Gas-lubricated Bearings Research Articles

The Role of the Working Fluid and Non-Ideal Thermodynamic Effects on Performance of Gas Lubricated Bearings

Abstract Small-scale turbomachinery operating at high rotational speed is a key technology for increasing the power density of energy and propulsion systems. A notable example is the turbine of an organic Rankine cycle turbogenerator for thermal recuperation from prime engines and industrial processes. Such systems typically operate with organic compounds characterized by complex molecular structures, to allow the design of efficient fluid machinery and flexibility in matching the heat source and sink temperature profiles. Gas bearings are considered advantageous compared to traditional oil-lubricated rolling element bearings for supporting the turbine rotor, enabling greater machine compactness and reduced complexity, and to avoid contamination of the working fluid. In certain operating conditions, however, the lubricant of the bearing is in thermodynamic states near the saturated vapor line or in the vicinity of the fluid critical point whereby non-ideal effects are relevant and may affect bearing performance. This work investigates the physics of thin film flows in gas bearings operating with fluids made by complex molecules. The influence of non-ideal thermodynamic effects on gas bearing performance is discussed by analysis of the fluid bulk modulus. Reduced values of the non-dimensional bulk modulus near the critical point or saturated vapor line decrease bearing performance. The main parameter characterizing the influence of molecular complexity on bearing performance is shown to be the acentric factor. For complex fluids with large acentric factors, the impact of non-ideal thermodynamic effects on non-dimensional bearing load capacity and rotor-dynamic characteristics is less pronounced.

Fabrication and tribological properties of WC-reinforced Inconel X-750 alloy at elevated temperature

The nickel-based superalloy Inconel X-750, valued for its exceptional mechanical properties, is used in gas-lubricated foil bearings. However, prolonged exposure to high temperatures can lead to wear failure, affecting their service life. Here, we propose a novel method named ultrasonic strengthening grinding (USG) that applies a WC coating on Inconel X-750. Friction tests reveal that at 600 °C, the friction coefficient and wear rate of the USG-treated samples were reduced by 30.2 % and 79.7 %, respectively. Detailed experiments and analysis demonstrate that the surface grain refinement and the WC-rich coating cooperate to improve the high-temperature tribological properties. These findings offer new insights into the design of wear-resistant coatings for enhancing the high-temperature tribological performance of Inconel X-750 Alloy.

Theoretical and Experimental Study on the Performance of Hermetic Diaphragm Squeeze Film Dampers for Gas-Lubricated Bearings

Low damping characteristics have always been a key sticking points in the development of gas bearings. The application of squeeze film dampers can significantly improve the damping performance of gas lubricated bearings. This paper proposed a novel hermetic diaphragm squeeze film damper (HDSFD) for oil-free turbomachinery supported by gas lubricated bearings. Several types of HDSFDs with symmetrical structure were proposed for good damping performance. By considering the compressibility of the damper fluid, based on hydraulic fluid mechanics theory, a dynamic model of HDSFDs under medium is proposed, which successfully reflects the frequency dependence of force coefficients. Based on the dynamic model, the effects of damper fluid viscosity, bulk modulus of damper fluid, thickness of damper fluid film and plunger thickness on the dynamic stiffness and damping of HDSFDs were analyzed. An experimental test rig was assembled and series of experimental studies on HDSFDs were conducted. The damper fluid transverse flow is added to the existing HDSFD concept, which aims to make the dynamic force coefficients independent of frequency. Although the force coefficient is still frequency dependent, the damping coefficient at high frequency excitation with damper fluid supply twice as that without damper fluid supply. The results serve as a benchmark for the calibration of analytical tools under development.

Study of the Static Characteristics of Gas-Lubricated Thrust Bearings Using Analytical and Finite Element Methods

