Proceedings of ASME Turbo Expo 2018: Turbine Technical Conference and Exposition, June 11-15, 2018, Oslo, Norway Paper GT2018-76224 EXPERIMENTAL FORCE COEFFICIENTS FOR TWO SEALED ENDS SQUEEZE FILM DAMPERS (PISTON RINGS AND O-RINGS): AN ASSESSMENT OF THEIR SIMILARITIES AND DIFFERENCES Luis San Andrés Mast-Childs Chair Professor ASME Fellow Texas A&M University Bonjin Koo Research Assistant Texas A&M University Sung-Hwa Jeung Compressor Design Engineer Compressor Technology & Development Ingersoll Rand Supported by Pratt & Whitney Engines and Turbomachinery Research Consortium Accepted for journal publication
Squeeze Film Dampers (SFDs) Anti-rotation pin Journal Lubricant film Shaft Ball bearing Housing Reduce rotor vibrations, suppress rotor instabilities, and provide mechanical isolation. Often coupled with bearings that lack damping or have too large stiffness. Too little damping may not be enough to reduce vibrations. Too much damping may lock damper & will degrade system rotordynamic performance. SFDs are designed with consideration of the entire rotor-bearing system. 2
Multiple-year research program Piston ring seals Piston ring seals To explore novel SFD designs & benchmark SFD empirical data. + Damper G (c G =373 mm(14.7 mil)) Piston ring and O-ring seals No end grooves Develop & validate SFD forced model.. Optimize SFD influence on rotor dynamics. 20+ papers 3
End seals for SFDs Reduce thru flow and increase damping. Most seal types cannot prevent air ingestion O-ring seal bearing bearing journal journal O-ring seal film film Piston ring seal bearing bearing journal journal film film End plate seal Industrial applications use O-rings, while jet engines implement piston rings (commercial). O-ring issues: Special groove machining, Material compatibility, Add visco-elastic effect. Piston ring issues: Cocking and locking Slits leak too much Design is highly empirical, except for end plate seals 4
Literature on sealed SFDs mostly experimental Miyachi et al. (1979): Damping coefficients for SFD sealed with O-rings and with piston rings. Meng et al. (1991): Tangential force and radial forces for short SFD with serrated piston ring seal (to avoid pressure distortions). Levesley and Holmes (1996): Compare performance of SFD sealed with a piston ring seal and a SFD with an end plate seal. De Santiago and San Andrés (1999): Report damping coefficients for integral- SFD with end plate seals (various gaps). Arghir and Defaye (2006): Report radial and tangential forces for a SFD with two types of piston ring seals: (a) w one slit and (b) with six openings. San Andrés and Seshagiri (2013): Quantify force coefficients in a SFD with a central feed groove and piston ring end seals. Above review spells many tests vs tests but does not aid to benchmark common seals in SFDs: O-rings vs. piston rings 5
The thrust of this paper A little about a lot. 1. Get damping and inertia coefficients for a SFD sealed with (a) O-rings and (b) piston rings (circular orbits, centered and off-centered). 2. Quantify effect of # of feed holes on SFD force coefficients. 3. Introduce a model for leakage thru PR slits. 4. Find force coefficients from film pressure measurements. 5. Show measured pressures and aspect of flow leaving damper. OR-SFD vs PR-SFD which one is better? One or more? How many for best? A PR is not a local end seal! Are these coefficients any good? Look at the oil outlet and believe! 6
SFD Test Rig Bearing mass, M BC Structure stiffness, K s damping, C s 15.2 kg 10 MN/m 0.9 kn-s/m SFD test bearing Designed and built by students at TAMU Two electro magnetic-shakers (2 kn or 550 lb f ). Static loader placed 45 o between X and Y axes. Customizable SFD test bearing. 7
