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APracticalApproachtoVibrationDetectionandMeasurement PhysicalPrinciplesandDetectionTechniques By: JohnWilson, theDynam ic Consultant, LLC Thistutorial addressesthephysicsofvibration; dynam ics ofaspringm ass system ; dam ping; displacem ent, velocity,andacceleration; andtheoperating principlesofthesensorsthat detect andm easure theseproperties. Vibrationisoscillatorym otion resultingfrom theapplicationofoscillatoryor varyingforcestoastructure. Oscillatorym otion reversesdirection. Asweshall see, theoscillationm ay becontinuousduringsom e tim e periodofinterest orit m ay be interm ittent. It m ay beperiodicornonperiodic, i.e., it m ay orm ay not exhibit aregularperiodofrepetition. Thenatureoftheoscillationdependsonthenatureofthe forcedrivingit andonthestructurebeingdriven. Motionisavectorquantity, exhibitingadirectionaswell asam agnitude. The directionofvibrationisusuallydescribedinterm s ofsom e arbitrarycoordinate system (typicallyCartesianororthogonal)whosedirectionsarecalledaxes. The originfortheorthogonal coordinatesystemofaxesisarbitrarilydefinedat som e convenient location.Most vibratoryresponsesofstructures canbem odeled assingle-degree-of-freedom springm ass system s, andm any vibrationsensorsuseaspringm ass system asthem echanical part oftheirtransductionm echanism . Inadditiontophysical dim ensions, aspring m ass system canbecharacterizedbythestiffnessofthespring, K, andthem ass, M, orweight, W, ofthem ass. Thesecharacteristicsdeterm ine not onlythestatic behavior(staticdeflection, d)ofthestructure, but alsoitsdynam ic characteristics. Ifgistheaccelerationofgravity: F=MAW=Mg K=F/d=W/dd=F/K=W/K=Mg/K DynamicsofaSpringMassSystem Thedynam ics ofaspringm ass system canbeexpressedbythesystem s behaviorin freevibrationand/orinforcedvibration. FreeVibration. Freevibrationisthecasewherethespringisdeflectedandthen releasedandallowedtovibratefreely.Exam ples includeadivingboard, abungee jum per, andapendulum orswingdeflectedandleft tofreelyoscillate. Twocharacteristicbehaviorsshouldbenoted. First, dam ping inthesystem causestheam plitude oftheoscillationstodecreaseovertim e. Thegreaterthe dam ping, thefastertheam plitudedecreases. Second, thefrequencyorperiod oftheoscillationisindependent ofthem agnitude oftheoriginal deflection(as longaselasticlim its arenot exceeded). Thenaturallyoccurringfrequencyofthefreeoscillationsiscalledthenatural frequency, fn: ForcedVibration. Forcedvibrationisthecasewhenenergyiscontinuously addedtothespringm ass system byapplyingoscillatoryforceat som e forcing frequency, ff. Twoexam ples arecontinuouslypushingachildonaswing andanunbalancedrotatingm achineelem ent. Ifenoughenergytoovercom e the dam ping isapplid, them otion willcontinueaslongastheexcitationcontinues. Forcedvibrationm ay taketheform ofself-excitedorexternallyexcitedvibration. Self-excitedvibrationoccurswhentheexcitationforceisgeneratedinoronthe suspendedm ass; externallyexcitedvibrationoccurswhentheexcitationforce isappliedtothespring. Thisisthecase, forexam ple, whenthefoundationtowhichthe springisattachedism oving. Transmissibility. Whenthefoundationisoscillating, andforceistransm itted throughthespringtothesuspendedm ass,them otion ofthem ass will bedifferent from them otion ofthefoundation. Wewillcall them otion ofthefoundationtheinput, I, andthem otion ofthem ass theresponse,R. TheratioR/Iisdefinedasthe transm issibility, Tr: Tr=R/I Resonance. At forcingfrequencieswell belowthesystem s natural frequency, RI, andTr 1. Astheforcingfrequencyapproachesthenatural frequency, transm issibility increasesduetoresonance.Resonanceisthestorageofenergyinthe m echanical system . At forcingfrequenciesnearthenatural frequency, energyisstored andbuildsup, resultinginincreasingresponseam plitude. Dam ping also