ML20147E653

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Experimental Investigation of Vibration Damping in Aluminum Electrical Conduit, Interim Rept
ML20147E653
Person / Time
Site: Browns Ferry  Tennessee Valley Authority icon.png
Issue date: 03/31/1986
From: March P
TENNESSEE VALLEY AUTHORITY
To:
Shared Package
ML18032A736 List:
References
WR28-4-900-176, NUDOCS 8803070119
Download: ML20147E653 (20)
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Text

GA. Record B41

'860327 003 Tennesuee Valley Authersty Office of Natural Resources anc Economic Development Divtston of Atr and Water Resources Engineering Laboratory I

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AN EXFERIMENTAL INVESTIGATION OF VIBRATION DAMPING IN ALUMINUM ELECTRICAL CONDUIT y ['

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1 TABLE OF CONTENTS INTRODUCTION..................................................

1 TECHNICAL BACKGROUND..........................................

1 TEST FACILITY AND INSTRUMENTATION..............................O i

Test Facility.............................................O Instrumentation...........................................O TEST PROCEDURES...............................................

5 E::ci tation Methocs and Procedures........................

5 Test Conditions......................,....................

5 O.

Data Analysis Procecures.................................

6 Verification Procedure...................................

6 Quality Assurance........................................

6 s

TEST RESULTS......s........................................... 6

)

Verification.............................................

6 Natural Frequency Resu1tc.................................E

'Results for Three-Ouarter Inch Conduit...................

8 Results for One and One-Half Inen Concuit.................S Results for Tnree-Incn Concuit............................S Results for Five-Inch Conduit...........................

1~

SUMMARY

, CONCLUEIONE, AND RECOMMENDATIONS....................

10 RE~ERENCES...................................................

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1

r INTRODUCTION

~-

Proper design of nuclear power plants in:ludes predicting the response of nucl ear plant system-8 and components to seismic e::c i t a t i on.

The dynamic response of an el ectrical conduit system, for e::a mp l e, will be influenced by the response of the entire plant to the sei smi c e::ci tati on. by the lccation of the system within the plant, and bv the characteristics of the system.

The damping, which is releted to the amcunt of energy dissipated per vibrational cycle (ANSI, 1971), is a particularly important parameter for estimating the. dynamic response of a system.

Additional damping information derivec from laboratory tests is necessary for accurate and reasonable sei smi c qualifications of electrical conduit systems.

Thic report describes the technical background, test facility, instrumentation, e:.:p er i men t a l procecures, data analysis procedures, and results for dynamic tests used to determine natural frequencies and damping values for aluminum electrical concuit.

Test parameters include type-of end restraint, conduit ciameter, span, wire loading, amplitude of e::c i t a t i on, and excitation method.

e TECHNICAL BACl: GROUND i

The dynamic behavior of a vibrational mode for a physical system can ofttn be adequately represented with a single degree-of-freecom model (see Den Hartog, 1056; Myklestad, 1956:

Mitchell, 1981; Lalanne, et al., 19E-).

The di f f erer.ti al equation of motior, for a single degree-of-freedom system in:

  • m ! + c:*. + k::

F(t)

(1)

=

Displacement of the where

=

structure m=

Effective mass c = Effective camping R = Effective stiffness F(t)

Fcccing function.

=

For the free vibration response typical of impact. snapback, and sine-decay tests, the forcing function becomes :ero:

mE + c:** + k::

0.

(2)

=

9 e

n.

2 This equation is satisited by'an e::ponenti all y decaying sinusold of the form:

~

= ::oe-s~a tc os (wat + $)

(3)

Initial def l ec ti on' where

c.

=

C = Damping ratio w

= Natural f requency - (rad /sec) n w.

= Damped natural frequency 4 = Pnase angle.

Additional definitions and relationships among variables are as follows:

y = c/c.

(4)

w. = wn(1 - 35)o 5
  • w (5) n I

2(km)o 5 = 2mw (6) c.

=

n 100) = Damping ratio

(*/.)

(7) w=

Onf (S)

= kotational frequency where w

(radians /second) f = Frequency (Hert:)

i

c. = Critical damping coefficient.

