Air Foil Bearings Research Articles

Stability of rigid rotors supported by air foil bearings: Comparison of two fundamental approaches

High speed direct drive motors enable the use of Air Foil Bearings (AFB) in a wide range of applications due to the elimination of gear forces. Unfortunately, AFB supported rotors are lightly damped, and an accurate prediction of their Onset Speed of Instability (OSI) is therefore important. This paper compares two fundamental methods for predicting the OSI. One is based on a nonlinear time domain simulation and another is based on a linearised frequency domain method and a perturbation of the Reynolds equation. Both methods are based on equivalent models and should predict similar results. Significant discrepancies are observed leading to the question, is the classical frequency domain method sufficiently accurate? The discrepancies and possible explanations are discussed in detail.

Development and Testing of Air Foil Bearing System for an Automotive Exhaust Gas Turbocharger

Lubricated bearings are usually used to support and guide the shafts in gas turbines, exhaust gas turbochargers and other turbomachines. The lubricant is also used for cooling the hot parts such as the turbine side of the rotor. The high temperature condition effects a contamination of the compressed air by evaporating the lubricant. In special applications an oil-free operation has to be guaranteed. In other applications an oil lubricated bearing system prevents an immediate engine stop. The use of air foil bearings eliminates the disadvantages of the oil lubricated bearings. An air foil bearing works self-adjusting the necessary gap which depends on relative speed of the rotor and the stator surfaces and on the viscosity of the lubricating fluid. A low rotor speed requires a small bearing gap, whereas the gap must be enlarged for high speed at constant viscosity of the lubricant. An air foil bearing works contact-free in a wide speed range even at small rotation speed depending on design. On an experimental basis an air foil bearing system was developed and tested for a standard automotive exhaust gas turbocharger. The developed bearings need no infrastructure for supplying with lubricant and its cooling and filtering. The air foil bearings was calculated and designed based on the estimated bearing loads. For the manufacturing of the radial wave springs a procedure was developed. A test facility was set up for the experiments. The modified rotor works at the standard rotation speed of 80000 rpm. The bearings support and guide the shaft contact-free (without wear) in a range of a few thousands of revolutions per minute up to the standard rotation speed.

200 마력급 터보 블로워 적용을 위한 자기베어링 설계

Recently, the development trend of turbomachinery is high capacity and high efficiency. Most of turbomachinery in the market are adopting ball bearings or air foil bearings. However, ball bearings have a limit for high speed product over 2.0×10SUP6/SUP DN(product of the inner diameter of the bearing in mm (D) and the maximum speed in rpm (N)). Air foil bearings have a limit for high axial load for high power products over 200~300 HP(horse power). Magnetic bearing is one of the solutions to overcome the limits of high speed and high axial load. Because magnetic bearings have no friction between the rotor and the bearings, they can reduce the load of the motor and make it possible to increase the rotating speed up to 5.0×10SUP6/SUP DN. Moreover, they can have high axial load capacity, because the axial load capacity of magnetic bearing depends on the capacity of the designed electromagnet. In this study, the radial and thrust magnetic bearings are designed to be applied to the 200 HP class turbo blower, and their performance was evaluated by the experiment. Based on the tests up to 26,400 rpm and 21,000 rpm under the no-load and load condition, respectively, it was verified that the magnetic bearings are stably support the rotor of the turbo blower.

On the nonlinear steady-state response of rigid rotors supported by air foil bearings—Theory and experiments

The demand for oil-free turbo compressors is increasing. Current trends are divided between active magnetic bearings and air foil bearings (AFB), the latter being important due to mechanical simplicity. AFB supported rotors are sensitive to unbalance due to low damping and nonlinear characteristics, hence accurate prediction of their response is important. This paper gives theoretical and experimental contributions by implementing and validating a new method to simulate the nonlinear steady-state response of a rotor supported by three pads segmented AFBs. The fluid film pressures, foil deflections and rotor movements are simultaneously solved, considering foil stiffness and damping coefficients estimated using a structural model, previously described and validated against experiments.

Experimental and theoretical analysis of a rigid rotor supported by air foil bearings

The popularity of compressors utilizing foil bearings is increasing. Their mechanical design is challenging, and an accurate prediction of the bearing coefficients is important. A mathematical model taking into account the foil structure, and the detailed geometry of a three pad foil bearing are presented. The steady state solution and dynamic coefficients are obtained through zeroth and first order perturbed equations respectively. Analysis of the foil structure reveals the importance of distinguishing between a static foil stiffness for the zeroth order equation and a dynamic stiffness for the first order equation. Calculated bearing coefficients are compared to experimental results obtained from a dedicated test rig. Generally, good agreement is observed and minor discrepancies for the damping coefficients are discussed.

Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate the computational performance, it is applied to the analysis of a compliant foil bearing modelled using the simple elastic foundation model. The model is derived and perturbed using complex notation. Top foil sagging effect is added to the bump foil compliance in terms of a close-form periodic function. For a foil bearing utilized in an industrial turbo compressor, the influence of boundary conditions and sagging on the pressure profile, shaft equilibrium position and dynamic coefficients is numerically simulated. The proposed scheme is faster, leading to the conclusion that it is suitable, not only for steady-state analysis, but also for non-linear time domain analysis of rotors supported by airfoil bearings.

Nonlinear Dynamic Analysis of High Speed Oil-Free Turbomachinery With Focus on Stability and Self-Excited Vibration

This paper presents a generic technique for the transient nonlinear dynamic analysis (TNDA) and the static equilibrium stability analysis (SESA) of a turbomachine running on foil air bearings (FABs). This technique is novel in two aspects: (i) the turbomachine structural model is generic, based on uncoupled modes (rotor is flexible, nonsymmetric and includes gyroscopic effects; dynamics of support structure can be accommodated) and (ii) the finite-difference (FD) state equations of the air films are preserved and solved simultaneously with the state equations of the foil structures and the state equations of the turbomachine modal model, using a readily available implicit integrator (for TNDA) and a predictor-corrector approach (for SESA). An efficient analysis is possible through the extraction of the state Jacobian matrix using symbolic computing. The analysis is first applied to the finite-element model of a small commercial automotive turbocharger that currently runs on floating ring bearings (FRBs) and is slightly adapted here for FABs. The results of SESA are shown to be consistent with TNDA. The case study shows that, for certain bearing parameters, it is possible to obtain a wide speed range of stable static equilibrium operation with FABs, in contrast to the present installation with FRBs. Application of the method to a test rig reported in the literature reveals a reasonable degree of correlation between theory and experiment.

Experimental research of oil-free support systems to predict the high-speed rotor bearing dynamics

In modern dissipated power generation systems, microturbines of power output ranging between 1 and 20 kW are applied. The development of a reliable bearing technology for high-speed small turbomachinery could be essential to these power-generating devices. In order to introduce this technology to common use, the optimal design selection from the viewpoint of machine reliability must be conducted. Therefore, one should analyze thoroughly the dynamics of the rotor-bearing-casing system in the whole operating range of the machine. The rotating system presented in the paper is supported in oil-free, airfoil bearings. Compliant surface foil gas bearings are a class of hydrodynamic bearings that use the ambient gas as their working fluid and thus require no dedicated lubrication systems, which makes their design much simpler. The article presents the development and experimental verification of a theoretical numerical model of the foil bearing for analysis of its dynamic characteristics (a sum of properties: two elastic elements connected in a series and their relative motion, friction that is related to this motion with respect to the elastic and cylindrical foils subjected to deformation) that will be an useable part of the study referring to numerical analyses oriented on developing a model of the high-speed rotor supported in bump-foil bearings.

Numerical and experimental investigation of bump foil mechanical behaviour

Corrugated foils are utilised in air foil bearings to introduce compliance and damping thus accurate mathematical predictions are important. A corrugated foil behaviour is investigated experimentally as well as theoretically. The experimental investigation is performed by compressing the foil, between two parallel surfaces, both statically and dynamically to obtain hysteresis curves. The theoretical analysis is based on a two dimensional quasi static FE model, including geometrical non-linearities and Coulomb friction in the contact points and neglects the foil mass. A method for implementing the friction is suggested. Hysteresis curves obtained via the FE model are compared to the experimental results obtained. Good agreement is observed in the low frequency range and discrepancies for higher frequencies are thoroughly discussed.

