Document type: International Standard Document subtype: Document stage: (60) Publication Document language: E H:\Secteur3\Normes en cours\ISO\ISO 6358-2\ISO-CD-6358-2_2017.doc STD Version 2.2
ISO TC 131/SC 5 N 796
Date: 2018-03-13
ISO 6358-2:2013(E)
ISO TC 131/SC 5/WG 3
Secretariat: AFNOR
Pneumatic fluid power -- Determination of flow-rate characteristics of components using compressible fluids -- Part 2: Alternative test
methods
Transmissions pneumatiques -- Détermination des caractéristiques de débit des composants traversés par un fluide compressible -- Partie 2: Méthodes d'essai alternatives
ISO 6358-2:2013(E)
ii © ISO 2013 – All rights reserved
Copyrightnotice
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ISO 6358-2:2013(E)
© ISO 2013 – All rights reserved iii
Contents Page
Foreword..............................................................................................................................................................iv
Introduction.........................................................................................................................................................v
1 Scope........................................................................................................................................................1
2 Normativereferences.......................................................................................................................2
3 Termsanddefinitions........................................................................................................................2
4 Symbolsandunits...............................................................................................................................2
5 Testinstallation....................................................................................................................................3
5.1Testcircuitfordischargetest..................................................................................................3
5.2Testcircuitforchargetest........................................................................................................3
5.3Generalrequirements................................................................................................................5
5.4Requirementsforthetank(item4)......................................................................................5
5.5Specialrequirements..................................................................................................................7
6Testprocedures.............................................................................................................................................8
6.1Testconditions..............................................................................................................................8
6.2Measuringprocedures...............................................................................................................9
6.3Calculationofcharacteristics................................................................................................11
7Presentationoftestresults.....................................................................................................................15
8Identificationstatement(referencetothisdocument).....................................................16
AnnexA(informative)Evaluationofmeasurementuncertainty....................................................17
AnnexB(normative)Testmethodtodetermineandcalibratethevolumeofanisothermaltank….23
AnnexC(informative)Isothermaltankstuffing..................................................................................29
AnnexD(informative)Testmethodtodetermineisothermalperformance............................32
AnnexE(informative)Equationsforcalculationofflow‐ratecharacteristics..........................35
AnnexF(informative)Proceduresforcalculatingcriticalback‐pressureratio,b,andsubsonicindex,m,bytheleast‐squaremethodusingtheSolverfunctioninMicrosoftExcel……………………….38
Bibliography.....................................................................................................................................................42
ISO 6358-2:2013(E)
iv © ISO 2013 – All rights reserved
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of nationalstandards bodies (ISO member bodies). The work of preparing International Standards is normallycarriedout through ISO technicalcommittees.Eachmemberbody interested ina subject forwhichatechnical committee has been established has the right to be represented on that committee.Internationalorganizations,governmentalandnon‐governmental,inliaisonwithISO,alsotakepartinthe work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on allmattersofelectrotechnicalstandardization.
The procedures used to develop this document and those intended for its further maintenance aredescribedintheISO/IECDirectives,Part1.Inparticularthedifferentapprovalcriterianeededforthedifferenttypesof ISOdocumentsshouldbenoted.ThisdocumentwasdraftedinaccordancewiththeeditorialrulesoftheISO/IECDirectives,Part2(seewww.iso.org/directives).
Attentionisdrawntothepossibilitythatsomeoftheelementsofthisdocumentmaybethesubjectofpatentrights. ISOshallnotbeheldresponsible for identifyinganyorallsuchpatentrights.DetailsofanypatentrightsidentifiedduringthedevelopmentofthedocumentwillbeintheIntroductionand/orontheISOlistofpatentdeclarationsreceived(seewww.iso.org/patents).
Anytradenameusedinthisdocumentisinformationgivenfortheconvenienceofusersanddoesnotconstituteanendorsement.
For an explanation on the voluntary nature of standards, the meaning of ISO specific terms andexpressions related to conformity assessment, as well as information about ISO's adherence to theWorldTradeOrganization(WTO)principlesintheTechnicalBarrierstoTrade(TBT)seethefollowingURL:www.iso.org/iso/foreword.html.
ThisdocumentwaspreparedbyTechnicalCommitteeISO/TC131,Fluidpowersystems,SubcommitteeSC5,Controlproductsandcomponents.
Thissecondedition,cancelsandreplacesISO6358‐2:2013,whichhasbeentechnicallyrevised.
AlistofallpartsintheISO6358seriescanbefoundontheISOwebsite.
ISO 6358-2:2013(E)
© ISO 2013 – All rights reserved v
Introduction
Inpneumaticfluidpowersystems,poweristransmittedandcontrolledthroughagasunderpressurewithinacircuit.Componentsthatmakeupsuchacircuitareinherentlyresistivetotheflowofthegasanditisnecessary,therefore,todefineanddeterminetheflow‐ratecharacteristicsthatdescribetheirperformance.
ISO6358:1989was developed to determine the flow‐rate characteristics of pneumatic valves, basedupon a model of converging nozzles. The method included two characteristic parameters: sonicconductance,C, and critical pressure ratio,b, used in aproposedmathematical approximation of theflow behaviour. The result described flow performance of a pneumatic valve from choked flow tosubsonicflow,basedonstaticpressure.Thisneweditionusesstagnationpressureinstead,totakeintoaccounttheinfluenceofflowvelocityonthemeasurementofpressures.
Experiencehasdemonstrated thatmanypneumatic valveshave converging–diverging characteristicsthatdonot fit theISO6358:1989modelverywell.Furthermore,newdevelopmentshaveallowedtheapplication of this method to additional components beyond pneumatic valves. However, this nowrequirestheuseoffourparameters(C,b,m,andΔpc)todefinetheflowperformanceinboththechokedandsubsonicflowregions.
This document describes a set of three flow‐rate characteristic parameters determined from testresults.Theseparametersaredescribedasfollowsandarelistedindecreasingorderofpriority:
— Thesonicconductance,C,correspondingtothemaximumflowrate(choked)isthemostimportantparameter.Thisparameterisdefinedbytheupstreamstagnationconditions.
— Thecriticalback‐pressureratio,b,representingtheboundarybetweenchokedandsubsonicflowissecond in importance. Its definition differs here from the one in ISO6358:1989 because itcorrespondstotheratioofdownstreamtoupstreamstagnationpressures.
— The subsonic index, m, is used if necessary to represent more accurately the subsonic flowbehaviour.Forcomponentswithafixedflowpath,misdistributedaround0,5.Inthesecases,onlythefirsttwocharacteristicparametersCandbarenecessary.Formanyothercomponents,mwillvarywidely.Inthesecases,itisnecessarytodetermineC,b,andm.
Several changes to the test equipmentweremade to overcome apparent violations of the theory ofcompressible fluid flow. This included expanded inlet pressure‐measuring tubes to satisfy theassumptionsofnegligibleinletvelocitytotheitemundertestandtoallowtheinletstagnationpressureto be measured directly. Expanded outlet tubes allow the direct measurement of downstreamstagnationpressure tobetteraccommodate thedifferent componentmodels.Thedifferencebetweenstagnationpressureatupstreamanddownstreamofcomponentmeansalossofpressureenergy.
ISO6358‐3 can be used to calculate without measurements an estimate of the overall flow‐ratecharacteristicsofanassemblyofcomponentsandpiping,usingthecharacteristicsofeachcomponentandpipingdeterminedinaccordancewiththisdocumentorISO6358‐1.
ThedischargeandchargetestmethodsspecifiedinthisdocumenthavethefollowingadvantagesoverthetestmethodspecifiedinISO6358‐1:
a) anairsourcewithalargeflow‐ratecapacityisnotrequired;
b) componentswithlargerflow‐ratecapacitycanbetestedmoreeasily;
c) energyconsumptionisminimised;and
d) testtimeisshortenedinthedischargeandchargetests,andnoiselevelisdecreasedinthechargetest.
ISO 6358-2:2013(E)
vi © ISO 2013 – All rights reserved
It should be noted that performance characteristics measured in accordance with this edition ofISO6358willdifferfromthosemeasuredinaccordancewithISO6358:1989.
Committee Draft ISO 6358-2:2013(E)
© ISO 2013 – All rights reserved 1
Pneumaticfluidpower‐‐Determinationofflow‐ratecharacteristicsofcomponentsusingcompressiblefluids‐‐Part2:Alternativetestmethods
1 Scope
Thisdocumentspecifiesadischargetestandachargetestasalternativemethodsfortestingpneumaticfluidpowercomponents thatusecompressible fluids, i.e. gases,and thathave internal flowpassagesthat canbeeither fixedorvariable insize todetermine their flow‐ratecharacteristics.However, thisdocumentdoesnotapplytocomponentswhoseflowcoefficientisunstableduringuse,i.e.componentsthatexhibitremarkablehystereticbehaviour(becausetheycancontainflexiblepartsthatdeformundertheflow)orthathaveaninternalfeedbackphenomenon(suchasregulators),orcomponentsthathaveacrackingpressuresuchasnon‐return(check)valvesandquick‐exhaustvalves.Inaddition,itdoesnotapplytocomponentsthatexchangeenergywiththefluidduringflow‐ratemeasurement,e.g.cylinders,accumulators,etc.
