Luis San AndrésMast-Childs Professor
Fellow ASME
ASME GT2011-45257ASME J. Eng Gas Turbines & Power (in print)
Thomas Abraham Chirathadam
Research Assistant
Texas A&M University
ASME TURBO EXPO 2011, Vancouver, Canada (June 2011)
Presentation available at http://rotorlab.tamu.edu
Metal Mesh Foil BearingEffect of Motion Amplitude, Rotor Speed, Static Load, and Excitation Frequency on
Force Coefficients
Oil-Free Bearings for Turbomachinery
JustificationCurrent advancements in vehicle turbochargers and midsize gas turbines need of proven gas bearing technology to procure compact units with improved efficiency in an oil-free environment.
DOE, DARPA, NASA interests range from applications as portable fuel cells (< 60 kW) in microengines to midsize gas turbines (< 250 kW) for distributed power and hybrid vehicles.
Gas Bearings allow• weight reduction, energy and complexity savings• higher temperatures, without needs for cooling air • improved overall engine efficiency
Ideal gas bearings
Simple – low cost, small geometry, low part count, constructed from common materials, manufactured with elementary methods.
Load Tolerant – capable of handling both normal and extreme bearing loads without compromising the integrity of the rotor system.
High Rotor Speeds – no specific speed limit (such as DN) restricting shaft sizes. Small Power losses.
Good Dynamic Properties – predictable and repeatable stiffness and damping over a wide temperature range.
Reliable – capable of operation without significant wear or required maintenance, able to tolerate extended storage and handling without performance degradation.
+++ Modeling/Analysis (anchored to test data) available
Gas Foil Bearings
Used in many oil-free rotating machinery: high load capacity (>20 psig), rotordynamically stable, tolerance of misalignment and shocks…….
: Bump spot weld X
Rotor spinning
Housing
Bump strip layer
Top foil
Gas film
Y
Top foil spot weld
Ω
Ө
…… but expensive with intellectual property restrictions. A low cost proven alternative needed.
Metal Mesh Foil Bearing (MMFB)
MMFB COMPONENTS: Bearing cartridge, metal mesh ring and top FoilHydrodynamic air film develops between rotating shaft and top foil.
Potential applications: ACMs, micro gas turbines, turbo expanders, turbo compressors, turbo blowers, automotive turbochargers, APUs
Large damping (material hysteresis) offered by metal mesh
Tolerant to misalignment, and applicable to a wide temperature range
Coatings needed to reduce friction at start-up & shutdown
Metal mesh foil bearing5 cm
Metal Mesh Ring
Top Foil Coated with MoS2
Bearing Cartridge
Rotor spinning
Slot
MMFB components
Top Foil
0.12 mm top foilChrome-Nickel alloyRockwell 40/45
Heat treated at ~ 450 ºC for 4 hours and allowed to cool. Foil retains arc shape after heat treatment
Sprayed with MoS2
sacrificial coating
Metal mesh pad
Compressed weave of copper wires
Compactness (density)=20%
Stiffness and damping of MMFB depend on metal mesh compactness
Bearing cartridge (+top foil+ metal mesh)
Metal mesh pad and top foil inserted in steel bearing cartridge.
Top foil firmly affixed in a thin slot made with wire-EDM machining
Simple to manufacture and assemble
Zarzour and Vance (2000) J. Eng. Gas Turb. & Power, Vol. 122Advantages 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) ASME GT-2001-0247Test metal mesh donut and squirrel cage( in parallel)Metal Mesh damping not affected by modifying squirrel cage stiffness
Choudhry and Vance (2005) ASME GT-2005-68641Develop design equations, empirically based, to predict structural stiffness and viscous damping coefficient
METAL MESH DAMPERS provide large amounts of damping. Inexpensive component.
Past work in Metal Mesh Dampers
Ertas &Luo (2008) ASME J. Gas Turbines Power, 130MM damper force coefficients not affected by shaft eccentricity (or applied static load)
Ertas (2009) ASME J. Gas Turbines Power, 131Two 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 2009-2521Shape memory alloy (NiTi) shows increasing damping with motion amplitudes. Damping from NiTi larger 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
Metal Mesh Dampers in Hybrid bearings
Past work in MMFBsSan Andrés et al. (2010) J. Eng. Gas Turb. & Power, 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 GT2009-59920Demonstrated operation to 45 krpm with early rotor lift off. Educated undergraduate students.
