作者：JohnWilson,動態(tài)顧問,這篇述振物、簧質(zhì)系的動學(xué)，位移速和速度并查振動擺動由振動或作用在機構(gòu)的力的變化引起振動的擺動。振動行動反向。由于機構(gòu)的多數(shù)振動的響應(yīng)可以用當做單度彈簧質(zhì)量系統(tǒng)模型，并且許多振動傳感器使可以用彈簧的剛度K，和質(zhì)量M，或者質(zhì)量的重量W等性能參數(shù)來阿描述。這些特征不僅決定來這機構(gòu)的靜態(tài)特性（靜變位d），而且決定來它的動態(tài)特性。如果g是重力的加速度:F=W=K=F/d=d=F/K=W/K= 振動被那情況情形哪里那彈簧是偏斜于是以及允許到地搖 迫振動頻率時的情形ff.兩個二例子連續(xù)地推一個孩子上去一個搖擺和一失衡旋轉(zhuǎn)電機元傳導(dǎo)能力當基礎(chǔ)正在振動，而且力整個彈簧被傳輸?shù)街兄沟馁|(zhì)量時候,質(zhì)量的動作將會是來自基礎(chǔ)的動作差積。會認為基礎(chǔ)的動作是輸入，I,,和質(zhì)量的動作響應(yīng),R.比率Tr=在力頻率好低于體系的固有頻率，RI,和Tr1。由于作用力的頻率接近那固發(fā)現(xiàn)當fffn.時最大傳遞率發(fā)生，這個情況被稱作fn，Rff1.414fn,RITr1頻率R<ITr1。在頻率當Ｒ<I質(zhì)量和剛性變更的效應(yīng)。從等式（1）可見固有頻率與剛度K的平方根成正比，并且與那 因為振動的位移最經(jīng)常按振蕩總振幅，全振幅的術(shù)語計量的，位移D＝2X：

V=A=22f2D=V/fD=A/22f21Hz,1in（英寸）0.05g（加侖）10in.0.5g1000Hz1g加速度僅僅是0.00002in.的位移；100g0.002in。 常>0.1英寸，到使他們成為現(xiàn)實的。有原來的入射光束。這由相位差形成的圖樣可以測量位移下至<100nm。NIST及其他國家一次校準機構(gòu)使用激光儀作為振動測試儀的一次校準在頻率直到25kHz。 電磁感應(yīng)式接近覺傳感器經(jīng)常被叫做渦流探針，因為最流行類型之一渦生在這接觸技術(shù)各式各樣的相對運動傳感器使用直接接觸用兩個目標來測量在他們之間的的位移傳感器這些裝置，隨后詳細地論述，是曾經(jīng)流行的但是現(xiàn)在是很少使用。 一些最早的"高頻"振動測量以電力學(xué)的速度被做感知器。這些是一個合并一個磁石的傳動器的型態(tài)支援了通一個軟式彈簧乳濁液系統(tǒng)造形的(彈簧質(zhì)量)系統(tǒng)。磁石的構(gòu)件在一個含有一或較多線的多旋轉(zhuǎn)線圈的殼中被中止。當殼在好的在彈簧過磁場的線圈速度的比例項。速度轉(zhuǎn)換器從10赫茲直至數(shù)百赫茲。他們通常是大的和重,44MHz)桿被與最初的桿和都移頻相較用來計算振動表面的速度。順序和疏遠距離是具決定性的。因為在位置，順序和距離方面的幾何學(xué)的約束，他們被限制到應(yīng)用程序。激光 靠的，和用途廣泛的加速度儀作為感知器而且整合他們的產(chǎn)量源自一個速度信號是實際的能被整合(速度)或雙重的整合(位移).一些加速度儀信號調(diào)節(jié)者為那一個目的有內(nèi)建的系統(tǒng)的一種變化,而且被歸類為的傳動器。振動的加速度儀原理所有的振動加速度儀使用一些變化一振動的或在一情況被一個加速。然后彈簧的位移，的位移這情形，否則力量傳輸在春天是傳感乘一電信號piezoresistive(對于大多數(shù)的應(yīng)用程序，個人偏向是向和的電子學(xué)的壓電加速計。這些裝置的相容。每個類型的加速度儀需要一個不同類型的訊號調(diào)節(jié)。加速度儀測定類 察元件提供一個電子的給定數(shù)目比例的給應(yīng)用應(yīng)力的數(shù)量。(piezein是一個希臘的字組意謂壓擠)許多肉色和人造的事物,大概晶體或窯業(yè)和一些聚合物,顯示這一個特性。這些事物有一個一般的結(jié)晶[性]的分子結(jié)構(gòu),藉由一個凈的進氣變更的分配當緊張的。當不重音的時候。在這些事物中，磁場能被來自應(yīng)力或溫度的形變產(chǎn)生,引起壓電的或焦熱度一起關(guān)聯(lián)的期數(shù)之上發(fā)生變更.聚合物PE事物有如熱擴散的他們本來被用的高焦熱電的產(chǎn)量。有三個熱電效應(yīng),將會在稍后被詳細地。個電場向前被產(chǎn)生雙偶體的方向時候,在面上的金屬電極在傾斜的生產(chǎn)品的可動裝仰賴被建立的電壓和在電極之間的電容.來自一個PE加速度儀的進氣通常單位的安培是微微庫倫,或10-12個庫侖,是某事超過6×106個電子。PE容)之中的一個交易,熱的系數(shù)，最大溫度，頻率特性和穩(wěn)定性。最好的S/牛頓比率通常自然地發(fā)生壓電晶體,像是電氣石或石英通常讓低要價靈敏度,有關(guān)一百分之一那那的網(wǎng)域(也就是,區(qū)域在哪一雙偶體自然地被排齊)是工極化的程序排齊的他們自己。極化非常地比較高地通常在溫度發(fā)生勝于操作溫度加速網(wǎng)域的順序程序。去極,或弛緩,極總是造成靈敏度的暫時或長備損失。電氣石，一個不去極的自然晶體,特別地是有用因為他們是自己，自動的意義產(chǎn)生,PE傳動器不能夠用來測量穩(wěn)定狀態(tài)加速度或力,這會把電子之遠,如同做感知器的內(nèi)電阻。(傳動器的高溫度或濕度會藉由減少電阻數(shù)值問題)。能量會被排出溝外，而且產(chǎn)量會,盡管固定的輸入加速度/力。PE傳動器電壓產(chǎn)量的外面測量需要對高壓線的動態(tài)行為和一前置放大器的輸入特性的特別注意。因為高壓線電容直接地信號振幅,高壓線的過度運動在測量期間能引起在它應(yīng)該在1000M的級上或比較高的確定充份的低周波響應(yīng)。限制是他們一定被"噪音對待的"高壓線用;以別的方式，高壓線的動作能移置摩擦電進大多數(shù)的PE傳動器高低不平。每一個各種不同的形而且按規(guī)定尺寸制作有效的帶它自己的性能妥協(xié)受到的影響。最通常類型的這一個傳動器是壓縮和剪設(shè)計。剪設(shè)計提供乙烯或者PR而言是較松的。IEPE加速度儀/力傳動器的靈敏度,與PR,不是被供給變化重要較起來沒有的電子學(xué)的設(shè)計,高阻抗版本將會總是有一個較高的平均無故障時間(MTBF)因此是有這些傳動器(一些設(shè)計相對地有高輸出阻抗)的關(guān)心。問題能被藉由在被制造業(yè)氣變換器。石英被用于電壓模態(tài),也就是,藉由來源從動件，因為它的小介質(zhì)常數(shù)比較地提進氣模態(tài)的頻率響應(yīng)中下垂。電壓模態(tài)的幅度頻率響應(yīng)相當平。矽應(yīng)變計一個功率加速度記錄器當應(yīng)變時，是一惠斯通電橋的電阻器合并一或多木頭支地用這輸入激勵電壓，要求一非常堅定的和的激勵供給。器和簡單把這輸出端直接地與一示波器連接在一起。如果鏡和激發(fā)單獨地被結(jié)束，這將不作。。)～置于地面(與和激發(fā)相等的接地),橋的一個支架被分路，而且整個的激發(fā)電壓被放置橫過那一個橋的支架。