David G. Havard, Ph.D., P.Eng.Havard Engineering Inc.

FATIGUE OF CONDUCTORS– A SUMMARY OF PRESENT KNOWLEDGE

January 12, 2010Conductors and Accessories WG Meeting

Disney Contemporary ResortOrlando, FL

OUTLINE OF PRESENTATION

Examples of conductor fatigueConductor typesClamp typesFretting behaviour in stranded conductorsDesign toolsAeolian vibration Assessment of vibration severity on actual linesDetermination of fatigue endurance capabilityExamples of conductor fatigue dataEvaluation of conductor residual lifeConductor and clamp types lacking fatigue data

EXAMPLE OF CONDUCTOR FATIGUE

Fatigue failure of a conductor next to a metal clamp

•Conductor fatigue occurs when wind induced vibration is not controlled

•Fatigue damage occurs most often next to the suspension clamp

•Fatigue usually takes many years to become apparent

•Steel core can fail by overheating after aluminum layers are separated

EXAMPLE OF FATIGUE DAMAGE

Conductor fatigue damage visible at a clamp due to aeolian vibration after five years service

• Showing the conductor after removing the clamp• Damage locations are at both ends of the keeper• Includes damage in the second layer

TYPICAL CONDUCTOR CONFIGURATIONS

Conductors comprise layers of strands wound in alternate directions around a central "king" wireThe conductor size is chosen to suit electrical and mechanical requirementsThe conductor cost is up to about 40% of total capital investment.The most common conductor type is ACSR (Aluminum Conductor Steel Reinforced)The ratio of steel to aluminum areas vary widely

SOME SPECIAL CONDUCTORS

Trapezoidal Z-shaped compact Self-damping ExpandedOptical Ground WireTP conductor

COMMON CONDUCTOR MATERIALS

Core:– Mainly galvanized steel (sometimes greased)– Some aluminized steel– Aluminum alloy 6201-T6– “Composite”

Outer layers:– Electrical grade aluminum (high conductivity, low

strength)– Aluminum alloy (higher strength, minor loss of

conductivity)– Annealed aluminum (ACSS) (low tensile and fatigue

strengths)

SOME CHARACTERISTICS METAL SUSPENSION CLAMPS

The ideal profile of the clamp body follows the natural curvature of the conductorThe ends of the clamp body and the keeper must be rounded to avoid indenting the conductorThe clamp incorporates a pivot either below, above or at the conductor axis to allow rotation in the plane of the conductor

OTHER SUSPENSION CLAMPS

Armor grip suspension (AGS)– Elastomeric bushing with

cage of preformed rods Metal clamp with elastomeric insertSpecial river crossing clamp– Long saddle to reduce

contact stress

CONTACT AREAS BETWEEN ROUND STRANDS

Fatigue of conductors is due to microslip movements of wires inducing fretting fatigueThe phenomenon is complex and its exact modelling has yet to be completedFatigue of conductors is due to microslip movements of wires Contact areas between round strands are ellipticalFretting and microslip occur in these contact areasFatigue cracks develop out of these contact areasFatigue cracks can occur on top and on bottom of the strand in the second layer

CONTACT AREAS BETWEEN TRAPEZOIDAL STRANDS

The knowledge on fatigue performance of conductors mostly relies on results of laboratory tests made on conductors in fixed short metallic clampsIt is not possible at the moment to determine the fatigue endurance of a conductor aloneThere is a wide diversity of design and geometry of conductors and supports

Contact areas between trapezoidal strands are diamond shapedStress levels are lower between trapezoidal strandsPoorly formed trap wire can have small contact areas and higher stresses

DESIGN TOOLS: AEOLIAN VIBRATIONS AND CONDUCTOR FATIGUE

There is no analytical solution that will predict fatigue of conductor-clamp systems due to the complex fatigue process and the variety of conductors and clampsApproximate engineering solutions have been developed and serve as reliable design tools When applied correctly, they lead to an acceptable level of control of the vibration to avoid fatigue The CIGRÉ report includes a review of those design tools and gives to the transmission line engineer a clear indication of the limits to their application

PREDICTION OF AEOLIAN VIBRATION AMPLITUDES

Many utilities have their own design rules (for number of dampers) based on past experienceVibration severity can also be measured on existing linesA useful analytical approach is the "Energy Balance Principle“ (EBP)The EBP leads to an estimate of conductor vibration amplitude based on equating the energy input from the wind with the energy absorption (damping) of the conductor and dampersThe EBP can also be used for the direct design of the damping system for a new lineThe estimate of the expected vibratory motion from EBP is considered an upper bound and is therefor a safe value

LIMITATIONS ON THE USE OF EBP

"The strains predicted by the different researchers exhibit considerable variability. Nevertheless analytical methods based on the EBP and shaker-based technology can provide a useful tool for use in design of damping systems for the protection of single conductors against aeolian vibrations. It should be used with circumspection and be supplemented by references to field experience. Greater accuracy can be obtained by evaluating damper dissipation on laboratory span rather than on the shaker"Ref: "Modelling of aeolian vibrations of a single conductor plus damper: assessment of technology "

CIGRÉ TF B2.11.01, Electra, No 223, December 2005, pp.28-36

CONDUCTOR PROFILE DURING AEOLIAN VIBRATION

Parameters describing conductor vibration include:

Bending amplitude Yb, Free loop amplitude ymax Bending angle β, Wave length λ and Loop length ℓ