San Andrés et al. (2010) J. Eng. Gas Turb. & Power, 132Start and shut down to measure torque and lift-off speed. Low friction factor ~ 0.01 at high speed 60 krpm.
San Andrés and Chirathadam (2011) J. Eng. Gas Turb. & Power, 133Rotordynamic coefficients from unidirectional impact loads. Estimated stiffness and damping force coefficients at 50 krpm.
EXPERIMENTS with a PRIOR MMFB (larger mesh thickness)
1. Structural stiffness and damping
2. Friction factor with airborne operation
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
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 dependent12.7 m
25.4 m38.1 m
Motion amplitude increases
San Andres et al., 2010, ASME J. Eng. Gas Turbines Power, 132 (3)
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
MMFB eq. damping vs. frequency
Amplitude increases
12.7 μm25.4 μm38.1 μm
MMFB equiv. viscous damping
decreases as the excitation
frequency increases and
as motion amplitude increases
Al-Khateeb & Vance modelSan Andres et al., 2010, ASME J. Eng. Gas Turbines Power, 132 (3)
Friction coefficient ( f )
decreases with increasing
static load
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
f rapidly decreases
initially, and then gradually
raises with increasing
rotor speedDry sliding Airborne (hydrodynamic)
Dead weight
(WD= 3.6 N)
Increasing static load (Ws) to 35.6 N (8 lb)
f = (Torque/Radius)/(Net static load)
CURRENT MMFB & ROTORDYNAMIC TEST RIG
MMFB dimensions & materials
Metal mesh foil bearing
Bearing axial length, L 38.0 mm
Journal diameter, D 36.5 mm
Bearing cartridge OD 63.57 mm
Bearing cartridge ID 42.07 mm
Copper mesh thickness, t 2.667 mm
mesh inner diameter 36.74 mm
Copper mesh density 20 %
Wire diameter 0.30 mm
Steel top foil thickness, tF 0.12 mm
Bearing diametral clearance
ID-2(t+tF)
~ 0.0 mm
5 cm
Top foil: Chrome nickel alloy
Metal mesh: copper
Bearing Cartridge:
Stainless steel
2.7mm
MMFB rotordynamic test rig
Max. operating speed: 75 krpmTurbocharger driven rotorRegulated air supply: 9.30bar (120 psig)
Test Journal: length 55 mm, 36.5 mm diameter
Journal press fitted on Shaft Stub
TC cross-sectional viewRef. Honeywell drawing # 448655
Twin ball bearing turbocharger, Model T25, donated by Honeywell Turbo Technologies
Bearing
Rotordynamic test rig
(X-Y 100 N shakers)
Dynamic load :25-100 N
Rotor speed 50 krpm
Freq. identification range:
200 to 400 Hz
Motion amplitudes : m, 25 m & 30
m
Static loads: 22 N (15.5 N along X & Y)
and 36N
Test rig schematic diagram
Squirrel cage affixed on turn-knob controlled
positioning table
Continuous supply of oil
lubricates ball bearings in
turbocharger center housing
Thermocouple measures bearing
outboard end temperature5 cm
TC center housing Oil inlet
Shaft stub
Air outlet
Oil outlet BEARING
Squirrel cage (Soft elastic support)
Static load
Y X
BEARING Stinger connection to shaker
Load sensor
Accelerometer
Static load along X
Static load along Y
Bearing weight
Net static load
Impact load tests : system mass & soft structure stiffness
Impact load along Y direction
Squirrel cage structure stiffness < 10% of bearing
stiffness
Damping ratio =0.024
R2 = 0.95
KSY = 21.2 kN/m
MSY = 0.88 kg
CSY = 6.6 Ns/m
Curve fit for the transfer Function
0 25 50 75 100 125 1500
5
10
15
20
25
ExperimentalCurve Fit
Frequency [Hz]
Acc
eler
ance
[(m
/s^2
) /N
]
2
1/ 22 22Y Y Y
Y
YS S S
a
FK M C
Accelerance function = physical
model equation
Estimated test system mass =0.88 kg
Y
Impact load
Bearing overhang on squirrel cage
Bearing
Sq. cage
Identification model
KS,CS: soft SQ stiffness
and damping
MS : effective mass
X
YKYY, CYY
KXY, CXY
Shaker force, FY
Bearing
Journal
KYX, CYX
KXX, CXX
Ω
X X X
Y Y Y
S X S X S XX XY XX XY X
YX YY YX YY YS Y S Y S
M a C v K X C C K K Fx x
C C K K FM a C v K Y y y
EOM:
Shaker force, FX
KSX, CSX
KSY, CSY
SoftSupport structure
Kij ,Cij: test bearing stiffness
and damping
Identification model
Forces: Sine sweep excitations (200-400 Hz), amplitude controlled
Responses: measure bearing accelerations and displacements relative to journal
Kij ,Cij : bearing stiffness and damping vs.
