Gas Journal Bearings Research Articles

Generalized maxwell velocity slip boundary model

For the gas flow of micro gas bearings in the near continuum and slip flow region where the squeezing velocity exists,a generalized Maxwell velocity slip boundary model is derived in detail using the velocity distribution function from the Grad thirteen moment approximation based on the conservation of momentum and energy fluxes in the Knudsen layer.The research shows that the generalized Maxwell velocity slip boundary model is consistent with the typical Maxwell velocity slip model when the temperature gradient along the surface and the squeezing velocity of gas flow are neglected.By applying the model in the control equation for micro gas journal bearings,the mathematical model for the gas-solid surface slip velocity boundary in the micro gas journal bearings has been obtained.

Real-Gas Effects in Foil Thrust Bearings Operating in the Turbulent Regime

In this study, an elastohydrodynamic model was created for predicting the pressure field in a compliant thrust bearing assembly lubricated by high pressure CO2. This application is of significance due to ongoing research into the closed-cycle supercritical CO2 turbine as a high-efficiency alternative to steam turbines. Hardware development for this concept has been led by Sandia National Laboratories, where turbomachinery running on gas foil thrust and journal bearings is being tested. The model accounts for the fluid velocity field, hydrodynamic pressure, and frictional losses within the lubrication layer by evaluating the turbulent Reynolds equation coupled with an equation for structural deformation in the bearings, and the fluid properties database RefProp v9.0. The results of numerical simulations have been compared with empirical correlations, with reasonable agreement attained. Of particular interest is the contrast drawn between the performance of high pressure CO2 as a lubricant, and ambient pressure air. Parametric studies covering a range of fluid conditions, operating speeds, and thrust loads were carried out to illustrate the value of this model as a tool for improved understanding and further development of this nascent technology.

Non-linear dynamic analysis of the ultra-short micro gas journal bearing-rotor systems considering viscous friction effects

Due to the micro-fabrication limitations and the low thickness of the silicon wafer, the length-to-diameter ratio (L/D) of the gas journal bearings in Power MEMS is about one order lower than that of the conventional bearings, which suggests that the viscous friction force in the micro-bearing is comparable to the load capacity. The effects of viscous friction force on non-linear dynamic characteristics of the ultra-short micro-bearing-rotor system are studied in this paper. The molecular gas-film lubrication model, which valid for arbitrary Knudsen numbers, is systematically coupled with the rotor kinetic equations and solved simultaneously to investigate the non-linear dynamic behavior of the system. The center orbits, phase portraits, Poincare maps, and FFT spectra of the system response at different L/D ratio, rotor mass, and bearing number, and the corresponding bifurcation diagrams for cases of ignoring and considering viscous friction force are inspected and compared. The results indicate that, if the viscous friction force is not taken into account in the case of low L/D ratio, the low-frequency large-amplitude self-excited whirl motion will be predicted as the increase of the rotor mass and the bearing number. However, when the viscous friction force is included in the non-linear dynamic model, the rotor motion becomes more stable under the same conditions, as the synchronous motion with smaller amplitude prevails.

824 大負荷回転軸用の自成絞り非対称給気式静圧ジャーナル気体軸受の特性(GS-10 振動(1))

824 大負荷回転軸用の自成絞り非対称給気式静圧ジャーナル気体軸受の特性(GS-10 振動(1))

C29 大負荷回転軸用の自成絞り非対称給気静圧ジャーナル軸受の特性(M-OS5-2 フルードパワーの基礎,M-OS5 フルードパワーの基礎と応用,「海を越え,国を越え,世代を超えて!」)

Rotating machineries have problems at bearings to support a rotor such as seismic ACROSS (Accurately Controlled Routinely Operated Signal System) transmitters. The rotor is supported by rolling contact bearings. The bearings in the transmitters, large heat generation occur caused by the high friction loss. In order to solve this problem, externally pressurized gas journal bearings with asymmetrically arranged inherent orifices has been developed for large load rotors. Numerical calculation of this bearing was carried out to obtain the characteristics using Divergence Formulation Method. Three types of bearing models have different placement of feed holes, respectively, i.e., Type A is the conventional symmetric type, which has eight feed holes in the bearing surface with equal distance. Type B is the proposed asymmetrical type, which has six feed holes at loading side of bearing surface and two feed holes at that of counter-loading side. Type C is also the proposed asymmetrical type, which has seven feed holes and one feed hole. The results showed that the proposed asymmetrical bearings have large load capacity and small flow rate compared with the conventional symmetric bearing.

Numerical analysis on the static performance of tilting pad–journal gas bearing in subsystems

For tilting pad–journal bearing, each pad and the journal form a subsystem with its own local parameters reflecting the relative position of the journal and pad. In this paper, tilting pad–journal gas bearing has been studied numerically in perspective of subsystems to prevent pad spragging. The effect of eccentricity, preload and gas compressibility on local parameters have been studied in this fluid–solid coupled problem. Finite element method is adopted to solve the compressible Reynolds equation, and the load between pads configuration is chosen as a specific example.