PR-SFD lubricant flow path Oil inlet in Y Feedholes θ=90 Static Loader θ=45 Piston rings θ=0 X PR slit θ=345 o Oil out ISO VG 2 oil Oil inlet temperature, T s = 23 o C Density, ρ = 799 kg/m 3 Viscosity μ at T s = 2.7 cpoise 8
OR-SFD lubricant flow path Oil inlet in Feedholes Y θ=90 Static Loader θ=45 O-rings Discharge tube θ=240 θ=0 X Oil out ISO VG 2 oil Oil inlet temperature T s = 23 o C Density ρ = 799 kg/m 3 Viscosity μ at T s = 2.7 cpoise 9
SFD geometry (L/D=0.2, D/c=340) Feedholes PR-SFD Y θ=90 Feedholes OR-SFD Y θ=0 X PR slit θ=345 o θ=90 Static Loader θ=45 Journal diameter, D Axial film land length, L Radial clearance, c Feedhole diameter, f in angular location, q in OR-SFD Discharge hole diameter, f exit hole location, q exit PR-SFD slit location, q slit 127 mm 25.4 mm 0.373 mm 2.5 mm 45 o, 165 o, 285 o 1.0 mm Max. v s =rw ~ 60 mm/s Re s =(r /m)wc 2 ~65 240 o 345 o θ=0 X Discharge tube θ=240
Y Displacement [μm] Test conditions: produce circular orbits Y and evaluate SFD force coefficients. Orbits with amplitude: Max. clearance (c) r=0.01c ~0.15c Y X CW X Y CCW X X Displacement [μm] 11
Shaker force F Estimation of SFD force coefficients from measurement of forces and displacements 12
Equation of motion and SFD coefficients EOM: Time Domain K L C L M L Unknown Parameters: Test system (lubricated) K L, C L, M L Stiffness Damping Inertia EOM: Frequency Domain 2 [ L iw L w L] MBC K C M z F a Measured variables: z, F, a, M BC SFD coefficients (K,C,M) SFD = (K,C,M) L (K,C,M) S SFD Test system (lubricated) Structure 13
DRY and LUBRICATED System Estimated Parameters Bearing mass, M BC Structure stiffness, K s damping, C s 15.2 kg 10 MN/m 0.9 kn-s/m f n =131 Hz, z =0.03 14
Parameters dry system (no oil) r=0.03c Dynamic stiffness ~ K-w 2 M K OR ~1.5 MN/m Quadrature stiffness ~ w C C OR ~0.8 kn.s/m O-rings produce significant stiffness and damping, not of viscous type. 15
Parameters for lubricated system (with oil) Dynamic stiffness ~ K-w 2 M Quadrature stiffness ~ w C OR-SFD PR-SFD OR-SFD PR-SFD r=0.15c, P s =69 kpa(g) OR-SFD shows larger stiffness and damping (K,C) L-OR than PR- SFD (K,C) L-PR. Inertia coefficients for OR-SFD and PR-SFD are nearly the same. 16
Y Prediction of SFD force coefficients X Orbit-model (2016) San Andres and Jeung,.. and a major departure *San Andres, L., and Jeung,S-H, 2016, Orbit-Model Force Coefficients for Fluid Film Bearings: A Step Beyond Linearization, ASME J. Eng. Gas Turb. Pwr., 138(2) 17
Flows thru orifice and PR-slit Extended Reynolds equation for squeeze film pressure 3 3 2 2 rh P rh P rh M rh rh 12 12 12 2 k R m R z m z t m t A M sk, Inlet/outlet mass flowrate(=rq k ) A Area k: in or exit k feedhole Q C A P P 2 in in in r s qin,0, t sk, k PR slit PR-slit Q 2 C A P, L exit, t P r q exit exit exit a 4 PR flow modeled as an orifice-like. A major departure from simple practice: Q ~ C seal DP Estimated from measurements: C in ~1.0, C exit ~0.8 Feedhole area ~ 4.9 mm 2, PR slit Area~ 2 mm 2, Discharge hole area for OR-SFD~ 0.8 mm 2 18
Journal center kinetics and forces Journal motion (X vsy) bearing reaction forces (F X vs F Y ). Y Journal center orbit (µm) Y Forces (N) Specify X (t), Y (t) Solve Reynolds equation find pressure P ω X X Integrate pressure field on journal surface find Forces F X, F Y Model not restricted to small amplitude motions. Continue to complete whole orbit path. Procedure reproduces experimental one and estimates (numerically) force coefficients over a wide frequency range. 19
