ASME GT2009-59315
Luis San AndrésMast-Childs Professor
Fellow ASME
Measurements of Structural Stiffness and Damping Coefficients in a Metal
Mesh Foil Bearing
Measurements of Structural Stiffness and Damping Coefficients in a Metal
Mesh Foil Bearing
June, 2009
ASME Turbo Expo 2009: Power for Land, Sea, and Air
ASME GT2009-59315
Supported by TAMU Turbomachinery Research Consortium
accepted for journal publication
Thomas Abraham ChirathadamResearch Assistant
Tae-Ho KimResearch Associate
Texas A&M University
ASME GT2009-59315
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
ASME GT2009-59315
MMFB Assembly
BEARING CARTRIDGE
METAL MESH RING TOP FOIL
Simple construction and assembly procedure
ASME GT2009-59315
TAMU past work on Metal Mesh Dampers
Zarzour and Vance (2000) J. Eng. Gas Turb. & Power, Vol. 122
Advantages of Metal Mesh Dampers over SFDsCapable of operating at low and high temperaturesNo 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
METAL MESH DAMPERS proven to provide large amounts of damping. Inexpensive. Oil-free
ASME GT2009-59315
Recent Patents: gas bearings & systems
A metal mesh ring is a cheap replacement for a “porous foil”
‘Air foil bearing having a porous foil’Ref. Patent No. WO 2006/043736 A1
Turbocharger with hydrodynamic foil bearingsRef. Patent No. US7108488 B2
Foil JournalBearings
Thrust foilBearing
ASME GT2009-59315Metal Mesh Dampers for Hybrid 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)
Recent work by OEM with MM dampers to maximize load capacity and to add damping in gas bearings
ASME GT2009-59315
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
ASME GT2009-59315
MMFB dimensions and specifications
Dimensions and SpecificationsBearing 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
Bearing cartridge
Top foil
Donut shaped metal mesh
Rotating shaft
Gas film
Ω
ASME GT2009-59315
Static load test setup
Lathe tool holder moves forward and backward : push and pull forces on MMFB
Lathe chuck holds shaft & bearing during loading/unloading cycles.
Lathe tool holder
Eddy Current sensor Load cell
Test MMFB
Stationary shaft
ASME GT2009-59315
-150
-100
-50
0
50
100
150
200
-0.12 -0.08 -0.04 0 0.04 0.08 0.12Displacement [mm]
Sta
tic
Lo
ad
[N
]
Push load
Pull load
Push load
Pull load
Static Load vs bearing displacement
3 Cycles: loading & unloading
Nonlinear F(X)
Large hysteresis loop : Mechanical
energy dissipation
MMFB wire density ~ 20%
Displacement: [-0.12,0.12] mmLoad: [-120, 150 ]N
Start
ASME GT2009-59315
0
0.5
1
1.5
2
2.5
3
-0.12 -0.08 -0.04 0 0.04 0.08 0.12
Displacement [mm]
Sti
ffn
es
s [
MN
/m]
Push loadPull load
Push load
Pull load
MMFB wire density ~ 20%
Derived MMFB structural stiffness
During Load reversal : jump
in structural stiffness
Max. Stiffness ~ 2.5 MN/m
Lower stiffness values for
small displacement
amplitudes
ASME GT2009-59315
Dynamic load tests
Motion amplitude controlled mode
Electrodynamic shaker
MMFB Accelerometer Force transducer
Test shaft FixtureTest shaftEddy Current sensors
MMFB motion amplitude (1X) is dominant
Waterfall of displacement
12.7, 25.4 &38.1 μm
Frequency of excitation :
25 – 400 Hz (25 Hz interval)
0
20
40
60
80
100
120
140
0 100 200 300 400
Frequency [Hz]
Dis
pla
cem
ent
[um
]
Increasing Frequency
400 Hz
25 Hz
1 X
ASME GT2009-59315
0
10
20
30
40
50
60
0 50 100 150 200 250 300 350 400
Frequency [Hz]
Dyn
amic
Loa
d [N
]
12.7 um25.4 um38.1 um
Around bearing natural frequency, less force needed to maintain same motion amplitude
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
38.1 μm
25.4 μm 12.7 μm
Motion amplitude decreases
ASME GT2009-59315
Parameter identification model
( )tM x K x C x F
Equivalent Test System
Meq
Keq
Ceq
Fext
x Lf =244 mm Lf =221 mm L= 248 mm
F(t)
X(t)
1-DOF equivalent mechanical system
ASME GT2009-59315
Harmonic force & displacements
Impedance Function
MaterialLOSS FACTOR
Viscous Dissipationor Hysteresis Energy
( ) i tx t X e ( ) i tF t F e
2( )F
Z K M i CX
2
disE K X
2
disE C X
Parameter identification (no shaft rotation)
KC
1
ImF
K X
ASME GT2009-59315
Model of metal mesh damping material
As force increases, more stick-slip joints among wires are freed, thus resulting in a greater number of spring-damper systems in series.
Stick-slip model (Al-Khateeb & Vance, 2002)
Stick-slip model
arranges wires in series connected by dampers and
springs.
