1. 1 Luis San Andres, Mast-Childs Professor Arian Vistahmer, Research Assistant Turbomachinery Laboratory Texas A&M University 8th IFToMM International Conference on Rotordynamics September 12-15, 2010, KIST, Seoul, Korea NONLINEAR ROTORDYNAMICS OF VEHICLE TURBOCHARGERS: PARAMETERS AFFECTING SUB HARMONIC WHIRL FREQUENCIES AND THEIR JUMP Paper P1113

2. 2 Increase internal combustion (IC) engine power output by forcing more air into cylinder Aid in producing smaller, more fuel-efficient engines with larger power outputs Turbochargers

3. 3 RBS Fully Floating Bearing RBS Semi Floating Bearing RBS Ball Bearing RBS: TC Rotor Bearing System(s) Increased IC engine performance & efficiency demands of robust & turbocharging solutions The driver:

4. 4 Bearing types Shaft Ball Bearing Squeeze Film Inner Race Locking Pin Outer Race Ball-Bearing Shaft Inner Film Outer Film Oil Feed Hole Floating Ring Locking Pin Semi-Floating Ring Bearing (SFRB) Floating Ring Bearing (FRB) Low shaft motion Relatively expensive Limited lifespan Economic Longer life span Prone to subsynchronous whirl

5. 5 Major challenges: extreme operating conditions - Low Oil Viscosity, e.g. 0W30 or 0W20 - High Oil Temperature (up to 150°C) - Low HTHS (2.9); Low Oil Pressure (1 bar) - Increased Maximum Turbocharger Speed - Variable Geometry Turbo Technology & Assisted e-power start up - High Engine Vibration Level - More Stringent Noise Requirements Water Need predictive too to reduce costly engine test stand qualification

6. 6 TC linear and nonlinear rotordynamic codes – GUI based – including engine induced excitations Realistic bearing models: thermohydrodynamic Novel methods to estimate imbalance distribution and shaft temperatures NL analysis for frequency jumps and noise reduction Measure ring speeds with fiber optic sensors Literature: San Andres and students Predictive tool for shaft motion benchmarked by test data 2004IMEchE J. Eng. Tribology 2005ASME J. Vibrations and Acoustics ASME DETC 2003/VIB-48418 ASME DETC 2003/VIB-48419 2007ASME J. Eng. Gas Turbines Power ASME GT 2006-90873 2007ASME J. Eng. Gas Turbines Power ASME GT 2005-68177 2007ASME J. Tribology IJTC 2006-12001 2007ASME DETC2007-34136 2010ASME J. Eng. Gas Turbines Power ASME GT2009-59108 2010IFToMM Korea

7. 7 ASME DETC2007-34136 Subsynchronous Components Synchronous Component Measured at compressor end Predicted at compressor end WATERFALLs of SHAFT MOTION TC testing: expensive and time consuming Predictive tool saves time and money Benchmarked against test data

8. 8 TC technical issue: frequency jump Shaft accelerates Top speed ~180 krpm (3 kHz) Oil inlet temp= 30  C Oil inlet pressure = 4 bar Jump from 1 st to the 2 nd subsynchronous whirl frequency increases TC noise Waterfall of center housing acceleration Objective: Study the bearing parameters and rotor characteristics affecting the frequency jump Rotor Speed Frequency (Hz) Bifurcation speed ~105 krpm (1.75 kHz) Mode 2: Cylindrical 22 3131 2222 Synchronous: 1X  11 Mode 1: Conical 2121  bifurcation =2  1 +  2 Jump

9. 9 Literature Review Noah and Sundararajan (1995 ) rotors supported on fluid film bearing display highly nonlinear behavior which linear analysis cannot predict Wang and Khonsari (2006) bifurcations: subcritical and supercritical, hysteresis evident in subcritical bifurcation Muszynska (1998) attributes hysteresis to fluid mean circumferential velocity (smaller during rotor acceleration than deceleration) Yamamoto (2001) and Nayfeh (1989 ) nonlinearities responsible for internal and combined resonances. These phenomena can couple the natural modes of a system and cause the exchange of energy among the natural modes Schweizer and Sievert (2009) note frequency jump in measured response, rotor supported on FRBs. Increased inlet pressure delays  bifurcation. Increased imbalance amount results in disappearance of the 2 nd subsynch whirl at high shaft speeds (~ 130 krpm) + OEM proprietary data show frequency jump

