CCM.P-K13 final report - BIPMFinal Report on CCM.P-K13, Version 4 of 2012-04-10 - 4 - - in Oct. 2008 in the range (100 to 500) MPa against 5 mm 2 PCU no. 10; - in Jan. 2009 in the

1 PTB: Physikalisch-Technische Bundesanstalt, Braunschweig, Germany 2 NIST: National Institute of Standards and Technology, Gaithersburg, USA 3 CENAM: Centro Nacional de Metrología, El Marqués, Mexico 4 NPLI: National Physical Laboratory India, New Delhi, India 5 NIM: National Institute of Metrology, Beijing, China 6 NMIJ: National Metrology Institute of Japan, AIST, Tsukuba, Japan 7 LNE: Laboratoire National d'Essais, Paris, France

Version 4 of 2012-04-10

Final Report on Key Comparison CCM.P-K13 in the Range 50 MPa to 500 MPa of Hydraulic Gauge Pressure

W. Sabuga1, D.A. Olson2, J.C. Torres3, S. Yadav4, Y. Jin5, T. Kobata6, P. Otal7

April 2012

ABSTRACT This report describes a CCM key comparison of hydraulic pressure standards of seven National Metrology Institutes, listed in the chronological order of their measurements, that was carried out in the period from December 2008 to March 2010 in order to determine their degrees of equivalence in the range 50 MPa to 500 MPa of the gauge pressure. The pilot laboratory was PTB. The primary pressure standards were pressure balances of different design equipped with piston-cylinder assemblies operated in free-deformation, controlled-clearance or re-entrant operation mode. The transfer standard was a piston-cylinder assembly in a pressure balance. The pressure-dependent effective areas of the transfer standard at specified pressures were reported by the participants and led to the reference values calculated as medians. Results of all participants excepting NIM agree with the reference values and with each other within the expanded uncertainties calculated with a coverage factor 2, most of them even within their standard uncertainties. In addition, the results were analysed in terms of the zero pressure effective area and the pressure distortion coefficient. Also for them agreement within expanded uncertainties (k=2) is observed. The results of the comparison demonstrate equivalence of the laboratory standards and of the Calibrating and Measurement Capabilities currently presented in the Key Comparison Data Base of BIPM.

Final Report on CCM.P-K13, Version 4 of 2012-04-10

- 1 -

Contents

1. INTRODUCTION ........................................................................................................ 2

2. LABORATORY STANDARDS AND MEASUREMENT METHODS OF THE PARTICIPANTS ...................................................................................................................... 2

2.1 PTB pressure balance and measurement method ................................................. 2

2.2 NIST pressure balance and measurement method ............................................... 4

2.3 CENAM pressure balance and measurement method .......................................... 6

2.4 NPLI pressure balance and measurement method ............................................... 8

2.5 NIM pressure balance and measurement method ................................................ 8

2.6 NMIJ pressure balance and measurement method ............................................ 10

2.7 LNE pressure balance and measurement method .............................................. 12

3. TRANSFER STANDARD ......................................................................................... 13

4. ORGANIZATION, CHRONOLOGY AND PROBLEMS DURING THE COMPARISON ...................................................................................................................... 15

5. MEASUREMENT PROCEDURES.......................................................................... 16

6. RESULTS .................................................................................................................... 18

6.1 Stability of the transfer standard .......................................................................... 18 6.2 Results of the participants ..................................................................................... 21

6.3 Reference value calculation ................................................................................... 27

6.4 Degree of equivalence ............................................................................................. 30

7. DISCUSSION .............................................................................................................. 31

8. SUPPLEMENTARY RESULTS ............................................................................... 32

9. CONCLUSIONS ......................................................................................................... 34

10. ACKNOWLEDGMENTS .......................................................................................... 34

11. REFERENCES ........................................................................................................... 34

12. ANNEX A: Relative deviations of the participants results’ from the reference value and the expanded uncertainties (k = 2) of these deviations at pressures 50 MPa to 500 MPa ................................................................................................................................... 36

13. ANNEX B: Relative differences between the participants’ results (dij) and their expanded uncertainties (U(dij)) (k = 2) at pressures 50 MPa to 500 MPa ......................... 41