NOTE This document does not provide a method to determine if a component has hysteretic behaviour;ISO6358‐1doesprovidesuchamethod.
Table1providesasummaryofwhichpartsofISO6358canbeappliedtovariouscomponents.
Table1—ApplicationofISO6358testmethodstocomponents
Components
Constantupstreampressuretest
Variableupstreampressuretest
ISO6358‐1constantupstream
pressuretest
ISO6358‐2chargetest
ISO6358‐1variableupstream
pressuretest
ISO6358‐2discharge
test
Group1 Directionalcontrolvalves yes yes yes yes
Flowcontrolvalves yes yes yes yes
Connectors yes yes yes yes
Valvemanifolds yes yes yes yes
Groupofcomponents yes yes yes yes
Group2 Filtersandlubricators yes no no no
Non‐return(check)valves yes no no no
Quick‐exhaustvalves yes no no no
Tubesandhoses yes no no no
Group3 Silencersandexhaustoilmistseparators
no no yes yes
Blownozzles no no yes yes
Cylinderendheads no no yes yes
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Thechargetestcannotbeperformedoncomponentsthatdonothavedownstreamportconnections.
Thisdocumentspecifiesrequirementsforthetestinstallation,thetestprocedure,andthepresentationofresults.
Evaluationofmeasurementuncertainties isdescribed inAnnexA.Requirements foramethod to testthe volume of an isothermal tank are given in AnnexB. Guidance on the isothermal tank is given inAnnexC.RequirementsforamethodtotestisothermalperformancearegiveninAnnexD.Guidanceonthe equation for calculating characteristics is given in AnnexE. Guidance on calculating flow‐ratecharacteristicsisgiveninAnnexF.
2 Normativereferences
The following documents are referred to in the text in such away that some or all of their contentconstitutes requirements of this document. For dated references, only the edition cited applies. Forundatedreferences,thelatesteditionofthereferenceddocument(includinganyamendments)applies.
ISO1219‐1, Fluidpower systemsandcomponents—Graphical symbolsandcircuitdiagrams—Part1:Graphicalsymbolsforconventionaluseanddata‐processingapplications
ISO5598,Fluidpowersystemsandcomponents—Vocabulary
ISO6358‐1, Pneumatic fluid power—Determination of flow‐rate characteristics of components usingcompressiblefluids—Part1:Generalrulesandtestmethodsforsteady‐stateflow
3 Termsanddefinitions
Forthepurposesofthisdocument,thetermsanddefinitionsinISO5598andISO6358‐1apply.
ISOandIECmaintainterminologicaldatabasesforuseinstandardizationatthefollowingaddresses:
— IECElectropedia:availableathttps://www.electropedia.org/
— ISOOnlinebrowsingplatform:availableathttps://www.iso.org/obp
4 Symbolsandunits
4.1 ThesymbolsandunitsshallbeinaccordancewithISO6358‐1andTable2.
Table2—Symbolsandunits
Reference Description Symbol Dimensiona SIunits Practicalunits
5.5.2 Time t T s s
5.4.3 Tankvolume V L3 m3 dm3
a T=time;L=length
4.2 The numerals used as subscripts to the symbols shall be in accordance with ISO6358‐1 andTable3.
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Table3—Subscripts
Subscript Meaning
3 Tankconditions
4.3 ThegraphicsymbolsusedinFigures1and2areinaccordancewithISO1219‐1.
5 Testinstallation
CAUTION—Figures1and2illustratebasiccircuitsthatdonotincorporateallthesafetydevicesnecessarytoprotectagainstdamageintheeventofcomponentfailure.Itisimportantthatthoseresponsibleforcarryingoutthetestgivedueconsiderationtosafeguardingbothpersonnelandequipment.
5.1 Testcircuitfordischargetest
AsuitabletestcircuitasshowninFigure1shallbeusedforthedischargetest.See5.3.5.
p3
p1 p2 1 2 3
4
13
7
12
9 8
14
15
16
11
5
6 10
NOTE SeeTable4forthekeytotestcircuitcomponents.
Figure1—Testcircuitfordischargetest
5.2 Testcircuitforchargetest
AsuitabletestcircuitasshowninFigure2shallbeusedforthechargetest.
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17 13
7 6 9 8
14 15
11 12 18 3
4
16 p3
p2 p1
10
5
NOTE SeeTable4forthekeytotestcircuitcomponents.
Figure2—Testcircuitforchargetest
Table4—KeytotestcircuitcomponentsshowninFigures1and2
Keyitem
number
Relevantsubclause
orparagraph
Description Additionalrequirements
1 5.3.2Compressedgassourceandfilterfordischargetest
2 ‐ Adjustablepressureregulatorfordischargetest
3 ‐ Shut‐offvalve
4 5.4 Tank
5 ‐ Temperature‐measuringinstrument
6 5.3.7 Upstreampressure‐measuringtube
7 5.3.7 Upstreamtransitionconnector
8 ‐ Componentundertest
9 5.3.7 Downstreamtransitionconnector
10 5.3.7 Downstreampressure‐measuringtube
11 5.3.10 Pressuretransducer
12 5.3.10 Pressuretransducer
13 5.3.4and5.3.9
Flowcontrolsolenoidvalve(optional) Thesonicconductanceofthisflowcontrolvalveshallbeaboutfourtimeslargerthanthatofthecomponentundertest.
14 ‐ Barometer
15 ‐ Digitalrecorder
16 5.3.10 Pressuretransducer
17 ‐ Suctionportforchargetest
18 ‐ Vacuumpumpforchargetest
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5.3 Generalrequirements
5.3.1 Thecomponentundertestshallbeinstalledandoperatedinthetestcircuitinaccordancewiththemanufacturer’soperatinginstructions.
5.3.2 Forthedischargetest,afiltershallbeinstalledwhichprovidesastandardoffiltrationspecifiedbythemanufacturerofthecomponentundertest.
5.3.3 Atestset‐upshallbeconstructedfromtheitemslistedinTable4.Items1through8,11,and14through16arerequiredforthedischargetest.Items3through12and14through18arerequiredforthechargetest.
5.3.4 If the componentunder test has no controlmechanism for shifting its position, install a flowcontrol solenoid valve (item13)upstreamof pressure‐measuring tube (item6) in order to start thetest.
5.3.5 Items9,10,and12arenotrequiredforthedischargetestwhenthecomponentundertestdoesnothaveadownstreamport.Seethespecialinstructionsin6.2.3.3.
5.3.6 Thedistancebetweenthetank(item4)andtheupstreampressure‐measuringtube(item6)forthedischargetest,orbetweenthetank(item4)anddownstreampressure‐measuringtube(item10)forchargetest,shallbeasshortaspossible.ThevolumesofallcomponentsandconductorsinFigures1and2betweenitems3and13(ifitem13isused)orbetweenitems3and8(ifitem13isnotused)shallbeaddedtothevolumeofthetank.
5.3.7 Thepressure‐measuringtubes(items6and10)andthetransitionconnectors(items7and9)shallbeinaccordancewithISO6358‐1.Itisnotnecessarytohaveatemperature‐measuringconnectioninthepressure‐measuringtubesbecausethetemperatureismeasuredinthetank.
5.3.8 Foranylocationswhereliquidcancollect,installationofadrainseparatorisrecommended.
5.3.9 Theshiftingtimeoftheflowcontrolsolenoidvalve(item13)shallbesufficientlyshorttolimitthetransienttimeatthebeginningoftestdatacollection.
5.3.10 Whenconnectingpressuremeasuringinstruments,thedeadvolumeshallbelimitedasmuchaspossibletoavoidlongresponsetime,delays,andphaselagformeasurements.
5.4 Requirementsforthetank(item4)
5.4.1 Structure
The tank shall be suitably structured as shown in Figure3 and consist of the components listed inTable5.DimensionsoftheflowportshallconformtothedimensionsgiveninTable6.
The tank shall conform to any local, national, and/or regional regulations and standards related topneumaticcontainers.
Theratiooftheheightofthetanktoitsdiametershouldnotexceed2:1.
Thejunctionoftheflowportwiththeinternalsurfaceofthetankshallbeconvergentshapedsoastoavoidpressureloss.Thedimensionsandarrangementofconnectionportsotherthantheflowportaredeterminedbythetestoperator.