Experimental Study on Journal Gas Bearing with Axial Slot for a Miniature Air Turboexpander

A new type of hydrostatic journal gas bearing with axial slot of tangential gas entry for miniature air turboexpander is firstly developed in this paper. This bearing configuration is presented and constructed to fit manufacture simplicity. The experimental investigations are carried out to reveal the relationship between bearing parameters and instability threshold speed. It is feasible to increase the stability of hydrostatic journal gas bearing by adopting this kind of configuration with axial slot of tangential gas entry. Some valuable tested results are obtained to reveal the optimum slot height and radial clearance for this miniature air turboexpander.

Numerical Solution to Reynolds Equation for Micro Gas Journal Bearings

Reynolds equation for gas bearings is a nonlinear partial differential one and its analytical solution usually is difficult to obtain. Therefore numerical method is an effective means to investigate the performance of gas-lubricated journal bearings. In this paper, firstly the modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The finite difference method (FDM) is employed to solve the modified Reynolds equation to obtain the pressure distribution for micro gas journal bearings under different reference Knudsen numbers. Numerical analysis shows that the pressure profiles for micro gas journal bearings decrease obviously with the reference Knudsen number increasing.

Asymmetric Supply Type Hydrostatic Journal Gas Bearings to Support Large Load Rotors

Asymmetric Supply Type Hydrostatic Journal Gas Bearings to Support Large Load Rotors

Performance Research on the Externally Pressurized Gas Journal Bearing under Different Working Gas Based on Finite Difference Method

Performance Research on the Externally Pressurized Gas Journal Bearing under Different Working Gas Based on Finite Difference Method

Active lubrication applied to radial gas journal bearings. Part 1: Modeling

Active bearings represent a mechatronic answer to the growing industrial need to high performance turbomachinery. The present contribution aims at demonstrate the feasibility of applying active lubrication to gas journal bearings. The principle of operation is to generate active forces by regulating radial injection of lubricant through the means of piezoelectric actuators mounted on the back of the bearing sleeves. A feedback law is used to couple the dynamic of a simplified rotor-bearing system with the pneumatic and dynamic characteristics of a piezoelectric actuated valve system. Selected examples show the considerable performance advantages of such new kind of bearing.

Application of a hybrid method to the bifurcation analysis of a relative short gas journal bearing system with herringbone grooves

Purpose – This paper employs a hybrid numerical method combining the differential transformation method (DTM) and the finite difference method (FDM) to study the bifurcation and nonlinear behavior of a rigid rotor supported by a relative short gas lubricated journal bearing system with herringbone grooves. The analysis reveals a complex dynamic behavior comprising periodic, subharmonic and quasi‐periodic responses of the rotor center. The dynamic behavior of the bearing system varies with changes in the rotor mass and bearing number. The current analytical results are found to be in good agreement with those of other numerical methods. This paper discusses these issues.Design/methodology/approach – In this paper, DT is used to deal Reynolds equation and is also one of the most widely used techniques for solving differential equations due to its rapid convergence rate and minimal calculation error. A further advantage of this method over the integral transformation approach is its ability to solve nonlinea...

On the modelling of hybrid aerostatic-gas journal bearings

Gas journal bearings have been increasingly adopted in modern turbo-machinery applications as they meet the demands of operation at high rotational speeds, in clean environment, and with great efficiency. Due to the fact that gaseous lubricants, typically air, have much lower viscosity than more conventional oils, carrying capacity and dynamic characteristics of passive systems are generally poorer. In order to enhance these characteristics, one solution is used to combine the aerodynamic effect with the addition of external pressurization. This study presents a detailed mathematical model for hybrid lubrication of a compressible fluid-film journal bearing. Additional forces are generated by injecting pressurized air into the bearing gap through orifices located on the bearing walls. A modified form of the compressible Reynolds equation for active lubrication is derived. By solving this equation, stiffness and damping coefficients can be determined. A multibody dynamics model of a global system comprised of rotor and hybrid journal bearing is built in order to study the lateral dynamics of the system. Campbell diagrams and stability maps are presented, showing the main advantages and drawbacks of this special kind of hybrid fluid-film bearing.

Study on the Performance of Gas Journal Bearings for Power MEMS

Gas journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in Power MEMS deriving from the extremely shallow structures. With the reference Knudsen number being included, the modified Reynolds equation for gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The boundary condition for modified Reynolds equation is given. The numerical method is employed to solve the modified Reynolds equation to obtain the pressure profiles, load capacities and attitude angles of gas journal bearings for Power MEMS under different reference Knudsen numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with the reference Knudsen number increasing, and the attitude angle changes conversely. Moreover, when the eccentricity ratio is smaller, the effect of gas rarefaction on the attitude angle is less.

