aeolian vibration aeolian vibration of damped …...1 1 aeolian vibration chuck rawlins • single...

1

1

Aeolian VibrationChuck Rawlins

• Single conductors• Bundled conductors• Ground wires• Insulators• Davit arms• Aircraft warning devices• Etc., etc., etc.

Single conductors with dampers

2

Prandtl & Tietjens 1934

Aeolian Vibration of Damped Single Conductors

1. Fundamentals

2. Waves, Dampers &Damping Efficiency

3. How the Technology Works

4. What to Do

3

( 0.2)Vf St StD

= ⋅ ≈(mph)(Hz) 3.26

(inches)Vf

D= ⋅

V = 2 to 15 mph

6 to 44 Hzf ≈Drake

Fujarra et al (1998)

1. Fundamentals

4

Koopman 1967

5

Koopman 1967

6

Fundamentals

2

7

P D

P

P

W

C

P W

P DP C- - = 00w c DP P P− − =

Fundamentals

8

Pick a wind velocity e. g. 10 mph.

Pick a conductor, e. g. Drake

10 mph3.26 29.4 Hz1.108 inches

f = ⋅ =

Fundamentals

9

Power Balance Components

Amplitude

Pow

er

P w

Power balance components

10 mphV =

Fundamentals

10

λ

1 /H mf

λ = ⋅

Drake @ 25% RS 11 to 80 feetλ ≈

Vibration loopsFundamentals

11

λ

1 /H mf

λ = ⋅

Self dampingFundamentals

12


Amplitude

Pow

er

P w

P c


10 mphV =

Fundamentals

3

13


Amplitude

Pow

er

P w

P c

P w - P c


10 mphV =

Fundamentals

14


Amplitude

Pow

er

P w

P D

P w - P c

Power balance

10 mphV =

Fundamentals

15


Amplitude

Pow

er

P D

P w - P c ( )w cp p L− ⋅

Power balance

10 mphV =

Fundamentals

16


Amplitude

Pow

erP D

( )w cp p L− ⋅6001000

1500

Effect of span length

10 mphV =

Fundamentals

17

aσ

N106 107 108

maxY

Fatigue curveFundamentals

max2a a amd E fYEI

πσ = ⋅

18


Amplitude

Pow

er

P D

( )w cp p L− ⋅6001000

1500

Protectable span length

10 mphV =

Fundamentals

4

19

Prot

ecta

ble

span

leng

th -

feet

Wind velocity - mph2 15

1000

2000

3000

Maximum safe span lengthFundamentals

20

2. Waves, Dampers & Damping Efficiency

21

Waves & Dampers

22

Waves & Dampers

23

Waves & Dampers

24

5

25

Waves & Dampers

26

∞

A

B

maxy A B= +

Waves & Dampers

( )2 2 20

12

P Z A Bω= −

2 20

12AP Z Aω= 2 2

012BP Z Bω=

Characteristic Impedance

0Z H m= ⋅

2 fω π=

Fixed rails

Frictionless roller

Z0 DashpotR

27

A

y max

B

0

2 2max 0 max

12

P Z yω=

( )2 2 20

12

P Z A Bω= −maxy A B= +

max

Damping efficiency PP

= A BA B−

=+

Waves & Dampers

0Z

28

Ymax

Ymin

Waves & Dampers

( )max 2Y A B= + ( )min 2Y A B= −

29

Fixed rails

R Dashpot

X

Waves & Dampers Damper resistance & reactanceF

30

Waves & Dampers

Damper Resistance

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30

Frequency - Hz

Res

ista

nce

- N

s/m

YD = 0.5 mm

1.01.5

2.0

2.5

6

31

Waves & Dampers

Damper Reactance

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

Frequency - Hz

Rea

ctan

ce -

Ns/

m 0.5 mm

YD =

1.0

1.52.02.5

32

A

B

T D SX X X= +

0/DR Zθ = 0/TX Zχ =

12 2

max

1 2tanh tanh2 1

DPP

θθ χ

−⎡ ⎤⎛ ⎞= ⎢ ⎥⎜ ⎟+ +⎝ ⎠⎣ ⎦

max

max

/DD P PYY θ

=

,D DR X

02cot D

SxX Z πλ

= −

Waves & Dampers

33

Damping efficiency measured in the laboratory

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4 0.5

Ymax

P D/P

max

6.7 911.1 13.215.1 16.118.6 2123 25.628 30.432.8 35.237.7 40.142.5 45

Waves & Dampers

34

D w cP P P= −

max max max

w cD P PPP P P

= −

2 2max 0 max

12

P Z yω=

35

1.0

50

Ymax/D0.5

P/Pmax

f

36

Waves & Dampers

(P w -P c )/P max

Y max /D

f50

0.5

0.5

max

( )w cp p LP− ⋅

7

37

Predicted Amplitudes

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50

Frequency - Hz

Ym

ax -

inch

es 2500300035004000

38

Power Balance at 32.8 Hz

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16Ymax

