Gas Bearings for Oil-Free Turbomachinery 29th Turbomachinery Consortium Meeting Dynamic Response of...

Gas Bearings for Oil-Free Turbomachinery29th Turbomachinery Consortium Meeting

Dynamic Response of a Rotor-Air Bearing System due to Base

Induced Periodic Motions

TRC-B&C-1-09

2009 TRC Project

GAS BEARINGS FOR OIL-FREE TURBOMACHINERY

Yaying NiuYaying NiuResearch Assistant

Luis San AndrésLuis San AndrésMast-Childs ProfessorPrincipal Investigator

Start date: Oct 1st, 2008

Gas Bearings for Oil-Free TurbomachineryMicro Turbomachinery (< 0.5 MW)

• Compact and fewer parts• Portable and easily sized• High energy density• Lower pollutant emissions• Low operation cost

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 Oil-Free TurbomachineryGas Bearings for MTM

• Small friction and power losses• Less heat generation • Simple configuration • High rotating speed (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 load carrying capacity• Prone to instability

GT 2009-59315

Gas Bearings for Oil-Free Turbomachinery

Rotor motion amplitude increases largely. Subsynchronous amplitudes larger than synchronous. Excitation of system natural frequency. NOT a rotordynamic instability!

Gas Bearings for MTM

Ps=2.36 bar (ab)

GT 2009-59199

2008: Intermittent base shock load excitationsDrop 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


• 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 the predictions to test results

2008-2009 Objectives

Evaluate the reliability of rotor-air bearing systems to withstanding base load excitations

Gas Bearings for Oil-Free Turbomachinery2009 Gas bearing test rig

Oscilloscope

Functiongenerator

Power amplifier

Test rig

Electromagnetic shakerTest table

Alignment bolts Rubber O-ringsEddy current

sensors

Trust pin

Imbalance plane

Infrared tachometer

Load cells

Test bearings Motor

Accelerometer

Support springs

Electromagnetic shaker

Test rig base

Air supply

Rotor

cm

The rod merely pushes on the base plate!

Rubber pad

Hingedfixture

Rotor

Bearing

y

x

Rotationdirection

10°

Coilspring (9 kN/m)

28 cm


Clearances ~42 m, Preload ~40%. Web rotational stiffness = 62 Nm/rad.Test rig tilts by 10°. NOT Load-on-Pad (LOP) !

Flexure Pivot Hybrid Bearings: Improved stability, no pivot wear.

Test rotor and gas bearings

45°

43° 72°

6.02.

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

• 0.825 kg in weight• 190 mm in length• Location of sensors and bearings noted

Rotor

Gas bearing

Gas Bearings for Oil-Free TurbomachineryShaker delivered accelerations

-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


Rubber pad

Hingedfixture

Rotor

Bearing

y

x

Rotationdirection

10°

Coilspring (9 kN/m)

28 cm

Due to electric motor

Shaker transfers impacts to the rig base! Super harmonic frequencies are 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


24 Hz

Rotor speed:

34 krpm (567 Hz)

Gas Bearings for Oil-Free TurbomachineryRotor speed coast down tests

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

Frequency [Hz]

Am

plit

ud

e [m

m]

35krpm

2krpm

1X

2X

0.05

0.045

0.04

0.035

0.03

0.025

0.02

0.015

0.01

0.005

0

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

30krpm

Left bearing

Rotor

Right bearing

LH RH

LV RV

Ps = 2.36 bar (ab)

Subsynchronous whirlingstarts beyond 30 krpm,fixed at system naturalfrequency 193 Hz

No base excitation

Slow roll compensatedSynchronous response

Rotor coasts down

from 35 krpm

No added imbalance

Pressure 2.36bar 3.72bar 5.08barNatural Freq 192Hz 217Hz 250Hz

Gas Bearings for Oil-Free TurbomachineryRotor speed coast down tests

2X

1X

Natural freq-193Hz

24Hz (2X12Hz-Excitation freq)

35krpm

2krpm

Frequency [Hz]

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Am

pli

tud

e [m

m]

0.05

0.045

0.04

0.035

0.03

0.025

0.02

0.015

0.01

0.005

0

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

Left bearing

Rotor

Right bearing

LH RH

LV RV

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


48 Hz

Ps = 2.36 bar (ab)

Subsynchronous response:1) 24 Hz (Harmonic of 12 Hz)2) Natural frequency 193 Hz

Shaker input frequency: 12Hz

Synchronous Dominant! Excitation of system natural frequency does NOT mean instability!


Rotor response amplitude at the system naturalfrequency decreases, as the feed pressure increases.

Fixed speed, increasing pressures

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

PressureincreasesPressureincreases

Shaker input 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

Gas Bearings for Oil-Free TurbomachineryFixed pressure, increasing speeds

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

Rotor response amplitude at the system naturalfrequency increases, as the rotor speed increases.

