scholarly journals Porous Gas Journal Bearings: An Exact Solution Revisited and Force Coefficients for Stable Rotordynamic Performance

2021 ◽  
Vol 11 (17) ◽  
pp. 7949
Author(s):  
Luis San Andrés ◽  
Jing Yang ◽  
Andrew Devitt
Keyword(s):  
Exact Solution ◽  
High Speed ◽  
Load Capacity ◽  
Computing Time ◽  
Radial Clearance ◽  
Stable Operation ◽  
Fe Model ◽  
Shaft Speed ◽  
Supply Pressure ◽  
Mechanical Elements

Having come of age, gas film bearings enable high-speed oil-free (micro) rotating machinery with gains in efficiency and reliability, longer maintenance intervals, and a reduction in contaminants released to the atmosphere. Among gas bearing types, porous surface gas bearings (PGBs) have proven successful for 50+ years and presently are off-the-shelf mechanical elements. This paper reviews the literature on PGBs since the 1970s and reproduces an exact solution for the performance of cylindrical PGBs. Both the analytical model and an accompanying finite-element (FE) model predict the performance for two PGBs, a commercially available 76 mm diameter bearing and a smaller 25 mm diameter laboratory unit whose experimental performance is available. As expected, the FE model results reproduce the analytical predictions obtained in a minuscule computing time. For a set external supply pressure, as the radial clearance increases, the flow rate through the bearing grows until reaching a peak magnitude. The PGB load capacity is a fraction of the product of the set pressure difference (pS − pa) and the bearing projected area with a significantly large centering static stiffness evolving over a narrow region of clearances. Operation with shaft speed enhances the bearing load capacity; however, at sufficiently high speeds, significant magnitude cross-coupled forces limit the stable operation of a PGB. At constant operating shaft speed, as the whirl frequency grows, the bearing effective stiffness (Keff) increases, while the effective damping (Ceff) becomes positive for whirl frequencies greater than 50% shaft speed. Similar to a plain hydrodynamic journal bearing, the PGB is prone to a half-frequency whirl, albeit the system natural frequency can be high, mainly depending on the external supply pressure. In essence, for the cases considered, PGBs are linear mechanical elements whose load capacity is proportional to the journal eccentricity.

Influence of geometric parameters on the bump foil bearing performance

2019 ◽  
Vol 234 (7) ◽  
pp. 1017-1026
Author(s):  
Sadanand Kulkarni ◽  
Soumendu Jana
Keyword(s):  
Carrying Capacity ◽  
High Speed ◽  
System Development ◽  
Load Capacity ◽  
Radial Clearance ◽  
Load Carrying Capacity ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Load Carrying ◽  
Lift Off

High-speed rotating system development has drawn considerable attention of the researchers, in the recent past. Foil bearings are one of the major contenders for such applications, particularly for high speed and low load rotating systems. In foil bearings, process fluid or air is used as the working medium and no additional lubricant is required. It is known from the published literature that the load capacity of foil bearings depend on the operating speed, viscosity of the medium, clearance, and stiffness of the foil apart from the geometric dimensions of the bearing. In case of foil bearing with given dimensions, clearance governs the magnitude of pressure developed, whereas stiffness dictates the change in radial clearance under the generated pressure. This article deals with the effect of stiffness, clearance, and its interaction on the bump foil bearings load-carrying capacity. For this study, four sets of foil bearings of the same geometry with two levels of stiffness and clearance values are fabricated. Experiments are carried out following two factor-two level factorial design approach under constant load and in each case, the lift-off speed is measured. The experimental output is analyzed using statistical techniques to evaluate the influence of parameters under consideration. The results indicate that clearance has the maximum influence on the lift-off speed/ load-carrying capacity, followed by interaction effect and stiffness. A regression model is developed based on the experimental values and model is validated using error analysis technique.