OR-SFD vs. PR-SFD Effect of number of open feed holes on SFD force coefficients Feedholes Piston ring (PR) Y θ=90 Static Loader θ=45 Plugged Shown next Bearing Cartridge θ=0 X Journal PR slit (q=345 o ) 20
Damping Coefficient, C [-] # of feedholes damping C SFD P s =69 kpa(g) 1.2 1 OR-SFD Prediction, 1 hole 1.2 1 PR-SFD Prediction, 1 hole 0.8 Prediction, 3 holes 0.8 0.6 0.4 0.2 3 feedholes 1 feedhole Test C XX C YY Prediction C XX =C YY 0 0.00 0.05 0.10 0.15 0.20 Orbit Amplitude (r/c) 0.6 0.4 0.2 0 Prediction, 3 holes 3 feedholes 1 feedhole Test C XX C YY Prediction C XX =C YY 0.00 0.05 0.10 0.15 0.20 Orbit Amplitude (r/c) Damper with one open feedhole produces 60% +damping than damper with three holes. For SFD with one feedhole, C PR-SFD < C OR-SFD due to air ingestion thru PR slits. 21
Added Mass Coefficient, M [-] # of feedholes inertia M SFD P s =69 kpa(g) 1.2 1 0.8 0.6 OR-SFD Prediction, 1 feedhole 1.2 1 0.8 0.6 PR-SFD Prediction, 1 hole Prediction, 3 holes 0.4 0.2 Prediction, 3 feedholes 3 feedholes 1 feedhole Test M XX M YY 0 0.00 0.05 0.10 0.15 0.20 Orbit Amplitude (r/c) Prediction M XX =M YY 0.4 0.2 3 feedholes 1 feedhole Test M XX M YY 0 0.00 0.05 0.10 0.15 0.20 Orbit Amplitude (r/c) Prediction M XX =M YY Damper with one feedhole produces + inertia (~80%) than damper with three feedholes. OR-SFD and PR-SFD produce same M. Although ends are sealed, test coefficients are 50% of long bearing model due to pressure distortions. 22
Pressure, P (bar) Predicted mid-plane (z=0) pressure field r=0.15c, w=60 Hz; P s =1 bar(g) Three feedholes Y Feedholes θ=90 Three feedholes θ=0 X PR slit θ=345 o Pressure wave distorts near feedholes One feedhole Y Feedhole θ=90 One feedhole pk-pk dynamic pressure drops Circ. coordinate, q ( o ) θ=0 X PR slit θ=345 o (C,M) SFD 23
SFD force coefficients obtained from experiments (a) Measurement of forces and displacements (benchmark) (b) Measurement of film dynamic pressures (at a fixed location) Do both methods deliver the same coefficients? 24
Forces from film dynamic pressure t Y v s =rw F t r F r b r Assumes pressure is invariant in rotating frame: X Radial and tangential forces: F P( q wt, z) P b z r L/2 2 L/2 0 ( b, z) F t sin b F P RL P (, ) cos b P R db dz r c s 1 F t s 1 Cv Ma P c 1 and P s 1 are components of pressure with fundamental frequency w. r C and M are damping and inertia coefficients for circular centered orbits. 25
Damping Coefficient, C [-] Damping Coefficient, C [-] Damping C SFD from F: forces & disp., P: pressure 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 C P at B C F C P at A Prediction 40 Hz 0 1 2 3 4 5 6 7 Supply pressure (barg) r=0.65c, v s =61 mm/s 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 C Prediction 0 1 2 3 Supply pre Forces from pressure deliver too large damping, not varying with supply pressure! Inlet orifice feedhole(s) & PR slits distort pressure field. 26
Added Mass Coefficient, M [-] Added Mass Coefficient, M [-] Inertia M SFD from F: forces & disp, P: pressure r=0.65c, v 1.4 1.4 s =61 mm/s M 1.2 P at A 1.2 1.0 1.0 0.8 0.8 Prediction 0.6 0.4 M F M P at B 0.6 0.4 0.2 0.0 Prediction 40 Hz 0 1 2 3 4 5 6 7 Supply pressure (barg) 0.2 0.0 0 1 2 3 Supply pr Forces from pressure deliver too large M that increases with supply pressure! Force/Disp procedure validates predictions. 27
SFD force coefficients (a) From forces and displacements (b) From film pressure Do both methods deliver the same coefficients? NO! Even coefficients derived from pressures at two angular locations (A&B) are different! 28
Y Film pressures and flow at the damper X discharge. prefer beer or orange juice? savor the last drop! 29
