Air Foil Bearings Research Articles

Elasto‐aerodynamic lubrication analysis of a self‐acting air foil journal bearing

ABSTRACTNowadays, air foil bearings find widespread use in very high speed, lightly loaded oil‐free rotating turbomachineries such as compressors and microgas turbines because they have theoretically no speed limitations and they are environmentally benign. In the design of such bearings, it is of cardinal importance to enhance their steady‐state and dynamic performance characteristics for the safety operation, especially against the external dynamic excitations. Most of elasto‐aerodynamic approaches under dynamic conditions proposed in the technical literature include only the static pressure induced deformation of foils. This paper presents a theoretical investigation on the effects of both static and dynamic deformations of the foils on the dynamic performance characteristics and stability of a self‐acting air foil journal bearing operating under small harmonic vibrations. For the dynamic deformations of foils to be taken into account, the perturbation method is used for determining the gas‐film stiffness and damping coefficients for given values of excitation frequency, compressibility number and compliance factor of the bump foil. The rotor‐dynamic coefficients serve as input data for the linear stability analysis of rotor‐bearing system. The nonlinear stationary Reynolds' equation is solved by means of the Galerkin's finite element formulation, whereas the finite differences method are used to solve the first‐order complex dynamic equations resulting from the perturbation of the transient compressible Reynolds' equation. As a first approximation, the corrugated subfoil is modelled as a simple elastic foundation, i.e. the stiffness of a bump is uniformly distributed throughout the bearing surface. It was found that the dynamic properties and stability of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition. Copyright © 2012 John Wiley & Sons, Ltd.

Ultra High Speed Motor Supported by Air Foil Bearings for Air Blower Cooling Fuel Cells

As accomplishing the research of the PM synchronous motor driven by 15 kW at the rated speed of 120,000 rpm, this paper represents an approach to minimize eddy current losses which occur prominently at high speed. Various simulation and testing techniques are therefore applied to determine the effect of design parameters. Here, the proposed parameters for analysis are winding types, slot opening width and sleeve thickness. This paper based on the obtained results, evaluates the optimum value of the most critical design parameters responsible for eddy current loss. Finally, this paper studies the developed model which represents a solution for minimizing the cause of eddy current loss by implementation of sinusoidal distribution of air-gap magnetic flux density. It comes to the conclusion that sleeve thickness should be chosen as considering a function of mechanical stress and critical speed of rotor. Furthermore, the critical speed of rotor is evaluated by rotor dynamics. The design efficiency is well accorded with the efficiency test, having a maximum error of 2.7%.

Microturbocharger with Air Foil Bearings for a 100-W Class Micro Power System and Improvement of Rotordynamic Performance

This article presents the experimental investigation of a microturbocharger supported on bump-type air foil bearings (AFBs) for a 100-W power generation. The microturbocharger was designed via thermodynamic cycle analyses as well as rotordynamic analyses and constructed using a centrifugal compressor and turbine with tip diameter of 10 mm. The tests for AFBs at rotating speeds up to 410 krpm driven by air showed a large subsynchronous motion at 100 Hz. However, AFBs with an additional viscoelastic film eliminated the subsynchronous response due to increased damping by the viscoelastic film. The compressor performance was evaluated numerically and experimentally.

Thrust Bump Air Foil Bearings with Variable Axial Load: Theoretical Predictions and Experiments

Thrust air foil bearings are critical components in high-efficiency turbomachinery, such as two-stage compressors subjected to large and irregular axial forces. In this article, a model of thrust bump foil bearings that predicts deflection with variable axial load is developed assuming no tilting effect of the thrust collar. To predict the air clearance, deflection of the elastic foundation was used in the air film height equation. Combined Dirichlet and Neumann-type boundary conditions were used for static load performance predictions. To verify the theoretical model, tests were performed with three different thrust air foil bearings with outer radii of 45, 50, and 55 mm. The rotating speed ranged from 10,000 to 25,000 rpm. From the test results, the model using nonlinear stiffness was in better agreement with the experimental results than the model using linear stiffness.

