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ISROMAC-12 Luis San Andres Mast-Childs Professor February 2008 Issues on Stability, Forced Nonlinear Response and Control in Gas Bearing Supported Rotors for Oil- Free Microturbomachinery Turbomachinery Laboratory, Mechanical Engineering Department Texas A&M University (http://phn.tamu.edu/TRIBGroup) The Twelfth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery

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Microturbomachinery as per IGTI ASME Paper No. GT2002-30404 Honeywell, Hydrogen and Fuel Cells Merit Review Automotive turbochargers, turbo expanders, compressors, Distributed power (Hybrid Gas turbine & Fuel Cell), Hybrid vehicles Drivers: deregulation in distributed power, environmental needs, increased reliability & efficiency International Gas Turbine Institute Max. Power ~ 250 kWatt

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Micro Gas Turbines MANUFACTURER OUTPUT POWER (kW) Bowman 25, 80 Capstone 30, 60, 200 Elliott Energy Systems 35, 60, 80, 150 General Electric 175 Ingersoll Rand 70, 250 Turbec, ABB & Volvo 100 Microturbine Power Conversion Technology Review, ORNL/TM-2003/74. Cogeneration systems with high efficiency Multiple fuels (best if free) 99.99X% Reliability Low emissions Reduced maintenance Lower lifecycle cost 60kW MGT www.microturbine.com Hybrid System : MGT with Fuel Cell can reach efficiency > 60% Ideal to replace reciprocating engines. Low footprint desirable

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Largest power to weight ratio, Compact & low # of parts High energy density Reliability and efficiency, Low maintenance Extreme temperature and pressure Environmentally safe (low emissions) Lower lifecycle cost ($ kW) High speed Materials Manufacturing Processes & Cycles Fuels Rotordynamics & (Oil-free) Bearings & Sealing Coatings: surface conditioning for low friction and wear Ceramic rotors and components Automated agile processes Cost & number Low-NOx combustors for liquid & gas fuels TH scaling (low Reynolds #) Best if free (bio-fuels) MTM – Needs, Hurdles & Issues Proven technologies with engineering analysis (anchored to test data) available for ready deployment

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Gas Bearings for Oil-Free Turbomachinery Thrust at TAMU : Investigate bearings of low cost, easy to manufacture (common materials), easy to install & align. Predictable Performance a must! Combine hybrid (hydrostatic/hydrodynamic) bearings with low cost coating for rub-free operation at start up and shut down. Major issues: Little damping, Wear at start & stop, Instability (whirl & hammer) / Nonlinearity Passenger vehicle turbocharger

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Gas Bearings for Oil Free Turbomachinery Gas Foil Bearings Advantages: high load capacity (>20 psig), tolerance of misalignment and shocks, high temperature capability with advanced coatings

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Simple elastic foundation model Heavy load, ASME J. Eng. Gas Turbines Power, 2008, 130; and high speed operation, ASME J. Tribol., 2006, 128. Finite element flat shell top foil models. 1D and 2D structural models, GT 2007-27249 Note sagging of top foil between bumps P/Pa W Uniform elastic foundation With top foil bending Top Foil Model: 2D Finite Elements Fast PC codes couple foil structure to gas film hydrodynamics – GUI driven

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Accuracy of Foil Bearing Model Predictions Prediction Shutdown Test data Startup Test data Prediction KIST test data (2003) Benchmarked computational model! Static load: 52 N Rotor speed decreases Driving motor Shutdowns Prediction 10,000 cycles Test data: 5,000 cycles AIAA-2007-5094

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Example 1: Subsynchronous motions Subsynchronous amplitude recorded during rotor speed coastdown from 132 krpm (2,200 Hz) Whirl amplitude remains ~ constant as subsynchronous frequency drops from 350 Hz to 180 Hz Heshmat (1994) - Maximum speed 132 krpm, i.e. 4.61 ×10 6 DN. - Stable limit cycle operation but with large amplitude subsynchronous motions. Whirl frequency tracks rotor speed

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Example 2: Subsynchronous motions Heshmat (2000) Flexible rotor- GFB system operation to 85 krpm (1.4 kHz): 1 st bending critical speed:34 krpm (560 Hz) Waterfall plot recorded during rotor speed coastdown test from 45 krpm (750 Hz) Rotor orbit shape at 45k rpm Large amplitude limit cycle motions above bending critical speed, whirl frequency = natural frequency (rigid body)

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Lee et al. (2003, 04): Flexible rotor supported on GFBs with viscoelastic layer Example 3: Subsynchronous motions Viscoelastic layer eliminates large motions at natural frequency & appearing above 1 st bending critical speed. 50 kRPM (833 Hz) Bump type GFB Viscoelastic GFB Synchronous vibration 1st bending mode Rigid body mode Bump type GFB Viscoelastic GFB Synchronous vibration