Samples of Recorded Film Dynamic Pressure bar P 225⁰ P 315 ⁰ Supply pressure increases PR slit θ=135 o Y θ=90 Feedhole θ=45 o θ=0 X Vapor cavitation Bubble collapse Air ingestion +Vapor cavitation P θ=225⁰ P θ=315⁰ Vapor cavitation P 225 ⁰ P 315⁰ No air ingestion or oil vapor Pressures show both oil vapor cavitation and large amplitude/high frequency spikes from air ingestion (bubbles collapse). Pressures are distorted & do NOT displace with whirl speed! bar 60 Hz, r=0.65c: v s ~90 mm/s Re s ~65
Discharge flow at the top side of SFD PR slit PR slit Air bubbles (foam) Scattered bubbles P s = 0.69 bar (Q s =0.8 LPM) Bubbly mixture makes a foam. (beer like) P s = 6.2 bar (Q s =2.8 LPM) Few bubbles appear. +Oil leaking thru PR slit avoids air ingestion. (orange juice like) 60 Hz, r=0.65c: v s ~90 mm/s Re s ~65 31
Conclusion OR-SFD vs PR-SFD GT2018-76224 (a) Test O-ring damper provides more damping as it avoids air ingestion. Also O-rings add stiffness and visco-elastic damping to test system. (b) For both PR-SFD and OR-SFD, the larger the # feed holes, the lower the damping coefficient. (c) Force coefficients extracted from dynamic film pressure are largely in error. Pressure field does not simply rotate! (d) Film pressures show oil vapor cavitation and persistent air ingestion for operation at a low supply pressure and/or with a large squeeze velocity (v s ). 32
Acknowledgements Thanks Pratt & Whitney Engines & Turbomachinery Research Consortium Questions (?) Cheers! Learn more at http://rotorlab.tamu.edu 33
OR-SFD vs. PR-SFD Effect of static eccentricity 0c & ¼ c on SFD force coefficients Y r= 0.15 c X 34
Damping Coefficient, C [-] Damping Coefficient, C [-] Static eccentricity (0 & 0.25c) C SFD P s =69 kpa(g) & three feed holes 1.2 1 0.8 Prediction, e s /c=0.25 OR-SFD Prediction, e s /c=0.0 1.2 1 0.8 Prediction, e s /c=0.0 PR-SFD Prediction, e s /c=0.25 0.6 0.6 0.4 Test Prediction C 0.2 XX C YY C XX =C YY e s /c=0 e 0 s /c=0.25 0.00 0.05 0.10 0.15 0.20 Orbit Amplitude (r/c) 0.4 Test Prediction C 0.2 XX C YY C XX =C YY e s /c=0 e 0 s /c=0.25 0.00 0.05 0.10 0.15 0.20 Orbit Amplitude (r/c) For PR-SFD, Damping C SFD ~ constant with eccentricity; whereas for OR-SFD, C SFD increases ~50%. Predictions OK for OR-SFD. 35
Added Mass Coefficient, M [-] Added Mass Coefficient,M [-] Static eccentricity (0 & 0.25c) M SFD P s =69 kpa(g) & three feed holes 1.2 OR-SFD 1.2 PR-SFD 1 0.8 Prediction, e s /c=0.25 Prediction, e s/c=0.0 1 0.8 Prediction, e s /c=0.0 Prediction, e s/c=0.25 0.6 0.6 0.4 0.2 Test M XX M YY Prediction M XX =M YY e s /c=0 0 e s /c=0.25 0.00 0.05 0.10 0.15 0.20 Orbit Amplitude (r/c) 0.4 0.2 Test M XX M YY Prediction M XX =M YY e s /c=0 0 e s /c=0.25 0.00 0.05 0.10 0.15 0.20 Orbit Amplitude (r/c) PR-SFD and OR-SFD show same added mass (M SFD ) not affected by static eccentricity. Predictions show the same. 36
SFD Test Rig cross section 37
End seals: Piston Rings & O-rings Reduce demand of flow or side leakage raise film dynamic pressures to increase damping while reducing air ingestion. End seals modeling is highly empirical! 38
Conclusion OR-SFD vs PR-SFD GT2018-76224 (a) Test O-ring damper provides more damping as it avoids air ingestion. Also O-rings add stiffness and visco-elastic damping to test system. (b) For both PR-SFD and OR-SFD, the larger the # feed holes, the lower the damping coefficient. (c) Damping C OR-SFD increases with static eccentricity (e s ); whereas M OR-SFD and (C,M) PR-SFD are nearly constant. (d) Force coefficients extracted from dynamic film pressure are largely in error. Pressure field does not simply rotate! (e) Film pressures show oil vapor cavitation and persistent air ingestion for operation at a low supply pressure and/or with a large squeeze velocity (v s ). 39