Evaluation of Foil Bearing Performance and Nonlinear Rotordynamics of 120 kW Oil-Free Gas Turbine Generator

This paper presents a design approach of air foil bearings (AFBs) for a 120 kWe gas turbine generator, which is a single spool configuration with gas generator turbine and alternator rotor connected by a diaphragm coupling. A total of four radial AFBs support the two rotors, and one set of double acting thrust foil bearing is located inside the gas generator turbine. The rotor configuration results in eight degree of freedom (DOF) rotordynamic motions, which are two cylindrical modes and two conical modes from the two rotors. Stiffness of bump foils of candidate AFB was estimated from measured structural stiffness of the bearing, and implemented to the computational model for linear stiffness and damping coefficients of the bearing and frequency-domain modal impedances for cylindrical and conical modes. Stiffness of the diaphragm coupling was evaluated using finite element analysis and implemented to nonlinear rotordynamic analyses of the entire engine. Analyses show the conical mode of the turbine rotor is the main source of instability of the entire engine when AFB clearance is not selected properly. Optimum AFB clearance is suggested from frequency domain modal analyses and nonlinear transient analyses.

Experimental Identification of Force Coefficients of Large Hybrid Air Foil Bearings

Foil bearing technology using air or gas as a lubricant has been around since the mid-1960s, and it made significant progress in its reliability, performance, and applications. Even if significant progress has been made to the technology, the commercial applications to relatively large machines with journal shaft diameter bigger than 100 mm was not reported. This paper presents dynamic characteristics of a hybrid (hydrodynamic + hydrostatic) air foil bearing (HAFB) with a diameter of 101.6 mm and a length of 82.6 mm. The test rig configuration in this work is a floating HAFB on a rotating shaft driven by electric motor, and the HAFB is under external load. HAFB stiffness coefficients were measured using both (1) time-domain quasi-static load-deflection curves and (2) frequency-domain impulse responses, and HAFB damping coefficients were measured using only impulse responses. The HAFB direct stiffness coefficients measured from both methods are close to each other in the range of 4∼7 MN/m depending on speed, load, and supply pressure, but frequency domain method shows larger scatter in the identified coefficients. HAFB coefficients simulated with the linear perturbation method using a bump stiffness matched to the load-deflection characteristics at 18,000 rpm show reasonably good agreements with experimentally measured values.

Simulation of Static Performance of Air Foil Bearings Using Coupled Finite Element and Computational Fluid Dynamics Techniques

The main objective of the current work is to determine a relationship between the top and bump foil's geometry and load-carrying capacity in a journal compliant generation I air foil bearing, as well as determining the effect of the thermohydrodynamic phenomena in the performance of the air foil bearing (AFB). Static and steady-state operation is assumed throughout the analysis. A finite element model is adopted in order to investigate the operational characteristics of the specific bearing. Bump foil's elastic behavior is modeled using two node linear link spring elements. During the hydrodynamic analysis, incompressible viscous steady state Navier–Stokes equations are numerically solved, due to the low bearing compressibility number. During the thermohydrodynamic analysis, compressible, viscous, steady-state Navier–Stokes equations were solved, coupled with the energy equation. The material used during the structural analysis is Inconel X750, and it is assumed that it has linear and elastic behavior. Constant ambient pressure is applied at the free faces of the fluid as well as no slip condition at the surface of the fluid that faces the top foil. Computational fluid dynamics (CFD) and structural models are solved separately. At the beginning of the analysis, the CFD problem is solved with the assumption that the top foil has not yet been deformed. After the solution of the CFD problem, the pressure distribution at the surface of the fluid that faces the top foil is applied at the top foil and then the structural problem is solved. Consequently, the deflections of the top foil are applied on the corresponding surface of the CFD model and the algorithm continues until convergence is obtained. As soon as the converged solution for the pressure distribution is obtained, numerical integration is performed along the surface of the bearing in order to calculate its load-carrying capacity. Static bearing performance characteristics, such as pressure distribution, bump foil deflection, and load capacity are calculated and presented. Furthermore, fluid film thickness, top foil deflection, and fluid pressure are investigated as functions of the bearing angle as well as load-carrying capacity as a function of the bump and top foil stiffness. The same procedure is repeated for the thermohydrodynamic analysis. Moreover, in order to estimate the heat flux from the top foil to the bump foil channel as a function of the top foil temperature, a simple finite element model of the bump foil–cooling channel is constructed.

Note: Radial-thrust combo metal mesh foil bearing for microturbomachinery

This Note proposes a novel radial-thrust combo metal mesh foil bearing (MMFB). Although MMFBs have advantages such as higher stiffness and damping over conventional air foil bearings, studies related to MMFBs have been limited to radial MMFBs. The novel combo MMFB is composed of a radial top foil, thrust top foils, and a ring-shaped metal mesh damper--fabricated by compressing a copper wire mesh--with metal mesh thrust pads for the thrust bearing at both side faces. In this study, the combo MMFB was fabricated in half-split type to support the rotor for a micro gas turbine generator. The manufacture and assembly process for the half-split-type combo MMFB is presented. In addition, to verify the proposed combo MMFB, motoring test results up to 250,000 rpm and axial displacements as a function of rotational speed are presented.