P/P m

ax

Damper

Wind - self damping

2500

30003500

4000

39

Power Balance at 40.1 Hz

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14Ymax

P/P m

ax

Wind - self dampingDamper

250030003500

4000

40


(a) A Look Under the Hood

(b) Road Test

41

Damper impedance

Damping efficiency on conductor

Vibration amplitudes

Incidence of conductor fatigue

Damper design

Conductor tension,mass & stiffness

Damper spacing

Conductor self-damping

Windpowerfunction

Spanlength

Conductor fatiguecharacteristics

42Courtesy Alcoa Laboratories

8

43

Tunnel throat

44

Brika & Laneville 1995

45

Specific Wind Power - Sine Loops

0.1

1

10

100

0.01 0.1 1ymax/D

P w/f3 D

4

Rawlins 1982Brika & Laneville 1995Polimi 2003Diana et al 2005

46

Reduced Decrement - Sine Loops

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8ymax/D

δr

Rawlins (1982)Brika & Laneville (1995)Polimi (2003)Diana et al (2005)

max /w

rP V LDSt

P mH mρ δ= ⋅ ⋅ ⋅

max max max

w cD P PPP P P

= −

47

Damper impedance




Damper design


Damper spacing


Windpowerfunction

Spanlength

Conductor fatiguecharacteristics

48

Alcoa MassenaMemorial University

of Newfoundland

Measuring self-damping

9

49Munaswamy & Haldar (1997)

Self damping of Drake at 25% RS

0.01

0.1

1

0 0.1 0.2 0.3 0.4

Ymax (in)

P C/P

max

per

100

0 fe

et

14.00 Hz

16.41

18.5423.5

28.2533.25

38.0143.25

48.2553.75

50

Self Damping of Hawk at 25%RS (4 Labs)

0.0

0.2

0.4

0.6

0.0 0.1 0.2 0.3 0.4 0.5Ymax inches

P C/P

max

per

100

0 fe

et

Frequency = 41 to 45 Hz

51

Courtesy GREMCA, University of Laval

52

Multilayer ACSR in Suspension or Clamps Bell-mouthedNo armor rods

0.00

0.10

0.20

0.30

0.1 1 10 100 1000

megacycles

fym

ax m

/s

53

Laws of motion

Cable/Damper Interaction

Power balance

Fatigue exposure

Damper impedance




Damper design


Damper spacing


Wind powerfunction

Locale Spanlength

Turb effects

Conductor fatigue characteristics

54

Power balance

Fatigue exposure

Damper impedance




Damper design


Damper spacing


Wind powerfunction

Locale Spanlength

Turb effects


Laws of motionF ma=


10

55

Power balance

Fatigue exposure

Damper impedance




Damper design


Damper spacing


Wind powerfunction

Locale Spanlength

Turb effects


12 2

max

1 2tanh tanh2 1

DPP

θθ χ

−⎡ ⎤⎛ ⎞= ⎢ ⎥⎜ ⎟+ +⎝ ⎠⎣ ⎦


Laws of motion

56

Fatigue exposure

Damper impedance




Damper design


Damper spacing


Wind powerfunction

Locale Spanlength

Turb effects


w D cP P P= +

Laws of motion


Power balance

57

Damper impedance




Damper design


Damper spacing


Wind powerfunction

Locale Spanlength

Turb effects

Conductor fatigue characteristicsend , 1i iD nσ σ σ≥ = >∑

Laws of motion


Power balance

Fatigue exposure

58

Damper impedance




Damper design


Damper spacing


Wind powerfunction

Locale Spanlength

Turb effects


Shaker test

Laws of motion


Power balance

Fatigue exposure

59

Damper impedance




Damper design


Damper spacing


Wind powerfunction

Locale Spanlength

Turb effects


Shaker test

Labspan test

Laws of motion


Power balance

Fatigue exposure

60

Damper impedance




Damper design


Damper spacing


Wind powerfunction

Locale Spanlength

Turb effects


Shaker test

Labspan test

Fieldrecordings

Laws of motion


Power balance

Fatigue exposure

11

61

Damper impedance




Damper design


Damper spacing


Wind powerfunction

Locale Spanlength

Turb effects


Shaker test

Labspan test

Fieldrecordings

Inspectionof line

Laws of motion


Power balance

Fatigue exposure

62

(b) Road Test!


