Fig1AphotographfortheDHWSNISonitsnalform2MHamdyetalIntJMetrolQualEng82020 partsasshowninFigure2thehigherpartleftsidecolumnrightsidecolumnbothofadiameter6mmandlength700mmdoubleshee ID: 960828
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recommendationwithanexpandeduncertaintyfrom1.0kg/mto1.4kg/mkg/m9].However,methodAinOIMLR111,2004uncertaintydownto0.1kg/mcanbereachedreached1].The(HWA-NIS)includesaweighingpansuspendedundersidetheelectronicdigitalbalancewitharodof6mmdiameterincludingasuspensionwirewith4mmdiameterattheregionofthesurfacetensioneffect.Thesuspensionwirediametercanaffectthesurfacetensionaroundthe4mmdiameteratthetimeofweighingthestandardandtheundertestmassinthedistilledwaterbyalargevalue.Itshouldbenotedthat,thegratedeffectforawireof1mmdiameterwillbe23mg[].Hencethisweighingpansuspensionwirewasaffectedwith92mgstandarduncertainty.Theweighingpanwasdesignedtocarryamasswithamaximumcapacityof10kgandtheoreticallyto20kg[]butstillitssuspensionwirediameterof4mmwhichgivesalargesurfacetensionuncertaintysourceeffectbyabout80%ofthetotalexpandeduncertainty.Themasshandlerofthe(HWA-NIS)wasdesignedwithtwopositions,bysuchdesignitwasnotpossibletohandlethegroupofindividualmassesatonceintheprocessofthedensityscalewhenitusedtotransferthetraceabilityfromtheprimarystandardtheSiliconSpheretothestandardmasses.Finally,thedensityofthe20kgmassesstillmeasuredatNISusingthemethodDinOIMLR111withanuncertaintyintheorderof±15kg/mkg/m1].Togetridofalltheseproblems,thisworkdevelopsandimprovesthe(HWA-NIS)tobeabletomanuallyandautomaticallyhandleandmeasurethedensityofuptofourmassesofanyshaperangingfrom2kgupto20kgwithastandarduncertaintycoverstheOIMLobjective[].Thedevelopmentincludesdesignandconstructionofanewalternativehydrostaticweighin
gparts,includesinnovativedesignforaweighingpanabletocarrymassesupto20kgwithfoursuspensionwireswithdiametersof0.3mmforeachoneattheregionoftheintersectionthedistilledwatersurfacewiththediameterofthesewiresatthetimeofweighinginthedistilledwatertoreducethelargeuncertaintyvalueduetosurfacetensioneffectandtobeabletoreachacceptedstandarduncertaintycoverstherequirementsofOIMLR111forthismethod.Theinnovativedesignforthe4-positionsmasshandlercancarryfourmasseswithamaximumcapacityof20kgforeachmass.Also,eachpositionwasdesignedwithapentagonalshapetobeabletocarrygroupsofindividualmassesagainstoneequivalentmassatonceatthetimeofthedensityscaleweighingprocess.Thestressanddeformationofthedevelopedpartswerecheckedusing3DFiniteElementAnalysis(FEA)[]SolidWorkssoftware.2TheDevelopedHydrostaticWeighingSystem(DHWS-NIS)TheNISdevelopedHydrostaticWeighingSystem(DHWS-NIS)upto20kgwasanobligatoryacomplementinsteadofthe10kgNISHydrostaticWeighingApparatus(HWA-NIS)thathasbeendesignedandconstructedbyNISintheyear2014[].Thedeveloped(DHWS-NIS)canbeusedformeasuringmassesdensityrangingfrom2kgupto20kgbasedonthehydrostaticweighing.TheNISdeveloped(DHWS-NIS)showninFigure1consistingoffourmainpartsnamely;(1)themaincabinetcarrieselectronicdigitalcomparatorbalanceofacapacity26kgandreadabilityof1mg.(2)The4-positionsmasshandlerisusedforloadingandunloadinguptofourstandardsincludingundertestmassesduringthehydro-staticweighingprocess.(3)Thedevelopedweighingpansuspendedundersideoftheelectronicdigitalbalanceandisusedforweigh