A study was conducted to develop a porous aerostatic rectangular thrust bearing model, with the aim of assessing how different operational conditions and geometric factors influence its static capabilities. Initially, the Reynolds equation was analytically solved. Subsequently, simulations were performed on the rectangular air bearing model. Analyzing the impact of throttle hole configurations, air film thickness, orifice size, and supply pressure revealed their significant effect on the bearing’s load capacity, air consumption, peak airflow speed in the air film gap, and rigidity. Experimental validations were further conducted on manufactured bearings, corroborating the theoretical findings. It was observed that extending the length of the rectangular throttle hole array progressively increases gas consumption and diminishes stability, while the load capacity and stiffness initially surge then taper off. A thinner air film enhances load capacity and reduces gas flow, contributing to increased stability. Conversely, enlarging the orifice diameter boosts both load capacity and stability but escalates mass flow and diminishes stiffness. Elevating gas supply pressure enhances load capacity, flow rate, and stiffness, albeit at the cost of reduced stability. A comparative analysis among experimental data, finite element analysis, and analytical solutions showed strong congruence, affirming the precision of the latter two methods for predicting the bearing’s performance. This investigation aids with refining bearing design for precision devices and offers insights to enhance bearing efficiency and lifespan and to reduce friction and wear. Given its lower computational demands, the analytical approach provides a rapid means to assess static characteristics, underscoring its utility alongside finite element techniques for optimizing aerostatic bearing parameters.

Influence of Geometrical Shape on the Lubrication Performance of Partially Micro-Grooved Gas-Lubricated Parallel Slider Bearings

The influence of grooving parameters and micro-groove cross-section shape on the lubrication performance of partially micro-grooved gas-lubricated parallel slider bearings is investigated in the present study. The solution procedure for the multi-grid finite element method is that the algebraic equations formed by the finite element method are in turn smoothed by the interpolation from the coarse grid to the fine grid and the restriction from the fine grid to the coarse grid. By adopting the multi-grid finite element method, the pressure distribution of partially micro-grooved gas-lubricated parallel slider bearings is obtained. The grooving parameters are optimized to obtain the maximum average pressure for different micro-groove cross-section shapes. The results show that the orientation angle of the micro-grooves, depth of the micro-grooves, width of the micro-grooves, area density of the micro-grooves, micro-grooved fraction, and cross-section shape of the micro-grooves have an important influence on the hydrodynamic pressure of partially micro-grooved gas-lubricated parallel slider bearings. The results of this study demonstrate that the lubrication performance of partially micro-grooved gas-lubricated parallel slider bearings can be obviously enhanced by adopting the appropriate grooving parameters and micro-groove cross-shape. The results of this study is beneficial for the design of partially micro-grooved gas-lubricated parallel slider bearings.

Parametric Studies on Performance of Oil-Free Thrust Foil Bearings at Lower Speeds

The present work involves an experimental analysis on gas-lubricated foil thrust bearing (FTB) that has major applications in food processing units at lower operating speeds. Parametric studies include testing thrust foil bearings with various foil configurations in terms of foil thickness, foil geometry, and foil material. Novel bearing testing apparatus designed and fabricated for the purpose supported a larger diameter (224 mm) thrust foil bearing, operated at speeds ranging from 10,000 rpm to 18,000 rpm. Performance of air foil thrust bearing (AFTB) concerning static structural stiffness and load bearing capability was determined in optimizing the best foil configuration. A novel dimensionless number was formulated that emphasizes the affecting factors of thrust foil bearing with respect to axial loads.

Fluid-structure coupling model and output characteristics of a diaphragm-type restrictor

The film stiffness of gas-lubricated hydrostatic bearings and seals are considered to be enhanced remarkably by proper design of a diaphragm-type restrictor. A fluid-structure coupling numerical model by coupling iteration of small deflection bending differential equation of circular thin plate and one-dimensional Reynolds equation was established, and the influence of different parameters, including pressure and geometrical parameters, on the flow output characteristics of a diaphragm-type restrictor was investigated numerically and experimentally. The results show that the correctness of established fluid-structure coupling numerical model is verified well by comparing calculated values of diaphragm deformation and output flow characteristics to the measured values. The optimum values of diaphragm thickness is 0.6–0.8 mm and initial throttle clearance is 20–35 μm for stable operation of diaphragm-type restrictor, while the optimum value of back pressure strongly depends on the diaphragm thickness.

