1. GT2009-59175 SFD Force Coefficients- Multiple Frequency I DENTIFICATION of SQUEEZE FILM DAMPER FORCE C OEFFICIENTS from MULTIPLE-FREQUENCY NON-CIRCULAR JOURNAL MOTIONS ASME GT2009-59175 Luis San Andrés Mast-Childs Professor Texas A&M University Adolfo Delgado Mechanical Engineer GE Global Research Center Supported by TAMU Turbomachinery Research Consortium 2009 ASME Turbo Expo Conference, June 2009 accepted for journal publication

2. GT2009-59175 SFD Force Coefficients- Multiple Frequency  housing journal lubricant film shaft ball bearing anti-rotation pin Typical squeeze film damper (SFD) configuration In aircraft gas turbines and compressors, squeeze film dampers aid to attenuate rotor vibrations and to provide mechanical isolation. Too little damping may not be enough to reduce vibrations. Too much damping may lock damper & degrades system rotordynamic performance SFD Operation & Design Issues In a SFD, the journal whirls but does not spin. The lubricant film is squeezed due to rotor motions, and fluid film (damping) forces are generated as a function of the journal velocity.

3. GT2009-59175 SFD Force Coefficients- Multiple Frequency  housing journal lubricant film shaft ball bearing anti-rotation pin Typical squeeze film damper (SFD) configuration SFD Operation & Design Issues Damper performance depends on a)Geometry (L, D, c) b)Lubricant (density, viscosity) c)Supply pressure and through flow d)Sealing devices e)Operating speed (frequency) Flow regimes: (laminar, superlaminar, turbulent) Type of lubricant cavitation: gaseous or vapor air ingestion & entrapment

4. GT2009-59175 SFD Force Coefficients- Multiple Frequency Intershaft dampers are subject to whirl motions resulting from the combined imbalance response of both the LP and the HP shafts. In multi-spool engines, intershaft dampers are located in the interface between rotating shafts Intershaft Dampers Schematic view of intershaft [*] Objective: to investigate the forced performance of SFD for non-circular motions with multi-frequencies [*] Gupta K., and Chatterjee S., 2007, “Dynamics of an Improved Inter Shaft Squeeze Film Damper: Theory and Experiment,” ASME paper No. GT2007- 27534. LP shaft HP shaft Multiple frequency excitation.

5. GT2009-59175 SFD Force Coefficients- Multiple Frequency Intershaft SFDs Della Pietra and Adilleta (2002): Comprehensive review of research conducted on SFDs over last 40 years. (1975) Hibner (1991) Al-Shafei (2008) Defaye et al. Parameter identification in SFDs: Tiwari et al. (2004): Comprehensive review of parameter identification in fluid film bearings. (1986) Roberts et al, (1990) Ellis et al., (1999) Diaz and San Andrés (2006-2008) San Andrés and Delgado (SFD & MECHANICAL SEAL) Relevant Past Work GT 2006-91238, GT 2007-24736, GT 2008-50528

6. GT2009-59175 SFD Force Coefficients- Multiple Frequency Bearing Assembly TRC SFD Vertical Test Rig Schematic view of test rig

7. GT2009-59175 SFD Force Coefficients- Multiple Frequency SFD bearing design Oil inlet O-rings Ring carrier Discharge groove Plexiglas Bearing Journal Housing Top plate Bottom plate Eddy current sensor O-rings Vertical plate Discharge orifice Pipe insert Shaft L=25.4 mm, D=127 mm, c=0.127 mm (5 mil) Open end configuration

8. GT2009-59175 SFD Force Coefficients- Multiple Frequency Open End Configuration Clearance c= 0.127 mm (5 mil) Diameter D = 127 mm (5 inch) Length L = 25.4 mm (1 inch) ISO VG 2 oil Flow through squeeze film land Feed plenum Inlet groove Squeeze film land Discharge groove

9. GT2009-59175 SFD Force Coefficients- Multiple Frequency Multiple frequency excitations Multiple frequency excitation force: X Displacement [  m] Y Displacement [  m] ISO VG 2 Feed pressure = 31 kPa Temperature (avg.) = 24 0 C Max. clearance: 127 mm 130 -130 65 -65 65 Low speed shaft: fixed frequency (25 Hz) + High speed shaft: sine sweep (30 Hz to 120 Hz) Three excitation vectors: Case 1 Low and high speed shafts in phase Case 2 Low and high speed shafts 90 deg out of phase Case 3 Excitation vector amplitude increases (constant amplitude response) -130

