ASME Turbo Expo 2009: Power for Land, Sea, and Air June, 2009 Measurements of Structural Stiffness and Damping Coefficients in a Metal Mesh Foil Bearing Luis San Andrés Mast-Childs Professor Fellow ASME Thomas Abraham Chirathadam Research Assistant Tae-Ho Kim Research Associate Texas A&M University ASME GT2009-59315 accepted for journal publication Supported by TAMU Turbomachinery Research Consortium 1

Metal mesh foil bearings Metal mesh ring and top foil assembled inside a bearing cartridge. Hydrodynamic air film will develop between rotating shaft and top foil. Metal mesh resilient to temperature variations Damping from material hysteresis Stiffness and viscous damping coefficients controlled by metal mesh material, size (thickness, L, D), and material compactness (density) ratio. Potential applications: ACMs, micro gas turbines, turbo expanders, turbo compressors, turbo blowers, automotive turbochargers, APU

Simple construction and assembly procedure MMFB Assembly Simple construction and assembly procedure BEARING CARTRIDGE METAL MESH RING TOP FOIL 3

TAMU past work on Metal Mesh Dampers METAL MESH DAMPERS proven to provide large amounts of damping. Inexpensive. Oil-free 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) MM 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

Recent Patents: gas bearings & systems Turbocharger with hydrodynamic foil bearings Ref. Patent No. US7108488 B2 Foil Journal Bearings Thrust foil Bearing ‘Air foil bearing having a porous foil’ Ref. Patent No. WO 2006/043736 A1 A metal mesh ring is a cheap replacement for a “porous foil” 5

Metal Mesh Dampers for Hybrid Bearings Recent work by OEM with MM dampers to maximize load capacity and to add damping in gas bearings Ertas &Luo (2008) ASME J. Gas Turbines Power., 130, pp. 032503-(1-8) MM damper force coefficients not affected by shaft eccentricity ( or applied static load) Ertas (2009) ASME J. Gas Turbines Power, 131 (2), pp. 022503-(1-11) Two metal mesh rings installed in a multiple pad gas bearing with flexural supports to maximize load capacity and damping. Bearing stiffness decreases with frequency & w/o external pressurization; and increases gradually with supply pressure Ertas et al. (2009) AIAA 2009-2521 Shape memory alloy (NiTi) shows increasing damping with motion amplitudes. Damping from NiTi higher than for Cu mesh (density – 30%) : large motion amplitudes (>10 um) 6

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) Cost effective Metal mesh tends to sag or creep over time Damping NOT viscous. Modeling difficulties

MMFB dimensions and specifications Bearing Cartridge outer diameter, DBo(mm) 58.15 Bearing Cartridge inner diameter, DBi(mm) Bearing Axial length, L (mm) 28.05 Metal mesh ring outer diameter, DMMo (mm) 42.10 Metal mesh donut inner diameter, DMMi(mm) 28.30 Metal mesh density, ρMM (%) 20 Top foil thickness, Ttf (mm) 0.076 Metal wire diameter, DW (mm) 0.30 Young’s modulus of Copper, E (GPa), at 21 ºC 110 Poisson’s ratio of Copper, υ 0.34 Bearing mass (Cartridge + Mesh + Foil), M (kg) 0.3160 ± PICTURE

Static load test setup Lathe chuck holds shaft & bearing during loading/unloading cycles. Load cell Eddy Current sensor Stationary shaft Lathe tool holder Test MMFB Lathe tool holder moves forward and backward : push and pull forces on MMFB

Static Load vs bearing displacement 3 Cycles: loading & unloading Nonlinear F(X) Large hysteresis loop : Mechanical energy dissipation Start Displacement: [-0.12,0.12] mm Load: [-120, 150 ]N MMFB wire density ~ 20%

Derived MMFB structural stiffness MMFB wire density ~ 20% During Load reversal : jump in structural stiffness Lower stiffness values for small displacement amplitudes Max. Stiffness ~ 2.5 MN/m

Dynamic load tests MMFB motion amplitude (1X) is dominant Motion amplitude controlled mode 12.7, 25.4 &38.1 μm Accelerometer Force transducer MMFB Frequency of excitation : 25 – 400 Hz (25 Hz interval) Waterfall of displacement Eddy Current sensors Electrodynamic shaker Test shaft Test shaft Fixture MMFB motion amplitude (1X) is dominant

Dynamic load vs excitation frequency Dynamic load decreases around bearing natural frequency, but increases with further increase in excitation frequency. Dynamic load decreases with increasing motion amplitudes Motion amplitude decreases 38.1 μm 25.4 μm 12.7 μm Around bearing natural frequency, less force needed to maintain same motion amplitude

Parameter identification model F(t) X(t) 1-DOF equivalent mechanical system Equivalent Test System 14

Parameter identification (no shaft rotation) Harmonic force & displacements Impedance Function Viscous Dissipation or Hysteresis Energy Material LOSS FACTOR 15

