Gas Foil Bearings Research Articles

Effects of Structure Parameters on Static Performance of Gas Foil Bearings Based on a New Fully Coupled Elastic–Aerodynamic Model

Abstract: Accurately predicting the performance of gas foil bearings (GFBs) is important. This paper presents a new fully coupled elastic–aerodynamic model for analyzing the static performance of gas foil journal bearings (GFJBs). The gas compressible lubrication model was solved in MATLAB to obtain the gas pressure. The foil structure deformation was solved in COMSOL by considering the Coulomb friction and allowing the contact surfaces to be separated from each other. Under given load and rotational speed conditions, the calculated minimum gas film thickness and attitude angle match well with the literature data, validating the accuracy of the developed model. Based on the model developed, a comprehensive and systematic analysis of the effects of the structural parameters on the static performance was performed. The results showed that as the bump height, top foil thickness, and bump foil thickness increased, the load capacity could be improved to different degrees. The bump foil thickness had the greatest effect on the load capacity. These results provide theoretical guidance for the structural design and practical applications of GFJBs.

Opportunities to Enhance sCO2 Power Cycle Turbomachinery with Bearingless Motor/Generators

Thermal power cycles using sCO2 as a working fluid place extreme demands on their turbomachinery components and their electric motors/generators. In this paper, new system topologies for sCO2 turbomachinery are proposed which take advantage of “bearingless” electric machine technology to improve performance. Bearingless motors/generators are a new type of electric machine which integrate the functionality of active magnetic bearings into the existing hardware of an electric motor/generator. The existing electromagnetic surfaces and materials are reused to enable controllable production of radial forces on the machine shaft. This is envisioned to improve hermetic direct-drive turbomachinery systems by either augmenting existing bearings (i.e., bearing assist) or replacing existing bearings (i.e., bearing removal). The state-of-the-art technologies for several bearing types (gas foil bearings, externally pressurized porous (EPP) gas bearings, and active magnetic bearings) and electric machines are reviewed to motivate the introduction of bearingless technology. Two system designs using bearingless machines are proposed and compared against existing commercial solutions in terms of maximum shaft weight, number of passthroughs into the hermetic environment, cost, and complexity. A case-study bearingless motor/generator is assessed via simulations and a hardware prototype to investigate practical considerations for using bearingless technology in sCO2 turbomachinery. The proposed bearingless solutions have potential to enable a new generation of sCO2 turbomachinery with improved reliability, reduced complexity, and lower cost. This paper shows that by transforming the motor/generator already present in turbomachinery into a bearingless motor/generator, the technical challenges involved with sCO2 can be overcome without adding significant cost.

Modular test rig for a rotor supported by gas foil bearings

AbstractFoil bearings for high speed turbomachinery are and have been studied in terms of load capacity and lift‐off speed, stability, thermal behaviour and manufacturing. This paper focuses on a modular rotor‐bearing test rig, with which design changes can easily be experimentally investigated. An exemplary design change is undertaken and its effects are studied. Furthermore, a simple procedure is introduced, with which rigid body modes of the rotor can be extracted from phase information derived from experimentally obtained time series data.

An experimental study on the applicability of acoustic emission to detection of lift-off state in gas foil bearings

Gas foil bearings (GFBs) are fluid dynamic bearings with applications in high-speed lightweight machinery. One of the important parameters in GFBs is the lift-off speed. It indicates a speed above which there is no occurrence of dry friction and wear between the rotor and bearing, the so-called lift-off state. There are various techniques for determination of the lift-off state. However, they come with major limitations and complexities for use in real-world applications, especially in high-speed machinery. In recent years, monitoring the lift-off condition in journal bearings based on acoustic emissions (AE) has been investigated and shown to be suitable for this type of bearing. Nevertheless, its applicability to GFBs is yet not known, as there has been no practical investigation on AE signals in GFBs. In the present work, the applicability of AE measurements to detection of lift-off state in GFBs is explored experimentally based on previous studies on journal bearings. The results demonstrate that AE measurements are a potential alternative to conventional methods in determining the lift-off state in GFBs. The comparison between features of AE signals, measured at two different locations on the bearing, with the friction torque as the reference exhibits the applicability of AE measurements to detection of lift-off state.