- 2 -

1. INTRODUCTION At the CCM High Pressure Working Group meeting held at BIPM on 21 April 2008, it was decided to carry out a new key comparison (KC) in the range of 500 MPa of hydraulic gauge pressure. This comparison is aimed to renew the equivalence statements derived from previous comparison CCM.P-K8, carried out in 1996 – 1999 and approved for provisional equivalence [1], which, for several reasons, is unsuitable to derive a reference value and to provide a link for RMOs' KCs recently conducted or being planned. The initially agreed group of participants included 9 National Metrology Institutes (NMIs) as specified above and, additionally, National Research Institute for Physicotechnical and Radio Engineering Measurements (VNIIFTRI), Mendeleevo, Russia, as well as Korea Research Institute of Standards and Science (KRISS), Daejeon, Korea. Therewith the original group of NMIs included 2 representatives from EURAMET, 2 from COOMET (PTB being a member of both EURAMET and COOMET), 2 from SIM and 4 from APMP. However, the laboratory standard of VNIIFTRI was damaged in the period of this KC so that VNIIFTRI could not participate in this KC. KRISS participated in the comparison, submitted reasonable results, which were evaluated within the Draft A report, but decided to withdraw them because their standard was destroyed after the comparison and the submitted results were estimated by KRISS as meaningless. The Physikalisch-Technische Bundesanstalt (PTB), Germany, was agreed to be a pilot laboratory in this KC. At the meeting of 21 April 2008, a piston-cylinder unit (PCU) without any pressure balance base was suggested as a transfer standard (TS) to minimise transportation costs. However later, it was agreed to include a pressure balance base to the TS to provide its better stability and because some participants did not have their own base for operation of the PCU. The PCU and the pressure balance of the TS were provided by PTB. All participants with the exception of NIM operated the TS with their own weights. For NIM, which did not have weights suitable for the TS, those were provided by PTB. The comparison was conducted in accordance with the Technical Protocol prepared by the PTB and approved by the participants. All uncertainties in this report are standard ones. 2. LABORATORY STANDARDS AND MEASUREMENT METHODS OF THE

PARTICIPANTS All laboratory standards (LS) used were pressure balances equipped with PCUs. Different methods were applied by the participants to compare their standards with the TS. 2.1 PTB pressure balance and measurement method The PTB standard used in this KC was a modified Harwood pressure balance with a total load mass of 500 kg [2] equipped with a 1 GPa PCU identified by no. 7594 manufactured by Desgranges et Huot and normally used in the Desgranges et Huot 1:10 1 GPa pressure multiplier (Table 1).


- 3 -

Table 1. PTB standard and measurement conditions

Manufacturer Pressure balance – Harwood, modified

PCU – Desgranges et Huot, ser. no. 7594 Measurement range in MPa 50 – 1000 Material of piston Tungsten carbide Material of cylinder Tungsten carbide with a sleeve of steel Operation mode, free-deformation (FD) or controlled-clearance (CC)

Both FD and CC are possible, CC was used

Zero-pressure effective area (A0) at reference temperature in mm2

4.902256 1)

Relative uncertainty of A0 in 10-6 13 Pressure distortion coefficient (λ) in MPa-1 0.437·10-6 Uncertainty of λ in MPa-1 0.05·10-6 Relative uncertainty of mass pieces in 10-6 0.6 Linear thermal expansion coefficient of piston (αp) in °C-1

4.5·10-6

Linear thermal expansion coefficient of cylinder (αc) in °C-1

4.5·10-6

Reference temperature (t0) in °C 20 Local gravity (g) in m/s2 9.812533 Relative uncertainty of g in 10-6 0.53 Height difference between laboratory standard (LS) and TS (h, positive if LS is higher than TS) in mm

-1.0

Uncertainty of h in mm 0.37 1) A0 as actualised in 2007 after a piston-cylinder remounting. Before the remounting, the

effective area was A0, before 2007 = 4.902107 mm2. The zero-pressure effective area (A0) of this assembly is traceable through a calibration chain to three primary 5 cm2 10 MPa piston-cylinder units [3]. The value of the distortion coefficient (λ) with associated uncertainty was determined by FEA [4-5] and an experimental method [6]. The value of A0 used before 2007 was based on the results of the following cross-float measurements:

- in Jan. 1998 against an 84 mm2 PCU identified by no. 701/2 [2] performed in a special pressure balance in the range (3 to 12) MPa,

- in Feb. 1999 in the range (40 to 400) MPa against an 8.4 mm2 PCU identified by no. 703/1 [2], which was used as a PTB standard in CCM.P-K7 and the respective KCs of EURAMET, COOMET and APMP;

- in Aug. 2000 in the range (130 to 940) MPa against a 5 mm2 PCU of the same design identified by no. 10 [2], which is traceable to PCU 703/1;

- in Jan. 2001 in the range (70 to 400) MPa against 8.4 mm2 PCU no. 703/1; - in May 2001 in the range (130 to 940) MPa against 5 mm2 PCU no. 10.

