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Luis San Andrés Mast-Childs Professor Fellow ASME Identification of Rotordynamic Force Coefficients of a Metal Mesh Foil Bearing using Impact Load Excitations ASME GT2010-22440 Supported by TAMU Turbomachinery Research Consortium ASME J. Eng Gas Turbines & Power (in print) Thomas Abraham Chirathadam Research Assistant Texas A&M University ASME TURBO EXPO 2010, Glasgow, Scotland, UK (June 2010)

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Metal Mesh Foil Bearing (MMFB) MMFB COMPONENTS: Bearing Cartridge, Metal mesh ring and Top Foil Hydrodynamic air film develops between rotating shaft and top foil Potential applications: ACMs, micro gas turbines, turbo expanders, turbo compressors, turbo blowers, automotive turbochargers, APU Large damping (material hysteresis) offered by metal mesh Tolerant to misalignment, and applicable to a wide temperature range Suitable tribological coatings needed to reduce friction at start-up & shutdown Cartridge Metal mesh ring Top Foil

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Metal Mesh Foil Bearings (+/-) No lubrication (oil-free). NO High or Low temperature limits. Resilient structure with lots of material damping. Simple construction ( in comparison with other foil bearings) Cheap! Metal mesh tends to sag or creep over time Damping NOT viscous. Modeling difficulties Unknown rotordynamic force coefficients

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Zarzour and Vance (2000) J. Eng. Gas Turb. & Power, Vol. 122 Advantages of Metal Mesh Dampers over SFDs Capable of operating at low and high temperatures No changes in performance if soaked in oil Al-Khateeb and Vance (2001) GT-2001-0247 Test metal mesh donut and squirrel cage( in parallel) Metal Mesh damping not affected by modifying squirrel cage stiffness Choudhry and Vance (2005) Proc. GT2005 Develop design equations, empirically based, to predict structural stiffness and viscous damping coefficient METAL MESH DAMPERS provide large amounts of damping. Inexpensive. Oil-free Past work in Metal Mesh Dampers

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Past work in MMFBs San Andrés et al. (2010) J. Eng. Gas Turb. & Power, Vol. 132(3) Assembled the first prototype MMFB (L=D=28 mm). Load vs Deflection with hysteresis shows large structural damping 0.7). Frequency dependent stiffness agree with predictions. San Andrés et al. (2009) ASME GT2009-59920 Demonstrated operation to 45 krpm with early rotor lift off. Educated undergraduate students. San Andrés et al. (2009) Proc. AHS 65 th Annual Forum, May, 2009 Start and shut down to measure torque and lift-off speed. Low friction factor ~ 0.01 at high speed 60 krpm.

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MMFB assembly BEARING CARTRIDGE METAL MESH RING TOP FOIL Simple construction and assembly procedure

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MMFB dimensions and specs Dimensions and Specifications Bearing Cartridge outer diameter, D Bo (mm)58.15 Bearing Cartridge inner diameter, D Bi (mm)42.10 Bearing Axial length, L (mm)28.00 Metal mesh donut outer diameter, D MMo (mm)42.10 Metal mesh donut inner diameter, D MMi (mm)28.30 Metal mesh density, ρ MM (%)20 Top foil thickness, T tf (mm)0.127 Metal wire diameter, D W (mm)0.30 Young’s modulus of Copper, E (GPa), at 21 ºC 114 Poisson’s ratio of Copper, υ0.33 Bearing mass (Cartridge + Mesh + Foil+sensors), M (kg) 0.380 PICTURE Mesh thickness= 7 mm

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Static load vs. MMFB deflection 3 Cycles: loading & unloading Nonlinear F(X) Large hysteresis loop : Mechanical energy dissipation MMFB Structural Characteristic (wire density ~ 20%) Displacement: [-0.12,0.12] mm Load: [-120, 150 ]N Start San Andres, L., Chirathadam, T.A., and Kim, T.H., 2010, ASME J. Eng. Gas Turbines Power, 132 (3), p.032503.

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MMFB structural stiffness K=dF/dx During Load reversal : jump in structural stiffness Max. Stiffness ~ 2.5 MN/m Lower stiffness values for small displacement amplitudes MMFB Structure Characterization (wire density ~ 20%) San Andres, L., Chirathadam, T.A., and Kim, T.H., 2010, ASME J. Eng. Gas Turbines Power, 132 (3)

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Al-Khateeb & Vance model: reduction of stiffness with force magnitude (amplitude dependent) MMFB structural stiffness vs. freq. At low frequencies (25-100 Hz), stiffness decreases At higher frequencies, stiffness gradually increases Bearing stiffness is frequency and motion amplitude dependent 12.7 um 25.4 um 38.1 um Motion amplitude increases San Andres, L., Chirathadam, T.A., and Kim, T.H., 2010, ASME J. Eng. Gas Turbines Power, 132 (3)

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MMFB eq. damping vs. frequency Amplitude increases 12.7 μm 25.4 μm 38.1 μm MMFB equiv. viscous damping decreases as the excitation frequency increases and as motion amplitude increases Predicted equivalent viscous damping coefficients in good agreement with measurements San Andres, L., Chirathadam, T.A., and Kim, T.H., 2010, ASME J. Eng. Gas Turbines Power, 132 (3)

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MMFB rotordynamic test rig Max. operating speed: 75 krpm Turbocharger driven rotor Regulated air supply: 9.30bar Journal: length 55 mm, 28 mm diameter, weight=0.22 kg Journal press fitted on Shaft Stub TC cross-sectional view Twin ball bearing turbocharger Model T25 MMFB

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Journal speed and torque vs time Rotor starts Constant speed ~ 65 krpm Valve open Valve close 3 N-mm Rotor stops Applied Load: 17.8 N Manual speed up to 65 krpm, steady state operation, and deceleration to rest Startup torque ~ 110 Nmm Shutdown torque ~ 80 Nmm Once airborne, drag torque is ~ 3 % of Startup ‘breakaway’ torque Top shaft speed = 65 krpm Iift off speed Lift off speed at lowest torque : airborne operation W D = 3.6 N San Andres, L., Kim, T.H., Chirathadam, T.A., and Ryu, K., 2009, Proc. AHS 65 th Annual forum, Grapevine, TX, May 27-29.