63

Damper design

Locale

Turb effects

Shaker test

Labspan test

Fieldrecordings

Inspectionof line

F ma=

DZ

0/DZ Z

max/DP P

w D cP P P= +

cP

wP

, , T m EI

Dx

L

01020304050

0.1 10 1000megacycles

σ

max , bY Y

end , 1i iD nσ σ σ≥ = >∑

64

CIGRE Study Committee B2 - Working Group 11Task Force 1 “Vibration Principles” / G. Diana

Assessments of the Technology

“Modeling of Aeolian Vibrations of Single Conductors - Assessment of the Technology,” Electra No. 181 (1998)

“Modeling of Aeolian Vibrations of a Single ConductorPlus Damper: Assessment of Technology,” Electra No.223 (2005)

The Source

65Photo courtesy of IREQ

IREQ’s Varennes Test Line The Course

66

IREQ Varennes Test Line near Montreal

The Course

12

67

Diana et al (University of Milan)

H-J Krispin (RIBE)

Leblond & Hardy (IREQ)

Rawlins (Alcoa Fujikura)

Sauter & Hagedorn (University of Darmstadt)

The Drivers

68

Damper design

Locale

Turb effects

Shaker test

Labspan test

Fieldrecordings

Inspectionof line

F ma=

DZ

0/DZ Z

max/DP P

w D cP P P= +

cP

wP

, , T m EI

Dx

L

01020304050

0.1 10 1000megacycles

σ

max , bY Y

end , 1i iD nσ σ σ≥ = >∑

Dampers A, B, C

Damper D

69

Benchmark Comparison - 15% Turbulence Rawlins

0

1

2

3

4

0 10 20 30 40Frequency (Hz)

Free

-Loo

p Si

ngle

Am

plitu

de (m

m)

Measured in test lineDamper ADamper BDamper C

Results

70

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20 25 30 35 40 45

Frequency [Hz]

Am

plitu

de 0

-Pea

k [m

m]

Measured

Damper C (0.5EJmax 15% turb.)

Damper B (0.5EJmax 15% turb.)

Damper A (0.5EJmax 15% turb.)

Electra Fig. 15

Results

71

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20 25 30 35 40 45

Frequency [Hz]

Am

plitu

de [m

m]

Measured

Damper C 15% turb. (Diana)

Damper C 15% turb. (Rawlins)

Electra Fig. 17

Results

72

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20 25 30 35 40 45

Frequency [Hz]

Am

p. [m

m]

Measured

Damper A 15% turb. (Diana)Damper A 15% turb. (Rawlins)Damper A 15% turb. (Krispin)

Damper A 15% turb. (S&H)Damper A 15% turb. (Leblond&Hardy)

Electra Fig. 18

Results

13

73

0

0.5

1

1.5

2

2.5

3

Raw

lins

- C T

15%

Dia

na -

C T

15%

0.5

*EJm

ax

Har

dy -

A c

on E

J

Raw

lins

- A T

10%

Raw

lins

- C T

10%

Dia

na -

B T

15%

0.5

*EJm

ax

Raw

lins

- A T

15%

Har

dy -

A fu

ne

Raw

lins

- A T

5%

Kris

pin

- A T

15%

EJm

in

Dia

na -

A T

15%

0.5

*EJm

ax

Kris

pin

- A T

15%

0.5

*EJm

ax

Raw

lins

- B T

15%

S&H

- A

T15

%

Kris

pin

- A T

10%

EJm

in

Raw

lins

- B T

10%

Kris

pin

- A T

10%

0.5

*EJm

ax

Dia

na -

A T

5% 0

.5*E

Jmax

Dia

na -

A T

5% 0

.05*

EJm

ax

Raw

lins

- C T

5%

Raw

lins

- B T

5%

S&H

- C

T1%

S&H

- B

T1%

Dia

na -

B T

5% 0

.5*E

Jmax

Dia

na -

C T

5% 0

.5*E

Jmax

Dia

na -

B T

5% 0

.05*

EJm

ax

Dia

na -

C T

5% 0

.05*

EJm

ax

S&H

- A

T5%

RM

S (E

rror

% (A

-M)/M

)

Electra Fig. 16

Best Runs

74

Differences between teams:1. Wind power functions.

2. Self damping models.

3. Secondary effects, e.g. stiffness.

4. Modeling damper/conductor in different ways.

A

B

75

Differences between teams:1. Wind power functions.