The "logarithmic decrement," representing the natural log of the ratio of successi ve ma::i mum ampli tudes, is f requently used to calculate the damping ratio (Den Hartog, 1956: Myklestad, 1056; La:an and Goodman, 1961; Lal anne, et al.,

1960: March, 1984; ANCO, 1985):

6. = (1/n ) l n (2:./::..n)

(9) b = 2nc (10) where 6 = Log decrament n = Number of cycles

. = D: spl ac ement at cycle m
..n = Displacement n cycles after cycle m.

Natural frequencies and damping ratios can also be computed by curve f itting the. f ree-response di spl acement dat+ to the single degree-of-freedom' response model given in Equation (C) (Hunter, Linton, and March, 1986; March, 1986).

l

3

, TEST FACILITY AND INSTRUMENTATION Test Facilitv A test f acility was constructec to reprcduce a mounting configuration typically-encountered in a plant.

Two twelve-inch by sin and one-half inch wide 41ange beams were mounted hori:ontally anc welded on eight-foot c, enters to tnree rigid vertical supports.

Two f our-i nch by fcur-inch bon beam sections were welded to the upper horizontal beam on ten-foot centers.

Sections of P-1000 Uni strut were welded beneath each bon beam.

Electrical conduit test spans were attached to the P-lOOO Unistrut sections with one-bolt or two-bolt Unistrut clamos and the corresponding Unistrut bolts and nuts.

In general, a ten-foot length of electrical conduit and a cne-foot lengtn of electrical conduit were joined with a standard threeced coupling and supported on ten-foot centers.

For the three-quarter inen conduit, an additional center support was,added, forming'two

  • five-foot spans.

Wires, clamps, couplings, and electrica) conduit sections were supplied by Browns Ferry Nuclear Plant personnel.

j Instrumentation These tests included enciting a dynamic response in the conduit, measuring the displacement response of the conduit as a function of time, and te or i vi ng the dynamic characteristics of the system from the measured free-response data.

Encitation methods included impacts and snapbacks.

Lateral displacement was measured witn a linear variable differential transducer (LVDT).

Lateral acceleretion was measured with a crystal-type accelerometer.

Impact force was measured with a crystal-type force cell located in an' impact hammer head.

Outputs from the displacement transcucer and from the accelerometer were scanned, digiti:ed, and stored on magnetic cisks for scaling, plotting, and analysis.

The microcomputer-

[

based data acquisition and analysi s system is she

  • in the photograph in Figure 1.

The minimum scan rate for data acquisition was 500 Hert: per channel.

Frequency snd damping values were determinec f rom the digiti:ed data using a simplen curve-fitting algorithm, as discussed in a subsequent section.

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s TEST FFOCEDURES

~~

Encitation Methods and Procedures Test pro edures w e similer_regarcless ci encitation Jonse was produced by snapback technique.

A dynamic encitation or-by an impact hammer with a soft rubber tip.

F c e-snapback encitation, the concult system was moved to its inattal i

displacement by using a turnbuckle, anc a colt cutter wan'uned to sever a connecting rod.

For impact entitation, the test concuit

-was struck in the l ateral - C.iori: ontal ) cirection at midspan with-

- the impact hammer.

Voltages corresponcing to the displacements and accelerations of-the conduit in renpsnse to the encitation

~

were digiti:ed and recorded for analysis.

- Test Conditions The three-quarter inch conduit was attached with Unistrut Type P1110B one-hole conduit clamps on five-foot centers.

The wire loading was 0.16 lbm/ft.

Impact encitation was used to provide initial deflections.

Tests were conducted on the

^

five-f oot section which 'incluced the threaded coupling and en the five-foot section which did not incluce a coupling.

The one and one-half inch conduit was tested with Unistrut Type P1115 ene-hol e conduit clamps and. span lengths of ten feet and nine feet.

Thi s concuit was also tested with Uni strut Type P2559-15 two-hole conduit clamps and a span length of nine 4eet.

The wire loading for all tests was 0. 66 lbm/f t.

Impact excitation was used te provide initial defle:tions.

The three-inen conduit was attachwd wi th Uni stre.t Type.

POSSS O two-hole condui', clamps and a span length of ten feet.

This canduit was tested with a wire-l oadi ng of ' 1. 59 l bm/f t and without wires.

Snapoack and impact excitation were used to provide initial deflections.