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Foil Bearing Test Rig Driving motor (1HP, 50 krpm) Flexible coupling Optical Tachometer Start motor (2HP, 25 krpm) Foil bearing housing Electro magnet loader Test rotor Centrifugal clutch (Engaged at ~50 krpm) Cluth shoes Spring Wear ring Ω Shaft Diameter = 1.500” mass = 2.2 lb

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Amplitudes of subsynchronous motions INCREASE as imbalance increases ( forced nonlinearity ) Example 4: TAMU test rig Speed (-) Imbalance + u = 7.4 μmu = 10.5 μm 26 krpm Limit cycle : large subsync motions aggravated by imbalance

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Example 4: TAMU test rig Large amplitudes locked at natural frequency (50 krpm to 27 krpm) …… but stable limit cycle! Rotor speed decreases

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Overview – GFB computational models All GFB models predict (linearized) rotordynamic force coefficients. No model readily available to predict nonlinear rotordynamic forced response What causes the subsynchronous motions? What causes the excitation of natural frequency?

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Foil Bearing: stiffness & dissipation FB structure is non linear (stiffness hardening), a typical source of sub harmonic motions for large (dynamic) loads. Hysteresis loop gives energy dissipation Kim and San Andrés (2007): Eight cyclic load - unload structural tests Loading Unloading F ≠ K X

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Simple FB model allows quick nonlinear rotordynamic predictions F = X (0.0675 -0.002 X + 0.0001 X2 ) Test data Prediction FB structural model AIAA-2007-5094

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Predicted nonlinear rotor motions Rotor speed: 30 →1.2 krpm (600 →20 Hz) Imbalance displacement, u = 12 μm (Vertical motion) Subsynchronous ( sub harmonic ) whirl motions of large amplitude AIAA-2007-5094 Major assumption – gas film of infinite stiffness

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Comparison to test measurements Rotor drive end, vertical plane. Structural loss factor, γ =0.14. Subsynchronous whirl frequencies concentrate in a narrow band around natural frequency (132 Hz) of test system. Large amplitude subsync motions cannot be predicted using linear rotordynamic analyses. Synchronous motions Test data Predictions Sync. and Subsync. Amplitudes Amplitude vs. whirl frequency Test data Predictions Frequency (Hz) AIAA-2007-5094

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WHIRL FREQUENCY RATIO Predictions and measurements show bifurcation of nonlinear response into distinctive whirl frequency ratios (1/2 & 1/3) Test data (San Andres et al, 2006) Predictions Test data (Kim and San Andres et al, 2007) Rotor speed (krpm ) Comparison to test data AIAA-2007-5094

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FB structure is highly non linear, i.e. stiffness hardening: a common source of sub harmonic motions for large (dynamic) loads. Subsynchronous frequencies track shaft speed at ~ ½ to 1/3 whirl ratios, locking at system natural frequency. Model predictions agree well with rotor response measurements (Duffing oscillator with multiple frequency response). Gas Foil Bearings Closure 1

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-FEED AIR PRESSURE: 40 kPa [6 psig] - 340 kPa [50 psig] AIR SUPPLY Rotordynamic tests with bearing side pressurization IJTC2007-44047 Typically foil bearings DO not require pressurization. Cooling flow needed for thermal management to remove heat from drag or to reduce thermal gradients in hot/cold engine sections Axial flow retards evolution of mean circumferential flow velocity within GFB, as in an annular seal

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Onset of subsynchronous whirl motions Rotor onset speed of subsyn- chronous whirl increases as side feed pressure increases (a) 0.35 bar (b) 1.4 bar (c) 2.8 bar Synchronous Subsynchronous N OS : 25 krpm N OS : 30.5 krpm N OS : 27 krpm

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FFT of shaft motions at 30 krpm (a) 0.35 bar (b) 1.4 bar (c) 2.8 bar Whirl frequency locks at rigid body natural frequency ( not affected by level of feed pressure For Ps ≥ 2.8 bar rotor subsync. whirl motions disappear; (stable rotor response) ω sub = 132 Hz ω sub = 147 Hz ω sub = 127 Hz Subsynchronous ω syn = 508 Hz Synchronous

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Original GFB Shimmed GFB Gas Foil Bearing with Metal Shims Original GFB Inserting metal shims underneath bump strips introduces a preload (centering stiffness) at low cost – typical industrial practice

