33rd Turbomachinery Research Consortium Meeting On the Forced Performance of a SFD Operating with Large Amplitude Orbital Motions: Measurements and Assessment of the Accuracy of the Linearized Force Coefficients Model TRC-SFD-01-2013 Luis San Andrés Mast-Childs Professor Sung-Hwa Jeung Graduate Research Assistant May 2013 TRC Project 32513/1519SF Linear Nonlinear Force Coefficients for SFDs

SFD with a central groove Lubricant supplied into a circumferential groove feeds uniformly the squeeze film lands. Feed groove oil inlet Whirl motion from the journal squeezes the lubricant film and generates dynamic pressures that aid to damp the rotor vibrations Typical squeeze film damper (SFD) with a central groove [1] Conventional knowledge regards a groove as indifferent to the kinematics of journal motion, thus effectively isolating the adjacent film lands.

SFD Test Rig – cut section in Bearing Cartridge Test Journal Main support rod (4) Journal Base Pedestal Piston ring seal (location) Flexural Rod (4, 8, 12) Circumferential groove Supply orifices (3)

Geometry (three feed holes 120o apart) SFD Test Rig – cut section Geometry (three feed holes 120o apart) Journal Diameter, D 12.7 cm (5.0 in) Land Length, LF 2.54 cm (1.0 in) Radial Land Clearance, c 251 μm (9.9 mil) Damper Axial Length (two lands + groove), L 6.35 cm (2.5 in) Feed orifice Diameter, ϕ 2.54 mm (0.1 inch) Central Groove Groove Axial length, LG 1.27 cm (0.5 inch) Groove Depth, dG 0.96 cm (0.38 inch)

Lubricant flow path ISO VG 2 oil Oil inlet Lubricant properties (ISO VG 2 ) Supply temperature, Tin 25 °C (77 °F) Lubricant viscosity @ Tin , μ 2.96 cP Lubricant density, ρ 785 kg/m3 (49 lb/ft3)

Funded TRC (2012-13) $ 28,470 Test damper with dynamic loads (20-300 Hz) inducing off-centered elliptical orbital motions to reach 0.8c. Identify SFD force coefficients from test impedances, and correlate coefficients with linear force coefficients and experimental coefficients for smallest whirl amplitude (0.05c). Perform numerical experiments, similar to the physical tests, to extract linearized SFD force coefficients from the nonlinear forces. Quantify goodness of linear-nonlinear representation from an equivalence in mechanical energy dissipation. Predictions: Effect of groove on SFD forced performance 6

Tests conducted Evaluate SFD dynamic force coefficients from Excitation frequencies 10 – 100 Hz Evaluate SFD dynamic force coefficients from Circular orbit journal motions with orbit amplitudes (r) from 8% to 71% of radial clearance (c). Static journal eccentricity (e) to 76% of radial clearance (c). Max. clearance (c) : 251 μm Y es = 0.76 c es = 0.51 c es = 0.25 c es= 0 c Y Displacement [μm] X X Displacement [μm]

Parameter identification procedure Step 1 : Model system (2-DOF) F Shaker force EOM: Time Domain KL CL ML EOM: Frequency Domain Measured variables: Unknown Parameters: KL, CL, ML SFD coefficients (K, C, M)SFD = (K, C,M)L – (K, C, M)S SFD Test system (lubricated) Structure

Test SFD damping coefficients Y X = 0 c = 0.25 c = 0.51 c = 0.76 c (eS/c) eS=0.76c eS=0.51c eS=0.25c eS=0.0c CXX SFD CXX ~CYY Findings: SFD damping coefficients increase with increasing orbit amplitude and static eccentricity. CXX increases dramatically above r/c > 50%

Test SFD added mass coefficients Y X = 0 c = 0.25 c = 0.51 c = 0.76 c MXX SFD eS=0.76c eS=0.51c eS=0.25c eS=0.0c (eS/c) MXX ~MYY Findings: SFD added mass coefficients increase with increasing static eccentricity; but decrease with increasing orbit amplitude. MXX decreases dramatically above r/c>50%

SFD effective force coefficients For circular orbits (only), SFD forces reduce to Y -Fradial rw X r -Ftangential

-Keff Test SFD effective stiffness es/c=0.0 structure es/c=0.0 Findings: SFD effective stiffness decreases with increasing excitation frequency and with orbit amplitude (a fluid inertia effect).