Dynamic behavior of self-acting gas-lubricated long journal bearing

Planar dynamics of a rotor supported by self-acting gas-lubricated journal bearing is investigated theoretically. Whirling of the shaft is one of the common problems in a gas-lubricated journal bearing system. As whirling increases, it becomes large enough to cause a destructive contact between the bearing surfaces. It is essential to predict the parameter range for the safe operation of the gas-lubricated journal bearing systems. An analytical model of the long, self-acting gas-lubricated journal bearing system is numerically integrated for analysis of steady-state solutions and limit cycle oscillations. Dynamic behavior of the system is analyzed with the variation of dimensionless bearing compressibility parameter Λ and dimensionless bearing stability parameter Λ2Ω. For a set of stability parameters Λ2Ω ranging from 0.01 to 1000, the critical value of Λ is determined which corresponds to angular speed ω of the rotor. With the decrease of parameter Λ2Ω, critical value Λ decreases. Limit cycles bifurcating from the equilibrium point at critical values are unstable for a low value of Λ2Ω=0.01 and stable for other higher values. In both the cases of stable and unstable limit cycles, limit cycles disappear beyond a compressibility parameter Λ and no further fold bifurcation of the limit cycle is detected. Results are presented as equilibrium point bifurcation and bifurcation of the limit cycle. The dynamics of the system and safe operating range are presented with diagrams. The results obtained are validated through trajectories of the journal center by numerical integration of the system of equations for different initial conditions presented in the figures.

Experimental study of different structural parameters on gas lubricated spiral groove thrust bearing for cryogenic turbo expander

With the development of high speed and miniaturization of turbo expander, the gas-lubricated spiral groove dynamic pressure gas bearing plays an important role. An experimental study on the gas-lubricated spiral groove gas thrust bearing is carried out to research the relationship between the bearing loading capacity and the structural parameters such as the spiral angle, the groove length ratio, the groove width ratio and the rotating speed. The contrast experiment of spiral groove structure on thrust disc and bearing end face was also carried out. The experimental results show that the optimum spiral angle is 20°, the optimum groove length ratio is 0.61∼0.68, the optimum groove width ratio is 0.5∼0.55, and the new structure of the spiral groove on the thrust disc will increase the bearing loading capacity by 7.6% than the traditional structure.

Research on clearance flow characteristics of gas-lubricated journal bearings using the lattice Boltzmann method

Gas-lubricated journal bearings (GLJBs) are widely utilized in rotating machines and the complex flow in ultra-thin clearances is a hot research topic. In this paper, the micro-clearance between the journal and housing of a GLJB was selected as the research object of a typically curved variable cross-section microchannel. In addition, the multiple-relaxation-time (MRT) model of the lattice Boltzmann method (LBM) was employed to analyze the shear flow characteristics. The generalized form of interpolation supplemented LBM (GILBM) based on the body-fitted grid was utilized due to complex geometry, and the Langmuir slip boundary model was introduced through the non-equilibrium extrapolation (NEE) method to simulate the rarefied airflow from the slip region to transition region. The velocity and pressure fields in the microchannel under different bearing parameters and operating conditions were described by the present model. What’s more, the gas backflow phenomenon was captured. Additionally, the effect of velocity slip on the performance characteristics of GLJBs was studied. It was found that with the increase of eccentricity ratio and rotor speed, or a decrease of clearance size, the load-carrying capacity and friction torque of GLJBs rise, and the occurrence of velocity slip weakens the static performances of GLJBs.

Nonlinear dynamic response and bifurcation of asymmetric rotor system supported in axial-grooved gas-lubricated bearings

Dynamic characteristics of the asymmetric rotor system supported in axial-grooved gas-lubricated bearings are studied. In order to solve nonlinear dynamic response of rotor system effectively, a hybrid numerical model is established by coupling the motion equation of rotor with the rational function model of the gas film forces. The rational function model of the gas film forces of gas-lubricated bearing is established based on vector fitting theory. By using the hybrid numerical model, the repeated calculations of the unsteady Reynolds equation and gas film forces are avoided; the continuous rotor trajectory and the dynamic gas film forces can be calculated simultaneously; and for the rotor system supported in the same bearings, the computing cost can be saved effectively. The nonlinear dynamic responses of asymmetric rotor system supported in axial-grooved gas-lubricated bearings are investigated by trajectory diagrams, frequency spectrum, Poincaré maps, and time series. The bifurcations are analyzed by the bifurcation diagrams with different rotating speeds and mass eccentricities. The dynamic behaviors of the asymmetric rotor system appear complex nonlinear dynamic phenomenon and specific bifurcation characteristics.

