Final Report APMP.M.P-S8 100412 - BIPM · Final Report on APMP.M.P-S8 Version 1.1 of 12 April 2010 2 preparation of a report on the comparison and the analysis of data on the basis

Final Report on APMP.M.P-S8 Version 1.1 of 12 April 2010

The Asia-Pacific Metrology Programme (APMP) and the European Association of National Metrology Institutes (EURAMET)

1000 MPa HYDRAULIC PRESSURE INTERLABORATORY COMPARISON

Final Report on Supplementary Comparison APMP.M.P-S8 in Hydraulic Gauge Pressure from 100 MPa to 1000 MPa

April 2010

Tokihiko Kobata1, Kazunori Ide1, Hiroaki Kajikawa1,

Wladimir Sabuga2, Steffen Scheppner2 and Wilfried Schultz2

Abstract This report describes the results of a supplementary comparison of hydraulic high-pressure standards at two National Metrology Institutes (NMIs), National Metrology Institute of Japan, AIST (NMIJ/AIST) and Physikalisch-Technische Bundesanstalt (PTB), Germany, which was carried out during the period January 2007 to March 2007 within the framework of the Asia-Pacific Metrology Programme (APMP) and the European Association of National Metrology Institutes (EURAMET) in order to determine their degrees of equivalence at pressures in the range 100 MPa to 1000 MPa for gauge mode. The pilot institute was NMIJ/AIST. NMIJ/AIST used a hydraulic pressure balance and a pressure multiplier, and PTB used a controlled-clearance pressure balance as their pressure standards. High-precision pressure transducers were used as a transfer standard. The sensing element of the transducers was a foil strain gauge. To ensure the reliability of the transfer standard, two pressure transducers were used on the transfer standard unit. At the beginning and the end of this comparison, the transfer standard was calibrated at the pilot institute. From the calibration results, the behavior of the transfer standard during the comparison period was characterized and it was presented that the capability of the transfer standard for the purpose of this supplementary comparison was sufficient. The degrees of equivalence of the national measurement standards were expressed in terms of deviations from the supplementary comparison reference values and from each other, considered in combination with associated uncertainties of these deviations. The hydraulic pressure standards in the range 100 MPa to 1000 MPa for gauge mode of the two participating NMIs were found to be equivalent within their claimed uncertainties. 1 NMIJ/AIST (Pilot institute): National Metrology Institute of Japan, AIST, AIST Tsukuba Central 3, 1-1, Umezono 1-Chome,

Tsukuba, Ibaraki, 305-8563 Japan 2 PTB: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany


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Contents: Page

1. Introduction ..................................................................................................................... 1 2. Participating institutes and their pressure standards .................................................. 3

2.1 List of participating institutes .................................................................................. 3 2.2 Pressure standards of participating institutes ......................................................... 3

2.2.1 Description of the NMIJ/AIST pressure standard ............................................. 4 2.2.2 Description of the PTB pressure standard ......................................................... 6

3. Transfer standard ............................................................................................................ 7 3.1 Pressure transducers and measuring amplifier ....................................................... 7 3.2 Structure of transfer standard .................................................................................. 9 3.3 Transfer package ..................................................................................................... 11

4. Circulation of the transfer standard ............................................................................ 12 4.1 Chronology of measurements .................................................................................. 12 4.2 Environmental conditions of the transfer standard during transportation .......... 12

5. Calibration ..................................................................................................................... 14 5.1 Preparation .............................................................................................................. 14 5.2 Head correction by height difference ...................................................................... 14 5.3 Calibration procedure .............................................................................................. 15

5.3.1 Complete measurement cycle ........................................................................... 15 5.3.2 Measurement at 0 MPa ..................................................................................... 16 5.3.3 Calibration at (100, 200, 300, 400, 500, 600, 700, 800, 900 and 1000) MPa... 16 5.3.4 Results to be reported ....................................................................................... 17

6. Analysis of reported data .............................................................................................. 18 6.1 Correction for zero-pressure offsets ........................................................................ 19 6.2 Correction for difference between nominal pressure and actual pressure ............ 19 6.3 Correction to reference temperature ....................................................................... 20 6.4 Correction for long-term shift in characteristics of transducer ............................. 24 6.5 Calculation of normalized mean ratio of participating institutes ......................... 26 6.6 Calculation of expected mean pressure of participating institute ......................... 28 6.7 Estimation of uncertainties ..................................................................................... 29

6.7.1 Uncertainty due to systematic effect in pressure standard ............................ 29 6.7.2 Uncertainty due to deviation from reference temperature ............................. 31 6.7.3 Uncertainty due to combined effect of short-term random errors .................. 33 6.7.4 Uncertainty arising from the long-term shift .................................................. 35 6.7.6 Combined uncertainty in expected mean pressure of institute ...................... 38


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7. Results for supplementary comparison APMP.M.P-S8 ................................................ 39 7.1 Calculation of APMP Supplementary Comparison Reference Values ................... 39 7.2 Evaluation of degrees of equivalence ...................................................................... 41

7.2.1 Deviation of institute’s value from APMP SCRV ............................................. 41 7.2.2 Difference between deviations for pairs of institutes ...................................... 44

8. Discussions .................................................................................................................... 46 9. Conclusions .................................................................................................................... 47 Acknowledgements ............................................................................................................ 48 References .......................................................................................................................... 49


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1. Introduction The National Metrology Institute of Japan, AIST (NMIJ/AIST), Japan, and the Physikalisch-Technische Bundesanstalt (PTB), Germany, the members of the Asia-Pacific Metrology Programme (APMP) and the European Association of National Metrology Institutes (EURAMET), respectively, both participants in the last CIPM 100 MPa key comparison CCM.P-K7 1 and 500 MPa key comparison CCM.P-K8 2, have organized this comparison to extend the pressure range up to 1 GPa, and finally, to study suitability of pressure transducers as transfers standards for high pressure comparisons.

NMIJ/AIST has been agreed by the Technical Committee for Mass and Related Quantities (TCM) in APMP to coordinate the interlaboratory comparison program for high-pressure as a pilot institute. The comparison has been identified as APMP.M.P-S8 by the Consultative Committee for Mass and Related Quantities (CCM) of the International Committee for Weights and Measures (CIPM), the International Bureau of Weights and Measures (BIPM). The objective of the comparison was to compare the performance of hydraulic pressure standards in the National Metrology Institutes (NMIs), in the pressure range 100 MPa to 1000 MPa for gauge mode using Di(2)-ethyl-Hexyl-Sebacate (DHS) as a transmitting fluid according to the guidelines3,4,5. Both participating institutes have the opportunity to get results in the comparison at a level of uncertainty appropriate for them6. The results of this comparison will be included in the Key Comparison Database (KCDB) of BIPM following the rules of CCM7. Those will also be used to support the declarations made for the 1 GPa pressure calibration and measurement capabilities (CMCs) of the NMIs for the Mutual Recognition Arrangement (MRA). The pilot institute proposed using high-precision electronic pressure transducers as a transfer standard for this comparison. To ensure the reliability of the transfer standard, two high-precision pressure transducers were used on the transfer standard unit. At the beginning and the end of the comparison, the transfer standard was calibrated at the pilot institute. From the calibration results, the behavior of the transfer standard during the comparison period was well characterized. A protocol was prepared by the pilot institute, which was an integral part of this comparison8,9. The transfer standard was circulated from January 2007 to March 2007. NMIJ/AIST used a hydraulic pressure balance and a pressure multiplier and PTB used a controlled-clearance pressure balance as their pressure standards. Both NMIs calibrated the transfer standard against their pressure standard following the protocol. The calibration results obtained at PTB have been submitted to the pilot institute. The


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preparation of a report on the comparison and the analysis of data on the basis of the results from the participants have been done by the pilot institute by trying to make a uniform treatment for both participants according to the guidelines3,4,5. This report gives the calibration results of the transfer standard carried out at the two NMIs. The following sections provide descriptions of the participating institutes and their pressure standards, the transfer standard, the circulation of the transfer standard, the general calibration procedure for the transfer standard, the method for analysis of the calibration data and the comparison results.


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2. Participating institutes and their pressure standards 2.1 List of participating institutes Two National Metrology Institutes (NMIs) participated into this comparison including the pilot institute. The participating institutes along with their addresses are listed in Table 2.1.

