Gas Journal Bearings Research Articles

High-speed tilting-pad gas journal bearing flow field analysis

Tilting-pad gas journal bearing are widely used in the field of high-speed turbine machinery, especially in the special environment of low temperature. However, the performance is limited by structure, so a clear understanding of the field is particularly important. In this paper, finite volume method is used to simulate the three-dimensional flow field of high-speed tilting-pad gas bearing, then the effects of shaft speed, eccentricity and gas film thickness on the bearing capacity are studied. The simulation results show that the two factors of shaft speed and gas film clearance play a decisive role in producing sufficient bearing capacity of tilting tile radial gas bearings compared with other factors.

Numerical Analysis on the Static Performance of Gas Journal Bearing by Using Finite Element Method

In this paper, finite element method is used to calculate the static performance of gas journal bearing, in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed. The results indicate that the average gas film thicknesses corresponding to the maximum load capacity and stiffness, and the minimum attitude angle increase with the growth of orifice diameter. Load capacity and stiffness significantly improved with the increase of rotation speed, eccentricity ratio and supply pressure when the bearing has thin average gas film thickness. Attitude angle increases with the growth of rotation speed, while the growth rate slows down or even decreases at high speed. The most effective way of reducing attitude angle is to increase supply pressure. It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices, while other parameters have the same effect by changing gas pressure at orifice outlet.

Study on the solution algorithm of Reynolds equation of self‐acting gas journal bearings based on a finite difference method

AbstractIt is very crucial to solve the Reynolds equation quickly and accurately using the numerical methods in the research field of fluid lubrication. For the static Reynolds equation of self‐acting gas journal bearings, the typical solution algorithm of the finite difference method is put forward and a new solution algorithm of the finite difference method is proposed. Secondly, the Reynolds equation is solved numerically with the same parameters and the pressure distribution of gas bearings is obtained. Finally, the numerical solution from the new solution algorithm can be obtained with less number of iterations and the less computing time under the different computational grids and bearing numbers. Therefore, the new solution algorithm of the finite difference method is superior to the typical solution algorithm of the finite difference method.

Investigations on bearing performances of metal rubber-bump foil gas journal bearing with three structure pads integrating stiffness and damping

Foil-type gas journal bearing has low load-carrying capacity and poor operational stability. Metal rubber-bump foil gas journal bearing with three structure pads (MR-BFGJBTSPs) are proposed to achieve satisfactory bearing characteristics. The equivalent stiffness model of metal rubber damping element is developed, considering the contact states of metal wires: separation state, sliding contact state, viscous contact state. The stiffness prediction model is presented based on the modified LuGre model, integrating the friction coefficients. The static and dynamic bearing performances of MR-BFGJBTSPs are analyzed, integrating the stiffness and damping of hybrid elastic support structure. Results show that the predicted structure stiffness Kc compares best to limited test data. The load-carrying capacity of MR-BFGJBTSPs increases when the friction coefficients μtb, μbh increase.

Fractional-order model and nonlinear vibration analyses of hybrid gas journal bearing–rotor system

It is important to propose a reasonable nonlinear dynamic model of gas dynamic bearing–rotor system for the stable operation of turbocharger. This paper presents a hybrid gas journal bearing (HGJBs)–rotor system with flexible supporting structure. A fractional-order dynamic model of the symmetrical flexible HGJB–rotor system is established. A tracking–alarming method is proposed to obtain the rotational speed ratio at the bifurcation point. The stable and unstable regions of the rotational speed ratio Ωω for both the rigid bearing–rotor system and flexible HGJB–rotor system are analyzed. The nonlinear dynamic behaviors of HGJB–rotor system versus the fractional order αd and rotational speed ratio Ωω are studied. Results show the fractional-order dynamic model can realize the reasonable prediction of nonlinear dynamic behaviors. An increase in the rotational speed ratio Ωω and the decrease of fractional order αd result in a growth of the vibration amplitude. The adoption of flexible supporting structure is a good strategy to increase the size of stable region.

