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 ?