53032276 aeolian vibration

7/29/2019 53032276 Aeolian Vibration

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Aeolian Vibration

Basics

November 2008

Part of a series of reference reports prepared byPreformed Line Products


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Aeolian Vibration BasicsContents Page

Abstract .............................................................................................................................1

Mechanism of Aeolian Vibrations ......................................................................................1

Effects of Aeolian Vibration ...............................................................................................3

Safe Design Tension with Respect to Aeolian Vibration....................................................5

Influence of Suspension Hardware....................................................................................5

Dampers: How they Work .................................................................................................6

Damper Industry Specifications.........................................................................................7

Damper: Laboratory Testing..............................................................................................8

Dampers: Field Testing .....................................................................................................9


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ABSTRACT

Wind induced (aeolian) vibrations ofconductors and overhead shield wires(OHSW) on transmission and distribution linescan produce damage that will negativelyimpact the reliability or serviceability of these

lines. Lines damaged by vibration may have tobe de-rated or even taken out of service untilrepairs can be made. This could have animpact on an entire network.

Understanding aeolian vibration and how itcan be managed or controlled is the key tominimizing its possible effect on a line ornetwork.

This report will present an executive summaryof the research and findings of industryexperts all over the world who havecontributed to the understanding of aeolianvibration and its control. The references citedwill provide a more detailed explanation ofindividual principles, findings andrecommendations.

MECHANISM OF AEOLIAN VIBRATION

When a smooth stream of air passes acrossa cylindrical shape, such as a conductor orOHSW, vortices (eddies) are formed on theleeward side (back side). These vorticesalternate from the top and bottom surfaces,

and create alternating pressures that tend toproduce movement at right angles to thedirection of the air flow. This is the mechanismthat causes aeolian vibration [1].

The term smooth was used in the abovedescription because unsmooth air (i.e., air withturbulence) will not generate the vortices andassociated pressures. The degree ofturbulence in the wind is affected both by theterrain over which it passes and the windvelocity itself. It is for these reasons thataeolian vibration is generally produced bywind velocities below 15 miles per hour

(MPH). Winds higher than 15 MPH usuallycontain a considerable amount of turbulence,except for special cases such as open bodiesof water or canyons where the effect of theterrain is minimal.

The frequency at which the vortices alternatefrom the top to bottom surfaces of conductorsand shield wires can be closely approximated

by the following relationship that is based onthe Strouhal Number [2].

Vortex Frequency (Hertz) = 3.26V / dwhere: V is the wind velocity component

normal to the conductor or OHSW

in miles per hour

d is the conductor or OHSWdiameter in inches

3.26 is an empirical aerodynamicconstant

One thing that is clear from the aboveequation is that the frequency at which thevortices alternate is inversely proportional tothe diameter of the conductor or OHSW.

For example, the vortex frequency for a 795kcmil 26/7 ACSR (Drake) conductor underthe influence of an 8 MPH wind is 23.5 Hertz.A 3/8 OHSW under the same 8 MPH wind willhave vortices alternating at 72.4 Hertz. Thefact that the vortex frequency for an OHSW ismuch higher than that for a conductor will beimportant to remember when the effects ofvibration are discussed later in this report.

To further illustrate the difference in vibrationfrequencies between conductor and OHSW,Figures 1 & 2 show actual vibration recordingsmade on a line in the western part of the U.S.The recordings were taken with an OntarioHydro Recorder on a 1400 span. Theconductor is 1272 kcmil 45/7 ACSR (Bittern)and the OHSW is 3/8 EHS. Plugging therecorded frequencies and diameters into theabove equation yields the same apparent windvelocity (4.5MPH) for both the conductor andOHSW.

Figure 1 Vibration Recorded on 1272 kcmil45/7 ACSR (11 Hertz)

1 Second


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Figure 2 Vibration Recorded on3/8 OHSW (41 HERTZ)

Sustained aeolian vibration activity occurswhen the vortex frequency closelycorresponds to one of the natural vibrationfrequencies of the span of conductor orOHSW. This sustained vibration activity takesthe form of discrete standing waves withforced nodes at the support structures andintermediate nodes spaced along the span atintervals that depend on the particular naturalfrequency (Figure 3).