Performance Analysis of Externally Pressurized Gas Journal Bearing Lubricated with Vapor of R134a in Centrifugal Compressor

The performance of an externally pressurized gas journal bearing lubricated with R134a vapor used in an oil-free refrigeration centrifugal compressor is calculated by solving Reynold equations with the finite difference method (CFD). The load capacity, stiffness and mass flow rate of refrigerant vapor under conditions of various operational parameters are obtained and compared with that in air gas bearings. In addition, the influences of the average clearance, eccentricity ratios and supply vapor pressure on the static characteristics of journal bearings are investigated and discussed in detail. It concluded that the optimal operation parameters of gas journal bearings lubricated with R134a vapor are different with air journal bearings. These factors should be considered in the design process of R134a refrigerant vapor gas journal bearings.

Influence of slip effect on viscous dissipation heat and lubrication characteristics of Gas Journal Bearing: A multiscale analysis

As operating under quite high bearing speed with quite narrow clearance, the slip effect generally inevitable exists and closely relates to the performance of Gas Journal Bearing (GJB). However, singly the conventional macroscopic method may not be capable of fully exploring the influence of slip effect and seize tiny details such as slip velocity and flow vortex. In this article, both the Lattice Boltzmann Method (LBM) and the Reynolds equation method are applied to analyze the distributions of lubricant viscous dissipation heat, velocity, slip velocity, pressure, journal position and film thickness versus different operating parameters at multiscale. It shows that the slip effect weakens the squeezing function on lubricant film, reduces the viscous dissipation heat peaks, consumes the maximum pressure peaks, and decreases the bearing capacity, which is more obvious at larger Knudsen number. At higher bearing speed, the high viscous dissipation heat and pressure zone rapidly magnifies, in contrast, under larger bearing load, the high viscous dissipation heat zone concentrates.

Unbalance Response Analysis of a Spindle Supported on Gas Bearings: A Comparison between Different Approaches

Gas journal bearings are widely employed in high-speed spindles for the micromachining industry. Compared to their oil and rolling counterparts, gas bearings have a longer life span, lower friction and a lower level of noise. In order to design accurate high-speed spindles supported by externally pressurized gas bearings, it is vital to analyze the characteristics of rotor bearing systems. In this paper, we present an analysis of the unbalance response of a high-speed spindle supported by gas journal bearings. A number of aspects to enhance the accuracy of the system are discussed. We performed the analysis by considering a nonlinear and a linearized numerical model validated through experimental measurements.

Experimental and numerical investigation of the unbalance behavior of rigid rotors supported by spiral-grooved gas journal bearings

The forced response of rigid rotors, supported by herringbone-grooved gas journal bearings are investigated numerically and experimentally. The rotor configurations are varied by using end cylinders, attached at both sides of the shaft. Three rotors with different center of mass positions relative to the bearing locations are investigated for a variation of unbalance conditions. The numerical predictions by a quasi-linear unbalance approach and a full transient analysis are compared with experimentally obtained data. Different unbalance configurations are tested for validating the numerical models at orbital motions larger than 50% of the clearance and for bearing compressibility numbers of up to Λ=42. The investigation shows a maximum difference of 19.5% between nominal model predictions and experimental data at maximum orbital motions. The influence of the center of mass position on the rotor motion is proven to be significant and agrees with the numerical predictions. Further, the test unit is operated at different tilt angles, allowing to investigate the influence of static loading due to gravitational force on the forced response. It is found, that under different static loading, the rotor orbital motion remains unaltered and its influence can be neglected in the unbalance analysis.

Effect of texture geometry on the performance of noncircular aerodynamic journal bearings