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Keya Measuringports(temperatureandpressure)b Sourceportc Flowport
Figure3—Structureofthetank
Table5—Keytotankcomponents
Keyitemnumber Description Comments
1 Lid
2 Tankbody
3 Gasket
4 Flangefastener(nutandbolt) Sixormorepieces,equallyarranged
5 Metalnet See5.4.2.
6 Stuffedmaterial See5.4.2.
7 Drainvalve
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Table6—Threadsizeofflowport
Tankvolume,V,inm3
Threadsize
V≤0,0025 G1/8
0,0025<V≤0,0063 G1/4
0,0063<V≤0,014 G3/8
0,014<V≤0,032 G1/2
0,032<V≤0,066 G3/4
0,066<V≤0,100 G1
0,100<V≤0,190 G11/4
0,190<V≤0,310 G11/2
0,310<V≤0,510 G2
0,510<V≤0,730 G21/2
0,730<V≤1,100 G3
5.4.2 Stuffedmaterial
The stuffed material, which is used to reduce the change in air temperature, shall be resistant tocorrosion and pressure and shall be distributed evenly in the tank. If copperwires are used as thestuffedmaterial,wiresofequivalentdiameter3×10−5mto5×10−5mshallbestuffedinthetankatadensityof3x102kg/m3.
NOTE The equivalent diameter means the diameter of the cross‐sectional area of a noncircular shapeassumedasequivalenttothediameterofthecross‐sectionalareaofacircularshape.
Thestuffedmaterialshallbewrappedwithametallicnettopreventitfromflowingoutoftheflowport.Itisdesirablethatasuitableframesupportsthestuffedmaterialtopreventitfromleaninginsidethetank.FurtherinformationisgiveninAnnexC.
5.4.3 Volume
Thevolumeofthetank,V,inm3shouldbecalculatedusingFormula(1):
55 10V C (1)
where
Cistheestimatedsonicconductanceofthecomponentundertest,inm3/(s∙Pa)(ANR).
NOTE1 Thetankvolumeisthenetvalueobtainedbysubtractingthevolumeofthestuffedmaterialfromthevolumeoftheemptyairtank.
NOTE2 ThetestmethodtodeterminethetankvolumeisgiveninAnnexB.
5.5 Specialrequirements
5.5.1 ThespecialrequirementsgivenISO6358‐1,5.6applyforthisdocument.
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5.5.2 ThedigitalrecordershallbesettosamplepressureatatimeintervaldeterminedinaccordancewithFormula(2)or(3).Approximately1000pressuredatapointswillbeobtainedduringdischargeorchargetests.Thesecriteriahaveaneffectonthecalculationsperformedin6.3.
— Fordischargetests:
82,5 10V
tC
(2)
— Forchargetests:
81,5 10V
tC
(3)
where
Δt isthetimeintervalforsamplingpressure,ins;
C istheestimatedsonicconductanceofthecomponentundertest,inm3/(s∙Pa)(ANR);
V isthetankvolume,inm3.
6 Testprocedures
6.1 Testconditions
6.1.1 Testfluid
6.1.1.1 Airshouldbeusedasthetest fluid.Ifadifferentfluidisused, itshallbestatedinthetestreport.
6.1.1.2 The gas shall be filtered and conditioned to comply with the recommendations of themanufacturerofthecomponentundertest.
6.1.2 Checks
Periodicallycheckthatthepressure‐tappingholesarenotblockedbyliquidsorsolidparticles.
6.1.3 Testmeasurements
6.1.3.1 Eachsetoftestreadingsshallberecordedaftersteady‐stateconditionsoftemperatureandpressureinthetankhavebeenreached.Thevariationsofpressuresandtemperatureindicationsshallnotexceedthelimitsgiveninthecolumn“Allowedtestconditionsvariation”ofTable7.
6.1.3.2 PressureandtemperatureshallbemeasuredwithinthemeasurementaccuracyspecifiedinTable7.
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Table7—Measurementaccuracyandallowedtestconditionofparameters
ParameterMeasurementaccuracy
Allowedtestconditionvariation
Volume ±1% ‐
Time ±1% ‐
Upstreampressure ±0,5% ±1%
Downstreampressure ±0,5% ±1%
Tankpressure ±0,5% ±1%
Temperature ±1K ±3K
6.1.3.3 Flow‐rateconditionsineachflowpathshallbemaintainedconstantwithinthecomponentwhiletakingmeasurementstoensurethereisnoinadvertentmovementofcomponentparts.
6.2 Measuringprocedures
6.2.1 Requirementsfortestingtopublishcatalogueratings
Ifdataaretobeusedforpublishingratingsinacatalogue,asampleconsistingofaminimumoffivetestunits selected from a random production lot shall be tested in accordance with the followingprocedures.
6.2.2 Selectionofmeasuringprocedure
Either the procedure described in 6.2.3 or the procedure described in 6.2.4 shall be selected inaccordancewiththescopeofthisdocument.
6.2.3 Measuringproceduresfordischargetest
6.2.3.1 Setthepressureofthepressureregulator(item2)at700kPa(7bar),andopentheshut‐offvalve(item3) tochargeair into the tank(item4).Leave the tank in this stateuntil temperatureandpressureinthetankreachsteady‐stateconditions.
6.2.3.2 Close the shut‐off valve (item3) and measure the initial pressure, p3, using pressuretransducer 16, initial temperature, T3, using the temperature‐measuring instrument (item 5) in thetank,andatmosphericpressureusingthebarometer(item14).
6.2.3.3 Open the component under test (item8) or the solenoid valve (item13) to discharge airfrom the tank (item4) into theatmosphere.Measurepressure in the tank,p3,upstreampressure,p1,anddownstreampressure,p2,duringdischargeusingthepressuretransducers(items16,11,and12),and record the values using the digital recorder (item15) as shown in Figure4. If the downstreamtransition connector cannot connect to a component under test, measure atmospheric pressure asdownstreampressure,p2.
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2
a b
3
1
4
X
Y
Key
X time
Y pressure
1 upstreampressure
2 downstreampressure
3 pressureinthetank
4 atmosphericpressurea chokedflowregionb subsonicflowregion
NOTE Thebrokenlineindicatestheupstreampressure,p1,whensolenoidvalve13isusedtostartthetest.Buttheupstreampressure,p1,beginsatthemaximumvalueifthecomponentundertestcanperformtheshifttostartthetest.
Figure4—Pressureresponseinthetankduringdischarge
6.2.4 Measuringproceduresforchargetest(seeFigure2)
6.2.4.1 Reduce the pressure in the tank (item 4) to approximately 2kPa absolute (0,02barabsolute)usingthevacuumpump(item18).Then,closetheshut‐offvalve(item3)andleavethetankinthisstateuntilthepressureinthetankreachessteady‐stateconditions.Measuretheinitialpressure,p3,using the pressure transducer (item 16), initial temperature, T3, using the temperature‐measuringinstrument(item5)inthetank,andtheatmosphericpressureusingthebarometer(item14).
6.2.4.2 Openthecomponentunder test(item8)or thesolenoidvalve(item13) tochargetheairfrom the atmosphere into the tank. Measure pressure in the tank, p3, upstream pressure, p1, anddownstream pressure,p2, during charge using the pressure transducers (items 16, 11, and 12), andrecordthevaluesusingthedigitalrecorder(item15)asshowninFigure5.
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b
4
a
2
1
3
X
Y
Key
X time
Y pressure
1 upstreampressure
2 downstreampressure
3 pressureinthetank
4 atmosphericpressurea chokedflowregionb subsonicflowregion
NOTE Thebrokenlineindicatestheupstreampressure,p1,whenasolenoidvalve13isusedtostartthetest.Buttheupstreampressure,p1,beginsatthemaximumvalueifthecomponentundertestcanperformtheshifttostartthetest.
Figure5—Pressureresponseinthetankduringcharge
6.3 Calculationofcharacteristics
6.3.1 Sonicconductance,C
6.3.1.1 Smoothingofpressureinthetank,p3
Performacalculationtosmooththerawpressuredatainthetankfroma21‐pointmovingaveragebyusingFormula(4).
10
3( ) 3( )10
1'
21
i j
j ii j
p p
(4)
where
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p3(i) isthepressureinthetank,inPa(i=1,2,···,n);
p’3(j) isthepressureinthetankaftermovingaverageprocessing,inPa(j=11,12,···,n‐10);
n isthenumberofpressuredatapointsmeasuredduringthedischargetestorthechargetest.
6.3.1.2 Conductancecharacteristicscurve
Calculate theconductance,Ce, foreachvalueof jover themeasuredregionshown inFigure4 for thedischarge test,orFigure5 for the charge test,byusingFormula(5)or (6).Describe the conductanceversusthepressureratioonthegraphasshowninFigures7or8:
— fordischargetest
3( 10) 3( 10)e( )
1( ) 0 0 3
' '
20
j jj
j
V p pC
p R t T T
(5)
— forchargetest
3( 10) 3( 10)e( )
1( ) 0 0 3
' '
20
j jj
j
V p pC
p R t T T
(6)
where
Ce(j) istheconductanceofacomponentundertest,inm3/(s∙Pa)(ANR)(j=21,22,…,n−20);seeFigure6foradescriptionofhowthesedataareorganized;
p1(j) istheupstreampressure,inPa;
p’3(j‐10) isthepressureinthetankaftersmoothingbefore10points,inPa;
p’3(j+10) isthepressureinthetankaftersmoothingafter10points,inPa;
V isthevolumeofthetank,inm3;
R isthegasconstant,inJ/(kg·K);[forair,R=287J/(kg·K)];
ρ0 isthemassdensityofairatthestandardreferenceatmosphere,inkg/m3;
T0 istheabsolutetemperatureatstandardreferenceatmosphere,inK;
T3 istheabsolutetemperatureinthetankatstartofdischarge,inK;
Δt isthetimeintervalforsamplingpressuredeterminedin5.5.2,ins.
