APracticalApproachtoVibrationDetectionandMeasurementPhysicalPrinciplesandDetectionTechniquesBy: JohnWilson, theDynam ic Consultant, LLCThistutorial addressesthephysicsofvibration; dynam ics ofaspringm asssystem ; dam ping; displacem ent, velocity,andacceleration; andtheoperatingprinciplesofthesensorsthat detect andm easure theseproperties.Vibrationisoscillatorym otion resultingfrom theapplicationofoscillatoryorvaryingforcestoastructure. Oscillatorym otion reversesdirection. Asweshall see,theoscillationm ay becontinuousduringsom e tim e periodofinterest orit m ay beinterm ittent. It m ay beperiodicornonperiodic, i.e., it m ay orm ay not exhibitaregularperiodofrepetition. Thenatureoftheoscillationdependsonthenatureoftheforcedrivingit andonthestructurebeingdriven.Motionisavectorquantity, exhibitingadirectionaswell asam agnitude. Thedirectionofvibrationisusuallydescribedinterm s ofsom e arbitrarycoordinatesystem (typicallyCartesianororthogonal)whosedirectionsarecalledaxes. Theoriginfortheorthogonal coordinatesystemofaxesisarbitrarilydefinedat som econvenient location.Most vibratoryresponsesofstructurescanbem odeled assingle-degree-of-freedom springm asssystem s, andm any vibrationsensorsuseaspringm ass system asthem echanical partoftheirtransductionm echanism . Inadditiontophysical dim ensions, aspringm ass system canbecharacterizedbythestiffnessofthespring, K, andthem ass, M,orweight, W, ofthem ass. Thesecharacteristicsdeterm ine not onlythestaticbehavior(staticdeflection, d)ofthestructure, but alsoitsdynam iccharacteristics. Ifgistheaccelerationofgravity:F=MAW=MgK=F/d=W/dd=F/K=W/K=Mg/KDynamicsofaSpringMassSystemThedynam ics ofaspringm ass system canbeexpressedbythesystem s behaviorinfreevibrationand/orinforcedvibration.FreeVibration. Freevibrationisthecasewherethespringisdeflectedandthenreleasedandallowedtovibratefreely.Exam ples includeadivingboard, abungeejum per, andapendulum orswingdeflectedandleft tofreelyoscillate.Twocharacteristicbehaviorsshouldbenoted. First, dam ping inthesystemcausestheam plitude oftheoscillationstodecreaseovertim e. Thegreaterthedam ping, thefastertheam plitudedecreases. Second, thefrequencyorperiodoftheoscillationisindependent ofthem agnitude oftheoriginal deflection(aslongaselasticlim its arenot exceeded).Thenaturallyoccurringfrequencyofthefreeoscillationsiscalledthenaturalfrequency, fn:ForcedVibration. Forcedvibrationisthecasewhenenergyiscontinuouslyaddedtothespringm ass system byapplyingoscillatoryforceat som e forcingfrequency, ff. Twoexam ples arecontinuouslypushingachildonaswingandanunbalancedrotatingm achineelem ent. Ifenoughenergytoovercom e thedam ping isapplid, them otion willcontinueaslongastheexcitationcontinues.Forcedvibrationm ay taketheform ofself-excitedorexternallyexcitedvibration.Self-excitedvibrationoccurswhentheexcitationforceisgeneratedinoronthesuspendedm ass; externallyexcitedvibrationoccurswhentheexcitationforceisappliedtothespring. Thisisthecase, forexam ple, whenthefoundationtowhichthespringisattachedism oving.Transmissibility. Whenthefoundationisoscillating, andforceistransm ittedthroughthespringtothesuspendedm ass,them otion ofthem ass will bedifferentfrom them otion ofthefoundation. Wewillcall them otion ofthefoundationtheinput,I, andthem otion ofthem ass theresponse,R. TheratioR/Iisdefinedasthetransm issibility, Tr:Tr=R/IResonance. At forcingfrequencieswell belowthesystem s natural frequency,RI, andTr 1. Astheforcingfrequencyapproachesthenatural frequency,transm issibility increasesduetoresonance.Resonanceisthestorageofenergyinthem echanical system . At forcingfrequenciesnearthenatural frequency, energyisstoredandbuildsup, resultinginincreasingresponseam plitude. Dam ping alsoincreaseswithincreasingresponseam plitude, however, andeventuallytheenergyabsorbedbydam ping, percycle,equalstheenergyaddedbytheexcitingforce, andequilibrium isreached. Wefindthepeaktransm issibility occurringwhenff fn. Thisconditioniscalledresonance.Isolation. Iftheforcingfrequencyisincreasedabovefn, Rdecreases. Whenff =1.414fn, R=IandTr=1; at higherfrequenciesR0.1in., tom ake them practical.Thechangeinintensityorangleofalight beam directedontoareflectivesurfacecanbeusedasanindicationofitsdistancefrom thesource. Ifthedetectionapparatusisfast enough, changesofdistancecanbedetectedaswell.Them ost sensitive, accurate, andpreciseoptical deviceform easuringdistanceordisplacem ent isthelaserinterferom