increaseswithincreasingresponseam plitude, however, andeventuallythe energyabsorbedbydam ping, percycle,equalstheenergyaddedbytheexciting force, andequilibrium isreached. Wefindthepeaktransm issibility occurringwhen ff fn. Thisconditioniscalledresonance. Isolation. Iftheforcingfrequencyisincreasedabovefn, Rdecreases. Whenff = 1.414fn, R=IandTr=1; at higherfrequenciesRIandTr1. At frequencies whenR0.1in., tom ake them practical.Thechangeinintensityorangleofa light beam directedontoareflectivesurfacecanbeusedasanindicationofits distancefrom thesource. Ifthedetectionapparatusisfast enough, changesof distancecanbedetectedaswell.Them ost sensitive, accurate, and preciseoptical deviceform easuringdistanceordisplacem ent isthelaser interferom eter. Withthisapparatus, areflectedlaserbeam ism ixed withthe original incident beam . Theinterferencepatternsform ed bythephasedifferences canm easure displacem ent downto1MHzinsom e PRshockaccelerom eters. Most contem porary PRsensorsarem anufactured from asinglepieceofsilicon. Ingeneral, theadvantagesofsculptingthewholesensorfrom onehom ogeneous block ofm aterial arebetterstability, lesstherm alm ism atch betweenparts, andhigher reliability. Underdam ped PRaccelerom eters tendtobelessruggedthan PEdevices. Single-crystal siliconcanhaveextraordinaryyieldstrength, particularly withhighstrainrates, but it isabrittlem aterial nonetheless. Internal frictionin siliconisverylow, soresonanceam plification canbehigherthanforPE transducers. Boththesefeaturescontributetoitscom parative fragility, althoughif properlydesignedandinstalledtheyareusedwithregularitytom easure shocks well above100,000g. TheygenerallyhavewiderbandwidthsthanPEtransducers (com paring m odels ofsim ilar full-scalerange), aswell assm aller nonlinearities, zeroshifting, andhysteresischaracteristics. BecausetheyhaveDCresponse, theyareusedwhenlong-durationm easurem ents are tobem ade. Inatypical m onolithic siliconsensingelem ent ofaPRaccelerom eter, the1m m squaresiliconchipincorporatestheentirespring, m ass, andfour-arm PRstraingauge bridgeassem bly. Thesensorism ade fromasingle-crystal siliconbym eans of anisotropicetchingandm icrom achiningtechniques. Straingaugesareform ed bya patternofdopant intheoriginallyflatsilicon. Subsequent etchingofchannels freesthegaugesandsim ultaneouslydefinesthem asses assim ply regionsof siliconoforiginal thickness. Thebridgecircuit canbebalancedbyplacingcom pensation resistor(s)inparallel orserieswithanyofthelegs, correctingforthem atching ofeithertheresistance valuesand/orthechangeofthevalueswithtem perature. Com pensation isanart; becausethePRtransducercanhavenonlinearcharacteristics, it isinadvisable tooperateit withexcitationdifferent fromtheconditionsunderwhichit was m anufactured orcalibrated. Forexam ple,PRsensitivityisonlyapproxim ately proportional toexcitation, whichisusuallyaconstant voltageor, insom e cases, constant current, whichhassom eperform ance advantages. Becausetherm al perform ance will ingeneral changewithexcitationvoltage, thereisnot aprecise proportionalitybetweensensitivityandexcitation. Anotherprecautionindealing withvoltage-drivenbridges, particularlythosewithlowresistance, istoverifythat thebridgegetstheproperexcitation. Theseriesresistanceoftheinput leadwires actsasavoltagedivider. Takecarethat theinput leadwireshavelowresistance, or that asix-wirem easurem ent bem ade (withsenselinesat thebridgetoallowthe excitationtobeadjusted)sothebridgegetstheproperexcitation. Constant current excitationdoesnothavethisproblem withseriesresistance. However, PRtransducersaregenerallycom pensated assum ing constant voltage excitationandm ight not givethedesiredperform ance withconstant current. The balanceofthePRbridgeisitsm ostsensitivem easure ofhealth, andisusually thedom inant featureinthetotaluncertaintyofthetransducer. Thebalance, som