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1 10 20 30
11 12 13
21 22 23
Measured pressure p3(i) n
… .
n-10
n-20
i=1,2,…, n
Smoothing pressure p’3(j)
j=11,12,…, n-10
Conductance C e(j)
j=21,22,…, n-20
Figure6—ValueofjinCe(i)
6.3.1.3 Calculationofsonicconductance,C
Calculatethesonicconductance,C,byaveragingthesaturatedregionoftheconductance,Ce,asshowninFigures7or8.Thesaturatedregionischaracterizedbyseveralvaluesoftheconductancethatareatmaximumvaluescomparedtoallothers.However,thisdoesnotincludethetransientvaluesobtainedimmediatelyafterstartingachargeordischarge.
IftheCecoefficientsvarysignificantlyinthechokedflowregion,thecomponentcouldbeconsideredtoexhibitpressuredependence. In this case, first repeat theprocedure in6.2.3.1 through6.2.3.3 at theupper limit of the pressure range of the component, then determine theKp andCmax. coefficients inaccordancewith6.3.3.
a
0
1
C
X
Y
Key
X back‐pressureratiop2/p1
Y conductanceCea saturatedregion
Figure7—Conductancecharacteristicsfordischargetest
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14 © ISO 2013 – All rights reserved
a
0 1
C
X
Y
Key
X back‐pressureratiop2/p1
Y conductanceCea saturatedregion
Figure8—Conductancecharacteristicsforchargetest
6.3.2 Criticalback‐pressureratio,b,andsubsonicindex,m
6.3.2.1 Calculatethecriticalback‐pressureratio,b,andsubsonicindex,m,fromFormula(7)bytheleast‐squaremethodusing all of pressure ratios,p2/p1, and conductance ratios,Ce/C, in the subsonicflow region determined in 6.3.1. See AnnexF for the calculation, giving attention to the secondparagraphinF.2.2.1.
22
e 111
mp
bC pC b
(7)
6.3.2.2 Ifthevalueofthesubsonicindex,m,calculatedin6.3.2.1isbetween0,48and0,52,itsvaluemaybecorrectedto0,5toreducethenumberofcharacteristicparameters.Inthiscase,recalculatethecorrespondingcriticalback‐pressureratio,b,inaccordancewith6.3.2.1,withm=0,5.
6.3.3 Pressuredependencecoefficient,Kp
Taking Cmax as the value of conductance for the maximum upstream pressure, plot the pressuredependenceasshowninFigure9usingthetestresultstatedin6.2.3.3,thenfindthecorrelativelineinthe range of the conductance ratio close to 1. The plot on this line can be considered to define thechokedflowregion.Theslopeofthislineisthevalueofthepressuredependencecoefficient,Kp.Whenselectingaconductanceratioandupstreampressureattwopositionsonthisline,KpcanbecalculatedbyusingFormula(8).
ISO 6358-2:2013(E)
© ISO 2013 – All rights reserved 15
low
maxp
1max 1low
1CC
Kp p
(8)
where
p1lowisthelowerupstreampressureofthelineardependence.
b c 0
1
a
3
1 2
4
X
Y
Key
X upstreampressurep1
Y conductanceratioCe/Cmax
1 firstdatapoint,takenatmaximumupstreampressure
2 secondpointontheline
3 correlativeline
4 testresultsa conductanceratioClow/Cmaxb upstreampressurep1lowc upstreampressurep1max
Figure9—Plotofconductanceratioversusupstreampressure
7 Presentationoftestresults
7.1 Allmeasurementsandtheresultsofcalculationsshallbetabulatedbythetestinglaboratory.
7.2 Ifdataare tobeused forpublishingratings inacatalogue, theaverageof results fromthe testunitsforeachcharacteristiclistedin7.3shallbereported.
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7.3 The followingperformancecharacteristicsrelated to flow‐ratecapacity,whicharecalculated inaccordancewith6.3,shallbestated:
a) sonicconductance,C,[alsoseeitemd)below],
b) criticalback‐pressureratio,b,
c) subsonicindex,m,and
d) ifnecessary,pressuredependencecoefficient,Kp,upstreampressure,p1max,andsonicconductance,Cmaxattheupstreampressurevaluep1max.
7.4 FromthesecharacteristicstheperformanceofthecomponentcanbepredictedusingFormula(E.1)and(E.2)ofAnnexEofISO6358‐1andcompared.
7.5 Therecordofthecalibrationofmeasuringdevicesshallbeavailable.
8 Identificationstatement(referencetothisdocument)
Use the following statement in test reports, catalogues, and sales literaturewhen electing to complywiththisInternationalStandard:
“Flow‐ratecharacteristicsofpneumaticcomponentsdeterminedinaccordancewiththedischargetestor charge test of ISO6358‐2, Pneumatic fluid power—Determination of flow‐rate characteristics ofcomponents—Part2:Alternativetestmethods”
ISO 6358-2:2013(E)
© ISO 2013 – All rights reserved 17
AnnexA(informative)
Evaluationofmeasurementuncertainty
A.1 General
The ISO guide of the uncertainty in measurement (GUM:2000) provides the current internationalconsensus method for estimating the measurement uncertainty. There are different possibilities toestimatemeasurement uncertainty, the strictmathematicalway is describedmost extensively in theGUM, but the other pragmatic methods that are in conformity with GUM can be used. The mostimportantruleis:effortandexpenditurefordeterminationofuncertaintiesshouldbeclearlyguidedbytheprinciple”fitforpurpose”,thatis,itshouldbegoodenoughtomeettherequirementsoftheuserofthemeasurementdata,but it shouldnotbeoverdone in lightof theapplication.Thisannexuses thisprinciple.
GUMgroupsuncertaintycomponentsintotypeAandtypeBaccordingtothewaydatawereobtained.Type A components are calculated by statistical means from repeated measurements, while type Bcomponents are taken from other sources, e.g. reference material, calibration certificates, acceptedvaluesofconstants,resolution,instability,environmentalconditions.
Inpractice,however,acombinedapproachwillbethemostsuitable;thiscombinedapproachwillapplyveryoften,asitisimpossibletoestimateeachuncertaintyindividually.Inthiscase,typeBwillbeusedwithreferencematerialsandqualitycontrolmaterialstoavoidsomesystematicmeasuringerror.Thesingle uncertainties are combined applying the law of propagation of uncertainty. The type Auncertaintyestimateisanestimatederivedfromthestatisticalanalysisofexperimentaldata.Thistypeofuncertaintyevaluationispreferredwhenthevalueofameasurandwillbetheaverageofseveraltestresultsorisinrelationwithnon‐independentvariables.
A.2 Evaluationofmeasurementuncertaintyofthesonicconductance,C,usingtypeB
A.2.1 Measurandconductance,Ce
According to this document, the most important flow‐rate characteristic parameter of a pneumaticcomponentisthesonicconductance,C.Theequationrelatingmeasurandconductance,Ce,andevolutionoftheconductanceduringthechargeordischargetestcanbeexpressedusingeitherFormula(E.3)or(E.8);followingtheseequations,thequantitysubjecttomeasurement,andinputquantitiesare:
3 3 3e 1 3
0 1 0 3
1( ) ( , , , )
T dp dpVC sign f p T V
p T RT dt dt (A.1)
A.2.2 Identificationofuncertaintyofinputquantities
AccordingtoFormula(A.1),theinputquantitiessubjecttomeasurementare:
a) p1–upstreamstagnationpressure
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18 © ISO 2013 – All rights reserved
Uncertaintyfollowstheaccuracyofmeasuringinstrument:±Δp1=±0,5%
Methodofmeasurementofstagnationpressure(walltaping):Δp1=+0,3%
b) T3–upstreamstagnationtemperature
Uncertaintyfollowstheaccuracyofmeasuringinstrument:±ΔT3=±1K
It must be noted here that all measurement instabilities are included in the previous limits ofuncertainty. If it is not, the reality in this range of instabilitymust be added at thepreviousΔT.However,thetemperaturevariation(decreasinginthedischargecaseorincreasinginchargecase)must be less than 3K from the isothermal tank. That is the condition for the validity of theisothermalassumptionofairinsidethetankandtheflowratecanbecalculatedbyonlyrecordingthepressureresponse.
c) V–volumeofisothermaltank
UncertaintieswillfollowtheevaluationofFormula(B.14)
d) dp3/dt–changeinpressureinthetank
Uncertaintywillfollowtheaccuracyofmeasuringinstrumentandthetimebase(samplingperiod).