10. 10 Development of software for prediction of (semi) floating ring bearing (S-FRB) static and dynamic forced response XLBRG Tool EXCEL & Fortran FEM code for prediction of FRBs and SFRBs forced response (static and dynamic ) Finite length bearing model with global thermal balance and shear thinning effects Interface to XLTRC 2 software for rotordynamics analysis THD Model of Semi-Floating Ring Bearings

11. 11 Models for fluid films - Balance of drag torques from outer and inner oil films - Thermal energy transport (heat conduction & convection) Ring Housing Shaft Inner oil film Outer oil film Y Outer film pressure, Po Inner film pressure, Pi Film thickness: X Reynolds Equations 2004 IMEchE J. Eng. Tribology

12. 12 Lumped Parameter Thermal Model shaft bearing Inner film Outer film Mechanical power by fluid shearing P ~ Torque x Rot Speed Inner film Temp Rise Outer film Temp Rise Oil energy increase ~ Heat flow Sp Heat x Mass flow x Temperature Difference Floating ring Energy convected to solids and conducted through shaft, ring and bearing 2004 IMEchE J. Eng. Tribology

13. 13 XL BRG ®: types of bearings shaft ring Oil inlet, P s, T S Half- moon groove Straight feed hole ring Oil inlet, P s, T S shaft Oil supply – outboard side Oil supply in bearing Types of oil supply Figures NOT to scale

14. 14 XLTRC² Rotordynamics Virtual Tool Beam Finite-Element Formulation Real Component-Mode Synthesis (CMS) model Multi-line Rotor/Housing Modeling Capability Linear and transient response nonlinear analyses Fully integrated with an extensive suite of support codes User-Friendly GUIs for rapid model development and report generation Integration of FRB and SFRB codes into nonlinear rotordynamics program Rotor-Bearing structural model General EOMs

15. 15 Finite Element Model for turbocharger structure Shaft: 43 elements, bearing: 13 elements Turbine and comp wheels as lumped inertias 4-plane imbalance distribution Bearing models fully integrated (instantaneous reaction forces) Shaft speed 30 krpm (500 Hz)-240 krpm (4,000 Hz) Rotor model in XLTRC 2 ™ SFRB Compressor Turbine Rotor C.G. Axial location Shaft radius Compressor bearing Turbine bearing

16. 16 Damped Natural Frequencies (Linear Eigenvalue Analysis) Damped natural frequencies Mode shapes at 95 krpm C T C T C T  =0.68  =0.24  =-0.09  =-0.05  =0.30 1 st elastic mode Conical, SFRB conical mode Cylindrical bending, SFRB cylindrical mode Conical mode Cylindrical bending mode C T C T 1X 75 krpm 50 krpm 2 nd mode unstable 3rd mode unstable Conical, SFRB conical Cylindrical bending, SFRB cylindrical Damping ratio

17. 17 Nonlinear Rotordynamic Analysis sampling time=100  s Ramp Rate Δf Time Segment Duration Time Steps per Segment Total Integration Time Number of Time Segments Total # of Time Steps Total CPU Time for Speed Transient [Hz/s][Hz][s]- -[hr]  500 4.880.55,0007.01470,000~9.0 Baseline Case Shaft speed 30 krpm (500 Hz) -240 krpm (4,000 Hz) Oil inlet pressure = 3.6 bar Oil inlet temperature = 120  C Speed ramp rate = 500 Hz/s Imbalance distribution = Static (in-phase) # FFT points = 2 11 (2,048)

