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
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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
Adiletta, G., Guido, A., and Rossi, C., 1997, Nonlinear Dynamics, 14
Steady 1X whirl
15
0
0.5
1
1.5
2
0 100 200 300Frequency (Hz)
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:
Measured orbit Predicted orbit
Horizontal plane Left end of rotor
LB RB
Adiletta, G., Guido, A., and Rossi, C., 1997, Nonlinear Dynamics, 14
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
0 100 200 300Frequency (Hz)
Mag (m
m)
Clearance circle
6 krpm
Measurement vs. PredictionCase 1
Measured orbit Predicted orbit
Horizontal plane Left end of rotor
LB RB
Adiletta, G., Guido, A., and Rossi, C., 1997, Nonlinear Dynamics, 14
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.
NL Transient Response Analysis
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)
Prediction Measurement
Measurement vs. predictionCase 2 5.6 krpm
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)
Prediction Measurement
Measurement vs. predictionCase 2 6.0 krpm
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
NL Transient Response Analysis
Help needed down the road: Email to [email protected]
Questions (?)