(J06-3 流体関連の騒音と振動(3))(J06 流体関連の騒音と振動)

K-1233 気体軸受の動的挙動の数値シミュレーション(J06-3 流体関連の騒音と振動(3))(J06 流体関連の騒音と振動)

On the Performance of Hybrid Foil-Magnetic Bearings

Recent technological advancements make hybridization of the magnetic and foil bearings both possible and extremely attractive. Operation of the foil/magnetic bearing takes advantage of the strengths of each individual bearing while minimizing each other’s weaknesses. In this paper one possible hybrid foil and magnetic bearing arrangement is investigated and sample design and operating parameters are presented. One of the weaknesses of the foil bearings, like any hydrodynamic bearing, is that contact between the foil bearing and the shaft occurs at rest or at very low speeds and it has low load carrying capacity at low speeds. For high speed applications, AMBs are, however, vulnerable to rotor-bending or structural resonances that can easily saturate power amplifiers and make the control system unstable. Since the foil bearing is advantageous for high speed operation with a higher load carrying capacity, and the magnetic bearing is so in low speed range, it is a natural evolution to combine them into a hybrid bearing system thus utilizing the advantages of both. To take full advantage of the foil and magnetic elements comprising a hybrid bearing, it is imperative that the static and dynamic characteristics of each bearing be understood. This paper describes the development of a new analysis technique that was used to evaluate the performance of a class of gas-lubricated journal bearings. Unlike conventional approaches, the solution of the governing hydrodynamic equations dealing with compressible fluid is coupled with the structural resiliency of the bearing surfaces. The distribution of the fluid film thickness and pressures, as well as the shear stresses in a finite-width journal bearing, are computed. Using the Finite Element (FE) method, the membrane effect of an elastic top foil was evaluated and included in the overall analytical procedure. Influence coefficients were generated to address the elasticity effects of combined top foil and elastic foundation on the hydrodynamics of journal bearings, and were used to expedite the numerical solution. The overall program logic proved to be an efficient technique to deal with the complex structural compliance of various foil bearings. Parametric analysis was conducted to establish tabulated data for use in a hybrid foil/magnetic bearing design analysis. A load sharing control algorithm between the foil and magnetic elements is also discussed. [S0742-4795(00)01201-1]

Numerical Analysis of Herringbone-Grooved Gas-Lubricated Journal Bearings Using a Multigrid Technique

In this paper, a multigrid technique is applied to the compressible Reynolds equation discretized by the divergence formulation in order to analyze both static and dynamic characteristics of herringbone-grooved gas-lubricated journal bearings. The developed code demonstrates quicker convergence than an optimized successive over-relaxation scheme, and the dominance in numerical efficiency is especially remarkable at higher values of bearing number where slow convergence is generally observed. Comparisons between the present nonlinear orbit solutions and previously published experimental results show reasonable agreement in both steady-state and dynamic stability performances.

Stability of Axially-Grooved Self-Acting Gas-Lubricated Journal Bearings.

Both experimental and numerical studies are conducted on half-frequency whirl (HFW) stability of axially-grooved self-acting gas-lubricated journal bearings. The studies demonstrate that 8-grooved bearings are unconditionally unstable with usual bearing clearance and rotational speed. On the other hand, 2 grooved bearings operate stably at relatively low values of bearing number which are obtained with usual clearance and speed. The physics of HFW stability is attributed to the pressure distribution geometry. Further, as a result of extensive numerical simulations, it is found that 3 grooved bearings with groove width ratio to total width of 0.3 through 0.5 give favorable stability performance.

Numerical prediction of the performance of gas-lubricated spiral groove thrust bearings

The objective of this paper is to develop an accurate numerical procedure for the analysis of nominally flat contacts with spiral grooves lubricated by gases. The numerical procedure, which is based on the control-volume method, enables the solutions of the non-linear Reynolds equation to be obtained without limitation in geometry and operating conditions. Satisfactory flow balance was achieved on the control volumes as well as on the whole boundary and the method was proved to be very accurate. Convergence of the method was quick for any compressibility number. Three types of contact with spiral grooves were analysed. They were hydrodynamic bearings without interior chambers, hydrodynamic bearings with interior chambers and hybrid bearings. The effects of spiral angle, groove geometry (length, depth and width) and compressibility on performances were investigated for all possible designs.