Novel Approach for Optical Characterization of Thrust Collar Lubricated Area: Experimental and Numerical Results

2021 ◽  
Vol 143 (1) ◽  
Author(s):  
Thomas Kerr ◽  
Adolfo Delgado
Keyword(s):  
High Speed ◽  
Pressure Field ◽  
Load Capacity ◽  
Fe Model ◽  
Cfd Model ◽  
Axial Loads ◽  
Test Rig ◽  
Efficient Operation ◽  
Oil Film ◽  
All Speeds

Abstract Thrust collars (TCs) are bearing elements used in geared machinery that transmit axial loads from one shaft to another. TCs are primarily used in integrally geared compressors (IGCs) but are also found in gearboxes and marine propulsion applications. TCs are hydrodynamic elements featuring a converging-diverging wedge to generate a pressure field that reacts axial loads. Accurate modeling requires knowledge of the film characteristics such as cavitation, turbulence, and air ingestion, all of which reduce load capacity. Current models in the literature do not include mass-conserving cavitation algorithms or turbulence flow. The following paper introduces a new test rig that optically characterizes the thin film region of a TC. The test rig geometries, speeds, and loads match those typically seen in IGC applications. The test rig utilizes a transparent acrylic window in conjunction with a high-speed camera (HSC) to obtain high-speed images of the oil film. Images are filtered and averaged to obtain areas of interest in the oil film. Cavitation and turbulence areas are measured for pinion speeds of 2.5, 5, and 7.5 krpm and axial loads of 0.5, 1, and 1.5 kN. Cavitation occurs in the diverging (upper) region of the TC and appears at pinion speeds over 5000 rpm but does not change in shape after that speed. The cavitation is independent of applied load. Turbulence at the inlet region (bottom) occurs at all speeds but increases to almost 35% of the total area at the highest speed. This paper also presents a finite element (FE) model that includes predictions for the static characteristics of the TC, specifically the cavitation area. The cavitation modeling uses an iterative Elord's method, which conserves mass. The model predicts a similar cavitation area for all speeds and loads. A computational fluid dynamics (CFD) study predicts a similar cavitation area and pressure field to the FE model. The CFD model predicts turbulence in the lower region that increases for increasing spin speed, which matches the experimental results. The CFD model tends to under-predict the turbulence area compared to the experiments. As IGCs move into new application areas to satisfy new needs, the increase in efficiency and capacity comes at a cost of more load and higher speed requirements on the TCs. This work will help original equipment manufacturers model TCs more accurately to ensure safe and efficient operation.

Measurements of Static and Dynamic Load Performance of a 102 mm Carbon-Graphite Porous Surface Tilting-Pad Gas Journal Bearing

2021 ◽  
Author(s):  
Luis San Andrés ◽  
Rachel Bolen ◽  
Jing Yang ◽  
Ryan McGowan
Keyword(s):  
Dynamic Load ◽  
Load Capacity ◽  
Stable Operation ◽  
Specific Load ◽  
Force Coefficients ◽  
Supply Pressure ◽  
Air Supply ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Gas Bearing

Abstract Aerostatic journal bearings with porous tilting pads enable shaft support with minute drag power losses. To date archival information on the static and dynamic load performance of this bearing type is scant. Thus, the paper presents measurements conducted with an air lubricated bearing with diameter d = 102 mm and comprising four tilting pads made of porous carbon-graphite, each with length L = 76 mm. Two nested Belleville washers resting on spherical pivots support each pad. At ambient temperature of ∼ 21°C, as the air supply pressure into the bearing pads increases, so does the bearing aerostatic specific load (F/(L·d)) that reaches 58% of the pressure difference, supply minus ambient. With an air supply pressure of 7.8 bar(a), the test bearing static stiffness KS = 13.1 MN/m, is independent of both shaft speed and static load. KS is just 63% of the washers’ stiffness KP = 20.6 MN/m (during loading). While operating with shaft speeds equal to 6 krpm and 9 krpm (150 Hz) and under specific loads to 115 kPa and 101 kPa respectively, dynamic load experiments with excitation frequencies up to 342 Hz show the test bearing supplied with air at 7.8 bar(a) has frequency independent stiffness (K) and damping (C) coefficients. For rotor speeds equaling 0, 6 and 9 krpm, the bearing direct stiffnesses KXX ∼ KYY range from 13.6 MN/m to 32.7 MN/m as the specific load increases from 0 kPa to 115 kPa. The direct damping coefficients CXX ∼ CYY are as large as 5.8 kN·s/m, though having a large experimental uncertainty. Bearing cross-coupled force coefficients are insignificant. The test porous gas bearing reached its intended load capacity, demonstrated a dynamically stable operation and produced force coefficients mainly affected by the pads’ pivot supports and the magnitude of air supply pressurization.