Table 2.1: List of participating institutes. Participating Institutes

Country: Japan Acronym: NMIJ/AIST (Pilot institute) Institute: National Metrology Institute of Japan, AIST Address: AIST Tsukuba Central 3, 1-1, Umezono 1-Chome, Tsukuba, Ibaraki, 305-8563 Japan Country: Germany Acronym: PTB Institute: Physikalisch-Technische Bundesanstalt Address: PTB, Working Group 3.23, Bundesallee 100, D-38116 Braunschweig,

Germany

2.2 Pressure standards of participating institutes NMIJ/AIST used a hydraulic pressure balance and a pressure multiplier, and PTB used a controlled-clearance pressure balance as their pressure standards to generate the hydraulic pressures. Each institute provided information about its standards against which the transfer standard was calibrated, including the pressure balance base, the type and material of piston-cylinder assembly and the effective area with its associated standard uncertainty at the reference temperature, see Tables 2.2 and 2.3. Details of the parameters used by each participating institute such as the local gravity, height difference between the reference levels of the participating institute’s standard and the transfer standard, and the power supply voltage used for the transfer standard are also listed in the tables. The pressure standard of each participating institute was operated at the normal operating temperature of the institute.


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2.2.1 Description of the NMIJ/AIST pressure standard The pressure standard up to 1 GPa using a precise pressure multiplier and a pressure balance has been developed at NMIJ/AIST. The multiplying ratio of the pressure multiplier, which is the ratio of high pressure to low pressure, is about 10. The pressure multiplier has low and high pressure ports and is capable of generating pressure of 1 GPa at the high pressure port when pressure of 100 MPa is applied to the low pressure port. The pressure for the low pressure port can be applied accurately using a pressure balance. The multiplying ratio of the multiplier was precisely measured as a function of pressure by applying known pressures to both the ports. Using the multiplying ratio measured, the pressure generated at the high pressure port was calculated up to 1 GPa. The methods for evaluating the multiplying ratio of the multiplier and for calculating the pressure generated using the pressure multiplier up to 1 GPa have been reported10. In this comparison, NMIJ/AIST used a simple type pressure balance from 100 MPa to 500 MPa, and the pressure system consisting of the precise pressure multiplier and a pressure balance from 600 MPa to 1000 MPa, as the pressure standards. Details of the pressure standards are given in Table 2.2.


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Table 2.2: Details of the pressure standards at NMIJ/AIST. All the uncertainties are expressed as standard uncertainties.

NMICountry

Pressure standardtype

Pressure balance (100 MPa to 500 MPa)Base

WeightsRelative uncertainty of mass pieces

Piston-cylinderMaterial of piston

Linear thermal expansion coefficient of piston / ℃-1

Material of cylinderLinear thermal expansion coefficient of cylinder / ℃-1

Piston rotation Effective area Value ui relative ui

A 0 / m2 1.961434 × 10-6

at 23 ℃3.1 × 10-11 1.6 × 10-5

λ / MPa-1 8.33 × 10-7 1.05 × 10-7 0.13Multiplier (500 MPa to 1000 MPa)

Piston-cylinderMaterial of piston (Low Pressure / High Pressure)

Material of cylinder (Low Pressure / High Pressure)Piston rotation Multiple ratio Value ui relative uiMultiple ratio 9.99842 2.0 × 10-4 2.0 × 10-5

λ / MPa-1 4.82 × 10-7 1.10 × 10-7 0.23Pressure balance [Used with Multiplier]

BaseWeights

Relative uncertainty of mass piecesPiston-cylinder

Material of pistonLinear thermal expansion coefficient of piston / ℃-1



A 0 / m2 9.80863 × 10-6

at 23 ℃1.3 × 10-10 1.3 × 10-5

λ / MPa-1 7.27 × 10-7 1.02× 10-7 0.14Parameters used for the compariton Value ui relative ui

Local gravity / m/s2 9.7994808 2.0 × 10-6 2.0 × 10-7

Density of medium ρ f / kg/ m3 Eq.(a) --- 1 × 10-2

Transfer Standard Value ui relative uiDifferential height of reference levels H 1 / mm 326.4 1.0 ---Differential height of reference levels H 2 / mm 344.7 1.0 ---Differential height of reference levels H 0 / mm 0.0 1.0 ---

Power supply 100VAC 50Hz --- ---

Eq(a): ρ f = [912.7 + 0.752 (p /MPa) - 1.645⋅10-3 (p /MPa)2 + 1.456⋅10-6 (p /MPa)3] × [1 - 7.8 × 10-4 (t/°C - 20)] kg/m3

(ρ f: density of Di(2)-ethyl-Hexyl-Sebacate (DHS), p : pressure, t : temperature)H 1: Differential height of the reference levels between the participating institute’s standard (100 MPa - 500 MPa) and the transfer standard

(Positive: if the level of the institute’s standard is higher).H 2: Differential height of the reference levels between the participating institute’s standard (600 MPa - 1000 MPa) and the transfer standard

(Positive: if the level of the institute’s standard is higher).H 0: Differential height between the reference level of the transfer standard and one end of vent valve (Positive: if the level of vent valve is higher).

Tungsten carbide / Tungsten carbide with a sleeve of steel

Tungsten carbide4.5 × 10-6

Tungsten carbide

10 rpm (by motor)

DescriptionNagano-Keiki (Modified)

Nagano-Keiki1 × 10-6

Nagano-Keiki 100 MPa

4.5 × 10-6

10 rpm (by hand)

Description

4.5 × 10-6

10 rpm (by hand)

Steel10.5 × 10-6

Tungsten carbide

DH 1 GPa multiplierTungsten carbide / Tungsten carbide

NMIJ/AISTJapan

Description

DH1 × 10-6

DH 5300

Simple type pressure balance and 1 GPa multiplierDescriptionDH 5316-02


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2.2.2 Description of the PTB pressure standard The pressure standard used in the comparison was the 1 GPa pressure balance11 equipped with a 1 GPa piston-cylinder assembly identified by no. 7594. In the pressure balance, Di(2)-ethyl-Hexyl-Sebacate (DHS) is used as a pressure-transmitting medium. The zero-pressure effective area (A0) of this assembly is traceable through a calibration chain to the three primary 5 cm2 10 MPa piston-cylinder units12. The value of the distortion coefficient (λ) with associated uncertainty was determined by FEA13,14 and an experimental method15. Details of the participating laboratory standard are given in Table 2.3. Table 2.3: Details of the pressure standard at PTB. All the uncertainties are expressed as standard uncertainties.

NMICountry

Pressure standardtype

Pressure balanceBase

WeightsRelative uncertainty of mass pieces

Piston-cylinderMaterial of piston

Linear thermal expansion coefficient of piston / ℃-1



A 0 / m2 4.902107× 10-6

at 20 ℃6.4× 10-11 1.3 × 10-5

λ / MPa-1 0.437 × 10-6 5.0 × 10-8 0.11Parameters used for the compariton Value ui relative ui

Local gravity / m/s2 9.812533 5.2 × 10-6 5.3 × 10-7

Density of medium ρ f / kg/ m3 Eq.(a) --- 1 × 10-2

Transfer Standard Value ui relative uiDifferential height of reference levels H / mm 313.0 1.0 ---Differential height of reference levels H 0 / mm 0.0 1.0 ---

Power supply 100VAC 50Hz --- ---

Eq(a): ρ f = [912.7 + 0.752 (p /MPa) - 1.645⋅10-3 (p /MPa)2 + 1.456⋅10-6 (p /MPa)3] × [1 - 7.8 × 10-4 (t/°C - 20)] kg/m3

(ρ f: density of Di(2)-ethyl-Hexyl-Sebacate (DHS), p : pressure, t : temperature)H : Differential height of the reference levels between the participating institute’s standard and the transfer standard

(Positive: if the level of the institute’s standard is higher).H 0: Differential height between the reference level of the transfer standard and one end of vent valve (Positive: if the level of vent valve is higher).

Controlled-clearance type pressure balanceDescription

Harwood 1.4 GPa (Modified)

PTBGermany

Description

4.5 × 10-6

6 rpm (by motor)

Tungsten carbide4.5 × 10-6

Tungsten carbide with a sleeve of steel

Harwood6 × 10-7

DH-Budenberg 1 GPa (Part of the 1 GPa multiplier)


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3. Transfer standard For this APMP 1000 MPa comparison, a transfer standard developed at

NMIJ/AIST was used. The transfer standard of this comparison included two 1 GPa foil strain gauge pressure transducers16, a measuring amplifier17, an electric device for measuring environmental conditions, a laptop computer and a program as described in the technical protocol of the comparison8,9. The details of the transfer standard are described below. 3.1 Pressure transducers and measuring amplifier Pressure transducers:

Two pressure transducers, which are listed in Table 3.1, were used on the transfer standard. The sensing element of the pressure transducers used is a foil strain gauge. The transducers used were specially developed by the manufacturer.

Table 3.1: Details of pressure transducer used. Type P3MB-TCJ

Manufacturer Hottinger Baldwin Messtechnik GmbH (HBM) Pressure type Absolute pressure

Principle of measurement Foil strain gauge Measuring range 1000 MPa

Nominal sensitivity 1 mV/V Dimensions Ø25 x 123 mm2 (without cable)

The serial number of each pressure transducer used is listed in Table 3.2.

