Dynamic Response of a Rotor-Hybrid Gas Bearing System due to
Base Induced Periodic Motions
Keun RyuResearch Assistant
Luis San AndrésMast-Childs Professor
Fellow ASME
TURBOMACHINERY LABORATORYTEXAS A&M UNIVERSITY
Supported by TAMU Turbomachinery Research Consortium
ASME paper GT2010-22277
Yaying NiuResearch Assistant
ASME TURBO EXPO 2010, Glasgow, Scotland, UK
Microturbomachinery (< 250 kW)
• Compact and fewer parts• Portable• High energy density• Lower emissions• Low operation/maintenance costs
Advantages
http://www.hsturbo.de/en/produkte/turboverdichter.html
Turbo Compressor100 krpm, 10 kW
Micro Turbo500 krpm, 0.1~0.5 kW
http://www.hsturbo.de/en/produkte/micro-turbo.html
Oil-free turbocharger120 krpm, 110 kW
http://www.miti.cc/new_products.html
Gas bearings for microturbomachinery
• Little friction and power losses• Simple configuration • High rotor speeds (DN value>4M)• Operate at extreme temperatures
Advantages
Gas Foil Bearing Flexure Pivot Bearing
Metal Mesh Foil Bearing
AIAA-2004-5720-984 GT 2004-53621
Issues• Small damping• Low static load capacity• Prone to instability
GT 2009-59315
Gas Bearing Research at TAMU
2001/2 - Three Lobe Bearings
2003/4 - Rayleigh Step Bearings
2002-09 - Flexure Pivot Tilting Pad Bearings
2004-10: Bump-type Foil Bearings
2008-10: Metal Mesh Foil Bearings
Stability depends on feed pressure. Stable to 80 krpm with 5 bar pressure
Worst performance to date with grooved bearings
Stable to 93 krpm w/o feed pressure. Operation to 100 krpm w/o problems. Easy to install and align.
Industry standard. Reliable but costly.Models anchored to test data.
Cheap technology. Still infant. Users needed
• Set up an electromagnetic shaker under the base of test rig to deliver periodic load excitations
• Measure the rig acceleration and rotordynamic responses due to shaker induced excitations
• Model the rotor-air bearing system subject to base motions and compare predictions to test results
Objective & tasks
Evaluate the reliability of rotor-air bearing systems to withstanding periodic base or foundation excitations
Positioning Bolt
X
Y
Load
LOP
Rotor/motor
Bearing
Sensors
Load cell
Air supply
Thrust pin
Rotor: 826 gramsBearings: L= 30 mm, D=29 mm
190 mm, 29 mm diam
Gas Bearing Test Rig
Clearance ~42 m, preload ~40%. Web rotational stiffness = 62 Nm/rad.Test rig tilted by 10°.
Flexure Pivot Hybrid Bearings: Improved stability, no pivot wear
Rotor and hybrid gas bearings
45°
43° 72°
6.0
2.0
33.2
62
.485
A
A
Rotation directionSection A-A
Load cells
Φ0.5 feed hole
Air supply
Flexure web
Pad
Y
X10°
Static Load
Eddy current sensor probe
Left bearing Right bearing
Vertical Vertical
Horizontal Horizontal
• 0.826 kg, 190 mm in length• Location of sensors and
bearings noted
Rotor
Rotor motion amplitudes increase with excitation of system natural frequency. NOT a rotordynamic instability!
Intermittent base shock load excitations
Ps=2.36 bar (ab)
Previous work (GT 2009-59199)
Drop induced shocks ~30 g. Full recovery within ~ 0.1 sec.