Study of Groove Parameters on the Hydrodynamic Behavior of Spiral-Grooved Thrust Bearing with Gas Lubricant

The gas-lubricated thrust bearing is widely used in agriculture mechanical systems, and the groove shape plays an important role on the hydrodynamic behavior of spiral-grooved thrust bearing (SGTB). Although the groove shape may change smaller, it is clear that the hydrodynamic response is very sensitive to the groove parameters. This paper proposes a computational method for the analysis of SGTB with gas lubricant, considering the effects of groove parameters. With the compressibility taken into account, the evaluation of lubrication performance for SGTB is obtained by the CFD technology. Also, the simulation results are compared with the published data, which indicates that the presented model of SGTB is able to obtain more realistic results of hydrodynamic characteristics of SGTB. Moreover, the mapping relationship between groove parameter and hydrodynamic behavior of SGTB is represented.

Influence of slip-flow phenomenon on thermohydrodynamic behaviour of gas foil thrust bearings

Gas foil bearings are often used in high-speed turbomachinery such as turboexpanders and turbochargers due to their merits over simple gas-lubricated bearings. The merits of gas foil bearings include their ability to tailor dynamic parameters such as stiffness and damping. Gas foil bearings usually have low clearance and operate at a high rotational speed, which eventually leads to velocity slip at the solid–fluid interface. This article investigates the effect of slip flow on various parameters of gas foil thrust bearings. A numerical model is formulated to predict pressure, film thickness and temperature distribution of helium lubricated gas foil thrust bearing at high rotating speed. The Reynolds equation is modified by assuming first-order slip coupled with the structural (compliant) and energy equation. The temperature-dependent viscosity and density of the fluid are also considered in the Reynolds equation to predict the thermohydrodynamic behaviour of gas foil thrust bearings. The numerical model thus developed uses a finite-difference method and the Newton–Raphson method to solve the Reynolds equation,whereas the successive over-relaxation method is used to solve the energy equation. Various performance parameters are compared for slip and no-slip conditions for gas foil thrust bearings. The results show a considerable difference between the two phenomena. Also, the conventional Reynolds equation tends to overestimate the load-carrying capacity.

Experimental Investigation of a Small-Scale Organic Rankine Cycle Turbo-Generator Supported on Gas-Lubricated Bearings

Abstract Waste heat recovery (WHR) is expected to contribute to reducing CO2 emissions from trucks. Organic Rankine cycle (ORC) systems show the highest potential for this application, but still lack efficient small-scale expansion devices, in practice. A novel turbogenerator (TG) supported on gas-lubricated bearings is presented in this paper. The device combines a single-stage radial-inflow turbine and a permanent-magnet machine in a single rotating part supported on aerodynamic bearings, lubricated with the working fluid (R245fa). The oil-free expander was tested within a dedicated ORC test setup. It was driven up to its nominal speed of 100 krpm, generated up to 2.3 kW of electrical power, and reached a peak overall efficiency of 67%. Although the prototype was not actively cooled, the mechanical losses of the rotor shaft and the iron loss of the electrical machine reached their nominal levels. Only the copper loss was at a part-load level. The electromechanical efficiency of the TG reached 91% and is expected to increase while testing the device at higher load. This proof of concept confirms the high-speed and low-loss potential of gas-lubricated bearings for small-scale dynamic expanders.

Multiscale simulation of flow in gas-lubricated journal bearings: A comparative study between the Reynolds equation and lattice Boltzmann methods

On account of varying tiny cross-sectional clearance and fairly high bearing speed, the feature of lubricant gas of gas-lubricated journal bearings (GLJBs) is a complex multiscale problem. In this research, both macroscopic Reynolds equation and mesoscopic lattice Boltzmann methods (LBM) are adopted to successfully establish models for restoring flow characteristics of GLJBs from continuum, slip to transition flow regimes. The influences of eccentricity ratios, bearing speeds and Knudsen numbers (Kn) on pressure, thickness, velocity distributions and flow fields of lubricant flow are investigated. The distinctions between the results through two methods, which can be complementary, are compared and analyzed with maximum error ≯9.6%. It indicates that keeping the eccentricity ratio or bearing speed at appropriate high levels is good for improving its working performance. When Kn is enhanced, the maximum and minimum pressure peaks will decrease and increase, respectively, whereas, the impact degree of rarefaction effect on the pressure distribution will reduce after Kn exceeding a certain level. Besides, an interesting backflow phenomenon in the lubricant flow field is demonstrated. This investigation enriches numerical models for GLJBs at different flow regimes, and provides new fruitful insights into the flow characteristics at multiscale.