Table 3.2: Serial numbers of pressure transducers.

Identification 1 2 Serial Number 091110318 091110317


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Measuring amplifier: The characteristics of the measuring amplifier used in this comparison are

listed in Table 3.3. The resolution of the measuring amplifier is 1 ppm of the full scale.

Table 3.3: Characteristics of measuring amplifier. Type DMP40S2

Manufacturer Hottinger Baldwin Messtechnik GmbH (HBM) Excitation voltage (used) 5.0 V Measuring range (used) 2.5 mV/V

Resolution (used) 10-6 mV/V (1 ppmFS) Signal type (used) Absolute

Dimensions 458 mm x 171 mm x 367 mm

To perform a reliable comparison, the effects on the readings of the transducers by setting parameter and environmental conditions were evaluated at the pilot institute before and during the comparison. The important characteristics for the transfer standard such as the temperature coefficient and the long-term stability of the span reading are evaluated quantitatively in section 6. Effect by power source In this comparison, both participating institutes used a power source with the voltage of 100 VAC and the frequency of 50 Hz using a power supply regulator. Therefore, the effect of the power source on the reading was considered to be negligible. Effect by attitude

In the protocol of this comparison, it was required that two transducers are set up in vertical position. Therefore, the effect of the attitude of pressure transducers on the reading was not included into the uncertainty estimation. Effect by transient response In the technical protocol8,9 of this comparison, it was required that all the calibrations should be performed in the time from fifteen minutes to twenty minutes after pressure change. The effect on the reading by the transient response of each pressure transducer was evaluated from our observation. The relative change in the reading of each pressure transducer between fifteen minutes to twenty minutes after applying pressure change at 1000 MPa was typically less than 10 × 10-6. The relative


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standard uncertainty of the effect was estimated as 10 × 10-6 / 2 3 = 2.9 × 10-6, which was sufficiently small compared with the target uncertainty of this comparison. In the case that the participants follow the procedure in the protocol, the effect on the reading by a transient response can be negligible. Therefore, the effect was not included into the uncertainty evaluation. 3.2 Structure of transfer standard For this APMP comparison, two pressure transducers were used in the transfer standard to ensure the reliability. The transfer standard consists of two pressure transducers, a measuring amplifier, a laptop computer, a device for measuring environmental conditions, a computer and connecting parts as shown in Figure 3.1.

PressureTransducer

2

Tee Tee

Connectingpipe

PressureTransducer

1

Transducer setup:Vertical

Measuringamplifier

LaptopComputer

Envi.Meas.Device

Connecting port

Participating Institute’sPressureStandard

Participating institute’s system

Vent valve V0 for

zero pressure

Transfer standard systemRef. Level of TS

Figure 3.1: Schematic drawing of transfer standard. It was required that two transducers are set up in vertical position. The

reference level of the transfer standard was represented by the vertical height of the connecting pipe.


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An electric device for measuring environmental conditions (Model TR-73U, T

& D corp.) was attached to the transfer standard to measure the environmental conditions during the comparison including the transportation. When it was used in measurement, the measured data was acquired by a computer and was used for data analysis. When it was transported, the measured data was recorded into the inside memory automatically. The data was extracted from the memory at the pilot institute. A laptop computer and the program developed were used for acquiring the measurement data, which were the readings of both pressure transducers and the environmental conditions.

Through a specified connecting port of the transfer standard, the transfer standard was connected to a participant’s pressure balance.

A vent valve, which was prepared by the participant, was used between the specified connecting port and the participant’s pressure balance as shown in Figure 3.1.

Figure 3.2 shows the photographs of the transfer standard used.

Figure 3.2: Photographs of transfer standard.

Measuring amplifier

Pressure transducers

Shock data logger

Envi. meas. device


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3.3 Transfer package The contents of the transfer package are listed in Tables 3.3 and 3.4. The two pressure transducers were carried by hand, and the measuring amplifier was sent. Figure 3.3 shows photographs of the transfer package for carrying the pressure transducers. An electric device for measuring environmental conditions (Model TR-73U, T & D corp.) and a shock data logger (Model IPK-01-4000-N, SANTEST CO., LTD.) were included in the box for measuring the conditions during transportation. A single metal box is used for transporting a measuring amplifier as shown in Figure 3.2.

Table 3.3: Contents of transfer package (Pressure transducers part).

Carrying box for pressure transducers part Transducers Two pressure transducers with connecting parts Shock data logger with connecting cable Envi. Meas. device with connecting cable Laptop computer with power cable

Table 3.4: Contents of transfer package (Measuring amplifier part). Carrying box for measuring amplifier part Amplifier with power cable Envi. Meas. device with connecting cable

Envi. Meas. Device Shock data logger

Figure 3.3: Photographs of transfer package (pressure transducers part) for APMP.M.P-S8.


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4. Circulation of the transfer standard According to the protocol8,9, the transfer standard was circulated during the

period January 2007 to March 2007 with calibrations at the pilot institute (NMIJ/AIST) at the start and end of the comparison. An ATA CARNET was prepared by the pilot institute to enable the circulation of the package. An inspection of the appearance and function of the devices was made when the package first arrived at and before the package departed from each participating institute. 4.1 Chronology of measurements

Table 4.1 presents the chronology of the measurements made with the transfer standard during the comparison loop. The arrival and departure dates, and dates during which calibration data was taken at each participating institute are listed. The total time required to complete the measurements phase of this comparison was about three months. There was no serious problem regarding the transportation during the course of the comparison.

Table 4.1: Chronology of measurements during supplementary comparison. Institute Country Arrival Departure Dates for calibrations

NMIJ/AIST Japan --- 2007/2/12 2007/1/30, 2/1, 2/2PTB Germany 2007/2/13 2007/2/21 2007/2/15, 2/16, 2/19

NMIJ/AIST Japan 2007/2/22 --- 2007/2/28, 3/1, 3/2 4.2 Environmental conditions of the transfer standard during transportation

As described in section 3, an electric device for measuring environmental conditions and a shock data logger were installed in the transfer package to monitor the environmental conditions during the transportation. Since the transfer package (pressure transducers) was carefully carried by hand, the environmental conditions including ambient temperature, relative humidity and atmospheric pressure could be kept in the appropriate range.

The acceleration measured in the transfer standard during the transportation is shown in Figure 4.1. The maximum value measured was approximately 50 m/s2, which was sufficiently small compared with the manufacturer’s specification. Therefore, it can be stated that the transfer standard did not suffer any serious shock during the whole comparison.


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0

10

20

30

40

50

2007/02/07 2007/02/12 2007/02/17 2007/02/22 2007/02/27

Acc

eral

atio

n / m

/s2

Date

Figure 4.1: Acceleration measured in the transfer package (pressure transducers part) during the transportation.


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5. Calibration The general procedure for this comparison is described in the protocol8,9. 5.1 Preparation It was agreed to use clean Di(2)-ethyl-Hexyl-Sebacate (DHS) as a working fluid. The pressure standard of each participating institute was operated at the normal operating temperature of the institute. The environmental conditions for calculating the pressure applied were measured using participant’s own devices.

For the preparation of the calibration, the followings were recommended: (i) at latest, twelve hours before starting the measurement procedure, the measuring amplifier was to be connected to a power supply and be turned on for warming up and stabilization. (ii) The power supply for the transfer standard was to be maintained during all the calibrations at the participating institute. (iii) Setting parameters of the measuring amplifier were to be set as listed in the protocol8. (iv) After the installation, the transfer standard system was to be pressurized using the system of each participant up to 1000 MPa and the function of each pressure transducer and the leak in the test system were to be checked. (v) During twelve hours before the start of each calibration cycle, no gauge pressure was to be applied to both pressure transducers. 5.2 Head correction by height difference

The pressure generated by a pressure standard at the reference level of the transfer standard, P, is represented by the following equation:

P = Pstd + (ρf − ρa)·gl·H (5.1)

where, Pstd is the pressure generated by the participant’s pressure standard at its reference level; (ρf − ρa)·g·H is the head correction, with ρf the density of the working fluid, ρa the air density, gl the local acceleration due to gravity, and H the vertical distance between the reference levels of the two intercompared standards (institute standard and transfer standard). H is positive if the level of the institute’s standard is higher. Each participant had to make appropriate corrections for the height difference between the reference levels and to include their contributions into the uncertainty of the applied pressure.


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5.3 Calibration procedure At nominal target pressures of 100 MPa, 200 MPa, 300 MPa, 400 MPa, 500

MPa, 600 MPa, 700 MPa, 800 MPa, 900 MPa, and 1000 MPa, the applied pressures were measured and the readings of the pressure transducers were recorded. The values, together with the respective measurement uncertainties, were the main basis of the comparison.