18. 18 Linear and Nonlinear Synchronous Response Preds. Discrepancies between linear and nonlinear responses due to large ring and shaft displacements (predicted by nonlinear response). Linear analysis assumes small amplitude motions Nonlinear fixed rotor speed analysis 500 Hz/s Nonlinear rotor speed transient analysis Linear rotordynamic analysis 45 krpm 110 krpm 49 krpm Compressor end

19. 19 Frequency (Hz) 1000 2000 3000 4000 30 krpm Horizontal direction Vertical direction Baseline Case Waterfalls of shaft motion (compressor end) Contour map Jump at 182 krpm (ramp down) Max speed, 240 krpm Jump at 165 krpm (ramp up) 1X ω1ω1 ω2ω2 Oil 3.6 bar, 120  C, 500 Hz/s

20. 20 Total shaft motion between 20% and 40% of max physical limit independent of rotor acceleration or deceleration Up & down at 500 Hz/s Baseline Case Total shaft motion (compressor end) Oil 3.6 bar, 120  C, 500 Hz/s

21. 21 Rotor accelerates (500 Hz/s) Rotor decelerates (-500 Hz/s) @ Ωb= 165krpm (2.75kHz) 5ω1 ~ 4ω2 3ω1 + ω2~ Ωb ω2 = 815 Hz Ωb= 165krpm Cylindrical bending rotor filtered whirling mode C T ω1 = 654 Hz Ωb= 165krpm Conical rotor filtered whirling mode C T JUMP 165 krpm JUMP 182 krpm UP @ Ωb=182krpm (~3kHz) 5ω1 ~ 4ω2 2ω1 + 2ω2~ Ωb DOWN ω2 = 845 Hz Ωb= 182krpm C T Cylindrical bending rotor filtered whirling mode ω1 = 674 Hz Ωb= 182krpm C T Conical rotor filtered whirling mode 0.1 (-) Baseline Case Subsynchronous frequency & amplitude vs shaft speed

22. 22 Rotor accelerates Whirl frequency at  bifurcation ~ ¼ rotor speed Baseline Case Rotor whirl frequency ratio (WFR) vs speed Oil 3.6 bar, 120  C, 500 Hz/s

23. 23 Nonlinear rotordynamic analyses Parameters varied: Oil inlet pressure = 3.6 bar (nominal), reduce by 33% Oil inlet temperature = 120  C, T low 120  C Bearing inner length increase by 15% Speed ramp rates = 250 Hz/s, 500 Hz/s, 750 Hz/s Imbalance distribution = Static (in-phase)Opposed couple Turbine-back-out-of-phase (TBOP)

24. 24 Effect of oil supply temperature Rotor subsynchronous frequency & amplitude versus shaft speed Rotor accelerates Oil 3.6 bar, T> 120  C, 500 Hz/s Bifurcation speed Oil inlet temperature

25. 25 Effect of oil temperature on frequency jump 30  C, 4 bar 100  C, 4 bar Waterfalls of center housing acceleration Bifurcation speed Bifurcation speed~ 1800 Hz (108 Krpm)  threshold ~2  1 +  2 Bifurcation speed 1400Hz (84 krpm) Oil inlet temperature * Provided by HTT test data*

26. 26 Effect of shaft speed ramp rate During rotor acceleration, increasing speed ramp rate delays onset of  bifurcation Higher speed ramp rate increases hysteresis in  bifurcation between speed ramp up and ramp down cases Rotor decelerates -750 Hz/s Rotor accelerates +750 Hz/s Rotor subsynchronous frequency & amplitude vs speed

27. 27 Effect of imbalance distribution Rotor accelerates Total shaft motion TBOP imbalance reduces total amplitude of shaft motion 160 krpm Subsynchronous motions disappear Rotor subsynchronous frequency & amplitude vs speed Oil 3.6 bar, 120  C, 500 Hz/s

28. 28 Effect of imbalance amount In TBOP imbalance distribution subsynch whirl motions disappear at ~ 100 krpm  No jump Rotor accelerates Synchronous motion only Imbalance amount doubled Total shaft motion Amplitude of synch response increases Rotor subsynchronous frequency & amplitude vs speed Oil 3.6 bar, 120  C, 500 Hz/s Double amount