Today, considerable uses of aerodynamic journal bearings have attracted the attention of many researchers in the field of tribology. Therefore, the theoretical and experimental analysis of their performance has been the subject of many researches. Growing application of the gas journal bearings is due to their capability in various engineering fields such as instrumentation and high-speed machines like spindles, small-scale turbomachines, and precision gyroscopes, dental milling machines, and many other rotor-bearing systems. Upgrading the performance of gas bearings by changing their geometry or using new compressible lubricants has always been one of the suggestions proposed by the tribology researchers. Recently, the development of new technologies such as laser milling and lithography increased the possibility of creating textured surfaces as a way to improve the performance of journal bearings. So, in this study, the effects of texture geometry on the steady-state performance of two-lobe noncircular aerodynamic journal bearings are presented. For this purpose, the governing Reynolds equation of hydrodynamic gas lubrication is analyzed by finite element method according to the changes of the lubricant film thickness in presence of the cubical, cylindrical, and ellipsoidal surface textures. Results show that the creation of textures on the lower lobe compared to the upper lobe or the whole surface is more effective on the performance of two-lobe aerodynamic bearings. Also, increasing both the dimple depth and the amount of bearings noncircularity, especially at shallow texture depth, cause more significant changes in the lubricant film pressure distribution and the bearing performance parameters such as load-carrying capacity, attitude angle, and frictional power loss. Further, it is obvious that the creation of cubical, cylindrical and ellipsoidal textures especially at shallow depth with an increase in the noncircularity of bearings’ geometry have a higher impact on the steady-state performance of the studied rotor-bearing system, respectively.

Chaotic Analysis and Machine Learning Diagnosis of Herringbone-grooved Journal Gas Bearing System

Chaotic Analysis and Machine Learning Diagnosis of Herringbone-grooved Journal Gas Bearing System

Experimental and theoretical investigation on rotodynamic characterization of hybrid porous tilting pad bearings

Porous journal gas bearings, which offer advantages of high load capacity and good stiffness compared to other types of hydrostatic gas bearings, will meet instability issues at high rotational speeds. Hybrid porous tilting pad bearings (HPTPBs) provide a possibility as a rotor supported in high-speed Turbomachinery. This study presents an experimental investigation of the dynamic responses of a rigid rotor supported with two HPTPBs. The rotor was successfully accelerated to 40 krpm. The supply pressure ratio of each pad is monitored separately, and the influence of the separate gas supply on the dynamic response is analyzed. Rotor dynamic tests with different unbalance mass and different supply pressure ratios were carried out. A mathematical model with the consideration of airflows in the porous materials and bearing clearance, pad motion, rotor motion, unbalance force were presented. Prediction results are accorded well with the test results.

Numerical analysis on the performance characteristics of a new gas journal bearing by using finite difference method

This paper proposes a novel gas journal bearing in which orifices are different in diameter and distribute unevenly. Finite Difference Method (FDM) combined with Linear Perturbation Method (LPM) is used to solve the unsteady-state Reynolds equation of the flow field in the bearing clearance. Moreover, four types of bearing structures are used to discuss the effects of orifices different in diameter and uneven distribution on the bearing performance. The results demonstrate that the new bearing has better static and dynamic performances compared with those of traditional bearing in which orifices are equal in diameter and distribute evenly. Moreover, thin gas film thickness, high supply pressure, and large eccentricity ratio are hopeful for improving load capacity of the new bearing. Furthermore, the stability of the novel bearing is improved if eccentricity ratio is 0.25–0.3.

Numerical Modeling and Experimental Validation of a Supercritical CO2-Lubricated Hydrodynamic Journal Bearing