ingthestandardandundertestmassesbelowthereferenceliquidsurface.(4)Themechanicalliftercarriesawaterbathcontains260litersofthedistilledwaterinwhichthestandardandundertestmassesaretobeimmersedduringthehydrostaticweighingprocess.Thetemperatureofthewaterbathiscontrolledtobewithin±0.01The(DHWS-NIS)containsasystemforambientconditionmeasurements.Thissystemisconsistingofatmosphericpressuremeasuringinstrumentwitharead-abilityof0.1Paandthermo-hygrometerformeasuringtheambienttemperaturewithreadabilityof0.001Candambientrelativehumiditywithreadabilityof0.01%[bothareneededforairdensitycalculations[].APT-100thermometerwitharesolutionof0.0010.00112]iskeptimmersedinthedistilledwaterandclosedtotheweighingpantoevaluatethetemperaturegradientofthedistilledwatertemperature[3DevelopedpartsforthehydrostaticweighingSystem3.1ThedevelopedweighingpanThedevelopedweighingpanissuspendedundersidetheelectronicdigitalbalancebystainlesssteelrodof6mmdiameter.Theweighingpanwasconstructedwithtwo Fig.1.Aphotographforthe(DHWS-NIS)onitsnalform.2M.Hamdyetal.:Int.J.Metrol.Qual.Eng.,8(2020) partsasshowninFigure2;thehigherpart(leftsidecolumn,rightsidecolumnbothofadiameter6mmandlength700mm,doublesheetmechanismand6mmdiameterstainlesssteelrod)istobeoperatedabovethedistilledwatersurfaceandonlyaffectedbytheairbuoyancy.Thelowerpart(leftsidecolumn,rightsidecolumnbothofadiameter6mmandlength400mm,doublesheetmechanismandpentagonshapeposition)istobeimmersedbelowthedistilledwatersurfaceandonlyaffectedbytheliquidbuoyancy.Thetwop
artsconnectedtoeachotherwithfourstainlesssteelsuspensionwireswithadiameterof0.3mmforeachoneandlengthof100mmasshowninFigure3.ThepreviousdesignoftheweighingpanisshowninFigure4anditssuspensionwirewithadiameterof4mmisshowninFigure5Allthecomponentofthedevelopedweighingpanaremanufacturedusingstainlesssteelmaterial304[].Solidworkssoftwareat3DanditsFEManalysisareusedtocheckthestressesandthedeformationofthedevelopedweighingpan.ThemaximumVonMisesstresswas137.3MPashowninFigure6withsafetyfactor1.5.Thevalueofthemaximumdeformationwascheckedwith0.72mmunderaloadof20kgasshowninFigure73.2Thedeveloped4-PositionsMassHandlerThemasshandlerintheprevious(HWA-NIS)showninFigure8wasdesignedwithtwopositionsformassesupto10kg.Thedeveloped4-positionsmasseshandlerwas Fig.2.Thedevelopedweighingpan. Fig.3.Thedevelopedsuspensionwire. Fig.4.previousweighingpan. Fig.5.Theprevioussuspensionwire.M.Hamdyetal.:Int.J.Metrol.Qual.Eng.,8(2020)3 OIMLR111-1standard[].Thehydrostatictechniquewasusedforrelatingthemassoftheundercalibrationtothemassofthereferencemassusedbothinairandinthereferenceliquid(distilledwater)ofknowndensity[undernearlythesameenvironmentalcondition.Thedistilledwaterwasselected,asitsdensityisawell-knownfunctionoftemperatureanditislowcost.Theuncertain-tieslessthan0.1kg/mwouldbereachedthroughthisBeforestartingtheweighing,Theundertestmasswasplacedonitsassociatedpositionsonthe4-positionsmasshandleragainstthestandardmassinthedistilledwaterforabout8hourstoreachthermalstabilization.Fivepre-weighingwerecar
