DAMPING AND INERTIA COEFFICIENTS FOR TWO END SEALED SUEEZE FILM DAMPERS WITH A CENTRAL GROOVE: MEASUREMENTS AND PREDICTIONS

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1 2013 ASME Turbo Expo Conference, June , San Antonio, TX, USA DAMPING AND INERTIA COEFFICIENTS FOR TWO END SEALED SUEEZE FILM DAMPERS WITH A CENTRAL GROOVE: MEASUREMENTS AND PREDICTIONS Luis San Andrés Mast-Childs Professor, Fellow ASME Texas A&M University Sanjeev Seshagiri Mechanical Engineer VYCON Inc, Cerritos, CA ASME Accepted for journal publication Supported by Pratt & Whitney Engines (UTC) 1

2 SFD operation & design Squeeze film dampers aid to attenuate rotor vibrations, suppress rotor instabilities and provide mechanical isolation Pinned SFD Y X Too little damping may not be enough to reduce vibrations. Too much damping may lock damper & will degrade system rotordynamic performance 2

3 End sealed & grooved SFD Shaft Oil inlet Groove Piston rings Ball bearing reports dynamic pressures in the central groove and shows groove does not isolate the film lands but contributes to increase dynamic fluid film reaction force. Film land Lubricant under pressure fills in the central groove and film lands. Piston rings seal lubricant exit path to ambient and produce large dynamic pressures.. 3

4 P&W SFD Test Rig Isometric view Electromagnetic shaker (Y direction) Static loader Electromagnetic shaker (X direction) Top view Shaker in Y direction Static loader Shaker in X direction SFD test bearing 4

5 Test rig description shaker Y Static loader Static loader shaker X Shaker Y Y Shaker X X SFD SFD Y Y Static loader base Base Support support rods F Y F s X X F X 5

6 SFD bearing design features Test Journal Circumferential groove Bearing Cartridge Flexural Rod (4, 8, 12) Pedestal Piston ring seal Supply orifices (3) Main support rod (4) Journal Base Geometry of SFD Journal diameter: 127 mm (5.0 inch) Film clearance: 0.127mm (5 mil) Max. Land length: 2 x 25.4 mm (2 x 1 inch) Support stiffness: MN/m ( klb f /in) End conditions: Open and sealed with piston rings in in in in 6

7 Flow through squeeze film lands Oil inlet Leakage across piston rings in ISO VG 2 oil Oil inlet temperature, T s = 25 o C Density, ρ = 785 kg/m 3 Viscosity μ at T s = 2.96 cpoise Flow rate, Q in = 1.4 LPM 7

8 Objective & tasks Evaluate dynamic load performance of a grooved SFD with end seals and compare to test results from open ends SFD. Dynamic load measurements with sealed ends SFD: circular orbits (centered and off centered) shows test SFD force coefficients for small amplitude orbits are indifferent to the type of motion (circular 1:1 or elliptical 5:1). Y Y c static load 45 o X X r e S =0 e S centered and offcentered circular orbits 8

9 Piston ring end seals Reduce lubricant side leakage, raise film dynamic pressures, increase the damping coefficient, and also reduce air ingestion. Leakage Journal Housing Lubricant Film Piston rings Piston ring design as a damper end seal is highly empirical.

10 SFD configurations tested Geometry & oil properties for sealed ends SFD Short SFD (B) Long SFD (A) Journal diameter, D 127 mm Land length, L 12.7 mm 25.4 mm Radial clearance, c C B = mm C A = mm Groove axial length, L G 12.7 mm Depth, d G 9.5 mm Oil wetted length, 2L + L G 38.1 mm 63.5 mm Support stiffness Ks = 18.7 MN/m Max. static load (976N), Max. amplitude dynamic load (2,240 N) Range of excitation frequencies: Hz (short), Hz (long) Re s c 2 = in film lands 0.76 bar (0.52 bar open ends) Groove static pressure, P G Oil inlet temperature, T s 25 o C Lubricant ISO VG 2 Density, ρ 785 kg/m 3 Viscosity μ at T s 2.96 cpoise 4.69 bar (0.72 bar open ends) Flow rate, Q in 1.32 LPM 1.40 LPM 10

11 Parameter Identification Y X x y 2 x ax y a 2 Y Cross-coupled Measured by displacement sensors Measured by accelerometer Direct Direct Journal also moves during excitation of the bearing *SFDs do not have stiffnesses,i.e., no reaction forces due to changes in static displacement Direct Direct Cross-coupled 11

12 Parameter Identification Single frequency circular orbits Applied Loads Two linearly independent load vectors F 1 and F 2 F F FX cos( t) F X i t Re e 1 1 FY sin( t) if Y 2 2 FX cos( t) F X i t Re e 2 2 FY sin( t) if Y CW CCW Y X Y X displacements & accelerations z x () t X e 1 1 y () t Y i t 1 a 2 a z x () t X 2 e 2 y () t Y i t Load F, displacement z and accelerations a recorded at each frequency 12

