外文翻译--对振动侦查和测量的一种实用方法物理原则和侦查技术 英文版.pdf
APracticalApproachtoVibrationDetectionandMeasurementPhysicalPrinciplesandDetectionTechniquesBy:JohnWilson,theDynamicConsultant,LLCThistutorialaddressesthephysicsofvibration;dynamicsofaspringmasssystem;damping;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=MAW=MgK=F/d=W/dd=F/K=W/K=Mg/KDynamicsofaSpringMassSystemThedynamicsofaspringmasssystemcanbeexpressedbythesystemsbehaviorinfreevibrationand/orinforcedvibration.FreeVibration.Freevibrationisthecasewherethespringisdeflectedandthenreleasedandallowedtovibratefreely.Examplesincludeadivingboard,abungeejumper,andapendulumorswingdeflectedandlefttofreelyoscillate.Twocharacteristicbehaviorsshouldbenoted.First,dampinginthesystemcausestheamplitudeoftheoscillationstodecreaseovertime.Thegreaterthedamping,thefastertheamplitudedecreases.Second,thefrequencyorperiodoftheoscillationisindependentofthemagnitudeoftheoriginaldeflection(aslongaselasticlimitsarenotexceeded).Thenaturallyoccurringfrequencyofthefreeoscillationsiscalledthenaturalfrequency,fn: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/IResonance.Atforcingfrequencieswellbelowthesystemsnaturalfrequency,RI,andTr1.Astheforcingfrequencyapproachesthenaturalfrequency,transmissibilityincreasesduetoresonance.Resonanceisthestorageofenergyinthemechanicalsystem.Atforcingfrequenciesnearthenaturalfrequency,energyisstoredandbuildsup,resultinginincreasingresponseamplitude.Dampingalsoincreaseswithincreasingresponseamplitude,however,andeventuallytheenergyabsorbedbydamping,percycle,equalstheenergyaddedbytheexcitingforce,andequilibriumisreached.Wefindthepeaktransmissibilityoccurringwhenfffn.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.DampingDampingisanyeffectthatremoveskineticand/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,andAccelerationSincevibrationisdefinedasoscillatorymotion,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:atanytime,t.VelocityEquation.Velocityisthetimerateofchangeofdisplacement,whichisthederivativeofthetimefunctionofdisplacement.Forinstantaneousvelocity,v:Sincevibratorydisplacementismostoftenmeasuredintermsofpeak-to-peak,doubleamplitude,displacementD=2X:Ifwelimitourinteresttothepeakamplitudesandignorethetimevariationandphaserelationships:where:V=peakvelocityAccelerationEquation.Similarly,accelerationisthetimerateofchangeofvelocity,thederivativeofthevelocityexpression:Andwhere:A=peakaccelerationItthuscanbeshownthat:V=fDA=22f2DD=V/fD=A/22f2Fromtheseequations,itcanbeseenthatlow-frequencymotionislikelytoexhibitlow-amplitudeaccelerationseventhoughdisplacementmaybelarge.Itcanalsobeseenthathigh-frequencymotionislikelytoexhibitlow-amplitudedisplacements,eventhoughaccelerationislarge.Considertwoexamples:At1Hz,1in.pk-pkdisplacementisonly0.05gacceleration;10in.is0.5gAt1000Hz,1gaccelerationisonly0.00002in.displacement;100gis0.002in.MeasuringVibratoryDisplacementOpticalOOOTechniques.Ifdisplacementislargeenough,asatlowfrequencies,itcanbemeasuredwithascale,calipers,orameasuringmicroscope.Athigherfrequencies,displacementmeasurementrequiresmoresophisticatedopticaltechniques.High-speedmoviesandvideocanoftenbeusedtomeasuredisplacementsandareespeciallyvaluableforvisualizingthemotionofcomplexstructuresandmechanisms.Thetwomethodsarelimitedbyresolutiontofairlylargedisplacementsandlowfrequencies.Strobelightsandstroboscopicphotographyarealsousefulwhendisplacementsarelargeenough,usually>0.1in.,tomakethempractical.Thechangeinintensityorangleofalightbeamdirectedontoareflectivesurfacecanbeusedasanindicationofitsdistancefromthesource.Ifthedetectionapparatusisfastenough,changesofdistancecanbedetectedaswell.Themostsensitive,accurate,andpreciseopticaldeviceformeasuringdistanceordisplacementisthelaserinterferometer.Withthisapparatus,areflectedlaserbeamismixedwiththeoriginalincidentbeam.Theinterferencepatternsformedbythephasedifferencescanmeasuredisplacementdownto<100