Experimental Versus Theoretical Characteristics of a High-Speed Hybrid (Combination Hydrostatic and Hydrodynamic) Bearing

1993 ◽  
Vol 115 (1) ◽  
pp. 160-168 ◽  
Author(s):  
K. Alan Kurtin ◽  
D. Childs ◽  
Luis San Andres ◽  
K. Hale
Keyword(s):  
High Speed ◽  
Load Capacity ◽  
Test Facility ◽  
Navier Stokes ◽  
Radial Clearance ◽  
Hydrodynamic Bearing ◽  
Speed Test ◽  
Discharge Coefficients ◽  
Hybrid Combination ◽  
Numerical Predictions

The high-speed test facility designed and installed at Texas A&M to study water lubricated journal bearings has been successfully used to test statically an orifice compensated five-recess-hybrid (combination hydrostatic and hydrodynamic) bearing for two radial clearance configurations. Measurements of relative-bearing position, torque, recess pressure, flow rate, and temperature were made at speeds from 10,000 to 25,000 rpm and supply pressures of 6.89 MPa (1,000 psi), 5.52 MPa (800 psi), and 4.14 MPa (600 psi). For speeds of 10,000 and 17,500 rpm, the bearing load capacity was also investigated. A pitching instability of the bearing limited the number of test cases. A 2-dimensional, bulk-flow, Navier-Stokes numerical analysis program was used for all theoretical performance predictions. Orifice discharge coefficients used in the program were calculated from measured flow and pressure data. Reynolds numbers for flow within the bearing lands due to shaft rotation and recess pressurization ranged from 6700 to 16,500. Predictions sensitivity to ±10 percent changes in the input parameters was investigated. Results showed that performance prediction sensitivities are high for changes in discharge coefficients and negligible for changes in relative roughness. The numerical predictions of relative bearing position, recess pressure, flowrate, and torque are very accurate, provided the selected orifice discharge coefficients are correct.

Imbalance Response of a Rotor Supported by Hybrid Air Foil Bearings

2011 ◽  
Author(s):  
Daejong Kim ◽  
Prajwal Shetty ◽  
Donghyun Lee
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Hydrodynamic Instability ◽  
High Reliability ◽  
Load Capacity ◽  
Damping Ratio ◽  
Foil Bearings ◽  
Supply Pressure ◽  
Bearing Stiffness ◽  
Frequency Ratios

Air foil bearings (AFB’s) are widely used in small to midsized turbomachinery. They are simple in construction, offer very low drag friction, and have very high reliability at high speed operations. This paper presents experimental imbalance response of a 4.84 kg rigid rotor (operating below bending critical speed) supported by two hybrid air foil bearings with 50 mm in diameter. The concept of “hybrid” in this paper utilizes the hydrostatic augmentation of the load capacity during the start up and shut down. The hybrid air foil bearings were designed with three top foils for enhanced stability. Imbalance responses in cylindrical mode are presented up to 44,000rpm with different supply pressures. As the supply pressure is increased from 2.67 to 4 bar, the bearing stiffness increases slightly, resulting in slightly larger vibration (and reduced damping ratio) during the trans-critical speed operation. Hydrodynamic instability was observed with whirl frequency ratios of about 0.17∼0.2 depending on the supply pressures. Tests were also conducted to investigate the effect of supply pressure on the rotordynamic stability. The test results show that the hybrid operation is very effective to suppress the subsynchronous vibrations at high speeds.

Measurements of Static and Dynamic Load Performance of a 102 MM Carbon-Graphite Porous Surface Tilting-Pad Gas Journal Bearing

2021 ◽  
Author(s):  
Luis San Andres ◽  
Jing Yang ◽  
Ryan McGowan
Keyword(s):  
Dynamic Load ◽  
Load Capacity ◽  
Stable Operation ◽  
Specific Load ◽  
Damping Coefficients ◽  
Supply Pressure ◽  
Air Supply ◽  
Frequency Independent ◽  
Stiffness And Damping ◽  
Gas Bearing