如的傳感器。低阻抗PR傳動器共享由IEPE提供的噪音免蝕態(tài)的利益,雖然PR的輸出阻抗時常夠大的它不能夠駕駛大的電容負載。標準是由于IEPE外殼,結(jié)果是在產(chǎn)量上的一個有低的規(guī)因數(shù);那是,電阻的比率對應(yīng)變的變化很小。他們的響應(yīng)被有柔性響應(yīng)支配。他對長度的數(shù)值比例項和反的比例到橫斷面面積。如果一個傳統(tǒng)的事物被展,當長度增加的時候，它的寬度減少。兩者的效應(yīng)增加電阻。1.6;1.6材料展覽品這一個效應(yīng),像壓電性強烈地是一個水晶取向的函數(shù)。喜歡其他的半導(dǎo)體性質(zhì),100小型化允許一些PR的自然頻率>1MHz加速度儀。加速度儀容易不比PE裝置高低不平。單一晶體矽能有特別的降伏強度,特別地以高的應(yīng)變他們被規(guī)律性用測量很好上述的100,000g。他們通常有較寬的頻帶寬度勝于PE傳動器(比較相似實物大小范圍的模型),連同較小的非線性，零的移位和磁滯特性。因為他在PR加速度儀的一個典型獨石矽可察元件中,1毫米角尺矽合并整個的彈簧，質(zhì)量一晶體矽做成的。應(yīng)變計被本來平的矽一個雜物的圖案造形。溝流的后來浸蝕規(guī)并且值及價值的變化用溫度的修正。補償是一種藝術(shù);因為PR傳動器能有非線性特性,用激發(fā)PR例激發(fā),通常是一個固定的電壓或,在一些外殼,定流中有一些性能利益。因為熱的性能將會大體上和激發(fā)電壓的變化,在靈敏度和激發(fā)之間沒有一個精密的比例。另外的預(yù)防在處理恒定電流激勵工作沒有這些用串聯(lián)電阻的問題。然而，PR傳動器通常被補整傲慢的固定電壓激發(fā)并且不可能用定流給被需要的性能。PR橋的平衡是它的健康最敏感衡量,而且ZMO(可測量產(chǎn)量,和0g的產(chǎn)量),能被通常是熱的特性或在或外面地誘導(dǎo)了感知器的應(yīng)變變化的一些效應(yīng)改變。傳動器外殼設(shè)計嘗試來自外面的應(yīng)變,像是熱的暫態(tài)，基本的應(yīng)變系數(shù)0.7技術(shù)是有用的只有在相對地低周波:阻尼成比例流過速度,而且適當?shù)牧髁克俣缺唤逵晌灰谱銐虼竽睦铩Ｕ硿枘峥梢杂行У爻シ糯舐剩娱L過量程的能力，并且比加倍有可變電 中屏從一個邊緣被把～建成懸臂式，因此，動作實際上是轉(zhuǎn)動;其他的屏在圓周的周圍被支允許空氣減震中間插進的腐蝕劑硅片。事實是空氣粘度變化由只有一點百分比在一寬的工作極其大加速度過量程的工況是1000倍的測量范圍。手指中止的一個硬的質(zhì)量。阻尼特性被位于質(zhì)量之上的孔氣體流量控制。規(guī)定尺寸制作關(guān)聯(lián)。同時,高頻電容檢波電路被用，而且一些高頻載波通常在產(chǎn)量信號上出 型是開環(huán)裝置在哪一產(chǎn)量由于可察元件的撓曲被直接地讀。在倍力器中-控制,或閉合回路，加速度儀,撓曲信號被用當一個身體上地驅(qū)動或再平衡返回平衡位的質(zhì)量電路的反饋。倍力器加速度儀制造業(yè)者建議仰賴位移(也就是,晶體和piezoresistive元件的繃皮操作)時質(zhì)量電再平衡保持小,將非線性減到最少。除此之外，閉合回路設(shè)計被說有較高的精確度勝于開環(huán)打字。然而，期間精確度的定義改變。以傳感器制造商校核。伺服加速度計可以APracticalApproachtoVibrationDetectionand——PhysicalPrinciplesandDetectionBy:JohnWilson,theDynamicConsultant,Thistutorialaddressesthephysicsofvibration;dynamicsofaspringmasssystem;dam;displacement,velocity,andacceleration;andtheoperatingprinciplesofthesensorsthatdetectandmeasuretheseproperties.Vibrationisoscillatorymotionresultingfromtheapplicationofoscillatoryorvaryingforcestoastructure.Oscillatorymotionreversesdirection.Asweshallsee,theoscillationmaybecontinuousduringsometimeperiodofinterestoritmaybeintermittent.Itmaybeperiodicornonperiodic,i.e.,itmayormaynotexhibitaregularperiodofrepetition.Thenatureoftheoscillationdependsonthenatureoftheforcedrivingitandonthestructurebeingdriven.Motionisavectorty,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=K=F/d=d=F/K=W/K=DynamicsofaSpringMassThedynamicsofaspringmasssystemcanbeexpressedbythesystem'sbehaviorinfreevibrationand/orinforcedvibration.FreeVibration.Freevibrationisthecasewherethespringisdeflectedandthenreleasedandallowedtovibratefreely.Examplesincludeadivingboard,abungeejumper,andndulumorswingdeflectedandlefttofreelyTwocharacteristicbehaviorsshouldbenoted.,daminthesystemcausestheamplitudeoftheoscillationstodecreaseovertime.Thegreaterthedam,thefastertheamplitudedecreases.Second,thefrequencyorperiodoftheoscillationisindependentofthemagnitudeoftheoriginaldeflection(aslongaselasticlimitsarenotexceeded).Thenaturallyoccurringfrequencyofthefreeoscillationsiscalledthenaturalfrequency,fn: (1)ForcedVibration.Forcedvibrationisthecasewhenenergyiscontinuouslytothespringmasssystembyapplyingoscillatoryforceatsomeforcingfrequency,ff.Twoexamplesarecontinuouslypushingachildonaswingandanunbalancedrotatingmachineelement.Ifenoughenergyto