Comparison of copper and tungsten carbide calibration spheres
Kenneth G. Foote
Instituteof Marine Research,5011 Bergen,Norway
David N. MacLennan
Marine Laboratory,•4berdeen,
Scotland
(Received1 April 1983;acceptedfor publication2 November1983)
The propertiesof calibrationspheresmadefrom electrical-grade
copper,denotedCu, and
tungstencarbidewith 6% cobaltbinder,denotedWC, are examinedtheoretically.Effectsof
variationsin material,medium,and equipmentparametersare determinedfor spheresintended
to calibrate38-kHz echosounders
whena targetstrengthof order -- 41.5 dB is required.The
derived30.4-mm-diamCu sphereand selected38.1-mm-diamWC ball bearingshowdifferent
dependences
onthevariedparameters.
Changes
in thematerialandequipmentparameters
within
widerangeswill not upseta precisioncalibrationwith expected_ 0. l-dB accuracy.Adjustment
of thecalibrationvalueof backscattering
crosssectionwith changing
temperature
is generally
necessary
for elasticspheres.
Thisisthecasefor thepresentWC sphere,butnotfor theCu sphere
by virtueof its optimizationwith respectto temperature.Greaterhardnessis foundto be
insufficient
for choosingbetweenthe two; the particularapplicationmustbe considered.
Pragmaticcriteria for sphereselectionare discussed.
PACS numbers: 43.85.Vb, 43.20.Fn, 43.30.Dr
precision
calibration,ashasfusedsilica,in whichis alsoa
INTRODUCTION
Interestin the useof solidmetalspheres
ascalibration
or referencetargetshas increasedsignificantlysincetheir
dismissal
for presumably
large-system
calibrations
by Wallaceet al? Dragonetteet aL2 haveusedtungstenearbide
spheres
forgaugingbackscattering
measurements
in thelaboratory.Similarspheres
havebeenexaminedin Scotlandfor
possible
application
to echosounder
calibrations?
Copper
hasalsorecei•;ed
muchattention.
3-•Spheres
machined
from
electrical-grade
copperare beingusedto calibratefisheries
groupIII materiallike copper,secondaryaimsof the study
are to emphasizethe futility of selectingmaterialssolelyon
the basisof their hardnessand to discourage
misuseof the
rigid-sphereapproximationin the calculationof scattering
I. SPHERE
SELECTION
Selectionof a spherefor calibratinganygivenacoustic
instrumentgenerallyinvolvesselectionof the materialand
echosounders
in Norwayandelsewhere.
7 Therehavealso
determination or selection of the diameter. This is now dis-
beenapplications
of solidmetalspheresin nonlinearacous-
cussed
bothforcopperandfor tungsten
carbide.As a practical example,the derivedspheresare to be suitablefor calibrating the 38-kHz echo sounderscommonlyusedin fish
stock estimation.The calibrationsare to be performed at
tics.8.9
Purely theoreticalconsiderationshave favored the socalled"groupII" materialsof AnsonandChivers'classifica-
tion.1øThisissomewhat
misleading,
for whiletheyaregen-
shortranges,
butin thefarfieldof thetransducer.
Furth•r-
erally hard and dense, they are also among the most
more, the target strengthis to be roughlyequalto that of a
ball;namely,about-- 41.5dB.•z
expensive
andhazardous,
nottomention
leastmachinabl•
of ping-pong
materials.
I 1.•2Someexamples
areberyllium,boron,sintered
diamond,iridium, niobium,osmium,platinum,rhenium,
ruthenium,
andtungsten
carbide?
3 "GroupIII" materials,
A. Copper
Thisnoblemetalhasmanyvirtues.
4'7It ischeap,
corro-
in contrast,whilelesshardandpossessing
morecomplicated
radiation functionsand backscatteringcrosssectionsthan
sionresistant,easyto machine,readilyavailablein a high
state of purity, and hard when cold-workedand unan-
the group lI materials,are generallymuch easierto fabricate. Copperbelongsto this class,as do aluminum,nickel,
nealed. •6
monelmetal,stainlesssteel,and zinc.•3
The pre•nt studydealswith pragmaticconsiderations
in thechoiceof materialfor fabricationinto spheresdesigned
for usein hydroacousticcalibrations.The objectmaterials,
copperand tungstencarbide,are convenientboth for their
immediateandpotentialapplications
andfor thdr representation of acousticallydissimilarmaterialsaccordingto Anson and Chivers' admittedly somewhatarbitrary classification.•øSincebothmaterialshavebeenusedsuccessfully
for
612
J. Acoust.Soc. Am. 75 (2), February1984
With respectto the elasticity,which with the density
determinesthe scatteringresponse
for a givenimmersion
medium, the elementalcompositionof commercialelectrical-gradecopperis important. The effectof trace clement
contentshouldbenegligible.
