rawlins avtutorialhandouts
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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
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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
Power Balance Components
Amplitude
Power
Pw
Pc
Power balance components
10 mphV=
Fundamentals
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Power Balance Components
Amplitude
Power
Pw
Pc
Pw
- Pc
Power balance components
10 mphV=
Fundamentals
14
Power Balance Components
Amplitude
Power
Pw
PD
Pw
- Pc
Power balance
10 mphV=
Fundamentals
15
Power Balance Components
Amplitude
Power
PD
Pw
- Pc
( )w c
p p L
Power balance
10 mphV=
Fundamentals
16
Power Balance Components
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
Power Balance Components
Amplitude
Power
PD
( )w c
p p L 600
1000
1500
Protectable span length
10 mphV=
Fundamentals
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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
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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
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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
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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
3. How the Technology Works
(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
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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
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
48
Alcoa Massena
Memorial University
of Newfoundland
Measuring self-damping
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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
Damping efficiency on conductor
Vibration amplitudes
Incidence of conductor fatigue
Damper design
Conductor tension,
mass & stiffness
Damper spacing
Conductor self-damping
Wind power
function
Locale Span
length
Turb effects
Conductor fatigue characteristics
54
Power balance
Fatigue exposure
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
function
Locale Span
length
Turb effects
Conductor fatigue characteristics
Laws of motionF ma=
Cable/Damper Interaction
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Power balance
Fatigue exposure
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
function
Locale Span
length
Turb effects
Conductor fatigue characteristics
1
2 2
max
1 2tanh tanh
2 1
DP
P
= + +
Cable/Damper Interaction
Laws of motion
56
Fatigue exposure
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
function
Locale Span
length
Turb effects
Conductor fatigue characteristics
w D cP P P= +
Laws of motion
Cable/Damper Interaction
Power balance
57
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
function
Locale Span
length
Turb effects
Conductor fatigue characteristics
end, 1i iD n = >
Laws of motion
Cable/Damper Interaction
Power balance
Fatigue exposure
58
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
function
Locale Span
length
Turb effects
Conductor fatigue characteristics
Shaker test
Laws of motion
Cable/Damper Interaction
Power balance
Fatigue exposure
59
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
function
Locale Span
length
Turb effects
Conductor fatigue characteristics
Shaker test
Lab
span test
Laws of motion
Cable/Damper Interaction
Power balance
Fatigue exposure
60
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
function
Locale Span
length
Turb effects
Conductor fatigue characteristics
Shaker test
Lab
span test
Field
recordings
Laws of motion
Cable/Damper Interaction
Power balance
Fatigue exposure
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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
function
Locale Span
length
Turb effects
Conductor fatigue characteristics
Shaker test
Lab
span test
Field
recordings
Inspection
of line
Laws of motion
Cable/Damper Interaction
Power balance
Fatigue exposure
62
(b) Road Test!
3. How the Technology Works
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
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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
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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=
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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
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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.
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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