AUTOMATED ANALYSIS OF TIME TRANSIENT RESPONSE IN …

AUTOMATED ANALYSIS OF TIME TRANSIENT RESPONSE IN NONLINEAR

ROTOR BEARING SYSTEMSQing Liu

Research Assistant, Ph.D.

Luis San AndresMast-Childs ProfessorPrincipal Investigator

32nd Turbomachinery Research Consortium Meeting

TRC 32513/1519X5

Year I

May 2012

2

Why a Transient Response Analysis?All Rotor Bearing Systems (RBS) undergo unsteady

or transient forcing loading:• Start and shut down events: influence of load and rotor speed on

transient behavior

• Sudden events: blade loss simulations (large imbalances), maneuver loads

• Support excitation: earthquake, engine motions and noise

• Beyond the threshold speed of instability: whirl frequency and limit cycle (orbit size)

• Highly NL rotating machines: turbochargers, rotors on foil bearing systems, electrical submersible pumps (ESP)

Trend in RBS design & analysis: conduct more & more preliminary studies (using fast virtual tools) to anticipate anyupsetting event to costly systems.

3

XLTRC² Rotordynamics Tool• Beam Finite-Element Formulation• Real Component-Mode Synthesis (CMS) model• Multi-line Rotor/Housing Modeling Capability• Linear and transient response nonlinear

analyses• Fully integrated with an extensive suite of support

codes• User-Friendly GUIs for rapid model development and

report generationGeneral EOMs

(t)QqKqGqCqM =+Ω−+

4

0 1 2 3 4 5 6 7-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

XLTRC² Transient Response Analysis• Restricted to simple NL models

(short length JB, dry friction)• Cumbersome to use: impossible

to understand• Time consuming: transient

response calculations take long times (unpredictable time)

• Repeat input for multiple cases• Tons of data output: no post-

processing tools

Typical case:~190,000 time steps

Objective: to create GUIs to automate transient RBS response prediction/analysis

5

Work to Date: June 2011-May 2012Current work:• Added click & run worksheets: multiple cases,

multiple loading conditions, multiple bearing configurations, efficient storage of data

• Post-processing tools: analyze tons of data (thousands of data points), make FFTS and waterfalls, filter responses to obtain 1X and any other sub or super-synchronous motions, filtered mode shapes at selected frequencies, etc.

• Setup test rig (flex rotor on JBs) to measure responses and to benchmark predictions of rotor NL dynamics.

Save time in diagnosing & troubleshooting

66

GUI Transient Response PredictionsUser input worksheet: Transient time response for rotor bearing system Multiple CONSTANT rotor speedsOutput data folder G:\work\trc report demo const\result

Set sampling rate

Option 1: Variable sampling rate

Total revolutions Samples/rev Total steps

16 16

Option 2: Constant sampling rate Chosen

Sample rate (Hz) Total elapsed time (s) Total steps

1000 1 1000

2 Constant sampling rate

Setup Multiple Runs Parameters of Transient Response for Rotor Bearing System CASES Transient Response Options

Output shaft TimeRun data file speed start

# name RPM T01 file 1 1000 02 file 2 2000 03 file 3 3000 0

Nonlinear connection # of Nlconn 2

NLconn from Stn NLconn to Stn NLconn type NLconn option

4 0

27 0

Default 3 Moes' impedance

Default 3 Moes' impedance

UserDef 8 Foil bearing

Default 2 Rub simulator

UserDef 8 Foil bearing

Nonlinear ConnectionsBearing #1 Moes' Impedance

Length Diameter Clearance Viscosity JB or SFD[in] [in] [in] [psi-s] =JrnlBrg, 0=SF

1.125 0.5 4.00E-03 2.03E-06 11.125 0.5 4.00E-03 2.03E-06 11.125 0.5 4.00E-03 2.03E-06 1

Update Parameters

Run Multiple Cases

1. Select folder to restore output data files

2. Set sampling time and rate 3. Choose NL connection location and model

4. Set file name, running speed for each case

5. Input NL connection parameters

Last step: Click buttons to update parameters and run cases

Find all output files in this folder. SAVE TIME

The worksheet looks complicated and confusing…

Friday morning: Please attend DEMO session showing usage of GUIs

GUI Transient Response Predictions

But actually they are NOT.