17-•ø
Thetwocommercial
electrical-gradeformsof copper,the oxygen-free
(OF} and the
electrolytictough-pitch(ETPI,maybeexpected
to havevery
similarelasticproperties.
21
Anotherpropertyof copperwhichis advantageous
to
itselasticity,
hencechoice,
isitscubicstructure.
Texturingis
0001-4966/84/020612-05500.80
¸ 1984 AcousticalSocietyof America
612
unlikelyto influencethis, which may explainthe evident
constancy
of therigiditymodulusof commercial
electrical-
gradecoppers.•s'22=a?
Thisappears
to beverynear47GPa,
wherecois thefrequency.
$, F, andH arenormallyexplicit
functions of co•
Inthecomputation
below,
Sisthespectrum
ofapulsed
whichcorresponds
to a Poisson's
ratioof 0.350,assuming
a
sinusold,
andfir isthereceiverresponse
functionof theSim-
Lamlparameter
• of 110GPa,or a density
of 8950kg/m3
tadEK-400/38echosounder.4
F depends
onthecharacter-
andlongitudinal
soundspeedof 4770m/s.
The constancy
in elasticityof OF andETP coppersallowstheacoustic
characteristics
of suchspheres
to becalculatedreliably.The factof copperbeinga groupIII material
and havinga frequency-sensitive
backscattering
crosssec-
isticsof boththe sphereandthemedium,in additionto the
frequency.
asForthechosen
homogeneous
elastic
materials,
the relevantpropertiesof the sphereare the radiusa, the
densityPl, the longitudinal
soundspeedG, and the transversesoundspeedca.The mediumpropertiesare expressed
tion and radiation force function is thus no drawback to its
throughthe densityp and the soundspeedc. The nominal
choice.
13Indeed,this featuremay be exploitedto obtain valuesof thesequantitiesare givenin Table I.
Variation of theseparametersis the basisof the comhigh,or low, valuesof backscattering
crosssectionor radiparison,for discoveryof an instabilityor otherseveredepenation forcefunctionfor a spheresize which could not be
denceof• wouldsuggest
thatthesphereisunsuitable
foruse
achievedwith the harder,moreacousticallyconstantgroup
II materials.
in precision
calibration.In orderto renderthecomparison
as
realisticas possible,the rangesof variationare chosenin
The diameterof thecoppersphereisdetermined
in acaccordance
with the followingprinciples.
cordance
withtheoptimization
scheme
developed
in Ref.4.
Ideally, the materialparameterswouldbe variedover
Thebackscattering
crosssectionisto varyaslittleaspossible
percentagerangescorresponding
to the larger of the oboverthe temperature
rangefrom0øto 30 'C in seawaterof
servedparameterrangesof the two materials.However,
salinity35 ppt. Giventhat the targetstrengthmustbeabout
knowledgeof the particulartungstencarbidein WC 38.1 is
-- 41.5 dB, the optimaldiameteris foundto be 30.40 ram.
extremelylimited,and generictungstencarbidesspantoo
Machininga sphereof this sizecanbe accomplished
quite
andelasticities
to bemeaningful
for
easilywitha tolerance
of 0. 1%, whichearlierinvestigations widea rangeof densities
theintended
comparisons.
a9'3ø
Moreisknownaboutvaria-
haveshown
tobeadequate.
4'7
tions
incopper,
andthepar•neter
ranges
aretherefore
de-
B. Tungsten carbide
rivedfromtheliteratureon high-puritypolycrystalline
cop-
Tungsten
carbidewith6% cobaltaddedasa binderwas
chosenasa promising
material.It isextremelyhard--tung-
pets.6Theseareshownin TableII.
sten carbide is 9.5 on the Mohs hardness scale--and it is
temperaturez and the salinity.The intendedapplicationis
marine,so the salinityis chosento be 35 ppt. Temperature
commerciallyavailablein the form of precisionball bearings.Only discretesizescan be procuredeasily,but others
canbeobtainedthroughtheusualsinteringprocess.
Off-theshelfball bearingsare availablein convenient
sizesfor the
purpose
ofcalibrating
theacoustic
equipment
usedin fisheries research,wherefrequencies
are typicallyin the range
from 30 to i 50 kHz.
