Mass Metrology

364 Pages·2012·3.885 MB·English

by  S. V. Gupta (auth.)

SpringerSeriesin
materials science
155
SpringerSeriesin
materials science
Editors: R.Hull C.Jagadish R.M.Osgood,Jr. J.Parisi Z.Wang
The Springer Series in Materials Science covers the complete spectrum of materials physics,
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S. V. Gupta
Mass Metrology
With 126 Figures
123
Dr. S. V. Gupta
Sector-8, Rohini 269/B-5
110085 Delhi
India
[email protected]
SeriesEditors:
ProfessorRobertHull ProfessorJu¨rgenParisi
UniversityofVirginia Universita¨tOldenburg,FachbereichPhysik
Dept.ofMaterialsScienceandEngineering Abt.Energie-undHalbleiterforschung
ThorntonHall Carl-von-Ossietzky-Straße9–11
Charlottesville,VA22903-2442,USA 26129Oldenburg,Germany
ProfessorChennupatiJagadish Dr.ZhimingWang
AustralianNationalUniversity UniversityofArkansas
ResearchSchoolofPhysicsandEngineering DepartmentofPhysics
J4-22,CarverBuilding 835W.DicknsonSt.
CanberraACT0200,Australia Fayetteville,AR72701,USA
ProfessorR.M.Osgood,Jr.
MicroelectronicsScienceLaboratory
DepartmentofElectricalEngineering
ColumbiaUniversity
SeeleyW.MuddBuilding
NewYork,NY10027,USA
SpringerSeriesinMaterialsScience ISSN0933-033X
ISBN978-3-642-23411-8 e-ISBN978-3-642-23412-5
DOI10.1007/978-3-642-23412-5
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber: 2012930378
©Springer-VerlagBerlinHeidelberg2012
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Dedicatedtomy wife,Mrs Prem Gupta
Childrenand Grandchildren
as
Theyallinspiremeto livelonger
•
Preface
FreshfromtheUniversityofAllahabadandjoiningNationalPhysicalLaboratoryin
1954,Ifoundmyselfinanaltogetherdifferentworld.Itappearedthatwhatwelearnt
at MSc level was differentfrom what we need at NPL. Naturally I started asking
manyquestionsas to why we are performingin a particularway. After prolonged
discussion,Iusedtohearthefinalansweras“NPLUKisdoingitthisway”.There
was hardly any detailed literature on mass measurement, except some notes from
NPL UK and a Dictionary of Applied Physics, at that time I vow to myself to
compilealltheavailableliteratureonMassMetrology.However,ittookmeanother
55 years to complete my dream. My conceptwas to give every available thing in
theliteratureormyownexperienceaboutmassmetrologyintheformofabook.In
theprocessIforgotwhatisrequiredinpresenttimesandnotnecessaryforpresent
generation.For example I included great details and mathematicsabout weighing
with a two-pan balance. My concept is that a very few books are available about
massmeasurementso I tried to includea lotof thingswhichmightnotbeneeded
inthecontemporarytime.Allsuchsuperfluousmaterialshavebeencurtailedonthe
recommendationofthereviewerofthebook.
Besides the routine chapters on unit of mass, mass measurement system in
India;two-andsingle-panbalancesandtheirmaintenanceandtesting,Ihavetaken
up the various transducers used for weighing and included their testing. I have
provedthat maximumpermissible error requirementsare the same for digital and
analoguebalances,andagreatdetailonenvironmentaleffectsonweightsfrombest
material is given. The methods for air density determination have been given in
detail. In the process, changed composition of argon in air discovered from the
measurementofairdensityinsitucarriedoutwithsolidobjectsandthatcalculated
from BIPM equation has been discussed. The methods of mass determination of
different weights in a set in terms of the mass of head weight are described in
detail with numerical examples. Optimisation of weighing designs and solution
of normal equations are described. A new chapter on the detection of small mass
differencestothe limitof zeptogram10(cid:2)21 g (massofa quarterofthegoldatom)
hasbeenproduced.Fabricationanddetectionoffrequencyusing nano-technology
are mentionedwith sufficientreferences. Details of micro-cantileversused for the
vii
viii Preface
purposearegiven.Theapplicationsofmicro-cantileverinotherfieldsareoutlined.
Themethodsofredefiningthekilogram,theunitofmass,intermsoffundamental
constantshavebeendescribed.Thechapterisconcludedwiththepresentstatusand
futureplantodefinethekilogram.
Special attention has been paid to the need of Legal Metrology.Special topics
suchasthemaintenanceandupkeepofstandardbalanceskeptatvariouslevelsand
effectofgravityonelectronicbalanceshavebeendiscussed.Thelimitsofmovement
of classes I to IV electronic balances in north–southdirection have been given in
detailforpracticallyallsituations.
I acknowledge the help of Dr R.S. Davis, Head of Mass Standards at BIPM.
I will fail in my duty if I do not express my most sincere thanks to the reviewer
of the book for his keen interest and suggestions. My thanks are also due to my
daughterMrsReetaGupta,Scientist,NationalPhysicalLaboratory,forhersincere