Figure 3 Standing Wave Vibration

The natural frequencies at which a conductoror OHSW under tension will vibrate in a seriesof standing waves are approximated by:

F = (Tg/w)1/2 x N/2S

where:F is the natural frequency in hertzT is the tension in poundsg is the gravitational constant of 32.2 ft/sec2

w is the conductor or OHSW weight per footN is the number of standing wave loopsS is the span length in feet

For example, the natural frequencies for an800 span of 795 kcmil 26/7 ACSR (Drake)conductor at a tension of 4,725# are given by:

F = 0.233 x N

It was stated earlier that sustained vibrationwill occur when the vortex shedding frequencyof the wind is equal to one of the naturalfrequencies of the span. Therefore, for thisexample, using 800 of Drake conductor at atension of 4,725#:

2.9422 x V = 0.233 Nor

12.6275 x V = N

For a wind velocity of about 8 MPH, the spanin this example would have 100 standingwaves (N=100), each about 8 in length (loop

length). At a higher wind speed near 12 MPHthe loop length will decrease to 5.3 (N=150).The importance of loop lengths will bediscussed in a later section dealing with theplacement of dampers.

The amplitude at which a span will vibrate(peak-to-peak movement at the anti-node inFigure 3) depends on a number of factorswhich include the energy that is transferred tothe span by the wind and the amount ofdamping in the span from the conductor orOHSW itself (self damping) or from additionaldampers installed in the span.

In most cases the maximum peak-to-peakamplitude of a vibrating conductor or OHSWwill not exceed its diameter.

Extensive research utilizing wind tunnelstudies has been used to determine theenergy imparted by the wind to a vibratingconductor [3], [4], [5], [6], [7], [8], [9].Collectively this research has shown that windenergy may be expressed in the general (non-linear) form:

P = L x d4 x f3 x fnc(Y/d)where:

P is the wind energy in wattsL is the span lengthd is the conductor diameterf is the vibration frequency in hertzY is the anti-node vibration (peak-to-peak)fnc(Y/d) is a function derived fromexperimentation

The above expression assumes completelylaminar wind flow, free of turbulence. Theeffects of turbulence will be discussed later inthis report.

The self damping characteristics of aconductor or OHSW are basically related tothe freedom of movement or loosenessbetween the individual strands or layers of theoverall construction. In standard conductorsthe freedom of movement (self damping) willbe reduced as the tension is increased. It is forthis reason that vibration activity is mostsevere in the coldest months of the year whenthe tensions are the highest.

1 Second

Node

Anti-node

LoopLength


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Some conductors designed with higher selfdamping performance use trapezoidal shapedouter strands that lock together to creategaps between layers. Other conductors, suchas ACSS (formerly SSAC), utilize fullyannealed aluminum strands that becomeinherently looser when the conductor

progresses from initial to final operatingtension.

Procedures have been established formeasuring self damping performance ofconductors and OHSW in the laboratory [10].

The energy absorbed by damping devicesadded to a span of conductor or OHSW is thesubject of a later section of this report.

EFFECTS OF AEOLIAN VIBRATION

It should be understood that the existence ofaeolian vibration on a transmission ordistribution line doesnt necessarily constitutea problem. However, if the magnitude of thevibration is high enough, damage in the formof abrasion or fatigue failures will generallyoccur over a period of time.

Abrasion is the wearing away of the surface ofa conductor or OHSW and is generallyassociated with loose connections betweenthe conductor or OHSW and attachmenthardware or other conductor fittings. Thelooseness that allows the abrasion to occur isoften the result of excessive aeolian vibration.

Abrasion damage can occur within the spanitself at spacers (Figure 4), spacer dampersand marker spheres, or at supportingstructures (Figure 5).

Figure 4 Abrasion Damage at Spacer

Figure 5 Abrasion Damage at LooseHand Tie

Fatigue failures are the direct result of bendinga material back and forth a sufficient amountover a sufficient number of cycles. Removingthe pull tab from a can of soda is a goodexample.