Identification of stiffness and damping characteristics of axial air-foil bearings

Air-foil bearings (AFBs) are self acting hydrodynamic bearings made from sheet metal foils comprised of at least two layers. The innermost “top foil” layer traps a gas pressure film that supports a load while the layer or layers underneath provide an elastic foundation. AFBs are currently used in many commercial applications, both terrestrial and in aerospace. AFBs provide a means to eliminate the oil system leading to reduce weight and enhanced temperature capability. Regardless of the application of the AFBs, the identification of the structural characteristics is important for successful design practice. In the present work, structural characteristics (stiffness and damping) of axial AFBs are indentified in the light of experimental results. Due to the initial high torque requirement of the AFB, the experimental setup using a single AFB is proposed instead of standard two-foil bearing setups. Experiments are carried out at maximum speed of 60,000 rpm. Sub-structuring approach is used for identification of the structural (stiffness and damping) characteristics of the AFB. The results have shown that the developed experimental procedure is able to identify the stiffness and damping characteristics of axial AFBs accurately.

Air Injection as a Thermal Management Technique for Radial Foil Air Bearings

A thermal management technique for radial foil air bearings was experimentally evaluated. The technique is based on injecting air directly into the internal circulating fluid-film to reduce bulk temperatures and axial thermal gradients. The tests were performed on a single top foil, Generation III, radial foil bearing instrumented with three thermocouples to monitor internal temperatures. A through hole in the bearing shell coincident with the gap between the top foil's fixed and free ends provided entry for the injection air. The tests were conducted at room temperature with the bearing operating at speeds from 20 to 40 krpm while supporting 222 N. Two different mass flow rates of injection air were evaluated for this method, 0.017 and 0.051 kg/min. Test results suggest that the air injection approach is a viable thermal management technique capable of controlling bulk temperatures and axial thermal gradients in radial foil air bearings.

Numerical and Experimental Investigation of Bump Foil Forming Process for Foil Air Bearings

In this paper, a simplified nonlinear finite element for bump foil forming process of foil air bearings is developed. The bump foil is dealt with as flexible deformable body, the upper die and lower die are considered as the rigid body without deformation. The friction model between bump foil and dies with velocity-dependent friction forces is described by arctan function. The forming process of SS304 Stainless Steel bump foil under different loads is investigated with rigid-plastic finite element method. The simulation results are compared with theoretical values and experimental results. Therefore more feasible process parameters are obtained to fabricate the bump foils.

Design and Performance Prediction of Hybrid Air Foil Thrust Bearings

Air foil bearings (AFBs) have been recognized as the most promising for oil-free turbomachinery. However, the applications of AFBs to the relatively large turbomachinery have many technical challenges due to limited load capacity and wear during start/stops. A hybrid air foil bearing (HAFB), which combines the benefits of AFB and hydrostatic air bearing, was introduced earlier by the authors, and the experimental studies showed much larger load capacity at low speeds and much lesser friction torque during start/stop than hydrodynamic counterpart. The benefit of HAFB was recognized through the experimental studies, and the concept of hybrid operation was further developed to thrust air foil bearings. This paper presents novel design features of the hybrid air foil thrust bearing (HAFTB) with radially arranged bump foils and preformed Rayleigh step contour, and presents simulated static and dynamic characteristics of the HAFTB. A 2D thin plate equation in cylindrical coordinate was solved with the finite difference method for the prediction of the top foil deflection. Parametric studies were performed to evaluate the effect of various design parameters on the static and dynamic performances of HAFTB. At low speeds, a design with orifice located at the center of land region showed the highest load capacity, while a design with orifice located near the leading edge of land region showed the highest load capacity at high speeds. Direct and coupled bearing coefficients were also calculated for various operating conditions. The direct stiffness increases with supply pressure but the direct damping decreases with supply pressure. In addition, typical hardening effect of gas film accompanying increase of stiffness and decrease of damping was predicted in high frequency excitations.

