Microsoft Wordghfgh

7/30/2019 Microsoft Wordghfgh

1/67

DKD-R 6-1 Calibration of Pressure Gauges

DEUTSCHER KALIBRIERDIENST

Guideline Calibration of

DKD-R 6-1 Pressure Gauges


2/67


Published by the Accreditation Body of the Deutscher Kalibrierdienst (DKD) at the Physika-lisch-Technische Bundesanstalt in co-operation with its Technical Committee "Pressure and

Vacuum."

Copyright 2003 by DKD

The work including all its parts is protected by copyright. Any exploitation outside the narrowconfines of the Copyright Act is inadmissible and liable to prosecution unless it has been ap-proved. This is valid in particular for reproductions, translations, microfilming as well as stor-age and processing in electronic systems.

The document and all its parts are protected by copyright. Any unauthorized use outside thenarrow limits set by the Copyright Act is inadmissible and liable to prosecution. This applies inparticular to copies, translations, microfilming and storage and processing in electronic sys-tems.

Objavljeno od strane akreditacionog tijela Njemakog kalibracionog servisa u

Fiziko-tehnikoj saveznoj agenciji u saradnji sa Tehnikim komitetom

,,Pritisak i vakuum.

Izdavaka prava zadrava 2003 DKD

Rad ,ukljuujui sve njegove djelove, je zatien autorskim pravima. Svako

korienje izvan uskih granica koje su odredjene od strane Zakona o

Autorskim pravima je nedopustivo i podlono krivinom gonjenju,osim ako je

odobreno. To vrijedi posebno za reprodukcije,prevode,mikrofiming i takodje za

skladitenje i procesuiranje u elektronike sisteme.

Dokment i svi njegovi djelovi su zatieni autorskim pravima. Svako

neovlateno korienje izvan uskih granica koje su odredjene od strane

Zakona o autorskim pravima je nedopustivo i podlono krivinom gonjenju. Tose posebno odnosi na kopije,prevode,mikrofiming i skladitenje i procesuiranje

u elektronike sisteme.


3/67


Deutscher Kalibrierdienst (DKD)

The DKD comprises calibration laboratories in industrial enterprises, research institutes, tech-nical authorities, inspection and testing institutes. They are accredited and supervised by theDKD. They calibrate measuring instruments and material measures for measurands andmeasurement ranges specified within the scope of accreditation. The DKD calibration certifi-cates issued by these laboratories prove traceability to national standards as required in theISO 9000 family and ISO/IEC 17025.

Calibrations carried out by DKD laboratories ensure that the user may rely on measurementresults. They increase the customers' confidence and competitiveness on the national andinternational markets and serve as a metrological basis for the inspection of measuring andtest equipment within the framework of quality assurance measures.

Calibrations offered by the DKD cover electrical measurands, length, angles and other geo-metrical quantities, roughness, coordinate and form measuring techniques, time and fre-quency, force, torque, acceleration, pressure, flowrate, temperature, humidity, medical meas-urands, acoustic measurands, optical measurands, ionizing radiation and other measurands.

Publications: see Internet

Address:

Deutscher Kalibrierdienst at the Physikalisch-Technische Bundesanstalt Bundesallee 100

D-38116 Braunschweig

P.O. Box 33 45 D-38023 BraunschweigOffice telephone +49 531 592 1901Fax +49 531 592 1905E-Mail d k d@p t b . deInternet www . d k d . in f o

Njemaki kalibracioni servis
mailto:[email protected]://www.dkd.info/http://www.dkd.info/mailto:[email protected]


4/67


Njemaki kalibracioni servis( DKD ) se sastoji od kalibracionih laboratorija u

industrijskim preduzeima,istrivakim institucijama,tehnikim

organima,nadzoru i ispitivanju instituta. Oni su akreditovani i pod nadzorom

DKD.

Oni kalibriu mjerne instrumente i uredjaje i materijalne mjere mjerenim i

mjernim rasponima koji su odredjeni u okviru akreditacije. U DKD kalibracioni

certifikati izdati od strane ovih laboratorija dokazuju sljedivost nacionalnih

standarda kako se to i zahtijeva u porodici ISO 9000 i ISO / IEC 17025.

Kalibracije koje se sprovode od strane DKD labratorija osiguravaju da se

korisnik moe osloniti na tanost rezultata.Oni poveavaju povjerenje klijenata

i konkurentnost na domaem i internacionalnom tritu i slue kao metroloka

baza za kontrolu mjerenja i testiranje opreme u okviru osiguranja kvaliteta

mjera.

Kalibracije koje nude DKD pokrivaju elektrino mjerenje,duinu,uglove,druge

geometrijske koliine,hrapavost,koordinira i formira tehnike mjerenja, vrijeme

i frekvenciju,silu,okretni

moment,ubrzanje,pritisak,protok,temperaturu,vlanost,medicinska

mjerenja,zvuna mjerenja,optika mjerenja,jonizujue zraenje i druga

mjerenja

Publikacije : vidi Internet

Adresa:

Deutscher Kalibrierdienst at the Physikalisch-Technische Bundesanstalt

Bundesallee 100 D-38116 Braunschweig P.O. Box 33 45 D-38023

Braunschweig

Office telephone +49 531 592 1901

Fax +49 531 592 1905

E-Mail [email protected]


5/67


Foreword

DKD Guidelines are application documents for the general criteria and procedures which arelaid down in DIN EN ISO/IEC 17025 and DKD publications. The DKD Guidelines describetechnical and organizational processes serving the calibration laboratories as a model for lay-ing down internal procedures and regulations. DKD Guidelines can become an integral part ofquality manuals of calibration laboratories. The application of the Guidelines supports equaltreatment of the devices to be calibrated at the different calibration laboratories and improvesthe continuity and verifiability of the work of the calibration laboratories.

The DKD Guidelines will not impede the further development of calibration procedures andsequences. Deviations from guidelines and new methods are permitted in agreement with theAccreditation Body if they are justified by technical aspects.

The present Guideline was prepared by the Technical Committee "Pressure and Vacuum" inco-operation with the PTB and adopted by the Advisory Board of the DKD. With its publicationit is binding for all DKD calibration laboratories unless separate procedural instructions ap-proved by the Accreditation Body are available.

Predgovor

DKD smjernice su aplikacioni (prijavni) dokumenti za glavne kriterijume i

procedure koje su utvrdjene u DIN EN ISO/IEC 17025 DKD publikacijama. DKD

smjernice opisuju tehnike i organizacijske procese sluei kalibracionim

laboratorijama kao model kojim se utvrdjuju

Interne procedure i propisi. DKD smjernice mogu postati sastavni dio

kvalitetnih prirunika kalibracionih laboratorija. Primjena Smjernica podrava

jednaki tretman uredjaja koji treba da se kalibrira u razliitim kalibracionimlaboratorijama i poboljava kontinuitet i povjerljivost ( verifikaciju ) rada u

kalibracionim laboratorijama.

DKD Smjernice nee onemoguiti dalji razvoj kalibracionih postupaka-

procedura i sekvenci-sljedivost.


6/67


Odstupanja od smjernica i novih metoda su doputena u sporazumu sa

Akreditacinim tijelom ako su opravdana tehnikim aspektima.

Sadanja Smjernica pripremio je Tehniki odbor ,,Pritisak i vakuum u saradnji

sa PTB i usvojena je od strane Savjetodavnog odbora DKD. Objavljivanje je

obavezujue za sve DKD kalibracione laboratorije,osim ako su dostupne

odvojene proceduralne smjernice

koje su odobrene od strane akreditacijskog tijela.

Contents

1 Purpose and scope of application .......................................................................... 5

2 Symbols and designations ..................................................................................... 5

2.1 Variables ............................................................................................................... 5

2.2 Indices .................................................................................................................. . 73 Reference and working standards.......................................................................... 7

4 Calibration item ...................................................................................................... 8

5 Calibratability.......................................................................................................... 9

6 Ambient conditions ................................................................................................. 9

7 Calibration methods ..............................................................................................10

8 Measurement uncertainty......................................................................................13

8.1 Definition ..............................................................................................................13

8.2 Procedure.............................................................................................................13

8.2.1 Evaluation model ..................................................................................................138.2.2 Sum/difference model...........................................................................................14

8.2.3 Product/quotient model.........................................................................................14

8.2.4 Input quantities .....................................................................................................15

8.2.5 Potential influence quantities, example.................................................................16


7/67

DKD-R 6-1 Calibration of Pressure Gauges8.3 Calibration of Bourdon tube pressure gauges.......................................................17

8.3.1 Evaluation model ..................................................................................................17

8.3.2 Uncertainty analysis..............................................................................................18

8.3.3 Load step-related uncertainty budget ...................................................................19

8.3.4 Single-number rating ............................................................................................20

8.4 Calibration of electrical pressure gauges ..............................................................208.5 Calibration of pressure transducers and pressure transmitters with electrical

output ...................................................................................................................20

8.5.1 Evaluation model ..................................................................................................20

8.5.2 Uncertainty analysis..............................................................................................22

8.5.3 Load step-related uncertainty budget ...................................................................23

8.5.4 Single-number rating ............................................................................................23

8.6 Determination of relevant parameters for uncertainty analysis .............................24

8.6.1 Resolution r..........................................................................................................24

8.6.1.1 Analog indicating devices ...............................................................................248.6.1.2 Digital indicating devices ................................................................................24

8.6.1.3 Fluctuation of readings ...................................................................................24

8.6.2 Zero deviationf0....................................................................................................24

8.6.3 Repeatability b'.....................................................................................................25

8.6.4 Reproducibility b ...................................................................................................25

8.6.5 Hysteresis h ..........................................................................................................25

9. Evaluation of measurement results and statements in the calibration certificate ...26

9.1 Determination of other parameters .......................................................................27

9.1.1 Mean values x .....................................................................................................279.1.2 Error span U........................................................................................................27

9.1.3 Conformity ............................................................................................................27

9.2 Visualization of calibration result...........................................................................28

9.2.1 Bourdon tube pressure gauges, electrical pressure gauges .................................28

9.2.2 Pressure transmitters with electrical output ..........................................................29

9.3 Limiting values for uncertainty statements ............................................................29

10. Other rules and standards.....................................................................................30

Annex A Estimate of measurement uncertainty to be attributed to the values of the pressure

balance under conditions of use...........................................................................31

Annex B Example Uncertainty budget for the calibration of a Bourdon tube pressure gauge .33

Annex C Example Uncertainty budget for the calibration of a digital electrical pressure

gauge ...................................................................................................................35

Annex D Example Uncertainty budget for the calibration of a pressure transmitter with

electrical output ....................................................................................................37

Annex E (informative) Measurement uncertainties of reference and working standards......41

Annex F Period of validity (recommended) ..........................................................................42

References .............................................................................................................................43


8/67


1 Purpose and scope of application

This Guideline serves to establish minimum requirements for the calibration method and theestimate of the measurement uncertainty in the calibration of pressure gauges. It applies toBourdon tube pressure gauges, electrical pressure gauges and pressure transmitters withelectrical output for absolute pressure, differential pressure and overpressure with negativeand positive values.