etim es calledbias, zerooffset, orZMO(zerom easurand output, theoutput with0 g), canbechangedbyseveral effectsthatareusuallytherm al characteristicsor internallyorexternallyinducedshiftsinstrainsinthesensors. Transducercase designsattem pt toisolatethesensorsfromexternal strainssuchastherm al transients, basestrain, orm ounting torque. Internalstrainchanges, e.g., epoxycreep, tendto contributetolong-term instabilities. Allthesegenerallylow-frequencyeffectsare m ore im portant forDCtransducersthanforAC-coupleddevicesbecausetheyoccur m ore ofteninthewiderfrequencybandoftheDC-coupledtransducer. Som e PRdesigns, particularlyhigh-sensitivitytransducers, aredesigned withdam ping toextendfrequencyrangeandoverrangecapability. Dam ping coefficientsof0.7areconsideredideal.Suchdesignsoftenuseoil orsom e other viscousfluid. Twocharacteristicsdictatethat thetechniqueisuseful onlyat relativelylowfrequencies: dam ping forcesareproportional toflowvelocity, and adequateflowvelocityisattainedbypum ping thefluidwithlargedisplacem ents. Thisisahappycoincidenceforsensitivetransducersinthat theyoperateat thelow accelerationfrequencieswheredisplacem ents areadequatelylarge. Viscousdam ping caneffectivelyelim inateresonanceam plification, extendthe overrangecapability, andm ore thandoubletheuseful bandwidth. However, because theviscosityofthedam ping fluidisastrongfunctionoftem perature, theuseful tem perature rangeofthetransducerissubstantiallylim ited. VariableCapacitance. VCtransducersareusuallydesignedas parallel-plateairgapcapacitorsinwhichm otion isperpendiculartotheplates. In som e designstheplateiscantileveredfromoneedge, som otion isactuallyrotation; otherplatesaresupportedaroundtheperiphery, asinatram poline. Changesin capacitanceoftheVCelem ents duetoaccelerationaresensedbyapairofcurrent detectorsthat convert thechangesintovoltageoutput. ManyVCsensorsare m icrom achined asasandwichofanisotropicallyetchedsiliconwaferswitha gaponlyafewm icrons thicktoallowairdam ping. Thefact that airviscosity changesbyjust afewpercent overawideoperatingtem perature rangeprovidesa frequencyresponsem ore stablethanisachievablewithoil-dam ped PRdesigns. InaVCaccelerom eter, ahigh-frequencyoscillatorprovidesthe necessaryexcitationfortheVCelem ents.Changesincapacitancearesensedbythe current detector. Output voltageisproportional tocapacitancechanges, and, therefore, toacceleration. Theincorporationofovertravel stopsinthegap canenhanceruggednessinthesensitivedirection, althoughresistancetooverrange intransversedirectionsm ust relysolelyonthestrengthofthesuspension, asistrueof all othertransducerdesignswithoutovertravel stops. Som e designscansurvive extrem ely highaccelerationoverrangeconditions-asm uch as1000full-scale range. Thesensorofatypicalm icrom achined VCaccelerom eter is constructedofthreesiliconelem entsbondedtogethertoform aherm etically sealedassem bly. Twooftheelem ents aretheelectrodesofanairdielectric, parallel-platecapacitor. Them iddleelem ent ischem ically etchedtoform a rigidcentral m ass suspendedbythin,flexiblefingers. Dam ping characteristics arecontrolledbygasflowintheorificeslocatedonthem ass. VCsensorscanprovidem any ofthebest featuresofthetransducertypes discussedearlier: largeoverrange, DCresponse, low-im pedance output, and sim ple external signal conditioning.Disadvantagesarethecost andsize associatedwiththeincreasedcom plexityoftheonboardconditioning. Also, high-frequencycapacitancedetectioncircuitsareused, andsom e ofthe high-frequencycarrierusuallyappearsontheoutput signal. It isgenerallynot even noticed, beinguptothreeordersofm agnitude (i.e., 1000)higherin frequencythantheoutput signals. Servo(ForceBalance). Althoughservoaccelerom eters areused predom inantly ininertial guidancesystem s,som e oftheirperform ance characteristics m ake