Experimental study on system characteristics of vapor compression refrigeration system using small-scale, gas-bearing, oil-free centrifugal compressor

Small-scale refrigeration centrifugal compressors hold the potential for superior efficiency compared to currently used positive displacement compressors. However, traditionally, centrifugal compressors have been employed in large refrigeration systems with cooling capacity of several hundred kilowatts or more. Conversely, the application of small-scale centrifugal compressors in smaller refrigeration systems, with cooling capacity in the tens of kilowatts, has largely remained theoretical, lacking practical experimental studies. For a better understanding of the operational characteristics of such systems, this study constructed a 45 kW R245fa refrigeration system test bench based on the small-scale oil-free centrifugal compressor utilizing gas foil bearings. The experimental investigation analyzed the impact of refrigerant charge amount, compressor speed, and coolant flow rate on system performance. Results indicate that the system achieves its peak cooling capacity of 49.73 kW with a system COP of 3.64 at 65,000 rpm. Moreover, at 50,000 rpm, the system demonstrates its highest system COP of 4.23 with a cooling capacity of 26.07 kW. In comparison to traditional positive displacement compressor refrigeration systems, it exhibits higher energy efficiency. Additional simulation studies were conducted to evaluate the effects of substituting R1233zd(E) for R245fa on the system performance and to assess the feasibility of such a substitution.

A Review on the Dynamic Performance Studies of Gas Foil Bearings

Gas foil bearings have important and wide applications in high-speed turbomachinery, generating low frictional lubricating gas film in series with underlying elastic foil structures to support the rotor system. Their dynamic performance is of vital significance in maintaining the rotor stability as well as in depressing rotor vibrations. This paper conducts a comprehensive review on dynamic performance studies conducted on gas foil bearings, including research on the dynamic stiffness and damping coefficients, bearing stability, nonlinear vibrations of the rotor–bearing system, and active methods for controlling rotor dynamic motions. This review provides clear observations towards the developments and iterations of the models, methods, and experiments of these studies.

Identification of dynamic coefficients of gas foil bearings by simulated excitation based on coupled fields

The dynamic coefficients (dynamic stiffness coefficient and dynamic damping coefficient) of gas foil bearings (GFBs) are important for transient dynamics calculation and stability analysis of the GFBs-rotor system. Although the perturbation method can be used to calculate the dynamic coefficients, it can only consider a single whirl ratio. Moreover, the whirl ratio is assumed and not practical. Therefore, this paper proposes an identification method of dynamic coefficients of GFBs by simulated excitation. Firstly, based on single journal-single GFB model considering gas-structure interaction by coupled fields, harmonic excitations were applied to the rotor to obtain the shaft orbit. Next, frequency response function method and equivalence coefficient method were used to identify dynamic coefficients. The former method is suitable for the case where response and excitation are same frequency, namely linear problem. The latter method is fit for the situation in which the response has multiple frequency components, namely nonlinear problem. Finally, examples were carried out, and the results from different methods were compared and analyzed. This research work lays a theoretical foundation for the design of the GFBs-rotor system.

Optimal Design of Boundary Angle for Gas Foil Thrust Bearing Thermal Performance

As the energy density and efficiency requirements of air compressors continue to increase, gas foil thrust bearings face a high risk of thermal failure due to their elevated speed and limited cooling space. This paper proposes a novel structure for gas foil thrust bearings with enhanced thermal characteristics. A thermo-elastic–hydrodynamic model is developed using a thermal-fluid–solid interaction approach to investigate aerodynamic and thermal performance. The load capacity and thermal characteristics of nine different boundary angles are analyzed. The model is validated, and the actual characteristics of gas foil bearings with various boundary angles are examined using a test rig. The results indicate that, compared to conventional gas foil thrust bearings with a boundary angle of 0°, the new structure with a boundary angle ranging from −10° to −5° not only maintains the load carrying capacity but also improves thermal characteristics. Furthermore, this improvement becomes more pronounced with higher rotational speeds. Therefore, the proposed optimization is advantageous in reducing the risk of thermal failure.

