Post on 14-Mar-2020
Analysis of a turbo generator rotor
Acir Edvam Ozelame
Celso Kenzo Takemori
Edmar Baars
About Vibroacústica
590 km
Partners
Problem descripton
• Turbo generator rotor
Problem description
• Estimate the influence of the bowed rotor and the machined flange on the vibration behavior using static structural results.
• Simple and accurate model.
• Extremely fast.
• “Field simulation”
• For example: – Oscillating loads on the supports
(bearings) can lead to vibration.
– Unbalanced mass due to rotor deformation.
Problem description
• Beam elements
• Model validation and verification
– Assembly requirements (manufacturer)
– Modal analysis
• Analysis
– Reaction forces
– Deflection shape
Problem description
Important note: Without CAD, only drawings on papers before 1990!
Methodology – Beam elements
#Station ID Length Outer diameter Inner diameter
1 130 640 80
2 280 280 80
3 130 640 80
4 180 355 80
5 175 355 80
6 135 420 80
7 210 530 80
...
• The mathematical model, and its results,
were compared to experimental data and
manufacturer information:
– Mass and center of mass
– Assembling alignment
– Deflection due to gravity
– Critical speeds
Results - Model validation and verification
Generator
Nominal 48000 kg
Model 47960 kg
LP Rotor
Nominal 43250 kg, CM 4345 mm (Reference plane #5)
Model 43233 kg, CM 4280 mm
HP-IP Rotor
Nominal 20300 kg, CM 3602 mm (Reference plane #5)
Model 20281 kg, CM 3585 mm
Mass and center of mass
-1,00
0,00
1,00
2,00
3,00
4,00
5,00
6,00
7,00
0 5000 10000 15000 20000 25000 30000
HP-IP Rotor, Cold assembly (+1.5mm onbearing #1)
LP Rotor, Cold assembly
Generator, Cold assembly (-0.05mm onbearing #5, +4.57mm on bearing #6)
+4.57 mm
-0.05
mm +1.5
mm
HP-IP
LP
Generator
Simulation: 0.27 mm Manufacturer data: 0.30 mm
Simulation: 4.57 mm Manufacturer data: ~5.00 mm
Length [mm]
Dis
pla
ce
me
nt [m
m]
Assembly configuration, before coupling,
deflection shape due to weight
Simulation: 0.15 mm Manufacturer data: 0.15 mm
HP-IP Rotor, Deflection shape only due to
weight
Bowed rotor model
• The effect of the permanent deformation of the HP-IP rotor was modeled using opposite moments.
• In the graph, measured data are identified as ‘bolt #7’ and ‘bolt #8’, and the bowed rotor mathematical model is the curve labeled ‘moment’. -20
-10
0
10
20
30
40
0 2000 4000 6000 8000
Ru
n-o
ut
[10
0th
of
mm
]
Length [mm]
Bolt #7
Bolt #8
Moment
Model verification
LP rotor modal analysis
18.9 Hz 28.9 Hz 43 Hz
48 Hz
71 Hz
? ? Rigid support
Flexible support 17 Hz 28 Hz 51 Hz 79 Hz
Model verification
Critical speeds
990 rpm
992 rpm
1650 rpm
1659 rpm 2112 rpm
2127 rpm
2761 rpm
2859 rpm
3651 rpm
3938 rpm
994 rpm
Contr
ol
panel
1687 rpm 2197 rpm 2944 rpm 3406 rpm
Pedestals (structural) and bearings (oil film)
stiffness must be theoretically and/or
experimentally estimated for accurate critical
speeds calculation.