10. GT2009-59175 SFD Force Coefficients- Multiple Frequency Parameter Identification Equations of motion SFD coefficients (function of instantaneous journal eccentricity e ) Non-circular whirl motions Dissipative non-linear force function of journal position e and velocity v Added mass coefficient constant for test journal amplitudes (< 60% c ) For parameter identification only 1x component is considered (dissipates mechanical energy)

11. GT2009-59175 SFD Force Coefficients- Multiple Frequency Parameter Identification For each excitation force frequency component (sine sweep) From two independent vectors with H ii1 = H ii2 ; i=x,y Dynamic stiffnesses Damping coefficients

12. GT2009-59175 SFD Force Coefficients- Multiple Frequency Excitation Force & Displacement X Displacement [  m] Y Displacement [  m] 130 -130 65 -65 65 Clearance: 127 mm Case 1 Time trace (Force) Fixed frequencyLinear sweep Case 1: LS & HS in phase Highly elliptical motions

13. GT2009-59175 SFD Force Coefficients- Multiple Frequency [1] Delgado, A., 2008, “A Linear Fluid Inertia Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Grooved Oil Seal Rings,” Ph.D. Dissertation, December, Texas A&M University, C/S, TX. Parameter Identification Re(H xx )= K xx -M xx  2 Identification Range Dynamic stiffness Frequency spectra Displacement Force 25 Hz Identification Range Sine sweep Single Frequency + Case 1 Classical theory predicts = 2.1 kg (3 times smaller) FREQUENCY DOMAIN Parameter xx yy IdentifiedMass, (M) 16.3 kg 16.1kg Squeeze film inertia (M SFD ) 6.1 kg 5.9 kg r 2 (goodness of curve fit) 0.97 0.98 Added mass coefficient from 6.6 kg [1]

14. GT2009-59175 SFD Force Coefficients- Multiple Frequency Parameter Identification Cross-coupled coefficients negligible (No lubricant cavitation) Im(H xx /  ) Predictions (circular centered orbits) Predictions (small radial motions about an off- centered position) Damping coefficients bracketed by predictions from full film short length SFD model (open ends) Case 1 e Damping coefficient [kN.s/m] Amplitude/clearance Damping coefficient

15. GT2009-59175 SFD Force Coefficients- Multiple Frequency Excitation Force & Displacement clearance: 127 mm Case 2 X Displacement [  m] Y Displacement [  m] 130 -130 65 -65 65 Fixed frequencyLinear sweep Case 2: LS & HS out of phase Non circular whirl motions Time trace (Force)

16. GT2009-59175 SFD Force Coefficients- Multiple Frequency Parameter Identification Case 2 Frequency spectra Re(H xx )= K xx -M xx  2 Force Displacement Similar added mass coefficients as in Case 1 FREQUENCY DOMAIN Dynamic stiffness

17. GT2009-59175 SFD Force Coefficients- Multiple Frequency Parameter Identification Case 2 e Damping coefficient [kN.s/m] Amplitude/clearance For excitation loads (F x, F y ) out of phase by 90 degree, identified damping coefficients are closer to predictions for circular (centered) motions Im(H xx /  ) FREQUENCY DOMAIN Damping coefficient Case 2: LS & HS out of phase

18. GT2009-59175 SFD Force Coefficients- Multiple Frequency Excitation Force & Displacement Similar to case 2 but with increasing amplitude of excitation load Case 3 3 constant motion amplitudes ~20 um, ~40 um, ~ 60 um Case 3: LS & HS out of phase

19. GT2009-59175 SFD Force Coefficients- Multiple Frequency Damping coefficient [kN.s/m] Amplitude/clearance Linear (single) damping coefficient e Im(H xx ) ~20 um ~40 um ~ 60 um Damping coefficient Case 3: LS & HS out of phase

20. GT2009-59175 SFD Force Coefficients- Multiple Frequency SFD force coefficients could be identified for multiple- frequencies when expressed as generic functions of journal position and velocity. The motion with amplitude at main excitation frequency is one that leads to dissipation of mechanical energy. Classical SFD (open ends) model predictions: centered circular orbits and small amplitude motions about off- centered position ENCLOSE the identified damping coeffs. Novel model added mass coefficient correlates well with test data. Classical theory predicts mass coefficients 3 times smaller than test values. Large mass due to effects of inlet and discharge grooves. Conclusions:

21. GT2009-59175 SFD Force Coefficients- Multiple Frequency Thanks to TAMU Turbomachinery Research Consortium Acknowledgments Questions ? Learn more at http://phn.tamu.edu/TRIBGrouphttp://phn.tamu.edu/TRIBGroup