Identification of dynamic properties of radial air-foil bearings

Air-foil bearings (AFBs) are self acting hydrodynamic bearings made from sheet metal foils comprised of at least two layers. The innermost “top foil” layer traps a gas pressure film that supports a load while the layer or layers underneath provide an elastic foundation. Air-foil bearings are currently used in many commercial applications, both terrestrial and aerospace. Air-foil bearings provide a means to eliminate the oil system leading to reduce weight and enhanced temperature capability. Regardless of the application of the air-foil bearings, the identification of the dynamic characteristics is important for successful design practice. In the present work, stiffness and damping of radial air-foil bearings are indentified in the light of experimental results. Due to the initial high torque requirement of the air-foil bearing, the experimental setup using single air-foil bearing is proposed instead of standard two-foil bearing setups. Experiments are carried out at maximum speed of 60,000 rpm. Sub-structuring approach is used for identification of stiffness and damping properties of the air-foil bearings. The results have shown that the developed experimental procedure is able to indentify the stiffness and damping properties of radial air-foil bearings accurately.

Design of Three-Pad Hybrid Air Foil Bearing and Experimental Investigation on Static Performance at Zero Running Speed

Air foil bearings (AFBs) have been explored for various micro- to midsized turbomachinery for decades, and many successful applications of the AFBs to small turbomachinery were also reported. As machine size increases, however, one of the critical technical challenges of AFBs is a wear on the top foil and rotor during starts/stops due to relatively heavy rotor weight compared with the size of the bearing. The wear on the foil increases with greater loading during starts/stops as a function of the coating performance. The hybrid air foil bearing (HAFB), which combines hydrodynamic pressure with hydrostatic lift, can help to minimize/eliminate the wear problem during the start/stops. This paper reports design and preliminary test results of hydrodynamically preloaded three-pad HAFB aimed for midsized airborne turbomachinery applications. Designed HAFB was manufactured and comprehensive parametric design simulations were performed using time-domain orbit simulations and frequency-domain linear perturbation analyses to predict performances of manufactured bearing. Static stiffness was measured at zero running speed to investigate the load capacity of hydrostatic operation when rotor is at stationary. The measured static stiffness showed good agreement with predictions.

Thermohydrodynamic Analyses of Bump Air Foil Bearings With Detailed Thermal Model of Foil Structures and Rotor

A new thermohydrodynamic analysis model for bump air foil bearings with a detailed thermal model of bump foil structures and rotor is presented. In the developed model, temperatures of lubricating air film, top foil, bump foils, bearing sleeve, and rotor are calculated simultaneously through an iterative process. Reynolds equation and 3D energy equation were applied to the air film, and energy equations were applied to all the other structures around the bearing. Energy and momentum equations were applied to cooling channels to predict spatial temperature distribution along the cooling channels. The thermal growth of the rotor, foil structure, bearing sleeve, and centrifugal growth of the rotor are also considered. For the accuracy of the model, effective heat transfer resistance between the top foil and bearing sleeve was measured for various conditions and implemented into the thermal analysis around the cooling channels. The model was also bench marked with published experimental results for verifications. Using a developed model, parametric studies were performed with different bearing nominal clearances, applied loads, rotating speeds, and cooling conditions through channels.

Thermohydrodynamic Study of Multiwound Foil Bearing Using Lobatto Point Quadrature

The applications of foil air bearings have been extended for use in a wide range of turbomachineries with high speed and high temperature. Lubricant temperature becomes an important factor in the performance of foil air bearings, especially at high rotational speeds and high loads or at high ambient temperature. This study presents a thermohydrodynamic (THD) analysis of multiwound foil bearing, in which the Reynolds’ equation is solved with gas viscosity as a function of temperature that is obtained from the energy equation. Lobatto point quadrature is utilized to accelerate the iteration process with a sparse mesh across film thickness. A finite element model of the foil is used to describe the foil elasticity. An iterative procedure is performed between the Reynolds equation, the foil elastic deflection equation, and the energy equation until convergence is achieved. A three-dimensional temperature prediction of air film is presented, and a comparison of THD to isothermal results is made to emphasize the importance of thermal effects. Finally, published experimental data are used to validate this numerical solution.