day-to-dayhelp.Iwishtorecordmyprofoundappreciationforthekeeninterestand
strenuouseffortsputinbyDrHabil.ClausAscheron,theExecutiveEditorPhysics,
formakingit possibleto bringthe manuscriptto the desiredleveland to Springer
VerlagGmbH,Germany,andinbringingthisbooktolight.
NewDelhi S.V.Gupta
August2011
Contents
1 UnitofMassandStandardsofMass..................................... 1
1.1 ConceptsofMass................................................... 1
1.1.1 GravitationalMass ..................................... 2
1.1.2 InertialMass............................................ 2
1.1.3 EqualityofInertialandGravitationalMass........... 3
1.2 MassandWeightofaBody ........................................ 3
1.2.1 ConventionalMass ..................................... 4
1.2.2 Variation of the Weight of a Body
onSurfaceofEarth..................................... 4
1.3 UnitofMass......................................................... 7
1.3.1 HistoryoftheUnitsofMetreandKilogram.......... 7
1.3.2 UnitofLength.......................................... 8
1.3.3 KilogramdeArchives.................................. 8
1.4 MetricConvention.................................................. 8
1.4.1 InternationalKilogram................................. 9
1.4.2 NationalPrototypesofKilogram...................... 11
1.4.3 NationalPrototypeKilogramandOther
StandardsinIndia ...................................... 11
1.4.4 CalibrationofTransferStandardsofMass............ 12
1.5 HierarchyofMassStandards....................................... 12
1.5.1 Nomenclature........................................... 12
1.5.2 MeasurementChain.................................... 14
1.5.3 TrackingtheMassValuesofStandards ............... 14
1.5.4 PeriodofVerificationorCalibration................... 15
1.5.5 MaximumPermissibleErrors.......................... 15
1.6 TraceabilityofMeasurements...................................... 15
1.6.1 Traceability ............................................. 15
1.6.2 CIPMMRA............................................. 17
References.................................................................... 17
ix
x Contents
2 Two-PanEqual-ArmBalances............................................ 19
2.1 Introduction......................................................... 19
2.2 BriefHistory ........................................................ 19
2.3 Other1-kgBalances ................................................ 20
2.3.1 Equal-ArmInterchangeablePan
BalanceUK............................................. 20
2.3.2 EqualArmwithDoubleInterchangeable
PanBalance............................................. 22
2.3.3 SubstitutionBalanceNPL-India....................... 22
2.3.4 ElectronicBalancewithAutomation
atNPL-India............................................ 23
2.3.5 HydrostaticBalance.................................... 24
2.4 InstallationofaBalance............................................ 26
2.4.1 ProperEnvironmentalConditions
forBalanceRoom ...................................... 26
2.4.2 RequirementsforLocationoftheBalance............ 26
2.5 EvaluationofMetrologicalDataforaBalance.................... 27
2.5.1 NeedforEvaluation.................................... 27
2.5.2 VisualExamination..................................... 29
2.5.3 Sensitivity............................................... 30
2.5.4 PeriodofSwingorTimePeriod....................... 32
2.5.5 AccuracyofRiderBar ................................. 33
2.5.6 Stability/Repeatability................................. 35
2.5.7 RepeatabilityofWeighing ............................. 35
2.5.8 EqualityofArmLengths............................... 36
2.5.9 CalculationofArmRatio,Repeatability
ofSingleandDoubleWeighing ....................... 37
2.5.10 RequirementforArmRatio
andRepeatabilityofWeighing......................... 39
2.5.11 TestforParallelismofKnifeEdges ................... 39
2.6 MethodsofWeighing............................................... 41
2.6.1 DirectWeighing........................................ 41
2.6.2 TranspositionWeighing................................ 41
2.6.3 SubstitutionWeighing.................................. 42
2.7 DoubleTranspositionandSubstitutionWeighing................. 42
2.7.1 DoubleTranspositionMethod......................... 42
2.7.2 DoubleTranspositionwithSimultaneous
DeterminationofS.R................................... 43
2.7.3 DoubleSubstitution .................................... 45
2.7.4 Double Substitution Weighing with
SimultaneousDeterminationofS.R. .................. 45
2.8 MaintenanceofStandardBalances ................................ 46
2.8.1 CategoryofBalances................................... 46
2.8.2 ReferenceBalances..................................... 46