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Original GFBs 0.35 bar (5 psig) Amplitude (μm) Rotor speed (krpm) Amplitude (μm, 0-pk) Frequency (Hz) Shimmed GFBs 0.35 bar (5 psig) Rotor speed (krpm) Amplitude (μm, 0-pk) Amplitude (μm) Frequency (Hz) Gas Foil Bearing with Metal Shims

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Rotor-bearing modeling Normalized 1X amplitudes: Predictions reproduce test measurements with great fidelity 0.35 bar (5 psig) XL2DFEFOILBEAR predicts synchronous bearing force coefficients Original GFBs Shimmed GFBs Imbalance increases by 1,2,3

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Validation of predicted force coeffs. Original GFBs Effective stiffness vs. measurement location Good agreement between predicted coefficients and GFB stiffness and damping estimated at natural frequency (10 krpm) Effective damping vs. measurement location Test dataPredictionsTest dataPredictions Imbalance masses: 55mg,110mg, 165mg 0.35 bar (5 psig)

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Predictions Test data Predictions Test data Stiffness vs. Frequency Damping vs. Frequency MTM GFB: 1X dynamic force coefficients 2008 Gen III GFB prediction tool developed by TAMU for MTM OEM Predictions agree with experimental dynamic force coefficients for Generation III Foil Bearing !

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Predictive foil bearing FE model (structure + gas film) benchmarked by test data. (Cooling) end side pressure reduces amplitude of whirl motions (+ stable) Preloads (shims) increase bearing stiffness and raise onset speed of subsync. whirl. Predicted rotor 1X response and GFB force coefficients agree well with measurements. Gas Foil Bearings Closure 2

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Gas Bearings for Oil Free Turbomachinery Flexure Pivot Bearings Advantages: Promote stability, eliminate pivot wear, engineered product with many commercial appls.

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Positioning Bolt LOP Rotor/motorBearingSensorsLoad cell Air supply Thrust pin Gas Bearing Test Rig

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As Pressure supply increases, critical speed raises and damping ratio decreases Displacements at RB(H) LOP 20 psig 40 psig 60 psig Effect of feed pressure on rotor response Question: If shaft speed regulates feed pressure, could large rotor motions be suppressed ?

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Coast down rotor speed vs time ~ 2 minute Long time rotor coast down speed: exponential decay, typical of viscous drag 2.36 bar 210 rpm/s Speed region for control of feed pressure

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Cheap Control of Bearing Stiffness Automatic adjustment of supply pressure

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Control of Feed Pressure into Gas Bearings Step increase in supply pressure Displacements at RB(H) 5.08 bar 2.36 bar Blue line: Coast down Red line: Set speed 2.36 bar 5.08 bar Rotor peak amplitude is completely eliminated by sudden increase in supply pressure

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Test & predicted rotor responses TESTPREDICT Excellent correlation – Reliable Predictive model !

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Flexure Pivot Hydrostatic Gas Bearings Closure: Stable to 99 krpm! Supply pressure stiffens gas bearings and raises rotor critical speeds, though also reducing system modal damping. CHEAP Feed pressure control of bearing stiffness eliminates critical speeds (reduce amplitude motions)! Models predict well rotor response; even for large amplitude motions and with controlled supply pressure!

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Dominant challenge for gas bearing technology Current research focuses on coatings (materials), rotordynamics (stability) & high temperature (thermal management ) –Bearing design & manufacturing process better known. Load capacity needs minute clearances since gas viscosity is low. –Damping & rotor stability are crucial –Inexpensive coatings to reduce drag and wear at low speeds and transient rubs at high speeds –Engineered thermal management to extend operating envelope to high temperatures Need Low Cost & Long Life Solution!

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Acknowledgments Thanks to Students Tae-Ho Kim. Dario Rubio, Anthony Breedlove, Keun Ryu, Chad Jarrett NSF ( Grant # 0322925 ) NASA GRC ( Program NNH06ZEA001N-SSRW2 ), Capstone Turbines, Inc., Honeywell Turbocharging Systems, Foster-Miller, & TAMU Turbomachinery Research Consortium (TRC) To learn more visit: http://phn.tamu.edu/TRIBGroup

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BACK UP SLIDES

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Funded by 2003-2007: NSF, TRC, Honeywell 2007-2009: NASA GRC, Capstone MT, TRC, Honeywell Research in Gas Foil Bearings Current work: experimentally validated predictive model for high temperature gas foil bearings

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Ideal gas bearings for MTM (< 0.25 MW ) Simple – low cost, small geometry, low part count, constructed from common materials, manufactured with elementary methods. Load Tolerant – capable of handling both normal and extreme bearing loads without compromising the integrity of the rotor system. High Rotor Speeds – no specific speed limit (such as DN) restricting shaft sizes. Small Power losses. Good Dynamic Properties – predictable and repeatable stiffness and damping over a wide temperature range. Reliable – capable of operation without significant wear or required maintenance, able to tolerate extended storage and handling without performance degradation. +++ Modeling/Analysis (anchored to test data) readily available