On the Breakdown Under Contact Conditions of Reynolds Equation for Gas Lubricated Bearings

For the analysis of gas lubricated bearings, Reynolds equation is available in a number of forms—the original version, first-order modified, second-order modified, one-and-a-half order modified, and Boltzmann-Reynolds. All of these variants are asymptotically examined for instances in which local contact occurs in a bearing. These asymptotics serve to identify the order of the respective singularities in pressures, and thus imply the possible consequences of using a particular version of Reynolds equation in the presence of contact.

On Fundamental Characteristics of a Hybrid Gas-Lubricated Journal Bearing with Surface-Restriction Compensation

The static and dynamic characteristics of a hybrid gas-lubricated journal bearing with surface-restriction compensation through multiple sawtooth grooves are analyzed by applying FEM. The design criteria of this bearing are discussed using the theoretical results of the fundamental bearing characteristics calculated under the variations of several bearing parameters. In particular, the optimum groove depths for the maximum static stiffness and for the maximum dynamic stiffness are clarified. The experimental research on this bearing is also presented in this paper. The theoretical and experimental results show that this bearing has a higher bearing performance and more applications in engineering compared with the traditional gas-lubricated bearing.

Transient Analysis of Gas-Lubricated Journal Bearing Systems by Differential Quadrature

This paper is an extension of an earlier work in which the present authors demonstrated the application of the differential quadrature method (DQM) to the steady-state analysis of incompressible and compressible lubrication problems. In the present work, the DQM is applied to the transient-state analysis of compressible lubrication problems. For this purpose, the analysis of gas-lubricated plain journal bearings under the conditions of nonuniform journal rotation is considered. The computed results from the solutions of the reference problem included in the paper provide a comparison of the convergence characteristics and computational efficiency of the differential quadrature and finite element methods.

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...

Fast Numerical Approach for Analyzing Self-Acting Gas-Lubricated Bearings Using a Multigrid Method.

A multigrid method has been introduced as a fast alternative to conventional relaxation methods for obtaining a solution to the Reynolds equation for self-acting gas-lubricated bearings. This paper verifies the procedure applied to both static and time-dependent dynamic analyses of plain-cylindrical journal bearings. The method gives successful results with less computational effort compared with single grid-oriented iterative methods. In addition, the new approach does not require a trial and error process to optimize the overrelaxation parameter unlike a successive overrelaxation method. The nonlinear orbit method which is an accurate but time-consuming transient analysis is expected to be reduced to a handy design tool for a complicated bearing system on incorporating the multigrid technique.

An Analysis of Gas-Lubricated, Multileaf Foil Journal Bearings With Backing Springs

This paper describes the development of a new analysis technique that was used to evaluate the performance of a class of gas-lubricated journal bearings. The surface of these bearings is made up of preformed, leaf-type, compliant foils that are anchored to the bearing housing by spacer keys. Each leaf overlaps an adjacent leaf. Beneath each foil and attached to the inside of the bearing housing is a strip of backing spring. The stiffnesses of various foil bearing structures are modeled and presented as influence coefficients. Unlike conventional approaches, the solution of the governing hydrodynamic equations dealing with compressible fluid is coupled with the structural resiliency of the bearing surfaces. The distribution of the fluid film thickness and pressures, as well as the shear stresses in a finite-width journal bearing, are computed. The solutions include values of bearing stiffness coefficients due to both structural and hydrodynamic stiffnesses. The analysis, which is conducted for multileaf configurations by varying the number of leaves, uncovers the effects that the various structural, geometric, and operational variables have on bearing behavior. Also discussed are design guidelines with regard to the number of leaves, the degree of compliance, and bearing operational parameters.

Advancements in the Performance of Aerodynamic Foil Journal Bearings: High Speed and Load Capability

An advanced-design, aerodynamic, air-lubricated foil journal bearing achieved a landmark speed of 2200 cps (132,000 rpm) and a major breakthrough in load performance of 673.5 kPa (97.7 psi). At 20°C (68°F) room temperature, normal ambient pressure, 995 cps (59,700 rpm) rotor speed, and with bearing projected pad area of 1081 mm2 (1.675 in2), the bearing demonstrated a load capacity of 727.8 N (163.6 lb). The bearing also exhibited low heat generation, with about 40°C (104°F) average side leakage temperature rise. For this demonstration, a highspeed spindle utilizing a pair of 35-mm (1.375-in.) bearings and supporting a test rotor with a mass of 1.545 kg (weighing 3.41 lb) and overall length of 211 mm (8.3 in.) was successfully taken to the limiting speed of the test apparatus. This speed was set by the maximum sound velocity (Mach 1) in the spindle’s turbine wheel. The rotor/bearing speed of 4.62 × 106 DN is beyond the capability of any advanced oil-lubricated ball bearings or conventional gas-lubricated bearings. The net result is a highly stable bearing at high operating speed. This paper presents the development of this air-lubricated foil journal bearing, the operational procedures used during testing, test results (dynamic analyses), and load performance characteristics.