SpeedincreasesSpeedincreases

Shaker input frequency: 12HzFeed pressure: 2.36 bar (ab)

180Hz180Hz

180Hz180Hz

193Hz193Hz

12Hz, 24Hz, 36hz, etc12Hz, 24Hz, 36hz, etc

Gas Bearings for Oil-Free TurbomachineryFixed speed and pressure, increasing input frequency

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

Rotor response amplitude at the system naturalfrequency increases, as the input frequency increases.

FrequencyincreasesFrequencyincreases

Rotor speed: 34 krpm (567Hz)Feed pressure: 2.36 bar (ab)

193Hz193Hz

NOT due to base motion!NOT due to base motion!

Same excitation magnitude for 6, 9, and 12 Hz


Prediction uses synchronous speed bearing force coefficients. In actuality, gas bearing force coefficients are frequency dependent!

XLTRC2 prediction

Shaft1232015105

Shaft11

Left bearing support Right bearing support

Test rig base

LH

LV

RH

RV

Base motion

Rotor speed 26 krpm 30 krpm 34 krpm

Conical 202 Hz 212 Hz 222 Hz

Cylindrical 185 Hz 193 Hz 201 Hz



Natural freq=13,338cpm (222Hz)Damping ratio=0.044Rotor speed=34 krpm

Conical mode

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

201 Hz

60 Hz

48 Hz

36 Hz

24 Hz

12 Hz

222 Hz

XLTRC2

Measured

Left bearing

Rotor

Right bearing

LH RH

LV RV

FE rotor model

Conical

Cylindrical

System Natural Freq

Input accelerationin XLTRC2, simulateactual acceleration.


XLTiltPadHGB™

Gas Bearings for Oil-Free TurbomachineryXLTRC2 prediction

Left bearing

Rotor

Right bearing

LH RH

LV RV Shaker input frequency: 12HzFeed pressure: 2.36 bar (ab)Rotor speed: 34 krpm (567 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]

Acc

eler

atio

n [

m/s

2]

Input acceleration

201 Hz

60 Hz

48 Hz

36 Hz

24 Hz

12 Hz

222 Hz

Input accelerationonly on VERTICAL direction

XLTRC2 predicts absolute rotor motions! Measured rotor response is relative to bearing housing.

Predicted natural frequencycomponent

Prediction frequency step:1.25 Hz.

0.01

0.1

1

10

100

1000

10 100 1000

Frequency [Hz]

Am

plit

ud

e [μ

m]

LV_34krpm_measurement_relative

LV_34krpm_XLTRC2 prediction_absolute

12Hz

24Hz

36Hz

48Hz

60Hz

201 & 222Hz

567Hz193Hz70~90Hz

Measured N.F. component

Gas Bearings for Oil-Free TurbomachineryRigid rotor model prediction

imb b bΜU GU CU KU = W F CU KU&& & & &




XLTRC2



Measured


Rigid rotor model

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

Left bearing

Rotor

Right bearing

LH RH

LV RV

System response equals to the superposition of unique single frequency responses.

System Natural Frequency:

Input acceleration in rigid rotor model, VERTICAL direction only!

Equations of Motion:Equations of Motion:

12 i i

Z K Μ G C F


Steady-State!

Absolute rotor response

r bZ Z U Relative rotor response

Rotor 1st bending mode: 1,917 Hz (115 krpm)


Rigid rotor model predicts relative rotor motions! The test rotor-bearing system shows good isolation.

Rigid rotor model prediction

Left bearing

Rotor

Right bearing

LH RH

LV RV Shaker input frequency: 12HzFeed pressure: 2.36 bar (ab)Rotor speed: 34 krpm (567 Hz)

Relative rotor motion

Predicted natural frequencycomponent

Above the natural frequency,the system is isolated!Above the natural frequency,the system 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

Measured N.F. component

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


• The recorded rotor response contains the main input frequency (5-12 Hz) and its super harmonics, and the rotor-bearing system natural frequency.

• The motion amplitudes at the natural frequency are smaller than the components synchronous with rotor speed.

• The rotor motion amplitude at the system natural frequency increases as the gas bearing feed pressure (5.08~2.36bar) decreases, as the rotor speed (26~34krpm) increases, and as the shaker input frequency (5~12 Hz) increases.

• Predicted rotor motion responses obtained from XLTRC2® and an analytical rigid rotor model show good correlation with the measurements. The system shows reliable isolation.

Conclusions

Reliability of rotor-air bearing system to withstanding base load excitations demonstrated

Gas Bearings for Oil-Free Turbomachinery 29th Turbomachinery Consortium Meeting Dynamic Response of...

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