力力矩压力测量E

力、力矩、压力测量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、转矩）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&instruments9一种伺服式测力系统。无外力作用时，系统处于初始平衡位置，光线全部被遮住，光敏元件无电流输出，力发生器不产生力矩。当被测力F作用在杠杆上时，系统失去平衡，杠杆发生偏转，窗口打开相应的缝隙。光线通过缝隙，照射到光敏元件上，光敏元件输出与光照成比例的电信号，经放大后加到磁电力矩发生器的旋转线圈上。载流线圈与磁场相互作用而产生电磁力矩，用于平衡被测力F与配重(标准质量m)力的力矩之差；使杠杆重新处于平衡状态。当杠杆处于新的平衡位置时，其转角与被测力F成正比，放大器输出电信号在采样电阻R上的电压U0与被测力F成比例。磁电式力平衡测力系统Forcebalancemethods10ElasticelementmethodsSensorsthatareusedformeasurementofforce,torqueorpressureoftencontainanelasticelementthatconvertsthemechanicalquantityintoadeflectionorstrainwhichcanthenbetransformedusinganothersensorintoanelectricalsignal.Electricalresistancestraingaugesarewidelyusedinthiscapacity.11Ingeneral,elasticelementsusedforthemeasurementofforcecanbeconsideredtorepresentedbythemodelshowninFig.Whenaforcef(t)actsonthemassofelement,adisplacementisproducedwhichvarieswithtimebeforeobtainingasteady-statevalue.Thedisplacementvariationwithtimeisdescribedbyasecondorderdifferentialequation.Inpractice,oftenitisnotthedisplacementitselftobemeasuredbutthestrainexperiencedbyastraingaugeattachedtowhatisequivalentofthespring.dampingspring12Diagramofstraingauge13Variousformsofelasticmembersareused.Thesimplestisjustaspringtomakeadevicecalledspringbalance.Theextensionofthespringrepresentstheforceapplied.Loadcells,i.e.elasticmemberswhichtransformforceintodisplacementorstrains,cantakemanyforms.14Thestructureoftypicalelasticelementanditsdesigningcalculationasfollows:Columnarloadcell15Provingring测力环BendingbeamAppliedforce16Therelativeextensionofstraingaugeinelasticelement:Δl-------Totalextensionofstraingaugel--------theoriginallengthofstraingaugeF------appliedforceA------workingareaofelasticelementE------Yangmodelofelasticelementσ------stressofelasticelement17Sensitivity:

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

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

压电式测力仪利用压电材料(石英晶体、压电陶瓷）的压电效应，将被测力经弹性元件转换为与其成正比的电荷量输出，通过测量电路测出输出电荷，从而实现对力值的测量。弹性元件感受力F时压电材料产生电荷Q输出dij:Piezoelectricconstant适用于动态力的测量19

由工业纯铁、硅钢等铁磁材料制成的铁心在机械力的作用下磁导率发生变化称为压磁效应，或称磁弹性效应。如图a所示，在铁心上安置一对线圈一励磁线圈和测量线圈。两线圈的平面相互垂直,若无外力作用，励磁线圈中心交流电流所建立的磁场对测量线圈没有输出，见图b。若外力作用在铁心上，铁心磁导率改变，则测量线圈被励磁线圈中的磁场交链而输出比例于外力大小的信号，见图c。

Piezomagneticdynamometry20Torquemeasurement

Torquemeasurementareusedforrotatingshaftstodeterminethepowertransmittedandalsotomonitoragainstfailureasaresultofshearstress.Themeasurementoftorqueisalwayslinkedwiththepowerandrotatingspeed.Theworkdoneistheproductoftheforceandthedistancetraveledinthedirectionoftheforce.Workdonepersecond=F×2