Model of metal mesh damping material Stick-slip model (Al-Khateeb & Vance, 2002) Stick-slip model arranges wires in series connected by dampers and springs. As force increases, more stick-slip joints among wires are freed, thus resulting in a greater number of spring-damper systems in series. 16

Design equation: MMB stiffness/damping Empirical design equation for stiffness and equivalent viscous damping coefficients (Al-Khateeb & Vance, 2002) Functions of equivalent modulus of elasticity (Eequiv), hysteresis coeff. (Hequiv), axial length (L), inner radius (Ri), outer radius (Ro), axial compression ratio (CA), radial interference (Rp), motion amplitude (A), and excitation frequency (ω) 17

Real part of (F/X) vs excitation frequency Frequency of excitation : 25 – 400 Hz ( 25 Hz step) 12.7 μm 25.4 μm Natural frequency of test system 38.1 μm Motion amplitude increases Real part of (F/X) decreases with increasing motion amplitude 18

MMFB structural stiffness vs frequency Frequency of excitation : 25 – 400 Hz (25 Hz step) At low frequencies (25-100 Hz), stiffness decreases At higher frequencies, stiffness gradually increases Motion amplitude increases 12.7 um 25.4 um MMFB stiffness is frequency and motion amplitude dependent 38.1 um Al-Khateeb & Vance model : reduction of stiffness with force magnitude (amplitude dependent) 19

Imaginary impedance (F/X) vs frequency Frequency of excitation : 25 – 400 Hz ( at 25 Hz interval) Motion amplitude increases Im(F/X) decreases with motion amplitude 12.7 μm 25.4 μm 38.1 μm

Predictions vs. test data: Damping MMFB equiv. viscous damping decreases as the excitation frequency increases and as motion amplitude increases Amplitude increases 12.7 μm 25.4 μm 38.1 μm Predicted equivalent viscous damping coefficients in good agreement with measurements

Loss factor vs excitation frequency Frequency of excitation : 25 – 400 Hz ( at 25 Hz step) Structural damping or loss factor is the largest around the MMFB natural frequency 25.4 μm 12.7 μm 38.1 μm Loss factor nearly similar for all motion amplitudes 22

Conclusions Static and dynamic load tests on MMFB show large mechanical energy dissipation and (predictable) structural stiffness MMFB stiffness and damping decreases with amplitude of dynamic motion MMFB equivalent viscous damping decreases with motion amplitude, and more rapidly with excitation frequency Large MMFB structural loss factor ( g ~ 0.7 ) around test system natural frequency Predicted stiffness and equivalent viscous damping coefficients are in agreement with test coefficients: Test data validates design equations 23

Acknowledgments Questions ? Thanks to TAMU Turbomachinery Research Consortium Honeywell Turbocharging Technologies Learn more at http://phn.tamu.edu/TRIBGroup Questions ?

Current work

MMFB rotordynamic test rig 15 10 5 cm Journal press fitted on Shaft Stub (a) Static shaft TC cross-sectional view Ref. Honeywell drawing # 448655 Max. operating speed: 75 krpm Turbocharger driven rotor Regulated air supply: 9.30bar (120 psig) Twin ball bearing turbocharger, Model T25, donated by Honeywell Turbo Technologies Test Journal: length 55 mm, 28 mm diameter , Weight=0.22 kg 26

Preloading using a rubber band Test Rig: Torque and Lift-Off Measurements Thermocouple Force gauge String to pull bearing Shaft (Φ 28 mm) Static load MMFB Top foil fixed end Positioning (movable) table Torque arm Preloading using a rubber band Eddy current sensor Calibrated spring 5 cm 27

Lift off speed at lowest torque : airborne operation Rotor speed and torque vs time Constant speed ~ 65 krpm Valve open Valve close 3 N-mm Applied Load: 17.8 N Rotor starts Rotor stops WD= 3.6 N Manual speed up to 65 krpm, steady state operation, and deceleration to rest Iift off speed Startup torque ~ 110 Nmm Shutdown torque ~ 80 Nmm Once airborne, drag torque is ~ 3 % of startup ‘breakaway’ torque Lift off speed at lowest torque : airborne operation Top shaft speed = 65 krpm 28

Varying steady state speed & torque Rotor starts Rotor stops Manual speed up to 65 krpm, steady state operation, and deceleration to rest 61 krpm 50 krpm 37 krpm 24 krpm Drag torque decreases with step wise reduction in rotating speed until the journal starts rubbing the bearing 57 N-mm 45 N-mm 2.5 N-mm 2.4 N-mm 2.0 N-mm 1.7 N-mm Side load = 8.9 N WD= 3.6 N Shaft speed changes every 20 s : 65 – 50 – 37 - 24 krpm 29

Bearing drag torque vs rotor speed Max. Uncertainty ± 0.35 N-mm Bearing drag torque increases with increasing rotor speed and increasing applied static loads. Lift-Off speed increases almost linearly with static load Lift-off speed 8.9 N (2 lb) 17.8 N (4 lb) 26.7 N (6 lb) 35.6 N (8 lb) Rotor accelerates 30