eter. Withthisapparatus, areflectedlaserbeam ism ixed withtheoriginal incident beam . Theinterferencepatternsform ed bythephasedifferencescanm easure displacem ent downto1MHzinsom e PRshockaccelerom eters.Most contem porary PRsensorsarem anufactured from asinglepieceofsilicon.Ingeneral, theadvantagesofsculptingthewholesensorfrom onehom ogeneous blockofm aterial arebetterstability, lesstherm alm ism atch betweenparts, andhigherreliability. Underdam ped PRaccelerom eters tendtobelessruggedthanPEdevices. Single-crystal siliconcanhaveextraordinaryyieldstrength, particularlywithhighstrainrates, but it isabrittlem aterial nonetheless. Internal frictioninsiliconisverylow, soresonanceam plification canbehigherthanforPEtransducers. Boththesefeaturescontributetoitscom parative fragility, althoughifproperlydesignedandinstalledtheyareusedwithregularitytom easure shockswell above100,000g. TheygenerallyhavewiderbandwidthsthanPEtransducers(com paring m odels ofsim ilar full-scalerange), aswell assm aller nonlinearities,zeroshifting, andhysteresischaracteristics.BecausetheyhaveDCresponse, theyareusedwhenlong-durationm easurem ents aretobem ade.Inatypical m onolithic siliconsensingelem ent ofaPRaccelerom eter, the1m msquaresiliconchipincorporatestheentirespring, m ass, andfour-arm PRstraingaugebridgeassem bly. Thesensorism ade fromasingle-crystal siliconbym eans ofanisotropicetchingandm icrom achiningtechniques. Straingaugesareform ed byapatternofdopant intheoriginallyflatsilicon. Subsequent etchingofchannelsfreesthegaugesandsim ultaneouslydefinesthem asses assim ply regionsofsiliconoforiginal thickness.Thebridgecircuit canbebalancedbyplacingcom pensation resistor(s)inparallelorserieswithanyofthelegs, correctingforthem atching ofeithertheresistancevaluesand/orthechangeofthevalueswithtem perature. Com pensation isanart;becausethePRtransducercanhavenonlinearcharacteristics, it isinadvisabletooperateit withexcitationdifferent fromtheconditionsunderwhichit wasm anufactured orcalibrated. Forexam ple,PRsensitivityisonlyapproxim atelyproportional toexcitation, whichisusuallyaconstant voltageor, insom e cases,constant current, whichhassom eperform ance advantages. Becausetherm alperform ance will ingeneral changewithexcitationvoltage, thereisnot apreciseproportionalitybetweensensitivityandexcitation. Anotherprecautionindealingwithvoltage-drivenbridges, particularlythosewithlowresistance, istoverifythatthebridgegetstheproperexcitation. Theseriesresistanceoftheinput leadwiresactsasavoltagedivider. Takecarethat theinput leadwireshavelowresistance, orthat asix-wirem easurem ent bem ade (withsenselinesat thebridgetoallowtheexcitationtobeadjusted)sothebridgegetstheproperexcitation.Constant current excitationdoesnothavethisproblem withseriesresistance.However, PRtransducersaregenerallycom pensated assum ing constant voltageexcitationandm ight not givethedesiredperform ance withconstant current. ThebalanceofthePRbridgeisitsm ostsensitivem easure ofhealth, andisusuallythedom inant featureinthetotaluncertaintyofthetransducer. Thebalance,som etim es calledbias, zerooffset, orZMO(zerom easurand output, theoutput with0g), canbechangedbyseveral effectsthatareusuallytherm al characteristicsorinternallyorexternallyinducedshiftsinstrainsinthesensors. Transducercasedesignsattem pt toisolatethesensorsfromexternal strainssuchastherm al transients,basestrain, orm ounting torque. Internalstrainchanges, e.g., epoxycreep, tendtocontributetolong-term instabilities. Allthesegenerallylow-frequencyeffectsarem ore im portant forDCtransducersthanforAC-coupleddevicesbecausetheyoccurm ore ofteninthewiderfrequencybandoftheDC-coupledtransducer.Som e PRdesigns, particularlyhigh-sensitivitytransducers, aredesignedwithdam ping toextendfrequencyrangeandoverrangecapability. Dam pingcoefficientsof0.7areconsideredideal.Suchdesignsoftenuseoil orsom e otherviscousfluid. Twocharacteristicsdictatethat thetechniqueisuseful onlyatrelativelylowfrequencies: dam ping forcesareproportional toflowvelocity, andadequateflowvelocityisattainedbypum ping thefluidwithlargedisplacem ents.Thisisahappycoincidenceforsensitivetransducersinthat theyoperateat thelowaccelerationfrequencieswheredisplacem ents areadequatelylarge.Viscousdam ping caneffectivelyelim inateresonanceam plification, extendtheoverrangecapability, andm ore thandoubletheuseful bandwidth. However, becausetheviscosityofthedam ping fluidisastrongfunctionoftem perature, theusefultem