All materials have a certain endurance limitrelated to fatigue. The endurance limit is thevalue of bending stress above which a fatiguefailure will occur after a certain number ofbending cycles, and below which fatiguefailures will not occur, regardless of thenumber of bending cycles.

In the case of a conductor or OHSW beingsubjected to aeolian vibration, the maximumbending stresses occur at locations where theconductor or OHSW is being restrained frommovement. Such restraint can occur in the

span at the edge of clamps of spacers, spacerdampers and stockbridge type dampers.However, the level of restraint, and thereforethe level of bending stresses, is generallyhighest at the supporting structures.

When the bending stresses in a conductor orOHSW due to aeolian vibration exceed theendurance limit, fatigue failures will occur(Figure 6). The time to failure will depend onthe magnitude of the bending stresses and thenumber of bending cycles accumulated [11],[12], [13].

Figure 6 Fatigue of Conductor Strands


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In a circular cross-section, such as aconductor or OHSW, the bending stress iszero at the center and increases to themaximum at the top and bottom surfaces(assuming the bending is about the horizontalaxis). This means that the strands in the outerlayer will be subjected to the highest level of

bending stress and will logically be the first tofail in fatigue.

The same principle applies to the addition ofArmor Rods to the conductor or OHSW atsupport locations. A portion of the bendingstress is applied to the Armor Rods, whichreduces the bending stress on the conductoror OHSW. Since the Armor Rods are locatedthe furthest from the center line of theconductor, they will be subjected to thehighest level of bending stress, and would beexpected to fatigue before the conductorstrands. However, with the use of bolted

suspension clamps this is not the usual modeof failure (Figure 7).

Figure 7 Fatigue Failure of Conductor UnderArmor Rods

The reason that a conductor will fail underArmor Rods is that the bolted suspensionclamp produces a substantial amount ofcompression load when it is installed. Thecompression between the keeper and theclamp body somewhat crushes theconductor (Figure 8).

Figure 8 Cut-Away of Suspension Clamp

The compression force produces notches inthe aluminum strands of conductors as theypass over each other (the strands in eachlayer are produced in the opposite laydirection). The resulting notches (Figure 9)create stress risers that substantially reducethe endurance limit of the affected strands.

Figure 9 Notching of Aluminum StrandsUnder Bolted Suspension Clamp

It is clear that care must be taken whenremoving Armor Rods from a line that hasbeen subjected to moderate or severe aeolianvibration activity.

Suspension assemblies, such as theARMOR-GRIP Suspension and theCUSHION-GRIP Suspension which use

elastomer cushions, with or without factory-formed rods, hold the conductor with aminimal amount of compression force(Figure 10).

Figure 10 Cut-Away of ARMOR-GRIPSuspension

The conductor in the elastomer cushionsbends gradually, compared to the abruptbending at the edge of a bolted clampskeeper, and notching of the aluminum strandsdoes not occur. The net result is that aconductor or OHSW in a suspension assemblythat uses elastomer cushions can withstandhigher levels of aeolian vibration activitywithout fatigue failure.


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SAFE DESIGN TENSION WITH RESPECTTO AEOLIAN VIBRATION

There are a number of factors taken intoaccount in choosing a design tension for atransmission or distribution line. These factorsinclude:

Average Span Length Overall Height of Structures Maximum Tension at Highest Wind

and/or Ice Loading Clearances at Highest Operating

Temperature Susceptibility to Aeolian Vibration

Of these factors the susceptibility to aeolianvibration has been the only one that is difficultto quantify. Beginning in the early 1960s, andbased on available field experience at thattime, the industry adopted a rule of thumb for

safe design tensions with respect to aeolianvibration [14]. It was suggested that theeveryday stress (EDS) be limited to 18% ofthe conductor rated breaking strength (RBS)to assure safe operation with regard to aeolianvibration. More recent surveys of theperformance of actual lines [15] that had beenin service for 10 to 20 years revealed that upto 45% of lines installed using an EDS


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Figure 12 ARMOR-GRIP Suspension(AGS)

Figure 13 CUSHION-GRIP Suspension(CGS)

As reported earlier Armor Rods will absorb aportion of the bending stress at the edges of

the suspension clamp, but do nothing toreduce the effects of the compression loadingand resulting notching of the aluminumstrands.