Abstract Aerostatic journal bearings with porous tilting pads enable shaft support with minute drag power losses. To date archival information on the static and dynamic load performance of this bearing type is scant. Thus, the paper presents measurements conducted with an air bearing with diameter 102 mm and comprising four tilting pads made of porous carbon-graphite, each with length = 76 mm. At ambient temperature of 21°C, as the air supply pressure into the bearing pads increases, so does the bearing aerostatic specific load that reaches 58% of the pressure difference. With a supply pressure of 7.8 bar(a), the test bearing static stiffness = 13.1 MN/m, is independent of both shaft speed and static load. While operating with shaft speeds = 6 krpm and 9 krpm and under specific loads to 115 kPa and 101 kPa respectively, dynamic load experiments with excitation frequencies up to 342 Hz show the test bearing supplied with air at 7.8 bar(a) has frequency independent stiffness and damping coefficients. For rotor speeds equaling 0, 6 and 9 krpm, the bearing direct stiffnesses range from 13.6 MN/m to 32.7 MN/m as the specific load increases from 0 kPa to 115 kPa. The direct damping coefficients are as large as 5.8 kN·s/m. The test porous gas bearing reached its intended load capacity, demonstrated a dynamically stable operation and produced force coefficients mainly affected by the pads' pivot supports and the magnitude of air supply pressurization.

Floating Ring Balance Analysis of Journal Floating Ring Hybrid Bearing in Turbulent Regime

2014 ◽  
Vol 672-674 ◽  
pp. 1637-1641
Author(s):  
Hong Guo ◽  
Shao Lin Zhang
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Flow Equation ◽  
Radial Clearance ◽  
Speed Ratio ◽  
Turbulent Regime ◽  
Shaft Speed ◽  
Eccentricity Ratio ◽  
Pressure Boundary Condition ◽  
Balance Analysis

An externally pressurized deep/shallow pockets hybrid journal floating ring bearing compensated by flat capillary restrictor which can meet the need of high speed rotating machinery is presented in this paper. Bases on turbulent flow theory, the equations governing the flow of inner and outer fluid film in the journal floating ring bearing are established. The control equations together with the pressure boundary condition and the restrictor flow equation are solved by using the Finite Element Method. The balance of floating ring is achieved by adjusting ring-to-shaft speed ratio, inner film radial clearance and inner film eccentricity ratio. It can be seen from simulation results that the ring-to-shaft speed ratio and inner film clearance vary slightly and the floating ring can keep balance under different speed and eccentricity ratio. The variation of static and dynamic performance with eccentricity and rotational speed are calculated and analyzed based on floating ring balance.

Analytical and Experimental Study of Hydroinertia Gas Bearings for Micromachine Gas Turbines

2005 ◽  
Author(s):  
Kousuke Isomura ◽  
Shin-ichi Togo ◽  
Kousuke Hikichi ◽  
Satoshi Goto ◽  
Shuji Tanaka
Keyword(s):  
Gas Turbine ◽  
Gas Turbines ◽  
High Speed ◽  
Load Capacity ◽  
Stable Operation ◽  
Test Rig ◽  
Suction Force ◽  
Gas Bearings ◽  
Bearing Stiffness ◽  
Gas Bearing

Hydro-inertia gas bearing is a type of static air bearing, which supports the rotor by suction force generated by supersonic flow in large bearing clearance [1]. A tool to analyze the flow inside the clearance of hydroinertia gas bearings have been developed, and validated by experiment. A tool to estimate the load capacity and the bearing stiffness of the hydroinertia gas bearing based on experimental data has also been developed. A micro spinner test rig has been fabricated to test an hydroinertia gas bearings designed by the developed tools, and stable operation of 4mm diameter shaft at 1,200,000 rpm has successfully been achieved. A micro-high-speed bearing test rig to test a rotor for micromachine gas turbine has been designed and fabricated. Current micromachine gas turbine’s configuration requires a rotor with 10mm diameter compressor and turbine impellers on each end of 4mm diameter shaft to operate stably at 870,000rpm. Based on the achievement of stable operation at the high-speed of 1,200,000 rpm, hydro-inertia gas bearing has been selected as a candidate for both the bearings for micromachine gas turbine. Currently, the rotor speed as high as 770,000rpm has been achieved in this test rig.