perature rangeofthetransducerissubstantiallylim ited.VariableCapacitance. VCtransducersareusuallydesignedasparallel-plateairgapcapacitorsinwhichm otion isperpendiculartotheplates. Insom e designstheplateiscantileveredfromoneedge, som otion isactuallyrotation;otherplatesaresupportedaroundtheperiphery, asinatram poline. ChangesincapacitanceoftheVCelem ents duetoaccelerationaresensedbyapairofcurrentdetectorsthat convert thechangesintovoltageoutput. ManyVCsensorsarem icrom achined asasandwichofanisotropicallyetchedsiliconwaferswithagaponlyafewm icrons thicktoallowairdam ping. Thefact that airviscositychangesbyjust afewpercent overawideoperatingtem perature rangeprovidesafrequencyresponsem ore stablethanisachievablewithoil-dam ped PRdesigns.InaVCaccelerom eter, ahigh-frequencyoscillatorprovidesthenecessaryexcitationfortheVCelem ents.Changesincapacitancearesensedbythecurrent detector. Output voltageisproportional tocapacitancechanges, and,therefore, toacceleration. Theincorporationofovertravel stopsinthegapcanenhanceruggednessinthesensitivedirection, althoughresistancetooverrangeintransversedirectionsm ust relysolelyonthestrengthofthesuspension, asistrueofall othertransducerdesignswithoutovertravel stops. Som e designscansurviveextrem ely highaccelerationoverrangeconditions-asm uch as1000full-scalerange.Thesensorofatypicalm icrom achined VCaccelerom eter isconstructedofthreesiliconelem entsbondedtogethertoform aherm eticallysealedassem bly. Twooftheelem ents aretheelectrodesofanairdielectric,parallel-platecapacitor. Them iddleelem ent ischem ically etchedtoform arigidcentral m ass suspendedbythin,flexiblefingers. Dam ping characteristicsarecontrolledbygasflowintheorificeslocatedonthem ass.VCsensorscanprovidem any ofthebest featuresofthetransducertypesdiscussedearlier: largeoverrange, DCresponse, low-im pedance output, andsim ple external signal conditioning.Disadvantagesarethecost andsizeassociatedwiththeincreasedcom plexityoftheonboardconditioning. Also,high-frequencycapacitancedetectioncircuitsareused, andsom e ofthehigh-frequencycarrierusuallyappearsontheoutput signal. It isgenerallynot evennoticed, beinguptothreeordersofm agnitude (i.e., 1000)higherinfrequencythantheoutput signals.Servo(ForceBalance). Althoughservoaccelerom eters areusedpredom inantly ininertial guidancesystem s,som e oftheirperform ance characteristicsm ake them desirableincertainvibrationapplications. All theaccelerom eter typesdescribedpreviouslyareopen-loopdevicesinwhichtheoutput duetodeflectionofthesensingelem ent isreaddirectly. Inservo-controlled, orclosed-loop,accelerom eters, thedeflectionsignal isusedasfeedbackinacircuit that physicallydrivesorrebalancesthem ass backtotheequilibrium position. Servoaccelerom eterm anufacturers suggest that open-loopinstrum ents that relyondisplacem ent (i.e.,strainingofcrystalsandpiezoresistiveelem ents) toproduceanoutput signal oftencausenonlinearityerrors. Inclosed-loopdesigns, internal displacem ents arekeptextrem ely sm all byelectrical rebalancingoftheproofm ass, m inim izing nonlinearity.Inaddition, closed-loopdesignsaresaidtohavehigheraccuracythanopen-looptypes.However, definitionoftheterm accuracyvaries. Checkwiththesensorm 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. Forceisusuallyprovidedbydrivingcurrentthroughcoilsonthem ass inthepresenceofam agnetic field. Inthependulousservoaccelerom eter withanelectrom agneticrebalancingm echanism , thependulousm ass developsatorqueproportional totheproduct oftheproofm ass andtheappliedacceleration. Motionofthem ass isdetectedbythepositionsensors(typicallycapacitivesensors), whichsendanerrorsignal totheservosystem . Theerrorsignaltriggerstheservoam plifier tooutput afeedbackcurrent tothetorquem otor,whichdevelopsanopposingtorqueequalinm agnitude totheacceleration-generatedtorquefrom thependulousm ass. Output istheapplieddrivecurrent itself(oracrossanoutput resistor), which, analogoustothedeflectionintheopen-looptransducers, isproportional totheappliedforceandthereforetotheacceleration.Incontrast totheruggedspringelem ents oftheopen-looptransducers, therebalancingforceinthecaseoftheclosed-loopaccelerom eter isprim arilyelectrical andexistsonlywhenpowerisprovided. Thespringsareasflim sy inthesensitivedirectionasfeasibleandm ostdam ping isprovidedthroughtheelectronics. UnlikeotherDC-responseaccelerom eters whosebiasstabilitydependssolelyonthecharacteristicsofthesensingelem ent