ethedamisapplid,themotionwillcontinueaslongastheexcitationcontinues.Forcedvibrationmaytaketheformofself-excitedorexternallyexcitedvibration.Self-excitedvibrationoccurswhentheexcitationforceisgeneratedinoronthesuspendedmass;externallyexcitedvibrationoccurswhentheexcitationforceisappliedtothespring.Thisisthecase,forexample,whenthefoundationtowhichthespringisattachedismoving.Transmissibility.Whenthefoundationisoscillating,andforceistransmittedthroughthespringtothesuspendedmass,themotionofthemasswillbedifferentfromthemotionofthefoundation.Wewillcallthemotionofthefoundationtheinput,I,andthemotionofthemasstheresponse,R.TheratioR/Iisdefinedasthetransmissibility,Tr:Tr=Resonance.Atforcingfrequencieswellbelowthesystem'snaturalfrequency,RI,andTr1.Astheforcingfrequencyapproachesthenaturalfrequency,transmissibilityincreasesduetoresonance.Resonanceisthestorageofenergyinthemechanicalsystem.Atforcingfrequenciesnearthenaturalfrequency,energyisstoredandbuildsup,resultinginincreasingresponseamplitude.Damalsoincreaseswithincreasingresponseamplitude,however,andeventuallytheenergyabsorbedbydam,percycle,equalstheenergyaddedbytheexcitingforce,andequilibriumisreached.Wefindthepeaktransmissibilityoccurringwhenfffn.Thisconditioniscalledresonance.Isolation.Iftheforcingfrequencyisincreasedabovefn,Rdecreases.Whenff=1.414fn,R=IandTr=1;athigherfrequenciesR<IandTr<1.AtfrequencieswhenR<I,thesystemissaidtobeinisolation.Thatis,someofthevibratorymotioninputisisolatedfromthesuspendedEffectsofMassandStiffnessVariations.FromEquation(1)itbeseenthatnaturalfrequencyisproportionaltothesquarerootofstiffness,K,andinverselyproportionaltothesquarerootofweight,W,ormass,M.Therefore,increasingthestiffnessofthespringordecreasingtheweightofthemassincreasesnaturalfrequency.Damisanyeffectthatremoveskineticand/orpotentialenergyfromthespringmasssystem.Itisusuallytheresultofviscous(fluid)orfrictionaleffects.Allmaterialsandstructureshavesomedegreeofinternaldam.Inaddition,movementthroughair,water,orotherfluidsabsorbsenergyandconvertsittoheat.Internalintermolecularorintercrystallinefrictionalsoconvertsmaterialstraintoheat.And,ofcourse,externalfrictionprovidesdam.Damcausestheamplitudeoffreevibrationtodecreaseovertime,andalsolimitsthepeaktransmissibilityinforcedvibration.ItisnormallycharacterizedbytheGreekletterzeta(),orbytheratioC/Cc,wherecistheamountofdaminthestructureormaterialandCcis"criticaldam."Mathematically,criticaldamisexpressedasCc=2(KM)1/2.Conceptually,criticaldamisthatamountofdamwhichallowsthedeflectedspringmasssystemtojustreturntoitsequilibriumpositionwithnoovershootandnooscillation.Anunderdampedsystemwillovershootandoscillatewhendeflectedandreleased.Anoverdampedsystemwillneverreturntoitsequilibriumposition;itapproachesequilibriumasymptotically.Displacement,Velocity,andSincevibrationisdefinedasoscillatorymotion,itinvolvesachangeofposition,ordisplacement(seeFigure1).Velocityisdefinedasthetimerateofchangeofdisplacement;accelerationisthetimerateofchangeofvelocity.SometechnicaldisciplinesusethetermjerktodenotethetimerateofchangeofSinusoidalMotionEquation.Thesingle-degree-of-freedomspringsystem,inforcedvibration,maintainedonstantdisplacementamplitude,exhibitssimpleharmonicmotion,orsinusoidalmotion.Thatis,itsdisplacementamplitudevs.timetracesoutasinusoidalcurve.GivenakdisplacementofX,frequencyf,andinstantaneousdisplacementx: (2)atanytime,VelocityEquation.Velocityisthetimerateofchangeofdisplacement,whichisthederivativeofthetimefunctionofdisplacement.Forinstantaneousvelocity,v: (3)Sincevibratorydisplacementismostoftenmeasuredintermsofpeak-to-peak,doubleamplitude,displacementD=2X: (4)Ifwelimitourinteresttothepeaplitudesandignorethetimevariationandphase (5)V=peakAccelerationEquation.Similarly,accelerationisthetimerateofchangeofvelocity,thederivativeofthevelocityexpression: (6) (7)A=peakItthuscanbeshownV A=22f2D=V/D=A/22Fromtheseequations,itcanbeseenthatlow-frequencymotionislikelytolow-amplitudeaccelerationseventhoughdisplacementmaybelarge.Itcsobeseenhigh-frequencymotionislikelytoexhibitlow-amplitudedisplacements,eventhoughaccelerationislarge.Considertwoexamples:At1Hz,1in.pk-pkdisplacementisonly~0.05gacceleration;10in.is~0.5g?At1000Hz,1gaccelerationisonly~0.00002in.displacement;100gis~0.002in.MeasuringVibratoryOpticalTechniques.Ifdisplacementislargeenough,asatlowfrequencies,itcanbemeasuredwithascale,calipers,orameasuringmicroscope.Athigherfrequencies,displacementmeasurementrequiresmoresophisticatedopticaltechniques.High-speedmoviesandcanoftenbeusedtomeasuredisplacementsandareespeciallyvaluableforvisualizingthemotionofcomplexstructuresandmechanisms.Thetwomethodsarelimitedbyresolutiontofairlylargedisplacementsandlowfrequencies.Strobelightsandstroboscopicphotographyarealsousefulwhendisplacementsarelargeenough,usually>0.1in.,tomakethempractical.Thechangeinintensityorangleofalightbeamdirectedontoareflectivesurfacecanbeusedasanindicationofitsdistancefromthesource.Ifthedetectionapparatusisfastenough,changesofdistancecanbedetectedaswell.Themos sitive,accurate,andpreciseopticaldeviceformeasuringdistanceordisplacementisthelaserinterferometer.Withthisapparatus,areflectedlaserbeamismixedwiththeoriginalincidentbeam.Theinterferencepatternsformedbythephasedifferencescanmeasuredisplacementdownto<100nm.NISTandothernationalprimarycalibrationagenciesuselaserinterferometersforprimarycalibrationofvibrationmeasurementinstrumentsatfrequenciesupto25kHz.ElectromagneticandCapacitiveSensors.Anotherimportantclassnoncontact,special-purposedisplacemen sorsisteralcategoryofproximitysensors.Theseareprobesthataretypicallybuiltintomachinerytodetectthemotionofshaftsinsidejournalbearingsortherelativemotionofothermachineelements.Thesensorsmeasurerelativedistanceorproximityasafunctionofeitherelectromagneticorcapacitive(electrostatic)couplingbetweentheprobeandthe.Becausethesedevicesrelyoninductiveorcapacitiveeffects,theyrequireanelectricallyconductive.Inmostcases,theymustbecalibratedforaspecificandspecificmaterialcharacteristicsinthegapbetweenprobeand.Electromagneticproximitysensorsareoftencallededdycurrentprobesbecauseoneofthemostpopulartypesuseseddycurrentsgeneratedintheasitsmeasurementmechanism.More