2. Self damping models.

3. Secondary effects, e.g. stiffness.

4. Modeling damper/conductor in different ways.

Differences with field data:

1. All of the above.

2. Modeling damper/conductor interaction.

76

Benchmark Results• The different teams differed widely in their

predictions of vibration amplitudes.• Some differences were due to different data bases

on wind power and self-damping.• None of the predictions agreed well with field

measurements.• This is mainly due to problems in the modeling of

the interaction of the damper with the conductor.

77

Locale

Turb effects

Shaker testDZ

0/DZ Z

max/DP P

w D cP P P= +

cP

wP

, , T m EI

Dx

L max , bY Y

Damper

Conclusion

This branch of the technology is notaccurate enough to use in specifyingvibration protection.

78

A

B

Accelerometers

Leblond & Hardy

DEAMSystem

( )2 2 20

12

P Z A Bω= −

14

79

0 5 10 15 20 25 30 35Frequency, (Hz)

0

4

8

12

16

20

Max

. ant

inod

e am

plitu

de, (

mm

)

Calculated from measured reflection coefficientMeasured

Leblond & Hardy80

Locale

Turb effects

Shaker testDZ

0/DZ Z

max/DP P

w D cP P P= +

cP

wP

, , T m EI

Dx

L max , bY Y

Damper

Conclusion

This branch may beaccurate enough touse in specifyingvibrationprotection.. Lab

span test

81

1. Why did I spend all this time presenting the technology, when I knew it wasn’t very useful to the designer?

2. OK, if that isn’t useful, what is?

82

4. What to Do?

2. OK, if that isn’t useful, what is?

83

Resources:

1. Your own experience. If it worked before (or didn’t), it will do the same again.

2. Experience of others. If it worked for them...

84

Alcoa Field Experience Case Collection - ACSR with Armor Rods

0

4

8

12

16

0 5 10 15 20 25 30 35 40 45 50

Tension (%RS) at average annual minimum temperature

KLs

bas

ed o

n ru

ling

span

No damageConductor fatigueExcessive wear

15

85

max /w

rP V LDSt

P mH mρ δ= ⋅ ⋅ ⋅

max

wr

P LDSt VP H m

ρ δ= ⋅ ⋅ ⋅ ⋅⋅

% 100 HTRS

= ⋅

DKRS w

=⋅

"Conductor Vibration - A Study of Field Experience," C. B. Rawlins,K. R. Greathouse & R. E. Larson, AIEE Conférence Paper CP-61-1090.

86

Alcoa Field Experience Case Collection - ACSR with Armor Rods

0

5

10

15

0 500 1000 1500 2000 2500 3000 3500H/m - meters

LD/m

No damageConductor fatigueExcessive wear

87

Safe Design Tension with Respect to Aeolian VibrationsCIGRE B2 WG11 TF4 - Claude Hardy, Convenor

Part 1: Single Unprotected Conductors Electra No. 186, October 1999

Part 2: Damped Single Conductors Electra No. 198, October 2001Part 3: Bundled Conductors Electra No. 220, June 2005

Overhead Conductor Safe Design Tensionwith Respect to Aeolian Vibrations,

CIGRE Technical Brochure No. 273, June 2005

88CIGRE Brochure 273, Fig. 5.4

Recommended Safe Tensions for Single Conductor Lines

89

Safe Design Zone

3

0 500 1000 1500 2000 2500 3000 3500H/w, (m)

0

5

10

15

L D

/ m

, (m

/kg)

Field casesTerrain #1

Terrain #2

Terrain #3

Terrain #4

SpecialApplication

Zone

Figure 4 : Ranking parameters of twin horizontal bundled lines in North America fittedwith non-damping spacers and end-span Stockbridge dampers in relation to estimated

safe boundaries.

Electra No. 220, June 2005 90

Resources:

1. Your own experience. If it worked before (or didn’t), it will do the same again.

2. Experience of others. If it worked for them...

3. Your friendly….

16

91 92

Why???!!All suppliers have some system for makingrecommendations.

They have the most comprehensive knowledge oftheir system’s performance.

They are well motivated to avoid repetition ofany unsatisfactory performance.

They are in the best position to maintain thesystem to achieve that.

93

Protection recommendations will not agree.

2. Their damper designs are different.

1. Suppliers have different technical approaches.

3. Their exposures to field experience have differed.

1. Why did I spend all that time presenting the technology, when I knew it wasn’t very useful?

94

The End

aeolian vibration aeolian vibration of damped …...1 1 aeolian vibration chuck rawlins • single...

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