Theoretical and Experimental Investigations of Oil-Free Bearings and their Application in Diagnostics of High-Speed Turbomachinery

In order to reduce the risk of failures, the optimal design selection from the viewpoint of machine reliability must be conducted. Therefore, one should analyze thoroughly the dynamics of the rotor-bearing-casing system in the whole operating range of the machine. The rotating system presented in the paper is supported in non-conventional bearings. The actual study consists in the investigation of new coating materials in the bearing design and the improvement in rotating system dynamics to increase the total efficiency, maintain the cleanness of the working medium and ensure operation of bearings in wide temperature ranges. Despite many advantages, air-foil bearings meet problems of friction and wear in critical moments of their operation, furthermore their complete theoretical model is difficult to establish. Different modeling theories of such bearing dynamic characteristics are shortly described. The current tendency in numerical and experimental methods for diagnostics of rotor support systems of low power rotating machinery is outlined.

Experimental Feasibility Study of Radial Injection Cooling of Three-Pad Air Foil Bearings

The foil bearing (FB) is one type of hydrodynamic bearing using air or another gas as a lubricant. When FBs are designed, installed, and operated properly, they are a very cost-effective and reliable solution for oil-free turbomachinery. Because there is no mechanical contact between the rotor and its bearings, quiet operation with very low friction is possible once the rotor lifts off the bearings. However, because of the high speed of operation, thermal management is a very important design factor to consider. The most widely accepted cooling method for FBs is axial flow cooling, which uses cooling air or gas passing through heat-exchange channels formed underneath the top foil. The advantage of axial cooling is that no hardware modification is necessary to implement it, because the elastic foundation structures of the FB serve as the heat-exchange channels. Its disadvantage is that an axial temperature gradient exists on the journal shaft and bearing. In this paper, the cooling characteristics of axial cooling are compared with those of multipoint radial injection, which uses high-speed injection of cooling air onto the shaft at multiple locations. Experiments were performed on a three-pad FB 49 mm in diameter and 37.5 mm in length, at speeds of 30,000 rpm and 40,000 rpm. Injection speeds were chosen to be higher than the journal surface speed, but the total cooling air flow rate was matched to that of the axial cooling cases. Experimental results show that radial injection cooling is comparable to axial cooling at 30,000 rpm, in terms of cooling performance. Tests at 40,000 rpm reveal that the axial cooling performance reaches saturation when the pressure drop across the bearing is larger than 1000 Pa, while the cooling performance of radial injection is proportional to the cooling air flow rate and does not become saturated. Overall, multipoint radial injection is better than axial cooling at high rotor speeds.

Aero‐elastic bearing effects on rotor dynamics: a numerical analysis

ABSTRACTIn recent decades, numerous models for airfoil bearings have been developed. However, these models are not sufficiently accurate for rotor response prediction in the presence of nonlinearities. It is essential to control the instabilities due to the nonlinear behaviour in order to quantify the energy dissipation in the bearings. By means of a variational approach, the flexible structure is modelled as a thin medium subject to a compressible fluid pressure, under isothermal conditions, in the laminar and turbulent regimes. The model is constructed using the finite element method for the structure response. Internal dry friction is taken into account with Coulomb's law and an updated Lagrangian method. The structure model is coupled with Reynolds equation to obtain the rotor displacement, using the equations of motion for the complete mechanical system.This work is performed to show the influence of the thin structure approach on the rotor behaviour and the field pressure. The link between deflection of the bumps and dry friction is established. The structure buckling is increased by both friction between the sheets and energy dissipation. A second objective is to identify the subsynchronous frequencies in order to establish the relevance of the new airfoil model for nonlinear and instability investigations. Copyright © 2012 John Wiley & Sons, Ltd.