13 Parameter Identification EOMs (2 DoF) time domain BC M a+ M M z K K z+ C +C z F s SFD s SFD s SFD EOM (Frequency Domain) 2 i K s KSFD C s +CSFD MSFD Ms z FM F MBC a Impedance function H (ω) Physical model H z z F M FM H H H F F z z XX XY M M HYX H YY 2 XX XX XX XX XX Re( ) ; Im( ) H K M H C 13

14 Parameter Identification IVF Method* Flexibility G H 1 function G (ω) = transfer functions (displacement/force) IVFM solution Iteration on weighed least squares to minimize the estimation error in: GH=I+e SFD force coefficients (K, C, M) SFD = (K, C, M) (K, C, M) S SFD coefficients Test system Support structure * Instrumental Variable Filter Method (IVFM) (Fritzen, 1986, J.Vib, 108) Measurement errors affect little identified parameters 14

15 Typ. impedances- lubricated SFD H YY C YY Short SFD e S =0; r =0.05c B DRY system tests show there is no contribution of piston rings to the support structure (stiffness & damping). Physical model Re(H XX )= K- 2 M and Im(H XX )=C reproduce test data. Damping C is constant over the frequency range 15

16 SFD force coeffs classical theory Assumes a centered journal (e s =0), full film, open ends. Ignores the effect of central groove & end seals. Damping 3 tanh L * * * R C CXX CYY 2 12π L 1 D c L D Inertia 3 * * * π LR M MXX MYY 2 1 c Stiffness K XX = K YY = K XY = K YX = 0 tanh L D L D * Y X *SFD fluid film does not generate stiffnesses 16

17 Normalization of force coefficients Force coefficients presented in comparison with predictions from classical theory: C C * M * C M M Long damper L=25.4mm, c = mm Short damper L= 12.7mm, c = mm C* A = 6.80 kn.s/m, M* A = 2.99 kg C* B = 0.92 kn.s/m, M* B = 0.38 kg Ratio ~ (L/c) 3 ~ 8 Experimental identification procedure shows NO cross-coupled coefficients for test SFD. 17

18 Experimental SFD force coefficients sealed ends short length damper 12.7 mm lands, c= mm mm Journal 12.7 mm 12.7 mm 18

19 SFD direct coefficients vs. static eccentricity Y XX, C YY c es 45 o X M XX, M YY C XX ~C YY and M XX ~M YY nearly invariant with static eccentricity. Short SFD (12.7 mm lands, c B =0.138 mm) Amplitude of motion, r = 7.5µm19 Maximum e S = 0.36c

20 SFD direct coefficients Comparison with open ends damper C XX, C YY 3.5 times more damping from sealed ends SFD. Twice the added mass from sealed ends SFD. M XX, M YY Test coefficients much larger than simple theory. Short SFD (12.7 mm lands, c B =0.138 mm) 20

21 Experimental SFD force coefficients sealed ends long damper 25.4 mm lands, c=0.141 mm mm Journal 25.4 mm 25.4 mm 21

22 SFD direct coefficients vs. static eccentricity Y XX, C YY c es 45 o X C XX ~C YY and M XX ~ M YY invariant with static eccentricity. M XX, M YY Long SFD (25.4 mm lands, c A =0.141 mm) Amplitude of motion, r = 7.6µm Maximum e S ~ 0.35c 22

23 SFD direct coefficients Comparison with open ends damper XX, C YY M XX, M YY 2.7 times more damping and 2.6 times more added mass from sealed ends SFD. Test coefficients much larger than simple theory. Long SFD (25.4 mm lands, c B =0.141 mm) 23

24 Dynamic film pressures Piezoelectric pressure sensor (PCB) locations Side view: Sensors located at middle plane of film lands Bearing Cartridge PCB groove PCB top land PCB bottom land Piezoelectric sensors: 2 in top land, 2 in bottom land 2 in groove 24

25 Dynamic pressures: films & groove Whirl frequency 80 Hz film lands Number of time periods groove 0 0 Top and bottom film lands show similar pressures. Larger pressures than with open ends SFD. Dynamic pressure in the groove is as large as in the film lands* Long SFD: e s =0, r=0.054c A, P G = 4.69 bar *A groove PCB sensor is located closer to the seal ring slit than the other, hence the difference in pressures 25

26 Dynamic pressures: films & groove Whirl frequency 250 Hz film lands Number of time periods groove Number of time periods 0 Film and groove dynamic pressures increase with excitation frequency. Seal rings prevent air ingestion even at high frequency, evidenced by noise-free pressure waves. Long SFD. e s =0, r=0.055c A. P G = 4.69 bar 26

27 Peak-peak dynamic film pressures Long damper with end seals Piezoelectric pressure sensor (PCB) location Bearing Cartridge groove groove top land bottom land Peak-peak pressures are twice as large as those in open ends damper. Pressures in groove are as large as those in the film lands. Mid-plane 27