-y +y
Gravity
Results – Bowed rotor, -y and +y definitions
-1
0
1
2
3
4
5
6
7
0 5000 10000 15000 20000 25000 30000
HP-IP Rotor, LP Rotor, Generator, Hotassembly (B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm,B#6+4.57mm)
HP-IP Rotor, LP Rotor, Generator, Bowedrotor -y (B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm,B#6+4.57mm)
HP-IP Rotor, LP Rotor, Generator, Bowedrotor +y (B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm,B#6+4.57mm)
HP-IP
LP
Generator
Length [mm]
Dis
pla
ce
me
nt [m
m]
+y
-y
On
ly
we
igh
t
Assembly configuration with
plastic deformation (HP-IP rotor bow)
Deflection shape due to weight
-0,5
0
0,5
1
1,5
2
0 2000 4000 6000 8000 10000 12000 14000
Weight only
Weight + rotor bow (-y)
Weight + rotor bow (+y)
Subtracting means this difference:
Weight+rotor bow (red and green curves) minus weight
only (dashed curve)
For easier
visualization, the
next two slides
shows only this
difference.
Deflected shape subtracting
the deformation due to weight
-0,20
-0,15
-0,10
-0,05
0,00
0,05
0,10
0,15
0,20
0 5000 10000 15000 20000 25000 30000
Bowed rotor +y
Bowed rotor -y
HP-IP
LP Generator
The HP-IP rotor bow add eccentricity to the centers of mass of the
equipment parts (“crankshaft” shape).
As the shaft is flexible, the resultant force of this out-of-center
masses will increase even more the eccentricity of the centers of
mass, and the effect will worsen.
Length [mm]
Dis
pla
ce
me
nt [m
m]
Deflected shape subtracting the
deformation due to weight
-0,02
-0,02
-0,01
-0,01
0,00
0,01
0,01
0,02
0,02
0 5000 10000 15000 20000 25000 30000
Bowed rotor +y
Bowed rotor -y
HP-IP
LP Generator
Even the LP rotor, that in this
analysis was considered straight,
will have an unbalanced behavior.
Length [mm]
Dis
pla
ce
me
nt [m
m]
Deflected shape subtracting
the deformation due to weight (expanded y axis)
92
120
186
225
245
226
99 90
211 223
245
226
0
50
100
150
200
250
300
Bearing #1 Bearing #2 Bearing #3 Bearing #4 Bearing #5 Bearing #6
HP-IP Rotor, LP Rotor, Generator, Bowed rotor -y(B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm, B#6+4.57mm)
HP-IP Rotor, LP Rotor, Generator, Bowed rotor +y(B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm, B#6+4.57mm)
During operation, reaction
forces on supports
oscillates between blue
and red values as the
shaft turn 180 degrees.
Fo
rce
[kN
] Assembly configuration with bowed rotor,
after coupling, reaction forces
-y +y
Bowed rotor and machined flange
-1
0
1
2
3
4
5
6
7
0 5000 10000 15000 20000 25000 30000
HP-IP Rotor, LP Rotor, Generator, Hotassembly, bowed rotor +y, machined flange0.08mm +y (B#1+1.55mm, B#2+0.05mm,B#3-0.25mm, B#4-0.25mm, B#5-0.05mm,B#6+4.57mm)
HP-IP Rotor, LP Rotor, Generator, Hotassembly, bowed rotor -y, machined flange0.08mm -y (B#1+1.55mm, B#2+0.05mm,B#3-0.25mm, B#4-0.25mm, B#5-0.05mm,B#6+4.57mm)
HP-IP Rotor, LP Rotor, Generator, Hotassembly (B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm,B#6+4.57mm)
HP-IP
LP
Generator
+y
-y
On
ly
we
igh
t
Length [mm]
Dis
pla
ce
me
nt [m
m]
Bowed rotor, machined flange
Deflected shape with gravity
-0,2
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0 5000 10000 15000 20000 25000 30000
Bowed rotor, machined flange, eccentricity +y
Bowed rotor, machined flange, eccentricity -y
HP-IP
LP Generator
Qualitatively we can expect
the same behavior of the
rotor without machining.
Length [mm]
Dis
pla
ce
me
nt [m
m]
Deflected shape subtracting the
deformation due to gravity
-0,20
-0,15
-0,10
-0,05
0,00
0,05
0,10
0,15
0,20
0 5000 10000 15000 20000 25000 30000
Bowed rotor +y
Bowed rotor, machined flange, eccentricity +y
HP-IP
LP Generator
The machined flange allows an angle between the HP-IP
rotor and the LP rotor, increasing the eccentricity of the
center of mass between bearings #2 and #3.