y,thistypeofsensorusestheenergydissipatedbytheeddycurrents.Thegreaterthedistancefromprobeto,thelesselectromagneticcoupling,thelowerthemagnitudeoftheeddycurrents,andthelessenergytheydrainfromtheprobe.Otherelectromagneticprobessensethedistortionofanelectromagneticfieldgeneratedbytheprobeandusethatmeasurementtoindicatethedistancefromprobeto.Capacitiveproximitysensorsystemsmeasurethecapacitancebetweentheprobeandtheandarecalibratedtoconvertthecapacitancetodistance.Capacitanceisaffectedbythedielectricpropertiesofthematerialintheg wellasbydistance,socalibrationcanbeaffectedbyachangeoflubricantorcontaminationofthelubricantinamachineenvironment.ContactTechniques.Avarietyofrelativemotionsensorsusedirectcontacttwoobjectstomeasurerelativemotionordistancebetweenthem.TheseincludeLVDTs,positiontransducers(stringpots),andlinearpotentiometers.Allofthesedevicesdependonmechanicallinkagesandelectromechanicaltransducers.SeismicDisplacementTransducers.Thesedevices,discussedindetaillater,wereoncepopularbutnowareseldomused.Theytendtobelarge,heavy,andshortlived.DoubleIntegrationofAcceleration.Withtheincreasingavailabilityanddecreasingcostofdigitalsignalprocessing,moreapplicationsareusingthemoreruggedandversatileaccelerometersassensors,thendoubleintegratingtheaccelerationsignaltoderivedisplacements.Whileolderogintegrationtechniquestendedtobenoisyandinaccurate,digitalprocessingcanprovidequitehigh-quality,high-accuracyresults.MeasuringVibratoryTransducers.Someoftheearliest"high-frequency"vibrationmeasurementswerewithelectrodynamicvelocitysensors.Theseareatypeofseismictransducerthatincorporatesamagnetsupportedonasoftspringsuspensionsystemtoformtheseismic(springmass)system.Themagneticmemberissuspendedinahousingthatcontainsoneormoremultiturncoilsofwire.Whenthehousingisvibratedatfrequencieswellabovethenaturalfrequencyofthespringmasssystem,themass(magnet)isisolatedfromthehousingvibration.Thus,themagnetisessentiallystationaryandthehousing,withthecoils,movespastitatthevelocityofthestructuretowhichitisattached.Electricaloutputisgeneratedproportionaltothevelocityofthecoilmovingthroughthemagneticfield.Velocitytransducersareusedfrom~10HzuptoafewhundredHz.Theytendtobelargeandheavy,andeventuallywearandproduceerraticoutputs.LaserVibrometers.Laservibrometersorlaservelocimetersarerelativelyinstrumentscapableofprovidinghighsensitivityandaccuracy.Theyuseafrequency-modulated(typicallyaround44MHz)laserbeamreflectedfromavibratingsurface.ThereflectedbeamiscomparedwiththeoriginalbeamandtheDopplerfrequencyshiftisusedtocalculatethevelocityofthevibratingsurface.Alignmentandstandoffdistancearecritical.Becauseofthegeometricconstraintsonlocation,alignment,anddistances,theyarelimitedtolaboratoryapplications.Oneversionoflaservibrometerscansthelaserbeamacrossafieldofvision,measuringvelocityateachpoint.Thecompositecanthenbedisplayedasacontourmaporacolorizeddisplay.Thevibrationmapcanbesuperimposedonaimagetoprovidetheumamountofinformationaboutvelocityvariationsonalargesurface.IntegrationofAcceleration.Aswithdisplacementmeasurements,low-digitalsignalprocessingmakesitpracticaltouserugged,reliable,versatileaccelerometersassensorsandintegratetheiroutputtoderiveavelocitysignal.MeasuringVibratoryMostmodernvibrationmeasurementsaremadebymeasuringacceleration.Ifvelocityordisplacementdataarerequired,theaccelerationd