A seconc, nominally identical, three inch conduit specimen was also testec under si mi l ar conditions.

For this specimen, the wire loading was 1.41 lbm/ft.

The five-inch conduit was attached with Unistrut Type PO558-50 two-hole concuit clamps and a span l engtr. o4 ten feet.

This conduit was tested witn a wire loeding cf 4;OB lom/ft.

Snapback and impe-t encitation we' 3 ased tc proviJe initial deflections.

S e

4

--'s

6 Data Analvsis Procedures Equation (0) provides A mathematical model for the free response of a linear, damped, single cegree-of-freedom system.

Natural frequencies and damping values are det ermined by using a steplen curve-fitting algorithm to fit this mathematical mocel to the f ree-response di spl acement data obtained during testing.

The si mpl en algorithm, a versatile. otrect-search procedure for minimi:1ng a multiple variabl e function,'is described in greater detail in Nelder and Mead (1965), Caceci and Cacherad (1984), and Hynter, Linton, and March (1966).

Convergence of the curve-fitting procedure can be accelerated when the natural frequency is determined in advance, f+her by using a Fourier transform method or by calculating directly f rom the time-domain data, and an enponential decay curve is fitted to the data peal:5.

Verification Procedure For the purpose of verif ying the curve-f i tti ng al ge.-i thm used in the data anal ysi s, data sqts correr?onding to natural frequencies of 10.00 Herte and 30.00 Herte and damping ratios of 1.0 %,

5.0%, 10.0%, and 15.0% were generated analytically f rom Equation (0).

The data analysis procedures were applied to this data, and natural frequencies and damping ratios were computed.

Ovalitv Assurance This study was concutted uncer WRE5 SP-15. Ol:-R1, "Quality Assurance Procedure for Ccncucting Physical Model Studies and Physical Testing Programs" (March, 1950).

TEST RESULTE Veri f i c at i on The full three parameter (i.e.,

amplitude, damping ratio, and frequency) cu-ve-fits to the anal yti cally generated data sets were enact to ten significant cigits, which corresponded to the level of orecision dictatec by the software implementation of the

~

simpleu al g ori thm.-

A typical example is presented in Figure O.

The two parameter. (i. e., amplituce and damping ratio), or "envel ope," curve

.f i ts were al so in encellent agreement with the analytically generatec data sets, as shown in Figure O.

P

i

.o Electric Conduit Damping Tests 200 100 IGO Generated Data Set

- Two Parameter Curve-Fit 340

+++++++++++ Threc Parameter Curve-Fit

^ 120 0

100 q E

so. N v

N p

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-40

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-so

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-100 n

-s2e 1

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.00

.05

.30

.35

.20-Time (Seconds) l Figure 2: Typical Result f rom Verification i

i

8 Natural Frecuenev Results Natural frequency values corresponding to the various test'

-conditions. appear in Table 1.

The conduit coupling' raised the' natural frequency of the five-foot spans of three-querter inch

[

.condult.

With the one end one-half inch conduit, higher natural frequencies were observed when the' test specimen was secured with the two-bolt conduit ciampu.

l Results for Three-Ouarter Inch Concuit i

l Damping ratios f or horicontal impact encitati on of the three quarter inch conduit, with and without a conduit coupling, are presented as a function of encitation amplitude in Figure O.

Damping rati o.results with the conduit coupling were simil ar to results without the conduit coupling.

Damping ratios increased with increased initial displacements.

At,the mantmum amplituce tested, damping ratios ranged from 27.5% to 01.8%.

At the minimum amplitude tested, damping ratios ranged from 6.5% to 11.8%.

1 Resul ts for One and One-Half Inch Conduit i

\\

Damping ratios for the one and one-half inch condu'it are presented as a f uncti on of encitation amplitude in Figure 4.

Damping ratio results obtained with a ten-foot span were similar j'

to results obtained with a ni n?-f oot span.

Damping ratios i

increased with increased ini ti al displacements.

Significantly lower damping ratios were obtained when the test specimen was secured with two-bolt conduit clamps.

At the manimum amplituce i

tested with the two-bolt clamps, camping ratios ranged 4 rom 20.Q%

i to 01.0%, and at the minimum amplitude testec, damping ratios ranged from 11.9% to 14.0%.