frequencyX
YKYY, CYY
KXY, CXY
Shaker force, FY
Bearing
Journal
KYX, CYX
KXX, CXX
Ω
Shaker force, FX
KSX, CSX
KSY, CSY
SoftSupport structure
X X
X
Y Y
Y
S S2SX XXX XX XY XY
YX YX YY YY S SY Y2S
C KMF AxK j C K j C j
yK j C K j C C KF AM j
( ) ( )
( ) ( )
( )
( )
Process data in frequency domain to obtain:
Y
W
X
Dynamic load and displacements
Static load resolved along X and Y = 15.5 N
Shaft speed=50 krpm (833 Hz)
15.5 N 15.5 N
Fixed end Force along X
Displacement along X
Displacement along Y
Dynamic load 25-100 NExcitation frequency 200- 400 Hz
Displacement along X ~ 30 m
Noticeable cross-directional motion
Net static load (static load-bearing weight) = 22 N along vertical direction
X Y
Forces & disps. vs. frequency
Static loads along X and Y =15.5 N
Shaft speed=50 krpm (833 Hz)
15.5 N 15.5 N
Fixed end
DFT amplitude of dynamic loads and bearing
displacements relative to rotor
Average of ten consecutive excitations
In frequency domain, displacement magnitude
decreases (force increases) with frequency
0 100 200 300 400 5000
5
10
15
20
XXXYYXYY
Frequency [Hz]
Fo
rce
[N]
Fo
rce
[N]
Frequency [Hz]
0 100 200 300 400 5000
2
4
6
XXXYYXYY
Frequency [Hz]
Disp
lacem
ents
[um
]
Dis
pla
cem
en
t [μ
m]
Frequency [Hz]
0 100 200 300 400 5000
2
4
6
XXXYYXYY
Frequency [Hz]
Dis
pla
cem
ents
[u
m]
0 100 200 300 400 5000
2
4
6
XXXYYXYY
Frequency [Hz]
Dis
plac
emen
ts [u
m]
200-400 Hz Force FYY
FXX
FXY
FYX
Displacement YY
XxXY
YX
N
m
X Y
-1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
es
s [
MN
/m]
-1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
es
s [
MN
/m]
-1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
es
s [
MN
/m]
-1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
es
s [
MN
/m]
K KK K
XX XYYYYX
MMFB stiffnesses: varying rotor speeds
22 N static load
50 krpm
40 krpm0 krpm
45 krpm
KxxKYY
KYX
KXY
KXXKYY
KYX
KXY
KXXKYY
KYX
KXY
Kxx
KYX
KXY
KYY
At rest (0 rpm) direct stiffness is
structural only. Direct K
decreases with rotor speed.
With rotation, KYX changes sign.
Small cross-stiffneses.