Filling up the worksheet takes only a few minutes. Next, click RUN, and XLTRC2 will do the work for ALL the cases.

0.E+00

1.E-07

2.E-07

3.E-07

4.E-07

0 50 100Frequency (Hz)

Am

p (m

)

GUI Transient Response Analysis• Get an overview• More detailed view if needed• Select a time range• Expand to view details• Calculate FFTs• Select a frequency &• Draw deflected rotor shape

-5.E-07-4.E-07-3.E-07-2.E-07-1.E-070.E+001.E-072.E-073.E-074.E-075.E-07

0.0 2.0 4.0 6.0 8.0 10.0

Time (s)

Dis

plac

emen

t (m

)

0200400600800100012001400160018002000

Rot

or s

peed

(RPM

)

displacement

rotorspeed

With low resolution: Plot every 10 data pts.

-6.E-07

-4.E-07

-2.E-07

0.E+00

2.E-07

4.E-07

6.E-07

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

Time (s)

Dis

plac

emen

t (m

)

0200400600800100012001400160018002000

Rot

or s

peed

(RPM

)

displacement

rotorspeed

With medium resolution: Plot every 5 data pts.

LB RB

FFT

at 25Hz (1X)

-6.E-07

-4.E-07

-2.E-07

0.E+00

2.E-07

4.E-07

6.E-07

5 5.2 5.4 5.6 5.8 6time (s)

Dis

plac

emen

t (m

)

XY

99

GUI Transient Response AnalysisFrequency analysis and filtering

012345678

0 100 200 300 400 500

Frequency (Hz)

Mag

(mil)

00.5

11.5

22.5

33.5

44.5

0 2000 4000 6000 8000 10000

Rotor speed (RPM)

Sync

hron

ous

& S

ubsy

nchr

onou

s R

espo

nse

Mag

nitu

de (m

il)

synchronoussubsynchronous

0

2000

4000

6000

8000

10000

0 50 100 150

Synch/Subsynch Resp Freq (Hz)

Rot

or s

peed

(RPM

)

synchronoussubsynchronous

0

20

40

60

80

100

0 2000 4000 6000 8000 10000

RPM

WFR

(%)

waterfall

Amplitudes vs. speed

Whirl frequencies vs. speed Whirl frequency ratio

1010

Nonlinear transient RBS response analysis cases:

• Rigid rotor supported on plain journal bearings, running at multiple constant rotor speeds.

• Flexible rotor supported on elliptical journal bearings, running at time-varying rotor speed.

NL Transient Response Analysis

1111

Rigid rotor on plain journal bearings

Adiletta, G., Guido, A., and Rossi, C., 1997, “Nonlinear Dynamics of a Rigid Unbalanced Rotor in Journal Bearings. Part II: Experimental Analysis”, Nonlinear Dynamics, 14, pp. 157-189.

Test rigLeft bearing Right bearingLB RB

measurement planes

imbalance planes

Rotor geometry

Case 1

1212

Physical Parameter Value

RotorMass (kg) 16.7Transverse moment of inertia (kg-m2) 0.24Polar moment of inertia (kg-m2) 0.0143

Plain Journal Bearings

length (mm) 16diameter (mm) 80radial clearance (mm) 0.25Bearings’ span (mm) 280Oil viscosity (cPoise) 17.6

Predic. first critical speed: ~2,500 rpm (41.6 Hz)

Experimentally observed subsynchronous motion starts at ~4,600 rpm (77 Hz = 1.85 x crit. speed)

L/D=0.2D/c=320

RBS configurationCase 1

Adiletta, G., Guido, A., and Rossi, C., 1997, Nonlinear Dynamics, 14

13

0

0.5

1

1.5

2

0 50 100 150 200 250 300

Frequency (Hz)

Mag (m

m)

13

Operating range: 3-10 krpmRBS begins to show subsynchronous motions at ~4.5 krpm.