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Bearing power loss vs rotor speed 8.9 N (2 lb) 17.8 N (4 lb) 26.7 N (6 lb) 35.6 N (8 lb) Rotor accelerates Power loss decreases to a minimum during mixed lubricationregime and then increases with increasing rotor speed Dead weight (W D = 3.6 N) Increasing static load (W s ) to 35.6 N (8 lb) Mixedlubrication Hydrodynamiclubrication

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Rotor accelerates 8.9 N (2 lb) 17.8 N (4 lb) 26.7 N (6 lb) 35.6 N (8 lb) Friction coefficient vs rotor speed f ~ 0.01 Friction coefficient ( f ) decreases with increasing static load Dry sliding Airborne (hydrodynamic) f = (Torque/Radius)/(Static load) f ~ 0.3-0.4 San Andres, L., Kim, T.H., Chirathadam, T.A., and Ryu, K., 2009, Proc. AHS 65 th Annual forum, Grapevine, TX, May 27-29.

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Impact loads Positioning table MMFB Journal (28 mm) Flexible string Force gauge Top foil fixed end 5 cm Accelerometer Eddy current sensor TC (FRONT VIEW) IMPACT HAMMER (SIDE VIEW) Identification of stiffness and damping coeff.

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Identification model Assembly mass, M = 0.38 kg Deliver impacts along Y direction only X Y K YY, C YY K XY, C XY Impact force, f Y Bearing Cartridg e Journal K YX, C YX K XX, C XX Ω Equations of motion: Record displacements (relative to rotor) and bearing acceleration

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Identification model: freq. domain Lightly loaded bearing (3.5N). Assume: SHAFT STATIONARY ( 1-DOF) SHAFT ROTATING (2-DOF) Multiple tests (10) : frequency averages

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Impact force and displacements Frequency domain averages of 10 impacts Y Time domain Frequency domain Shaft not rotating Rapid decay of MMFB displacement indicates large material damping

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Impact force and displacements Time domain Frequency domain Time domain Shaft speed = 50 krpm Y direction X direction Synchronous response, 1X Appreciable cross directional motions (X) X direction

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Bearing acceleration & relative disp. SHAFT STATIONARY SHAFT speed = 50 krpm (833 Hz) Acceleration derived from bearing displacement relative to shaft, |- ω 2 Y |, is not equal to bearing acceleration since the TC shaft stub is rather flexible. Important to measure both: displacements and accelerations (X,Y) Acceleration from displacement relative to shaft, |ω 2 Y| Bearing acceleration Acceleration from displacement relative to shaft Measured Y direction X direction

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Test MMFB stiffnesses (K, k) Direct stiffness K at 50 krpm < structure stiffness ( ~ 25 % reduction at 200 hz) Applied load = 3.5 N. Weight=3.5 N Shaft speed=50 krpm Direct and cross coupled stiffnesses (airborne) and bearing structuralstiffness increase with frequency Structure K ( No rotation) Direct K Cross k

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MMFB direct viscous damping C are similar, with and without shaft rotation. Metal mesh provides ++ damping Equivalent viscous damping decays rapidly with increasing frequency Cross c Direct C Structure C Test MMFB damping (C, c) Applied load = 3.5 N. Weight=3.5 N Shaft speed=50 krpm

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Loss factor is large ~ 0.5, with little variation in frequency Large loss factor magnitude = large energy dissipation mechanism γ=C ω/K 50 krpm No rotation Test MMFB loss factor ( ) Applied load = 3.5 N. Weight=3.5 N Shaft speed=50 krpm

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Not all measurements showed acceptable rotordynamicperformance.At certain speeds, rotor-bearing system shows largesubharmonic motions.Is this behavior a typical rotordynamic instability or a forced nonlinearity ? Waterfalls of start up

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Subharmonic whirl motions of large amplitudes locked at system natural frequency H load =3.5 N ½ frequeny whirl for lightly loaded bearing Bearing displacements relative to shaft

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H load = 18 N Large sub harmonic motions locked at natural frequency ½ frequeny whirl absent with larger applied loads

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Conclusions Metal mesh foil bearing assembled using cheap, commercially available materials. While airborne, bearing power loss increases with rotor speed (little friction). Min power loss found. MMFB direct stiffness (airborne) slightly < structural stiffness. Cross-stiffness small. MMFB viscous damping nearly independent of shaft speed though decreasing fast with frequency. LOSS factor is large (~0.50) Start up shows ½ frequency whirl=natural frequency for low static loads & speeds < 50 krpm MMFBs are promising inexpensive bearings for oil-freeturbomachinery

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Acknowledgments Thanks support of Turbomachinery Research Consortium Honeywell TurboCharging Systems Learn more http://rotorlab.tamu.edu Questions ?

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Current work: rotordynamic test rig X-Y 100 N shakers) Test bearing Positioning table Force gauge Rubber belt Steel frame/ shield

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Current work: rotordynamic test rig Shakers Test bearing TC X Y Applicable to foil bearings & metal mesh bearings

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