Consequently, there is negligible influence ofArmor Rods on the recommendations for safedesign tensions (with or without dampers).

The use of elastomer cushions on highperformance suspensions, such as the AGSand CGS, provide two benefits. First, withinthe elastomer cushion the vibrating conductoris bent in a gradual manner along the cushion,

rather than bending abruptly at the edge of ametallic keeper (suspension clamp).

Secondly, the elastomer cushions, with orwithout externally applied rods (as with theAGS) minimize or eliminate the compressionloading on the conductor, which causesnotching of the aluminum strands.

As a result high performance suspensions willallow higher safe design tensions (H/w) andhave a positive influence on the protectablespan length of a damper.

The amount of positive influence andadditional protection provided by performance

suspensions is difficult to reduce to a simpletable. Contact PLP with specific line designand environmental (terrain and temperatures)data for more information.

DAMPERS: HOW THEY WORK

Dampers of many different types have beenused since the early 1900s to reduce the levelof aeolian vibration within the span and, moreimportantly, at the supporting structures.

The damper most commonly used forconductors is the Stockbridge type damper,

named after the original invention by G.H.Stockbridge about 1924. The original designhas evolved over the years but the basicprinciple remains: weights are suspended fromthe ends of specially designed andmanufactured steel strand, which is secured tothe conductor with a clamp (Figure 14).

Figure 14 VORTX Damper

When the damper is placed on a vibratingconductor, movement of the weights willproduce bending of the steel strand. Thebending of the strand causes the individualwires of the strand to rub together, thusdissipating energy. The size and shape of theweights and the overall geometry of thedamper influence the amount of energy thatwill be dissipated for specific vibrationfrequencies. Since, as presented earlier, aspan of tensioned conductor will vibrate at anumber of different resonant frequenciesunder the influence of a range of windvelocities, an effective damper design musthave the proper response over the range offrequencies expected for a specific conductorand span parameters.


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Some dampers, such as the VORTX Damper(Figure 14), utilize two different weights andan asymmetric placement on the strand toprovide the broadest effective frequency rangepossible.

An effective damper is capable of dissipating

all of the energy imparted to a conductor bythe wind (ranging from 2 to 15 MPH) for thespecified protectable span length. The sameapplies to longer spans where multipledampers are required to dissipate the energyfrom the wind.

Placement programs, such as thosedeveloped by PLP for the VORTX Damper,take into account span and terrain conditions,suspension types, conductor self-damping,and other factors to provide a specific locationin the span where the damper or dampers willbe most effective.

For smaller diameter conductors (< 0.75),overhead shield wires, and optical groundwires (OPGW), a different type of damper isavailable that is generally more effective thana Stockbridge type damper. The SpiralVibration Damper (Figure 15) has been usedsuccessfully for over 35 years to controlaeolian vibration on these smaller sizes ofconductors and wires.

Figure 15 Spiral Vibration Damper

The Spiral Vibration Damper is an impacttype damper made of a rugged non-metallicmaterial that has a tight helix on one end thatgrips the conductor or wire. The remaininghelixes have an inner diameter that is largerthan the conductor or wire, such that theyimpact during aeolian vibration activity. Theimpact pulses from the damper disrupt andnegate the motion produced by the wind.

The Spiral Vibration Damper is so effectivebecause it can be placed anywhere in thespan and has no specific resonantfrequencies. It responds to all frequencies,especially the high frequencies associatedwith smaller diameter conductors and wires(see MECHANISM OF AEOLIAN VIBRATION

section).

The Spiral Vibration Damper also has a limit tothe length of the span protected by onedamper. Longer spans require more than onedamper per span (see Table 2). Up to threeSpiral Vibration Dampers can be spuntogether during installation to avoid having toreach further out into the span.