riedoutbeforestartingtheweighingcomparisonsformakingacenteringtothestandardmassandtheundertestmassontheweighingpan.FiveReference-Test-Reference(RTR)cycleswereperformed.ThebalancereadingwastakenatthetimeofweighingviaLabVIEWsoftwareafterstabilizationtime.4.1MeasurementprocedureWeighingthereferencemass()intheairofdensity)andrecordthebalancereading(Weighingthemassundercalibration()intheairofdensity()andrecordthebalancereading(Weighingthereferencemass()underthesurfaceofthedistilledwaterofdensity()andrecordthebalancereading(Weighingthemassundercalibration()underthesurfaceofthedistilledwaterofdensity()andrecordthebalancereading(Measurethetemperatureofthedistilledwaterattheweighingreadings( Fig.10.Aphotographforthe4-PositionsMassHandler. Fig.11.TheMassHandlercarriesindividualmasses. Fig.12.TheVonMissesstressdistributionforthe4-PositionMassHandler. Fig.13.Themaximumdeformationforthe4-PositionMassM.Hamdyetal.:Int.J.Metrol.Qual.Eng.,8(2020)5 4.2CalculationsThedensityofthemassundercalibration()isthencalculatedusingequation ðÞ whereCarethecorrectionsfactorsforthebuoyancyforce,canbecalculatedusingtheequations( rarrð2ÞCl¼1 :thedifferentbetweentheweighingofthereferencemassandthemassundercalibrationinairandcanbecalculatedusingequation:Thedifferentbetweentheweighingofthereferencemassandthemassundercalibrationintheliquidandcanbecalculatedusingequationisthebuoyancyforcecorrectionfactor,canbecalculatedusingequation :Densityofthesensitivitymass,:Airdensityduringcalibrationoftheusedbalance.T
hesubscriptswereforair,liquid,referencemass,massundercalibrationandweighingprocessrespectively.Thedensityofthemassundercalibration()canbecalculatedatreferencetemperature20Cfromequationasfollowing:ðÞ¼½ð:thecoefcientofthermalexpansionforthemassundercalibration(4.8:thetesttemperature,:thereferencetemperature(204.3UncertaintysourcesevaluationTheuncertaintysourceswereevaluatedbasedonthemethod(A)inOIMLR111[].TypeAandtypeBuncertaintycomponentsandevaluationwerecalculatedaccordingtotheGUMstandard[TypeAuncertaintycomponentsandevaluation:Repeatability()intheunitof(g/cmIsthestandarddeviationofsuccessivedensitymeasure-mentsofanundercalibrationmasscarriedoutunderthesameconditionsofmeasurement,dividedbythenumberofmeasurementsandcanbeobtainedfromequation :isthestandarddeviation,:isthenumberofTherepeatabilityhasanormalprobabilitydistributionwithadivisor=1andsensitivitycoefcient()=1.TypeBuncertaintycomponentsandevaluation:Theuncertaintyinmeasuringthedensitydistilledwater)ing/cmTheuncertaintyinmeasuringthedensityofreference)ing/cmTheuncertaintyinmeasuringthemassvalueofthereferencemass)ingTheuncertaintyduetotheweighingdifferenceindistilledwaterbetweenreferencemassandundercalibrationmass)ingTheuncertaintyduetothesurfacetensioneffect)ingTheprobabilitydistributionsoftheuncertaintycomponents(1and2)arenormaldistributionswithdivisors=1whiletheprobabilitydistributionsoftheuncertaintycomponents(3,4and5)arerectangulardistributionswithdivisors=Thesensitivitycoefcients()oftheuncertaintycomponen