1X

Waterfall plot for predicted responseHorizontal plane, Left end of rotorImbalance: 51.4 g-cm at each imbalance plane, in phase

LB RB

3.0 krpm

10 krpm

Predicted RBS transient responseCase 1

4.5 krpm

½ X¼ X ¾ X

Experiments show rotor ½ frequency whirls starts at ~4.6 krpm

14

-0.3

-0.15

0

0.15

0.3

-0.3 -0.15 0 0.15 0.3X- Response (disp), mm

Y- R

espo

nse

(dis

p), m

m

0

0.5

1

1.5

2

0 100 200 300Frequency (Hz)

Mag (m

m)

3 krpm

Clearance circle

Measurement vs. PredictionCase 1Horizontal plane Left end of rotor

Measured orbit Predicted orbit

LB RB


Steady 1X whirl

15

0

0.5

1

1.5

2


Mag (m

m)

-0.3

-0.15

0

0.15

0.3

-0.3 -0.15 0 0.15 0.3X- Response (disp), mm

Y- R

espo

nse

(dis

p), m

m

4.5 krpm

Clearance circle

Measurement vs. PredictionCASE 1:


Horizontal plane Left end of rotor

LB RB


Start of ½ whirl frequency motions

16

-0.3

-0.1

0.1

0.3

-0.3 -0.1 0.1 0.3X- Response (disp), mm

Y- R

espo

nse

(dis

p), m

m

0

0.5

1

1.5

2


Mag (m

m)

Clearance circle

6 krpm

Measurement vs. PredictionCase 1


Horizontal plane Left end of rotor

LB RB


Large amplitude (~c) ½ whirl frequency motions

1717

Nonlinear transient RBS response analysis cases:

• Rigid rotor supported on plain journal bearings, running at multiple constant rotor speeds.

• Flexible rotor supported on elliptical journal bearings, running at time-varying rotor speed.


1818

measurement planes

imbalance planes

LB RBLeft bearing

Right bearing

Test rig in Turbomachinery Lab

Rotor geometry

Flexible rotor on elliptical bearingsCASE 2:

1919

Physical Parameter Value

RotorMass (lbm) 28.4Transverse moment of inertia (lbm-in2) 1023Polar moment of inertia (lbm-in2) 120

Elliptical Bearings

length (in) 1.125diameter (in) 1Radial pad clearance (mil)preload

40.5

Bearings’ span (in) 21Lubricant viscosity (cPoise) 16.5

L/D=1.125D/c=250½ W/LD

=12.6 psi(light load)

Pin-pin mode critical speed: ~ 4.8 krpm (80 Hz)

Experimentally observed subsynchronous ½ whirl motions start at ~5.25 krpm (just 25% above crit. speed)

RBS configurationCase 2

LB RBLB RB

20

0 50 100 150 200 250 3000

10

20

30

40

50

frequency (Hz)

Y (m

il)

20

5.25 krpm

6.6 krpm

3.0 krpm

LB RB

RBS shows subsynchronous whirl motion from ~5.25 krpm (87 Hz) (25% above crit. Speed = 80 Hz)

Waterfall plot for measured responseHorizontal planeCenter of rotor

Measured transient responseCase 2

1X

0 50 100 150 2000

10

20

30

40

50

frequency (Hz)

Y (m

il)

2121

-4 -2 0 2 4-4

-2

0

2

4

X (mil)

Y (m

il)

4.8 krpm

Measurement vs. predictionCase 2

0 50 100 150 2000

0.5

1

1.5

frequency (Hz)

Y (m

il)

0 50 100 150 200Frequency (Hz)

Prediction

4.8 krpm

Measurement1X 1X

1

0.5

0

orbit

LB RBLB RB

Am

p (m

il)

1XSteady 1X whirl

22220 50 100 150 2000

10

20

30

40

50

frequency (Hz)

Y (m

il)

-4 -2 0 2 4-4

-2

0

2

4

X (mil)

Y (m

il)

5,250rpm

0 50 100 150 2000

0.5

1

1.5

frequency (Hz)

Y (m

il)

0 50 100 150 200

Frequency (Hz)

Prediction Measurement

Measurement vs. predictionCase 2 5.25 krpm

1X1X

orbit

LB RBLB RB

1

0.5

0

Am

p (m

il)

0.5 X

1XMeasurements: start of ½ X whirl.Prediction: steady 1X whirl.