Abstract The supercritical carbon dioxide (sCO2) Brayton cycle is an attractive thermal cycle for compact power generation applications due to its high efficiency and power density. Hydrodynamic gas journal bearings are attractive for this application due to their simplicity. Lubricating the bearings with sCO2 from the primary loop would be ideal, as this would eliminate the need for a separate lubricant source or complex seals and pumps to reduce the bearing lubricant pressure below the operating pressure of the primary loop. However, few studies in the literature have examined the behavior of a hydrodynamic journal bearing lubricated with supercritical fluid and none have experimentally demonstrated the operation of such a bearing. This paper describes the development of a simple numerical model of a hydrodynamic journal bearing operating under laminar conditions. The model incorporates the real gas properties of sCO2 and therefore can be used to qualitatively investigate the impact of operation near the critical point and the scaling relationships between inlet pressure and the bearing drag and stiffness. The model predictions are compared to results that would be obtained by assuming constant fluid properties in order to assess the effects on bearing performance of the large gradients in properties that occur near the critical point and to determine over what range of inlet conditions the constant-property simplification is valid. The modeling results show that bearing drag and stiffness rise linearly throughout the subcritical regime, but sharply rise by approximately 50% at the critical pressure. However, the behavior predicted by the real gas model closely matches those obtained from the constant-property model (CPM) for all conditions that are more than 3 kPa away from the critical pressure. To validate the prediction that bearing operation follows the same scaling relationships near the critical pressure as at low pressure, a test assembly consisting of a turbomachine driven by a motor and supported on tilt-pad hydrodynamic gas journal bearing was operated in a CO2 environment at 35 °C with pressures up to 7.336 MPa. The bearing operated smoothly and did not exhibit signs of instability such as whirl. Coast down measurements were conducted to estimate the bearing drag at various pressures up to 5.612 MPa. The bearing coefficient of friction, f, inferred from these tests increased with system pressure from 0.359 at atmospheric pressure to 0.619 at 5.612 MPa. The peak bearing Reynolds number during operation was approximately 400. These results indicate that hydrodynamic bearing operation using sCO2 is possible without significant reduction in bearing performance; however, further testing should be carried out in order to validate the model results concerning bearing stiffness.

Gas foil bearings with radial injection: Multi-domain stability analysis and unbalance response

Gas Foil Bearings (GFBs) possess significant potential for oil-free and environmentally friendly support of high-speed rotating machinery in a wide range of applications. Advances in GFB design and solid lubricants have significantly improved the capabilities of GFBs, but application in heavier machinery still leaves many technical limitations to be overcome. A possible path is through hybridization with radial gas injection as commonly applied in rigid gas journal bearings. From a modelling perspective, modifications of the well-documented Reynolds Equation have previously been proposed to include injection, but the mass flow itself is difficult to predict. In the literature, this is often described using idealized analytical expressions with carefully defined/calculated/identified correction factors. In the present work, a parameter-map approach is presented where the injection flow is interpolated from a five-dimensional pre-generated map of mass flows calculated using a CFD sub-model for the injector valve. This allows injection to be added into a fully coupled simultaneous GFB simulation framework. Non-controlled hybrid mode simulations are presented for a yet-to-be-built version of an existing industrial scale GFB test rig augmented with an existing injection system. The presented results comprise multi-domain mode shape visualizations, Campbell diagrams, and unbalance responses indicating significant improvements attainable already from the hybrid mode. The addition of actively controlled injection is thus considered feasible and may allow hybrid GFBs to support heavier rotors than permissible using the currently available passive variants.

Effects of new micro-pocketed bore surface topographies on the performance behaviours of aerodynamic journal bearing

This paper presents the exploration for improving the static and dynamic performance behaviours of a self-acting rigid gas journal bearing employing some new conceived micro-depth pocketed surface topographies at the bore. The conceived micro-pockets comprise of relatively large size rectangular pocket having micro-depth at bearing bore in the converging zone followed by placing of different designs of sub-pockets at the trailing edge of the previous one in the direction of journal rotation. The form of equation achieved from Patir and Cheng’s model for the case of hydrodynamic lubrication regime and the related dynamic pressure equations have been solved using the finite volume method discretisation scheme followed by the solution of the algebraic equations using the Gauss-Seidel iterative method. The minimum film thickness, frictional force, side leakage, bearing dynamic coefficients, effective stiffness, effective damping, and critical mass parameters have been investigated with each new bore surface topography and compared with the performances of conventional aerodynamic journal bearing. Substantial improvements in both static and dynamic performances have been found with the new micro-pocketed bore surface topographies as compared to conventional one. Moreover, the established best bore design has produced significant increase (21%) in minimum film thickness, substantial reduction (12%) in coefficient of friction, and excellent improvement (170%) in the stability parameter (critical mass) as compared to the conventional case.