rn=(Powertransmittedbyarotatingshaft=2

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

45、135

:thestrainsalongthedirectionof45o、135orelatedtoaxisoftheshaft.241.电阻应变式转矩仪在转轴上或直接在被测轴上，沿轴线的45。或135。方向将应变片粘贴上，当转轴受转矩M作用时，应变片产生应变，其应变量与转矩M成线性关系。对空心圆柱形轴：对方形截面轴：G为转轴的弹性模量25Whenthetorqueismeasuredforarotatingshaft,itisnecessarytoobtaintheoutputsignalfromthebridgeconnectionofthestraingaugeswhichareontherotatingshaftandprovidethed.c.supplyvoltageforthebridge.Onemethodofdoingthisisviasliprings.Aproblemwithsuchanarrangementisthenoisegeneratedbyvariationsincontactresistancebetweentheringsandthebrushes.26Analternativemethodistomounttheentirebridge,togetherwithitsvoltagesupply,ontherotatingshaftandusethebridgeoutputtomodulatearadiosignalwhichisthentransmittedtonearby,stationary,equipmentfordisplayorrecording.272829(2)力平衡法它是利用平衡转矩M0去平衡被测转矩M，从而求得M的方法。当转轴受转矩作用时，机体上必定同时作用着方向相反的平衡力矩(或称支座反力矩)，因此测量出机体上的平衡力矩就可以知被测转矩大小。30图为反力法测量小转矩的测试系统。由测量轴2、静压空气支承3、角位移传感器5、力矩电动机4和标准电阻Ro及电路组成。31(3)能量转换法这是按能量守恒定律来测量力矩的仪器。它是通过测量其它与转矩有关的能量系数(如电能系数)来确定被测力矩大小的。根据能量转换法制作的测力矩仪一般多用于测量各种电机的转矩。因其影响因素较多测量误差大，所以只有测量电参数的电机转矩测量仪应用较多。32PressuremeasurementTogetherwithtemperatureandflow,pressureisthemostimportantparametersinindustrialprocesscontrolTheunitofpressureisthePascal(Pa)with1Pabeing1N/m2Atthesurfaceoftheearth,theatmosphericpressureisgenerallyabout100KPa.Thisissometimesreferredtoasapressureof1bar.331.Manometers（液体式压力计）U-tubemanometerThecisternmanometerTheinclinedtubemanometer2.Diaphragms(薄膜，弹性式压力计）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

(磁阻隔膜压力计）Thedisplacementofthecentralpartofthediaphragmincreasesthereluctanceofthecoilononesideofthediaphragmanddecreasesitontheother.Withthetwocoilsconnectedinoppositearmsofana.c.bridge,theoutofbalancevoltageisrelatedtothepressuredifferencecausingthediaphragmdisplacement46Capacitancepressuretransducerswereoriginallydevelopedforuseinlowvacuumresearch.Thiscapacitancechangeresultsfromthemovementofadiaphragmelement.Thediaphragmisusuallymetalormetal-coatedquartzandisexposedtotheprocesspressureononesideandtothereferencepressureontheother.Dependingonthetypeofpressure,thecapacitivetransducercanbeeitheranabsolute,gauge,ordifferentialpressuretransducer.47Thediaphragmisbetweentwofixedplatesanditsmovementthusincreasesthecapacitancewithrespecttoonefixedplateanddecreasesitwithrespecttotheother.

AsshowninFigure，thedeflectionofthediaphragmcausesachangeincapacitancethatisdetectedbyabridgecircuit.Thecapacitorcanalsoformpartofthetuningcircuitofafrequencymodulatedoscillatorandsogiveanelectricaloutputrelatedtothepressuredifferenceacrossthediaphragm.48式中，E为弹性膜片的弹性模量；u为材料的泊松比49PotentiometricPressureTransducer

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

现在真空技术在生产、科研中的用途愈来愈广，在整个真空范围内所采用的测量方法也是多种多样的。按测量方法的原理来分可以分为：基于力的作用原理：U形管，波登管式，波纹管式，膜片式；基于压缩作用原理：麦氏真空计；基于导热作用原理：电阻真空计，热电偶真空计；基于电离作用原理：热阴极式，冷阴极式，放射性真空计。52

U形管真空计是最简单的真空计。其结构原理如图所示。一根由玻璃管制成的U形管中盛上水银或油,U形管一端接到真空系统上，另一端为大气。随着系统中真空度的升高，U形管真空侧的液面在大气作用下随之上升。这样，依据两管中校面的高度差，就可以测得真空系统中的真空度，即p=pa-h，其中p为系统中真空度，pa为大气压值，h为两液面之差。53（2）压缩真空计

利用波义耳定律，将被测真空系统中一定的残余气体加以压缩，比较压缩前后体积、压力的变化，即能算出真空度。玻义耳-马略特定律

它反映气体的体积随压强改变而改变的规律。对于一定质量的气体，在其温度保持不变时，它的压强和体积成反比；或者说，其压强P与它的体积V的乘积为一常量，即PV=C（常数）（T不变时）或P1V1＝P2V2=…=PnVn实际气体只是在压强不太高、温度不太低的条件下才服从这一定律。54麦克劳真空计麦氏计是一种绝对真空计，测量范围为1.3xl03－1.3×10－8帕，精度较高，可作为其它真空计的标准。它是于1874年由麦克劳研制的，故命名为麦克劳真空计，简称麦氏计。其结构如图3．2所示。主要由毛细管A、毛细管B、玻璃泡、导液管、水银瓶构成。55毛细管A、玻璃泡及下面一段管子(到a-a面为止)的体积为V1。测量前需用油封机械泵将水银瓶抽真空，使水银面处于a-a位置。这时，玻璃泡与真空系统相通，其压强与真空系统相同，均为p。转动切换阀门，切断油封机械泵，使水银瓶与干燥空气相通。此时，水银瓶中水银在干燥空气压力作用下，沿导液管上升，充满玻璃泡．然后沿毛细管A上升，使玻璃泡和毛细管A中气体被压缩到毛细管A的顶部，其体