29. 29 Effect of imbalance on frequency jump Waterfalls of center housing acceleration Low imbalance amount 100  C, 4 bar Increased imbalance amount Imbalance amount 2 nd subsynch whirl disappears No frequency jump * Provided by HTT test data*

30. 30 Summary of internal and combined resonances Case  b (Hz) ω 1 (Hz) ω 2 (Hz) Internal relation Combined relation Baseline (up  ) 2,7506548155ω 1 ~4ω 2 3ω 1 +ω 2 ~  b Baseline (down ) 3,0306748455ω 1 ~4ω 2 2ω 1 +2ω 2 ~  b Reduced Pressure (up)1,9804937323ω 1 ~2ω 2 ω 1 +2ω 2 ~  b Reduced Pressure (down)2,0005087323ω 1 ~2ω 2 ω 1 +2ω 2 ~  b Reduced Temperature (up)2,7506848205ω 1 ~4ω 2 N/A Reduced Temperature (down)2,7206598205ω 1 ~4ω 2 3ω 1 +ω 2 ~  b Increased Temperature (up)2,5006208014ω 1 ~3ω 2 N/A Increased Temperature (down)3,0306458404ω 1 ~3ω 2 2ω 1 +2ω 2 ~  b Increased Inner Length (up)2,700762786N/A Increased Inner Length (down)2,720762796N/A Low Acceleration (+250Hz/s)2,5006358404ω 1 ~3ω 2 N/A Low Deceleration (-250Hz/s)2,6206458114ω 1 ~3ω 2 N/A High Acceleration (+750Hz/s)3,1207138506ω 1 ~5ω 2 2ω 1 +2ω 2 ~  b High Deceleration (-750Hz/s)2,1505527863ω 1 ~2ω 2 ω 1 +2ω 2 ~  b Opposed Couple Imb Dist. (up)3,0006548404ω 1 ~3ω 2 2ω 1 +2ω 2 ~  b Opposed Couple Imb Dist. (down)2,4206017764ω 1 ~3ω 2 N/A TBOP Imb Dist. (up)2,5005917914ω 1 ~3ω 2 3ω 1 +ω 2 ~  b TBOP Imb Dist. (down)2,0005137573ω 1 ~2ω 2 ω 1 +2ω 2 ~  b Linear combination of whirl frequencies at jump frequency (shaft speed)

31. 31 ramp rate hysteresis in  bifurcation Conclusions Oil inlet pressure = 3.6 bar (nominal), reduce by 33% Oil inlet temperature = 120  C, T low 120  C Bearing inner length increase by 15% Speed ramp rates = 250 Hz/s, 500 Hz/s, 750 Hz/s Imbalance distribution = P supply delays  bifurcation T supply  bifurcation, multiple jumps No jump, smooth transition For TBOP imbalance, 2 nd whirl (ω 2 ) disappears Static (in-phase)Opposed couple Turbine-back-out-of-phase (TBOP)

32. 32 Other conclusions Total amplitude of motion reduces for TBOP imbalance. Large imbalances increases the synchronous amplitude motions, and at times, favor the disappearance or attenuation of large amplitude subsynchronous whirl motions. Qualitative agreement between test data (reported by HTT and Schweizer) and nonlinear predictions Linear rotordynamics analyses cannot predict the large amplitude, multiple-frequency responses obtained with the nonlinear analysis Test data (by Schweizer & Sievert) and predictions show a raise in supply pressure delays  bifurcation. Also, supply temp  bifurcation. An increase in speed ramp rate delays  bifurcation Study further the effect of bearing clearances, ring rotation, lubricant type, and bearing outer film length on frequency jump phenomenon. Validate predictions (quantitative comparison) against test data. Recommendations

33. 33 Acknowledgements Learn more at http://rotorlab.tamu.edu Honeywell Turbocharging Technologies (2000-2008), Dr. Kostandin Gjika TAMU Turbomachinery Laboratory Turbomachinery Research Consortium (XLTRC 2® ) KIST Energy Mechanics RC Questions?