High-Speed Bearing Technologies for Wastewater Treatment Applications

High-Speed Bearing Technologies for Wastewater Treatment ApplicationsReview of High-Speed magnetic and airfoil bearings history and development is presented. Principles of operation of each technology are then explained in detail. A discussion on application of both technologies to the wastewater treatment blowers follows. Airfoil bearings offer a low cost but higher risk high-speed bearing solution for turbo blowers, whereas magnetic bearings offer dynamic...Author(s)Aleksandra IrvingJoseph IbetsSourceProceedings of the Water Environment FederationDocument typeConference PaperPublisherWater Environment FederationPrint publication date Oct, 2013ISSN1938-6478DOI10.2175/193864713813667458Volume / Issue2013 / 20Content sourceWEFTECCopyright2013Word count91

Parallel Iterative Solution Schemes for the Analysis of Air Foil Bearings

AbstractIn an air foil bearing analysis the model is usually solved iteratively due in part to the nonlinearity of the modeling Reynolds equation and the compliance of the bearing surface. The solution procedure requires a multiple-level-deep nested iteration, which involves extended solution time and convergence difficulty. In this study, a simple air foil bearing model is used and the compressible-fluid Reynolds equation for modeling gas lubrication is linearized by Newton's method. The discretized equation is solved by one of the two parallel iterative methods, red-black or strip partition successive-over-relaxation (SOR) method. The parallel programming is conducted using OpenMP programming in an eight-core work-station. Then, a numerical damping scheme for the film-profile convergence is presented. Finally, a root-finding process is conducted to iteratively attain the eccentricity of the bearing for a given load. It is found that the numerical damping step is crucial, which allows the use of a larger relaxation factor to have a fast rate of convergence. Both the parallel SOR methods are easy to implement and the red-black SOR method exhibits better efficiency in the studied cases. This study presents a parallel computing scheme for analyzing air foil bearing of bump-type by today's shared-memory multicore platforms.

Imbalance Response and Stability Characteristics of a Rotor Supported by Hybrid Air Foil Bearings

This article presents the imbalance response of a 4.84-kg rotor of 49 mm in diameter supported by hybrid air foil bearings (HAFBs). In this work, hybrid means hydrostatic injection of pressurized air into the air film. Previous experimental works by the authors on HAFBs with different designs (elastic supports, overall size, number of top foils) considered the load capacity at low speeds and the cooling effectiveness of the hybrid operation. The current article investigates the rotordynamics performance of HAFBs. The HAFB in this work has three top foils with hydrodynamic preload with a clearance distribution similar to traditional three-lobe bearings. The imbalance response in cylindrical mode is presented with different supply pressures (2.67–4.67 bar). Imbalance responses near the critical speeds do not clearly show the effect of increased pressure on the bearing stiffness, natural frequency, and damping around the critical speeds. However, the frequency of subsynchronous vibrations (considered to be the natural frequency of the rotor-bearing system) at high speeds increases slightly with the pressure. The increased supply pressure is more effective in suppressing the subsynchronous vibrations at high speeds rather than affecting the modal stiffness and natural frequencies. Prediction using modal impedance curves calculated from a linear perturbation method slightly overpredicts (4–9%) the measured natural frequencies.

Extended Three-Dimensional Thermo-Hydrodynamic Model of Radial Foil Bearing: Case Studies on Thermal Behaviors and Dynamic Characteristics in Gas Turbine Simulator

Environment-friendly microturbomachinery has its broad current and future applications in fuel cells, power generation, oil-free industrial blowers and compressors, small aero propulsions engines for missiles and small aircrafts, automotive turbo chargers, etc. Air foil bearings (AFBs) have been one of the popular subjects in recent years due to ever-growing interests in the environment-friendly oil-free turbomachinery. AFBs have many noticeable attractive features compared to conventional rigid-walled air/gas bearings such as improved damping and tolerance to minor shaft misalignment and external shocks. In addition, the low viscosity of air or gas allows very low power consumption even at high speeds. A turbine simulator mimicking 50 kW power generation gas turbine was designed. The turbine simulator can generate the same thermodynamic conditions and axial thrust load as the actual gas turbine. In this paper, the 3-D thermo-hydrodynamic (THD) model developed for single radial AFB was further extended to the turbine simulator configuration by extending the solution domain to the surrounding structures including two plenums, bearing sleeve, housing, and rotor exposed to the plenums. In addition, a computational fluid dynamic (CFD) model on the leading edge groove region was developed for better prediction of inlet thermal boundary conditions for the bearing. Several case studies are presented through computer simulations for hydrodynamically preloaded three-pad radial AFB in the hot section. It is found that both bearing and rotor should be provided with cooling air to maintain the temperature of both the rotor and top foil below 300 °C. It is also found that the higher thermal contact resistance between the rotor and hot impellers reduces the axial temperature gradient of the rotor. Dynamic performance of the bearing was evaluated using the linear perturbation method for operation at elevated temperature. The softening effect of the bump foil at elevated temperature results in a decrease of both stiffness and damping coefficients compared to the values at room temperature.