2 Symbols and designations

The symbols are subject-related, i.e. as a rule, they are given in the order in which they ap-pear in the text.

1 Svrha i oblast primjene

Ove Smjernice slue da se uspostave minimalni zahtjevi za kalibracionemetode i procjenu mjerne nesigurnosti u kalibraciji manometra. To se odnosi i

na Bourdone cijevi,manometre,elektrine manometre i transmitere pritiska sa

elektrinim izlazom za apsolutni pritisak,diferencijalni pritisak,nadpritisak sa

negativnim i pozitivnim vrijednostima.

2 Simboli i oznake

Simboli su predmetno vezani,to jest,kao pravilo ,oni su po redu kojim e se pojavljivati utekstu.

2.1 Promjenljive

2.1 Variables

2.1 PromjenljiveM1 ... M6 Measurement series

max. load Highest value (of calibration range)

Y Output quantity


9/67


X Value-determining input quantity

X Unknown measurement deviation

K Correction factor

x Estimate of input quantity

y Estimate of output quantity

c Sensitivity coefficient

k Expansion factor

a Half-width of a distribution

P Probability

E[...] Expected value

u Standard uncertainty

U Expanded uncertainty

w Relative standard uncertainty

W Relative expanded uncertainty


10/67


p Pressure - pritisak

pSystematic measurement deviation of the quantity of

pressure

p Unknown measurement deviation of the quantity of

pressure

S Transmission coefficient (of pressure transducer)

SSystematic deviation of transmission coefficient from

single-number rating ( S= S- S)

V Voltage

G Amplification factor

r Resolution

f0 Zero deviation

b' Repeatability

b Reproducibility

h Hysteresis

U Error span

W Relative error span

S' Slope of a linear regression function

pe Excess pressure

m Mass of load masses

g Acceleration due to gravity

DensityA Effective cross section of piston-cylinder system

Deformation coefficient of piston-cylinder system

Linear thermal expansion coefficient of piston

Linear thermal expansion coefficient of cylinder

t Temperature of piston-cylinder system

hDifference of pressure reference levels of reference

instrument and the instrument tobe calibrated


11/67


2.2 Indices

Supply Supply voltage

j Number of measurement point

m Number of measurement series

n Number of measurement cycles

a Air

Fl Medium

m Load mass

0 Reference conditions t = 20C

ref Reference conditions

cond. of use Conditions of use

corr Correction (of measurement value)


12/67


3 Reference and working standards

The calibration takes place by direct comparison of the measurement values for the calibration

item with those of the reference or working standard which has been directly or indirectlytraced back to a national standard.

The reference standards used are pressure gauges of long-time stability such as pressurebalances and liquid-level manometers. They are calibrated at the PTB at regular intervals anda calibration certificate is issued for them stating the expanded uncertainty under referenceconditions (standard acceleration due to gravity, 20C).

When a calibration is carried out outside the reference conditions, corrections are to be ap-plied to the pressure calculation. The measurement uncertainties to be attributed to these cor-rections due to influence quantities are to be taken into account as further contributions in theuncertainty budget.

The working standards documented in the quality manual of the DKD laboratory are calibratedin an accredited laboratory and a calibration certificate is issued for them stating the expandeduncertainty under reference conditions. The working standard is subject to approval by thePTB. The working standards can be different as regards their type.

Reco mm enda t ion:The measurement uncertainty which is attributed to the measurement values of the referenceor working standard should not exceed 1/3 of the uncertainty aimed at

1, which will probably be

attributed to the measurement values of the calibration item.


13/67


1The measurement uncertainty aimed at is the uncertainty which can be achieved when specified

calibration efforts are made (uncertainty of the values of the standard, number of measurementseries, etc.). It is normally greater than the smallest uncertainty which can be stated.

3 Reference i radni standardi

Kalibracija se odvija direktnim poredjivanjem mjernih vrijednosti za kalibracionutaku onim referencamaIli radnim standardima koje su direktno ili indirektno prouavane (do ) nacionalinimstandardima.Korieni referentni standardi su manometri za dugogodinju stabilnost,kao to su vage pod pritiskom,teni nivo-rang manometri.Oni su kalibrisani po PTB u redovnim razmacima i kalibracioni certifikat se izdaje zanjih uz navodjenje proirene nesigurnosti uz referentne uslove( standardno ubrzanje zbog gravitacije,200 C ). Kad se kalibracija sprovodi izvanreferentnih uslova,korekcije e se primjenjivati na armaturni obraun.Mjernu nesigurnost koju treba pripisati ovim korekcijama zbog uticaja koliina kojetreba uzeti u obzir kao dalji doprinos u nesigurnosti prorauna.Radni standardi dokumentovani u priruniku kvaliteta za DKD laboratoriju sukalibrisani u akreditovanoj laboratoriji i kalibracioni certifikat se izdaje za njih uznavodjenje proirene nesigurnosti pod referentnim uslovima. Radni standardipodlijeu odobravanju od strane PTB. Radni standardi mogu biti razliiti o obzirom nanjihov tip.

Preporuka:

Mjerna nesigurnost kojoj je pripisana mjerna vrijednost reference ili radnog stadardane smije prelazilti 1/3 od neizvjesnosti sa ciljem 1 ,koja e vjerovatno biti pripisana

mjernim vrijednostima kalibracione take.

1 Mjerna nesigurnost usmjerena je na nesigurnost koja se moe postii kad sunapravljeni navedeni kalibracioni napori ( nesigurnost vrijednostistandarda,broj serija mjerenja itd ) . To je uobiajeno vie od najmanjeneizvjesnosti koja moe biti navedena. 4. Kalibracione takeKalibracione take tri vrste manometara predstavljenje su na slici 1.


14/67


Slika 1: Tipovi manometara


15/67


4 Calibration item

The calibration items are pressure gauges of the three types represented in figure 1.

Kalibracione take manometra ova tri tipa prikazane su na slici 1


16/67


Figure 1: Types of pressure gauges

Type Standard Calibration itemAuxiliary

measuring devices

(1)

Burdon tubepressuregauge

Referenceor workingstandard

Burdon tubepressure gauge

(2) Voltage source

Electricalpressuregauge


p

U,I,f

p Indication

(3)

Pressuretransmitter withelectrical output


p

U,I,f

Auxiliary power

Indication


17/67

In contrast to electrical pressure gauges (2) for which only auxiliary power needs to be pro-vided, auxiliary measuring devices of the DKD laboratory must be used for the calibration ofpressure transmitters with electrical output (3). These devices serve to convert the electricalsignal into a readable indication. The measurement uncertainty attributed to the measurement

values of the auxiliary measuring devices is to be taken into account in the uncertainty analy-sis. To ensure traceability, the auxiliary measuring devices must have been calibrated and astatement on the measurement uncertainty to be attributed to the measurement values mustbe available. When selecting the test equipment it is to be ensured that the measurement un-certainty attributed to the measurement values of the auxiliary measuring devices can bestated according to the measurement uncertainty aimed at for the calibration item.If the calibration item has a digital interface (e.g. RS232, RS485, IEEE488, etc.), this interfacecan be used in the place of the indication. It is to be ensured that the data read out are une-quivocally interpreted and processed.

Za razliku od elektrinog manometra ( 2 ) za koji samo pomono napajenje treba biti

osigurano,pomoni mjerni uredjaj DKD laboratorije mora biti korino za kalibracijupriteska transmitera sa elektrinim izlazom ( 3 ). Ovi uredjaji slue da konvertujuelektrini signal u itljivu indikaciju. Mjerna nesigurnost pripisana mjernimvrijednostima pomonih mjernih uredjaja moe se uzeti u obzir u analizi nesigurnosti.Kako bi se osigurala sljedivost pomoni mjerni uredjaji moraju biti kalibrisani i izjava omjernoj nesigurnosti kojij se pripisuju mjerne vrijednositi mora biti dostupna. Prilikomodabira test opreme potrebno je osigurati da se mjerna nesigurnost koja se pripisujemjernim vrijednostima pomonog mjernog uredjaja moe izraziti u skaldu sa ciljem/usmjerenjem kalibracione take. Ako kalibraciona taka ima digitalnu unutranjost ( naprimjer RS232, RS485, IEEE488, itd ),ova povrina moe biti iskoriena u mjestoindikacije. Potrebno je osigurati da podaci koji se itaju van budu jednoznano

intrepretirani/tumaeni i obradjeni.


