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.