The actual value of A0 used since 2007 is based on the results of the following cross-float measurements:

- in Jan. 2007 in the range (130 to 940) MPa against 5 mm2 PCU no. 10; - in Jan. 2008 in the range (70 to 400) MPa against 8.4 mm2 PCU no. 703/1;


- 4 -

- in Oct. 2008 in the range (100 to 500) MPa against 5 mm2 PCU no. 10; - in Jan. 2009 in the range (70 to 400) MPa against 8.4 mm2 PCU no. 703/1; - in Mar. 2010 in the range (70 to 400) MPa against 8.4 mm2 PCU no. 703/1.

All the measurements before and after 2007 did not show any essential change of λ in respect to its uncertainty, but showed a relative increase in A0 of 3·10-5. This change has been explained by a remounting of this PCU performed before the measurements in 2007. The connection of the PCU to the tubing is realised by a metal-to-metal contact at the 60°-tapered bore of the cylinder. As an FEM analysis has shown, the contact force between the tubing and the PCU can produce a relative change in A0 of the order 10-5. In all measurements before 2007 the same piece of tubing was attached to the PCU without remounting it between the measurements. Before the measurements in 2007, after a modification of the tubing in the pressure balance, another tubing piece had to be attached to the PCU which presumably affected its A0. After the reattachment, the PCU has always been used with the new tubing piece, and the stability of its A0 was controlled by the several measured listed above. In particular, the stability of its A0 was controlled every time before the PTB measurements within the actual KC in 2008, 2009 and 2010. This PTB pressure standard was used in the following comparisons: EURAMET.M.P-K7 (500 MPa, 2005-2007), APMP.M.P-S8 (1 GPa, 2007-2008), EURAMET.M.P-S5 (500 MPa, 2007-2010) and EURAMET.M.P-K13 (500 MPa, 2008-2010). For an adequate link between these comparisons and the actual CCM comparison it should be taken into account that A0, before 2007 was used in EURAMET.M.P-K7, APMP.M.P-S8 and EURAMET.M.P-S5, and A0, after 2007 was used in EURAMET.M.P-K13. The magnetisation of the piston and cylinder of the TS was measured at the beginning of the KC in 2008 and at the end in 2010. At the beginning in 2008, the magnetic flux density was <30 µTesla at the piston and <170 µTesla at the cylinder. The cylinder was demagnetised and measured again with the result <50 µTesla. In 2010, the magnetic flux density of <30 µTesla at the piston and <70 µTesla at the cylinder was found. The pressure measurements were performed in accordance with the Technical protocol. However, only 60 total points were taken in 2008, only 70 in 2009 and full 100 points in 2010. The TS was directly connected to the LS, with di(2-ethylhexyl) Sebacate (DHS) being used as a pressure-transmitting liquid in both standards, and the measurements were performed by the cross-float method using the pistons fall rates as the equilibrium criterion. The typical sensitivity of the cross-float in terms of the smallest effective mass loaded on the piston of the TS was (20, 50, 100, 200 and 400) mg at pressures (50, 150, 250, 400 and 500) MPa, respectively. The piston fall rates measured at (50, 250 and 500) MPa were in mm/min: 0.06, 0.32, 0.49 in 2008; 0.03, 0.35, 0.64 in 2009 and 0.02, 0.34, 0.75 in 2010. 2.2 NIST pressure balance and measurement method Measurements of the TS effective area vs. pressure were made by crossfloat comparison to NIST Laboratory Standard piston gauge known as PG21. The characteristics of the LS and measurement conditions are given in Table 2. The characteristics (zero-pressure area and distortion coefficient) of the LS were most recently established in 1996 from calibrations against two primary standard controlled clearance gauges. A calibration of LS against another Laboratory Standard in 2008 confirmed the characteristics of the LS.