28 Comparisons to predictions from a modern model 28

29 Model SFD with a central groove SFD geometry and nomenclature Lubricant in orifice Bearing do Uses effective depth d = Xc Lubricant in dg groove LG L c : clearance film land End seal Lubricant out Journal z D, diameter recirculation zone Solve modified Reynolds equation (with fluid inertia) d Effective groove depth separation line streamline Lubricant out 2 3 P P 3 2 h h 12 h h h 2 R R z z t t Model uses experimentally derived end seals flow conductance. * San Andrés & Delgado, GT

30 Damping coefficients Short SFD Predicted coefficients agree well with test data, with gradual increase with static eccentricity C XX ~C YY Test coefficients are ~ larger than simple formula (open ends). circular orbits r/c =

31 Inertia coefficients Short SFD Predictions match well the test data. Inertia coefficients are ~ constant with static eccentricity. Predicted M XX = M YY Test M XX > M YY at low e S Static eccentricity (e/c) Test coefficients are ~ larger than simple formulas. circular orbits r/c =

32 Damping coefficients Long SFD Predicted coefficients increase with static eccentricity and agree well with test data. Test coefficients are ~ 8-10 larger than simple formula (open ends). circular orbits r/c =

33 Inertia coefficients Long SFD Inertia coefficients under predicted by 25%. Predicted coefficients are constant with static eccentricity (e S ). Test coefficients are ~ higher than simple open end SFD formula. circular orbits r/c =

34 Conclusions The piston rings are effective end seals reducing through flow, increasing damping and preventing air ingestion. Sealed short length damper has ~4 times more damping and twice the added mass as the open ends short damper. The sealed long damper shows ~ 3 times more damping and added mass than the open ends SFD. Dynamic pressures in the groove are as large as in the lands. Predicted coefficients agree well with test values for the sealed short damper. The added mass coefficients are under predicted by 25% for the long sealed damper Conventional knowledge = classical lub. formulas deliver too little damping and too small inertia. 34

35 Acknowledgments Thanks to Pratt & Whitney Engines students Paola Mahecha, Adolfo Delgado, Shraddha Sangelkar, Sara Froneberger, Brian Butler, Logan Havel, James Law. Questions (?) Learn more at 35

36 Relevant Past Work Della Pietra and Adilleta, 2002, The Squeeze Film Damper over Four Decades of Investigations. Part I: Characteristics and Operating Features, Shock Vib. Dig, (2002), 34(1), pp. 3-26, Part II: Rotordynamic Analyses with Rigid and Flexible Rotors, Shock Vib. Dig., (2002), 34(2), pp Zeidan, F., L. San Andrés, and J. Vance, 1996, "Design and Application of Squeeze Film Dampers in Rotating Machinery," Proceedings of the 25th Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, September, pp Zeidan, F., 1995, "Application of Squeeze Film Dampers", Turbomachinery International, Vol. 11, September/October, pp Vance, J., 1988, "Rotordynamics of Turbomachinery," John Wiley and Sons, New York Parameter identification: Tiwari, R., Lees, A.W., Friswell, M.I Identification of Dynamic Bearing Parameters: A Review, The Shock and Vibration Digest, 36, pp

37 TAMU references SFDs 2012 San Andrés, L., 2012, Damping and Inertia Coefficients for Two Open Ends Squeeze Film Dampers with A Central Groove: Measurements and Predictions, ASME J.Eng Gas Turbines Power, Vol. 134 (10), p (ASME Paper No. ) 2011 San Andrés, L., and Delgado, A., A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically, ASME Paper GT Delgado, A., and San Andrés, L., 2010, A Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Grooved Oil Seal Rings, ASME Journal of Tribology Vol Delgado, D., and San Andrés, L., 2010, Identification of Squeeze Film Damper Force Coefficients from Multiple- Frequency, Non-Circular Journal Motions, ASME J. Eng. Gas Turbines Power, Vol. 132 (April), p (ASME Paper No. GT ) 2009 Delgado, A., and San Andrés, L., 2009, Nonlinear Identification of Mechanical Parameters on a Squeeze Film Damper with Integral Mechanical Seal, ASME Journal of Engineering for Gas Turbines and Power, Vol. 131 (4), pp (ASME Paper GT ) 1997 Arauz, G., and L. San Andrés, 1997 "Experimental Force Response of a Grooved Squeeze Film Damper," Tribology International, Vol. 30, 1, pp San Andrés, L., 1996, "Theoretical and Experimental Comparisons for Damping Coefficients of a Short Length Open-End Squeeze Film Damper," ASME Journal of Engineering for Gas Turbines and Power, Vol. 118, 4, pp

38 Select effective groove depth Predictions overlaid with test data to estimate effective groove depth Short sealed ends SFD Long sealed ends SFD d η + c B = 3.5 c B d η + c A = 3.5 c A d η = 2.5c B d η = 2c A 38

39 End seal flow conductance Side leakage (flow rate)= C SEAL pressure ( D) Q T Hydraulic network Q R TS R TL R BL Q=Q T +Q B R BS Q B Short SFD Long SFD C SEAL = 5.83 x (m 2 /s)/pa C SEAL = 6.25 x (m 2 /s)/pa 39