18/67

5 Calibratability

Handling of a calibration task presupposes calibratability (suitability of the calibration item), i.e.the state of the calibration item at the time of calibration should comply with the generally ac-cepted rules of technology and with the particular specifications of the manufacturer's docu-mentation. The calibratability is to be ascertained by external inspections and function tests.

External inspections cover for example:- visual inspection for damage (pointer, threads, sealing surface, pressure channel)- contamination and cleanness- visual inspections of inscriptions, readability of indications- test whether the documents necessary for calibration (technical data, operating instruc-

tions) have been submitted.

Function tests cover for example:- tightness of tube system of calibration item- electrical function- perfect function of actuators (e.g. zero adjustability)- setting elements in defined position- faultless execution of self-checking and/or self-setting functions; if needed, internal ref-

erence values are to be read out via the EDP interface- torque dependence (zero signal) during mounting

No t e:If repair or adjustment work has to be carried out to ensure calibratability, this work has to beagreed upon between customer and calibration laboratory.

6 Ambient conditionsThe calibration is to be carried out after temperature equalization between calibration item andenvironment. A period for warming up the calibration item or potential warming-up of the cali-bration item due to the supply voltage is to be taken into account.The calibration is to be performed at an ambient temperature stable to within 1 K; this tem-perature must lie between 18C and 28C and is to be recorded.

No t e:If the air density has an effect on the calibration result, not only the ambient temperature butalso the atmospheric pressure and the relative humidity are to be recorded.


19/67

Kalibartibilnost-podobnost kalibracije

Upravljanje kalibracionim zadatkom podrazumijeva kalibratibilnost

( pogodnost/prikladnost kalibracione take ) tj.stanje kalibracione take u trenutkukalibracije treba biti u skladu sa opteprihvaenim tehnolokim pravilima ( pravilimatehnologije ) i sa odredjenim odredbama u dokumentaciji proizvodjaa. Kalibratibilnost semoe utvrditi spoljanjim pregledima I funkcijskim( funkcionalnim ) testovima.Spoljanji pregledi obuhvataju na primjer:-vizuelni pregled zbog oteenja ( pokaziva,navoji,zaptivanje( zatvaranje )povrine,kanal pritiska)-kontaminacija i istoa,-vizuelni pregled natpisa,itljivost oznaka,-testiranje da li su dokumenti neophodni za kalibraciju(tehniki podaci,operativnauputstva) dostavljeni.

Funkcijski testovi pokrivaju na primjer:

-nepropusnost( stezanje ) cijevi sistema kalibracione take,-elektrina funkcija,-savreno funkcionisanje pogona ( npr. nula prilagodljivost-podesivost )-postavljanje ( podeavanje ) elemenata u definisanom poloaju,-bezprijekorno izvravanje( izvodjenje ) automatskih provjera ( samoispitivanje ) i/ili samo-podeavanja funkcija,ako je potrebno,unutranje referentne vrijednosti treba oitati prekoEDP SUELJA,

-okretni moment zavisnosti ( nula signal ) tokom montae.

Napomena:

Ako se treba sprovesti popravka ili podeavanje ( prilagodjavanje ) rada kako bi seosigurala kalibratibilnost,ovaj posao mora biti dogovoren izmedju klijenta u kalibracionelaboratorije.

6. Uslovi okoline

Kalibracija se sprovodi nakon to se izjednai temperatura izmedju kalibracione take i

okoline. Treba uzeti u obzir i period zagrijavanja kalibracione take ili potencijalnozagrijavanje kalibracione take zbog napona napajanja.Kalibracija treba da bude izvedena na stabilno sobnoj temperatura unutar 1 K,ovatemperatura mora biti izmedju 18 o C i 28 o C i treba se zabiljeiti.

Napomena:Ako vlanost vazduha ima uticaj na rezultat kalibracije,ne samo temperaturu okoline negoi atmosferski pritisak i relativnu vlanost treba zabiljeiti.


20/67

7 Calibration methods- The pressure gauge is to be calibrated as a whole (measuring chain), if possible.- The specified mounting position is to be taken into consideration- The calibration is to be carried out in measurement points uniformly distributed over the

calibration range.- Depending on the measurement uncertainty aimed at, one or several measurement se-

ries are necessary.- If the behaviour of the calibration item as regards the influence of the torque during

mounting is not sufficiently known, the calibration item has to be clamped once again todetermine the reproducibility. In this case, the torque is to be measured and docu-mented.

Upon application, further influence quantities (e.g. temperature effects from other measure-ment series at different temperatures) can be determined.The comparison between the measurement values for calibration item and reference or work-ing standard can be performed by two different methods:

- adjustment of the pressure according to the indication of the calibration item,- adjustment of the pressure according to the indication of the standard.

The time for preloading at the highest value and the time between two preloadings should beat least 30 seconds. After preloading and after steady-state conditions have been reached and the calibration item permitting -, the indication of the calibration item is set to zero. Thezero reading is carried out immediately afterwards. For the pressure step variation in a meas-

urement series, the time between two successive load steps should be the same and not beshorter than 30 seconds and the reading should be made 30 seconds after the start of thepressure change at the earliest. Especially Bourdon tube pressure gauges have to be slightlytapped to minimize any frictional effect of the pointer system. The measurement value for theupper limit of the calibration range is to be recorded prior to and after the waiting time. Thezero reading at the end of a measurement series is made 30 seconds after complete relief atthe earliest.

The calibration effort is shown in table 1 and figure 2 in dependence on the measurement un-certainty aimed at (see

1on page 7). Figure 2 shows the sequence of the calibration.

7 Kalibracione metode

-Manometar treba kalibrisati u cjelini (mjerni lanac ) ako je mogue,-Naznaeni ( odredjenu,navedenu ) poloaj ugradnje treba uzeti u obzir( treba razmotriti )

-Kalibraciju treba sprovoditi unutar mjernih taaka koje su ravnomjerno rasporedjene pokalibracionom nizu,-U zavisnosti od cilja mjerne nesigurnosti,potrebno je uraditi jednu ili nekoliko serijamjerenja,


21/67

-Ako ponaanje kalibracione take u pogledu uticaja okretnog momenta,u tokumontae,nije dovoljno poznato,treba kalibracionu taku sigurnije privrstiti kako bi se opetutvrdila ponovljivost.U tom sluaju okretni momenat treba izmjeriti i dokumentovati.Nakon prijave,dalje uticajne veliine ( npr.temperaturni efekti iz drugih serija mjerenja prirazliitim temperaturama ) mogu se odrediti.

Poredjenje izmedju mjernih vrijednosti za kalibracionu taku i referenci ili radnogstandarda moe se izvriti pomou dvije razliite metode :-podeavanje pritiska u skladu sa naznakom kalibracione take,-podeavanje pritiska u skladu sa naznakom( navodjenjem ) standarda.Vrijeme uitavanja na najveoj vrijednosti i vrijeme izmedju dva uitavanja treba da budenajmanje 30 sekundi.Nakon oitavanja i nakon to su postignuti stabilni uslovi-kalibraciona takadoputena( dozvoljena ) pokazivanje kalibracione take je postavljeno na nulu.Oitavanje nule se sprovodi odmah posle toga.Za varijacije pritiska u koraku sa serijama mjerenja ,vrijeme izmedju dva uzastopnaoitavanja koraka treba da bude isto i ne krae od 30 sekundi i oitavanje treba napraviti

30 sekundi nakon poetka najranije promjene pritiska.Pogotovo Bourdon cijevi manometri moraju biti lagano izabrani kako bi se smanjio bilokakav efekat trenja sistema pokazivaa.Mjernu vrijednost za gornju granicu kalibracionog raspona treba zabiljeiti prije i nakonvremena itanja.Oitavanje nule na kraju serije mjerenja je napravljeno 30 sekundi nakon potpunogolakanja uz to manje kanjenje.

Kalibracioni napor je prikazan u tabeli 1 i slika 2 zavisno od cilja mjerne nesigurnosti( vidjeti 1 na strani 7 ) . Slika 2 pokazuje redosljed kalibracije.

Tabela 1. Kalibracioni redosljed

Table 1: Calibration sequences

Calibra-tionse-

quence

Measurementuncertainty aimed

at, in % ofthe

measurementspan

Numberofmeasure-

mentpoints

Numberofpre-

loadings

Load change+ waiting time

Waiting time atupper limit ofmeasurement

range

(***)

minutes

Numberofmeasurement

series

(*) with zero

up/down

(**)

seconds up down

A < 0,1 9 3 > 30 2 2 2

B 0,1 ... 0,6 9 2 > 30 2 2 1

C > 0,6 5 1 > 30 2 1 1

(*) Reference to the span was used to allow the sequence (necessary calibration effort) tobe selected from the table, as the accuracy specifications of the manufacturers are usu-ally related to the measurement span.

(**) One has in any case to wait until steady-state conditions (sufficiently stable indication ofstandard and calibration item) are reached.


22/67

(***) For Bourdon tube pressure gauges, a waiting time of five minutes is to be observed. Forquasi-static calibrations (piezoelectric sensor principle), the waiting times can be re-duced.

No t e:For the calibration of items with a range of measurement greater than 2500 bar, calibrationsequence A is in principle to be used. If clamping effects are observed, the calibration is to berepeated clamping the calibration item anew.

(*) Upuivanje na rasponu je korieno kako bi se omoguio niz ( potrebni kalibracioninapor ) koji se bira iz tablice ,kao i tanost (preciznost ) tehnikih podataka proizvodjaakoja se obino odnose na mjerni raspon.(**) Neko treba u svakom sluaju da saeka dok se stabilni uslovi ( dovoljno stabilnipokazatelji standarda i kalibracione take ) ne postignu.