Analytical Solution for Electromagnetic Performance Analysis of Permanent Magnet Synchronous Motor with a Parallel Magnetized Cylindrical Permanent Magnet

High-speed direct-drive permanent magnet synchronous motors (PMSMs), supported by elastic foil gas bearings, have broad applications, such as in microcompressors. However, some problems remain to be solved for the electrical performance analysis of PMSMs. For example, there is presently no related analytical model that can be used in rotor dynamics expression for this type of PMSM. This study aimed to establish theoretical models for electromagnetic force density and torque. The process involved both theoretical and experimental research. The analytic models of air gap magnetic density, electromagnetic force density, and electromagnetic performance were established for a PMSM with a parallel magnetized cylindrical permanent magnet. The analytic calculation was conducted, and the results of the analytic model were obtained. The analytical model of the electromagnetic torque and force can be applied in theoretical research on rotor dynamics. The model provides a theoretical basis and method for studying the influence of the electromagnetic load on rotor dynamics. A finite element simulation analysis of the electrical performance of the PMSM was carried out. An electrical performance experiment was conducted. The deviation between the experimental result and the theoretical value was less than 4%. This result indicated that the analytic models could be used in a dynamics analysis of compressors that are directly driven by a PMSM for application in engineering and industrial contexts.

Numerical investigation on the rotordynamics of a high-speed air compressor supported by gas foil bearings

Gas foil bearings are particularly suitable for supporting rotors of hydrogen fuel cell air compressors. Based on Reynolds equation and elastic mechanics theory, a fluid-structure interaction model of gas foil bearings is introduced. A series of perturbation equations are developed and solved to obtain stiffness and damping coefficients of the foil bearings at different rotational speeds. A lumped model of the bearing-rotor system is developed and the rotor stability is analysed by innovatively applying Riccati transfer matrix method. The natural frequencies of the rotor are calculated and then the Campbell diagram is plotted. Subsequently, the critical speeds and the corresponding vibration modes are obtained. The predicted values of the proposed model are highly consistent with the reported experimental results and finite element results, indicating the accuracy of the model. Based on the calculation of rotor unbalance response, further investigation on the effects of unbalance parameters on unbalance response is conducted. The results obtained in this paper could provide theoretical reference for the design of foil bearing supported rotors.

Impact of Gas Foil Bearings, Labyrinth Seals, and Impellers on the Critical Speed of Centrifugal Compressors for Fuel Cell Vehicles: A Comprehensive Investigation

The critical speed is a crucial factor that impacts the stability of high-speed compressors. However, limited research has simultaneously considered the influence of gas foil bearings (GFBs), labyrinth seals, and impellers on critical speed. In this study, we develop a rotordynamic model that incorporates the aerodynamic forces of GFBs, labyrinth seals, and impellers to explore the effects of each component on the critical speed. To validate the developed model, experimental tests are conducted on a centrifugal compressor test bed, and the results exhibit a high level of agreement with the model calculations. By comparing the model calculations that include different components, we comprehensively analyze the influence of each component on the critical speed. The findings reveal that, for centrifugal compressors used in fuel cell vehicles, the rotordynamic coefficients resulting from GFBs are significantly larger than those resulting from impellers and labyrinth seals. Thus, it is reasonable to disregard the aerodynamic forces caused by impellers and labyrinth seals when calculating the critical speed. Furthermore, substituting rigid gas bearings for GFBs as a means to simplify the calculations has only a very slight impact on the results. This study aims to optimize the design process of centrifugal compressors for fuel cell vehicles and offers valuable insights for designing compressors of similar sizes.