Note: Increase number of dampers by 50% forspans crossing rivers or canyons.

Table 2 Spiral Vibration DamperRecommendations

DAMPER: INDUSTRY SPECIFICATIONS

The most up-to-date and comprehensiveindustry specification for aeolian vibrationdampers is IEC 61897:1998, Overhead Lines Requirements and Tests for StockbridgeType Aeolian Vibration Dampers.

IEC 61897:1998 describes the requirementsfor materials and protective coatings used inthe manufacture of a damper, and laboratoryand field testing to demonstrate theeffectiveness and durability of a damper. Thetesting includes:

Damper Fatigue Clamp Slip Load Weight Slip Load Damper Response Laboratory In-Span Damper

Performance Electrical (Corona) Performance Field Performance

Standard Hi-Mass

100' to 800' 2 1

800' to 1600' 4 21600' to 2400' 6 3

Span

Length

Dampers per Span


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The damper response test is performed beforeand after the fatigue test on a number ofdampers in the laboratory to confirm that theresponse of the damper will not change duringits service life in the field.

DAMPER: LABORATORY TESTING

The damper response test is performed in thelaboratory by attaching the damper to a shaker(Figure 16).

Figure 16 Damper Response Test Set-Up

By exciting the damper over a range offrequencies the force between the damper andthe shaker can be measured and plotted(Figure 17).

Figure 17 Damper Response Curve

Figure 17 shows the power (in watts) deliveredto the damper by the shaker (vertical axis)over a range of frequencies. The results areshown for three of the same damper design,along with the average. This plot shows fourdistinct peaks in the power curve. Theserepresent the resonant frequencies of thedamper weights. Each weight has tworesonant frequencies: one where the furthestend of the weight has the maximum

movement, and the other where the endnearest the clamp has the maximummovement (higher frequency). The VORTXDamper shown in the curve has two differentweights, each with different resonantfrequencies, which accounts for the four peaksin the curve.

The damper response test is not a measure ofa dampers effectiveness in a span, but istypically used to assure that the basic designhas a correct frequency range for theconductors on which it will be used, and tocompare dampers before and after beingsubjected to fatigue testing.

The damper fatigue testing uses the same testset-up, without the force transducer betweenthe shaker and the damper. In this test thedamper is vibrated for 10 million cycles at ashaker amplitude of 1mm (peak-to-peak) for

the highest resonant frequency of the damper.

The in-span damper performance testing inthe laboratory gives a clear indication of theanticipated performance of the damper in thefield. For this test the damper is attached to atensioned conductor and positioned where itwould be on a span in the field. Blocks of steelplates with grooves for the conductor are usedto eliminate any effects from the dead-endhardware (Figure 18).

Figure 18 In-Span Damper PerformanceTest

The power dissipated by the damper over arange of frequencies was determined by theInverse Standing Wave method in accordancewith IEEE Standard 664-1993, IEEE Guidefor Laboratory Measurement of the PowerDissipation Characteristics of AeolianVibration Dampers for Single Conductors.

VSD4032 Damper Comparison

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

Frequency (Hz)

Power(W)

VSD4032-0001-A VSD4032-0001-B VSD4032-0001-C AverageofDampers


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Sensitive equipment was used to determinethe vertical movement of the span at one ofthe free nodes and anti-nodes. The outputfrom the measurement equipment wasanalyzed by a computer system (Figure 19) tocalculate the power dissipated over thefrequency range.

Figure 19 Computer Analysis System

The results of the testing produce a plot of thepower dissipated by the damper, in watts(vertical axis) for a number of frequencies (orequivalent wind velocities) in the rangeexpected for the conductor being tested. Byplotting the wind energy for the maximumprotectable span length for each frequency,the effectiveness of the damper is clearlyshown (Figure 20).

Figure 20 In-Span Performance Test Results

In the above figure, the lower curve is the windenergy for a 900 (275meter) span, and the top

curve is the energy dissipated by the damper.For the entire range of frequencies, thedamper can dissipate at least, and generallymore than, the wind can impart on the span.