Load cell
Pressurized air supply
Eddy current sensors
Alignment Bolt
Hitting rod
Test table
Load cell
Rubber pad
Accelerometer (A1)
Accelerometer (A2)
Plunger
Solenoid
RotorGas bearing
Hinged fixture
cmcm Plastic pad
Test table
Load cell
Pressurized air supply
Eddy current sensors
Alignment Bolt
Base plate
Rubber pad
Rotor
Gas bearing
Hinged fixture
cmcm
Electromagnetic shaker
Coil spring (9kN/m)10º
x
y
28cm
Rotational direction
cmcm
Electricmotor
Load cells
Infrared tachometer
Pressurized air supply
Thrust pin
Flexure pivot pad bearing
Eddy current sensors
Alignment Bolts
Imbalance plane
LB RB
Test table
Rotor
Support springs
Electromagnetic shaker
Accelerometer
Rubber O-rings
Gas bearing test rig
Front and side views (not to scale)
Base excitation
Shaker & rod push base of test rig
Hybrid gas bearing test rigOscilloscope
Functiongenerator
Power amplifier
Test rig
Electromagnetic shakerTest table
Rod pushes base plate!(no rigid connection)
Waterfalls in coast down Ps = 2.36 bar
No base excitation
0
10
20
30
40
50
60
0 200 400 600 800 1000 1200 1400
Frequency [Hz]
Am
pli
tud
e [
µm
]
35 krpm
2krpm
1X
2X
LV
30 krpm
Subsynchronous whirl > 30 krpm,fixed at system natural frequency = 193 Hz
Left bearing
Rotor
Right bearing
LH RH
LV RV
Rotor speed coast down tests (35 krpm)
0
5
10
15
20
25
0 5 10 15 20 25 30 35 40
Speed [krpm]
Am
pli
tud
e (p
k-p
k) [
μm
]
LV_2.36bar (ab)
LV_3.72bar (ab)
LV_5.08bar (ab)
192Hz (11.5krpm) @ 2.36bar
217Hz (13krpm) @ 3.72bar
250Hz (15krpm) @ 5.08bar
Left bearing
Rotor
Right bearing
LH RH
LV RV
Feed pressure increases natural frequency and lowers damping ratio
No base excitation
1X response
Pressure 2.36bar 3.72bar 5.08barNatural Freq 192Hz 217Hz 250Hz
Left bearing housing
Right bearing housingMotor
casing
Base plate
Accelerometer
Imp
act
cm
Natural frequency whole test rig (5 Hz)
Soft mounts (coils) produce low natural frequency
0
0.1
0.2
0.3
0.4
0 20 40 60 80 100
Frequency [Hz]
Acc
eler
atio
n [g
]
Test rig base plate
Motor casing
Left bearing housing
Right bearing housing
5 Hz - Natural freq of the test rig
Acc
eler
atio
n (g
)
Delivered excitations (6 Hz)
-2
-1
0
1
2
3
0 0.1 0.2 0.3 0.4 0.5
Time [sec]
Acc
eler
atio
n [
g]
Acceleration
0.17 sec (6 Hz)
Excitation frequency: 6 Hz
0
0.05
0.1
0.15
0.2
0.25
0.3
0 200 400 600 800 1000
Frequency [Hz]
Acc
eler
atio
n [g
]
Acceleration
6 Hz
12 Hz
18 Hz624 Hz
51 Hz
Excited frequencies
Excitation frequency: 6 Hz
Due to electric motor
Shaker transfers impacts to rig base! Super harmonic frequencies excited
0
0.05
0.1
0.15
0.2
0.25
0.3
0 20 40 60 80 100
Frequency [Hz]
Acc
eler
atio
n [
g]
Acceleration
6 Hz12 Hz 18 Hz
51 Hz
Excited frequencies
Excitation frequency: 6 Hz
24 Hz
Rotor speed: 34 krpm (567 Hz)
Acc
eler
atio
n (g
)A
ccel
erat
ion
(g)
Acc
eler
atio
n (g
)
zoom
Test table
Load cell
Pressurized air supply
Eddy current sensors
Alignment Bolt
Base plate
Rubber pad
Rotor
Gas bearing
Hinged fixture
cmcm
Electromagnetic shaker
Coil spring (9kN/m)10º
x
y
28cm
Rotational direction
Waterfalls in coast down
Ps = 2.36 bar (ab)
Shaker frequency: 12Hz
0
10
20
30
40
50
60
0 200 400 600 800 1000 1200 1400
Frequency [Hz]
Am
plit
ud
e [µ
m]
Series1
35 krpm
2krpm
Natural frequency:193 Hz
24 Hz (2×12Hz: Excitation frequency)
1X
2X
LV
Rotor speed coast down
0
5
10
15
20
0 100 200 300 400 500 600
Frequency [Hz]
Am
pli
tud
e [μ
m]
Amplitude_LV
Synchronous response
Natural frequency
212 Hz
Ps = 2.36 bar (ab)
Subsynchronous frequencies:1) 24 Hz (2 x 12 Hz)2) Natural frequency 193 Hz
Shaker frequency: 12Hz
Synchronous motion dominates! Excitation of system natural frequency
does NOT mean instability!