Length [mm]
Dis
pla
ce
me
nt [m
m]
Comparison between the deflected
shape of the unmachined and machined flange
-0,02
-0,02
-0,01
-0,01
0,00
0,01
0,01
0,02
0,02
0 5000 10000 15000 20000 25000 30000
Bowed rotor +y
Bowed rotor, machined flange, eccentricity +y
HP-IP
LP
Generator
The eccentricity of the LP
rotor center of mass is also
increased.
Length [mm]
Dis
pla
ce
me
nt [m
m]
Comparison between the deflected shape of the
unmachined and machined flange (expanded y axis)
92
120
186
225
245
226
99 90
211 223
245
226
0
50
100
150
200
250
300
Bearing #1 Bearing #2 Bearing #3 Bearing #4 Bearing #5 Bearing #6
HP-IP Rotor, LP Rotor, Generator, Bowed rotor -y(B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm, B#6+4.57mm)
HP-IP Rotor, LP Rotor, Generator, Bowed rotor +y(B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm, B#6+4.57mm)
The difference between –y and +y is what we call “Reaction forces
oscillations”
Reaction forces [kN]
Bowed rotor, unmachined flange
96 97
208
222
245
226
94
113
190
226
244
226
0
50
100
150
200
250
300
Bearing #1 Bearing #2 Bearing #3 Bearing #4 Bearing #5 Bearing #6
HP-IP Rotor, LP Rotor, Generator, Hot assembly,bowed rotor +y, machined flange 0.08mm +y(B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm, B#6+4.57mm)
HP-IP Rotor, LP Rotor, Generator, Hot assembly,bowed rotor -y, machined flange 0.08mm -y(B#1+1.55mm, B#2+0.05mm, B#3-0.25mm, B#4-0.25mm, B#5-0.05mm, B#6+4.57mm)The difference between –y and +y
is what we call “Reaction forces oscillations”
Reaction forces [kN]
Bowed rotor, machined flange
7
30
25
2
0 0
2
17
19
4
1 0
0
5
10
15
20
25
30
35
Bearing #1 Bearing #2 Bearing #3 Bearing #4 Bearing #5 Bearing #6
Bowed rotor, amplitude of the reacton forcesoscillations
Bowed rotor, machined flange, amplitude of thereacton forces oscillations
As we have some sort of
“knee” on the machined
flange, the reaction forces
are decreased.
Fo
rce
[kN
] Reaction forces oscillations [kN]
Comparison between unmachined and machined flange
-y +y
Straight rotor and machined flange
-0,04
-0,03
-0,02
-0,01
0
0,01
0,02
0,03
0,04
0 5000 10000 15000 20000 25000 30000
Machined flange +y
Machined flange -y
Length [mm]
Dis
pla
ce
me
nt [m
m]
Deflected shape subtracting the
deformation due to weight
5
13
6
2
0 0
0
2
4
6
8
10
12
14
16
Bearing #1 Bearing #2 Bearing #3 Bearing #4 Bearing #5 Bearing #6
Straigth rotor, machined flange, amplitude of thereacton forces oscillationsF
orc
e [kN
]
Reaction forces oscillations [kN]
Conclusions
• Mathematical model description and verification. – This model shows a good agreement with supplied data like
• assembling alignment,
• deformation due to gravity,
• LP rotor modal analysis and
• critical speeds.
• Effect of bowed rotor. – The summed effect of the rotor bow and gravity leads to an asymmetrical
load on supports (bearings).
– The unbalanced force due to mass eccentricity of a bowed rotor is much higher than that loads oscillations.
• Effect of bowed rotor and machined flange. – Positive effect on the reaction forces.
– Negative effect on the deflected shape.
• Effect of machined flange. – Increase oscillating forces on supports.
– Increase mass eccentricity due to rotor deformation.
Next steps
• Oil film and pedestals stiffness.
• Rotor dynamics.