- 5 -

Table 2. NIST standard and measurement conditions Manufacturer Ruska Instrument Corporation Measurement range in MPa 14 – 280 Material of piston Tungsten carbide Material of cylinder Tungsten carbide Operation mode, free-deformation (FD) or controlled-clearance (CC)

FD, re-entrant


8.402894

Relative uncertainty of A0 in 10-6 16.0 Pressure distortion coefficient (λ) in MPa-1 -2.744·10-6

Uncertainty of λ in MPa-1 See note 1 Relative uncertainty of mass pieces in 10-6 2.89 Linear thermal expansion coefficient of piston (αp) in °C-1

4.11·10-6


4.11·10-6


0

Uncertainty of h in mm 1 Notes: 1. NIST reports a single value for the uncertainty in the effective area of the Laboratory Standard over the measurement range. The uncertainty in λ is not separated from the uncertainty in A0. 2. Method to determine A0 and λ for Laboratory Standard: A0 and λ for the LS were determined by crossfloat calibration against two NIST piston gauge primary standards, both of the controlled clearance type. The two sets of data were combined and fit together to provide values for A0, λ, and the uncertainty in effective area. 3. Further details on Laboratory Standard: The LS is designated at NIST as PG21. It is a Ruska type 2450-700 piston gauge, serial number V-538. It operates in Spinesstic 22 hydraulic oil. The NIST LS operated in Spinesstic 22 oil and the TS operated in DHS provided by the pilot lab. To prevent cross-contamination of the fluids during the calibration measurements, the pressure balancing technique described in [7] and [8] was used. NIST refers to this technique as Transducer Assisted Crossfloat (TAC). The LS and the TS were each isolated by constant volume valves (CVVs). In the horizontal hydraulic line connecting the CVVs was a high precision absolute pressure transducer made by Paroscientific. The reference level of the CVVs, the LS, and the TS were the same to within 1 mm. During a measurement, the CVVs associated with the LS and TS were alternately opened to the pressure transducer. A computer controlled the opening and closing of the CVVs such that they were never both open at the same time.


- 6 -

The difference in pressure measured at the transducer was used to adjust the mass on the LS such that the standards were generating the same pressure to within 1 kPa or less. Then, 5 sets of pressure difference were performed with no further mass adjustment. Following a switching of the valve states, the computer waited 90 seconds before reading the pressure transducer to allow pressure transients to decay. The 5 difference measurements were averaged and added to the pressure generated by the LS to give the pressure at the TS. The standard deviation of the 5 difference measurements was typically 100 to 200 Pa, and was used to evaluate the additional uncertainty introduced by the TAC method. The method has previously been evaluated in unpublished work at NIST for use with different fluids in the two pressure balances. The TS was operated with the motor-drive on. The motor was switched on at least 30 minutes prior to the first measurement of a calibration cycle. Prior to the measurements of the 5 calibration cycles, the fall rate was measured at 50 MPa and 250 MPa with both the low and high pressure shut-off valves of the TS pressure balance closed. A manual valve on the outlet of the TS pressure balance was also closed. At 250 MPa, the fall rate was about 0.35 mm/min. At 50 MPa, the fall rate was too small to measure but was clearly less than 0.05 mm/min. The resistance of the TS thermometer was measured with an HP 3457A digital voltmeter set on offset compensated 4-wire ohms, 100 power line cycles, with a current through the sensing resistor of 1 mA. The magnetization of the piston and cylinder was measured at the end of the 5 cycles (the Gauss meter was not available at the beginning of the cycles). The piston magnetization was less than 0.4·10-4 Tesla and the cylinder magnetization was less than 0.5·10-4 Tesla. Ambient air pressure, relative humidity, and temperature were measured with a Ruska 2455-ADM. The standard uncertainties of the air pressure, relative humidity, and temperature were 100 Pa, 2.4 %, and 0.1 ºC, respectively. The TS was measured in 5 cycles against the LS on 29 January, 2 February, 3 February, 4 February, and 6 February 2009. Each cycle (day) consisted of observations made at 5 pressures in the ascending direction and 5 pressures in the descending direction. The 5 pressures were (50, 100, 150, 200, and 250) MPa. Due to the pressure limit of the NIST CMCs, measurements were not made over the full range of the protocol. There were 50 measurements in total. The LS was operated at mid-stroke and the TS was operated at the reference level indicated by the displacement indicator. The piston, bell, and masses of the LS were rotated at 20 to 30 rpm. The reference temperature for the LS was 23 ºC and the measured temperature was between 22.53 ºC and 22.75 ºC. The measured temperature for the TS was between 22.62 ºC and 23.70 ºC, with the temperature increasing from the beginning to the end of a cycle. The ambient air temperature varied from 23.1 ºC to 23.4 ºC over the 5 cycles. 2.3 CENAM pressure balance and measurement method The CENAM standard used in this KC was a DH pressure balance equipped with a PCU serial number 4923 with the properties given in Table 3.


