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ISROMAC-12

ISROMAC-12. February 2008. The Twelfth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery. Issues on Stability, Forced Nonlinear Response and Control in Gas Bearing Supported Rotors for Oil-Free Microturbomachinery. Luis San Andres Mast-Childs Professor.

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ISROMAC-12

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

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

  3. Micro Gas Turbines 60kW MGT www.microturbine.com 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 Hybrid System : MGT with Fuel Cell can reach efficiency > 60% Ideal to replace reciprocating engines. Low footprint desirable

  4. MTM – Needs, Hurdles & Issues 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) Proven technologies with engineering analysis (anchored to test data) available for ready deployment

  5. Gas Bearings for Oil-Free Turbomachinery Thrust at TAMU: Investigatebearings 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. Passenger vehicle turbocharger Major issues:Little damping, Wear at start & stop, Instability (whirl & hammer) / Nonlinearity

  6. 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

  7. Top Foil Model: 2D Finite Elements W 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 With top foil bending Uniform elastic foundation Fast PC codes couple foil structure to gas film hydrodynamics – GUI driven P/Pa Note sagging of top foil between bumps

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

  9. Example 1: Subsynchronous motions Whirl amplitude remains ~ constant as subsynchronous frequency drops from 350 Hz to 180 Hz Heshmat (1994) - Maximum speed 132 krpm, i.e. 4.61 ×106 DN. - Stable limit cycle operation but with large amplitude subsynchronous motions. Whirl frequency tracks rotor speed Subsynchronous amplitude recorded during rotor speed coastdown from 132 krpm (2,200 Hz)

  10. Example 2: Subsynchronous motions Rotor orbit shape at 45k rpm Waterfall plot recorded during rotor speed coastdown test from45 krpm (750 Hz) Heshmat (2000) Flexible rotor- GFB system operation to 85 krpm (1.4 kHz): 1st bending critical speed:34 krpm (560 Hz) Large amplitude limit cycle motions above bending critical speed, whirl frequency = natural frequency (rigid body)

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

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

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

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

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

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

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

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

  19. Test data Sync. and Subsync. Amplitudes Test data Predictions Predictions Comparison to test measurements Rotor drive end, vertical plane. Structural loss factor, γ=0.14. AIAA-2007-5094 Amplitude vs. whirl frequency Synchronous motions Frequency (Hz) 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.

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

  21. Gas Foil Bearings Closure 1 • 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).

  22. Rotordynamic tests with bearing side pressurization -FEED AIR PRESSURE:40 kPa [6 psig] - 340 kPa [50 psig] 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 AIR SUPPLY Axial flow retards evolution of mean circumferential flow velocity within GFB, as in an annular seal

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

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

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

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

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

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

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

  30. Gas Foil Bearings Closure 2 • 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 coefficientsagree well with measurements.

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

  32. Gas Bearing Test Rig Rotor/motor Load cell Bearing Sensors Thrust pin Air supply Positioning Bolt LOP

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

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

  35. Cheap Control of Bearing Stiffness Automatic adjustment of supply pressure

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

  37. Test & predicted rotor responses TEST PREDICT Excellent correlation – Reliable Predictive model !

  38. 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!

  39. Dominant challenge for gas bearing technology • 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 • Engineeredthermal managementto extend operating envelope to high temperatures Current research focuses on coatings (materials), rotordynamics (stability) & high temperature (thermal management) Need Low Cost & Long Life Solution!

  40. 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

  41. BACK UP SLIDES

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

  43. Ideal gas bearingsfor MTM(< 0.25 MW ) Load Tolerant – capable of handling both normal and extreme bearing loads without compromising the integrity of the rotor system. Simple – low cost, small geometry, low part count, constructed from common materials, manufactured with elementary methods. 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

  44. Gas Foil Bearings – Bump type • 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

  45. Test Bump-Type Foil Bearing Reference:DellaCorte (2000) Rule of Thumb 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)

  46. 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

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

  48. Top Foil Model: 2D Finite Elements Test data, Ruscitto, et al. 1978 (mid plane) Prediction (mid plane, 2D) Prediction (1D) Prediction (simple model) Test data, Ruscitto, et al. 1978 (edge) Prediction (edge, 2D) 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

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

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

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