A.2.3 Sensitivitycoefficient
Sensitivitycoefficientsareobtainedfrompartialderivativesofthemodelfunctionfwithrespecttotheinputquantities.Fortheevolutionofconductance,Ce:
3 32
1 0 30 1
1 T dpf Vp T RT dtp
fortheinputp1 (A.2)
3
3 3 030 1
0
1
2
dpf VT RT T dtT
pT
fortheinputT3 (A.3)
3
3 0 1 0 3
1 Tf Vdp p T RTdt
fortheinput 3dpdt
(A.4)
A.2.4 Expressionofabsolutestandarduncertainty
Theabsolutestandarduncertaintyforthemeasuredconductance,Ce,isgivenby:
3e 1 3
31 3
dpf f fC p T
dpp T dtdt
(A.5)
Iftherelativeorpercentagestandarduncertaintyisdesired,itisgivenby:
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© ISO 2013 – All rights reserved 19
ee
e% 100
CC
C
(A.6)
A.3 Evaluationofmeasurementuncertaintyofthesonicconductance,C,usingTypeA
A.3.1 Measurandsonicconductance,C
According to this document, the most important flow‐rate characteristic parameter of a pneumaticcomponent is thesonicconductance,C.Theevolutionof conductance,Ce, isdefinedbyFormula(A.1)canbeplottedovertheratioofdownstreampressuretoupstreampressure,p2/p1.Thesecurvesshowcorrelativelythepressurevariationandtheconductancecharacteristicsvariation.See6.3.1.3t.
A.3.2 Expressionofstandarduncertainty
If themeasurementpoints inthechokedflowregionareconsidered,anestimateofthemeasurandisobtainedthatwillbetheaverageofseveraldatapoints,asfollows:
1
1 n
ii
C Cn
(A.7)
where
n isnumberofmeasurementpointsinthechokedflowregion(n>1);
Ci istheresultofdatameasurementati.
The experimental standard deviation, sc, characterizes the variability of observed values, Ci, in thechokedflowregion,asfollows:
21
c 1
i n
ii
C C
sn
(A.8)
This experimental standard deviation of the sonic conductance measurement can be taken as anestimateofuncertainty(typeA).
A.4 Evaluationofmeasurementuncertaintyofthecriticalback‐pressureratio,b,andsubsonicindex,m,usingtypeB
A.4.1 Measurands
According to this document, the second most important flow‐rate characteristic parameter of apneumaticcomponentisthecriticalback‐pressureratio,b.Thesubsonicindex,m,iseventuallyusedtorepresent the subsonic flow behaviour. The equation relatingmeasurands b andm, i.e. the quantitysubjecttomeasurement,andinputquantitiesis:
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20 © ISO 2013 – All rights reserved
22
e 111
mp
bC pC b
(A.9)
Thisequationissolvedbythenonlinearleastsquaremethod(NLLSQ)withthevariablesasfollows:
ei
Cy
C (A.10)
2,
1,
ii
i
px
p (A.11)
Thedifferencebetweenanobservedvalueandthevaluegivenbythemodelis:
2
11
m
ii i
x by
b
(A.12)
The sum of squared difference will be the least values (see AnnexG). The NLLSQ are conceptuallyinadequatetogenerateastatisticalestimatorofuncertainty.ApragmaticwaytoestimatethevariabilityofbandmcanbetousetheNLLSQwiththeminimumandmaximumvaluesofCfoundinA.3.2.
A.4.2 Identificationandexpressionofuncertainty
AsmentionedinA.4.1,thefunctionalrelationshipbetweenthemeasurandsbandmandtheinfluencequantities is an arduous task. In this paragraph, two calculationswill focus on the upper and lowerlimitsofthesecharacteristics.Theuncertaintyoftheseflow‐ratecharacteristicswillbedefinedhereaslimitsassociatedwiththeNLLSQcalculationresults frommaximumandminimumsonicconductancedeterminedinthechokedflowregion.Intheseconditions:
c min,
CC s NLLSQ b m (A.13)
c max,
CC s NLLSQ b m (A.14)
From these calculation results, themaximumabsolute differences between these limits and the bestvaluesattributabletothesemeasurandsarethetwovalues:
maxb and
maxm .Thesevaluesarenow
consideredastheuncertaintyoftheresultofameasurement,whichisexpressedas:
maxb b forthecriticalback‐pressureratio (A.15)
maxm m forthesubsonicindex (A.16)
NOTE Thesecalculationsshowthat:
a) concerningthechokedflowregionoftheconductancecurve,thecomparisonofresultscanbedonedirectlybycomparingthevaluesofsonicconductance,C;but
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© ISO 2013 – All rights reserved 21
b) concerning thesubsonic flowregionof theconductancecurve, thecomparisonofeachparameterb andmindependently is not sufficient to compare the results. It is necessary to add a graphical comparison ofconductance curves, because the variations of each parameter C, b, and m can compensate to give anequivalentsubsonicflowregionoftheconductancecurve.
A.5 Repeatabilityandreproducibility
Asimplemethodforbasinguncertaintyestimatesonrepeatabilityandreproducibilitycanbemadebystatisticalmeansfromrepeatedmeasurements.Thismethodhasagreatadvantageinthatmosttestinglaboratoriesarealreadyacquaintedwithrepeatabilityandreproducibilityexperiments,butthismethodassumes that all significant systematic effects have been identified and either eliminated orcompensatedforbytheapplicationofsuitablecorrections.
Forcompletedetails,seeISO5725(inparticularISO5725‐2)andISO21748.
A.6 Practicaluncertaintyduetotankvolume
In the discharge test and charge test, flow rate is calculated by a tank volume,V, and the change inpressureinthetankfromdp3/dtinFormula(A.1).UncertaintyofCfromthedischargeandchargetestswhen the tank volume varies is shown in FigureA.1. The abscissa is V/C, which is tank volume, V,dividedby sonic conductance,C. This value represents an indicator of discharge or charge time. ThevalueofC ismorevariablewhenthetankvolume is toosmall forboththedischargetestandchargetest. When V/C>5×105, as described in 5.4.3, variations in C, b, and m due to tank volume areminimised.
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22 © ISO 2013 – All rights reserved
-2
-1,5
-1
-0,5
0
0,5
1
1,5
2
0 5 10 15 20
σ
-σ
×105
X
Y
Key
X V/C[m3/(s.Pa)(ANR)]
Y C[%]
dischargetest
mean
chargetest
mean
FigureA.1—Distributionsoftankvolumeandpracticaluncertainty
A.7 Practicaluncertaintyduetotemperature
Inthedischargetest,thecalculationofsonicconductance,C, isbasedonthetemperatureofairinthetankatthestartofdischarge,eventhoughthetemperatureintheisothermaltankwillslightlydecreaseduring discharge. Similarly, in the charge test, the temperature in the isothermal tank will slightlyincrease. The error of this decrease or increase of temperature is shown in Formula(A.17). In thedischargetest,Ciscalculatedtobesmallerthanatruevalueby0,5%whentemperaturedecreasesby3KataCcalculationpoint.Inthechargetest,C iscalculatedtobelargerthanatruevalueby0,17%whenthetemperaturerisesby1K.
'3 3
33
1ISO %
2 2T T
TT
(A.17)
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© ISO 2013 – All rights reserved 23
A.8 Errorduetotransientchangeoftemperature
Formula(A.1)ofthedischargetestignoresthetemperaturechangeoftheisothermaltankasdescribedinAnnexE.Whenconsideringthetransientchangeoftemperature,thesecondtermappearsasshowninFormula(A.18),whereMdenotesthemassofair.Inanactualtest,thetemperaturewilldecreasebyafewKevenwhenanisothermaltankisused,andsodT/dtwillbecomethemaximumvaluewhenthedischarge starts. Therefore, in accordancewith this part of ISO6358,C is calculated to be larger byapproximately1%atinitialdischarge.
However, if this transient interval is eliminated in the calculation of C as described in 6.3.1.3, itsinfluenceonthecalculatedCbecomessmall.Also,inthechargetest,Ciscalculatedtobeslightlysmallerduetotemperatureincreaseatinitialcharge,butthisresultwillhavelittleeffectonthecalculation.
3
0 1 0 3 0 1 0 3
dpV M dTC
dt dtp R T T p T T (A.18)
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24 © ISO 2013 – All rights reserved
AnnexB(normative)
Testmethodtodetermineandcalibratethevolumeofanisothermaltank
B.1 Testcircuit
ThetestcircuitshowninFigureB.1shallbeused.
1 2 3
12
9 10 8 7 11 5 6 4 4b 4a 8a 8b
Key
1 compressedgassourceandfilter
2 adjustablepressureregulator
3,7,and11 shut‐offvalve
5and9 temperaturemeasuringinstrument
6and10 pressuretransducer
4 isothermaltankundertest
4aand4b piping
8 referencetank(ofaknownvolume)
8aand8b piping
12 barometer
FigureB.1—Testcircuit
B.2 Generalrequirements
B.2.1 VolumeVi of the isothermal tank includes the volume of piping 4a and 4b. VolumeVs of thereference tank includes the volume of piping 8a and 8b. These piping volumes shall be determinedseparately,sothatthesedatacanbeusedwithothertanks.
