力力矩壓力測(cè)量E

力、力矩、壓力測(cè)量17.1Introduction7.1.1Force(1)Whatistheforce?Forceisoneofthemostimportantphysicalparameters.Variousmechanicalmotionisvirtuallythetransmissionofforceortorque.Forcepossessesthecapabilityinbothstaticanddynamicphenomenon:itcanchangethebody’smotionstatusorcausebody’sdeformation.2(2)unitofforceN(Newton):istheforcewhichwhenappliedtoamassofonekilogramgivesitanaccelerationof1m/s2.(3)Weight:istheforceexertedonabodyofmassmduetoearthgravity.G=mg;gisthelocalgravityacceleration,typicallyabout9.8m/s2.Weightmeasurementisusuallyspecifiedintermsofthemass.3(4)Torque(力矩、扭矩、轉(zhuǎn)矩）Torqueissometimescalledmoment.Itistheproductofaforceanditsarm.Forarotatingshaftofradiusr,thetorqueTappliedtotheshafttocauseittorotateisF×r,whereFisthetangentialforceattheradiusr.Whenashaftistwistedasaresultoftheapplicationofatorque,shearstressesandstrainareproducedintheshaftmaterial.4(5)PressureAforceFperpendiculartoanareaA,thepressurePisP=F/Aunit:Pascal(Pa)

1Pa=1N/m2

Atmosphericpressure:theatmospheresurroundingtheearthexertsaforceontheunitearthsurface,thatisthepressurecausedbytheweightoftheatmosphere.Itvarieswithweathercondition,theheightabovesealevel,latitude.5Positivepressure:thegaugepressurehigherthantheatmosphericpressure.Gaugepressure:thepressuremeasuredrelative

totheatmosphericpressure.Thedifferentialpressurebetweentheabsolutepressureandtheatmosphericpressure.Absolutepressure:usedforthepressure

measuredrelativetozeropressure.6Negativepressure:thegaugepressurelowerthantheatmosphericpressure.Vacuum:theabsolutepressurelowerthanatmosphere.77.2Measurementmethods7.2.1Forcemeasurementmethods(1)AccordingtostaticordynamiceffectStaticeffect-----thestaticforcecausesmechanicaldeformation.Bymeasuringthedeformationorusingsomeinnerstressorforcerelatedphysicaleffects.Dynamiceffect----accordingtotheNewton2ndlaw,theforceisassociatedwithacceleration.Knowingmassandaccelerationmeasured,theforcecanbedefined:F=ma8ForcemeasurementLeverbalancemethodsBasedontheprincipleofmomentsi.e.atstaticequilibriumthealgebraicsumoftheclockwisemomentsaboutanaxisequalstheanticlockwisemoments.Themomentofaforceaboutanaxisistheproductoftheforceandtheperpendiculardistancefromitslineofactiontotheaxis.Thismethodistypicallyusedforweightsupto1000Kg.2.Forcebalancemethods3.Elasticelementmethods4.Pressuremethods(2)accordingtothemethodsusingdifferentstructure&instruments9一種伺服式測(cè)力系統(tǒng)。無(wú)外力作用時(shí)，系統(tǒng)處于初始平衡位置，光線全部被遮住，光敏元件無(wú)電流輸出，力發(fā)生器不產(chǎn)生力矩。當(dāng)被測(cè)力F作用在杠桿上時(shí)，系統(tǒng)失去平衡，杠桿發(fā)生偏轉(zhuǎn)，窗口打開(kāi)相應(yīng)的縫隙。光線通過(guò)縫隙，照射到光敏元件上，光敏元件輸出與光照成比例的電信號(hào)，經(jīng)放大后加到磁電力矩發(fā)生器的旋轉(zhuǎn)線圈上。載流線圈與磁場(chǎng)相互作用而產(chǎn)生電磁力矩，用于平衡被測(cè)力F與配重(標(biāo)準(zhǔn)質(zhì)量m)力的力矩之差；使杠桿重新處于平衡狀態(tài)。當(dāng)杠桿處于新的平衡位置時(shí)，其轉(zhuǎn)角與被測(cè)力F成正比，放大器輸出電信號(hào)在采樣電阻R上的電壓U0與被測(cè)力F成比例。磁電式力平衡測(cè)力系統(tǒng)Forcebalancemethods10ElasticelementmethodsSensorsthatareusedformeasurementofforce,torqueorpressureoftencontainanelasticelementthatconvertsthemechanicalquantityintoadeflectionorstrainwhichcanthenbetransformedusinganothersensorintoanelectricalsignal.Electricalresistancestraingaugesarewidelyusedinthiscapacity.11Ingeneral,elasticelementsusedforthemeasurementofforcecanbeconsideredtorepresentedbythemodelshowninFig.Whenaforcef(t)actsonthemassofelement,adisplacementisproducedwhichvarieswithtimebeforeobtainingasteady-statevalue.Thedisplacementvariationwithtimeisdescribedbyasecondorderdifferentialequation.Inpractice,oftenitisnotthedisplacementitselftobemeasuredbutthestrainexperiencedbyastraingaugeattachedtowhatisequivalentofthespring.dampingspring12Diagramofstraingauge13Variousformsofelasticmembersareused.Thesimplestisjustaspringtomakeadevicecalledspringbalance.Theextensionofthespringrepresentstheforceapplied.Loadcells,i.e.elasticmemberswhichtransformforceintodisplacementorstrains,cantakemanyforms.14Thestructureoftypicalelasticelementanditsdesigningcalculationasfollows:Columnarloadcell15Provingring測(cè)力環(huán)BendingbeamAppliedforce16Therelativeextensionofstraingaugeinelasticelement:Δl-------Totalextensionofstraingaugel--------theoriginallengthofstraingaugeF------appliedforceA------workingareaofelasticelementE------Yangmodelofelasticelementσ------stressofelasticelement17Sensitivity:

----poisonconstantofelasticelementTotalstrainofelasticelement:Outputofelectricalbridge:Ingeneral,selectk=2

,Voltagesensitivity(mv/v):18Otherprincipleofforcemeasurement(1)Piezoelectricdynamometry

壓電式測(cè)力儀利用壓電材料(石英晶體、壓電陶瓷）的壓電效應(yīng)，將被測(cè)力經(jīng)彈性元件轉(zhuǎn)換為與其成正比的電荷量輸出，通過(guò)測(cè)量電路測(cè)出輸出電荷，從而實(shí)現(xiàn)對(duì)力值的測(cè)量。彈性元件感受力F時(shí)壓電材料產(chǎn)生電荷Q輸出dij:Piezoelectricconstant適用于動(dòng)態(tài)力的測(cè)量19

由工業(yè)純鐵、硅鋼等鐵磁材料制成的鐵心在機(jī)械力的作用下磁導(dǎo)率發(fā)生變化稱為壓磁效應(yīng)，或稱磁彈性效應(yīng)。如圖a所示，在鐵心上安置一對(duì)線圈一勵(lì)磁線圈和測(cè)量線圈。兩線圈的平面相互垂直,若無(wú)外力作用，勵(lì)磁線圈中心交流電流所建立的磁場(chǎng)對(duì)測(cè)量線圈沒(méi)有輸出，見(jiàn)圖b。若外力作用在鐵心上，鐵心磁導(dǎo)率改變，則測(cè)量線圈被勵(lì)磁線圈中的磁場(chǎng)交鏈而輸出比例于外力大小的信號(hào)，見(jiàn)圖c。

Piezomagneticdynamometry20Torquemeasurement

Torquemeasurementareusedforrotatingshaftstodeterminethepowertransmittedandalsotomonitoragainstfailureasaresultofshearstress.Themeasurementoftorqueisalwayslinkedwiththepowerandrotatingspeed.Theworkdoneistheproductoftheforceandthedistancetraveledinthedirectionoftheforce.Workdonepersecond=F×2

rn=(Powertransmittedbyarotatingshaft=2

nT=T)F:TangentialforceataradiusrT:Torqueappliedtoashafttocauseittorotate.21Basicmethodsoftorquemeasurement：（1）Transmissionmethod(扭軸法）（2）Forcebalancemethod（3）Powertransformationmethod22(1)Whenatorqueappliedtoanelasticshaft,asaresult,theshaftistwistedandshearstressandstrainsareproducedintheshaftmaterial.G:shearmodelofmaterial；:TorsionangleIP:polarsecondmoment(極慣性矩)23Whenthetorsionanglemeasured:Whentheshearstressofshaftmeasured:Whenthestrainofshaftmeasured:

45、135

:thestrainsalongthedirectionof45o、135orelatedtoaxisoftheshaft.241.電阻應(yīng)變式轉(zhuǎn)矩儀在轉(zhuǎn)軸上或直接在被測(cè)軸上，沿軸線的45?；?35。方向?qū)?yīng)變片粘貼上，當(dāng)轉(zhuǎn)軸受轉(zhuǎn)矩M作用時(shí)，應(yīng)變片產(chǎn)生應(yīng)變，其應(yīng)變量與轉(zhuǎn)矩M成線性關(guān)系。對(duì)空心圓柱形軸：對(duì)方形截面軸：G為轉(zhuǎn)軸的彈性模量25Whenthetorqueismeasuredforarotatingshaft,itisnecessarytoobtaintheoutputsignalfromthebridgeconnectionofthestraingaugeswhichareontherotatingshaftandprovidethed.c.supplyvoltageforthebridge.Onemethodofdoingthisisviasliprings.Aproblemwithsuchanarrangementisthenoisegeneratedbyvariationsincontactresistancebetweentheringsandthebrushes.26Analternativemethodistomounttheentirebridge,togetherwithitsvoltagesupply,ontherotatingshaftandusethebridgeoutputtomodulatearadiosignalwhichisthentransmittedtonearby,stationary,equipmentfordisplayorrecording.272829(2)力平衡法它是利用平衡轉(zhuǎn)矩M0去平衡被測(cè)轉(zhuǎn)矩M，從而求得M的方法。當(dāng)轉(zhuǎn)軸受轉(zhuǎn)矩作用時(shí)，機(jī)體上必定同時(shí)作用著方向相反的平衡力矩(或稱支座反力矩)，因此測(cè)量出機(jī)體上的平衡力矩就可以知被測(cè)轉(zhuǎn)矩大小。30圖為反力法測(cè)量小轉(zhuǎn)矩的測(cè)試系統(tǒng)。由測(cè)量軸2、靜壓空氣支承3、角位移傳感器5、力矩電動(dòng)機(jī)4和標(biāo)準(zhǔn)電阻Ro及電路組成。31(3)能量轉(zhuǎn)換法這是按能量守恒定律來(lái)測(cè)量力矩的儀器。它是通過(guò)測(cè)量其它與轉(zhuǎn)矩有關(guān)的能量系數(shù)(如電能系數(shù))來(lái)確定被測(cè)力矩大小的。根據(jù)能量轉(zhuǎn)換法制作的測(cè)力矩儀一般多用于測(cè)量各種電機(jī)的轉(zhuǎn)矩。因其影響因素較多測(cè)量誤差大，所以只有測(cè)量電參數(shù)的電機(jī)轉(zhuǎn)矩測(cè)量?jī)x應(yīng)用較多。32PressuremeasurementTogetherwithtemperatureandflow,pressureisthemostimportantparametersinindustrialprocesscontrolTheunitofpressureisthePascal(Pa)with1Pabeing1N/m2Atthesurfaceoftheearth,theatmosphericpressureisgenerallyabout100KPa.Thisissometimesreferredtoasapressureof1bar.331.Manometers（液體式壓力計(jì)）U-tubemanometerThecisternmanometerTheinclinedtubemanometer2.Diaphragms(薄膜，彈性式壓力計(jì)）ReluctancediaphragmgaugeCapacitancediaphragmgaugeStraingaugediaphragmgaugeForce-balancediaphragmgaugePiezoelectricdiaphragmgauge3.Bourdontubes34Dead-WeightTesterSchematic