Numerical and experimental investigation on the performance of hybrid porous gas journal bearings

AbstractAs the progress of the high‐speed performance requirement for porous gas journal bearings continuing, the aerodynamic effect, which plays a key role in the state of lubrication, causes the porous gas journal bearings being gradually to be used as hybrid bearings. This paper firstly presents a theoretical analysis on the lubrication mechanism of the hybrid bearings. The gas flow in the porous and clearance is modelled by using the mass continuity equation. Two experimental test rigs are designed to systematically test the static and dynamic characteristics of the hybrid bearings. The numerical results are corroborated by the experimental data. Results show that there is optimal clearance for hybrid bearings to obtain maximum load capacity. The load capacity of the hybrid bearings is increased by the aerodynamic effect to be higher than that of pure aerostatic bearings especially at higher rotational speed and larger eccentric ratio. However, due to the occurrence of the aerodynamic effect, the hybrid bearings show clear cross‐coupling dynamic coefficients, which may lead to bearing instability. It is interesting to note that the direct dynamic stiffness and damping coefficients are both influenced by the aerodynamic and aerostatic effects. Higher rotational speed and external supply pressure will result in higher direct dynamic coefficients.

Prediction of the reaction forces of spiral-groove gas journal bearings by artificial neural network regression models

This paper presents neural network regression models for predicting the nonlinear static and linearized dynamic reaction forces of spiral grooved gas journal bearings. The partial differential equations (PDEs) are sampled, based on a full factorial and randomly spaced parameter set. Feed-forward neural network (FNN) architectures are developed for modeling the PDEs and therefore replacing the time-consuming discrete and iterative solution procedure used to this date. A significant speed-up factor of >103 in computation time is achieved, compared to solving the PDE numerically. Furthermore, the FNN allows for multi-dimensional interpolation, which makes global system optimization easily possible. This is demonstrated by a real-case rotordynamic system optimization. By using the neural network meta-models, a complete rotordynamic system optimization time reduction of factor 300 is achieved.

Nonlinear transient analysis of rigid rotor mounted on externally pressurized double-layered porous gas journal bearings accounting velocity slip

The present work aims at estimating the journal center trajectories of a rigid rotor mounted on a hybrid, finite gas lubricated journal bearings with double-layered porous bushing using nonlinear transient analysis. To consider velocity slip in the film at the interface between film and porous region, Reynolds equation is modified using the Beavers–Joseph boundary condition. The governing equations of flow at clearance, porous regions are discretized using finite volume method. The variable values at cell-face centers are obtained using interpolation scheme of third order. Those discretized equations coupled with equations of rigid rotor motion are solved by third-order total variation diminishing Runge–Kutta scheme. Influence of velocity slip and design parameters on critical mass parameter values were explored. The observations are presented in the form of graphs that serves as a reference during the design of such bearings.

Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

The nonlinear behavior of a rigid rotor supported by herringbone grooved journal gas bearings (HGJBs) was investigated in this study. The two-dimensional narrow groove theory (2D-NGT) was adopted to model the HGJBs. A set of integrated rotor-bearing state equations were built by coupling the rotor motion equations and the bearing Reynolds equation. An implicit integrator with adaptive time step method was used to solve those state equations continuously. Two low-stability HGJBs were implemented to experimentally demonstrate and analyze the appearance of self-excitation motions. The theoretical model was successfully validated by the experimental data on predicting the onset speed of the sub-synchronous vibration of the HGJB-rotor system and the whirl frequency ratio. The predicted limit cycle amplitude increases as the speed increases until the rotor contacts with the bearing surface, which leads to a bearing failure. Forward conical mode dominates the self-excited motion during the whole speed range of self-excited motion. The prediction shows that the HGJB-rotor system can still operate in a stable, even though the rotor is installed vertically, i.e., without static load on the bearings. This is a distinct advantage in comparison to plain bearings. As the static load applies on the bearings increases, the onset speed of sub-synchronous vibration increases as well. For the investigated rotor-bearing system, an increase of the onset speed of sub-synchronous vibration from 36 krpm to 75 krpm is predicted as the static load increases from 0 to 4 times of the rotor weight. This indicates an increased HGJB stability with increased static load. The rotor orbits show complex shapes when the imbalance excitation is considered in the simulation. Both synchronous frequency and whirl frequency are shown in the spectral analysis. Moreover, the speed range of self-excited motion reduces from [38,48] krpm to [40,42] krpm as the imbalance increases from 0 to 40 mgmm.