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7/22/2019 Rawlins AVTutorialHandouts

1/16

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)V

f 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


2/16

7

PD

P

P

W

C

PW

PDPC- - = 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 Hz

1.108 inchesf = =

Fundamentals

9

Power Balance Components

Amplitude

Power

Pw

Power balance components

10 mphV=

Fundamentals

10

1/H m

f=

Drake @ 25% RS11 to 80 feet

Vibration loopsFundamentals

11

1/H m

f=

Self dampingFundamentals

12


Amplitude

Power

Pw

Pc


10 mphV=

Fundamentals


3/16

13


Amplitude

Power

Pw

Pc

Pw

- Pc


10 mphV=

Fundamentals

14


Amplitude

Power

Pw

PD

Pw

- Pc

Power balance

10 mphV=

Fundamentals

15


Amplitude

Power

PD

Pw

- Pc

( )w c

p p L

Power balance

10 mphV=

Fundamentals

16


Amplitude

Power

PD

( )w c

p p L 600

1000

1500

Effect of span length

10 mphV=

Fundamentals

17

a

N

106 107 108

maxY

Fatigue curveFundamentals

max2

a a a md E fY EI

=

18


Amplitude

Power

PD

( )w c

p p L 600

1000

1500

Protectable span length

10 mphV=

Fundamentals


4/16

19

Protectablespan

length

-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


5/16

25

Waves & Dampers

26

A

B

maxy A B= +

Waves & Dampers

( )

2 2 2

0

1

2P Z A B=

2 2

0

1

2A

P Z A= 2 20

1

2BP Z B=

Characteristic Impedance

0Z H m=

2 f =

Fixed rails

Frictionless roller

Z0 DashpotR

27

A

ymax

B

0

2 2

max 0 max

1

2P Z y=

( )2 2 201

2P Z A B=

maxy A B= +

max

Damping efficiencyP

P=

A B

A B

=

+

Waves & Dampers

0Z

28

Ymax

Ymin

Waves & Dampers

( )max 2Y A B= + ( )min 2Y A B=

29

Fixed rails

R Dashpot

X

Waves & DampersDamper resistance & reactance

F

30

Waves & Dampers

Damper Resistance

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30

Frequency - Hz

Resistance

-Ns/m

YD= 0.5 mm

1.01.5

2.0

2.5


6/16

31

Waves & Dampers

Damper Reactance

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

Frequency - Hz

Reactance-Ns/m 0.5 mm

YD=

1.0

1.52.0

2.5

32

A

B

T D SX X X= +

0/DR Z= 0/TX Z=

1

2 2

max

1 2tanh tanh

2 1

DP

P

= + +

max

max

/DD

P PY

Y =

,D DR X

0

2cot D

S

xX Z

=

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

PD

/Pmax

6.7 9

11.1 13.2

15.1 16.1

18.6 21

23 25.6

28 30.4

32.8 35.2

37.7 40.1

42.5 45

Waves & Dampers

34

D w cP P P=

max max max

w cD P PP

P P P=

2 2

max 0 max

1

2P Z y=

35

1.0

50

Ymax/D

0.5

P/Pmax

f

36

Waves & Dampers

(P w -P c )/P max

Ymax/D

50

0.5

0.5

max

( )w c

p p L

P


7/16

37

Predicted Amplitudes

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50

Frequency - Hz

Ymax-inches

2500

3000

3500

4000

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 0.16

Ymax

P/P

max

Damper

Wind - self damping

2500

3000

3500

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 0.14

Ymax

P/P

max

Wind - self damping

Damper2500

30003500

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

Wind

power

functionSpan

length

Conductor fatigue

characteristics

42Courtesy Alcoa Laboratories


8/16

43

Tunnel throat

44

Brika & Laneville 1995

45

Specific Wind Power - Sine Loops

0.1

1

10

100

0.01 0.1 1

ymax/D

Pw

/f3D

4

Rawlins 1982

Brika & Laneville 1995

Polimi 2003

Diana et al 2005

46

Reduced Decrement - Sine Loops

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8

ymax/D

r

Rawlins (1982)

Brika & Laneville (1995)

Polimi (2003)

Diana et al (2005)

max /

wr

P V LDSt

P mH m

=

max max max

w cD P PP

P P P=

47

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind

power

functionSpan

length

Conductor fatigue

characteristics

48

Alcoa Massena

Memorial University

of Newfoundland

Measuring self-damping


9/16

49

Munaswamy & 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)