- 7 -

Table 3. CENAM standard and measurement conditions Manufacturer DH Measurement range in MPa 1 – 500 Material of piston Steel Material of cylinder Tungsten carbide Operation mode, free-deformation (FD) or controlled-clearance (CC)

FD


1.961313


10.5·10-6


4.5·10-6


-0.16

Uncertainty of h in mm 1 The cylinder of the assembly is made of tungsten carbide, and the piston is made of steel with the following Young’s modulus (E) and Poisson’s coefficient (µ): piston, steel: E = 200 GPa, µ = 0.3; cylinder, tungsten carbide: E = 620 GPa, µ = 0.218. The traceability of the effective area is through a chain of pressure calibrations (cross floating) up to the CENAM national pressure primary standard which was calibrated dimensionally and in mass at the corresponding laboratories at CENAM. The previous calibration of the standard used for the comparison was performed in 2009 (internally at CENAM, CNM-CC-720-122/2009) at the following conditions: temperature 20.27 °C ± 0.2 ºC, atmospheric pressure 81.0 kPa ± 0.1 kPa, relative humidity 35% ± 5%. The medium was oil (Sebacate). The standards involved in the calibration chain as a reference are: - DHI piston-cylinder assembly serial no. 6319 operated in a pressure balance model

6316 serial no. 6367, mass set serial no. 3345 and carrying bell serial no. 3345. This standard was calibrated internally at CENAM in 2009 (calibration certificate CENAM-CNM-CC-720-121/2009).

- DHI piston-cylinder assembly serial no. 5716, pressure balance model 5306-02 serial no. 5715, mass set serial no. 3348; carrying bell serial no. 3348. This standard was calibrated internally at CENAM in 2009 (calibration certificate CENAM-CNM-CC-720-168/2009).

- DHI piston-cylinder assembly serial no. 228, pressure balance model PGA-7601 serial no. 507, mass set serial no. 2003, carrying bell serial no. 2003. This standard was calibrated internally at CENAM in 2009 (calibration certificate CENAM-CNM-CC-720-150/2009).

- DHI piston-cylinder assembly serial no. 108A, pressure balance model PGA-7601 serial no. 574, mass set serial no. 3345/2018, carrying bell serial no. C-737. This last standard


- 8 -

(the national pressure primary standard) was calibrated dimensionally in 2009 (calibration certificate CNM-CC-740-156/2009; ; U = 8.8·10-9 m2, k = 2. The mass calibration certificate CNM-CC-730-003/2008; U = 1.0·10-7 kg, k = 2).

2.4 NPLI pressure balance and measurement method The NPLI laboratory standard (LS) used in the comparison is a simple design type piston gauge with the properties and measurement conditions given in Table 4. Table 4. NPLI standard and measurement conditions Manufacturer DH-Budenberg Measurement range in MPa 1 – 500 Material of piston Steel Material of cylinder Tungsten carbide Operation mode, free-deformation (FD) or controlled-clearance (CC)

FD


1.960786

Relative uncertainty of A0 in 10-6 9.2 Pressure distortion coefficient (λ) in MPa-1 8.23·10-7 Uncertainty of λ in MPa-1 8.25·10-9 Relative uncertainty of mass pieces in 10-6 0.5 Linear thermal expansion coefficient of piston (αp) in °C-1

10.5·10-6


4.5·10-6


0

Uncertainty of h in mm 0.5 This LS is traceable to the Controlled Clearance Piston Gauge (CCPG) Type National Primary Pressure Standard through unbroken chain of national standards of mass, length and pressure. A0 and λ are obtained by cross floating the LS against the national pressure standard. The pressure transmitting fluid used in the measurements is DHS. The classical fall rate method is used to achieve the balancing equilibrium condition. The TS is then cross floated against LS using the same pressure transmitting fluid and classical fall rate method for balancing operations. 2.5 NIM pressure balance and measurement method A piston gauge model DHI-PG7000 with the range (5 – 500) MPa was used as the Laboratory Standard (LS) whose details are given in Table 5.