anbeintegrated(velocity)ordoubleintegrated(displacement).Someaccelerometersignalconditionershavebuilt-inintegratorsforthatpurpose.Accelerometers(accelerationsensors,pickups,ortransducers)areavailableinawidevarietyofsizes,sh s,performancecharacteristics,andprices.Thefivebasictransducertypesareservoforcebalance;crystal-typeorpiezoelectric;piezoresistiveorsiliconstraingaugetype;integralelectronicspiezoelectric;andvariablecapacitance.Despitethedifferenectromechanicaltransductionmechanisms,alluseavariationofthespringmasssystem,andareclassifiedasseismicSeismicAccelerometerPrinciple.Allseismicaccelerometersusesomevariationofaseismicorproofmasssuspendedbyaspringstructureinacase(seeFigure3).Whenthecaseisaccelerated,theproofmassisalsoacceleratedbytheforcetransmittedthroughthespringstructure.Thenthedisplacementofthespring,thedisplacementofthemasswithinthecase,ortheforcetransmittedbythespringistransducedintoanelectricalsignalproportionaltoacceleration.Accelerometers.Transducersdesignedtomeasurevibratoryaccelerationarecalledaccelerometers.Therearemanyvarietiesincludingstraingauge,servoforcebalance,piezoresistive(siliconstraingauge),piezoelectric(crystal-type),variablecapacitance,andintegralelectronicpiezoelectric.Eachbasictypehasmanyvariationsandtradenames.Mostmanufacturersprovideexcellentapplicationsengineeringassistancetohelptheuserchoosethebesttypefortheapplication,butbecausemostofthesesourcessellonlyoneortwotypes,theytendtobiastheirassistanceaccordingly.Formostapplications,my albiasistowardpiezoelectricaccelerometerswithinternalelectronics.Theprimarylimitationofthesedevicesistemperaturerange.Althoughtheyexhibitlow-frequencyroll-off,theyareavailablewithextremelylow-frequencycapabilities.Theyprovideapreamplifiedlow-impedanceoutput,simplecabling,andsimplesignalconditioning,andgenerallyhavethelowestoverallsystemcost.MostimportanttotheuseraretheperformanceandenvironmentalspecificationsandtheWhat'sinsidetheboxisirrelevantiftheinstrumentmeetstherequirementsoftheapplication,butwhenaddingtoexistinginstrumentationitisimportanttobesurethattheaccelerometeriscompatiblewiththesignalconditioning.Eachtypeofaccelerometerrequiresadifferenttypeofsignalconditioning.AccelerometerTypes.Themostcommonseismictransducersforshockandvibrationmeasurementsare:Piezoelectric(PE);high-impedanceIntegralelectronicspiezoelectric(IEPE);low-impedancePiezoresistive(PR);siliconstraingaugeVariablecapacitance(VC);low-level,low-ServoforcePiezoelectric(PE)sensorsusethepiezoelectriceffectsofthesensingelement(s)toproduceachargeoutput.Because