Direct stiffnesses gradually
increase with frequency
-500
-250
0
250
500
200 250 300 350 400
Frequency [Hz]
-500
-250
0
250
500
200 250 300 350 400
Frequency [Hz]
Eq
. v
isc
ou
s d
am
pin
g [
Ns
/m]
-500
-250
0
250
500
200 250 300 350 400
Frequency [Hz]E
q.
vis
co
us
da
mp
ing
[N
s/m
]
-500
-250
0
250
500
200 250 300 350 400
Frequency [Hz]
Eq
. v
isc
ou
s d
am
pin
g [
Ns
/m]
C C
C CXX XY
YX YY
MMFB damping: varying rotor speeds
40 krpm0 krpm
50 krpm45 krpm
CYX
CYY CXX
CXY
CXXCYY
CXY
CYX
CYY
CXYCYX
CXX CXXCYY
CYX CXY
22 N static load
Rotor speed does not affect
damping. Major effect is from
metal mesh hysteresis.
Direct C increases with
frequency.
At rest (0 rpm) direct damping is
structural only. Direct C
decreases with frequency.
-1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
ess
[MN
/m]
-1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
ess
[MN
/m]
K KK K
XX XY
YX YY
-1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
es
s [
MN
/m]
MMFB stiffnesses: varying motion amplitudes
20 m 25 m
30 m
KXX
KYX
KXY
KYY KXX
KYX
KXY
KYY
KXX
KYX
KXY
KYY Direct stiffnesses decrease with increasing motion amplitudes.
Similar to structural test results San Andres et al (2009)
At highest displacement amplitude (30 m), cross-coupled stiffness
magnitude is large at ~-0.4 MN/m
22 N static load
50 krpm Rotor speed
(833 Hz)
-500
-250
0
250
500
200 250 300 350 400
Frequency [Hz]
Eq
. vis
cou
s d
amp
ing
[N
s/m
]
-500
-250
0
250
500
200 250 300 350 400
Frequency [Hz]
-500
-250
0
250
500
200 250 300 350 400
Eq
. vis
cou
s d
amp
ing
[N
s/m
]
XYYX YY
-500
-250
0
250
500
200 250 300 350 400
Frequency [Hz]
Eq
. vis
cou
s d
amp
ing
[N
s/m
]
C CC C
XX XYYX YY
MMFB damping: varying motion amplitudes
30 m
25 m20 m
CYX
CXXCYY
CXY
CXX
CYY
CYX CXY
CXY
CYYCXX
CYX
Direct damping decreases slightly with increasing motion amplitude.
Direct C increases with frequency.
With increasing motion amplitude, cross-damping CYX decreases
22 N Static
load
50 krpm Rotor speed
(833 Hz)
MMFB K & C: varying applied static load
22 N
36 N
36 N
22 N
For increasing static load: force
coefficients are similar in
magnitude and show same trend
in frequency.
KXX
KYX
KXY
KYY
KXX
KYX
KXY
KYY
CXY
CYYCXX
CYX CXY
CYYCXX
CYX
50 krpm Rotor speed
(833 Hz)
Net static load = 22 N ( W/LD=0.16
bar) & 36 N ( W/LD=0.26 bar)
W
-1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
es
s [
MN
/m]
-1
-0.5
0
0.5
1
200 250 300 350 400
K KK K
XX XYYX YX -1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
ess
[MN
/m]
-1
-0.5
0
0.5
1
200 250 300 350 400
K KK K
XX XYYX YX
-500
-250
0
250
500
200 250 300 350 400
Frequency [Hz]
-500
-250
0
250
500
200 250 300 350 400
Eq
. vis
cou
s d
amp
ing
[N
s/m
]
XYYX YY
-1
-0.5
0
0.5
1
200 250 300 350 400
C CC C
XX XYYX YX
-1
-0.5
0
0.5
1
200 250 300 350 400Frequency [Hz]
Sti
ffn
ess
[MN
/m]
-1
-0.5
0
0.5
1
200 250 300 350 400
C CC C
XX XYYX YX
MMFB: estimation of loss factor
Proportional structural damping C K
T T
t T t T
V M
t t
E dt E dt
z Cz z K zEnergy (material damping) = Energy (viscous damping)
2 2
2 2
XX X YY Y
XX X YY Y
C V C V
K V K V
For elliptical orbits:
For circular orbits, XX YY
XX YY
C C
K K
Energy dissipation in MMFB largely due to mechanical hysteresis. A
loss factor (γ) best represents the material damping
Material loss factor
is frequency dependent.
does not depend greatly on
displacement amplitudes, rotor
speed or static loads
MMFB: Loss factor vs. frequency
> 1.0 for all test cases. MMFB has more
damping than other types of FBsTypical BFB loss factor ~ 0.1-
0.4Kim et al. (2008)
Waterfalls of force and displacement
Dominant displacement amplitude corresponds to excitation frequency
No sub-synchronous whirl detected.