ASME GT2009-59315
Design equation: MMB stiffness/damping
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)
, ,equiv o i A pK E f L R R f C f R f A f
, ,equiv o i A pC H g L R R g C g R g A g
2/325 21 4 10 1 2.96 10 1pA
equiv k ko i o i o i
RCL AK E
R R L R R R R
3/ 2 2/325 21 8.7 10 1 1.8 10 1
cpA
equiv co i o i o i n
RCL AC H
R R L R R R R
Empirical design equation for stiffness and equivalent viscous damping coefficients (Al-Khateeb & Vance, 2002)
ASME GT2009-59315
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 100 200 300 400Frequency [Hz]
Rea
l par
t o
f Im
ped
ance
F/X
[M
N/m
] 12.7 um25.4 um38.1 um
K - Mω 2
Real part of (F/X) decreases with increasing motion amplitude
Real part of (F/X) vs excitation frequency
Natural frequency of test system
Frequency of excitation :
25 – 400 Hz ( 25 Hz step)
12.7 μm
25.4 μm
38.1 μm
Motion amplitude increases
ASME GT2009-59315
0
0.5
1
1.5
2
2.5
0 100 200 300 400Frequency [Hz]
Str
uctu
ral s
tiffn
ess
[MN
/m]
12.7 um25.4 um38.1 um12.7 um Prediction25.4 um Prediction38.1 um Prediction
Al-Khateeb & Vance model : reduction of stiffness with force magnitude (amplitude dependent)
MMFB structural stiffness vs frequency
At low frequencies (25-100 Hz), stiffness
decreases
At higher frequencies, stiffness
gradually increases
MMFB stiffness is frequency and
motion amplitude dependent
Frequency of excitation :
25 – 400 Hz (25 Hz step)
12.7 um
25.4 um38.1 um
Motion amplitude increases
ASME GT2009-59315
0
0.2
0.4
0.6
0.8
1
0 100 200 300 400Frequency [Hz]
Imag
inar
y pa
rt o
f Im
peda
nce
F/X
[MN
/m]
12.7 um25.4 um38.1 um
Im(F/X) decreases with motion
amplitude
Imaginary impedance (F/X) vs frequency
Frequency of excitation :
25 – 400 Hz ( at 25 Hz interval)C K
12.7 μm
25.4 μm
38.1 μm
Motion amplitude increases
ASME GT2009-59315
10
100
1000
10000
100000
0 100 200 300 400Frequency [Hz]
Equi
vale
nt v
isco
us d
ampi
ng [N
s/m
]
12.7 um25.4 um38.1 um12.7 um Prediction25.4 um Prediction38.1 um Prediction
Predictions vs. test data: Damping
Amplitude increases
12.7 μm
25.4 μm38.1 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
ASME GT2009-59315
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 100 200 300 400Frequency [Hz]
Str
uc
tura
l Lo
ss
Fa
cto
r
12.7 um25.4 um38.1 um
Loss factor nearly similar for all motion amplitudes
Loss factor vs excitation frequency
Structural damping or loss
factor is the largest around the MMFB natural frequency
Frequency of excitation :
25 – 400 Hz ( at 25 Hz step)
12.7 μm
25.4 μm
38.1 μm
ASME GT2009-59315
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 ( ) around test system natural frequency
Predicted stiffness and equivalent viscous damping coefficients are in agreement with test coefficients: Test data validates design equations
ASME GT2009-59315
Thanks to
TAMU Turbomachinery Research Consortium
Honeywell Turbocharging Technologies
Acknowledgments
Questions ?
Learn more at http://phn.tamu.edu/TRIBGroup
ASME GT2009-59315
Current work
ASME GT2009-59315MMFB rotordynamic test rig
(a) Static shaft
Max. operating speed: 75 krpmTurbocharger driven rotorRegulated air supply: 9.30bar (120 psig)
Test Journal: length 55 mm, 28 mm diameter , Weight=0.22 kg
Journal press fitted on Shaft Stub
TC cross-sectional viewRef. Honeywell drawing # 448655
Twin ball bearing turbocharger, Model T25, donated by Honeywell Turbo Technologies
MMFB
ASME GT2009-59315
Positioning (movable) table
Torque arm
Calibrated spring
MMFB
Shaft (Φ 28 mm)
String to pull bearing
Static load
Eddy current sensor
Force gauge
Top foil fixed end
Preloading using a rubber band
5 cm
Test Rig: Torque and Lift-Off Measurements
Thermocouple
ASME GT2009-59315
Rotor 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
WD= 3.6 N
ASME GT2009-59315
Varying steady state speed & torque
Rotor starts
61 krpm
Rotor stops
50 krpm
37 krpm
24 krpm
2.5 N-mm
57 N-mm 45 N-mm
2.4 N-mm 2.0 N-mm 1.7 N-mm
Manual speed up to 65 krpm, steady state operation, and
deceleration to rest
Drag torque decreases with step wise reduction in
rotating speed until the journal starts rubbing the
bearing
Shaft speed changes every 20 s : 65 – 50 – 37 - 24 krpm
Side load = 8.9 N
WD= 3.6 N
ASME GT2009-59315
Bearing drag torque vs rotor speed
Lift-off speed
8.9 N (2 lb)
17.8 N (4 lb)
26.7 N (6 lb)
35.6 N (8 lb)
Max. Uncertainty ± 0.35 N-mm
Rotor accelerates
Bearing drag torque increases with increasing rotor speed and increasing applied static loads. Lift-Off speed increases almost linearly with static load
0
20
40
60
80
0 5 10 15 20 25 30Time [sec]
Sp
ee
d [
krp
m]
0
50
100
0 5 10 15 20 25 30Time [sec]B
ea
rin
g t
orq
ue
[N
-mm
]