Flexible Support for Gas-Lubricated Bearing Bushings

Herringbone-grooved journal bearings (HGJBs) for high-speed turbo-machinery are often supported on O-rings due to their favorable stiffness and damping characteristics for stability and alignment reasons. They yield limited lifetime at high temperatures, insufficient assembly repeatability, and dynamic characteristics that are difficult to measure and to tune, however. In order to overcome these shortcomings, a parametric model has been developed with the aim to design a flexible membrane bushing support that offers tunable tilting and radial stiffness and that can be coupled to various concepts to provide suitable damping levels to support a gas-lubricated bearing bushing. Three damping concepts have been investigated that offer independent tuning of the support damping coefficient in combination with the novel flexible bearing bushing support. The new flexible membrane support was manufactured and its stiffness in radial and tilting directions was measured before it was successfully implemented in a prototype. Test results obtained from the new prototype with membrane support show a significant improvement in bushing alignment quality compared to O-rings as well as stable operation up to the design rotor speed of 250 krpm.

An Instrumented High-Speed Rotor With Embedded Telemetry for the Continuous Spatial Pressure Profile Measurement in Gas Lubricated Bearings: A Proof of Concept

Abstract Pressure is the constitutive quantity governing the flow field in gas lubricated bearings. Knowledge of the pressure is of principal importance in the fundamental understanding of such bearings as well as for the validation of their models. Pressure measurements can be done from the bearing side using pressure taps, yet, several details will not be captured. In order to acquire a continuous scan of the pressure field inside the bearing, it is necessary to measure from the rotor side. This paper presents an instrumented measurement high-speed rotor with embedded pressure probes and a wireless telemetry that is capable of the continuous pressure field measurement within the gas film of journal bearings. The rotor was tested on externally pressurized gas journal bearings (EPGJBs) (D = 40 mm and L/D = 1), and pressure profile measurements were acquired up to 37.5 krpm (DN 1.5 M). Measurements at discrete points using pressure taps inside the test bearing were also performed for comparison. The measurements from both sides (bearing and rotor) were in good agreement at quasi-static conditions. At higher operational speeds, it was necessary to perform an in situ system identification and calibration for the embedded pressure probes using the bearing side measurements as a reference. The in situ system identification technique was successful to reconstruct the attenuated pressure signals for a wide range of supply pressures (amplitudes) and rotor speeds (excitation frequencies). The instrumented rotor was proven qualified to perform time-resolved pressure measurements within the gas film of journal bearings up to 37.5 krpm.

Увеличение ресурса подшипников на газовой смазке судового энергетического оборудования с помощью антифрикционных покрытий

Увеличение ресурса подшипников на газовой смазке судового энергетического оборудования с помощью антифрикционных покрытий

Stability of rotor with gas-lubricated journal bearing

Stability of rotor with gas-lubricated journal bearing

A Review of Grooved Dynamic Gas Bearings

Abstract This paper offers an extensive review of publications dealing with the modeling, the design, and the experimental investigation of grooved dynamic gas-lubricated bearings. Recent years have witnessed a rise in small-scale and high-speed turbomachinery applications. Besides the well-known gas foil bearings, grooved bearings offer attractive advantages, which unveil their potential in particular at small scale due to the structural simplicity as well as satisfying predictability. This paper starts with a general background of the application of gas-lubricated bearings and introduces and compares the different gas bearing topologies. Further, the state-of-the-art modeling of grooved gas-lubricated bearings is introduced, systematically assessing the advantages and inconveniences of two major approaches, i.e., the narrow groove theory (NGT) and direct discretization method. Since the NGT method is an elegant and efficient approach to model the complex effects of periodic grooves, a critical section is dedicated to the NGT. In a second phase, different models to include additional physical phenomena such as real gas lubrication, rarefaction, or turbulence effects are reviewed. The paper concludes with a critical assessment of the state-of-the-art and indicates potential fields of research that would allow to shed more light into the understanding of these bearings, as well as with some thoughts on the integrated design methodologies of gas bearing supported rotors.