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