B.2.2 ThevolumesViandVsof,respectively,theisothermaltankundertest(item4)andthereferencetank(item8)shallbeselectedusingFormula(B.1).
i
s0,1 10
VV
(B.1)
B.2.3 The location of the isothermal tank under test (item 4), the reference tank (item 8), thetemperature measuring instruments (items 5 and 9), and the pressure gauges (items 6 and 10) in
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© ISO 2013 – All rights reserved 25
FigureB.1maybechanged.Inthatcase,thereferencestotheisothermaltankundertest(item4)andthereference tank(item8) inB.3.1andB.3.3shallbereplacedwithreferences to thereference tank(item8)andtheisothermaltankundertest(item4).
B.2.4 Beforeconductingmeasurements,ensurethatnoneofthecomponentsinFigureB.1,fromitem3toitem11,leak.
B.3 Measurementprocedures
B.3.1 Closethefirsttwoshut‐offvalvesinthecircuit(items3and7),andopenthethirdshut‐offvalve(item11).Setthepressureofthepressureregulator(item2)at700kPa(7bar),andopenthefirstshut‐offvalve(item3)tochargetheair intothe isothermaltankundertest(item4).Aftercharging,allowsufficienttimeforthetemperatureandpressureinthetanktoreachsteady‐stateconditions.
B.3.2 Closethefirstandlastshut‐offvalves(items3and11).Measuretheatmosphericpressure,pa,usingthebarometer(item12),andmeasuretheinitialpressure,ps1,usingthepressuregauge(item10)andinitialtemperature,Ts1,usingthetemperaturemeasuringinstrument(item9)inthereferencetank(item8).Measuretheinitialpressure,pi1,usingthepressuregauge(item6)andinitialtemperature,Ti1,usingthetemperaturemeasuringinstrument(item5)intheisothermaltankundertest(item4).
B.3.3 Open the second shut‐off valve (item7) todischarge air from the isothermal tankunder test(item4)intothereferencetank(item8).Aftercharging,allowsufficienttimeforthetemperatureandpressureinthetankstoreachsteady‐stateconditions.
B.3.4 Measurethepressures,pi2andps2,usingthepressuregauges(items6and10),respectively,andthe temperature, Ti2 and Ts2, using the temperature measuring instruments (items 5 and 9),respectively,intheisothermaltankundertest(item4)andthereferencetank(item8).
B.3.5 Openthethirdshut‐offvalve(item11)todischargetheairfromtheisothermaltankundertest(item4)andthereferencetank(item8)totheatmosphere.
B.4 Calculationoftankvolume
UseFormula(B.2),which isbasedon theequationof state, tocalculate thevolumeof the isothermaltankundertest(item4),Vi.
s2 s1
s2 s1i s
i1 i2
i1 i2
p pT T
V Vp pT T
(B.2)
where
pi1 istheinitialpressureintheisothermaltankundertest(item4),inkPa;
pi2 is the pressure in the isothermal tank under test (item 4) when the second shut‐off valve(item7) is opened and the temperature and pressure in the tanks reach steady‐stateconditions,inkPa;
ps1 istheinitialpressureinthereferencetank(item8),inkPa;
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26 © ISO 2013 – All rights reserved
ps2 isthepressureinthereferencetank(item8)whenthesecondshut‐offvalve(item7)isopenedandthetemperatureandpressureinthetanksreachsteady‐stateconditions,inkPa;
Ti1 istheinitialtemperatureintheisothermaltankundertest(item4),inK;
Ti2 isthetemperatureintheisothermaltankundertest(item4)whenthesecondshut‐offvalve(item7) is opened and the temperature and pressure in the tanks reach steady‐stateconditions,inK;
Ts1 istheinitialtemperatureinthereferencetank(item8),inK;
Ts2 is the temperature in the reference tank (item8)when the second shut‐off valve (item7) isopenedandthetemperatureandpressureinthetanksreachsteady‐stateconditions,inK;
Vs istheknownvolumeoftank8,indm3.
B.5 Evaluationofmeasurementuncertaintyofthevolumeofisothermaltank(TypeBoftheGUM)
B.5.1 MeasurandvolumeVi
Formula(B.3)relatesthemeasurandVi,i.e.thequantitysubjecttomeasurement,andinputquantities:
1s2 s1 i1 i2
i ss2 s1 i1 i2
p p p pV V
T T T T
(B.3)
i s s1 s2 s1 s2 i1 i2 i1 i2, , , , , , , ,V f V p p T T p p T T (B.4)
B.5.2 Identificationofuncertaintyofinputquantities
AccordingtoFormulae(B.3)and(B.4),theinputquantitiessubjecttomeasurementare:
a) Vsvolumeofreferencetank
— Uncertaintyfollowingaccuracyofmeasuringinstrument:±ΔVs={±1%}
b) psandpistagnationpressuresofreferenceandisothermaltanks
— Uncertaintyfollowingaccuracyofmeasuringinstrument:±Δps={±0,5%}
— Uncertaintyfollowingaccuracyofmeasuringinstrument:±Δpi={±0,5%}
c) TsandTistagnationtemperatureofgasinreferenceandisothermaltanks
— Uncertaintyfollowingaccuracyofmeasuringinstrument:±ΔTs={±1K}
— Uncertaintyfollowingaccuracyofmeasuringinstrument:±ΔTi={±1K}
Allmeasurement instabilities are included in theprevious limits of uncertainty. If it does not reflectreality,thisrangeofinstabilityshallbeaddedtothepreviousΔT.
Theseinputquantitiesareindependentvariables,andthesensitivitycanbecalculated.
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© ISO 2013 – All rights reserved 27
B.5.3 Sensitivitycoefficient
Sensitivitycoefficientsareobtainedfrompartialderivativesofthemodelfunctionfwithrespecttotheinput quantities. For the volume of the isothermal tank under test (item 4), the following can beobtainedbyusingFormulae(B.5)through(B.13),inclusive:
1s2 s1 i1 i2
s s2 s1 i1 i2
p p p pfV T T T T
fortheinputVs (B.5)
1s i1 i2
s1 s1 i1 i2
V p pfp T T T
fortheinputps1 (B.6)
1s i1 i2
s2 s2 i1 i2
V p pfp T T T
fortheinputps2 (B.7)
1s1 i1 i2
s 2s1 i1 i2s1
p p pfV
T T TT
fortheinputTs1 (B.8)
1s2 i1 i2
s 2s2 i1 i2s2
p p pfV
T T TT
fortheinputTs2 (B.9)
2s s2 s1 i1 i2
i1 t1 s2 s1 i1 i2
V p p p pfp T T T T T
fortheinputpi1 (B.10)
2s s2 s1 i1 i2
i2 i2 s2 s1 i1 i2
V p p p pfp T T T T T
fortheinputpi2 (B.11)
2s i1 s2 s1 i1 i22
i1 s2 s1 i1 i2i1
V p p p p pfT T T T TT
fortheinputTi1 (B.12)
2s i2 s2 s1 i1 i22
i2 s2 s1 i1 i2i2
V p p p p pfT T T T TT
fortheinputTi2 (B.13)
B.5.4 Expressionofabsolutestandarduncertainty
Theabsolutestandarduncertaintyforthemeasuredvolumeoftheisothermaltankundertest(item4)isgivenbyFormula(B.14):
i s s1 s2 s1 s2 i1 i2 i1 i2
s s1 s2 s1 s2 i1 i2 i1 i2
f f f f f f f f fV V p p T T p p T T
V p p T T p p T T
(B.14)
Iftherelativeorpercentagestandarduncertaintyisdesired,itisgivenbyFormula(B.15):
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28 © ISO 2013 – All rights reserved
ii
i% 100
VV
V
(B.15)
B.6 Exampleoftestresult
FiguresB.2andB.3showthetestresultforthevolumeofanisothermaltankwithanominalvolumeof20dm3.TableB.1showsanexampleofuncertaintycalculation.
FiguresB.2andB.3alsoshowthe test resultofdischarge fromthe isothermal tankunder test to thereferencetankandviceversa.Thevolumeofreferencetankwasmeasuredinadvance.InFigureB.2,thepressure in the isothermal tankunder testwas set at about790kPa (7,9bar), and inFigureB.3, thepressureinthereferencetankwassetatabout655kPa(6,55bar).Initialpressures,pi1andps1,initialtemperatures,Ti1 andTs1, and the atmospheric pressureweremeasured. Pressures, pi2 and ps2, andtemperatures,Ti2 andTs2,weremeasured10minafterdischarge.Thevolumeof the isothermal tankundertestwascalculatedusingFormula(B.1)basedonthemeasuredvalue.