Static Analysis of Flying Characteristics of the Head Slider by Using an Optimization Technique

This paper suggests a method to predict the static solution for gas-lubricated slider bearings in a hard disk drive (HDD) by using an optimization technique. The modified Reynolds equation for the hydrodynamic lubrication theory under the slip condition is used to describe the compressible fluid flow within the gas bearing, and a factored implicit finite difference (FIFD) scheme is applied for pressure calculations. An optimization technique is employed to find the solution at which the forces and moments acting on the gas bearing are in a state of equilibrium. The proposed method is more general and robust than the conventional update schemes since it exploits the automatic update capability of the optimization technique instead of using an empirical approach, and may be more efficient than the transient FIFD approach since it directly searches for static solutions instead of tracking the time-dependent equations asymptotically to steady state. Results obtained for several typical head slider models are reported, showing the effectiveness of the proposed method.

Finite Element AnalysiH of Gas-Lubricated Grooved Journal Bearings. 1st Report, Analysis method.

This paper describes the development of a finite element analysis program for the nonlinear and time-dependent Reynolds equation based on an incremental formulation. This program can be utilized to predict the dynamic behavior of gas-lubricated grooved journal bearings. The accuracy of the program is clearly demonstrated through some analyses of both non-grooved and grooved journal bearings.

Study on si electrostatic and electroquasistatic micromotors

An electrostatic variable-capacitance micromotor and an electroquasistatic induction micromotor are discussed. Both the micromotors, with rotors of 160 μm diameter, have been fabricated by the surface micromachining of polysilicon. In order to reduce the friction in the micromotors, the application of a gas-lubricated bearing is proposed. An aerodynamic in-pumping spiral grooved thrust microbearing with a groove width of 4 μm and a groove depth of 300 nm has been designed and used in the micromotors.

Regular and Reversible Rotation-Type Gas-Lubricated Circular-Disk Grooved Thrust Bearings.

A new pump-in and pump-out type of gas-lubricated circular-disk grooved thrust bearing, which produces a gas film bearing pressure with shaft rotation in either direction, is proposed in this paper. A numerical analysis of the bearing characteristics with the narrow groove theory confirmed that the load capacity and stiffness of this bearing equal half those of the conventional bearing and that the damping coefficient equals twice that of the conventional bearing. Optimum bearing parameters which maximize the load capacity and the stiffness were also determined numerically and influence of the squeeze number was clarified.

Gas-lubricated microbearings for microactuators

This paper proposes the scaling-down of gas-lubricated bearings and their special application in microelectromechanical systems (MEMS). A gas bearing could eliminate the friction problem in microactuators and micromotors because its rubbing surfaces are completely separated by a film of gas. Two kinds of microbearings, the aerodynamic spiral-grooved type and an externally pressurized type, have been designed and fabricated by processes derived from IC fabrication processes. They have been used in micromotors with a rotor diameter of 160 μm and a hub diameter of 48 μm.

Statics of Gas-Lubricated Slider Bearings in Magnetic Recording Disk Files

This paper presents theoretical and experimental analyses of the static characteristics of gas-lubricated slider bearings. An implicit scheme, based on the Patankar-Spalding method, which is commonly utilized in the numerical heat transfer and fluid flow, is developed for the numerical solution of the Reynolds equation. Further investigations on the steady static minimum flying height and the pitch angle are presented by use of a transient response analysis. Theoretical results are experimentally verified to be correct and reliable. By comparing a grooved slider with a non-grooved one in the surface of bearing rails, it is concluded that the grooves in the surface of bearing rails may effectively improve statics of gas-lubricated slider bearings in magnetic disk storages.

Effects of Gas Inertia Forces on Dynamic Characteristics of Externally Pressurized Gas-Lubricated Thrust Bearings. 3rd Report. Inertia Effects on the Dynamic Performance of Externally Pressurized Gas-Lubricated Circular Thrust Bearings with a Capillary Restrictor.

In this report, the authors investigated theoretically and experimentally the inertia effects on the dynamic performance of externally pressurized gas-lubricated circular thrust bearings with a capillary restrictor in a turbulent regime. From the experiment, it is concluded that the effects of the inertia forces are considerable when the diameters of the capillary and the bearing clearance are large, and that the presented analysis yields good predictions of both the bearing stiffness and the damping coefficient.