5.3.1 Complete measurement cycle One complete measurement cycle consisted of pressure and environmental records for the transfer standard and the pressure standard at twenty-two pressure points of eleven pressure points from 0 MPa to 1000 MPa in steps of 100 MPa in ascending order and eleven points from 1000 MPa to 0 MPa in steps of 100 MPa in descending order as shown in Figure 5.1. The results of the measurements were recorded on the measurement results sheet prepared in the appendix9. One complete measurement cycle was performed during one day. A total of three calibration cycles was required, with each cycle being on a separate day.

Pressure

Time

0 MPa

1000 MPa

Figure 5.1: One complete measurement cycle.


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5.3.2 Measurement at 0 MPa At the beginning and the end of each cycle, zero-pressure readings for the pressure transducers were recorded. These data were used to correct calibration data for zero-pressure offsets. To apply zero gauge pressure to the pressure transducers, the vent valve V0 was opened (See Figure 3.1). After the waiting of fifteen minutes, within five minutes, the readings of both pressure transducers and the environmental conditions, which are the resulting averages for the 12 measurements (Interval: 10 sec.) and their corresponding standard deviations were measured using the measurement software developed for this comparison. Those data were recorded in the cells of the forms annexed to the protocol8,9. 5.3.3 Calibration at (100, 200, 300, 400, 500, 600, 700, 800, 900 and 1000) MPa The pressure generated by the participant’s standard was applied to the transfer standard after closing valve V0. The position of the piston of the pressure balance was kept in the floating range to maintain the pressure using the device such as a hand pump. It was required that the difference between the actual pressure realized at the transfer standard by the participant’s pressure standard and the target pressure should be within a thousandth of the target pressure. After the waiting of fifteen minutes, within five minutes, the readings of both pressure transducers and the environmental conditions, which are the resulting averages for the 12 measurements (Interval: 10 sec.) and their corresponding standard deviations were measured using the measurement software developed for this comparison. Then, the applied pressure with the associated standard uncertainty at the reference level of the transfer standard was calculated. Any influence quantity for the institute system was taken into account in the uncertainty estimation appropriately by each participant. The correction by the height difference between the reference levels of the participating institute’s standard and the transfer standard was considered. These data were recorded in the cells of the forms annexed to the protocol8,9 as presented in Table 5.1. In the table, P is the pressure applied by the participant’s standard at the local gravity gl and the local air density ρa and calculated at the reference level of the transfer standard using equation (5.1), and u(P) is the standard uncertainty of P.


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Table 5.1: Example of data recording at target pressure. Nom.

Pres.

[MPa]

Local

Time

Atmo

Temp.

[C]

Atmo

R.H.

[%]

Atmo

Pres.

[kPa]

Reading

R_a [MPa]

Reading

R_b [MPa]

Applied

Pressure

P [MPa]

u(P)

[MPa]

(k=1) Average σ Average σ

0 8:30 23.0 50.0 101.2

……

1000 12:00 23.0 50.0 101.2

1000 13:00 23.0 50.0 101.2

……

0 16:30 23.0 50.0 101.2

5.3.4 Results to be reported After the measurements were completed at the participating institute, the calibration results were transmitted to the pilot institute. The pilot institute, NMIJ/AIST, collected the following data and information using the sheets annexed to the protocol8,9.

(i) Measured and calculated values at the nominal pressures specified, each with an uncertainty in the measurement and the date(s) on which calibration cycle was undertaken [three cycles].

(ii) Details of the participating institute’s standard(s) against which the transfer standard was calibrated and the parameters used for the comparison, which were local gravity, height difference between the reference levels of the participating institute’s standard and the transfer standard, density of working fluid, the voltage and frequency applied to the transfer standard (presented in Tables 2.2 and 2.3).

(iii) Uncertainty budget for the pressure generated, which was to be estimated and combined following GUM6 under the responsibility of the participating institute. The uncertainties were evaluated at a level of one standard uncertainty at the participating institute.

Also, an uncertainty estimation for each pressure transducer calibrated was to be reported optionally.


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6. Analysis of reported data Data obtained from one complete measurement cycle consist of the records of the pressure and temperature obtained from the transfer standard, the pressure applied by the pressure standard and environmental parameters at twenty-two pressure points of eleven pressure points from 0 MPa to 1000 MPa in steps of 100 MPa in ascending sequence, one point 0 MPa, and eleven points from 1000 MPa to 0 MPa in steps of 100 MPa in descending sequence. Therefore, the following data sets were obtained from the reported results.

( ) ( ) ( ){ }iwyjtiwyjPiwymjR b ,,,,,,,,,,,, where the meanings of the parameters are as follows:

R [mV/V]: Raw reading of pressure transducer, P [MPa]: Applied pressure at the reference level of the transfer standard by

pressure standard j, tb [C]: Temperature measured around the transfer standard, j : Index for participating institute, m : Index for pressure transducer a or b, m = 1 or 2, y : Index for measurement cycle, w : Index for indicating ascending or descending measurements, w = 1 or 2, i : Index for indicating pressure, i × 100 MPa, i = 0 – 10,

In this section, the reduction and analysis of the data are performed by the following procedure: 6.1 Correction for zero-pressure offsets, 6.2 Correction for difference between nominal pressure and actual pressure, 6.3 Correction to reference temperature, 6.4 Correction for long-term shift in characteristics of transducer, 6.5 Calculation of normalized mean ratio of participating institute, 6.6 Calculation of expected mean pressure of participating institute, 6.7 Estimation of uncertainties.


19

6.1 Correction for zero-pressure offsets There were two 0 MPa pressure points in one measurement cycle. The readings

for ascending and descending pressure points of each cycle are offset by the readings at first and last 0 MPa points of each cycle, respectively. By subtracting the offset from the raw reading R, the corrected reading Rc0 is obtained as follows:

( ) ( ) ( )0,,,,,,,,,,,,0 wymjRiwymjRiwymjRc −= (6.1)

6.2 Correction for difference between nominal pressure and actual pressure

Rc0 is the reading of pressure transducer when the actual pressure realized at the transfer standard by the participant’s pressure standard, P, is applied. Since the readings of pressure transducers are nearly linear, the ratios of the readings of the pressure transducers to the actual pressures are practically independent of pressure within the small pressure ranges corresponding to the allowed deviations of the actual pressures from the nominal target pressures. As described in the protocol8, the difference between actual pressure applied and the nominal target pressure was adjusted to be within a thousandth of the nominal pressure. The ratios can be used to correct the readings for deviations of the pressure standard from the nominal pressure. When an exact nominal pressure Pn is applied to the pressure transducer, the predicted reading, Rc1, is calculated by

( ) ( )( ) ( )iP

iwyjPiwymjRiwymjR n

cc ⋅=

,,,,,,,,,,, 0

1 ,

(6.2) where Rc0 and P are the simultaneous readings of pressure transducer and the actual pressure applied, respectively.


20

6.3 Correction to reference temperature Rc1 is the reading of each pressure transducer when the surrounding temperature is tb. Since the reading is affected by the temperature, the reading should be corrected. During the comparison, the effect of the temperature on the reading was evaluated by the pilot institute. Here, the temperature coefficient of each pressure transducer at each target nominal pressure, β(m,i) [C-1], is calculated by the following equation from the calibration data obtained at the pilot institute j = 1:

( ) ( ) ( )( ) ( ) ( )[ ]∑∑∑

= = = −⋅

−⋅=

3

1

2

1

3

10

011

,,,1,,,1,,,,1,,,,1

181,

q w y bqbn

cqc

iwytiwytiPiwymRiwymR

imβ

(6.3)

where qbt is the measured temperature on the transfer standard obtained from the

calibration results performed at around 23 C for q = 0, 20 C for q = 1, 21 C for q = 2 and 22 C for q = 3, respectively, and q

cR 1 is the corresponding reading of each pressure transducer. Table 6.1 and Figure 6.1 present the calculated temperature coefficients of each pressure transducer for nominal target pressures. From the results, the average values are calculated for each pressure transducer as follows:

( ) ( )∑=

⋅=10

1

,101

i

imm ββ

(6.4) In the following analysis, the temperature coefficient obtained from equation (6.4) is used. It has been confirmed that the reading of pressure transducer can be corrected appropriately using the temperature coefficient. The standard uncertainty of the coefficient was estimated as ( ){ } 310=mu β ×

10-6 C-1.


21

Table 6.1: Temperature coefficients of each pressure transducer.

i MPa

1 100 19.6 34.72 200 26.2 20.43 300 25.7 26.74 400 27.0 24.75 500 21.7 20.66 600 21.9 28.27 700 20.5 25.88 800 23.5 26.29 900 24.2 28.210 1000 32.1 35.1

24.2 27.1

Temperature coefficient, β / 10-6 C-1

m1 2

Average

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000

Tem

pera

ture

coe

ficie

nt /

10-6

C-1

Pressure / MPa

m = 1

m = 2

Figure 6.1: Calculated temperature coefficients of each pressure transducer as a function of nominal target pressure.