The remaining laboratory tests (weight andclamp slip on strand, and corona) are selfexplanatory, but equally important in theoverall assessment of a damper.

DAMPER: FIELD TESTING

Beginning in the late 1950s considerable workwas completed on the development of ruggedequipment for the field measurement ofaeolian vibration [16], and on the interpretationand presentation of the results [17], [18], [19].

In 1966 the IEEE Committee on OverheadLine Conductors published a standardizedmethod for measurement and presentation ofresults [18] that is still used today.

The field vibration recorder developed byOntario Hydro in the early 1960s (Figure 21) isan analog device that is still being utilized.Recorders more recently developed use digitaltechnology to record and store the data.

Figure 21 Ontario Hydro Vibration RecorderMounted on ARMOR-GRIP Suspension

The best way to understand the process ofrecording and interpreting field vibration datais to follow the process that is used with theOntario Hydro Recorder (analog). In this wayyou will understand the steps that are doneautomatically in the newer (digital) recorders.

As shown in Figure 21 special mountinghardware is used to establish a very rigidattachment between the recorder and thesuspension hardware. The recorder measuresthe differential displacement between thesuspension and the conductor during vibrationactivity. The input arm of the recorder issecured to the conductor (or Armor Rod orAGS Rod) at a specified distance from thesuspension hardware. The IEEErecommended distance is 3.5 from the edgeof a keeper on a bolted suspension clamp. Alarger distance is required for AGS due to thearea where the rods transition from theconductor to the outer surface of theelastomer cushions (Figure 21). The distance

Damper Efficiency - VSD40B @ 150 micro-strain level Damper Placement = 39"

from Rigid Clamp

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60

Frequency (Hz)

Power(W)

Dissipated Power (Damper B) Wind Power input (275m Span)


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used in the field is recorded and taken intoaccount in the interpretation of the data.

Looking inside the Ontario Hydro vibrationrecorder (Figure 22), the arm connected to theconductor is connected to an assembly oflinkages that multiply the vertical

displacement. At the end of the assembly is athin plate with a sharp stylus that is positionedover the clear Mylar film.

Figure 22 Ontario Hydro Recorder(Inside View)

The clock (lower right side) works with a microswitch and a timing circuit to switch on themotor (top center) and advance the film for aone second period once every 15 minutes (96traces per day). At the same time an electromagnet pulls the stylus down onto the Mylarfilm. The rechargeable battery (upper right) iscapable of operating the recorder for a two-week period, even at extremely coldtemperatures.

Each one-second trace on the Mylar film(Figure 23) is an actual representation of themotion of the conductor (differentialdisplacement) during that period.

Figure 23 Vibration Recorded on 1272 kcmil45/7 ACSR Conductor (11 Hertz)

The Mylar tapes are read with a calibratedmagnified viewer that allows the technician torecord the number of cycles in the one-secondperiod (frequency), and the maximumamplitude (in mils) of the conductor movement(differential displacement).

The next step is to summarize, or add up thetotal number of recorded traces for eachfrequency and amplitude. When donemanually this procedure is referred to as a dotplot because the technician adds a dot in abox that represents a specific frequency andamplitude for each trace. When all the tracesare read and recorded, the dots are added upto get the total number of occurrences foreach frequency and amplitude. The newerdigital recorders determine the frequency andamplitude for each record (one per 15-minuteperiod) automatically and add them to a built-in histogram that can be downloaded into a

computer when the recorder is removed fromthe line. The only advantage of the analogrecorder is that it is possible to determine theapproximate time and date for each individualtrace.

It is assumed that the vibration activity that iscaptured in each one-second trace isindicative of the vibration during the entire15-minute period. Using this it is possible tocalculate the number of total cycles in the15-minute period (based on the frequency) foreach specific amplitude recorded during thestudy period.

The bending strain (in micro-strain) on theconductor for each amplitude is determinedfrom the Poffenberger-Swart equation [17],with consideration given to the distancebetween the suspension hardware and theattachment to the conductor.