them desirableincertainvibrationapplications. All theaccelerom eter types describedpreviouslyareopen-loopdevicesinwhichtheoutput duetodeflectionofthe sensingelem ent isreaddirectly. Inservo-controlled, orclosed-loop, accelerom eters, thedeflectionsignal isusedasfeedbackinacircuit that physically drivesorrebalancesthem ass backtotheequilibrium position. Servoaccelerom eter m anufacturers suggest that open-loopinstrum ents that relyondisplacem ent (i.e., strainingofcrystalsandpiezoresistiveelem ents) toproduceanoutput signal often causenonlinearityerrors. Inclosed-loopdesigns, internal displacem ents arekept extrem ely sm all byelectrical rebalancingoftheproofm ass, m inim izing nonlinearity. Inaddition, closed-loopdesignsaresaidtohavehigheraccuracythanopen-looptypes. However, definitionoftheterm accuracyvaries. Checkwiththesensor m anufacturer. Servoaccelerom eters cantakeeitheroftwobasicgeom etries: linear(e.g., loudspeaker)andpendulous(m eterm ovem ent). Pendulousgeom etry ism ost widelyusedincom m ercial designs. Until recently, theservom echanism wasprim arily basedonelectrom agnetic principles. Forceis usuallyprovidedbydrivingcurrentthroughcoilsonthem ass inthepresence ofam agnetic field. Inthependulousservoaccelerom eter withanelectrom agnetic rebalancingm echanism , thependulous m ass developsatorqueproportional totheproduct oftheproofm ass andtheapplied acceleration. Motionofthem ass isdetectedbythepositionsensors(typically capacitivesensors), whichsendanerrorsignal totheservosystem . Theerrorsignal triggerstheservoam plifier tooutput afeedbackcurrent tothetorquem otor, whichdevelopsanopposingtorqueequalinm agnitude totheacceleration-generated torquefrom thependulousm ass. Output istheapplieddrivecurrent itself(oracrossan output resistor), which, analogoustothedeflectionintheopen-looptransducers, is proportional totheappliedforceandthereforetotheacceleration. Incontrast totheruggedspringelem ents oftheopen-looptransducers, the rebalancingforceinthecaseoftheclosed-loopaccelerom eter isprim arily electrical andexistsonlywhenpowerisprovided. Thespringsareasflim sy inthe sensitivedirectionasfeasibleandm ostdam ping isprovidedthroughthe electronics. UnlikeotherDC-responseaccelerom eters whosebiasstability dependssolelyonthecharacteristicsofthesensingelem ent(s), it isthefeedback electronicsintheclosed-loopdesignthatcontrolsbiasstability. Servo accelerom eters thereforetendtoofferlesszerodrifting, whichisthem ajor reasonfor theirusesinvibrationm easurem ents. Ingeneral, theyhaveauseful bandwidthof 1000Hzandaredesignedforuseinapplicationswithcom paratively low accelerationlevelsandextrem ely lowfrequencycom ponents. References1. A. Chu. ZeroShift ofPiezoelectric Accelerom eters inPyroshockMeasurem ents, EndevcoTPNo. 293. 2. Shock& VibrationMeasurem entTechnology.1987. Endevco. 3. MeasuringVibration.1982. Bruel &Kjaer. 4. C. Harris. 1995. ShockandVibrationHandbook, 4thEd., McGrawHill. 5. General GuidetoICPInstrum entation.March1973. PCBPiezotronics, #G-0001. 6. IntroductiontoPiezoelectricSensors.March1985. PCBPiezotronics, #018. 7. ApplicationofIntegrated-CircuitElectronicstoPiezoelectricTransducers. March1967. PCBPiezotronics, #G-01. 8. IsotronInstructionManual.1995.Endevco, IM31704. 9. InstructionManual forEndevcoPiezoresistiveAccelerom eters. 1978. Endevco, #121. 10. EntranAccelerom eter InstructionandSelectionManual.1987. EntranDevices. 11. R. Sill. TestingTechniquesInvolvedwiththeDevelopm ent ofHighShock AccelerationSensors.Endevco, TP284. 12. R. Sill. Minim izing Measurem entUncertaintyinCalibrationandUseof Accelerom eters. Endevco, TP299. 13. P.K. Stein. TheConstant CurrentConcept forDynam ic Strain Measurem ent. SteinEngineeringServices,Inc., Lf/MSEPublication46. 14. B. Link. ShockandVibrationMeasurem ent UsingVariable Capacitance.Endevco, TP296.