22

Using the temperature coefficient calculated by equation (6.3), the mean reading corrected to a reference temperature, Rc2, can be calculated by taking the average for ascending and descending pressures of three cycles as follows:

( ) ( ) ( ) ( )[ ]{ }∑∑= =

−⋅+⋅⋅=2

1

3

112 ,,,1,,,,

61,,

w yrbcc tiwyjtmiwymjRimjR β .

(6.5) where rt is the reference temperature which is determined as stated in the followings. The average temperature of the transfer standard measured by the electric device for measuring environmental conditions at each nominal target pressure for the participating institutes, ( )ijtb , , is calculated from

( ) ( )∑∑= =

⋅=2

1

3

1

,,,61,

w ybb iwyjtijt

(6.6) For the pilot institute, j = 1, the average temperature is calculated from

( ) ( )∑∑∑= = =

⋅=2

1

2

1

3

1,,,1

121,1

l w y

lbb iwytit

(6.7) where l

bt is the temperature on the transfer standard obtained from l-th calibration data set (two data sets in total) performed at the pilot institute. Table 6.2 and Figure 6.2 present the average temperatures calculated from equations (6.6) and (6.7). Since the reference temperature was not described in the protocol8, it was chosen to be fair for both participants. The average of all the values in Table 6.2 is 21.78 C. Therefore, by rounding the value up slightly, the reference temperature of this comparison was

determined as rt = 21.8 C so that the maximum temperature deviation of the

participating institutes from the reference temperature was minimized. Since calibrations were performed at different temperatures, the uncertainty due to the deviation from the reference temperature is included as described in later subsection.


23

Table 6.2: Average temperatures measured around the transfer standard at the participating institutes for nominal target pressures.

1 2i MPa NMIJ/AIST PTB

0 0 23.20 20.37

1 100 23.18 20.42

2 200 23.18 20.43

3 300 23.13 20.48

4 400 23.07 20.47

5 500 23.08 20.47

6 600 23.08 20.47

7 700 23.08 20.47

8 800 23.10 20.43

9 900 23.12 20.4210 1000 23.17 20.42

23.13 20.44

Average temperature / C

Average

j

19

20

21

22

23

24

25

0 200 400 600 800 1000

Ave

rage

tem

pera

ture

/

C

Pressure / MPa

1

2

Figure 6.2: Average temperatures measured around the transfer standard at the participating institutes as a function of nominal target pressure.


24

6.4 Correction for long-term shift in characteristics of transducer At the pilot institute, one calibration set from three cycle measurements were performed two times. The relative difference obtained from two calibration results,

2cdR , is calculated from

( ) ( ) ( )( )∑

=

⋅

−= 2

12

12

22

2

,,121

,,1,,1,,1

l

lc

ccc

imR

imRimRimdR .

(6.8)

where lcR 2 is the mean reading corrected to a reference temperature obtained from l-th

calibration data set (two data sets in total) performed at the pilot institute. Table 6.3 and Figure 6.3 present the relative difference between two calibration results calculated by equation (6.8).

Table 6.3: Relative difference of lcR 2 measured at the pilot institute, 2cdR .

i MPa

1 100 17.1 19.1

2 200 16.3 25.2

3 300 -12.0 19.1

4 400 9.9 26.6

5 500 2.9 29.0

6 600 -3.7 26.5

7 700 1.5 34.7

8 800 -1.2 39.1

9 900 -0.4 37.9

10 1000 14.1 49.5

mRelative difference dR c2(1,m ,i ) / 10-6

21


25

-60

-40

-20

0

20

40

60

0 200 400 600 800 1000

Rel

ativ

e dev

iatio

n d

R c2

/ 10

-6

Pressure / MPa

1

2

Figure 6.3: Relative difference of lcR 2 measured at the pilot institute, 2cdR , as a

function of nominal target pressure.

As shown in Table 6.3 and Figure 6.3, the relative difference for pressure transducer m=1 is less than 18×10-6 in the pressure ranges between 100 MPa and 1000 MPa, and that for pressure transducer m=2 is less than 40×10-6 in the pressure ranges between 100 MPa and 900 MPa and 50×10-6 at maximum at 1000 MPa. The relative differences obtained are taken into consideration to calculate the uncertainty of the comparison results.

It has been confirmed that the shifts were due to the characteristics of the transducers and were not due to the pressure standards of the pilot institute. The stability of the pressure standard of the pilot institute had been checked by cross-float comparison against other standard pressure balances during this comparison and it was confirmed that there was no systematic shift in the primary pressure standard.

In the following analysis, the average reading corrected to a reference temperature for the pilot institute, Rc2, is calculated by averaging the two results of Rc2 obtained at the pilot institute using equation (6.9).


26

( ) ( )∑=

⋅=2

122 ,,1

21,,1

l

lcc imRimR

(6.9) 6.5 Calculation of normalized mean ratio of participating institutes By taking the ratio of Rc2 at j-th participating institute to the mean Rc2 obtained from both participating institutes, the normalized mean ratio for each calibration point, s0, is calculated as

( ) ( )( )∑

=

⋅= 2

12

20

,,21

,,,,

jc

c

imjR

imjRimjs

(6.10) There were two pressure transducers on the transfer standard. By taking the average of s0 for the two pressure transducers, the normalized mean ratio, S, is calculated as

( ) ( )∑=

⋅=2

10 ,,

21,

m

imjsijS

(6.11)

Ratio S provides a common basis for comparing the results reported by participants.

The normalized mean ratios, ( )imjs ,,0 and ( )ijS , , were obtained using

equations (6.10) and (6.11). Table 6.4 and Figure 6.4 present the deviations from the normalized mean ratios of the institutes from unity, ( ) 1, −ijS , as a function of nominal target pressure.


27

Table 6.4: Deviations of the normalized mean ratios, ( )imjs ,,0 and ( )ijS , , from unity

for nominal target pressures.

s 0 s 0 s 0 s 0 S S1 1 2 2 Average Average1 2 1 2 1 2

i MPa NMIJ/AIST PTB NMIJ/AIST PTB NMIJ/AIST PTB

1 100 23.2 -23.2 4.8 -4.8 14.0 -14.0

2 200 7.5 -7.5 -6.7 6.7 0.4 -0.4

3 300 6.0 -6.0 0.0 0.0 3.0 -3.0

4 400 7.0 -7.0 -1.2 1.2 2.9 -2.9

5 500 5.1 -5.1 -1.6 1.6 1.7 -1.7

6 600 6.4 -6.4 0.9 -0.9 3.7 -3.7

7 700 6.0 -6.0 -4.4 4.4 0.8 -0.8

8 800 -9.0 9.0 -19.5 19.5 -14.2 14.2

9 900 -10.4 10.4 -21.1 21.1 -15.7 15.7

10 1000 -5.0 5.0 -15.8 15.8 -10.4 10.4

Deviation of normalized mean ratio from unity / 10-6

jm

s 0 or S

-60

-40

-20

0

20

40

60

0 200 400 600 800 1000

Dev

iatio

n fr

om u

nity

/ 1

0-6

Pressure / MPa

NMIJ m=1

PTB m=1

NMIJ m=2

PTB m=2

NMIJ Aver.

PTB Aver.

Figure 6.4: Deviations of the normalized mean ratios of the institutes from unity as a function of nominal target pressure.


28

6.6 Calculation of expected mean pressure of participating institute Expected mean pressure of participating institute, ( )ijp , , is calculated by

( ) ( ) ( )iPijSijp n⋅= ,, . (6.12)

where ( )iPn is the nominal target pressure. ( )ijp , is taken as an indicator of the expected pressure actually generated by the pressure standard of the participating institute when the institute claims the nominal target pressure. The results for ( )ijp , from individual institutes are presented in Table 6.5.

Table 6.5: Expected mean pressures of the institutes for nominal target pressures.


1 100 100.0014 99.9986

2 200 200.0001 199.9999

3 300 300.0009 299.9991

4 400 400.0012 399.9988

5 500 500.0009 499.9991

6 600 600.0022 599.9978

7 700 700.0006 699.9994

8 800 799.9886 800.0114

9 900 899.9858 900.0142

10 1000 999.9896 1000.0104

jMean pressure, p (j ,i ) / MPa


29

6.7 Estimation of uncertainties In this subsection, all the uncertainties are expressed as the standard ones. The relative combined standard uncertainty in the normalized mean ratio of j-th participating institute, S(j,i), may be estimated from the root-sum-square of four component uncertainties.