At the manimum amplituce tested with the one-bolt clamps, camping ratios ranged from 00.0% to 06.6%,

and at the minimum amplitude tested, damping ratios ranged from 16.8% to 00.0%.

Results for Th ee-In:h Conduit Damping ratios for the three-inen conduit are presented as a l

function of excitation amplitude in Figure 5.

Results obtainec using impact encitation are consistent with results obtained i

using snapback encitation.

Results for both conduit specimens are also 21milar.. At the aanimum emplituce tested,' damping ration rangec from 17.4% to 00.5%.

At the minimum amplitude tested, damping ratios ranged from 4.9% to 6.0%.

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9 TABLE 1 Summary of Measured Single Span Natural Frequencies Aluminum Electrical Condut

  • Tests Diameter Test Condition

_ Span Average-Nat.

(inches)

Lenotn (ft) req.

(Hert:)

~

0.75 1-hol e cl amps, with 5

50.0 coup 1.ng, wire loading 0.~16 lbm/ft i

O.75 1-hole clamps, no 5

48.5-coupling, wire loading 0.16 lbm/ft 1.50 1-hole. clamps, no 9

04.0 coupling, wire loading 0.66 lbm/ft 1.50 0-hol e cl amps, no 9

07. !-

coupling, wire loading 0.66 lbm/ft 1.50 1-hole clamps, with 10 10.0 coupling, wire loading 0.66 lbm/f t 3.00 2-hol e cl amps, with 10 02.7 coupling,vgre y

4 y Ibm /ft, 5

loading 4 test specimen #1 0.00 2-hol e cl amps, with 10 4.1 coupling, no wires, test specimen #1 bb.9 0.00 O-hole clamps, with 10 coupling, wire l oadi ng si.,41 lbm/ft, test specimen #2 0.00 O-hole clamps, wi tt 10

~.!.

8, coupling, no wires, test specimen #2 5.00 O-hcle clamps, with IQ

'9.9

~

coupling, wire loading 4.05 lbm/ft

.+,,,,

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Electrical Conduit Damping Tests 50 i

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  • 2-0 50 100 150 200 250 300 350 Initial Displacement (Miis)

Figure 3: Damping Results f or.7 5 inch Conduit

J t

Electrical Conduit Damping Tests 50 r

.r.

r 1.5s Nino Ft. Span, 1-Bolt Clamps 43 l.5d Nino Ft. Span, 2-Dolt C1ampe

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4 _ __ _ ! -. _. _._..i _.__. _ __. i 0

0 50 100 150 200 250 300 350 Initial Displacement (Mils)

Figure 4: Damping Results f o'r 1.5 inch Conduit i

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a 13 The presence'of the wiring within'the conduit contributes signi f i cantl y to the damping,

as Indicated in Figure S.

The damping. ratio results for the three-inch condult displayed the general trend of increased damping with increased 'ini tial displacement.

Bel ow about 50 mils of initial displacement, damping decreased as displacement _ decreased..

Between about 50 ma i s and _000 mil s, damping remained relatively constant.

Beyond about 200 mils, the damping ratloc f or specimens wi th wiring.and with no wiring increaswd with increased,dtsplacement at-approximatel y.the same. slope.

These results suggest that a variety of damping mechanisms contribute to_the damping ratios [

depending:on the magnitude of the oscillation.

Results for Five-Inch Conduit Damping ratios for the five-ibch conduit are presented as a

. function of excitation amplitude in-Figure 6.

-Damping ratios were relatively constant as a f uncti on of. initial amplituce of 3

e::c s t ati on.

The measured damping ratios ranged from 8.1% to i

10.4%.

t

SUMMARY

, CONOLUSIONS, AND RECOMMENDATIONS This report presents camping values determined from snapback and impact tests conducted' wi th three-quarter inch, one and one-half inch, three-inch, and five-inch aluminum electrical conduit.

Test parameters included conduit diameter, type of 4

j conduit clamp, span, wiro loacing, amplitude of e::c a t ati on, and J

type of excitation.

Important results are summart:ed belows 1.

The test methodclogy provided consistent, reproducible J

results.

2.

Under similar conditions, snapback results and impact test results were in good agreement.

O.