Tungsten
carbideisa groupII material.The frequency
dependence
of its form functionfollowsthat of the ideally
hardsphereup to a w•venumber-radius
productof about
The mediumparameters
p and c both dependon the
variations from 00to 30 øCare considered,as in earlier stud-
ies.4'?The mediumdensityand the soundspeedare determined by the hydrographicparametersin the usualmanner.31.32
Sincethe echosoundermay haveto be calibratedin an
untunedconditionand mightbe usedwith differentpulse
durations,theseparametersare varied over the ranges
shownin Table II. The variationof the spherediameteris
redundant
insofar
asthescattering
isa function
ofthewave-
six.•
number-radius
product.Thusthesameproportional
change
Thediameter
ofthesphere
ischosen
fromthestandard in frequencyor diametershouldproducethesamechangein
rangeofballbearing
sizestoobtainthetargetstrength
near- form function. The examined0.20-mm range in diameter
estto -- 41.5 dB. The selecteddiameteris thus38.1 mm, i.e.,
1.5 in., and the diameter tolerance is better than 0.01%.
TABLE I. Parameters
andtheirnominalvaluesfor thetwospheres,
immersionmedium,andequipment.
II. METHOD
The objectsof the comparisonare a 30.40-mm-diam
spheremadefromelectrical-grade
copper,denotedCu 30.4,
anda 38.l-mm-diamsphereformedof tungstencarbidewith
Sphere
Type
Name
Symbol Units Cu 30.4 WC 38.1
Sphere
Diameter
2a
6% cobalt binder, denoted WC 38.1. Since these are intended for use in the calibration of 38-kHz echo sounders, the
Sphere
Density
p•
g/½m
3 8.94• 14.900
Sphere
c•
-km/s
operationallydefinedbackscattering
crosssectioncris the
Sphere
Longitudinal
soundspeed
Transverse
c•
km/s
naturalquantityforcomparison?
ThisisrelatedtotheincidentsignalspectrumS, the backscattering
form functionF,
and the frequencyresponse
functionH by the well-known
formula:
613
ISFHIa
ISHIarico,
J. Acoust.Soc.Am.,Vol.75, No.2, February1984
(1)
mm
sound
speed
30.4
38.1
4.760
6.864
2.2885 4.1612
•
Medium
D•nsity
p
g•/cm
3
Medium
Equipment
Soundspeed
Center
frequency
Pulseduration
c
f
km/s
kHz
i.490
38.0
T
ms
1.00
Equipment
1.027
K.G. FooteandD. N. MacLennan:
Comparison
ofcalibration
spheres
613
TABLE IL Rangesof parametervariations.
IlL RESULTS AND DISCUSSION
The effectsof varyingthematerialparameters
fromthe
nominalvaluesare shownin Fig. 1. In eachcase,the effects
p,
ñ 1%
for the tungstencarbidesphereareobserved
to bemuchless
c,
_ 5%
than
the
corresponding
ones
for
the
copper
sphere.
This is a
c:
ñ 3%
consequence
of
tungsten
carbide
being
much
harder,
in an
•
[0, 301'c
f
-t-0.5 kHz
acousticsense,
thancopperat frequencies
near38 kHz. In no
T
+0.5 ms
casearethevariationslarge,althoughtheexaminedparam2a
-t- 0.1 mm
eter rangesare considerable.
In the worstcase,that of the
coppersphereCu 30.4 whenthe transverse
soundspeedis
varied, the maximum changefrom the nominal target
variationis muchlargerthanthemanufacturing
tolerance, strengthis -F 0.1 dB. Thus, evenif the transversesound
but it is relativelysmallcompared
to the variationin the speedwerepOOrlyknown,useof thenominaltargetstrength
shouldallowa calibration
to beperformed
withanaccuracy
centerfrequency.
of +_0.1 dB.
The temperaturevariationrestfitsin largerchangesin
thebackscattering
crosssection.Theseareseenfrom Fig. 2
to be greaterfor the tungstencarbidespherethan for the
coppersphere.Of course,thediameterof thecoppersphere
was calculatedto minimizethe temperaturedependence.
The diameterof the tungstencarbidespherewasmerelyse*
!ectedfromthelimitedrangeavailablein off-the*shelf
items.
WC3•.1
Were the tungstencarbidesphereto be optimizedin the
7.3
mannerof the coppersphere,then costlyor nonstandard
fabricationby machiningor Sinteringwouldbe necessary.