Design Characteristics of an Aerodynamic Foil Bearing With Adaptable Bore Clearance

2018 ◽  
Author(s):  
Hossein Sadri ◽  
Henning Schlums ◽  
Michael Sinapius
Keyword(s):  
Gas Turbines ◽  
High Speed ◽  
Load Capacity ◽  
Functional Model ◽  
Operating Conditions ◽  
Radial Clearance ◽  
Static Properties ◽  
Advantages And Disadvantages ◽  
Aerodynamic Pressure ◽  
Foil Bearing

Aerodynamic foil bearings are suitable to support light, high-speed rotors under extreme operating conditions such as very low or very high temperatures, e.g. in cooling turbines, small gas turbines or exhaust gas turbochargers. The required bearing load capacity is generated by an aerodynamic pressure build-up in the corresponding lubrication gap. Due to the high dependence of the bearing performance on the bore geometry, the rotordynamic behavior (e.g. bearing stability) and static properties (e.g. load capacity) as a function of radial clearance and hydrodynamic preload are one of the main points of interest in recent studies. The outcome of both the experimental and the numerical investigations show the advantages and disadvantages of the various configurations of the bearing bore in different operating conditions. These observations lead to the basic idea of an adaptive air foil bearing (AAFB) in which, depending on the operating conditions, the bearing bore contour is changed by means of piezoelectric actuators applied to the compliant supporting shell. Similar to other shape morphing approaches, optimization with regard to various components of the mechanism is the next step in the design process after targeting the design pattern. This paper concentrates on an AAFB as an efficient approach to actively shape the contour of the bore clearance in a 3-pad bearing. Numerous FEM analyses of a functional model for an AAFB in addition to the experimental efforts reveal the main concerns of the design. Finally, the result of this study is a working graph for the AAFB under various loading conditions while operating with different input voltages of the actuators.

Novel Approach for Optical Characterization of Thrust Collar Lubricated Area: Experimental and Numerical Results

2020 ◽  
Author(s):  
Thomas Kerr ◽  
Adolfo Delgado
Keyword(s):  
High Speed ◽  
Pressure Field ◽  
Load Capacity ◽  
Fe Model ◽  
Cfd Model ◽  
Axial Loads ◽  
Test Rig ◽  
Efficient Operation ◽  
Oil Film ◽  
All Speeds

Abstract Thrust collars (TCs) are bearing elements used in geared machinery that transmit axial loads from one shaft to another. TCs are primarily used in integrally geared compressors (IGCs), but are also found in gearboxes and marine propulsion applications. TCs are hydrodynamic elements featuring a converging-diverging wedge to generate a pressure field that reacts axial loads. Accurate modeling requires knowledge of the film characteristics such as cavitation, turbulence, and air ingestion, all of which reduce load capacity. Current models in the literature do not include mass-conserving cavitation algorithms or turbulent flow. The following paper introduces a new test rig that optically characterizes the thin film region of a thrust collar. The test rig geometries, speeds, and loads match those typically seen in IGC applications. The test rig utilizes a transparent acrylic window in conjunction with a high-speed camera to obtain high-speed images of the oil film. Images are filtered and averaged to obtain areas of interest in the oil film. Cavitation and turbulence areas are captured for pinion speeds of 2.5, 5, and 7.5 krpm, and axial loads of 0.5, 1, and 1.5 kN. Cavitation occurs in the diverging (upper) region of the TC and appears at pinion speeds over 5,000 rpm, but does not change in shape after that speed. The cavitation is independent of applied load. Turbulence at the inlet region (bottom) occurs at all speeds, but increases to almost 35% of the total area at the highest speed. This paper also presents a finite element (FE) model that includes predictions for the static characteristics of the TC, specifically the cavitation area. The cavitation modeling uses an iterative Elord’s method, which conserves mass. The model predicts a similar cavitation area for all speeds and loads. A computation fluid dynamics (CFD) study predicts a similar cavitation area, and pressure field to the FE model. The CFD model predicts turbulence in the lower region that increases for increasing spin speed, which matches the experimental results. The CFD model tends to underpredict the turbulence area when compared to the experiments. As IGCs move into novel application areas to satisfy new needs, the increase in efficiency and capacity comes at a cost of more load and higher speed requirements on the TCs. This work will help original equipment manufacturers model TCs more accurately to ensure safe and efficient operation.

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