The Dynamic Performance Analysis of Foil Journal Bearings Considering Coulomb Friction: Rotating Unbalance Response

The dynamic performance of air foil bearings relies on a coupling between a thin air film and the frictional motion of a foil structure. A number of successful analytical techniques to predict their performance have been developed. However, the evaluation of their dynamic characteristics is still not adequate because of the mechanical complexity of the foil structure and the strong nonlinear behavior of the friction force. This work presents a nonlinear transient analysis method to predict the dynamic performance of foil bearings considering Coulomb friction. In this method, the time-dependent Reynolds equation is solved to calculate pressure distribution and a finite element method is used to simulate bump motion. The analysis is treated with a direct implicit integration technique that can handle nonlinear problems and an algorithm to solve for stick-slip motion of bump foil is applied. Using this method, the hysteretic behavior and dissipative characteristics of bump foil resulting from the unbalance excitation is observed. In addition, a number of parametric studies are performed to evaluate the effects of design parameters on the unbalance response. The parameters are friction coefficient, bump half wavelength, amount of mass unbalance, and the number of bump foil strips. The predictions of the unbalance response show that the foil bearing is very effective on the restriction of the vibration at the resonance frequency and there exist optimum values of design parameters such as friction coefficient, bump foil stiffness, and the number of bump foil strips with regard to minimizing the amplitude at the resonance frequency.

Hydrostatic air foil bearings: Analytical and experimental investigation

Air foil bearings have been used in various micro-turbomachinery applications. One of the critical technical challenges in extending the operating envelope of the air foil bearing to larger systems than current applications is the issue of coating wear on the top foil and rotor during starts/stops. This paper reports the design, construction, and testing of the first hydrostatic air foil bearing (HAFB). The HAFB showed higher load capacity with much less air consumption than the hydrodynamic counterpart, which is a noticeable advantage of HAFB in efficiency and cooling capacity. In addition, start torque was very small and comparable to the friction torque of steady-state hydrodynamic operation. The small start torque clearly indicates that the HAFB can help to eliminate the wear problem that has been a chronic failure mode in heavily loaded air foil bearings. A simple analytical model for prediction of top foil deflection and sagging effects under hybrid (both hydrostatic and hydrodynamic) mode was developed. The new top foil deflection model showed very good agreement with published experimental data. The top-foil deflection model and associated bump dynamics were integrated into time-domain orbit simulations to predict imbalance responses of a rigid rotor supported by HAFBs.

Parametric Studies on Dynamic Performance of Hybrid Airfoil Bearing

Airfoil bearings offer many advantages over oil-lubricated bearings, but they have reliability issues during start∕stops (wear) and limited heat dissipation capability. To address these issues, a hybrid airfoil bearing (HAFB) combining hydrodynamic airfoil bearing with hydrostatic lift was introduced previously by one of the authors of this paper. Their studies show that HAFB has superior performance compared to its hydrodynamic counterpart in load capacity and cooling performance. In this article, the bearing stiffness and damping coefficients of HAFB are calculated using a linear perturbation method developed for HAFB. Simulations showed that feed parameter and supply pressure affect the dynamic characteristics of HAFB. With an increase in either the supply pressure or the feed parameter, the rotor centers itself and hence one sees a decrease in direct stiffness. Simulations showed that the cross-coupled stiffness could be reduced by increasing either the supply pressure or the feed parameter. Direct damping showed increasing trend with the supply pressure and the feed parameter. Frequency-domain analysis of the bearing coefficients was also performed. The direct damping showed marginal changes with supply pressure but showed rapid increase with increasing excitation frequencies. The damping converged to null values for all the pressures for supersynchronous excitations. The loss in damping with high stiffness values for high frequency excitation is a typical hardening effect of gas bearings. In almost all the cases, there are rapid decreases in cross-coupled stiffness and damping and the values show converging trends in supersynchronous regime.

Performance Analysis of Double-Bump Air Foil Bearings

This paper presents a theoretical model for the analysis of double-bump air foil bearings (AFBs). The stiffness and damping coefficients of the double bump vary depending on the external load and its friction coefficient. In the case of a lightly loaded condition where only the upper bump contributes to deformation, the double bump is in the single active region. In the case of a heavily loaded condition where both the upper and lower bumps contribute to deformation, the double bump is in the double active region. So the double bump can be either in the single or double active region depending on vertical deflection. The equivalent stiffness and damping coefficients of the bump system are derived from the vertical and horizontal deflection of the bump, including the friction effect. A static and dynamic performance analysis is carried out by using the finite difference method and the perturbation technique. The results of the performance analysis for a double-bump AFB are compared with those obtained for a single-bump AFB. This paper successfully proves that a double-bumped AFB has higher load capacity, stiffness, and damping than a single-bump AFB in a heavily loaded condition.