( ){ } ( ){ } ( ){ } ( ){ } ( ){ }ijSuijSuijSuijSuijSu ltsrdmtemstdc ,,,,, 2222 +++=

(6.13) where ustd{S} is the uncertainty in S due to systematic effects in pressure standard j, utem{S} is the uncertainty in correcting the readings to equivalent values at the reference temperature, urdm{S} is the uncertainty due to combined effect of short-term random errors of transfer standard used and pressure standard j during calibration and ults{S} is the uncertainty arising from long-term shift in the characteristics of the transducers on the transfer standard. 6.7.1 Uncertainty due to systematic effect in pressure standard The relative standard uncertainty due to systematic effect in pressure standard j,

( ){ }ijSu std , , can be estimated from

( ){ } ( ){ }( )iP

ijPuijSu

n

stdstd

,, =

(6.14) where ( )iPn is the nominal target pressure. Table 6.6 and Figure 6.5 present the estimated relative standard uncertainties arising from systematic effects in the pressure standards used in the comparison, as reported by the participating institutes for nominal target pressures. The uncertainty due to the hydrostatic head correction was considered as included in the uncertainty of the pressure standard. The main contributions in this uncertainty came from the effective area and the pressure distortion coefficient of the pressure standard of the participating institute.


30

Table 6.6: Relative standard uncertainties, as claimed by the participants, due to systematic effects in their pressure standards. All the uncertainties are expressed as the standard ones.


1 100 19.8 14.0

2 200 26.6 16.5

3 300 35.4 20.0

4 400 44.9 24.0

5 500 54.8 28.2

6 600 73.6 32.7

7 700 83.1 37.3

8 800 93.1 42.1

9 900 103.4 46.8

10 1000 113.9 51.6

ju std {S (j ,i )} / 10-6

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000

Rel

ativ

e sta

ndar

d un

certa

inty

/ 1

0-6

Pressure / MPa

NMIJ/AIST

PTB

Figure 6.5: Relative standard uncertainties, as claimed by the participants, due to systematic effects in their pressure standards as a function of nominal target pressure.


31

6.7.2 Uncertainty due to deviation from reference temperature The uncertainty in correcting the reading at the temperature realized at j-th participating institute to equivalent value at the reference temperature, u{Stem}, can be estimated from

( ){ } ( ){ }( ) ( ) rb

ntem tijt

iPiuijSu −⋅= ,, β

(6.15) where ( ){ }iu β is the calculated standard uncertainty in the temperature coefficient, which was estimated as ( ){ } 310=iu β × 10-6 C-1 in the former subsection. ( )ijtb , is the average temperature measured on the transfer standard by the participating institutes for nominal target pressures calculated from equations (6.6) or (6.7), rt is the reference temperature of this comparison determined as rt = 21.8 C. The uncertainty in ( )ijtb , may also contribute an uncertainty to u{Stem}. However this systematic contribution was much smaller than the uncertainty evaluated by equation (6.15), and therefore it was not included. Table 6.7 and Figure 6.6 present the estimated standard uncertainties, u{Stem}, calculated from equation (6.15).


32

Table 6.7: Standard uncertainties in correcting the readings to equivalent values at the reference temperature. All the uncertainties are expressed as the standard ones.

j 1 2i MPa NMIJ/AIST PTB

1 100 8.1 8.3

2 200 8.0 8.0

3 300 8.0 7.9

4 400 7.7 7.6

5 500 7.4 7.7

6 600 7.4 7.7

7 700 7.4 7.7

8 800 7.4 7.7

9 900 7.5 7.9

10 1000 7.6 8.0

u tem {S (j ,i )} / 10-6

0

1

2

3

4

5

6

7

8

9

10

0 200 400 600 800 1000

Rel

. unc

er. b

y de

vi. f

rom

ref

. tem

per.

/ 1

0-6

Pressure / MPa

NMIJ/AIST

PTB

Figure 6.6: Standard uncertainties in correcting the readings to equivalent values at the reference temperature as a function of nominal target pressure.


33

6.7.3 Uncertainty due to combined effect of short-term random errors The standard uncertainty in S due to combined effect of short-term random errors of the transfer standard calibrated, u{Srdm}, can be estimated from the corresponding uncertainties in the normalized mean ratios by statistical methods. For j-th non-pilot participating institute, the uncertainty is obtained from

( ){ } ( ){ }[ ]∑∑= =

⋅=2

1

2

10

22 3/,,,41,

m wrdm iwmjsijSu σ

(6.16) where ( ){ }iwmjs ,,,0σ is the standard deviation of three values (y = 1 – 3) of

( )iwymjs ,,,,0 about its mean. For the pilot institute j = 1, the uncertainty is calculated from

( ){ } ( ){ }[ ]∑∑∑= = =

⋅=2

1

2

1

2

10

22 3/,,,181,1

l m w

lrdm iwmsiSu σ

(6.17)

where ( )iwymsl ,,,,10 is the normalized mean ratio obtained from l-th simultaneous

calibration set (two sets in total) performed at the pilot institute, ( ){ }iwms l ,,,10σ is the

standard deviation of three values (y = 1 – 3) of ( )iwymsl ,,,,10 about its mean. The

multiple calibrations at the pilot institute tend to reduce the influence of uncorrelated uncertainties arising from short-term variability for the pilot institute18. Table 6.8 and Figure 6.7 present the estimated standard uncertainties due to combined effect of short-term random errors calculated from equations (6.16) and (6.17).


34

Table 6.8: Standard uncertainties in the normalized mean ratios due to combined effects of short-term random errors. All the uncertainties are expressed as the standard ones.


1 100 16.2 12.3

2 200 8.2 8.2

3 300 5.5 3.8

4 400 3.5 3.8

5 500 4.2 3.2

6 600 3.8 4.1

7 700 4.0 4.1

8 800 2.4 6.5

9 900 4.9 3.0

10 1000 6.8 11.8

ju rdm {S (j ,i )} / 10-6

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

Stan

dard

unc

erta

inty

/ 1

0-6

Pressure / MPa

NMIJ/AIST

PTB

Figure 6.7: Standard uncertainties in the normalized mean ratios due to short-term random errors as a function of nominal target pressure.


35

6.7.4 Uncertainty arising from the long-term shift The long-term shift of a pressure transducer between calibrations should be considered in the uncertainties. The standard uncertainty in the normalized mean ratio of j-th participating institute due to long-term shift, ( ){ }ijSults , , was estimated as follows:

( ){ } ( )[ ]∑=

⋅=2

1

22

2 ,,121,

mclts imdRuijSu

(6.18) where ( )[ ]imdRu c ,,12 is the standard uncertainty arising from the instability of each pressure transducer and is evaluated using equation (6.19).

( )[ ] ( )3

,,1,,1 2

2

imdRimdRu c

c =

(6.19) where ( )imdRc ,,12 is the relative difference obtained from equation (6.8). Table 6.9 and Figure 6.8 present the estimated standard uncertainties due to the long-term shift in characteristics of pressure transducers calculated from equation (6.18).


36

Table 6.9: Standard uncertainties in the normalized mean ratios due to long-term shift in characteristics of pressure transducers. All the uncertainties are expressed as the standard ones.

u lts {S (j ,i )} / 10-6

i MPa u {dR c2}(m = 1) u {dR c2}(m = 2) u lts

1 100 9.9 11.0 10.5

2 200 9.4 14.5 12.2

3 300 6.9 11.0 9.2

4 400 5.7 15.4 11.6

5 500 1.7 16.8 11.9

6 600 2.1 15.3 10.9

7 700 0.9 20.0 14.2

8 800 0.7 22.6 16.0

9 900 0.2 21.9 15.5

10 1000 8.1 28.6 21.0

u {dR c2 (1,m ,i )} / 10-6

0

5

10

15

20

25

30

0 200 400 600 800 1000

Stan

dard

unc

erta

inty

/ 1

0-6

Pressure / MPa

u{dRc2}(m = 1)

u{dRc2}(m = 2)

ults

Figure 6.8: Standard uncertainties in the normalized mean ratios due to the long-term shift in characteristics of pressure transducers as a function of nominal target pressure.


37

6.7.5 Combined uncertainty in normalized mean ratio of institute The combined standard uncertainty in the normalized mean ratio of the institute is estimated by combining the component uncertainties using the “root-sum-squares” method according to equation (6.13) and is presented in Table 6.10 and Figure 6.9. Table 6.10: Combined standard uncertainties in normalized mean ratios of institutes, uc{S}. All the uncertainties are expressed as the standard ones.