Installation details of the electrical conduit can have a significant influence on its natural frequency and damping.

L.

Increased damping with increased amplitude of e::ci t &ti en was generally observed.

5 6.

The presence,of wiring significantly increased

  • damping.

7.

Decreasing d'amping ratios and decreasing amplitude dependence were observed with increasing Conduit diameter.

i

'4 '\\s

+.

s

Electrical Conduit Damping Tests 50 r-,

r r

45 5d Ten Ft. Span, 2-DoIt CIamps-on n

x 33 v

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It' 25 m

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.__.t__.

.._.__i._.._...._..____..=..__-_._.t______.-.

i. _._ e._._ _ _

0 50 800 150 200 250 300 350 Initial Displacement (Mils)

Figure 6: Damping Results f or 5 inch Conduit-i

~*

.' AS p

8.. A variety of 4.mplitude-dependent damping mechanisms are present.

4 9.

Damping ratt o resul ts are summart:ed in Figure 7.

Additional testing-would provide a broacer statistical basis for estimating the significance of observed differences and trends in the damping values.

The tests reported here, for e:: a mp l e, should be suoplemented wi th test results for three-quarter inch. conduit nd a ten-foot span.

Also, results should be obtained f or all si:es and both clamp types at a common ten-foot span.

Surveyt of field. installations, utili:ing a si mi l ar test methocology (March, 1996), could be conducted and compared with laboratory results.

Investigations could also be conducted to determine the relative contribution and the amplituce depencence o4 various damping mechanisms, such as Coulomb damping, material dampi ng, and damping due to wire l

loading.

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Electrical Conduit Damping Tests So 4

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9 50 100 150 200 250 300 350 Initial DispIacement (Miis)

Figure 7: Summary of Aluminum Conduit Results s

2

17 REFERENCEL American National Standards Institute. "American Nettonal Standard Methods for Analysis anc F'esentaticn of shock and Vibration Date," ANSI S2.10, 1971.

ANCO Engineers, "High-Amp 11tude Dynamic Tests of Prototypical Nuclear P i p i n g G y s t e.r. s, " Electric Fower Research Institute Report No. NF-0916, Februa.v 19ES.

Caceci, M.

S.,

and W.

P.

Cacher1s, "Fitttng Curves to Data,"

Bvte. May 1984, pp. 040-062.

Den Hartog, J.

P.,

Mechanical Vibrations. New Yori:t McGraw-Hill Book Company, 1956.

Hunter, K.

W.,

C.

M.

Linton, and P.

A.

M a r rc h, "An Improved Technicue f or Snapbacl-E::ci tat i on Usi ng Multipl e Force Inputs " Proceedings of the 4th International Modal Anal vs t s Conterence, Los Angeles, California, February 198c.

Lalanne, M.,

P.

Berthier, and J.

Der Hagopian, Mechanical Vibratiens for Enoineers. New York:

John Wil ey and sons, 1960.

'Lacan, B.

J.,

and L.

E.

G.o o d m an, "Material and Interface Damping," in C.

M.

Harris and C.

E.

Crece, ecs.,

Shock and Vibration Handbook. Volume 0:

Data Analvsts, Testing. anc Methocs of Control. New Yc r l;;

McGraw-Hill Bool: Company, 19o1.

March, P.,

"A Preliminary Study of Vibration Damping in Electrical Conduit," TVA Engineering Leboratory Report No. WR25-4-900-140, Octocer 1954 (revised March 19G6).

March, P.,

"Instrumentation and Methodology for in Situ Determination of Damping Values in Electrical Conduit,"

TVA Engineering Laboratory Report No. WR26-3-900-166, January 1986.

Mar.h, P., "Ouality Assurance Frocedure for Concocting Physical Model Studies anc Physical Testing Programs,"

WRE5-5F-15.01, Fevision 1,

August 1980.

Mi t chel l, J..'s., An Introduction to Machinerv Analvsis anc M3n'atorinc. Tulsa, Oklahoma:

Pennwell Fublisning Company, 1981, o

\\

18 Myl;l rGt ad,

N.

O.,

Fundementals of Vibeat1on Analvstt. New Y o r i:t

'McGraw-Hill bool. Company, 195c.

Nelder, J.

A.,

and R.

Meac, "A

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