Pneumatic fluid power -- Determination of flow-rate...

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

This ISO document is a Draft International Standard and is copyright‐protected by ISO. Except aspermittedundertheapplicablelawsoftheuser'scountry,neitherthisISOdraftnoranyextractfromit may be reproduced, stored in a retrieval system or transmitted in any form or by any means,electronic,photocopying,recordingorotherwise,withoutpriorwrittenpermissionbeingsecured.

RequestsforpermissiontoreproduceshouldbeaddressedtoeitherISOattheaddressbeloworISO'smemberbodyinthecountryoftherequester.

ISOcopyrightoffice

Casepostale56•CH‐1211Geneva20

Tel.+41227490111

Fax+41227490947

E‐[email protected]

Webwww.iso.org

Reproductionmaybesubjecttoroyaltypaymentsoralicensingagreement.

Violatorsmaybeprosecuted.

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

ISO 6358-2:2013(E)

2 © ISO 2013 – All rights reserved

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.

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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


13 5.3.4and5.3.9

Flowcontrolsolenoidvalve(optional) Thesonicconductanceofthisflowcontrolvalveshallbeaboutfourtimeslargerthanthatofthecomponentundertest.

14 ‐ Barometer

15 ‐ Digitalrecorder


17 ‐ Suctionportforchargetest

18 ‐ Vacuumpumpforchargetest

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


b

4

a

2

1

3

X

Y

Key

X time

Y pressure

1 upstreampressure


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

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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

ISO 6358-2:2013(E)


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)


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.

ISO 6358-2:2013(E)


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)


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

ISO 6358-2:2013(E)


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:

ISO 6358-2:2013(E)


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:

ISO 6358-2:2013(E)


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

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


-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)

ISO 6358-2:2013(E)


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)

ISO 6358-2:2013(E)


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

ISO 6358-2:2013(E)


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;

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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):

ISO 6358-2:2013(E)


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)

ISO 6358-2:2013(E)


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%

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


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

ISO 6358-2:2013(E)


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):

ISO 6358-2:2013(E)


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

ISO 6358-2:2013(E)


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)

ISO 6358-2:2013(E)


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)

ISO 6358-2:2013(E)


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.

ISO 6358-2:2013(E)


1

2

2

a b

3

1

4

X

Y

5

Key

X time

Y pressure

1 upstreampressure


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.

ISO 6358-2:2013(E)


FigureF.3—StartofSolver

FigureF.4—Calculationofbandm

ISO 6358-2:2013(E)


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

Date post:	23-May-2018
Category:	Documents
Upload:	trinhnhan
View:	213 times
Download:	0 times

Pneumatic fluid power -- Determination of flow-rate...

Documents