rotordynamics_8

1Bernhard BettigMechanical Design Research Lab

Mechanical Engineering - Engineering Mechanics Dept.Michigan Technological UniversityWeb site: http://www.me.mtu.edu/~mdrl

2with locations of displacement transducers shown

3Turbine Shaft: Generator Shaftr

r

h

K

K

xT

T

1

2

9

10

13.5 in.

17.75 in.

= 5.5 in.

1.9x10 lbf / in.

9.2x10 in - lbf / rad

=

=

=

=

r

r

h

K

K

xG

G

1

2

9

10

13.5 in.

18.06 in.

= 5.69 in.

1.8x10 lbf / in.

9.0x10 in - lbf / rad

=

=

=

=

1 1 1

9.2x10 lbf / in8

K K K

K

x xT xG

x

= +

=

1 1 1

4.5x10 in - lbf / rad10

K K K

K

T G

= +

=

4 is the material density

= , =2 12 1

1 1bt t

R Ra t bR

7

part m (lb) I (lb-ft2) J (lb-ft2)

Exciter 5200 5800 11600 Thrust Bell 21,000 46,000 91,000 Generator Rotor 330,000 11,000,000 22,000,000 Turbine Blades 35,000 570,000 1,150,000 Runner Cone 2600 6000 12,000

8 Upper Generator Guide Bearing

Lower Generator Guide Bearing

Turbine Guide Bearing

Cxx (lbf/(ft/s)) 8.0 x 107 9.3 x 107 1.3 x 106 Cxy (lbf/(ft/s)) -1.6 x 105 -1.7 x 105 7.8 x 103 Cyx (lbf/(ft/s)) -1.6 x 105 -1.7 x 105 7.8 x 103 Cyy (lbf/(ft/s)) 8.3 x 107 9.5 x 107 1.3 x 106 Kxx (lbf/ft) -1.0 x 106 -1.0 x 106 7.8 x 104 Kxy (lbf/ft) -5.8 x 108 -6.7 x 108 -9.7 x 106 Kyx (lbf/ft) 6.0 x 108 6.9 x 108 9.5 x 106 Kyy (lbf/ft) 1.5 x 106 1.7 x 106 2.6 x 104

An arbitrary 0.001 misalignment was input for the turbine guide bearing Y direction, to achieve bearing pressures.

9Parameter Value

Rated Power Line Voltage Armature Reactance (xd)

Armature Reactance (xq) Armature Resistance (ra) Power Factor for Load Test Rotor Diameter Rotor Gap Height Number of Rotor Poles Number of Stator Slots Carter Coefficient Turns per Phase Pole Pitch () Slots per pole per phase (n) Slot Pitch () Winding factor (k) Average Air Gap Rotor Center Offset Stator Center Offset

34 MW (43.0 MVA at 0.79 pf) 11 kV 4.39 Ohms (118% on 32.5 MVA base or 3.72 Ohm base) 2.65 Ohms (71.3% of base) 0.01077 Ohms 1.0 20.5 ft 52 in. 52 432 1.0 432 96.3 % (or 173 electrical) 2.77 6.02 % (or 21.7 electrical) 0.949 0.409 in. 0.00707 in. @ 135 X: -0.0169 in. Y: 0.0132 in.

10

Turbine Guide Bearing Probe (TGB) Upper Generator Guide Bearing Probe (UGB) Predom.

Freq. (Hz)

Predom. Freq. (x speed)

filtered 1xampl. (mil p-p)

filtered 1x phase (deg)

Predom. Freq. (Hz)


filtered 1x ampl. (mil p-p)


Bump Test (X) a 7.22 (Y) 6.90

(X) 7.53

Mech. Run 9 RPM

.83

1

(X) 2.53 (Y) 1.94

226 131

.83

1

105 RPM (X) 6.67 (Y) 7.22

4.0 4.3

(X) 2.68 (Y) 2.23

208 127

1.68 1 (X) 2.34 (Y) 1.09

27 285

127 RPM (X) 9.31 (Y) 9.59

4.4 4.5

2.1 1

134 RPM (X) 8.56 (Y) 8.47 (Y) 31.8

3.8 3.8 14.2

(X) 2.78 (Y) 2.69

193 104

2.2 1 (X) 1.57 (Y) 1.48

59 308

166 RPM (Overspeed)

(Y) 10 1.5 2.78

3.6 0.54 1.0

2.8 1

11

Turbine Guide Bearing Probe (TGB) Upper Generator Guide Bearing Probe (UGB) Predom.

