机械专业外文文献翻译对振动侦查和测量的一种实用方法Word文档格式.docx

机械专业外文文献翻译对振动侦查和测量的一种实用方法Word文档格式.docx

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displacement,velocity,andacceleration;

andtheoperatingprinciplesofthesensorsthatdetectandmeasuretheseproperties.

Vibrationisoscillatorymotionresultingfromtheapplicationofoscillatoryorvaryingforcestoastructure.Oscillatorymotionreversesdirection.Asweshallsee,theoscillationmaybecontinuousduringsometimeperiodofinterestoritmaybeintermittent.Itmaybeperiodicornonperiodic,i.e.,itmayormaynotexhibitaregularperiodofrepetition.Thenatureoftheoscillationdependsonthenatureoftheforcedrivingitandonthestructurebeingdriven.

Motionisavectorquantity,exhibitingadirectionaswellasamagnitude.Thedirectionofvibrationisusuallydescribedintermsofsomearbitrarycoordinatesystem（typicallyCartesianororthogonal）whosedirectionsarecalledaxes.Theoriginfortheorthogonalcoordinatesystemofaxesisarbitrarilydefinedatsomeconvenientlocation.

Mostvibratoryresponsesofstructurescanbemodeledassingle-degree-of-freedomspringmasssystems,andmanyvibrationsensorsuseaspringmasssystemasthemechanicalpartoftheirtransductionmechanism.Inadditiontophysicaldimensions,aspringmasssystemcanbecharacterizedbythestiffnessofthespring,K,andthemass,M,orweight,W,ofthemass.Thesecharacteristicsdeterminenotonlythestaticbehavior（staticdeflection,d）ofthestructure,butalsoitsdynamiccharacteristics.Ifgistheaccelerationofgravity:

F=MA

W=Mg

K=F/d=W/d

d=F/K=W/K=Mg/K

DynamicsofaSpringMassSystem

Thedynamicsofaspringmasssystemcanbeexpressedbythesystem'

sbehaviorinfreevibrationand/orinforcedvibration.

FreeVibration.Freevibrationisthecasewherethespringisdeflectedandthenreleasedandallowedtovibratefreely.Examplesincludeadivingboard,abungeejumper,andapendulumorswingdeflectedandlefttofreelyoscillate.

Twocharacteristicbehaviorsshouldbenoted.First,dampinginthesystemcausestheamplitudeoftheoscillationstodecreaseovertime.Thegreaterthedamping,thefastertheamplitudedecreases.Second,thefrequencyorperiodoftheoscillationisindependentofthemagnitudeoftheoriginaldeflection（aslongaselasticlimitsarenotexceeded）.Thenaturallyoccurringfrequencyofthefreeoscillationsiscalledthenaturalfrequency,fn:

（1）

ForcedVibration.Forcedvibrationisthecasewhenenergyiscontinuouslyaddedtothespringmasssystembyapplyingoscillatoryforceatsomeforcingfrequency,ff.Twoexamplesarecontinuouslypushingachildonaswingandanunbalancedrotatingmachineelement.Ifenoughenergytoovercomethedampingisapplid,themotionwillcontinueaslongastheexcitationcontinues.Forcedvibrationmaytaketheformofself-excitedorexternallyexcitedvibration.Self-excitedvibrationoccurswhentheexcitationforceisgeneratedinoronthesuspendedmass;

externallyexcitedvibrationoccurswhentheexcitationforceisappliedtothespring.Thisisthecase,forexample,whenthefoundationtowhichthespringisattachedismoving.

Transmissibility.Whenthefoundationisoscillating,andforceistransmittedthroughthespringtothesuspendedmass,themotionofthemasswillbedifferentfromthemotionofthefoundation.Wewillcallthemotionofthefoundationtheinput,I,andthemotionofthemasstheresponse,R.TheratioR/Iisdefinedasthetransmissibility,Tr:

Tr=R/I

Resonance.Atforcingfrequencieswellbelowthesystem'

snaturalfrequency,R

I,andTr

1.Astheforcingfrequencyapproachesthenaturalfrequency,transmissibilityincreasesduetoresonance.Resonanceisthestorageofenergyinthemechanicalsystem.Atforcingfrequenciesnearthenaturalfrequency,energyisstoredandbuildsup,resultinginincreasingresponseamplitude.Dampingalsoincreaseswithincreasingresponseamplitude,however,andeventuallytheenergyabsorbedbydamping,percycle,equalstheenergyaddedbytheexcitingforce,andequilibriumisreached.Wefindthepeaktransmissibilityoccurringwhenff

fn.Thisconditioniscalledresonance.

Isolation.Iftheforcingfrequencyisincreasedabovefn,Rdecreases.Whenff=1.414fn,R=IandTr=1;

athigherfrequenciesR<

IandTr<

1.AtfrequencieswhenR<

I,thesystemissaidtobeinisolation.Thatis,someofthevibratorymotioninputisisolatedfromthesuspendedmass.

EffectsofMassandStiffnessVariations.FromEquation

（1）itcanbeseenthatnaturalfrequencyisproportionaltothesquarerootofstiffness,K,andinverselyproportionaltothesquarerootofweight,W,ormass,M.Therefore,increasingthestiffnessofthespringordecreasingtheweightofthemassincreasesnaturalfrequency.