ConditionMeasuredresult Calculated
resultIsothermaltankundertest Referencetank
Initialconditionpi1=789,88kPa(7,8988bar)
Ti1=300,8K
ps1=100,90kPa(1,009bar)
Ts1=299,9K
Afterdischargingpi2=220,32kPa(2,2032bar)
Ti2=298,5K
ps2=220,37kPa(2,2037bar)
Ts2=300,5K
Vi=21,38dm3
pi1→ pi2
Ti1 → Ti2
Vi
Isothermal tank under test Reference tank
ps1→ ps2
Ts1 → Ts2
Vs
Vs=101,67dm3
Atmosphericpressure=100,836kPa(1,00836bar)
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© ISO 2013 – All rights reserved 29
FigureB.2—Exampleoftestresult(dischargefromIsothermaltankundertesttoreferencetank)
Condition
MeasuredresultCalculatedresultReferencetank Isothermaltankunder
test
Initialcondition
ps1=655,07kPa(6,5507bar)
Ts1=301,2K
pi1=100,97kPa(1,0097bar)
Ti1=299K
Afterdischarging
ps2=557,56kPa(5,5756bar)
Ts2=300,4K
pi2=557,52kPa(5,5752bar)
Ti2=300,8K
Vi=21,38dm3
Isothermal tank under test
Reference tank
pi1→ pi2
Ti1 → Ti2
Vi
ps1→ ps2
Ts1 → Ts2
Vs
Vs=101,67dm3
Atmosphericpressure=100,860kPa(1,0086bar)
FigureB.3—Exampleoftestresult(dischargefromreferencetanktoisothermaltankundertest)
TableB.1—Exampleofcalculationofuncertainty
Inputquantities EvaluationofmeasurementuncertaintyofthevolumeMeasuredvalue Accuracy
Vs 101,67 dm3 ±ΔVs ±0,1 dm3 sVf 0,210
ps1 100,90 kPa ±Δps ±1 kPa s1pf ‐0,180 dm3/kPa
ps2 220,37 kPa s2pf 0,179 dm3/kPa
pi1 789,88 kPa i1pf ‐0,038 dm3/kPa
pi2 220,32 kPa i2pf 0,038 dm3/kPa
Ts1 299,9 K ±ΔTs ±1 K s1Tf 0,060 dm3/K
Ts2 300,5 K s2Tf ‐0,131 dm3/K
Ti1 300,8 K i1Tf 0,099 dm3/K
Ti2 298,5 K i2Tf ‐0,028 dm3/K
iV 0,774 dm3
%iV 3,621%
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30 © ISO 2013 – All rights reserved
AnnexC(informative)
Isothermaltankstuffing
C.1 General
Thetemperaturechangeinthetankduringcharginganddischargingtheaircanberegulatedbystuffingthetankwithmaterialthathasalargeheatcapacity.Thisallowsthetestconditionstobekeptconstant,andthesonicconductancecanbecalculatedbyusingasimpleequation.Also,thisallowsthestabilizingtimeofthetemperatureinthetanktobereduced,whichresultsinshortertestingtime.
C.2 Massdensityandisothermalperformanceofstuffedmaterial
FigureC.1showsthetestresultsfortemperaturedropintankswithinsidevolumesof10,20,50,and100dm3, respectively, by changing the volume of stuffed material, in this case, copper wire with adiameterof 50μm.The figure showshow the temperaturedrops in the respective tank sizeswith achargepressureof700kPa(7bar)duringairreleaseforapproximately15s,whichmeansamaximumrate of pressure drop of approximately 100kPa/s (1bar/s). TableC.1 shows test results for a tankvolumeof5dm3;thevaluesoftheheatcapacityofcopperwireandairandtheratiobetweenthevalueshavebeencalculatedandgiven for referenceonly. Inorder tomaintain the temperaturedropwithin3K,useofastuffedmaterialwithamassdensityof0,3kg/dm3ormoreisnecessary.
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Key
X stuffedmass[kg/dm3]
Y temperaturedrop[K]
tankvolume10dm3
tankvolume20dm3
tankvolume50dm3
tankvolume100dm3
FigureC.1—Influenceofthemassofstuffedmaterialontemperaturedrop
TableC.1—Temperaturedropwithcopperwirestuffedmaterial
Massdensityofcopperwire
stuffedmaterial
[kg/dm3]
Percentageofstuffedvolume
[%]
Heatcapacityofcopperwire
[J/K]
Heatcapacityofair(at700kPa)
[J/K]
Ratioofheatcapacitiesofcopperand
air
Temperaturedrop
[K]
0,399 4,47% 770,0 39,86 19,3 1,3
0,349 3,91% 673,8 40,09 16,8 1,9
0,299 3,35% 577,5 40,33 14,3 2,5
0,250 2,79% 481,3 40,56 11,9 3,0
0,200 2,24% 385,0 40,79 9,4 5,5
0,150 1,68% 288,8 41,02 7,0 7,7
0,100 1,12% 192,5 41,26 4,7 15,4
0,050 0,56% 96,3 41,49 2,3 28,5
0,000 0,00% 0,0 41,72 0,0 45,8
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C.3 Stuffedmaterial
C.3.1 TableC.2showsthetemperaturedropwhenthetestisconductedwith4kgofcopperwireandstainlesssteelwirewithdiametersof,respectively,30and50μmstuffedat0,40kg/dm3inatankwithaninsidevolumeof10dm3.Thetestisconductedunderthesameconditionsasabove.
TableC.2—Temperaturedropwithmetallicwire
WirematerialWirediameter
30μm 50μm
Copper 1,5K 1,8K
Stainlesssteel — 1,1K
C.3.2 TableC.3 shows the temperature drop when the test is conducted with polyester fibre withdiameterof20 to50μmstuffed intoa tankwitha volumeof5dm3.When thedensityof the stuffedmaterialis0,04kg/dm3ormore,thetemperaturedropwillbe3Korless.
TableC.3—Temperaturedropwithpolyesterfibre
Massdensityofstuffedmaterial
[kg/dm3]
Percentageofstuffedvolume
[%]
Heatcapacityofpolyester
fibre
[J/K]
Heatcapacityofair(at700kPa)
[J/K]
Ratioofheatcapacitiesoffibreandair
Temperaturedrop
[K]
0,08 5,8% 537,6 39,31 13,7 1,5
0,04 2,9% 268,8 40,52 6,6 2,3
0,02 1,5% 134,4 41,12 3,3 6,2
0,00 0,0% 0,0 41,72 0,0 45,8
C.3.3 Pelletsmadeofmaterialssuchasporousglassorceramicmayalsobeusedasstuffedmaterial.
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AnnexD(informative)
Testmethodtodetermineisothermalperformance
D.1 Purpose
The purpose of this test is to determine if the isothermal tank and its stuffing material keep thetemperatureofthegasfromchangingbymorethan3K.
D.2 Testcircuit
ThetestcircuitshowninFigure1shallbeused.Inaddition,atimerthatiscapableofsettingtimesforopeningandclosingthesolenoidvalveshallbeinstalled.
NOTE The sonic conductance of the component under test and volumeof the tank shall be determined inaccordancewithFormula(1)in5.4.3.
D.3 Testprocedure
D.3.1 Settheinitialtankpressureat700kPa(7bar)usingthepressureregulator(item2)andleavethetankinthisstateuntilthetemperatureandpressureinthetankreachthesteady‐statecondition.
D.3.2 Close the shut‐off valve (item3) and measure the initial pressure, pi1, using the pressuretransducer(item16)andinitialtemperature,Ti1,usingthetemperaturemeasuringinstrument(item5)inthetank(item4).
D.3.3 Open the solenoid valve (item13) for 0,5s using the electrical control mechanism. Detectpressurechangeduringdischargeandreturntothesteady‐stateconditioninthetank(item4)usingthepressuretransducer(item16),andrecorditusingthedigitalrecorder(item15)asshowninFigureD.1.
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pi1
pi3
pi2
0
a
X
Y
Key
X time
Y pressure
a timeonvalveclosed
FigureD.1—Pressureresponsewhenstoppingdischarge
D.3.4 Afterthedischarge,allowsufficienttimeforthepressureintank(item4)toreachasteady‐statelevel.Then,recordthestabilizedpressure,pi3,andthepressure,pi2,whenthesolenoidvalve(item13)isclosed.
D.3.5 UseFormula(D.1),whichisbasedonCharles’Law,tocalculatetheaveragetemperature,Ti2,inthetankatthetimeofclosingthesolenoidvalve:
i2i2 i1
i3
pT T
p (D.1)
where
Ti1 istheinitialtemperature,inK;
pi2 isthepressurewhenthesolenoidvalveisclosed,inkPa;and
pi3 isthestabilizedpressure,inkPa.
D.3.6 Increasetheopeningtimeofthesolenoidvalveby0,5s(i.e.to1s)asstatedinD.3.3,andrepeatD.3.1throughD.3.5untilthepressureinthetankiscompletelydischarged.
D.4 Confirmationofisothermalization
Plot the average temperature in the tank obtained in D.3.5 in graphical form. FigureD.2 shows theexampledescribed fromTableC.2.A temperaturedropwithin3Kproducesamaximumdeviationof0,5% in the conductance, Ce. Thus, if the temperature drop is within 3K, the tank volume can beconsideredasanisothermalvolume.