This representation applies to metal clamps, not to elastomer lined clamps

The bending amplitude Yb is the most practical field measurement :

The peak to peak displacement of the conductor at 89 mm (3.5 inch) from the last point of contact with the clamp

Recommended by IEEE in 1966 (also in the 2007 revision IEEE P1368)Recommended in CIGRÉ SC22 WG04 1979 and SC22 WG11 TF02 1995

MEASUREMENT OF CONDUCTOR MOTIONS

MEASUREMENT OF CONDUCTOR MOTIONS

Pavica

Ontario Hydro Recorder Vibrec 400ALCOA Scolar III

Vibration recorders sample conductor vibration for a few seconds every 15 minutes

Each record is summarized as the maximum peak to peak amplitude and the average frequency

The records are stored for subsequent analysis

An idealized bending stress in the top-most outer-layer strand in the plane of the last point of contact) is calculated from the bending amplitude (Poffenberger-Swart formula)

Ea: modulus of elasticity of outer wire material (N/mm2)d: diameter of outer layer wire (mm)H: conductor tension at average temperature during test period (N)EI: sum of flexural rigidities of individual wires in the cable (N mm2)x: distance from the point of measurement to the last point of

contact between the clamp and the conductor.

ANALYTICAL REPRESENTATION OF THE FATIGUE PHENOMENON

( ) bpxa

a Ypxe

pdE+−

= − 14

2σ

EIHp =

The same idealized bending stress can be derived from the free loop amplitude, ymax, which is the vibration parameter often measured in indoor test spans

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 (N.mm2)

maxaa fyEImEdπσ =

ANALYTICAL REPRESENTATION OF THE FATIGUE PHENOMENON

LABORATORY FATIGUE TESTS ― RESONANT TYPE TEST BENCHES

Pneumatic tensioning system

Slider

DynamometerAmplitude measuring system

Rubber dampers

Wire break detectionVibrator

Active length : 7 m2 m 2 m

Suspension clamp

End clamp

Turnbuckle

5.5

• Constant amplitude excitation• Measurement of the bending amplitude Yb and/or the free loop amplitude ymax• Most tests with conductors supported in short metallic clamps• Clamps usually held in a fixed position on the test bench

The results of fatigue tests ultimately lead to the presentation of a fatigue (S-N) curveNote scatter in the dataThe endurance limit is determined at 500 megacyclesIdealized bending stress at conductor surface vs megacycles to failureEndurance limits– 22.5 MPa for single-layer ACSR– 8.5 MPa for multi-layer ACSR

FATIGUE ENDURANCE DATA

FATIGUE OF TWO LAYER ACSR CONDUCTORS

FATIGUE OF THREE LAYER ACSR CONDUCTORS

FATIGUE OF ALDREY AND 6201 ALUMINUM ALLOY CONDUCTORS

CONDUCTOR ENDURANCE LIMITS (IN METAL CLAMPS)

CONDUCTOR TYPE ENDURANCE LIMITσa ksi fymax in/sec

ALL ALUMINUM 3.19 5.04ALL 5005 ALLOY 3.19 5.04ALL ALDREY or 6201 2.18 3.43ACSR (Except 7/1) 3.19 4.65ACSR (7/1) 3.19 5.87COPPER (Cu) 5.08 3.39COPPERWELD (Cw) 5.08 4.616 Cu/1 Cw 5.08 3.662 Cu/1 Cw 5.08 3.82EHS Steel (Galv) 27.85 15.16EHs Steel (Aluminized) 19.58 10.71ALUMOWELD 19.58 10.87

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 =1The accuracy of the resulting estimate of lifetime is between 50% and 200%

EVALUATION OF CONDUCTOR RESIDUAL LIFE (CIGRÉ)

RULE OF THUMB APPROACH TO INTERPRETING FATIGUE DATA (IEEE)

Widely used set of empirical criteria (“Guide for Aeolian Vibration Field Measurements of Overhead Conductors”, IEEE P1368, 2007)The bending amplitude may exceed the endurance limit during no more than 5% of total cyclesNo more than 1% of total cycles may exceed 1.5 time the endurance limitNo cycle may exceed 2 times the endurance limit

CONDUCTOR AND CLAMP TYPES LACKING FATIGUE DATA

The extrapolation of fatigue data available to other types of conductors or to different types of support is not recommendedBending amplitude method is valid only for armored or unarmored conductors fitted with solid metal-to-metal clampsNot valid for cushioned clamps (armored or unarmored)Little test data for conductors except ACSR and aluminum alloysSome data for ACSR conductors with armor rodsThere is a need for more published data on conductor fatigue

CONDUCTOR FATIGUE - SOURCES

“Engineering Guidelines Relating to Fatigue Endurance Capability of Conductor/Clamp Systems”, CIGRÉ Technical Brochure No. 332, 2007

“EPRI Transmission Line Reference Book: Wind–Induced Conductor Motion”, (The Orange Book), Second Edition, Chapter 3 Fatigue of Conductors, 2006

“Guide for Aeolian Vibration Field Measurements of Overhead Conductors”, IEEE P1368, 2007 (a revision of IEEE 1966 Report)

SPEAKER’S CONTACT INFORMATION

President: Havard Engineering Inc.Tel: 1-905-273-3076Fax: 1-905-273-5402E-Mail: dhavard@rogers.comWeb Page: www.havardengineering .comAddress: 3142 Lindenlea DriveMississauga, OntarioCanada, L5C 2C2