1 100 28.8 22.9

2 200 31.4 23.5

3 300 37.8 23.7

4 400 47.1 28.0

5 500 56.7 31.7

6 600 74.9 35.5

7 700 84.8 40.8

8 800 94.8 46.2

9 900 105.0 50.0

10 1000 116.3 57.5

jCombined standard uncertainty, u c{S (j ,i )} / 10-6

0

20

40

60

80

100

120

140

0 200 400 600 800 1000

Com

bine

d st

anda

rd u

ncer

tain

ty /

10-6

Pressure / MPa

NMIJ/AIST

PTB

Figure 6.9: Combined standard uncertainties in normalized mean ratios of institutes as a function of nominal target pressure.


38

6.7.6 Combined uncertainty in expected mean pressure of institute The combined standard uncertainty of the expected mean pressure of participating institute, ( ){ }ijpuc , , is calculated from ( ){ }ijSuc , by

( ){ } ( ){ } ( )iPijSuijpu ncc ⋅= ,, . (6.20)

where ( )iPn is the nominal target pressure. ( ){ }ijpuc , is presented in Table 6.11 and Figure 6.10. Table 6.11: Combined standard uncertainties in expected mean pressures of institutes, uc{p}. All the uncertainties are expressed as the standard ones.


1 100 2.88 2.29

2 200 6.29 4.713 300 11.34 7.11

4 400 18.85 11.19

5 500 28.3 15.866 600 44.9 21.3

7 700 59.3 28.68 800 75.9 36.9

9 900 94.5 45.0

10 1000 116.3 57.5

jCombined standard uncertainty, u c {p (j ,i )} / kPa

0

20

40

60

80

100

120

140

0 200 400 600 800 1000

Com

bine

d st

anda

rd u

ncer

tain

ty /

kPa

Pressure / MPa

NMIJ/AIST

PTB

Figure 6.10: Combined standard uncertainties in expected mean pressures of institutes as a function of nominal target pressure.


39

7. Results for supplementary comparison APMP.M.P-S8 The results for supplementary comparison APMP.M.P-S8 are analyzed in this section independently and are processed by the following procedure:

7.1 Calculation of APMP Supplementary Comparison Reference Values (APMP SCRVs), 7.2 Evaluation of degrees of equivalence.

7.1 Calculation of APMP Supplementary Comparison Reference Values The comparison reference value is interpreted as an estimate of the measurand on the basis of the measurements provided by the participating institutes. In the guidelines4, it is described that “In calculating the comparison reference value, the pilot institute will use the method considered most appropriate for the particular comparison.” Several methods for defining a comparison reference value have been proposed19. The typical methods are (i) the unweighted mean method, (ii) the weighted mean method and (iii) the median method. Each method has some advantages and disadvantages. For this APMP comparison, an unweighted mean method was selected as a reasonable procedure to obtain reference values for this supplementary comparison. The unweighted mean value of the expected mean pressures obtained from all participating institutes is calculated at the nominal target pressure as the APMP SCRV for this supplementary comparison, p(SCRV, i), using similar ways as given in the key comparisons CCM.P-K418 and APMP.M.P-K520. This means that the SCRV is numerically equal to the target pressure by the following equation:

( ) ( )iPiSCRVp n=, (7.1)

The combined uncertainty in p(SCRV, i) can be estimated from20:

( ){ } ( ){ }∑=

≅2

12

22

2,,

j

c ijpuiSCRVpu

(7.2) where ( ){ }iSCRVpu , is the standard uncertainty of ( )iSCRVp , . Table 7.1 presents the APMP SCRVs and their combined standard uncertainties calculated for the expected mean pressures.


40

Table 7.1: APMP Supplementary comparison reference values and their combined standard uncertainties calculated for the expected mean pressures. All the uncertainties are expressed as the standard ones.

Nom. Tar. Pressure p (KCRV ,i ) u {p (KCRV ,i )}/ MPa / MPa / kPa

1 100 100.00000 1.842 200 200.0000 3.93 300 300.0000 6.74 400 400.0000 11.05 500 500.0000 16.26 600 600.000 257 700 700.000 338 800 800.000 429 900 900.000 52

10 1000 1000.000 65

i


41

7.2 Evaluation of degrees of equivalence In the MRA, the term “degree of equivalence of the measurement standards” is taken to mean the degree to which a standard is consistent with a key comparison reference value or with a measurement standard at another institute3. Therefore, the degrees of equivalence of the pressure standards for this comparison are expressed using the expected mean pressures quantitatively in two ways: (1) Deviations of participating institute’s values from APMP SCRVs, (2) Differences between deviations for pairs of participating institutes. 7.2.1 Deviation of institute’s value from APMP SCRV By comparing the expected mean pressure of j-th participating institute relative to a SCRV, the relative deviation from the reference value, ( )ij,Δ , is calculated by the following equation:

( ) ( ) ( )( )iSCRVp

iSCRVpijpij,

,,, −=Δ

(7.2) For this APMP comparison, the number of participants is two and ( )iSCRVp , is obtained from the average of the ( )ijp ,

( ) ( ) ( )( )iSCRVp

ipipi,2,2,1,1

⋅−

=Δ , ( ) ( ) ( )( )iSCRVp

ipipi,2,1,2,2

⋅−

=Δ

(7.2) and the relative expanded uncertainty of ( )ij,Δ , ( ){ }ijU ,Δ , is estimated from

( ){ } ( ){ }

( ){ }

( )( ){ }

( )iSCRVpiSCRVpu

iSCRVp

ijpu

kijukijU j

c

c ,,

,2

,

,,

2

12

2

=⋅=Δ⋅=Δ∑

=

(7.3) where ( ){ }ijuc ,Δ is the combined standard uncertainty of the relative deviation, k is the coverage factor and k = 2 is adopted, ( ){ }ijpuc , and ( ){ }iSCRVpu , are the combined uncertainties in the expected mean pressure of the institute and the reference value. Table 7.2 presents the relative deviations from reference values, ( )ij,Δ , the expanded (k = 2) uncertainties of the relative deviations, ( ){ }ijU ,Δ , and the degrees of


42

equivalence expressed by the ratios, ( ) ( ){ }ijUij ,, ΔΔ , for individual NMIs. Figure 7.1 presents ( )ij,Δ with ( ){ }ijU ,Δ graphically for the participating institutes as a function of nominal target pressure. Figure 7.2 provides a measure of the degree of equivalence by the relative magnitude of the deviation, ( ) ( ){ }ijUij ,, ΔΔ . For the present comparison, the condition ( ) ( ){ } 1,, ≤ΔΔ ijUij was established for both participating institutes at all target pressures. Table 7.2: Deviations from the APMP SCRVs, ( )ij,Δ , the expanded (k = 2) uncertainties of the deviations, ( ){ }ijU ,Δ and the degrees of equivalence as expressed by the ratios, ( ) ( ){ }ijUij ,, ΔΔ .

Pressure Δ (j,i ) U {Δ (j,i )}

/ MPa / 10-6 / 10-6

100 14 37 0.38200 0 39 0.01300 3 45 0.07400 3 55 0.05500 2 65 0.03600 4 83 0.04700 1 94 0.01800 -14 105 -0.13900 -16 116 -0.14

1000 -10 130 -0.08100 -14 37 -0.38200 0 39 -0.01300 -3 45 -0.07400 -3 55 -0.05500 -2 65 -0.03600 -4 83 -0.04700 -1 94 -0.01800 14 105 0.13900 16 116 0.14

1000 10 130 0.08

PTB

NMI Δ / U {Δ }

NMIJ/AIST


43

-200

-150

-100

-50

0

50

100

150

200

0 200 400 600 800 1000

Δ(j,

i) /

10-6

Pressure / MPa

-200

-150

-100

-50

0

50

100

150

200

0 200 400 600 800 1000

Δ(j,

i) /

10-6

Pressure / MPa

Figure 7.1: Deviations from the APMP SCRVs, ( )ij,Δ , and the expanded uncertainties of ( )ij,Δ , ( ){ }ijU ,Δ . The points show deviations ( )ij,Δ and the error bars refer to expanded (k = 2) uncertainties ( ){ }ijU ,Δ . [Upper] NMIJ/AIST, [Lower] PTB.


44

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000

Δ(j,

i) / U

{Δ(j,

i)}

Pressure / MPa

NMIJ/AIST

PTB

Figure 7.2: Degrees of equivalence of the participating institutes with respect to supplementary comparison reference values. Ratios ( ) ( ){ }ijUij ,, ΔΔ for the participating institutes are plotted as a function of nominal target pressure. 7.2.2 Difference between deviations for pairs of institutes The relative difference between pairs of pressure standards j and j’ is calculated by the following equation:

( ) ( ) ( ) ( ) ( )( )iSCRVp

ijpijpijijijj,

,,,,,,′−

=′Δ−Δ=′δ

(7.4) where ( )ij,Δ and ( )ij ,′Δ are the deviations from the reference value of j-th and j’-th institutes, respectively.