Ceff Test SFD effective damping es/c=0.0 Findings: SFD effective damping increases with orbit amplitude. Little dependency with frequency.

Pressure sensors in housing 14

Film dynamic pressure profiles Central groove Film lands es/c=0.0, 100 Hz Magnitude of peak pressure increases with orbit amplitude. Top and bottom film lands show similar pressures. Dynamic pressure in the groove is not nil. Air ingestion region

Film dynamic pressure profiles A uniform pressure zone indicates air entrainment.

Model SFD with a central groove SFD geometry and nomenclature Use effective depth Solve modified Reynolds equation (with temporal fluid inertia) h : fluid film thickness P : hydrodynamic pressure μ : lubricant viscosity R : journal radius

Damping: predictions and test data Y 45o c for small size orbits (r/c=0.08). predictions agree with test coefficients until es=0.5 c. At es/c=0.76 predictions are too large (~28%) es X classical theory (1.2 kN.s/m) Test data much larger than simple theory CXX Prediction Test data CYY Model by San Andres (2011)

Added mass: predictions & test data Y 45o classical theory (1.67 kg) es c X Model predictions agree well with experimental results. Predicted added masses increase slightly with static eccentricity Test data much larger than simple theory MXX Prediction Test data MYY Model by San Andres (2011)

Over a full period of motion SFD mechanical energy dissipation SFD reaction forces Actual force Linearized force Mechanical work Over a full period of motion

Work=Energy dissipation 100 Hz EDIS<0 is negative work = energy dissipated by SFD Findings: SFD work increases with increasing orbit amplitude.

Mechanical energy difference 100 Hz 0~5% ~23% Findings: Energy difference increases with increasing static eccentricity and orbit amplitude. For r/c≤0.4 and es/c≤0.25, Ediff < ~5%

Conclusions From circular orbit tests Goodness of linear force model (a) SFD damping coefficients increase with increasing orbit amplitude and static eccentricity. (b) SFD added mass coefficients increase with increasing static eccentricity and decrease with increasing orbit amplitude. Predictions correlate very well with test results for static eccentricity es<0.5c and deviate with increasing orbit amplitude and static eccentricity. Goodness of linear force model By means of comparing mechanical work in a period of motion; for r/c≤0.4 and es/c≤0.25, linearized SFD forced parameters represent well the actual SFD system TRC-SFD-01-2013

2013 proposal to TRC Justification Ultra-short SFD (L/D < 0.2) Aircraft engines must endure sudden maneuver loads (blade loss event, etc.) Large size grinding machines require quick dissipation of mechanical energy from sudden plunging motions (tool contacts the working piece, etc.) Ultra-short SFD (L/D < 0.2) save space & weight; with lighter lubricants to save fuel and reduce contamination; and with tighter clearances because of better materials & manufacturing.

2013 proposal to TRC Objectives Conduct experiments to characterize the forced response of a short length SFD (L/D=0.2) with sudden loads (400 lbf max). Build predictive tool to simulate SFD dynamic forced performance. Record SFD forced performance due to sudden impulsive loads (amplitude and time varying). Sudden load

TRC Budget 2013-2014 Year III 2013-2014 Year III $ 40,666 Support for graduate student (20 h/week) x $ 2,200 x 12 months $ 26,400 Fringe benefits (0.6%) and medical insurance ($197/month) $ 2,378 Travel to (US) technical conference $ 1,200 Tuition & fees three semesters ($227/credit hour) $ 8,688 Machine components and data storage $ 2,000 2013-2014 Year III $ 40,666 The TAMU SFD research program is the most renown in the world. The proposed research is of interest of SFD applications in gas turbines, hydrodynamic bearings in compressors, cutting tool and grinding machines.

Thank you Questions (?) Acknowledgments Learn more at Thanks to TAMU Turbomachinery Research & Pratt & Whitney Engines Questions (?) Learn more at http://rotorlab.tamu.edu 27