0
0.05
0.1
0.15
0.2
0.25
0.3
0 20 40 60 80 100
Frequency [Hz]
Acc
eler
atio
n [
g]
Acceleration
12 Hz 24 Hz 36 Hz
51 HzExcited frequencies
Excitation frequency: 12 Hz
48 Hz
0
10
20
30
40
50
60
0 200 400 600 800 1000 1200 1400
Frequency [Hz]
Am
plit
ud
e [µ
m]
Series1
35 krpm
2krpm
Natural frequency:193 Hz
24 Hz (2×12Hz: Excitation frequency)
1X
2X
LV
Rotor motion amplitude at system naturalfrequency decreases as feed pressure increases
Effect of feed pressure
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 100 200 300 400 500 600 700
Frequency [Hz]
Am
pli
tud
e [
mm
]
LV_2.36barLV_3.72barLV_5.08bar
Natural frequency
70~90Hz
Excitation frequency: 12Hz; Speed: 34krpm
Synchronousfrequency 567Hz(34 krpm)
Excitedfrequency and harmonics
2.36 bar
3.72 bar
5.08 bar
Left bearing
Rotor
Right bearing
LH RH
LV RV Shaker frequency: 12HzRotor speed: 34 krpm (567 Hz)
193Hz193Hz
215Hz215Hz
243Hz243Hz
12Hz, 24Hz, 36hz, etc12Hz, 24Hz, 36hz, etc
NOT due to base motion!NOT due to base motion!
Offset by0.01 mm
Ps: 2.36, 3.72 & 5.08 bar
PressureincreasesPressureincreases
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 100 200 300 400 500 600 700
Frequency [Hz]
Am
pli
tud
e [m
m]
LV_26krpm
LV_30krpm
LV_34krpm
567Hz (34krpm)
500Hz (30krpm)
433Hz (26krpm)
Excitation frequency: 12Hz; Feed pressure: 2.36bar (ab)
Natural frequency
70~90Hz
Excited frequencyand harmonics
26 krpm
30 krpm
34 krpm
Left bearing
Rotor
Right bearing
LH RH
LV RV
SpeedincreasesSpeedincreases
Shaker frequency: 12HzFeed pressure: 2.36 bar (ab)
180Hz180Hz
180Hz180Hz
193Hz193Hz
12Hz, 24Hz, 36hz, etc12Hz, 24Hz, 36hz, etc
Effect of rotor speed 26, 30 & 34 krpm
Rotor motion amplitude at system naturalfrequency increases as rotor speed increases
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 100 200 300 400 500 600 700
Frequency [Hz]
Am
pli
tud
e [m
m]
LV_W/O LV_5HzLV_6Hz LV_9HzLV_12Hz
Synchronousfrequency 567Hz(34 krpm)
Excited frequencyand harmonics
Feed pressure: 2.36bar (ab); Speed: 34krpm
Natural frequency
70~90 HzNo excitation
5Hz
6Hz
9Hz
12Hz
Left bearing
Rotor
Right bearing
LH RH
LV RV
FrequencyincreasesFrequencyincreases
Rotor speed: 34 krpm (567Hz)Feed pressure: 2.36 bar (ab)
193Hz193Hz
NOT due to base motion!NOT due to base motion!