Freq. (Hz)


filtered 1xampl. (mil p-p)


Predom. Freq. (Hz)


filtered 1x ampl. (mil p-p)


Load Test 100 % gate (29 MW)

2.3

1

(X) 5.89 (Y) 6.53

141 54

2.3

1

90 % (28.5 MW)

2.3 1 (X) 5.44 (Y) 6.07

138 56

2.3 1 (X) 3.10 (Y) 2.49

47 309

80 % (28 MW)

2.3 1 (X) 4.99 (Y) 5.47

139 58

2.3 1 (X) 3.17 (Y) 2.49

51 306

70 % (25.4 MW)

2.3 1 (X) 4.42 (Y) 4.78

144 58

2.3 1 (X) 3.05 (Y) 2.47

51 310

60 % (18.5 MW)

(X&Y)2.3 (X) .46 (Y) .49

1 .20 .21

(X) 3.73 (Y) 3.70

143 52

2.3 1 (X) 2.87 (Y) 2.41

53 311

50 % (9.3 MW)

(X&Y) 2.3 (X) 8.00 (Y) 8.42

1 3.5 3.7

(X) 2.68 (Y) 2.59

163 76

2.3 1 (X) 2.77 (Y) 2.23

55 313

40 % (1 MW)

(X) 8.79 (Y) 8.93

3.8 3.9

(X) 3.35 (Y) 3.56

191 111

2.3 1 (X) 2.57 (Y) 2.24

55 315

12

Using the method of influence coefficients applied using the rotor model:

13

Since we know ai,j from the model, and we know ri, we can calculate uj.

If i is greater than j, then the method of least squares is employed.

14

Item Magnitude Angle (deg)

Diameter Mass on circ. (lb)

Imbalances Exciter

0

Thrust Bell 0 Generator 6660 lb-ft 346 20.5 ft 650 Runner 97 lb-ft 74 200 in. 12

Misalignments Coupling (lateral)

.00066 in.

341

Coupling (angular)

.0043 deg. 219

15

Rotation Speed (rpm)

S

y

s

t

e

m

N

a

t

.

F

r

e

q

.

(

H

z

)

0

5

10

15

20

25

30

0 50 100 150 200

18


R

e

s

p

o

n

s

e

A

m

p

l

i

t

u

d

e

(

i

n

.

p

-

p

)

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0 50 100 150 200 250

TGBX&YUGBX&YTGB XTGB YUGB XUGB Y

Markers show actual readings

Real (in. p-p) I

m

a

g

.

(

i

n

.

p

-

p

)

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

-0.004 -0.002 0 0.002 0.004

TGBUGBTGB XTGB YUGB XUGB Y

TGB X

TGB Y

UGB X

UGB Y

Markers showactual readings

19


R

e

s

p

o

n

s

e

A

m

p

l

i

t

u

d

e

(

i

n

.

p

-

p

)

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0.005

0 100 200 300

TGBX&YUGBX&YTGB XTGB YUGB XUGB Y

Markers show actual readings

Real (in. p-p) I

m

a

g

.

(

i

n

.

p

-

p

)

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

-0.006 -0.004 -0.002 0 0.002

TGB Y

TGB X

UGB Y

UGB X

20

Misalignment Magnitude (in.)

R

e

s

p

.

A

m

p

.

(

i

n

.

p

-

p

)

0

0.001

0.002

0.003

0.004

0.005

0 0.02 0.04 0.06 0.08

TGBUGB

Real (in. p-p)

I

m

a

g

.

(

i

n

.

p

-

p

)

-0.004-0.003-0.002-0.001

00.0010.0020.0030.0040.005

-0.007 -0.002 0.003 0.008

UGB X

UGB YTGB X

TGB Y


R

e

s

p

.

A

m

p

.

(

i

n

.

p

-

p

)

00.0020.0040.0060.0080.01

0.012

0 50 100 150 200

TGB X&YTGB XTGB Y

.001 in.

.010 in. Y Offset

Real (in. p-p)

I

m

a

g

.

(

i

n

.

p

-

p

)

-0.008-0.006-0.004-0.002

00.0020.0040.0060.0080.01

-0.01 -0.005 0 0.005

.001 in.

.010 in.

TGB X

TGB Y

21

Bearing Radial Clearance (in.)

R

e

s

p

.

A

m

p

.

(

i

n

.

p

-

p

)

0

0.05

0.1

0.15

0.2

0.25

0.005 0.015 0.025 0.035 0.045

TGBUGB

Bearing Radial Clearnace (in.)

N

a

t

u

r

a

l

F

r

e

q

.

(

H

z

)

02468

1012141618

0.005 0.015 0.025 0.035 0.045

22

Power Output (MW)

R

e

s

p

o

n

s

e

A

m

p

l

i

t

u

d

e

(

i

n

.

p

-

p

)

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 20 40 60

TGB XTGB Y ActualUGB XUGB YTGB XTGB YUGB XUGB Y

Real (in. p-p) I

m

a

g

.

(

i

n

.

p

-

p

)

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

-0.008 -0.003 0.002

Model TGB X TGB Y UGB X UGB Y

TGB X

TGB Y

UGB X

UGB Y

rotordynamics_8

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