ts(1and2)areequalto1whilethesensitivitycients()oftheuncertaintycomponents(3,4and5)areobtainedfromthepartialderivativeofthemathemati-calmodelpresentedinequationCombinedstandarduncertaintyuc(IsobtainedusingtheindividualstandardmeasurementuncertaintiesassociatedwiththeinputquantitiesinthemathematicalmodelshowninequationandcanbecalculatedusingequationSeeequationExpandeduncertaintyU(Representtheproductofthecombinedstandardmeasurementuncertaintyandacoveragefactor=2atacondencelevelof95%whichcanbecalculatedfrom5ResultsanddiscussionThedensityandvolumeoffourmasseswithnominalvaluesof2kg,5kg,10kgand20kgwerecalculatedusing drtdmruðmrÞþ drtdDmwluðDmwlÞþ 6M.Hamdyetal.:Int.J.Metrol.Qual.Eng.,8(2020) WeighingSystem(DHWS-NIS)wasusedtodeterminethedensityoffourmasseswithnominalvaluesof2kg,5kg,10kgand20kgwithimprovedexpandeduncertaintyof0.149kg/m,0.092kg/m,0.081kg/mand0.078kg/mrespectively.Thisexpandeduncertaintywasimprovedbyvetimedfromitsinitialvalueduetoreducingtheeffectofsurfacetensionviathedevelopeddesign.1.InternationalOrganizationofLegalMetrology(OIML)R77(2004)2.C.Buchner,Automatictestingfacilityfordeterminingliquidsandsolidsdensity;anddeterminingthevolumeofweights,in20thIMEKOTC3Int.Conf.Meas.Force,MassTorque,20073.S.V.Gupta,PracticalDensityMesurementandHydrometery(BritishLibraryCataloguing,2002)4.M.Thi
esen,T.A.M.InternationalBureauofWeightsandMeasures,19755.H.A.Bowman,R.M.Schoonover,J.Res.Natl.Bur.Stand.Sect.CEng.Instrum.,179(1967)6.FederalInstituteofMetrology(METAS),PreciseDetermi-nationofVolumeandDensityofSolidBodies,17.C.Buchner,DevelopmentandrealisationofafullyautomatictestingfacilityfordeterminingthevolumeofE1weightsupto50kgbasedonhydrostaticweighing,in19thIMEKOWorldCongress2009(2009),vol.1,pp.1828.Y.J.Lee,W.G.Lee,M.Abdurahman,K.P.Kim,Densitymesurementsystemforweightsof1kgto20kgusinghydrostaticweighing,Int.J.Mod.Phys.Conf.Ser.1to13600266(2013)9.B.M.Sayed,B.S.Azzam,M.Z.Abdou,A.A.Eltawil,Adv.Mater.Res.,127134(2014)10.B.M.Sayed,A.B.S.Azzam,B.M.Z.Abdou,A.A.Eltawil,Design,controlandoptimizationoftheweighingmechanismfortheHWA-NISupto20kg,inProc.20163rdInt.Conf.Inf.Sci.ControlEng.ICISCE2016,2016,pp.30211.G.Richard,Budynas,J.KeithNisbett,Mech.Eng.Des.12.M.H.Mohamed,M.A.Bayoumi,A.A.Eltawil,A.E.Abuelezz,Int.J.Innov.Res.Sci.Eng.Technol.,1273512741(2014)13.A.Picard,R.S.Davis,M.Gläser,K.Fujii,Metrologia155(2008)14.M.Tanaka,G.Girard,R.Davis,A.Peuto,N.Bignell,,301309(2001)15.J.E.Bringas,Handbookofcomparativeworldsteelstandards(ASTMDS67B).LibraryofCongressCataloging(2004)16.S.Bell,ABeginnersGuidetoUncertaintyofMeasurement(NationalPhysicalLaboratory,2001)Citethisarticleas:MohamedHamdy,MohamedA.Bayoumi,AliE.Abuelezz,AlaaeldinA.Eltawil,DevelopingtheNISsoliddensityhydrostaticweighingsystemupto20kg,Int.J.Metrol.Qual.Eng.,8(2020)8M.Hamdyetal.:Int.J.Metrol.Qual.Eng.,8(2020) RESEARCHART