(***) Za Bourdon cijevi manometra,vrijeme ekanja od pet minuta treba biti potovano. Zakvazi statiku kalibraciju ( princip piezoelektrini senzor ) vrijeme ekanja moe bitismanjeno.Napomena:Za kalibracionu taku sa rasponom mjerenja koje je vee od 2 500 bara,kalibracioni nizAu principu treba koristiti. Ako se primijete efekti stezanja,kalibraciju treba ponovitiponovnim stezanjem kalibracione take.


23/67

Figure 2: Visualization of the calibration sequences Vizualizacija kalibracijskih nizova

max. load

pM1

2 minM2

Z

M3 M4

zero setting

preloadings

t

M1 ... M6 measurement series

Additional reproducibility measurement with 2nd

clamping

(e.g. if the effect of torque is estimated during the calibration)Dodatna ponovljivost mjerenja sa 2. stezanja(npr. ukoliko se efekt okretnog momenta procjenjuje tokom kalibracije)

p M5 M6

Sequence B Niz B t

pM1 M2 M3

Sequencnce C Niz C

p M1 M2

tZ

30 s 30 s

2 min

t readings

for Bourdon tube

pressure gau-ges: 5 min


24/67

8 Measurement uncertainty2

8.1 Definition

Parameter which is stated jointly with the measurement result, i.e. which is attributed by the

measurement to the measurement result and characterizes the interval of values which canbe reasonably assigned to the measurand on the basis of the measurement.

8.2 Procedure

8.2.1 Evaluation model

For the uncertainty analysis the sequence described in Publication DKD-3 is on principle fol-lowed. This publication uses the following terms and calculation rules on condition that no cor-relations between the input quantities are to be allowed for:

8. Kalibraciona nesigurnost 2

8.1 Definicija

Parametar koji se navodi zajedno sa mjernim razultatom,odnosno koji se

pripisuje mjerenjem prema mjernom rezultatu i karakterie interval

vrijednosti koji se moe razumno dodijeliti mjerenoj veliini na osnovu

mjerenja.

8.2 Postupak

8.2.1 Procjena modela

Za analize nesigurnosti redosljed opisan u publikacij DKD-3 se u principu

slijedi. Ova publikacija koristi sljedee odredbe i pravila prorauna uz uslov da

nema povezanosti izmedju ulaznih veliina koje treba dopustit za :

Model function y =f(x1,x2, ...,xN)

Standard

uncertaintyu(xi)

ci

ui

y

u(y)

standard uncertainty attributed to theinput quantity

sensitivity coefficient

contribution to the standard uncer-tainty attributed to the result, due tothe standard uncertainty u(xi) of the

input quantityxi

standard uncertainty attributed to theresult

cf

ix i

ui

y ci

u xi

2N

2u y ui

y

i 1

N

u y u2

yii 1


25/67

Expanded

uncertaintyU(y)

k

expanded uncertainty

coverage factor

U y k u y

k= 2for a measurand oflargelynormal distribution and a

coverage probability of95%

2For the terminology, see DIN V ENV 13005.


26/67

p

If relative measurement uncertainties are used, the variables u, Uare replaced with the vari-ables w, W.

With complex models, the calculation rule rapidly leads to an analytical determination of thesensitivity coefficient which is no longer manageable. As a result, the sensitivity coefficientswill have to be determined numerically with the aid of a computer.

Besides this general calculation rule, two particular rules are available which lead to sensitivitycoefficients ci = 1 and thus to the simple quadratic addition of the uncertainties of the inputquantities. This simplifies the uncertainty analysis and makes EDP program support unneces-sary.

No t e:The "simple" model, too, must of course correctly reflect the physical measurement/calibrationprocess. If appropriate, complex relations must be represented in a suitable model (no specialcase) in a separate uncertainty budget (see Annex A: Estimate of measurement uncertainty to

be attributed to the values of the pressure balance under conditions of use)

8.2.2 Sum/difference model

N

Y X /Xi

i 1

(1)

Y measurand or output quantityX input quantity/quantities according to the

functional relationship Y=f(X1,X2, ...Xn)

Xi unknown measurement deviation(s)

E [ Xi ] = 0 expected value[the components do not contribute to the determination of the outputquantity (corrections are not applied) but they make a contributionto the measurement uncertainty]

e.g. model for determining the measurement deviation of the indication:N

p pind pstandard / i

i 1

(2)

This model is most suitable for calibration items with an indication of their own in pressureunits (e.g. Bourdon tube pressure gauge, electrical pressure gauge). Here the measurementuncertainties are also stated in the unit of the physical quantity of pressure (pascal, bar, etc.).

8.2.3 Product/quotient model

N

Y X Ki

i 1

(3)

Y output quantityX value-determining input quantity/quantities

Ki = (1 + Xi ) correction factor(s)Xi unknown deviation(s)


27/67

K

E [ Xi ] = 0; E [Ki] = 1 expected values[the components do not contribute to the determination of the outputquantity (corrections are not applied) but they make a contributionto the measurement uncertainty]

e.g. model for determining the transmission coefficient of a pressure transducer(strain-gauge transducer):

S X

out

Vind NG Vsupply

i(4)

Xin


28/67

p

pstandard i 1

Ako su koriene relativne mjere nesigurnosti onda se varijable u,U

zamjenjuju sa varijablama w,W.

Sa sloenim modelima proraunsko pravilo brzo dovodi do analitikogodredjivanja osjetljivosti koeficijenta kojim se vie ne rukuje Kao rezultat toga

osjetljivost koeficijenata morat e se numeriki utvrditi uz pomo raunara.

Osim ovog glavnog pravila prorauna,dostupna su jo i dva posebna pravila

koja dovode do osjetljivosti koeficijenta ci=1 i tako do jednostavnog kvadratnogsabiranja nesigurnosti ulaznih veliina.

Ovo pojednostavljuje analizu nesigurnosti i program podrke EDP ini nepotrebnim.

Napomena :,,Jednostavni model se mora se naravno,isto pravilno odravati fiziko mjernim /kalibracionim procesima. Ako je potrebno , sloeni odnosni moraju biti zastupljeni uodgovarajuem modelu (ne poseban sluaj ) u odvojenim proraunima nesigurnosti( vidjeti Annex-Prilog A Procjena mjerne nesigurnosti kojoj treba pripisati vrijednostiravnotee pritiska pri uslovima korienja).

8.2.2 Model zbir/razlikaN

Y X /Xii 1

(1)

Y Mjerne ili izlazne veliineX izlazna veliina/veliine prema

Funkcionalnom odnosu

Y=f(X1,X2, ...Xn)

Xi nepoznato mjerno odstupanjeE [ Xi ] = 0 oekivana vrijednost

[komponente ne doprinose odredjivanju izlaznih veliina(korekcije se ne primjenjuju ) ali doprinose mjernojnesigurnosti ]

npr.model za odredjivanje mjernog odstrupanja od indikacije :N

p

pind

pstandard / ii 1

(2)

Ovaj model je najpogodniji za kalibraciju predmeta sa njihovom vlastitom indikacijomu u jedinicama pritiska(npr. Bourdon cijevi manometar, elektrini manometar). Ovdjesu takodje mjerne nesigurnosti navedene u jedinicama fizikih veliina pritiska (paskal,bar, itd.).

8.2.3 Modelproizvod/kolinik

NY X Ki

i 1

(3)


29/67

Y izlazne veliineX odredjivanje vrijednosti ulazne veliine/veliinaKi = (1 + Xi ) korekcioni factor (s)

Xi nepoznato odstupanje(s)


30/67

K

E [ Xi ] = 0; E [Ki] = 1 oekivane vrijednosti[ove komponente ne doprinose odredjivanju izlaznih veliinaof(korekcije se ne primjenjuju)ali doprinose odredjivnaju mjenenesigurnosti

]Npr. Model za odredjivanje prenosnog koeficijenta od pritiska transduktora(naprezanje-mjeraa sonde):

S X

out

Vind

NG Vsupplyi (4)

Xin pstandard i 1

This model is most suitable for calibration items without an indication of their own (e.g. pres-sure transmitter with electrical output) using related measurement uncertainties (dimension-less).

8.2.4 Input quantities

The measurement uncertainties attributed to the input quantities are subdivided into two cate-gories as regards their determination:

Type A: For the determination of the value and the standard uncertainty attributed to it,analysis methods from statistics for measurement series under repeatability con-ditions ( n 10 ) are applied.

Type B: The determination of the value and of the standard uncertainty attributed to it isbased on other scientific findings and can be estimated from the following infor-mation:

data from previous measurements,general knowledge and experience regarding the characteristics and thebehaviour of measuring instruments and materials,manufacturer's specifications,calibration and other certificates,reference data from manuals.

In many cases, only the upper and lower bounds a+ and a- can be stated for thevalue of a quantity, whereby all values within the bounds can be consideredequally probable. This situation can best be described by a rectangular probabilitydensity.

With a+

- a-

= 2 a (5)

the estimate of the input quantity

x1

a ai2

(6)

and the attributed standard uncertainty

are obtained.

au xi 3

(7)


31/67

Ovaj model je najpogodniji za kalibraciju taki bez indikacije njihovih

( npr.transmiter pritiska sa elektrinim izlazom) korienjem povezanih

mjernih nesigurnosti.

8.2.4 Ulazne veliine

Mjerne nesigurnosti pripisane ulaznim veliinama podijeljene su u dvije

kategorije s obzirom na njihovom odredjivanje:

Tip A : Za odredjivanje vrijednosti i standardne nesigurnosti koje su

pripisane,primjenjuju se metode analiziranja iz statistike serija mjerenja pod

uslovima ponovljivosti ( n 10 ) .