Static, Dynamic, and Thermal Properties of Compressible Fluid Film Journal Bearings

Modern turbo-machinery applications, high-speed machine tools, and laboratory equipment require ever-growing rotational speeds and high degree of precision and reliability. Gas journal bearings are often employed because they meet the demands of high-speed performance, in a clean environment, and work great efficiency. A great deal of literature has concentrated on the analysis and prediction of the static and dynamic performance of gas bearings, assuming isothermal conditions. The present contribution presents a detailed mathematical modeling for nonisothermal lubrication of a compressible fluid film journal bearing, in order to identify when this type of analysis should be of concern. Load capacity, stiffness, and damping coefficients are determined by the solution of the standard Reynolds equation coupled to the energy equation. Numerical investigations show how bearing geometry, rotational speed and load influence the bearing performance. Comparisons between isothermal and thermohydrodynamic models and discrepancies are quantified for three different types of bearing geometries.

Split-Type Herringbone-Grooved Hydrodynamic Journal Gas Bearings for Small Ultra-High-Speed Rotary Machines

A split-type herringbone-grooved journal gas bearing has been developed to support the high-frequency rotations of a practical rotor for a micro machine such as a palmtop gas turbine generator currently in development. For this particular application, the critical mass of the rotor and the operable clearance of the journal and thrust bearings are designed to rotate at over 14 kHz ( 840,000 rpm ). The test journal bearing and rotor have a radial clearance of 0.008 mm and a mass of 0.0042 kg. The roundnesses of the test journal bearing under the processed and reassembled conditions were measured using a 3-D coordinate measuring machine and compared to verify the repeatability of the bearing assembly; the difference in the measured roundness between each condition was about 0.003 mm, which includes axial assembly error. A rotational test of the rotor supported by the bearings was performed on a test rig. In this bearing, the maximum rotational frequency of the rotor reached 13.4 kHz ( 804,000 rpm ). Therefore, the operational stability of the system was verified.

Nonlinear dynamic analysis of a relatively short spherical gas journal bearing system

This paper studies the nonlinear dynamic behavior and bifurcation of a rigid rotor supported by two relatively short spherical gas journal bearings. The modified Reynolds equation is solved by a hybrid numerical method combining the differential transformation method (DTM) and the finite difference method (FDM). The analytical results reveal a complex dynamic behavior comprising periodic, subharmonic and quasi-periodic responses as the rotor mass and bearing number are increased. The results obtained using the hybrid DTM&FDM scheme are found to be in good agreement with those of a hybrid scheme comprising the successive over relaxation (SOR) method and the FDM scheme. Therefore, the DTM&FDM method provides an effective means of gaining insights into the nonlinear dynamics of relatively short spherical gas rotor-bearing systems.

Nonlinear Dynamic Behaviors and Bifurcation of Symmetrical Rotor System Supported by Self-Acting Gas Jounal Bearings

The unbalanced response and corresponding bifurcation behavior of the rotor dynamic system supported by gas journal bearings are investigated. A time-dependent mathematical model is used to describe the pressure distribution of gas journal bearing with nonlinearity. The rigid Jeffcott rotor with self-acting gas journal bearing supports is modeled. The finite difference method and the Successive Over Relaxation (S.O.R.) method are employed to solve the time-dependent Reynolds equation of gas journal bearings. The bifurcation of unbalanced responses of the rotor is analyzed by a Poincaré map. The numerical results reveal periodic, period-doubling, quasi-periodic, and chaotic motion of rich and complex non-linear behaviors of the system.

Effects of rarefaction on the characteristics of micro gas journal bearings

Given the definition of the reference Knudsen number for micro gas journal bearings, the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first-order slip boundary condition is proposed that takes into account the gas rarefaction effect. The finite difference method (FDM) is adopted to solve the modified Reynolds equation to obtain the pressure profiles, load capacities and attitude angles for micro gas journal bearings at different reference Knudsen numbers, bearing numbers and journal eccentricity ratios. Numerical analysis shows that pressure profiles and non-dimensional load capacities decrease markedly as gas rarefaction increases. Attitude angles change conversely, and when the eccentricity ratio is less than 0.6, the attitude angles rise slightly and the influence of the reference Knudsen number is not marked. In addition, the effect of gas rarefaction on the non-dimensional load capacity and attitude angle decreases with smaller bearing numbers.

G1100-1-6 小型回転機械用超高速分割型溝付き動圧ジャーナル気体軸受の回転特性([G1100-1]機素潤滑設計部門一般講演(1))

G1100-1-6 小型回転機械用超高速分割型溝付き動圧ジャーナル気体軸受の回転特性([G1100-1]機素潤滑設計部門一般講演(1))