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Series of corrugated foil structures (bumps) assembled within a bearing sleeve. Integrate a hydrodynamic gas film in series with one or more structural layers. Applications: ACMs, micro gas turbines, turbo expanders Reliable with load capacity to 100 psi) & high temperature Tolerant to misalignment and debris Need coatings to reduce friction at start-up & shutdown Damping from dry-friction and operation with limit cycles Gas Foil Bearings – Bump type

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Test Gas Foil Bearing Generation II. Diameter: 38.1 mm 5 circ x 5 axial strip layers, each with 5 bumps (0.38 mm height) Reference: DellaCorte (2000) Rule of Thumb Test Bump-Type Foil Bearing

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Oil-Free Bearings for Turbomachinery Justification Current advancements in automotive turbochargers and midsize gas turbines need of proven gas bearing technology to procure compact units with improved efficiency in an oil-free environment. DOE, DARPA, NASA interests range from applications as portable fuel cells (< 60 kW) in microengines to midsize gas turbines (< 250 kW) for distributed power and hybrid vehicles. Gas Bearings allow weight reduction, energy and complexity savings higher cavity temperatures, without needs for cooling air improved overall engine efficiency

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FB viscous damping OR dry friction –Dynamic load (Fo) from 4 - 20 N, –Test temperatures from 25°C to ~115°C F = F o cos(w.t) x Eq. Viscous Damping [N.s/m] Frequency [Hz] F o increases T = 25ºC Friction coefficient, m Frequency [Hz] F o increases San Andres et al., 2007, ASME J. Eng. Gas Turbines Power Viscous damping reduces with frequency. Natural frequency easily excited at super critical speed

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Simple elastic foundation model Heavy load, ASME J. Eng. Gas Turbines Power, 2008, 130; and high speed operation, ASME J. Tribol., 2006, 128. Finite element flat shell top foil models. 1D and 2D structural models, GT 2007-27249 Test data, Ruscitto, et al. 1978 (mid plane) Prediction (edge, 2D) Prediction (mid plane, 2D) Test data, Ruscitto, et al. 1978 (edge) Prediction (1D) Prediction (simple model) Top Foil Model: 2D Finite Elements

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EOMs: rigid rotor & in-phase imbalance condition Assumption: minute gas film with infinite stiffness x y Rotor motions Li & Flowers, AIAA 96-1596 Equations of motion

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Equations of Rotor Motion Numerical integration of EOMs for increasing rotor speeds to 36 krpm (600 Hz), with imbalance (u) identical to that in experiments. Natural frequency of rotor-GFB system for small amplitude motions about SEP: Solutions obtained in a few seconds. Post- processing filters motions and finds synchronous and subsynchronous motions = 132 Hz

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Comparison to test measurements Rotor drive end, vertical plane. Structural loss factor, γ =0.14. Good agreement between predictions to test data. Large amplitude subsynchronous motions cannot be predicted using linear rotordynamic analyses. Synchronous motions Test data Predictions Test data Predictions Subsynchronous motions Sync. and Subsync. Amplitudes

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Amplitude & Frequency of Subsync. Motions Comparison to test data Rotor drive end, vertical plane. Structural loss factor, γ =0.14. Subsynchronous whirl frequencies concentrate in a narrow band enclosing natural frequency (132 Hz) of test system Amplitude vs. frequency Frequency vs. rotor speed Test data Predictions Test data Predictions Rotor speed (krpm) Frequency (Hz)

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Model & Tests: Stability vs feed pressure 30 krpm operation Stability analysis: threshold speed of instability in good agreement with test data (onset speed of subsynchronous motion ) Prediction Test data

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Side feed pressure: 60 psig (4.1 bar) External pressurization reduces dramatically the amplitude of subsynchronous rotor motions. 1.4 bar 4.1 bar 2.8 bar 0.34 bar Side pressure increases Amplitude (μm, 0-pk) Whirl frequency (Hz) Rotor speed (krpm) Frequency (Hz) Amplitude (μm) Shimmed GFB Waterfall responses: Shimmed GFBs with side pressurization

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MTM bearing: prediction vs. test data * Bearing prediction tool (Computer software & GUI) developed for MTM OEM Structural static coefficients Predictions agree with identified static load performance of Micro Gas Turbine Foil Bearings! Displacement vs. load Test data 3 Test data 1 Loading Test data 2 Unloading Loading Prediction

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