The relative expanded uncertainty of the difference, ( ){ }ijjU ,, ′δ , is estimated from

( ){ } ( ){ }( ){ } ( ){ }

( )iSCRVp

ijpuijpukijjukijjU c ,

,,,,,,

22 ′+⋅=′⋅=′ δδ

(7.5)


45

where ( ){ }ijjuc ,, ′δ is the combined standard uncertainty of the difference, k is the coverage factor and k = 2 is adopted, ( ){ }ijpu , and ( ){ }ijpu ,′ are the combined uncertainties in the expected mean pressure of j-th and j’-th institutes, respectively. Table 7.3 presents a summary of results of the differences, ( )ijj ,, ′δ , the expanded (k = 2) uncertainties of the differences, ( ){ }ijjU ,, ′δ , and the degrees of equivalence expressed by the ratios, ( ) ( ){ }ijjUijj ,,,, ′′ δδ , for the participating institutes. A measure of the degree of equivalence is provided by the relative magnitude of the deviation as ( ) ( ){ } 1,,,, ≤′′ ijjUijj δδ . For the present comparison, the condition was established for all the pairs of the participating institutes at all nominal target pressures. Table 7.3: Differences, ( ) ( ) ( )ijijijj ,,,, ′Δ−Δ=′δ , expanded (k = 2) uncertainties of differences, ( ){ }ijjU ,, ′δ ’ and degrees of equivalence expressed by ratios,

( ) ( ){ }ijjUijj ,,,, ′′ δδ .

j'NMI

Pressure δ (j,j',i ) U {δ (j,j',i )} δ (j,j',i ) U {δ (j,j',i )}

/ MPa / 10-6 / 10-6 / 10-6 / 10-6

100 28 74 0.38200 1 79 0.01300 6 89 0.07400 6 110 0.05

1 500 3 130 0.03600 7 166 0.04700 2 188 0.01800 -28 211 -0.13900 -31 233 -0.14

1000 -21 259 -0.08100 -28 74 -0.38200 -1 79 -0.01300 -6 89 -0.07400 -6 110 -0.05

2 500 -3 130 -0.03600 -7 166 -0.04700 -2 188 -0.01800 28 211 0.13900 31 233 0.14

1000 21 259 0.08

PTB

j NMI

1 2NMIJ/AIST PTB

δ / U {δ } δ / U {δ }

NMIJ/AIST


46

8. Discussions Both participants calibrated two pressure transducers in the transfer standard against their pressure standards following the protocol8,9. The results presented in this report are based on data originally submitted to the pilot institute for preparation of the draft A report. From the calibration data of each participating institute, the expected mean pressures for each participating institute were calculated with associated uncertainties. In this report, the APMP.M.P-S8 reference values were calculated using the unweighted mean method.

The degrees of equivalence with respect to the APMP.M.P-S8 reference values and the degrees of equivalence between pairs of participating institutes in APMP.M.P-S8 were presented as the main result.

This comparison was originally identified as Key comparison, APMP.M.P-K8. Then in March 2010, the comparison type was changed to Supplementary comparison and the identifier was changed to APMP.M.P-S8.


47

9. Conclusions Two National Metrology Institutes (NMIs) participated into this APMP supplementary comparison of hydraulic high-pressure standards from 100 MPa to 1000 MPa for gauge mode. In order to ensure the reliability of the comparison, the transfer standard using two pressure transducers was circulated for the whole comparison. The transfer standard was calibrated at the pilot institute (NMIJ/AIST) at the beginning and the end of this comparison. The stability of the transfer standard during the comparison period was evaluated from the pilot institute calibration results and it is shown that the transfer standard was sufficiently stable to meet the requirements of this supplementary comparison. The degrees of equivalence of the hydraulic high-pressure standards at the two participating NMIs were obtained. They were expressed quantitatively by two terms, deviations from the APMP supplementary comparison reference values and pair-wise differences between the participating institutes. The hydraulic high-pressure standards in the range 100 MPa to 1000 MPa of the two participating NMIs (NMIJ/AIST and PTB) were found to be equivalent compared with their claimed expanded uncertainties.


48

Acknowledgements The invaluable advice by Dr. A.K. Bandyopadhyay and Dr. Samyong Woo, the former and present chairpersons of the Technical Committee on Mass and Related Quantities (TCM) of APMP, and Dr. J. C. Legras and Dr. J. C. Torres-Guzman, the former and present chairpersons of the High Pressure Working Group (HPWG) of CCM, are gratefully acknowledged. Contributions by several of the staff in the pressure and vacuum standards section at the NMIJ/AIST and in particular, Dr. A. Ooiwa and Dr. H. Akimichi are gratefully acknowledged for their help and encouragement.


49

References 1. Sabuga W. et al., Final Report on Key Comparison CCM.P-K7 in the range 10 MPa to

100 MPa of hydraulic gauge pressure, Metrologia, 2005, 42, Tech. Suppl., 07005. 2. Legras J. C. et al., EUROMET Intercomparison in the Pressure Range 100 MPa to 700

(1000) MPa, Metrologia, 1993/94, 30, 721-725. 3. Mutual recognition of national measurements standards and of calibration and

measurement certificates issued by national metrology institutes (MRA), Technical Report, International Committee for Weights and Measures, 1999 (http://www.bipm.org/pdf/mra.pdf)

4. Guidelines for CIPM key comparisons, Appendix F to Mutual recognition of national measurements standards and of calibration and measurement certificates issued by national metrology institutes, Technical Report, International Committee for Weights and Measures, 1999 (http://www.bipm.org/pdf/guidelines.pdf)

5. Formalities required for the CCM key comparisons (2nd revised draft), 2001. 6. Guide to the Expression of Uncertainty in Measurement (GUM), 2nd ed., Geneva,

International Organization for Standardization, 1995. 7. Entering the details and results of RMO key and supplementary comparisons into the

BIPM key comparison database, 2000. 8. Kobata T., Protocol of “APMP, EUROMET 1000 MPa Hydraulic Pressure

Interlaboratory Comparison, APMP.M.P-K8”, Edition 1.1, 4 January 2007. 9. Kobata T., Appendix of Protocol of “APMP, EUROMET 1000 MPa Hydraulic Pressure

Interlaboratory Comparison, APMP.M.P-K8”, Edition 1.0, 5 January 2007. 10. Kobata T. and Ide K., Development of Pressure Standard up to 1 GPa using a Precise

Pressure Multiplier, Proceedings of SICE-ICASE International Joint Conference 2006, Oct. 18-21, 2006, Busan, Korea.

11. Jäger J., Schoppa G., Schultz W., The standard instruments of the PTB for the 1 GPa range of pressure measurement. PTB-Report W-66, Braunschweig, October 1996. ISSN 0947-7063, ISBN 3-89429-783-2.

12. Jäger J., Sabuga W., Wassmann D., Piston-cylinder assemblies of 5 cm2 cross-sectional area used in an oil-operated primary pressure balance standard for the 10 MPa range. In: Metrologia, 1999, 36(6), p. 541-544.

13. Sabuga W., Bergoglio M., Buonanno G., Legras J. C., Yagmur L. Calculation of the distortion coefficient and associated uncertainty of a PTB 1 GPa pressure balance using Finite Element Analysis – EUROMET Project 463. In: Proceedings of International Symposium on Pressure and Vacuum, IMEKO TC16, Beijing, September 22-24, 2003, Acta Metrologica Sinica Press, 92-104.


50

14. Sabuga W., Molinar G., Buonanno G., Esward T., Legras J.C., Yagmur L. Finite element method used for calculation of the distortion coefficient and associated uncertainty of a PTB 1 GPa pressure balance – EUROMET project 463. In: Metrologia, 2006, 43, 311-325.

15. Sabuga W., Determination of the pressure distortion coefficient of pressure balances using a modified experimental method. In: Proceedings of NCSL International Workshop and Symposium, San Diego, August 4-8 2002, 17 p

16. Hottinger Baldwin Messtechnik GmbH (HBM), Data sheet for P3MBP, High-pressure Transducer 10000 bar, Special Version TCJ, 2005.

17. Hottinger Baldwin Messtechnik GmbH (HBM), Operating Manual for DMP40, DMP40S2.

18. Miiller A. P. et al., Final Report on Key Comparison CCM.P-K4 in Absolute Pressure from 1 Pa to 1000 Pa, Metrologia, 39, Tech. Suppl., 07001, 2002.

19. Cox M. G., The evaluation of key comparison data, Metrologia, 39, 589-595, 2002. 20. Kobata T. et al., Final Report on Key Comparison APMP.M.P-K5 in differential

pressure from 1 Pa to 5000 Pa, Metrologia, 2007, 44, Tech. Suppl., 07001.

Documents

Final Report APMP.M.P-S8 100412 - BIPM · Final Report on APMP.M.P-S8 Version 1.1 of 12 April 2010 2 preparation of a report on the comparison and the analysis of data on the basis