Tip B: Odredjivanje vrijednosti i standardne nesigurnosti koje su pripisanezasnivaju se i na drugim naunim nalazima ( istraivanjima ) i mogu se

procijeniti iz sljedeih informacija:

-podaci prethodnih mjerenja,

-osnovno znanje i iskustvo vezano za karakteristike i ponaanje mjernih

instrumenata i materijala,

-specifikacije proizvodjaa,

-kalibracija i drugi sertifikati,

-referentni podaci iz prirunika.

U mnogim sluajevima, samo gornja i donja granica a+ i a- mogu se navesti zaodreenu vrijednost veliine, pri emu se sve vrijednosti unutar granica mogu smatratijednako vjerojatnim. Ova situacija moe biti najbolje opisana pravouganom vjerovatnoigustina

Od a+ - a- = 2 a (5)

Procjene ulaznih veliina

x1

a ai2

(6)

i pripisane standardna nesigurnost

dobijene.

au xi 3(7)


32/67

If the values more likely lie in the centre or at the border of the interval, it is rea-sonable to assume a triangular or U-shaped distribution. Ako vrijednost lei vise u

centru ili na granici interval,onda je razumno pretpostaviti trouglastu ili U-oblik raspodjelu.

Table 2: Other type B distribution shapes

Distribution Standard uncertainty

triangular ua

6

U-shaped u

a

2

etc.

8.2.5 Potential influence quantities, example

For establishing the evaluation model it is advisable to set up a block diagram showing thecause-effect development. The example of the representation below shows the potential influ-ence quantities for the calibration of a pressure gauge against a pressure balance.

8.2.5 Potnencijalno uticajne veliine

Za utvrdjivanje modela evaluacije poeljno je postaviti blok diagram koji

pokazuje uzrono posljedini razvoj. Primjer zastupljenosti ispod pokazujepotencijalni uticaj veliine ua kalibrsianje manometra protiv pritiska

ravnotee.

Figure 3: Influence quantities in the calibration of a pressure gauge

difference of both reference levels interpolation deviation

conversionstemperatureair density

temperaturereference level

temperaturereference level

resolution , ENOBs *

local accelerationdue to gravity

density power supplyposition

drift roundings

pressurestandardpressure balance

tube

system

reference level

sensor adapter,

output unit

pressure gauge

evaluation

measurementuncertainty attributed - pressure-transmitting unit characteristics

measurementuncertainty

to the values underreferenceconditions

- hoses- fittings- valves- pressure-transmittingfluid

of the sensor- zero deviations- repeatability- reproducibility- hysteresis- drift

attributed to thevalues of theadapter, output unit


33/67

* Effective Number of Bits; see IEEE 1057-1994 IEEE Standard for Digitizing WaveformRecorders

No t e:It sometimes is helpful for the initial approach to subdivide the influence quantities accordingto whether they are associated with the standard, the procedure or the calibration item.

The measurement uncertainties which are attributed to the values of the standard, the adapterand the output unit are taken from calibration certificates (generally normally distributed, k= 2).Napomena:

Ponekad je korisno za poetni pristup podijeliti uticajne veliine prema tome

da li su povezani sa standardom,procedurom ili kalibracionom takom.

Mjerna nesigurnost kojo su pripisane vrijednosti standarda,adaptera i izlaznih

veliina su uzete iz kalibracionih certifikata ( generalno normalna distribucija

k=2 )


34/67

Y= p...

X1 =pind,..

2 standard

u u u u

p p p

p p p p

k

(*)

8.3 Calibration of Bourdon tube pressure gauges


A simple sum/difference model is suitable for determining the measurement deviation of theindication separate for the measurement values in the direction of increasing pressure andfor the measurement values in the direction of decreasing pressure.

8.3 Kalibracija manometra sa Burdonovom cijevi

8.3.1 Model vrednovanja

Jednostavni zbir/razlika model prikladan je za odredjivanja mjernih odstupanjaoznake,

pup/down

pind, up/down

2

pstandard

/i

i 1

pind, up/down

pstandard

/ zero deviation / repeatability (8)

measurand; measurement deviation of indicationIndex ... stands for up/down or mean (cf. eqs. 8 and 9)

indication of pressure gaugeIndex ... stands for up/down or mean (cf. eqs. 8 and 9)

X =p value of reference standard3

X3 = pzero deviation unknown measurement deviation due to zero deviation

X4 = prepeatability unknown measurement deviation due to repeatability

and for the mean values:

pmean

pind, mean

3

pstandard / i

i 1

pind, mean

pstandard

/ zero deviation / repeatability / hysteresis (9)

pmean

pind,up

pind, down

2(10)

X5 = physteresis unknown measurement deviation due to hysteresis

When the increasing and decreasing series are taken separately, the expanded uncertainty Uwith k=2 is: Kada se poveavanja ili smanjenja serija uzimaju odvojeno,onda je proirenamjerna nesigurnost U sa k=2 je

Uup/down

Uup/down

k uup/down

2standard

2

resolution

2zero deviation

2

repeatability

(11)


35/67

3The value of the reference standard allows for the use of the pressure balance under conditions of

use (application of corrections). Therefore the uncertainty analysis, too, contains uncertaintycontributions from the pressure balance both under reference conditions and conditions of use. Thelatter contribution is determined in uncertainty budgets (see Annex A: Estimate of measurementuncertainty to be attributed to the values of the pressure balance under conditions of use) for theeffects of temperature, of the thermal linear expansion coefficient, acceleration due to gravity, airdensity, deformation coefficient (pressure balance) or for density, acceleration due to gravity, altitude(difference in altitude).

Vrijednost referentnog standarda omoguuje korienje pritiska ravnoteepod uslovima koritenja (primjenom korekcija). Stoga analiza nesigurnosti,takoe, sadri nesigurnosti doprinose od ravnotee pritiska i podreferentnim uslovima i uslovimama koritenja.Kasniji doprinos utvruje se unesigurnosti prorauna (vidi Prilog A: Procjena mjerne nesigurnosti biti

pripisana na vrijednosti pritiska ravnotee u uslovima korienja) zadjelovanja temperature, od tolotne linearne ekspanzije koeficijenta,ubrzanja zbog gravitacija, gustoe vazduha, deformacije koeficijente(ravotenog pritiska) ili gustine, ubrzanje zbog gravitacije, visine (razlika uvisini).


36/67

U

u u

U

and a so-called error span4

allowing for the systematic deviation:

I takozvani raspon greke4 omoguavajui radi sistemskog odstupanja'up/down Uup/down pup/down (12)

When the mean values from increasing and decreasing series are used, the expanded un-certainty Uwith k=2 is calculated at:

Kada se srednje vrijednosti od poveanja i smanjenja niza koriste,proirena nesigurnost U sa k= 2 rauna se na:

Umean

k 2up/down

2

hysteresis (13)

where for the calculation of the measurement uncertainty uup/down the larger value of the re-peatability is to be entered. gdje za raunanje mjerne nesigurnosti gore/ dolje vee vrijednosti

ponovljivosti upisuje.

The associated error span is determined at:

Povezani raspon greke odredjuje se:'

mean Umean pmean (14)


37/67

8.3.2 Uncertainty analysis

The knowledge of the input quantities is preferably given in a table.

Analiza nesigurnostiPoznavanje poeljih ulaznih veliina dato je u tabeli:

4As error span the maximum difference to be expected between the measured value and the

conven- tional true value of the measurand is referred to. The error span can be used to characterizethe accuracy.

Kao kod raspona greke maksimalne razlike oekuju su izmedju izmjerene vrijednosti ikonvencionalne prave vrijednosti koje se spominju. Raspon greke se moe koristiti zakarakterizaciju tanosti.


38/67

1 pind, ... pi, ind, ... 2r rectangle 32

u r1 2r

3 21 ur bar

2 pstandardp

normal 2 u(standard) -1 ustandard bar

3/p

0 f0 rectangle 31 f

2

u f 003 2

1 u f0 bar

4 /prepeatability 0 b rectangle 32

u b1 b

3 21 ub bar

5 /physteresis 0 h rectangle 32

u h1 h

3 21 uh bar

Table 3: Uncertainty analysis for the calibration of a Bourdon tube pressure gauge

Cont.No.

Quantity Estimate

Width ofdistrib-

ution

Probabilitydistribution

DivisorStandard

uncertainty

Sensiti-vity coef-

ficient

Uncer-tainty con-

tribution

Unit5

Xi xi 2a P(xi) u(xi) ci ui(y)

i, standard

zero deviation

Y p ... u(y) bar

8.3.3 Load step-related uncertainty budgetThe estimate of the measurement uncertainty has to be made for each calibration value, i.e.for each load step. For reasons of clearness, the following tabular representation is recom-mended for increasing, decreasing and mean values:

8.3.3 Optereenje korak-vezane nesigurnosti prorauna

Procjena mjerne nesigurnosti mora biti izraena za svaku kalibracionu vrijednosti, odnosno zasvaki korak optereenja. Zbog preglednosti, sljedee tabelarni prikaz se preporuuje zapoveanje, smanjivanje i srednje vrijednosti:

Table 3: Uncertainty budget

Pressure

bar

Measure-ment de-viation

Standard uncertainty

u

Expanded

uncertainty

U(k= 2)

Errorspan

U

barbar

Contrib-ution 1

...Contrib-ution n

barbar

min.

...

max.


39/67

5

It is advisable to carry over the unit of the uncertainty contributions (unit of physical quantity, unitofindication, related (dimensionless) quantity, etc.)

Poeljno je da se prenose jedinice nesigurnosti doprinosa (jedinica fizike koliine,

jedinina pokazivanja, povezana (bezdimenzijska) koliina, itd.)