sensordoesnotrequireanexternalpowersourceforoperation,itisconsideredself-generating.The"spring"sensingelementsprovideagivennumberofelectronsproportionaltotheamountofappliedstress(piezeinisaGreekwordmeaningtosqueeze).Manynaturalandman-madematerials,mostlycrystalsorceramicsandafewpolymers,displaythischaracteristic.Thesematerialshavearegularcrystallinemolecularstructure,withanetchargedistributionthatchangeswhenstrained.Piezoelectricmaterialsmayalsohaveadipole(whichisthenetseparationofpositiveandnegativechargealongaparticularcrystaldirection)whenunstressed.Inthesematerials,fieldscanbegeneratedbydeformationfromstressortemperature,causingpiezoelectricorpyroelectricoutput,respectively.Thepyroelectricoutputscanbeverylargeunwantedsignals,generallyoccurrin thelongtimeperiodsassociatedwithmosttemperaturechanges.PolymerPEmaterialshavesuchhighpyroelectricoutputthattheywereoriginallyusedasthermaldetectors.Therearethreepyroelectriceffects,whichwillbediscussedlaterindetail.Chargesareactuallynot"generated,"butratherjustdisplaced.(Likeenergyandmomentum,chargeisalwaysconserved.)Whenanelectricfieldisgeneratedalongthedirectionofthedipole,metallicelectrodesonfacesattheoppositeextremesofthegradientproducemobileelectronsthatmovefromoneface,throughthesignalconditioning,totheothersideofthesensortocancelthegeneratedfield.Thetyofelectronsdependsonthevoltagecreatedandthecapacitancebetweentheelectrodes.Acommonunitofchargefromaccelerometeristhepicocoulomb,or10-12coulomb,whichissomethin er6×106electrons.ChoosingamongthemanytypesofPEmaterialsentailsatradeoffamongchargesensitivity,dielectriccoefficient(which,withgeometry,determinesthecapacitance),thermalcoefficients,umtemperature,frequencycharacteristics,andstability.ThebestS/Nratiosgenerallycomefromthehighestpiezoelectriccoefficients.Naturallyoccurringpiezoelectriccrystalssuchastourmalineorquartzgenerallylow-chargesensitivity,aboutone-hundredththatofthemorecommonlyusedferroelectricmaterials.(Buttheselow-chargeoutputmaterialsaretypicallyusedinthevoltagemode,whichwillbediscussedlater.)Allowingsmallersizeforagivensensitivity,ferroelectricmaterialsareusuallyman-madeceramicsinwhichthecrystallines(i.e.,regionsinwhichdipolesarenaturallyaligned)arethemselvesalignedbyaprocessofartificialpolarization.Polarizationusuallyoccursattemperaturesconsiderablyhigherthanoperatingtemperaturestospeedtheprocessofalignmentofthes.Depolarization,orrelaxation,canoccuratlowertemperatures,butatverymuchlowerrates,andc sooccurwithappliedvoltagesandpreloadpressures.Depolarizationalwaysresultsintemporaryorpermanentlossofsensitivity.Tourmaline,anaturalcrystalthatdoesnotundergodepolarization,isparticularlyusefulatveryhighBecausetheyareself-generating,PEtransducerscannotbeusedtomeasuresteady-stateaccelerationsorforce,whichwouldputafixedamountofenergyintothecrystal(aone-waysqueeze)andthereforeafixednumberofelectronsattheelectrodes.Conventionalvoltagemeasurementwouldbleedelectronsaway,asdoesthesensor'sinternal.(Hightemperatureorhumidityinthetransducerwouldexacerbatetheproblembyreducingthevalue.)Energywouldbedrainedandtheoutputwoulddecay,despitetheconstantinputExternalmeasurementofPEtransducervoltageoutputrequiresspecialattentiontothecable'sdynamicbehavioraswellastheinputcharacteristicsofthepreamplifier.Sincecablecapacitancedirectlyaffectsthesignalamplitude,excessivemovementofthecableduringmeasurementcancausechangesinitscapacitanceandshouldbeavoided.Closeattentionshouldalsobepaidtothepreamp'sinputimpedance;thisshouldbeontheorderof1000M