PC

/Pmaxper100

0feet

14.00 Hz

16.41

18.54

23.528.25

33.2538.01

43.25

48.25

53.75

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 0.5

Ymax inches

PC

/Pmaxper1000feet

Frequency = 41 to 45 Hz

51

Courtesy GREMCA, University of Laval

52

Multilayer ACSR in Suspension or Clamps Bell-mouthed

No armor rods

0.00

0.10

0.20

0.30

0.1 1 10 100 1000

megacycles

fymax

m/s

53

Laws of motion

Cable/Damper Interaction

Power balance

Fatigue exposure

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind power

function

Locale Span

length

Turb effects

Conductor fatigue characteristics

54

Power balance

Fatigue exposure

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind power

function

Locale Span

length

Turb effects


Laws of motionF ma=



10/16

55

Power balance

Fatigue exposure

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind power

function

Locale Span

length

Turb effects


1

2 2

max

1 2tanh tanh

2 1

DP

P

= + +


Laws of motion

56

Fatigue exposure

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind power

function

Locale Span

length

Turb effects


w D cP P P= +

Laws of motion


Power balance

57

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind power

function

Locale Span

length

Turb effects


end, 1i iD n = >

Laws of motion


Power balance

Fatigue exposure

58

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind power

function

Locale Span

length

Turb effects


Shaker test

Laws of motion


Power balance

Fatigue exposure

59

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind power

function

Locale Span

length

Turb effects


Shaker test

Lab

span test

Laws of motion


Power balance

Fatigue exposure

60

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind power

function

Locale Span

length

Turb effects


Shaker test

Lab

span test

Field

recordings

Laws of motion


Power balance

Fatigue exposure


11/16

61

Damper impedance




Damper design

Conductor tension,

mass & stiffness

Damper spacing


Wind power

function

Locale Span

length

Turb effects


Shaker test

Lab

span test

Field

recordings

Inspection

of line

Laws of motion


Power balance

Fatigue exposure

62

(b) Road Test!


63

Damper design

Locale

Turb effects

Shaker test

Lab

span test

Field

recordings

Inspection

of line

F ma=

DZ

0/DZ Z

max/DP P

w D cP P P= +

cP

wP

, ,T m EI

Dx

L

0

10

20

30

40

50

0.1 10 1000megacycles

max , bY Y

end, 1i iD n = >

64

CIGRE Study Committee B2 - Working Group 11

Task 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 Conductor

Plus Damper: Assessment of Technology,Electra No.

223(2005)

The Source

65Photo courtesy of IREQ

IREQs Varennes Test Line The Course

66

IREQ Varennes Test Line near Montreal

The Course


12/16

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

Lab

span test

Field

recordings

Inspection

of line

F ma=

DZ

0/DZ Z

max/DP P

w D cP P P= +

cP

wP

, ,T m E I

Dx

L

0

10

20

30

40

50

0.1 10 1000

megacycles

max, bY Y

end, 1i iD n = >

Dampers A, B, C

Damper D

69

Benchm ark Comparison - 15% Turbulence Rawlins

0

1

2

3

4

0 10 20 30 40

Frequency (Hz)

Free-LoopSingleAmplitude(mm)

Measured in test lineDamper A

Damper B

Damper 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]

Amplitude0-Peak[mm]

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]

Amp

litu

de

[mm

]

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]

Amp.

[mm

]

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


13/16

73

0

0.5

1

1.5

2

2.5

3

Rawlins-CT15%

Diana-CT15%

0.5

*EJmax

Hardy-AconEJ

Rawlins-AT10%

Rawlins-CT10%

Diana-BT15%

0.5

*EJmax

Rawlins-AT15%

Hardy-Afune

Rawlins-AT5%

Krispin-AT15%

EJmin

Diana-AT15%

0.5

*EJmax

Krispin-AT15%

0.5

*EJmax

Rawlins-BT15%

S&H-AT15%

Krispin-AT10%

EJmin

Rawlins-BT10%

Krispin-AT10%

0.5

*EJmax

Diana-AT5%

0.5

*EJmax

Diana-AT5%

0.0

5*EJmax

Rawlins-CT5%

Rawlins-BT5%

S&H-CT1%

S&H-BT1%

Diana-BT5%

0.5

*EJmax

Diana-CT5%

0.5

*EJmax

Diana-BT5%

0.0

5*EJmax

Diana-CT5%

0.0

5*EJmax

S&H-AT5%

RMS(Error%

(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 E I

Dx

L max, bY Y

Damper

Conclusion

This branch of the technology is not

accurate enough to use in specifying

vibration protection.

78

A

B

Accelerometers

Leblond & Hardy

DEAM

System

( )2 2 201

2P Z A B=


14/16

79

0 5 10 15 20 25 30 35

Frequency, (Hz)

0

4

8

12

16

20

Max.antinodeamplitu

de,

(mm)

Calculated from measured reflection coefficient

Measured

Leblond & Hardy

80

Locale

Turb effects

Shaker testD

Z

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 be

accurate enough touse in specifying

vibration

protection.. Labspan test

81

1. Why did I spend all this time presenting the technology,

when I knew it wasnt very useful to the designer?

2. OK, if that isnt useful, what is?

82

4. What to Do?

2. OK, if that isnt useful, what is?

83

Resources:

1. Your own experience. If it worked before

(or didnt), 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

KLsbasedonrulingspan

No damage

Conductor fatigue

Excessive wear


15/16

85

max /

wr

P V LDSt

P mH m

=

max

wr

P LD

St VP H m =

% 100 H

TRS

=

DK

RS w=

"Conductor Vibration - A Study of Field Experience," C. B. Rawlins,K. R. Greathouse & R. E. Larson, AIEE Confrence 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 3500

H/m - meters

LD/m

No damage

Conductor fatigue

Excessive 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 2001

Part 3: Bundled Conductors

Electra No. 220, June 2005

Overhead Conductor Safe Design Tension

with 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 3500

H/w, (m)

0

5

10

15

LD

/m,

(m/

kg)

Field cases

Terrain #1

Terrain #2

Terrain #3

Terrain #4

SpecialApplication

Zone

Figure 4 : Ranking parameters of twin horizontal bundled lines in North America fitted

with 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 didnt), it will do the same again.

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

3. Your friendly.


16/16

91 92

Why???!!

All suppliers have some system for making

recommendations.

They have the most comprehensive knowledge of

their systems performance.

They are well motivated to avoid repetition of

any unsatisfactory performance.

They are in the best position to maintain the

system 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 wasnt very useful?

94

The End

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