40/67

6/p

reproducibility 0 b rectangle 31 b

2

3 21 ub bar

u u u u uk

8.3.4 Single-number rating

In addition to the error span for each load step, the customer can be informed of the maxi-mum error span in the range for which the calibration is valid (in the unit of the pressure re-lated to the measurement value or the measurement span). Also, the conformity can be con-

firmed (cf. 9.1.3).8.3.4 Pojedinani broj ocjena

Uz raspon greke za svaki korak optereenja, kupac moe biti obavijeten o maksimalnomrasponu greke u rasponu za koji je kalibracija vrijedi (u jedinici pritiska pvezana na vrijednostimjerenja ili mjereni raspon ). Takoe, konformizam moe biti potvren (usp. 9.1.3).

8.4 Calibration of electrical pressure gauges

The evaluation model and the uncertainty budget for the calibration of Bourdon tube pressuregauges can also be used for the calibration of an electrical pressure gauge (numerically cor-rect indication in units of pressure). If necessary, a component for "reproducibility b when re-peatedly mounted is to be taken into account.

8,4 Kalibracija elektrinih manometara

Procjena modela i nesigurnost prorauna za kalibraciju mjerila Bourdon cijevi pritisak setakoe moe koristiti za kalibraciju elektrinih manometara (brojano tana indikacija ujedinicama pritiska). Ako je potrebno, komponentu za "obnovljivosti b kada je vie putasastavljan" treba uzeti u obzir.

X6

/preproducibility unknown measurement deviation due to reproducibility

Table 5:Additional component of uncertainty analysis for calibration of an electrical pressuregauge Dodatna komponenta analize nesigurnosti za kalibraciju elektrinogmanometra

Cont.No.

Quantity Estimate

Widthof dis-

trib-ution

Probabilitydistribution

DivisorStandard

uncertainty

Sensi-tivity

coef-ficient

Uncer-tainty con-

tributionUnit

Xi xi 2a P(xi) u(xi) ci ui(y)

u b

The expanded uncertainty (k=2) for the increasing and decreasing series is determined asfollows:

Uup/down

Uup/down

k uup/down

2

standard

2

resolution

2zero deviation

2

repeatability

2

reproducibility

(15)

The determination of the associated error span for the increasing and decreasing series andof the expanded uncertainty and the error span for the mean value is made in analogy to theprocedure for the Bourdon tube pressure gauge.

8.5 Calibration of pressure transducers and pressure transmitters with electricaloutput


A simple product/quotient model, for example, is suitable for determining the transmissioncoefficient separately for the measurement values in the direction of increasing pressure


41/67

and for those in the direction of decreasing pressure:

8,5 Kalibracija transduktera pritiska i transmitera pritiska sa elektrinim izlazom

8.5.1 Procjena modela

Jednostavan proizvod / kolinik model, na primjer, je pogodan za utvrivanje prenosakoeficijenta - odvojeno za vrijednosti mjerenja u smjeru poveanja pritiska i za one u smjerusmanjenja pritiska

Vind, up/down

Xout, up/down

G Vsupply

3

Sup/down

Ki

Sup/down

Xin

Vind,up/down

G Vsupply

pstandard

Kzero deviation

i 1

Krepeatability

Kreproducibility

(16)p

standard


42/67

...

X1 = Vind, ...

w w w w u u (u

W

)

'

Y= S measurand, transmission coefficientIndex ... stands for up/down or mean value (cf. eqs. 16 and 17)

indication of output unit (U, I, f)Index ... stands for up/down or mean value (cf. eqs. 16 and 17)

X2 = G transmission coefficient of adapter (amplifier made available)

X3 = Vsupply value of supply voltage (auxiliary device)

X4 =pstandard value of reference standard

X5 =Kzero deviation correction factor due to zero deviation

X6 =Krepeatability correction factor due to repeatability

X7 =Kreproducibility if applicable, correction factor due to reproducibility

For the mean values the following is valid: Za srednje vrijednosti validno je sljedee:

Xout, mean

Vind, mean

G Vsupply

4

Smean

Ki

Xin

Vind, mean

pstandard i 1

G Vsupply

Smean

pstandard

Kzero deviation

Krepeatability

Kreproducibility

K

hysteresis

(17)

X8 =Khysteresis correction factor due to hysteresis

When the increasing and decreasing series are taken separately, the relative expanded un-certainty (k=2) is determined at: Kada poveanja i smanjenja serija uzimaju odvojeno, relativnaproirena nesigurnost (k = 2) odreuje se na:

Wup/down

k wup/down

(18)Wup/down

k 2standard2ind

2amplifier

2supply

2zero deviation

2repeatability

2reproducibility

and the associated error spans at:

'

up/down Wup/downSup/down

S'

(19)

with the systematic deviation

Sup/down Sup/down S (20)

S'preferably representing the slope of the regression line through all measurement valuesand through the zero point of the output signal of the measuring transmitter.

When the mean value from increasing and decreasing series is used, the relative expandeduncertainty (k=2) is calculated at:

Spoeljno predstavlja nagib regresijske linije kroz sve mjerne vrijednosti i kroz nulte takeizlaznog signala mjernog odailjaa.Kad se srednja vrijednost od poveanja i smanjenja niza koristi, relativna proirenanesigurnost (k = 2) izraunava se na:


43/67

w wWmean k2up/down

2hysteresis (21)


44/67

1 Vind, ... Vi, ind normal 2 w(indicator) 1 wind #

2 G G normal 2 w(amplifier) -1 wamplifier #

3 Vsupply Vsupply normal 2 w(supply) -1 wsupply #

4 pstandard pi, standard normal 2 w(standard) -1 wstandard #

5 Kzero deviation 16)f0 rectangle 3

2

w f 1 f0

3 21 wf #

6 Krepeatability 1 b rectangle 32

w bb1

3 21 wb #

7 Kreproducibility 1 b rectangle 3b

2

w b1

3 21 wb #

8 Khysteresis 1 h rectangle 32

hw h

13 2

1 wh #

W

0

'

where for the calculation of the measurement uncertainty wup/down the larger value of the re-peatability is to be inserted.

gdje je za izraun w gore dolje mjerne nesigurnosti vee vrijednosti ponovljivosti treba da buduumetnute.

The associated error span is determined at:

Povezani razmaci greke odredjuju se:'

mean

with

Wmean

Smean

S'

(22)

Smean

Smean

S

(23)

ForS', cf. above.

8.5.2 Uncertainty analysis Analiza nesigurnosti

The knowledge of the input quantities is preferably given in a tabular form.Poznavanje ulaznihveliina je poeljno dati u tabelarnom prikazu

Table 6: Uncertainty analysis for the calibration of a pressure transmitter with electrical outputAnaliza nesigurnosti za kalibraciju transmitera pritiska sa elektriniom izlazom

Cont.

No.Quantity Estimate

Width

of dis-trib-

ution

Probability

distributionDivisor

Standard

uncertainty

Sensi-

tivitycoef-

ficient

Uncer-

tainty con-tribution

Unit

Xi xi 2a P(xi) w(xi) ci wi(y)

0 0

Y S... w(y) #

6)The characteristics f, b', b and h here are relative quantities, i.e. quantities related to the measure-


45/67

ment value (indication) which are not defined at the pressure zero.Karakteristuine fo,b,b I h su relativne veliine Itdveliine povezane sa mjernim vrijednostima( indikatorima ) koje nisu definisane na nultni pritisak.


46/67

8.5.3 Load step-related uncertainty budget

The estimate of the measurement uncertainty has to be made for each calibration value, i.e.for each load step. For reasons of clearness, the following tabular representation is recom-mended for increasing, decreasing and mean values:

Uitaj korak-povezane nesigurnosti proraunaProcjena mjerne nesigurnosti mora biti izraena za svaku kalibraciju, odnosno za svaki korakoptereenja. Zbog preglednosti, sljedee tabelarni prikaz se preporuuje za poveanje,smanjivanje i srednje vrijednosti:

Table 7: Uncertainty budget

PressureRel. standard uncertainty

w

Rel. expandeduncertainty W

(k=2)

Contribution1 ...

Contributionn

bar # #

min.

...

max.

8.5.4 Single-number rating

T r ans m ission coe fficient as slope ofa linear r e g r ession f unc t ion

For the use of the pressure transducer it is common practice not to apply different transmis-sion coefficients for the individual load steps (= calibration pressures) but one single transmis-sion coefficient for the whole range for which the calibration is valid. This preferably is theslope of the regression line through all measurement values and through the zero point of theoutput signal of the measuring transmitter (fitting without absolute term).

When this characteristic of the pressure transducer is used, a statement of conformity is sub-stituted for the measurement uncertainties attributed to the individual values measured for thetransmission coefficient (cf. 9.1.3).

For this purpose, the upper limiting amounts of the deviation are to be defined. This can bemade on the basis of the calibration results by calculation of the error spans according to8.5.1 ("self-determined conformity," definition on the basis of manufacturer's statements, cf.below). In this operation,

- the measurement uncertainties attributed to the individual measurement values of thetransmission coefficient and

- the deviations of these values from the single-number rating of the transmission coeffi-

cientare to be taken into account.


47/67

Jedan- broj ocjena

Transmisioni koeficijent kao pad linearne regresijske funkcije

Za koritenje transduktera pritiska uobiajena je praksa da ne primjenjuju razliiti transmisionikoeficijenti za pojedina optereenja koraka (= kalibracije pritiska), ali jednom transmisionom

koeficijentu koeficijent vrijedni za cijeli kalibracioni niz. Ovdje je poeljan je pad regresijske linijepreko svih mjernih vrijednosti i kroz nultne take izlaznog signala mjernog odailjaa (sklapanjebez apsolutnpg pojma-roka).