020406080
100120140160
0 200 400 600 800 1000
Frequency[Hz]
Fo
rce
[N
]
0
10
20
30
40
50
60
0 200 400 600 800 1000
Frequency [Hz]
Dis
pla
ce
me
nt
[um
]
400 Hz
200 Hz
200 Hz
400 HzSynchronous ( 833 Hz)
15.5 N 15.5 N
Fixed end 22 N static
load
50 krpm Rotor speed
(833 Hz)
MMFB CONCLUSIONS
MMFB shows large energy dissipation, >~ 1.0
Rotordynamic force coefficients estimated for various rotor speeds, motion amplitudes and static loads:
a) MMFB stiffness and damping decrease with increasing bearing displacements.
b) MMFB direct stiffness and damping largest without journal rotation (structural values). With rotation, cross-stiffnesses are small
c) MMFB direct stiffness increases with frequency while damping increases when rotor spins.
d) Similar force coefficients obtained for two static loads: 22 N and 36 N
e) MMFB loss factor is nearly independent of motion amplitude, rotor speed or applied static load
ASME GT2011-45257
MMFB CONCLUSIONS ASME GT2011-45257
Rule-of-thumb (ROT) model (Dellacorte, 2010)Typical foil bearing stiffness coeff. K~ 2,500-7,500 (L x D)
lbf/in3
damping coeff. C~ 0.1-1.0 (L x D) lbf-s/in3
MMFB stiffness coeff. K~ 1,330 (Lx D) lbf/in3 [360 MN/m3] damping coeff. C~ 0.93 (L x D) lbf-s/in3 [252 MN/m3]
Test MMFB is structurally soft with large damping: Mid-range of rule of thumb (ROT)
Net static load (applied load-bearing weight) 22 N ( W/LD=0.16 bar) and 36 N ( W/LD=0.26 bar)
Acknowledgments/ Thanks to
http://rotorlab.tamu.eduLearn more at:
Honeywell Turbocharging Technologies
Turbomachinery Research Consortium
Questions (?)
Extra slides - >
Rotor acceleratesRotor accelerates
Comparison: MMFB&BFB Friction factor vs rotor speed
f = (Torque/Radius)/(Static load)
f ~ 0.03
f ~ 0.03
Friction coefficient decreases with increasing applied static loads and rotor speed (due to lift-off)
MMFB BFB
Static load
0.01
0.1
1
0 10 20 30 40 50 60 70
Rotor speed [krpm]
Fri
ctio
n f
acto
r [-
]
35.6N
26.7N
17.8N
0.01
0.1
1
0 10 20 30 40 50 60 70
Rotor speed [krpm]
Fri
cti
on
facto
r [-
]
35.6N
26.7N
17.8N
Future work: MMFB force coefficient prediction
Θ
Θl
Θt
Θp
X
Y
eY
eX
h
r
r
p
r+c
m
r+c
Metal mesh
Rotor
Top foil radius with assembled clearance
Top foil
Fixed end
Rectangular finite element with 4 nodes
1 2
4 3
Km w
p
x
y
z
Metal mesh
Top foil
Analysis steps:1. Obtain stiffness matrix for MMFB structure + top foil using FEM.2. Assume small amplitude motions about a static position.3. Solve Reynolds equations for isothermal, isoviscous ideal gas.4. Predict force coefficients using dynamic (perturbed) pressure fields
Unwrapped Metal mesh and top foil
Demonstrate high temperature reliable operation of MMFB with adequate thermal management.
a) Construct two MMFB fitting existing test rig dimensions. b) Measure rotor response for temperature as high as 200 ºC, rotor speed up to 50
krpmc) Compare thermal performance of MMFBs with Gen. I bump-foil bearings
Future work: High temperature operation
Metal Mesh Foil Bearing