Calibrationofthepressuregaugesintheregionof20Pato2000kPaisgenerallybymeansoftheDead-weighttester.Pressureisproducedbywindinginapiston.Thepressureisdeterminedbyaddingweightstotheplatformsothatitremainsataconstantheight.35P2P1ThebasicmanometerconsistsofaU-tubecontainingaliquid.Apressuredifferencebetweenthegasesabovetheliquidinthetwolimbsproducesadifferencehinverticalheightsoftheliquidinthetwolimbs.Ifoneofthelimbsisopentotheatmospherethenthepressuredifferenceisthegaugepressure.Manometers36Water,alcoholandmercuryarecommonlyusedmanometricliquids.U-tubemanometersaresimpleandcheapandcanbeusedforpressuredifferencesintherange20Pato140KPa.Theaccuracyistypicallyabout1%.Temperatureaffect---------liquidexpansion37ThusthepressurewhenmeasuredbyaU-tubemanometeratatemperature,whenthemanometerliquiddensityat0°Cisknown,isgivenby:38CisternmanometerAnindustrialformoftheU-tubemanometeriscisternmanometer.Ithasoneofthelimbswithamuchgreatercross-sectionalareathantheother.Adifferenceinpressurebetweenthetwolimbscausesadifferenceinliquidlevelwithliquidflowingfromonelimbtotheother.HhdP1P2A2A139Thisformofmanometerthusonlyrequirethelevelofliquidinonelimbtobemeasuredfromafixedpoint.40TheinclinedtubemanometerTheinclinedtubemanometerisaU-tubemanometerwithonelimbhavingalargercross-sectionthantheotherandthenarrowerlimbbeinginclinedatsomeangletothehorizontal.ItisgenerallyusedforthemeasurementofsmallpressuredifferencesandgivesgreateraccuracythantheconventionalU-tubemanometer.

41

HdhxP1P2SinceA2ismuchgreaterthanA1,theequationapproximatesto:Initialzerolevelwithnopressuredifference42Bourdontubes43Thebourdontubemaybeintheformofa“C”,aflatspiral,ahelicalspiral.Inallforms,anincreaseinthepressureinthetubecausesthetubetostraightenouttoanextentwhichdependsonthepressure.Thisdisplacementmaybemonitoredinavarietyofways,forexample,todirectlymoveapointeracrossascale,tomoveasliderofapotentiometer,tomovethecoreofanLVDT.44Withdiaphragmpressuregauges,adifferenceinpressurebetweentwosidesofadiaphragmresultsinitblowingouttoonesideortheother.Ifthefluidforwhichthepressureisrequiredisadmittedtoonesideofthediaphragmandtheothersideisopentotheatmosphere,thediaphragmgaugegivesthegaugepressure.Iffluidsatdifferentpressuresareadmittedtothetwosidesofthediaphragm,thegaugegivesthepressuredifference.Diaphragms451Reluctancediaphragmgauge

(磁阻隔膜壓力計(jì)）Thedisplacementofthecentralpartofthediaphragmincreasesthereluctanceofthecoilononesideofthediaphragmanddecreasesitontheother.Withthetwocoilsconnectedinoppositearmsofana.c.bridge,theoutofbalancevoltageisrelatedtothepressuredifferencecausingthediaphragmdisplacement46Capacitancepressuretransducerswereoriginallydevelopedforuseinlowvacuumresearch.Thiscapacitancechangeresultsfromthemovementofadiaphragmelement.Thediaphragmisusuallymetalormetal-coatedquartzandisexposedtotheprocesspressureononesideandtothereferencepressureontheother.Dependingonthetypeofpressure,thecapacitivetransducercanbeeitheranabsolute,gauge,ordifferentialpressuretransducer.47Thediaphragmisbetweentwofixedplatesanditsmovementthusincreasesthecapacitancewithrespecttoonefixedplateanddecreasesitwithrespecttotheother.