As a rule, error spans result whose magnitudes decrease with increasing pressure. As theupper limiting amounts of the deviation

- the maximum calculated error span can be selected (in this case, the upper limitingamounts of the deviation are represented in the calibration diagram as straight linesparallel to the pressure axis, cf. 9.2, pressure transmitters with electrical output signal,figure 5, upper details) or

- the upper limiting amounts of the deviation are described by suitable curves such ashyperbolas or polynomials (cf. 9.2, pressure transmitters with electrical output signal,figure 5, lower details).


48/67

No t e :The use of pressure-dependent upper limiting amounts of the deviation is not common prac-tice. In pressure measurements with the calibrated device in the upper part of the measure-ment range, it allows, however, smaller measurement uncertainties to be stated.

For calibration items whose nominal parameter (e.g. 2 mV/V) has been balanced by themanufacturer, the upper limiting amounts of the deviation can alternatively be determinedfrom the associated parameter tolerance. In this case, it is, however, always to be checkedwhether the values of the transmission coefficients determined in the calibration, includingtheir attributed measurement uncertainties and systematic deviations from the single-numberrating of the parameter do not exceed the upper limiting amounts of the deviation.

8.6 Determination of relevant parameters for uncertainty analysis

8.6.1 Resolution r

8.6.1.1 Analog indicating devicesThe resolution of the indicating device is obtained from the ratio of the pointer width to thecentre distance of two neighbouring graduation lines (scale interval). 1/2, 1/5 or 1/10 is rec-ommended as ratio. If 1/10 is chosen as the ratio (i.e. the estimable fraction of a scale inter-val), the scale spacing must be 2,5 mm or greater (cf. also DIN 43790).

No t e:The best estimate for an analog indicating device is determined by visual interpolation. Thesmallest estimable fraction of a scale interval is the interpolation component (r) by which themeasurement values can be distinguished. The variation interval for the best estimate (x) thusis a+ =x + rand a- =x - rwith the width of the rectangular distribution being 2a = 2r.

8.6.1.2 Digital indicating devices

If the indication varies by one digital step at most when the pressure gauge is not loaded, theresolution corresponds to the digital step.

No t e:For the determination of the uncertainty contribution, half the value of the resolution (a = r/2)is assigned to the half-width of the rectangular distribution. This uncertainty contribution doesnot explicitly appear in section 8.5 as it is contained in the measurement uncertainty of theoutput unit (display) (statement in calibration certificate).

8.6.1.3 Fluctuation of readings

If the readings fluctuate by more than the value previously determined for the resolution withthe pressure gauge not being loaded, the resolution r is to be taken as half the span of thefluctuation, additionally added with a digital step.

8.6.2 Zero deviationf0

The zero point can be set prior to every measurement cycle consisting of an increasing and adecreasing series and must be recorded prior to and after every measurement cycle. Thereading is to be made with the instrument being completely relieved.


49/67

b

b

b max b ,

The zero deviation is calculated as follows:

f0 = m a

x

x 2 ,0 x1,0 , x 4 ,0 x 3 ,0 , x 6 ,0 x 5 ,0 (24)

The indices number the measurement values x read in the zero points of the measurementseries M1 to M6.

8.6.3 Repeatability b'

The repeatability with the mounting not being changed is determined from the difference ofthe zero signal-corrected measurement values of corresponding measurement series.

'

up, j

'

down,j

x3, j

x4, j

x3, 0

x4, 0

x1, j

x2, j

x1, 0

x2,0 (25)'

mean, j

'

up, j

'

down, j

The indexj numbers the nominal values of the pressure (j = 0: zero point).

8.6.4 Reproducibility b

The reproducibility with the instrument being mounted repeatedly and the conditions not beingchanged is determined from the difference of the zero signal-corrected measurement valuesof corresponding measurement series.

bup, j x5, j x5, 0 x1, j x1, 0

bdown, j

x6, j

x6, 0

x2, j

x2, 0 (26)

bmean, j

max bup, j

,bdown, j

For indexj, see above.

8.6.5 Hysteresis h

When mean values are stated, the hysteresis is determined from the difference of the zeropoint-corrected measurement values of the increasing and decreasing series as follows:

1h

mean, jn

x2, j

x1, 0

x1, j

x1, 0

x4, j

x3, 0

x3, j

x3, 0

x6, j

x5, 0

x5, j

x5, 0

(27)

For indexj, see above. The variable n stands for the number of the complete measurementcycles.


50/67

9. Evaluation of measurement results and statements in the calibrationcertificate

The main components of the pressure gauge are each provided with a calibration mark; de-vices belonging to a measuring chain are each provided with a calibration mark.

In addition to the requirements in DKD-5, the following information is to be stated in the cali-bration certificate:

- calibration method (DKD-R 6-1 sequence A, B, C or EN 837 parts 1 and 3)- pressure-transmitting medium- pressure reference plane on calibration item- position of calibration item for calibration- selected settings on calibration item

The calibration certificate should contain a table of all measurement values, e.g.:

Table 8: Measurement values

Pressure

pstandard

Value displayedpind

Calibration sequence AMeasurement with 2nd

clamping

Calibration sequence B

Calibration sequence C

M1 (up) M2 (down) M3 (up) M4 (down) M5 (up) M6 (down)

bar,Pascal,

...

bar, Pascal, A, V, mV/V, Hz, ...

min. min. min. min. min. min. min.

max. max. max. max. max. max. max.

Column 1 contains the pressure values measured for the standard. Columns 2 to 7 containthe corresponding measurement values displayed by the calibration items according to figure 1(Bourdon tube pressure gauge, electrical pressure gauge, pressure transmitter with electricaloutput) in units of pressure or output in other physical quantities (current, voltage, voltage ra-tio, frequency, ...) or already converted into the quantity of pressure.

The further evaluation of the measurement values can encompass the following characteris-tics:- mean values- measurement deviation of display- zero deviation- repeatability- reproducibility, if applicable- hysteresis- error span- single-number rating

- conformity-


51/67

9.1 Determination of other parameters

9.1.1 Mean values x

The mean values x i,j with i = up/down, mean are calculated as follows:

1xup, j

l m

1xdown, j

l

xm, j

xm,j

m

xm, 0

x(m -1), 0

for m

for m

1, 3, 5

2, 4, 6 (28)

xmean

xup, j

xdown, j

2

where variable lgives the number of measurement series.

9.1.2 Error span U

The error span is the sum of the expanded uncertainty (k=2) and the amount of the systematicdeviation. Due to the systematic component, the error span is assigned rectangular distribu-tion as distribution shape. The error span is to be determined according to the requirementsfor the mean values of the increasing and decreasing series and the mean value:

e.g.: U = U+ p (29)

The relative error span W'is formed accordingly.

e.g.: W' WS

S' (30)

Note:cf. also

4on page

18.

9.1.3 Conformity

If the error span and the transmission coefficients with attributed measurement uncertainty liewithin the error limit stated by the manufacturer, the conformity according to DKD-5 can beconfirmed. The range for which it is valid is also to be stated.


52/67

2QU GZEGUURTGUUWTGKP DCT

FGXKCVKQP OGCUWTGOGPVWPEGTVCKPV[WRRGT NQYGTNKOKVQHFGXKCVKQP

2QU GZEGUURTGUUWTGKP DCT


&GXKCVKQP

YKVJOGCUWTGOGPV

WPEGTVCKPV[TGNCVGFVQ

OGCUW

TGOGPVXCNWG

&GXKCVKQP

YKVJO

GCUWTGOGPV

WPEGTVCKPV[TGNCVGFVQ

OGCUWTGOG

PVURCP

&GXKCVKQP

YKVJOGCUW

TGOGPV

WPEGTVCKPV[

KPD

CT

'TTQT

URCPTGNCVGF

VQOGC

UWTGOGPV

XCNWG

'TTQT

URCPTGNCVGF

VQOGCUWT

GOGPV

URCP

'TTQT

URCP

KP

DCT

9.2 Visualization of calibration result

For better understanding and ease of overview, the calibration result can also be given in agraphical form.

9.2.1 Bourdon tube pressure gauges, electrical pressure gaugesThe systematic deviation with the expanded measurement uncertainty or the resulting errorspan, respectively, are to be represented with reference to the upper limiting amount of thedeviation (error limit), in the unit of the physical quantity and/or as a related quantity. The rep-resentation of related parameters can be made in a form which is typical of the kind of device(related to the measurement span, related to the measurement value).

Figure 4: Visualization of the calibration result for a Bourdon tube pressure gauge or an elec-trical pressure gauge

2QU GZEGUURTGUUWTG KP DCT 2QU GZEGUU RTGUUWTG KP DCT


GTTQT URCP WRRGT NQYGTNKOKVQHFGXKCVKQP

2QU GZEGUU RTGUUWTGKP DCT

GTTQT URCP WRRGT NQYGTNKOKVQHFGXKCVKQP

2QU GZEGUURTGUUWTG KPDCT

GTTQTURCP WRRGT NQYGTNKOKVQHFGXKCVKQP


53/67

GTTQTURCP UGNH FGVGTOKPGFWRRGT NQYGTNKOKVQHFGXKCVKQP

2QU GZEGUU RTGUUWTG KPDCT

GTTQTURCP UGNH FGVGTOKPGFWRRGT NQYGTNKOKVQH FGXKCVKQP

6TCPUOKUUKQPEQGHHKEKGPV

KP

O88

DCT

6TCPUOKUUKQPEQGHHKEKGPV

KPO88

DCT

'TTQT

URCP

KP

O88

DCT

'TTQT

URCP

KP

O88

DCT

9.2.2 Pressure transmitters with electrical output

The transmission coefficients and the attributed measurement uncertainties are representedwith reference to the upper limiting amounts of the deviation (error limits according to manu-facturer's specification or self-determined limit).

