1. 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 GT
accepted for journal publication
Supported by TAMU Turbomachinery Research Consortium 1

2. 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

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

4. 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
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

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

6. 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 (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 (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
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

7. 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

8. 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) ±
PICTURE

9. 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

10. 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%

11. 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

12. 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

13. 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

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

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

16. 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

17. 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

18. 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

19. MMFB structural stiffness vs frequency
Frequency of excitation :
25 – 400 Hz (25 Hz step)
At low frequencies ( 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

20. 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

21. 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

22. 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

23. 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

24. Acknowledgments Questions ? Thanks to
TAMU Turbomachinery Research Consortium
Honeywell Turbocharging Technologies
Learn more at
Questions ?

25. Current work

26. MMFB rotordynamic test rig15 10 5 cm
Journal press fitted on Shaft Stub
(a) Static shaft
TC cross-sectional view
Ref. Honeywell drawing #
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

27. 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

28. 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

29. 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 – krpm 29

30. 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