Effect of base frequency 0, 5, 6, 9, 12 Hz
Rotor motion amplitude at natural frequency increases as excitation frequency increases
Rigid rotor model
imb b bΜU GU CU KU = W F CU KU&& & & &Left bearing
Rotor
Right bearing
LH RH
LV RV
System response = superposition of single frequency responses
12i ii i
Z K Μ G C F
Rotor 1st elastic mode: 1,917 Hz (115 krpm)
Equations of motion (linear system)
K, C: bearing stiffness and damping from gas bearing model (San Andres, 2006)
U, Ub: rotor and base (abs) motions, Z=U-Ub
M,G: rotor inertia and gyroscopic matricesW: rotor weight Fimb: imbalance “force” vector
b b imbΜ Z U G Z U CZ KZ = W F&& && & & &
imb b bΜZ GZ CZ KZ = F F ΜU GU&& & & && &
Rework equations in terms of measured variables:
Rigid rotor model
Rotor speed 26 krpm 30 krpm 34 krpm
Conical 191 Hz 200 Hz 208 Hz
Cylindrical 184 Hz 192 Hz 200 Hz
Measured from 1X response tests
Cylindrical 180 Hz 182 Hz 193 Hz
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 50 100 150 200 250 300
Frequency [Hz]
Ac
cele
rati
on
[m
/s2
]
Input acceleration
200 Hz
60 Hz
48 Hz
36 Hz
24 Hz
12 Hz
209 Hz
Left bearing
Rotor
Right bearing
LH RH
LV RV
Good agreement shows predicted bearing force coefficients are accurate
Predicted natural frequencies
For predictions: input RECORDED
BASE accelerations (vertical)
Predictions in good agreement! Test rotor-bearing system shows good isolation.
Predictions vs. measurements
Shaker input frequency: 12HzFeed pressure: 2.36 bar (ab)
Rotor speed: 34 krpm (567 Hz)
Above natural frequency,RBS is isolated!
Above natural frequency,RBS is isolated!
0.01
0.1
1
10
100
1000
10 100 1000
Frequency [Hz]
Am
plit
ud
e [μ
m]
LV_34krpm_code prediction_relative
LV_34krpm_measurement_relative
12Hz
24Hz36Hz
48Hz
60Hz
200 & 208Hz
567Hz193Hz70~90Hz
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 50 100 150 200 250 300
Frequency [Hz]
Acc
eler
atio
n [
m/s
2]
Input acceleration
200 Hz
60 Hz
48 Hz
36 Hz
24 Hz
12 Hz
209 Hz
Nat freq. 1XExcitation freqs.
Left bearing
Rotor
Right bearing
LH RH
LV RV
• Rotor response contains 1X, excitation frequency (5-12 Hz) and its super harmonics and system natural frequency.
• Rotor motion amplitudes at natural frequency are smaller than synchronous amplitudes.
• Excited rotor motion amplitude at system natural frequency increases as gas bearing feed pressure (5.08~2.36bar) decreases, as rotor speed (26~34krpm) increases, and as the shaker input frequency (5~12 Hz) increases.
• Predicted rotor motion responses obtained from rigid rotor model show good correlation with test data.
Conclusions
Demonstrated isolation of rotor-air bearing system to withstand base excitations at low freqs.
Base Excitations on Gas-Rotor Bearing Syst
AcknowledgmentsThanks support of• TAMU Turbomachinery Research Consortium• Bearings+ Co. (Houston)
Learn morehttp://rotorlab.tamu.edu
Questions ?