Thermohydrodynamic Analysis of a Controllable Stiffness Foil Bearing With Shape Memory Alloy Springs: Experimental Tests and Theoretical Predictions

Abstract Shape memory alloy (SMA)-gas foil bearings (SMA-GFBs) are novel gas bearings comprising top foil, SMA springs, and housing. The radial clearance, stiffness, and damping coefficients of SMA-GFBs can be regulated by the bearing temperature which is determined by the electric heating of SMA springs and the cooling flow. A 3D thermohydrodynamic model (THD) considering the conduction and convection of the top foil, bearing housing, and hollow rotor, and the heat energy of heated SMA springs is presented to simulate the temperature distribution of SMA-GFBs at different rotational speeds, heating powers, and cooling flows. Centrifugal growth of the rotor and thermal expansions of the rotor, SMA springs, and bearing housing are also considered. A test rig is built to measure the bearing temperature and to validate the effectiveness of the theoretical model and circumferential cooling mode. Parametric studies are conducted with different speeds, heating powers, and cooling flows. The heat transfer ratios of the rotor and substructure are also compared. Compared to the temperature differences of the bearing temperature in the circumferential or axial directions, the effects of rotational speed and cooling flow on the bearing temperature are more apparent. The phase transition process of SMA spring can be controlled by adjusting the rotor speed and the cooling flow reasonably, and then the temperature characteristics of SMA-GFB can be changed. The temperature depending on the compressed gas film and heated SMA springs and cooling flow can be adjusted to confirm the feasibility of actively altering the performance of the bearing-rotor system.

Rotordynamics of a rotor radially and axially supported by active bump-type foil bearings and bump-type thrust foil bearings

The rotordynamics of a rotor supported by gas foil bearings (GFBs) has been studied, focusing mainly on the relation between radial loads and lateral vibration. Nevertheless, the various axial loads occurring during operation must be compensated by thrust GFBs. Their effect on lateral and axial vibrations of the rotor must be addressed. This research studied the effect of axial load on the rotordynamics of a rotor supported by active bump-type foil bearings (ABFBs). Two ABFBs and a pair of bump-type thrust foil bearings (BTFBs) supported a rigid rotor along the radial and axial directions, respectively. The 5 degree of freedom nonlinear dynamic model for the rigid rotor is shown in this paper and was validated through experimental measurements. The study considered the coupling of the time-variant nonlinear bearing forces of ABFBs and BTFBs. The rotordynamic behaviors of a rotor under various axial loads, rotor unbalances, and voltages are predicted. Moreover, the effects of various disk misalignments on the minimum gas film thickness of the BTFBs are discussed.

Numerical and experimental studies on feasibility of a cryogenic turboexpander rotor supported on gas foil bearings

Numerical and experimental studies on feasibility of a cryogenic turboexpander rotor supported on gas foil bearings

Nonlinear Dynamic Responses of Rigid Rotor Supported by Thick Top Foil Bearings

This study focuses on thick top foil bearings (TTFBs), which can prevent top foil from sagging and significantly reduce the load capacity of gas foil bearings (GFBs). However, the limited research on the dynamic responses of TTFB-rotor systems has hindered their wide application of TTFBs with high load capacity. To address this, an integrated nonlinear dynamic model is developed to analyze the linear dynamic responses of a rigid rotor supported on TTFBs. The model incorporates time domain orbit simulation, considering unsteady Reynolds equations, foil deformation equations, thick top foil motion equations, and rotor motion equations. A symmetrical test rig is used to validate the model, and three types of TTFBs with different bump foil stiffness are tested, with experimental results aligning with the model predictions. This study also investigates the effects of nominal clearance, static load, and unbalance on TTFB-rotor systems. The results indicate that unbalance has minimal impact on subsynchronous vibrations. However, larger bump foil stiffness, increased normal clearance, and higher static load contribute to improved stability and higher maximum stable speed of the TTFB-rotor system. Moreover, other relevant parameters reducing the bearing attitude angle can further enhance the system’s stability.