AsshowninFigure，thedeflectionofthediaphragmcausesachangeincapacitancethatisdetectedbyabridgecircuit.Thecapacitorcanalsoformpartofthetuningcircuitofafrequencymodulatedoscillatorandsogiveanelectricaloutputrelatedtothepressuredifferenceacrossthediaphragm.48式中，E為彈性膜片的彈性模量；u為材料的泊松比49PotentiometricPressureTransducer

(forcebalancebellowgauge)50Measurementoflowpressures(vacuum)Vacuumtendstobeusedforpressureslessthantheatmosphericpressure,namely1.013×105Pa.Aunitthatisoftenusedforsuchpressureisthetorr(托）,thisbeingthepressureequivalenttothatgivenbyacolumnofmercuryofheight1mm.1mmHg=133.322Pa=1torrAtmosphericpressureisabout760mmHgThelowertheabsolutepressureis,thehigherthedegreeofvacuumis.51

現(xiàn)在真空技術(shù)在生產(chǎn)、科研中的用途愈來(lái)愈廣，在整個(gè)真空范圍內(nèi)所采用的測(cè)量方法也是多種多樣的。按測(cè)量方法的原理來(lái)分可以分為：基于力的作用原理：U形管，波登管式，波紋管式，膜片式；基于壓縮作用原理：麥?zhǔn)险婵沼?jì)；基于導(dǎo)熱作用原理：電阻真空計(jì)，熱電偶真空計(jì)；基于電離作用原理：熱陰極式，冷陰極式，放射性真空計(jì)。52

U形管真空計(jì)是最簡(jiǎn)單的真空計(jì)。其結(jié)構(gòu)原理如圖所示。一根由玻璃管制成的U形管中盛上水銀或油,U形管一端接到真空系統(tǒng)上，另一端為大氣。隨著系統(tǒng)中真空度的升高，U形管真空側(cè)的液面在大氣作用下隨之上升。這樣，依據(jù)兩管中校面的高度差，就可以測(cè)得真空系統(tǒng)中的真空度，即p=pa-h，其中p為系統(tǒng)中真空度，pa為大氣壓值，h為兩液面之差。53（2）壓縮真空計(jì)

利用波義耳定律，將被測(cè)真空系統(tǒng)中一定的殘余氣體加以壓縮，比較壓縮前后體積、壓力的變化，即能算出真空度。玻義耳-馬略特定律

它反映氣體的體積隨壓強(qiáng)改變而改變的規(guī)律。對(duì)于一定質(zhì)量的氣體，在其溫度保持不變時(shí)，它的壓強(qiáng)和體積成反比；或者說(shuō)，其壓強(qiáng)P與它的體積V的乘積為一常量，即PV=C（常數(shù)）（T不變時(shí)）或P1V1＝P2V2=…=PnVn實(shí)際氣體只是在壓強(qiáng)不太高、溫度不太低的條件下才服從這一定律。54麥克勞真空計(jì)麥?zhǔn)嫌?jì)是一種絕對(duì)真空計(jì)，測(cè)量范圍為1.3xl03－1.3×10－8帕，精度較高，可作為其它真空計(jì)的標(biāo)準(zhǔn)。它是于1874年由麥克勞研制的，故命名為麥克勞真空計(jì)，簡(jiǎn)稱麥?zhǔn)嫌?jì)。其結(jié)構(gòu)如圖3．2所示。主要由毛細(xì)管A、毛細(xì)管B、玻璃泡、導(dǎo)液管、水銀瓶構(gòu)成。55毛細(xì)管A、玻璃泡及下面一段管子(到a-a面為止)的體積為V1。測(cè)量前需用油封機(jī)械泵將水銀瓶抽真空，使水銀面處于a-a位置。這時(shí)，玻璃泡與真空系統(tǒng)相通，其壓強(qiáng)與真空系統(tǒng)相同，均為p。轉(zhuǎn)動(dòng)切換閥門，切斷油封機(jī)械泵，使水銀瓶與干燥空氣相通。此時(shí)，水銀瓶中水銀在干燥空氣壓力作用下，沿導(dǎo)液管上升，充滿玻璃泡．然后沿毛細(xì)管A上升，使玻璃泡和毛細(xì)管A中氣體被壓縮到毛細(xì)管A的頂部，其體