The standard IEEE representation of theresults of a field vibration study is a graph withthe number of millions of cycles per day(MC/day) on the vertical axis, and the micro-strain level on the horizontal axis (see Figure24 for an example).

Figure 24 shows the recorded field vibrationon a test line with a single 795 kcmil 26/7ACSR (Drake) conductor on one phase andtwin (18 horizontal separation, with spacers)on a second phase. The tensions were thesame for the purpose of this study.

1 Second


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Figure 24 Example of IEEE Output for FieldVibration Study

It is clear from this study that the vibrationlevels on a single conductor are higher thanthe levels for a twin configuration (withspacers) under the same conditions.

It is common to use a similar comparison ofcurves to show the effectiveness of vibrationdampers in the field.


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REFERENCES

[1] Electric Power Research Institute, Transmission Line Reference Book, Wind Induced ConductorMotion, Research Project 795, 1978

[2] V. Strouhal, On Aeolian Tones, Annalen der Physik und Chemie, Band V, 1878, p. 216

[3] E. Bate, The Vibration of Transmission Line Conductors, Transactions of the Institution ofEngineers (Australia), Vol XI, 1930, pp. 277-290

[4] E. Bate and J. Callow, The Quantitative Determination of the Energy Involved in the Vibration of

Cylinders in an Air Stream, Transactions of the Institution of Engineers (Australia), Vol XV, No 5,1934, pp. 149-162

[5] J.S. Carroll, Laboratory Studies of Conductor Vibration, Electrical Engineering, May 1936

[6] F.B. Farquharson and R.E. McHugh, Wind Tunnel Investigation of Conductors Vibration UsingRigid Models, IEEE Transaction Paper, October 1956, pp. 871-877

[7] G. Diana and M. Falco, On the Forces Transmitted to a Vibrating Cylinder by a Blowing Fluid,

Meccanica, Vol VI, No 1, 1971

[8] C.B. Rawlins, Wind Tunnel Measurement of the Power Imparted to a Model of a VibratingConductor, IEEE Transactions on Power Apparatus & Systems, Vol PAS-102, No 4, April 1983,pp 963-971

[9] D.U. Noiseux, S. Houle and R. Beauchemin, Study of Effective Aeolian Wind Power Imparted to

Single Conductor Spans, Report on CEA R&D Project 146 T 328, 1986

[10] IEEE Std 563-1978 (Reaff 1991), IEEE Guide on Conductor Self Damping Measurements

[11] P.W. Dulhunty, A. Lamprecht and J. Roughan, The Fatigue Life of Overhead Line Conductors,

CIGRE SC22-WG04 Task Force Document, 1982

[12] CIGRE Study Committee 22, Working Group 04, Endurance Capability of Conductors, Final

Report, July 1988

[13] C.B. Rawlins, Exploratory Calculations of the Predicted Fatigue Life of Two ACSR and OneAAAC, Report CIGRE SC-22, WG11, TF4-96-5, April 1996

[14] O.D. Zetterholm, Bare Conductors and Mechanical Calculation of Overhead Conductors, CIGRE

Session Report #223, 1960

[15] CIGRE Report #273, Overhead Conductor Safe Design Tension with Respect to AeolianVibrations, Task Force B2.11.04, June 2005

[16] A.T. Edwards and M. Boyd, Ontario Hydro Live-Line Vibration Recorder for Transmission

Conductors, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-82, 1963, pp. 269-273

[17] J.C. Poffenberger and R.L. Swart, Differential Displacement and Dynamic Conductor Strain, IEEE

Transactions on Power Apparatus and Systems, Vol. PAS-84, 1965, pp. 281-289 and 508-509

[18] IEEE Committee Report, Standardization of Conductor Vibration Measurements, IEEE

Transactions on Power Apparatus and Systems, Vol. PAS-85, Jan. 1966, pp. 10-20

[19] R.A. Komenda and R.L. Swart, Interpretation of Field Vibration Data, IEEE Transactions on PowerApparatus and Systems, Vol. PAS-87, pp. 1066-1073


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53032276 aeolian vibration

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