Thermal Management Techniques for Oil-Free Turbomachinery Systems

Tests were performed to evaluate three different methods of utilizing air to provide thermal management control for compliant journal foil air bearings. The effectiveness of the methods was based on bearing bulk temperature and axial thermal gradient reductions during air delivery. The first method utilized direct impingement of air on the inner surface of a hollow test journal during operation. The second, less indirect method achieved heat removal by blowing air inside the test journal parallel to the shaft axis to simulate air flowing axially through a hollow shaft. The third method emulated the most common approach to removing heat by forcing air axially through the bearing's support structure. Internal bearing temperatures were measured with three type K thermocouples embedded in the bearing that measured general internal temperatures and axial thermal gradients. Testing was performed in a 1 atm, 260°C ambient environment with the bearing operating at 60 krpm, and supporting a load of 222 N. Air volumetric flows of 0.06, 0.11, and 0.17 m3/min at approximately 150 to 200°C were used. The tests indicate that all three methods provide thermal management but at different levels of effectiveness. Axial cooling of the bearing support structure had a greater effect on the bulk temperature for each air flow and demonstrated that the thermal gradients could be influenced by the directionality of the air flow. Direct air impingement on the journal's inside surface provided uniform reductions in both bulk temperature and thermal gradients. Similar to the direct method, indirect journal cooling had a uniform cooling effect on both bulk temperatures and thermal gradients but was the least effective of the three methods.

Foil Gas Bearing With Compression Springs: Analyses and Experiments

A new foil gas bearing with spring bumps was constructed, analyzed, and tested. The new foil gas bearing uses a series of compression springs as compliant underlying structures instead of corrugated bump foils. Experiments on the stiffness of the spring bumps show an excellent agreement with an analytical model developed for the spring bumps. Load capacity, structural stiffness, and equivalent viscous damping (and structural loss factor) were measured to demonstrate the feasibility of the new foil bearing. Orbit and coast-down simulations using the calculated stiffness and measured structural loss factor indicate that the damping of underlying structure can suppress the maximum peak at the critical speed very effectively but not the onset of hydrodynamic rotor-bearing instability. However, the damping plays an important role in suppressing the subsynchronous vibrations under limit cycles. The observation is believed to be true with any air foil bearings with different types of elastic foundations.

Rotordynamic characteristics of a micro turbo generator supported by air foil bearings

The rotordynamic characteristics of a micro power system supported by air foil bearings were investigated. Stability analysis was performed by a finite element method with the predicted dynamic coefficients of the foil bearings. A preliminary test rig was developed to simulate the operating characteristics of the micro power system. It consisted of a rotor supported by two air foil journal bearings and two air foil thrust bearings, and an impulse driven turbine. The foil journal bearings had a diameter of 7 mm and a length of 7 mm (L/D = 1). The test rig was operated stably under various situations and speeded up to 300 000 rpm. The main portion of the rotor response was synchronous and the amplitude of synchronous vibration was about 5–20 µm. Further, theoretical and experimental results for the unbalance response were compared. From this study, we showed the possibility of stable performance for the micro power system supported by air foil bearings.

고분자 전해질 연료 전지용 공기공급계의 동특성 및 성능에 대한 연구

Turbo-blower as an air supply system is one of the most important BOP (Balance of Plant) systems for FCV(Fuel Cell Vehicle). For generating and blowing compressed air, the motor of air blower consumes maximum 25% of net power, and fuel cell demands a clean air. In this study, turbo-blower supported by air foil bearings is introduced as the air supply system used by 80kW proton exchange membrane fuel systems. The turbo-blower is a turbo machine which operates at high speed, so air foil bearings suit their purpose as bearing elements. Analysis for confirming the stability and endurance is conducted. The rotordynamic stability was predicted using the numerical analysis of air foil bearings and it is verified through experimental works. In spite of various transient dynamic situation, the turbo-blower had stable performances. After the performance test, results are presented. The normal power of driving motor has about 1.6 kW with the 30,000 rpm operating range and the flow rate of air has maximum 160 SCFM. The test results show that the aerodymic performance and stability of turbo-blower are satisfied to the primary goals.