陕科大包装技术基础双语课件13机械冲击理论

Lesson13

MechanicalShockTheory

第13课机械冲击理论IntroductionThroughoutthedistributionsystem,packagesaremanhandledandmishandledinvariousways:dropped,thrown,kickedandotherwiseroughlyabused;fallfromconveyorsorforkliftsandcrashtothefloor;subjectedtoavarietyof

vehicleimpacts;trucksstarting,stopping,hittingchuckholesandrailroadcrossings,railcarhumping,joltingandothermoderatelyviolentactions;suffersanimpactwithanotherobject：floor,truckbed,pallet,bulkheadoranotherpackage.Amechanicalshockoccurswhenanobject'sposition,velocityor

accelerationsuddenlychanges.Suchashockmaybecharacterizedbyarapidincreaseinaccelerationfollowedbyarapiddecreaseoveraveryshortperiodoftime.Figure13.1:theaccelerationversustimeplotformostshocksFigure13.1RepresentationofmechanicalshockApackageshockmaytypicallybe20milliseconds(0.020seconds)longandhaveamagnitudeor"height"of150g's.

needtoknowboththemagnitudeoftheaccelerationandthedurationoftheshock.TheFreeFallingPackage

thelengthoftimeittakesapackagetofallfromadropheight,h

thedownwardvelocityatwhichitwillbetravelingamomentbeforeimpact;,theimpactvelocity:

AsisshowninFigure13.2.Apackagewillreboundalittleoralotdependingonthenatureofthepackageandthesurfaceithits.

Figure13.2Afallingpackage

coefficientofrestitution,e,describesthereboundvelocityasafunctionoftheimpactvelocity

13.1

totalvelocitychange:

13.2

13.3

Because01(typicalvaluesfallinginthe0.3to0.5range):

13.4

velocitychangeisalsonumericallyequaltotheareabeneaththeshockpulseasshowninFigure13.3.Figure13.3TherelationshipamongshockparametersPackagedamageisrelatedtothethreefactorsinvolvedinmechanicalshock:PeakAccelerationDurationVelocityChangeMechanicalShockTheory

ShowninFigure13.4,theproduct-packagesystemconsistsoffourbasiccomponents:theoutercontainer,thecushion,theproduct,andacriticalelement.showninFigure13.5:theproduct-packagemodel:

Figure13.4Asimpleproduct-packagesystemFigure13.5Aspring-massmodelfortheproduct-packagesystem

M2-themassoftheproduct

M1-representsthemassofthecriticalelementorCE

M3-representsthemassoftheoutercontainer

kl-thelinearspringconstantofthesprint-masssystemrepresentingthecriticalelement

k2-thelinearspringconstantofthecushionsystemAssumptionsforsimplicity:a.ignorethemassoftheoutercontainerandassumethatitprovidesnospringaction;b.thecushionhasnomassordampingandsuffersnopermanentdeflectionfromashock;c.theproduct-packagesystemimpactsaperfectlyrigidfloor;d.,themassofthecriticalelementisnegligiblecomparedtothemassoftheproduct.InFigure13.6,theimpactofaproduct-package:Figure13.6Theimpactofaproduct-packagesystemAtPointA,theproductisreadytofall.Thepotentialenergyatthismomentis:

13.5

where

AtPointC,thekineticenergyofthesystemisgivenby

13.6

13.7

whichshowthatthekineticenergyatthismomentisequaltotheinitialpotentialenergyofthesystem.

Inthemomentsfollowingtheinitialcontactofthecontainerwiththeimpactsurface,theamountofenergyabsorbedbythelinearcushionis:

13.8whereX2isthedownwarddisplacementoftheproductonthecushion.

AtPointD,thecushionhasabsorbedallofthesystem'skineticenergy

13.9

wheremaximumdynamiccompression,dm=maximumvalueofx2.

Themaximumamountofenergyabsorbedbythecushionmustequalthesystem'skineticenergyatimpact:

13.10

forthemaximumdynamiccompression:

13.11Thestaticdeflectionoftheproductonthelinearcushionis:

soEquation13.11mayalsobewrittenas:

13.12

Themaximumforceexertedupwardbythecushionagainsttheproductoccurswhen:

13.13

Themaximumacceleration(ordeceleration)experiencedbytheproduct,Gm,maybefoundfromtherelationship:

13.14

13.15

whereGmisunitless,butisunderstoodtobeinunitsof1g.

13.16

Gmisproportionaltothesquarerootofthedropheight:

Thismeansthatifwedoublethedropheight,themagnitudeoftheshockisnotdoubled,butratherincreasedbyafactorof(about1.4).

Equation13.15mayberearrangedtoproduceanexpressionfor:

13.17

Equation13.11mayalsoberearrangedtoproduceanequivalentexpression:

13.18

13.19

givingusanexpressionforthemaximumdynamiccompressionasafunctionofthemaximumaccelerationandthedropheight.

Conclusions:

1.

isrelatedtothedropheight,thespringinessofthecushionandtheweightoftheproduct.

2.Thestifferthespringorcushion,thelargerthevaluefor.

3.Thehigherthedropheight,thelargerthevaluefor().

4.Theheaviertheproduct,thesmallerthevalueofaslongasthespringorcushionisworking.

ShockDuration

Wemayapproximatethedisplacementoftheproductonthecushion,,atanytimeduringtheimpactwiththefunction:13.20where

13.21

f2-thenaturalfrequencyoftheproduct(M2)onthecushion(k2).Figure13.7ShockdurationandmaximumdisplacementFigure13.8ShockdurationandthenaturalperiodofvibrationT2-Theperiodofthefreevibrationoftheproductonthecushion:

13.22

where-thetimelengthordurationoftheshock.

Foranyshockofknownperiod,wemaycalculatetheequivalentshockfrequency:

13.23

theshockduration:

13.24

13.25

ShockAmplificationandtheCriticalElementDefine:

Ge-themaximumaccelerationexperiencedbythecriticalelement,resultingfromashock(Gmand),asshowninFigure13.9.Am-anamplificationfactor,analogoustovibrationmagnificationrelatingtheinputandoutputshocklevels:13.26

Ge=AmGm13.27Figure13.9ShocktransmissionDuringtheimpact,theamplificationfactorisgivenbytheexpressi