7.2-1.0 -.5•
•
• -I-G2./,
The precisionof a marinecalibrationwith the copper
1.0
spherewill not besignificantly
affectedby the weaktemperaturedcpendence
of thetargetstrength.The sameisnottrue
of thetungsten
carbidesphere,for itstargetstrengthvaries
by0.3 dB overtheinvestigated
temperature
range.Sincethe
temperature
rangefrom0• to 5 øCcontributes
0.2 dB to this
variation,however,a singlevalueof targetstrengthcan be
found which will ensurea precisioncalibrationover the
rangefrom5øto 30øC.Thetemperature
duringa calibration
Parameter
Rangeof variation
10.9
•
, , .-&0.62
,o.?,, , ,
7./,' ' ' t-62'3
0
2
/.
AC
1(ø14
CU30A
11.0
-&0.5
11.2
%0.6
10.8
11.0
-60.6
-/,0.7
10.6
10.8
-/+0.7
I
e• 10./•
10.6
I
8.0
-•.2.0
WC38.1
7.8
7.6
,•
38.1
7.3
7.2_3 -2 -1
I
I
I
-62.3
-/+2.1
7.6
-&2.2
7./+
-•,2.3
3
•c2
7.2
FIG. !. Effectsof materialparametervariationson thebackscattering
cross
sections
•yof twocah'bration
spheres.
Pl is thedensity,
cl thelongitudinal
soundspeed,
andc2thetransverse
soundspeed.
Nominalvalues
oftheseand
otherparameters
aregivenin TableI. TS denotes
thetargetstrength,
definedas 10logo•/(4•r),whereo is givenin inksunits.
614
-&O.B•
d.Acoust.Soc.Am.,Vol.75, No.2, February1984
0
10
20
- -•,2./+
30
TIøC)
FIG. 2. Effectsof temperature0') variationon the backscattering
crosssectionsof two calibrationsphereswhen they are immersedin seawater of
nominalsalinity35 ppt.
K.G. FooteandD. N. MacLennan:
Comparison
ofcalibration
spheres
614
couldbemeasured,
of course,
andthetargetstrength
value
adjusted,
ffnecessary.
Variationsin the equipmentparameters
are seenfrom
Fig. 3 to producesimilareffectson thebackscattering
cross
sectionsof both sphere..As in the caseof the materialparameters,
thecomputed
changes
in targetstrengtharesmall
enoughnot to upseta precisioncalibration.The sameconclusionappliesto the diametervariations,whoseeffects,as
notedabove,aresimilarto thoseof frequency.
It isnotedthatthecoppersphereisa strongeracoustic
taxgetthan the physicallylargertungstencarbidesphere.
The nominaltargetstrengthsare - 40.7 and -- 42.4 dB,
respectively.
This illustratesthe greaterflexibilityafforded
by group III materialslike copper,comparedto thoseof
groupII, suchastungstencarbide.In the caseof the harder,
groupII materials,whichmightapriori beconsidered
more
desirable
for calibrationapplications,
therangeof variation
in backscattering
crosssectionissmallerthanthatof materials in groupIII. The elasticityof theselesshard materials
maybeexploitedin a mannernot possible
with comparably
sizedspecimens
of hardermaterials.
IV. CONCLUSIONS
The effectsof variationsin materialandequipmentparametersare generallysmallfor boththe copperand tungstencarbidespheres.
The greaterhardness
of the tungsten
carbidesphereresultsin the targetstrengthhavingan extremelyweakdependence
onthematerialparameters.
However,thisconfersno particularadvantage
with respectto
variationsin the equipmentparameters,for whichthe two
spheresshowcomparableeffects.
Temperaturehasa greatereffectthantheotherconsideredparameters,especiallyin the caseof the tungstencarbidespherebelow5 øC.Insofaras the temperaturecan be
measuredor otherwisedeterminedin a calibrationexercise,
corrections
to thenominaltargetstrength
maybecomputed
in orderto preserve
the0.1-dBprecision.
Bothcopperandtungsten
carbideareexcellentmaterialsfor precision
calibrationspheres.
Suchconsiderations
as
cost,the needfor a particulartargetstrength,andacoustic
10.9
I' ' '"1••
-40'62
WC
CU 30./,
-40.68
10.7I
robustness,
amongothers,must dictatethe choicebetween
thesein any particularapplication.It is evidentthat hardnessisnot theonly,or eventhemostimportant,propertyto
be considered
in selectinga referencetargetfor the calibration of acousticsystems.
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spheres616