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0
100
200
300
400
500
600
700
800
0 5 10 15 X
282
283
284
285
286
287
288
289
290
0 5 10 15 X
Y2
Y1
Key
X time[s]
Y1 pressure[kPa]
Y2 temperature[K]
wirediameter30μm
wirediameter50μm
FigureD.2—Influenceofwirediameteronisothermalperformance
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AnnexE(informative)
Equationsforcalculationofflow‐ratecharacteristics
E.1 Equationsfordischargetest
E.1.1 Calculationmodel
ConsiderFigureE.1asamodelofthetestcircuitinFigure1.ThepressuresinadischargeprocessareshowninFigure4.Thevolumeoftheupstreampressure‐measuringtubehasbeenignoredbecauseitismuch smaller than the volumeof the tank.Because the temperature in the isothermal tank isnearlyconstantduringdischarge,thechangeofstateoftheaircanbeconsideredisothermal.Themassflowrate through the component under test, qm, can be calculated using Formula(E.1), based on theequationofstate:
3m
3
dpVq
RT dt (E.1)
V
Tank 4
T3 p1
qm
p2 p3
Component under test 8
FigureE.1—Modelofdischargetestcircuit
E.1.2 Calculationofmassflowrate,qm
The mass flow rate of the component under test, qm, throughout the entire discharge regime isexpressedbyFormula(E.2):
0m 0 1
3e
Tq C p
T (E.2)
where
Ceistheconductanceofthecomponentundertest.
BysolvingFormulae(E.1)and(E.2),theconductance,Ce,isexpressedbyFormula(E.3):
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3e
1 0 0 3
dpVC
dtp R T T (E.3)
Formula(5)in6.3.1.2forcalculatingtheconductance,Ce,forthedischargetestisobtainedbymodifyingFormula(E.3) by the central difference method. The sonic conductance, C, is calculated from thesaturatedregionoftheconductance,Ce,asshowninFigure7.
E.1.3 Calculationofcriticalback‐pressureratio,b,andsubsonicindex,m
Formula(E.5)forconductanceratioinsubsonicflowisobtainedfromFormula(E.4)formassflowrateinsubsonicflowregionand(E.2).Criticalback‐pressureratio,b,andsubsonicindex,m,arecalculatedfrom the ratio of conductance, Ce, and sonic conductance, C, except in the saturated region, usingFormula(E.5)andtheleast‐squaremethod.
22
0 1m 0 1
31
1
mp
bT p
q C pT b
(E.4)
22
e 111
mp
bC pC b
(E.5)
E.2 Equationsforchargetest
E.2.1 Calculationmodel
Consider FigureE.2as amodel of the test circuit in Figure2. The pressures in a charge process areshowninFigure5.Becausethetemperatureintheisothermaltankisnearlyconstantduringcharge,thechangeofstateofaircanbeconsideredisothermal.Themassflowratethroughthecomponentundertest,qm,canbecalculatedusingFormula(E.6),basedontheequationofstate:
3m
3
dpVq
RT dt (E.6)
V
Tank 4
p1
qm
p2 p3
Component under test 8
T3
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FigureE.2—Modelofchargetestcircuit
E.2.2 Calculationofmassflowrate,qm
Themassflowrateofthecomponentundertest,qm,throughouttheentirechargeregionisexpressedbyFormula(E.7)
0m e 0 1
a
Tq C p
T (E.7)
where
Ce istheconductanceofthecomponentundertest,and
Ta istheatmospherictemperature.
Consider that the temperature in the tank, T3, is the same as the atmospheric temperature, Ta. BysolvingFormulae(E.6)and(E.7),theconductance,Ce,isexpressedbyFormula(E.8):
3e
1 0 0 3
dpVC
dtp R T T (E.8)
Formula(6) in 6.3.1.2 for calculating the conductance, Ce, for charge test is obtained by modifyingFormula(E.8) by the central difference method. The sonic conductance, C, is calculated from thesaturatedregionoftheconductance,Ce,asshowninFigure8.
E.2.3 Calculationofcriticalback‐pressureratio,b,andsubsonicindex,m
Formula(E.10)fortheconductanceratioinsubsonicflowisobtainedfromFormula(E.9)formassflowrate insubsonic flowregionandFormula(E.7).Criticalback‐pressureratio,b,andsubsonic index,m,arecalculatedfromtheratiooftheconductance,Ce,andsonicconductance,C,exceptinthesaturatedregion,usingFormula(E.10)andtheleast‐squaremethod.
22
0 1m 0 1
a1
1
mp
bT p
q C pT b
(E.9)
22
e 111
mp
bC pC b
(E.10)
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AnnexF(informative)
Proceduresforcalculatingcriticalback‐pressureratio,b,andsubsonic
index,m,bytheleast‐squaremethodusingtheSolverfunctioninMicrosoftExcel
F.1 Usingdatainthesubsonicflowregion
Criticalback‐pressureratio,b,andsubsonicindex,m,arecalculatedbytheleast‐squaremethodusingEquation(F.1),back‐pressureratio,xi=p2/p1andconductanceratio,yi=Ce/C.Npointsaremeasuredinthesubsonicflowregion,asshowninTableF.1.
TableF.1—Pressureandconductanceratiosinthesubsonicflowregion
Measuredvalue
p2/p1 Ce/C
x1 y1
x2 y2
xN yN
2e 1
1
m
iC x bC b
(F.1)
Determine b andm so that the total sum, E [see Equation(F.3)], becomes the least of the squareddifference,δi [seeEquation(F.2)]betweenconductanceratio,Ce/C,or 21 / 1
m
ix b b , calculatedby
substitutingthemeasuredback‐pressureratio,xi,inEquation(F.1),andconductanceratio,yi,obtainedin6.3.1.2and6.3.1.3.AnexamplecalculationisshowninF.2.
2
11
m
ii i
x by
b
(F.2)
2 2 22 2 2N
2 1 2 N1 2 N
1
1 1 11 1 1
m m m
ii
x b x b x bE y y y
b b b
L
(F.3)
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F.2 UsingtheSolverfunctionbuiltinMicrosoftExcel
F.2.1 Function
SolverisafunctionavailableinthesoftwareprogramMicrosoftExcel.Usingassumedinitialvaluesforthevariablestobecalculated,theSolverfunctionvariestheseinitialvaluesinthebaseequationtogiveabestfittothedataenteredforthebaseequation.
F.2.2 Calculationofcriticalback‐pressureratio,b,andsubsonicindex,m
F.2.2.1 Enterthevaluesofpressureratio,p2/p1,andconductanceratio,Ce/C,inTableF.1inthecellsfromC4andD4untiltheendofthedata(seeFigureF.1).EnterEquation(F.2)inthecellsfromE4untiltheendofthedatatocalculatethedifferencebetweenthemeasuredconductanceratioandcalculatedconductanceratio.EnterthesquaredcolumnEinthecellsfromF4untiltheendofthedatatocalculatethe squared difference. Enter Equation (F.3) in the target cell G4 to calculate the total sum of thesquareddifference.Thevaluesofb(incellA4)andm(incellB4)areconsideredsolvedwhenthevalueintargetcellG4becomestheminimum.Avalueof0,5isenteredbothforbincellA4andformincellB4asinitialvalues.
FigureF.1—Inputofdata
Pressure data in the region close to the atmospheric pressure level could result in pressure ratiosgreater than 1 because of pressure sensor errors and signal noise, as shown in FigureF.2. Data thatresultinpressureratiosgreaterthan1canbeignored.
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© ISO 2013 – All rights reserved 41
1
2
2
a b
3
1
4
X
Y
5
Key
X time
Y pressure
1 upstreampressure
2 downstreampressure
3 pressureinthetank
4 atmosphericpressure
5 crossing
a chokedflowregion
b subsonicflowregion
FigureF.2—Illustrationofthepossibilityofpressurecrossingnearatmosphericconditions
F.2.2.2 StartSolver(seeFigureF.3)asfollows:
a) gotoTool(T)andselectSolver(V).Ifthe“Tool(T)”menudoesnotdisplaythe“Solver”command,consult“Help(H)”inExceltoinstalltheSolvertoExcel;then
b) specifythetargetcellG4,thetargetvalue(minimumvalue),andthecellsforvariables(A4andB4)onthe“SolverParameter”screenandclick“Solve(S)”,asshowninFigureF.3.
F.2.2.3 The values in cells A4 and B4 are varied (see FigureF.4), and the values ofb andm areobtained.
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42 © ISO 2013 – All rights reserved
FigureF.3—StartofSolver
FigureF.4—Calculationofbandm
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© ISO 2013 – All rights reserved 43
Bibliography
[1] ISO5725‐2, Accuracy (trueness and precision) ofmeasurementmethods and results— Part2:Basicmethodforthedeterminationofrepeatabilityandreproducibilityofastandardmeasurementmethod
[2] ISO21748, Guidance for the use of repeatability, reproducibility and trueness estimates inmeasurementuncertaintyestimation