230 50 100 150 2000

10

20

30

40

50

frequency (Hz)

Y (m

il)

23

0

4

3

3

3

0 50 100 150 200Frequency (Hz)

5,600rpm

0 50 100 150 2000

0.5

1

1.5

2

2.5

frequency (Hz)

Y (m

il)

-4 -2 0 2 4-4

-2

0

2

4

X (mil)

Y (m

il)



1X 1X2

1

0

LB RBLB RB

orbit

0.5 X 0.5 X

Am

p (m

il)

1X

-5

-4

-3

-2

-1

0

-2 0 2 4X (mil)

Y (m

il)

½ whirl motion

24240 50 100 150 2000

10

20

30

40

50

frequency (Hz)

Y (m

il)

-5 0 5-4

-2

0

2

4

X (mil)

Y (m

il)

6,000rpm

0 50 100 150 2000

0.5

1

1.5

2

2.5

3

frequency (Hz)

Y (m

il)

0 50 100 150 200

Frequency (Hz)



1X1X543210

LB RBLB RB

orbit

Am

p (m

il) 0.5 X0.5 X

1XOrbit size of ½ X whirl increases.

2525

Predicted deflected shapesCase 2

0 50 100 150 200Frequency (Hz)

Rotor shape at synchronous frequency

(93 Hz)

Rotor shape at subsynchronous whirl frequency ( ½ X) 46 Hz

2

1

0

Am

p (m

il)

5.6 krpm

1X

LB RBLB RBPin-pin mode

½ X

26

Proposed work 2012-2013Include realistic NL bearing models in XLTRC2©Pressure dam bearing, elliptical bearing, multiple-pad bearings.

Simulate NL responses for various rotor-bearing systems (RBS)Electrical submersible pumps (ESP), CO2 turbo-alternator on foil bearings, turbochargers.

Measure nonlinear RBS in test rigand compare to nonlinear predictions – simulate sudden imbalance (blade loss).

Proposed work 2012-2013Transient response analysis for ESP• Widely used in oil drilling.• Limited operational life.• Expensive installation, repairing, and replacing parts, especially in subsea applications.

System reliability and availability are compromised

Speed Drive

Pump

Seal

Motor

Why a NL response analysis for an ESP? • Long thin rotor in a flexible casing• Plain journal bearings induce oil whirl/whip with large amplitude motions that damage seal & bearings• Complicated working environment: mixture of oil, gas and even solids.

http://www.openelectrical.org/wiki/index.php?title=Electrical_Submersible_Pump

Example: whirl in a vertical pump

Corbo, M., Stefanko, D., and Leishear, R., 2002, “Practical Use of Rotordynamic Analysis to Correct a Vertical Long Shaft Pump’s Whirling Problem”, Proc. of 19th

Int. Pump Users Symp.

roto

r spe

ed

1X

Crit speed (nat.freq.

Whirl frequency = natural freq.

29

TRC BudgetYear II

Support for graduate student (20 h/w) x $ 2,200 x 12 months $ 26,400Fringe benefits (0.6%) and medical insurance ($197/month) $ 2,522Travel to (US) technical conference $ 1,200Tuition & fees three semesters ($227/credit hour) $ 9,262Other (PC-DAQ, HD storage, test rig supplies) $ 2,100

2012-2013 Year II $ 41,484

GUIs in XLTRC2 code will help Users to model NL rotordynamics with actual bearing types and to analyze responses in the frequency domain.

2012-2013 Year II

3030

Friday morning: Attend DEMO session showing usage of GUIs


Help needed down the road: Email to [email protected]

Questions (?)

Documents

AUTOMATED ANALYSIS OF TIME TRANSIENT RESPONSE IN …