ASTM D4728_2001
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thatoccuraccordingtotheGaussiandistribution,itiscalled
“Gaussianrandomvibration.”Gaussianrandomvibrationhas
thepropertythatthermslevelisequaltothestandard
deviation,or1sigma,andthattheamplitudewillfallwithin3
sigma,or3timesthermslevel,99.7%ofthetime.
3.2.12root-mean-square(rms)—thesquarerootofthe
mean-squarevalue.Intheexclusivecaseofasinewave,the
rmsvalueis0.707timespeakvalue.
3.2.13sigmadrivesignalclipping—aconditionwherethe
maximumamplitudeofthedriveoroutputsignaltoavibration
systemislimitedtoasigmavalue,ormultipleofthermsvalue.
Fordriveclippingatthe3sigmalevel,themaximumampli-
tudewillnotexceed3timesthermsvalue.
3.2.14sinusoidalvibration—aperiodicoscillationhavinga
sinusoidalwaveformofonlyonefrequency.
3.2.15spectrum—adefinitionofthemagnitudeofthe
frequencycomponentswithinaspecifiedfrequencyrange.
3.2.16statisticaldegreesoffreedom(DOF)—asrelatedto
PSDcalculation,thedegreesoffreedomisameasureofthe
statisticalaccuracyofthePSDestimation.ThenumberofDOF
isdeterminedbytheanalysisbandwidth(frequencyresolution)
andtotaltimeofthesample(determinedbyfrequencyresolu-
tionandnumberofaverages).Itisdefinedbytheformula
DOF=2BT,whereBistheanalysisbandwidthinHz,andTis
thetotalrecordlengthinseconds.
3.2.17transferfunction—thedynamicrelationshipbetween
outputandinput.Intermsofavibrationsystem,itistheratio
ofoutputresponsetoaconstantinputoveradefinedfrequency
range.
4.SignificanceandUse
4.1Shippingcontainersareexposedtocomplexdynamic
stressesinthedistributionenvironment.Approximatingthe
actualdamage,orlackofdamage,experiencedinreallifemay
requiresubjectingthecontaineranditscontentstorandom
vibrationtests.Inthisway,manyproductandcontainer
resonancesaresimultaneouslyexcited.
4.2Resonancebuildupsduringrandomvibrationtestsare
lessintensethanduringsinusoidalresonancedwellorsweep
tests.Therefore,unrealisticfatiguedamageduetoresonance
buildupisminimized.
4.3Randomvibrationtestsshouldbebasedonrepresenta-
tivefielddata.Whenpossible,confidencelevelsmaybe
improvedbycomparinglaboratorytestresultswithactualfield
shipmenteffects.RefertoPracticeD4169forrecommended
randomvibrationtests.(SeeAppendixX1andAppendixX2
forrelatedinformation.)
4.4Thereisnodirectequivalencebetweenrandomvibra-
tiontestsandsinusoidalvibrationtests.Equivalenttests
betweensineandrandom,inageneralsense,aredifficultto
establishduetononlinearities,dampingandproductresponse
characteristics.
4.5Vibrationexposureaffectstheshippingcontainer,its
interiorpacking,meansofclosure,andcontents.Thistest
allowsanalysisoftheinteractionbetweenthesecomponents.
Designmodificationtooneorallofthesecomponentsmaybe
usedtoachieveoptimumperformanceintheshippingenviron-
ment.
4.6Randomvibrationtestsmaybesimultaneouslyper-formedwithtransientorperiodicdatatosimulateknown
stressesofthistype,thatis,railjoints,potholes,etc.
4.7Randomvibrationmaybeconductedinanyaxis(verti-
calorhorizontal)orinanypackageorientation.However,
differenttestlevelsmaybeutilizedforeachaxisdependingon
thefieldenvironmentthatistobesimulated.
5.Apparatus
5.1VibrationTestSystem—Thevibrationtestsystem
(shaker)shallhaveavibrationtableofsufficientstrengthand
rigiditysothattheappliedvibrationsareessentiallyuniform
overtheentiretestsurfacewhenloadedwiththetestspecimen.
Thevibrationtableshallbesupportedbyamechanismcapable
ofproducingsingleaxisvibrationinputsatcontrolledlevelsof
continuouslyvariableamplitudethroughoutthedesiredrange
offrequencies.Suitablefixturesandguidestorestrictundes-
iredmovementofthetestspecimensshallbeprovided.
5.2ElectronicControls—Controlsshallprovidethecapa-
bilityofgeneratingvibrationsystemdriveinputsnecessaryto
producethedesiredpowerspectraldensityatthetablesurface
adjacenttothetestspecimen.Thefollowingmethodsprovide
thiscapabilitywithvaryingdegreesofaccuracyandversatility.
5.2.1MethodA,ClosedLoop–AutomaticEqualization—A
closedloopcontrollerisrequired,whichallowstheoperatorto
enterdesiredPSDdata.Thecontrollerautomaticallygenerates
equalizedvibrationtestsystemdrivesignalstoachievethe
desiredPSDthusmaintainingclosedloopcontrol.Theequal-
izeddrivesignalsautomaticallycompensateforspecimenand
vibrationtestsystemcharacteristics.Typical
systemsinclude
ananalogtodigitalconverterforconditioningfeedback
signals,adigitaltoanalogconvertertoproducedrivesignals,
adigitalprocessorwithrealtimeanalysiscapability,random
vibrationcontrolsoftwareprograms,agraphicsdisplaytermi-
nal,hardcopyprinter,andahardorflexible,orboth,diskdrive
unit.
NOTE2—RandomvibrationsystemstypicallycreateadrivesignalthatfollowstheGaussiandistribution.Manysystemshavea“driveclipping”capability,whichissometimesemployedtoprotectthevibrationsystemortestspecimenfromhighinstantaneousamplitudesthatmightcausedamage.
5.2.2MethodB,OpenLoop-DataStorageMedia—Data
storagemediaopenloopcontrolsystemsenableprerecorded