Figure 5: Visualization of the calibration result for a pressure transmitter with electrical output

2QU GZEGUURTGUUWTGKPDCT

6TCPUOKUUKQPEQGHHKEKGPV OGCUWTGOGPV WPEGTVCKPV[

UKPING PWODGTTCVKPI $ UGNHFGVGTOKPGFNKOKVQHFGXKCVKQP

2QU GZEGUURTGUUWTGKPDCT

transmiss ion coefficient measurement uncertainty

s ingle-numberrating (B) s elf-determinedupper/ lower limit of deviation

9.3 Limiting values for uncertainty statements7

For all calibration sequences (A, B, C) the measurement uncertainty is calculated in accor-dance with section 8. Independently of the result of the calibration, the measurement uncer-tainty is stated

for cal. sequence B not smaller than 0,04% of measurement spanand for cal. sequence C not smaller than 0,30% of measurement span.

For the statement of the error span in a conformity statement according to DKD-5, the valuemust be given

for cal. sequence B not smaller than 0,06% of measurement spanand for cal. sequence C not smaller than 0,60% of measurement span.

7for the present not valid for measuring transmitters


54/67

10. Other rules and standards

If appropriate, the following rules are to be taken into account for the calibration of pressuregauges. It may also be agreed to carry out the calibration in accordance with individual sec-tions of some of these rules.

EN 837 part 1 Druckmegerte mit RohrfedernMae, Metechnik, Anforderungen und Prfung(Pressure gauges with Bourdon tubes; measures, measuringtechnique, requirements and test)February 1997 edition

EN 837 part 3 Druckmegerte mit Platten- und Kapselfedern Mae,Metechnik, Anforderungen und Prfung (Pressuregauges with diaphragm and capsule elements;measures, measuring technique, requirements and test)February 1997 edition

DIN 16086 Elektrische Druckmegerte

Druckaufnehmer, Druckmeumformer, DruckmegerteBegriffe und Angaben in Datenblttern(Electrical pressure gauges; pressure transducers, pressuretransmitters, pressure gauges; terms and statements in datasheets)May 1992 edition

DIN 43790 Grundregeln fr die Gestaltung von Strichskalen und Zeigern(Basic rules for the design of line scales and pointers)January 1991 edition

EA-10/03 Calibration of Pressure BalancesEdition 1, July 1997

DKD-R 3-6 Richtlinie zur Auswahl und Kalibrierung von elektrischenReferenzdruckmegerten fr die Anwendung inDKD-Laboratorien(Guideline for the selection and calibration of electrical refer-ence pressure gauges for use in DKD laboratories)November 1993 edition

EA 10/17 EA Guidelines on the Calibration of ElectromechanicalManometers (rev. 00)July 2002


55/67

Temperature tK a t rectangle 31

u t a2

3t ct = - 2 p ut = ct u(t) bar

Thermallinear

expansioncoefficient

a rectangle 3 u1

a2

3c = -2 t- 20C p u = c u( ) bar

Acceleration

due togravity g ag rectangle 3

1

u g a2

3g cg =p g ug = cg u(g) bar

Deformation

coefficienta rectangle 3

1 2u3

a 2 u = c u( ) bar

i

Annex A Estimate of measurement uncertainty to be attributed to the values of

the pressure balance under conditions of use8

The values and the attributed expanded uncertainty Ustandard, ref for a pressure balance underreference conditions are to be taken from the calibration certificate (issued, for example, by

the PTB). When the instrument is used under conditions of use, corrections for the relevantinfluence quantities are to be applied to the values and to these values, too, an uncertaintyhas to be attributed.

Evaluation model9:

n

m g 1i 1

pe

a

m , ig h (31)

A0

1 p 1 t 2 0 C

Fl a(32)

Uncertainty analysis

with the influence quantities relevant to the pressure value of the standard: temperature,thermal linear expansion coefficient of piston and cylinder, acceleration due to gravity anddeformation coefficient. The sensitivity coefficients were calculated with the approximationsusual for practical applications and for the most common case = .

Table 9

Quantity

Xi

Esti-

mate

xi

Half-

width

a

Probability

distribution

P(xi)

Divisor

Standard

uncertainty

u(xi)

Sensitivity coefficient

ci

Uncertainty

contribution

ui(y)

Unit

c = -p

Y yu u

2u

2u

2u2

corr1 t . g

bar

8cf.

3on page 17

9cf. also EA-10/03 Annex B


56/67

Y y2 2 2

u u u

No t e :1. In calibration certificates issued by the PTB for pressure balances, the contribution of the

uncertainty of the numerical value of the deformation coefficient to the uncertainty of thepressure measurement at reference temperature generally has already been taken intoaccount.

2. Portable measuring instruments allow the local acceleration due to gravity at a certain lo-cation to be measured with a relative uncertainty of a few ppm. If such an exact measure-ment value is available, it may be permissible to neglect the uncertainty contribution of theacceleration due to gravity as the relative uncertainty of the value of the cross sectionalarea is in most cases substantially higher.

3. Related to the force of inertia g m acting in the vacuum, the buoyancy correction is of theorder of 1,5 10

-4. Changes in the air density at a particular location due to the weather

normally do not exceed 2 % corresponding to a relative contribution to the measurementuncertainty of 3 ppm. In relation to the uncertainty of the cross sectional area of 50 ppmusually given in calibration certificates, this contribution is negligible and generally does notjustify the metrological efforts made to determine it (cf. 6 Ambient conditions, Note).

Uncertainty analysiswith the influence quantities relevant to the determination of the hydrostatic pressure due to adifference between the reference level of the standard instrument and the instrument to becalibrated.

Table 10

Quantity

Xi

Esti-

mate

xi

Half-

width

a

Probability

distribution

P(xi)

Divisor

Standard uncertainty

u(xi)

Sensitivity

coefficient

ci

Uncertainty

contribution

ui

y

Unit

Determina-

tion ofdensity

difference

a a

aFl

rectangle 31 2 2u a

!a!

3 a Flc =g h u = c u( ) bar

Determina-

tion ofaccel-

eration due to

gravity

g ag rectangle 3 u g1

a2

3g

cg

h ug

cg

u g bar

Determina-

tion ofdiffer-

ence in alti-

tude

h ah rectangle 3 u h1

a2

3h

ch

g uh

ch

u(h) bar

ucorr2 u ug uh bar

Expanded uncertainty (k=2) for the values realized by a pressure balance under conditions ofuse:

Ustandard, cond. ofuse

k 2standard, ref

2corr1

2corr2 (33)

No t e :Besides the corrections given here as an example, further corrections and associated contri-butions to the measurement uncertainty are to be taken into account, for example the uncer-tainty of the residual gas pressure measurement for pressure balances for absolute pressure

or the pressure dependence of the density of the pressure-transmitting medium in the meas-urement of major hydraulic pressures.


57/67

Annex B ExampleUncertainty budget for the calibration of a

Bourdon tube pressure gauge

Calibration effort for calibration sequence CStatement of mean value (Miw) with measurement deviation ( p) and hysteresis (h)

Calib r a t ion it em

Gauge pressure measuring equipment with elastic sensing element (Bourdon tube pressuregauge)Accuracy stated by manufacturer : DIN cl. 1,0Scale interval : 0,5 bar (with fifth estimate)

S t anda r d de v ice

Designation : xxx

Expanded uncertainty : 1 10-4

p but not smaller than 0,4 mbarCalib r a t ion condit ions

Pressure-transmitting medium : purified nitrogen

Fl(20C,1bar) : 1,15 kg/mh : (0 m 0,005) m

tamb : (21,6 1) Cpamb : (990 1) mbar

Table 11: Result

PressureReading from calibration

item (indication)Mean value

Measure-ment devia-

tion

p

Miw-pe

HysteresisExpanded

uncertainty

pstandard pind Miw h U

M1 M2 (M1+M2)/2 |M2-M1|

bar bar bar bar bar bar bar

0,00 0,0 0,0 0,0 0,0 0,0 0,12

12,02 12,1 12,2 12,2 0,2 0,1 0,12

24,03 24,2 24,2 24,2 0,2 0,0 0,12

36,04 36,1 36,2 36,2 0,2 0,1 0,13

48,04 48,1 48,1 48,1 0,1 0,0 0,12

60,05 60,0 60,1 60,1 0,0 0,1 0,13


58/67

pstandard60,05bar

2 3,00*10 bar -1 3,00*10 9,02*10

pstandard, t 0,999997 2 K 3-15,77*10 K -1,32*10

-3

bar/K-47,63*10 5,82*10

-7

pstandard, h * 0-21,0*10 m 3

-32,89*10 m -6,74*10-3

bar/m-51,95*10 3,79*10

-10

pind60,05

0,1 bar 3-2

5,77*10 bar 1-2

5,77*10-3

3,33*10

pzero deviation 0 0,0 bar 3 0 1 0 0

prepeatability 0 0,0 bar 3 0 1 0 0

physteresis 0 0,1 bar 3-22,89*10 bar 1 -22,89*10 8,33*10

-4

Table 12: Uncertainty budget for load step p=60,05 bar

QuantityEsti-mate

Width ofdistribu-

tionDivisor

Uncer-tainty

Sensitivitycoefficient

Uncer-tainty

contrib.Variance

Xi xi 2a u(xi) ci u(y) u2

bar bar

-3 -3 -6

bar

p 0,00 bar u = 6,46*10-2 u

2

4,17*103

i

p 0,00 bar U= k u (k= 2) 0,13 bar

*allowing for the pressure-dependent gas density (approximation)

p, t 20 C,1bar

pabs

T

1bar T

20K

twith T=273,15K

For the correction of the pressures realized by the standard device, the following d

Microsoft Wordghfgh

Documents