orhighertoensuresufficientlow-frequencyresponse.Inpractice,achargeamplifierisnormallyused Insteadofmeasuringvoltageexternally,achargeshouldbemeasuredwithachargeItisahigh-impedanceopampwithacapacitorasitsfeedback.Itsoutputisproportionaltothechargeattheinputandthefeedbackcapacitor,andisnearlyunaffectedbytheinputcapacitanceofthetransducerorattachedcables.Thehigh-passcornerfrequencyissetbythefeedbackcapacitorandresistorinachargeconverter,andnotthetransducercharacteristics.(Thetransducerchangesnoisecharacteristics,notthefrequency.)Iftimeconstantsarelongenough,theAC-coupledtransducerwillsufficeformostvibrationmeasurements.Perhapsthemostimportantlimitationofhigh-impedanceoutputPEtransducersisthattheymustbeusedwith"noise-treated"cables;otherwise,motioninthecablecandisplacetriboelectriccharge,whichaddstothechargemeasuredbythechargeconverter.Triboelectricnoiseisacommonsourceoferrorfoundintypicalcoaxialcables.MostPEtransducersareextremelyrugged.Eachofthevarioussh sandsizesavailablecomeswithitsownperformancecompromises.Themostcommontypesofthistransducerarecompressionandsheardesigns.Sheardesignoffersbetterisolationfromenvironmentaleffectssuchasthermaltransientandbasestrain,andisgenerallymoreexpensive.Beam-typedesign,avariationofthecompressiondesign,isalsoquitepopularduetoitslowermanufacturingcost.Butbeamdesignisgenerallymorefragileandhaslimitedbandwidth.IntegralElectronicsPiezoelectric(IEPE).Manypiezoelectricaccelerometers/forcetransducersincludeintegralminiaturehybridamplifiers,which,amongotheradvantages,donotneednoise-treatedcable.Mostrequireanexternalconstantcurrentpowersource.Boththeinputsupplycurrentandoutputsignalarecarriedoverthesametwo-wirecable.Thelow-impedanceoutputoftheIEPEdesign(seeFigure5)providesrelativeimmunitytotheeffectsofpoorcableinsulation,triboelectricnoise,andstraysignalpickup.Output-to-weightratioofIEPEishigherthanwithPEtransducers.Additionalfunctionscanbeincorporatedintotheelectronics(seeFigure6),includingfilters,overlorotection,andself-LowercostcableandconditioningcanbeusedsincetheconditioningrequirementsarecomparativelylaxcomparedtoPEorPR.ThesensitivityofIEPEaccelerometers/forcetransducers,incontrasttoPR,isnotsignificantlyaffectedbysupplychanges.Instead,dynamicrange,thetotalpossibleswingoftheoutputvoltage,isaffectedbybiasandcompliancevoltages.Onlywithlargevariationsincurrentsupplywouldtherebeproblemswithfrequencyresponsewhendrivinghigh-capacitanceAdisadvantageofbuilt-inelectronicsisthatitgenerallylimitsthetransducertoanarrowertemperaturerange.Incomparisonwithanidenticaltransducerdesignthatdoesnothaveinternalelectronics,thehigh-impedanceversionwillalwayshaveahighermebetweenfailures(MTBF)rating.Inaddition,thenecessarilysmallsizeoftheamplifiermayprecludesomeofthedesirablefeaturesofferedbyafull-blownlaboratoryamplifier,suchastheabilitytodrivelongcable.Slewlimitingisthereforeaconcernwiththesetransducers(somedesignshaverelativelyhighoutputimpedance)whendrivinglonglinesorothercapacitiveloads.Theproblemcanberemediedbyincreasingtheamountofdrivecurrentwithinthelimitspecifiedbythemanufacturer.Thecircuitsneedno