fatigue endurance capability of conductor/clamp … · 2 conseil international des grands rÉseaux...
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07
Fatigue Endurance Capability Fatigue Endurance Capability of Conductor/Clamp Systemsof Conductor/Clamp SystemsUpdate of Present KnowledgeUpdate of Present Knowledge
Technical BrochureTechnical Brochure
Presentation to SC B2,Presentation to SC B2,Helsinki, July 2007Helsinki, July 2007
Louis Cloutier, Louis Cloutier, ConvenorConvenorAndré Leblond, André Leblond, SecretarySecretary
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
Fretting fatigue has long been recognized as being the cause of strand failures in outer as well as inner layers of the conductorsIn planes where conductor motion is constrained, the curvatures are much larger than in the free spanInterstrand microslip amplitude increases, small cracks are generated and some propagate up to complete strand failures
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
Strand failures occur mainly at suspension clamps where such singular conditions are created
To a lesser extent, a similar phenomenon can occur at damper, marker or spacer clamps
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
The main cause of conductor fatigue strand failures is the presence of Aeolian vibrations:
A phenomenon far from having a nice constant sinusoïdal formSmall vibration amplitudes exceeding rarely one conductor diameterIn the frequency range of 3 to 150 HzFor winds of 1 to 7 m/s (2 to 15 mph)
Other wind-induced conductor motions such as Wake-induced oscillations and Galloping may also be responsible for fatigue conductor strand failures.
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
Conductor vibration and its detrimental effects has been the subject of several studies for many decades
The following aspects have been of particular interest to the transmission line engineer :In situ measurement of conductor motionsSimple analytical representation of the fatigue phenomenonCharacterization of the fatigue behaviour of a conductorEvaluation of the conductor residual life
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
It permits a measure of the differential displacement of the conductor at 89mm from the last point of contact with the clamp.Introduced by Tebo in 1941Pursued by Edwards and Boyd in 1963Recommended by IEEE in 1963 (also in the 2006 revision of the IEEE Guide)Recommended in CIGRE SC22 WG04 1979 and SC22 WG02 1995
Several methods to measure the vibration intensity of a conductor have been employed.The bending amplitude Ybmethod finally comes out as the most practical :
In situ measurement of conductor motions (I)
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
The reverse bending amplitude was presented as an alternative to permit the installation of the vibration recorder directly onto the conductorThe bending amplitude method suits particularly well the configuration of a conductor supported in a short metallic clampThe last point of contact is easily locatedThe bending amplitude method must be interpreted correctly when cushioned clamps are used
In situ measurement of conductor motions (II)
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
In situ measurement of conductor motions (III)
Pavica
HILDAOntario Hydro RecorderTVM 90
Ribe LVRVibrec 400
Scolar III
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
The conductor/clamp system is represented as a cantilever beamBending amplitude method is valid only for armored or unarmored conductors fitted with solid metal-to-metal clampsInvalid for cushioned clamps (armored or unarmored)
Simple Analytical Representation of the Fatigue Phenomenon (I)
Xb=89mm
Yb
b boraσ or aε
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
An idealized bending stress (Poffenberger-Swart formula) is calculated in the top-most outer-layer strand in the plane of the last point of contact (LPC)
Ea: modulus of elasticity of outer wire material (N/mm2)d: diameter of outer layer wire (mm)p = (H/EI)½
H: conductor tension at average temperature during test period (N)EI: sum of flexural rigidities of individual wires in the cable (Nmm2)x: distance from the point of measurement to the last point of
contact between the clamp and the conductor.
Simple Analytical Representation of the Fatigue Phenomenon (II)
( ) bpxa
a Ypxe
pdE+−
= − 14
2σ
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
The free loop amplitude of vibration, ymax, is also a useful practical parameter
The Poffenberger-Swart formula becomes:
Ea: Young’s modulus for the outer-layer strand material (N/mm2)d: diameter of outer layer wire (mm)f: frequency of the motion (Hz)m: conductor mass per unit length (kg/m)EI: sum of flexural rigidities of individual wires in the cable (Nmm2)
Simple Analytical Representation of the Fatigue Phenomenon (III)
LPC
maxaa fyEImEdπσ =
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
Laboratory fatigue tests ― Resonant type test benches
Characterization of the fatigue behaviour of a conductor (I)
Pneumatic tensioning system
Slider
DynamometerAmplitude measuring system
Rubber dampers
Wire break detectionVibrator
Active length : 7 m2 m 2 m
Suspension clamp
End clamp
Turnbuckle
5.5E
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
Important test parametersConstant amplitude excitationMeasurement of the bending amplitude Yb and/or the free loop amplitude ymaxMost tests done with conductors supported in short metallic clampsClamps usually held in a fixed position on the test bench
Characterization of the fatigue behaviour of a conductor (II)
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
The results of such tests ultimately lead to the presentation of a fatigue (S-N) curveThe endurance limit is determined at 500 megacycles
Characterization of the fatigue behaviour of a conductor (III)
s
107 108 109
N
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
Fatigue Endurance Data
Idealized bending stress (Poffenberger-Swart formula) at conductor surface vsmegacycles to failureEndurance limits
22.5 MPa for single-layer ACSR8.5 MPa for multi-layer ACSR
Evaluation of the conductor residual life (I)
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
Statistical analysisS-N curves without wire failure
Average95% probability of survival
Evaluation of the conductor residual life (II)
1 10 100 1000N = Megacycles to failure
0
10
20
30
40
Poffen
berg
er-
Sw
art
str
ess
rel
ativ
e to
Yb
(MP
a)
Average S-N curve (50%)95% probability of survival curve
Multi-Layer ACSR Fatigue Endurance Data
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
Based on Cumulative damage theory (Miner’s rule)Total damage D at several stress levels σi cumulates linearly:
D = Σ ni/Ni
Failure is predicted when
D = Σ ni/Ni =1
Evaluation of the conductor residual life (III)
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CONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUESCONSEIL INTERNATIONAL DES GRANDS RÉSEAUX ÉLECTRIQUES TF B2.11.07TF B2.11.07FATIGUE ENDURANCE CAPABILITY OF CONDUCTOR/CLAMP SYSTEMS
UPDATE OF PRESENT KNOWLEDGE
Some important recent contributionsGuide for Aeolian Vibration Field Measurements of Overhead Conductors, IEEE P1368, 2007 (a revision of IEEE 1966 Report)Transmission Line Reference Book, Wind Induced Conductor Motion, Second Ed. EPRI 2007 (Chapter 3, Fatigue of Overhead Conductors), a revision of the 1979 “Orange Book”
IEC TC7 approved recently :Method for Conductor Fatigue Testing, Project 451(sec)/NP 94-08
CIGRE SCB2 intends to complete the following:Fatigue Endurance Capability of Conductor/Clamp Systems ― Engineering Guidelines and Recommendations