Alternative linear dynamic analysis method for gas foil bearing rotor systems using bearing [formula omitted]-domain impedance

Linear dynamic analysis of bearing rotor systems is a basic content of system design. For gas foil bearings (GFBs), the force coefficients method remains the most popular method in engineering practice. However, applying the force coefficients method in the modal analysis of damped free vibrations gives inaccurate modal parameters and, more importantly, leads to missing some important modes. This paper proposes a new linear dynamic analysis method using bearing s-domain (complex frequency-domain) impedance. The bearing s-domain impedance matrix is derived for the first time to characterize the linear dynamic characteristics of GFBs. Then, the linear dynamic analysis method of the GFB rotor system using bearing impedance is presented. The standard eigenvalue problem can be established based on the state–space representation of the bearing impedance matrix. It is found that the combined complex form of force coefficients is the bearing impedance evaluated on the imaginary axis in the s-plane, and the bearing impedance can be identified using the force coefficient data. This makes the proposed method possess the main advantage of the force coefficients method. The proposed method has no inherent error because the state variables relating to gas film and foil are preserved. The error only comes from the impedance fitting process and is controllable. Numerical examples have verified the effectiveness of the proposed method. This method can serve as an alternative to the force coefficients method.

Numerical Investigation of Bump Foil Configurations Effect on Gas Foil Thrust Bearing Performance Based on a Thermos-Elastic-Hydrodynamic Model

The performance of gas foil thrust bearings is critical to the successful design and operation of the high axial load rotatory machines that employ gas foil bearings. However, our understanding of gas foil thrust bearings remains incomplete. To enhance our understanding and predict the performance of gas foil thrust bearings, we have established a detailed three-dimensional thermo-elastic-hydrodynamic model of a gas foil thrust bearing based on a fluid-thermal-structure interaction approach in this study. To validate the accuracy of our model, a gas foil thrust bearing test rig was developed. Moreover, we present a numerical investigation of the influence of bump foil configurations on gas foil thrust bearing performance. The results show that the gas foil thrust bearing that fixes the bump foil at the trailing edge and splits the bump foil into several strips exhibits a 36.4% increase in load capacity compared to the gas foil thrust bearing that fixes a whole piece of bump foil at the leading edge. Fixing the bump foil at the trailing edge and splitting it into several strips effectively decreases power loss and reduces the risk of bearing thermal failure.

Investigation on the effect of coating properties on transient mixed lubrication of gas foil bearing

To reveal the effect of coating properties on the mixed lubrication evolution during the start–stop process of gas foil bearing (GFB), a transient gas mixed lubrication-wear model for coating surface is established. In the developed model, a method of the extended equivalent modulus by the film thickness ratio is proposed, which can extend the classic Greenwood and Tripp contact model for homogeneous materials to the coating contact involving layered materials. Moreover, a gas foil bearing start–stop experiment is conducted to verify the predicted results of the developed model. The effects of coating materials and standard deviation of coating surface on the start–stop performance of GFB are investigated. Within the scope of this article, the results show that during start-up, the gas film pressure first increases and then decreases with the increase in time, the minimum film thickness increases, while the asperity contact decreases. The opposite evolution is observed during shut-down. Compared with uncoated GFB, the friction torque and lift-off speed of GFB with polyimide (PI) and polytetrafluoroethylene (PTFE) are reduced, with PI reducing friction torque by 24.27% and PTFE by 49.03%. The minimum lift-off speed with PTFE is the smallest. The lift-off speed, friction torque, and wear volume increase with the increase in the standard deviation of coating surface. The friction torque and lift-off speed decrease as the start–stop cycle increases until both reach stability. This paper can provide theoretical guidance for the design of the top foil coating surface of GFB.

Modeling and characteristic investigation of practical gas dynamic bearings with stacked perforated foils

this paper presents a stacked perforated foil bearing to address plastic deformation and complex processes of traditional gas foil bearing, which consists of a top foil, three stacked perforated foils and a bearing sleeve. Three layers of perforated foils are stacked to form a stacked perforated foils as the elastic structure of the SPFB, providing sufficient structural deformation and multi-point friction. The theoretical model of the SPFB, which couples a structural model based on a single supported beam with Reynolds equation, is solved using FDM, and the predicted results are validated against experimental results. The static and dynamic characteristics of the SPFB are analyzed under multiple structural and operational parameters, which improves the theoretical basis for commercial application.

Instantaneous angular speed estimation in gas foil bearings from vibration signal

Instantaneous angular speed estimation in gas foil bearings from vibration signal