>> P.160
EffectofChangingSupportMethodandOrientation(Unit:μm)Changingthesupportmethodand/ororientationofamicrometerafterzerosettingaffectssubsequentmeasuringresults.Thetablesbelowhighlightthemeasurementerrorstobeexpectedinthreeothercasesaftermicrometersarezero-setinthe‘Supportedatthebottomandcenter’case.Theseactualresultsshowthatitisbesttosetandmeasureusingthesameorientationandsupportmethod.SupportingmethodSupportedatthebottomandcenterSupportedonlyatthecenterAttitudeMaximummeasuringlength(mm)325425525625725825925102500000000-5.5-2.5-5.5-11.0-9.5-18.0-22.5-26.0SupportingmethodSupportedatthecenterinalateralorientation.Supportedbyhanddownward.AttitudeMaximummeasuringlength(mm)3254255256257258259251025+1.5+2.0-4.50-9.5-5.0-14.0-5.0-4.5-10.5-10.0-5.5-19.0-35.0-27.0-40.0Abbe’sPrincipleℓLεθRAbbe’sprinciplestatesthat“maximumaccuracyisobtainedwhenthescaleandthemeasurementaxesarecommon”.Thisisbecauseanyvariationintherelativeangle()ofthemovingmeasuringjawonaninstrument,suchasacaliperjawmicrometer,causesdisplacementthatisnotmeasured=-Linthe)tovary,andtheerrorontheinstrument’sscaleandthisisanAbbeerror(diagram).Spindlestraightnesserror,playinthespindleguideorvariationofmeasuringforcecanallcause(increaseswithR.Hooke'sLawHooke’slawstatesthatstraininanelasticmaterialisproportionaltothestresscausingthatstrain,providingthestrainremainswithintheelasticlimitforthatmaterial.Hertz'sFormulaeHertz’sformulaegivetheapparentreductionindiameterofspheresandcylindersduetoelasticcompressionwhenmeasuredbetweenplanesurfaces.Theseformulaeareusefulfordeterminingthedeformationofaworkpiececausedbythemeasuringforceinpointandlinecontactsituations.(μm)Assumingthatthematerialissteelandunitsareasfollows:Modulusofelasticity:E=205GPaAmountofdeformation:Diameterofsphereorcylinder:D(mm)Lengthofcylinder:L(mm)Measuringforce:P(N)a)Apparentreductionindiameterofsphereb)Apparentreductionindiameterofcylinder1=0.094·P/L3√1/D2=0.823√P2/D2δδδσPPδ22LøD22δSøD(a)Spherebetweentwoplanes(b)CylinderbetweentwoplanesMicrometerExpansionduetoHoldingFramewiththeBareHand300200100502468101520Time(minutes)3014131211109876543210Expansion(µm)Theabovegraphshowsmicrometerframeexpansionduetoheattransferfromhandtoframewhentheframeisheldinthebarehandwhich,ascanbeseen,mayresultinasignicantmeasurementerrorduetotemperature-inducedexpansion.Ifthemicrometermustbeheldbyhandduringmeasurementthentrytominimizecontacttime.Aheatinsulatorwillreducethiseffectconsiderablyiftted,orglovesmaybeworn.(Notethattheabovegraphshowstypicaleffectsandisnotguaranteed.)LengthStandardExpansionwithChangeofTemperature(for200mmbarinitiallyat20˚C)31°C27°C21°C458Lapseoftime(minutes)76910012320151050Thermalexpansion(µm)Theaboveexperimentalgraphshowshowaparticularmicrometerstandardexpandedwithtimeaspeoplewhosehandtemperaturesweredifferent(asshown)heldtheendofitataroomtemperatureof20°C.Thisgraphshowsthatitisimportantnottosetamicrometerwhiledirectlyholdingthemicrometerstandardbuttomakeadjustmentsonlywhilewearingglovesorlightlysupportingthelengthstandardbyitsheatinsulators.Whenperformingameasurement,notealsothatittakestimeuntiltheexpandedmicrometerstandardreturnstotheoriginallength.(Notethatthegraphvaluesarenotguaranteedvaluesbutexperimentalvalues.)DifferenceinThermalExpansionbetweenMicrometerandLengthStandard0°C52520°C10°C225325425Nominallength(mm)125+3+2+10-1-2-3Differenceinexpansion(µm)Intheaboveexperiment,afterthemicrometeranditsstandardwereleftataroomtemperatureof20ºCforabout24hoursfortemperaturestabilization,thestartpointwasadjustedusingthemicrometerstandard.Then,themicrometerwithitsstandardwereleftatthetemperaturesof0ºCand10ºCforaboutthesameperiodoftime,andthestartpointwastestedforshift.Theabovegraphshowstheresultsforeachofthesizesfrom125through525mmateachtemperature.Thisgraphshowsthatboththemicrometeranditsstandardmustbeleftatthesamelocationforatleastseveralhoursbeforeadjustingthestartpoint.(Notethatthegraphvaluesarenotguaranteedvaluesbutexperimentalvalues.)02-79
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