Damping

Dampingisanyeffectthatremoveskineticand/orpotentialenergyfromthespringmasssystem.Itisusuallytheresultofviscous（fluid）orfrictionaleffects.Allmaterialsandstructureshavesomedegreeofinternaldamping.Inaddition,movementthroughair,water,orotherfluidsabsorbsenergyandconvertsittoheat.Internalintermolecularorintercrystallinefrictionalsoconvertsmaterialstraintoheat.And,ofcourse,externalfrictionprovidesdamping.

Dampingcausestheamplitudeoffreevibrationtodecreaseovertime,andalsolimitsthepeaktransmissibilityinforcedvibration.ItisnormallycharacterizedbytheGreekletterzeta（

）,orbytheratioC/Cc,wherecistheamountofdampinginthestructureormaterialandCcis"

criticaldamping."

Mathematically,criticaldampingisexpressedasCc=2（KM）1/2.Conceptually,criticaldampingisthatamountofdampingwhichallowsthedeflectedspringmasssystemtojustreturntoitsequilibriumpositionwithnoovershootandnooscillation.Anunderdampedsystemwillovershootandoscillatewhendeflectedandreleased.Anoverdampedsystemwillneverreturntoitsequilibriumposition;

itapproachesequilibriumasymptotically.

Displacement,Velocity,andAcceleration

Sincevibrationisdefinedasoscillatorymotion,itinvolvesachangeofposition,ordisplacement（seeFigure1）.

Figure1.Phaserelationshipsamongdisplacement,velocity,andaccelerationareshownonthesetimehistoryplots.

Velocityisdefinedasthetimerateofchangeofdisplacement;

accelerationisthetimerateofchangeofvelocity.Sometechnicaldisciplinesusethetermjerktodenotethetimerateofchangeofacceleration.

SinusoidalMotionEquation.Thesingle-degree-of-freedomspringmasssystem,inforcedvibration,maintainedataconstantdisplacementamplitude,exhibitssimpleharmonicmotion,orsinusoidalmotion.Thatis,itsdisplacementamplitudevs.timetracesoutasinusoidalcurve.GivenapeakdisplacementofX,frequencyf,andinstantaneousdisplacementx:

（2）

atanytime,t.

VelocityEquation.Velocityisthetimerateofchangeofdisplacement,whichisthederivativeofthetimefunctionofdisplacement.Forinstantaneousvelocity,v:

（3）

Sincevibratorydisplacementismostoftenmeasuredintermsofpeak-to-peak,doubleamplitude,displacementD=2X:

（4）

Ifwelimitourinteresttothepeakamplitudesandignorethetimevariationandphaserelationships:

（5）

where:

V=peakvelocity

AccelerationEquation.Similarly,accelerationisthetimerateofchangeofvelocity,thederivativeofthevelocityexpression:

（6）

and

（7）

A=peakacceleration

Itthuscanbeshownthat:

V=

fD

A=2

2f2D

D=V/

f

D=A/2

2f2

Fromtheseequations,itcanbeseenthatlow-frequencymotionislikelytoexhibitlow-amplitudeaccelerationseventhoughdisplacementmaybelarge.Itcanalsobeseenthathigh-frequencymotionislikelytoexhibitlow-amplitudedisplacements,eventhoughaccelerationislarge.Considertwoexamples:

•At1Hz,1in.pk-pkdisplacementisonly~0.05gacceleration;

10in.is~0.5g•At1000Hz,1gaccelerationisonly~0.00002in.displacement;

100gis~0.002in.

MeasuringVibratoryDisplacement

OpticalTechniques.Ifdisplacementislargeenough,asatlowfrequencies,itcanbemeasuredwithascale,calipers,orameasuringmicroscope.Athigherfrequencies,displacementmeasurementrequiresmoresophisticatedopticaltechniques.

High-speedmoviesandvideocanoftenbeusedtomeasuredisplacementsandareespeciallyvaluableforvisualizingthemotionofcomplexstructuresandmechanisms.Thetwomethodsarelimitedbyresolutiontofairlylargedisplacementsandlowfrequencies.Strobelightsandstroboscopicphotographyarealsousefulwhendisplacementsarelargeenough,usually>

0.1in.,tomakethempractical.

Thechangeinintensityorangleofalightbeamdirectedontoareflectivesurfacecanbeusedasanindicationofitsdistancefromthesource.Ifthedetectionapparatusisfastenough,changesofdistancecanbedetectedaswell.

Themostsensitive,accurate,andpreciseopticaldeviceformeasuringdistanceordisplacementisthelaserinterferometer.Withthisapparatus,areflectedlaserbeamismixedwiththeoriginalincidentbeam.Theinterferencepatternsformedbythephasedifferencescanmeasuredisplacementdownto<

100nm.NISTandothernationalprimarycalibrationagenciesuselaserinterferometersforprimarycalibrationofvibrationmeasurementinstrumentsatfrequenciesupto25kHz.

ElectromagneticandCapacitiveSensors.Anotherimportantclassofnoncontact,special-purposedi