- 9 -

Table 5. NIM standard and measurement conditions Manufacturer DHI Measurement range in MPa 5 – 500 Material of piston Tungsten carbide Material of cylinder Tungsten carbide Operation mode, free-deformation (FD) or controlled-clearance (CC)

FD


1.962185


4.5·10-6


4.5·10-6

Reference temperature (t0) in °C 20 Local gravity (g) in m/s2 9.801260 Relative uncertainty of g in 10-6 1 Height difference between laboratory standard (LS) and TS (h, positive if LS is higher than TS) in mm

-85

Uncertainty of h in mm 5 A0 of the LS is traceable to the primary standard by cross-float method. Because the range of the primary standard is (0.1 – 10) MPa, it is difficult to directly compare the LS with the primary standard. For this reason another piston gauge designated KY100 with the range (1 – 100) MPa was used for the link as a transfer standard. The effective area of the primary standard is determined by means of dimensional measurements. The Mass and Density Laboratory of NIM calibrated mass and density of the weights of the LS. The relative standard uncertainty of mass is 8·10-7, the standard uncertainty of density is 20 kg/m3. PCU temperature was measured by a platinum resistance thermometer (PRT) built into the LS mounting post. The temperature sensor was calibrated by the Temperature Lab. Pressure distortion coefficient of LS and it’s uncertainty come from the certificate of manufacturer, λ is 7.31·10-7/MPa with standard uncertainty 3.7·10-8/MPa. The multimeter, thermometer, hygrometer and barometer were calibrated either. When TS arrived at NIM, it was checked for damage and completeness of its components. Then, the piston fall rate was measured at (500, 250 and 50) MPa with the results (0.55, 0.34 and 0.06) mm/min, respectively. The magnetisation of the piston and cylinder was checked by the Division of Electricity and Quantum Metrology of NIM. The magnetic flux density at their surfaces did not exceed 1·10-4 Tesla. Originally, the LS and TS were connected through a three-ways valve with a digital pressure gauge having an upper limit of 280 MPa. Both, the piston fall rate method and the pressure indicator method were planned to monitor equilibrium between the LS and TS. But practically it was found that the piston fall rate method provides a better resolution of the measurement.


- 10 -

The system ran normally below 400 MPa, but there were some leak appeared at pressures higher than 400 MPa after one measurement cycle. After failing to solve the leaking problem, it was decided to complete the five measurement cycles with pressure not higher than 400 MPa (50, 100,150, 200, 250, 300 350, 400) MPa with the three-ways valve still being in the line between the LS and TS. Then, the LS and TS were connected directly and the 5 measurement cycles were completed at pressures of 450 MPa and 500 MPa. Each time the system was pressurised up to 400 MPa step by step, trying to keep a similar situation as in the normal procedure and it was waited at least 1 hour to get a stable deformation. The temperature of the TS was measured by a PRT connected to a multimeter. A laser displacement sensor was used to measure the position of the piston. The measurement was performed according to the procedure given in the Technical Protocol. The height difference was measured after LS and TS connected and level adjusted. A 30 minutes warm up run was performed. Load weight masses were adjusted to generate pressures not deviating from the nominal values by more than 0.1 MPa. To float both pistons, pressure was added by the pressure generator of the TS. At least 5 minutes were waited, the pistons rotated and pressure adjusted ensuring that the pistons of the TS and LS do not deviate from their working positions by more than 0.5 mm. The piston of LS was rotated by an internal motor to get the initial rotation. When the rotation speed reached 30 to 35 rpm, the motor was disconnected. Considering the rotating motor of TS could disturb the cross-float, the rotation pin on the piston was taken off and the piston was rotated by hand in the counter clockwise direction with the rotation speed lying between 30 and 35 rpm, with the motor being always on. The classical fall rate method was used to control the equilibrium. 2.6 NMIJ pressure balance and measurement method The NMIJ national pressure standard used in this KC was a PCU with serial no. 1093 whose properties are given below together with measurement conditions.


- 11 -

Table 6. NMIJ standard and measurement conditions Manufacturer DH Instruments, a Fluke Company Measurement range in MPa 5 – 500 Material of piston Tungsten carbide alloy Material of cylinder Tungsten carbide alloy Operation mode, free-deformation (FD) or controlled-clearance (CC)

FD


1.960899

Relative uncertainty of A0 in 10-6 15.5 Pressure distortion coefficient (λ1) in MPa-1 7.53·10-7 Uncertainty of λ1 in MPa-1 5.6·10-8 Pressure distortion coefficient (λ2) in MPa-2 5.8·10-11 Uncertainty of λ2 in MPa-2 6.5·10-11 Relative uncertainty of mass pieces in 10-6 0.5 Linear thermal expansion coefficient of piston (αp) in °C-1

4.5·10-6


4.5·10-6


-1.69

Uncertainty of h in mm 0.5 The effective area of the LS was determined by cross-float measurements with several piston-cylinders: FD piston-cylinder (1 MPa/kg up to 100 MPa) and NMIJ CC piston-cylinders (0.2 MPa/kg and 0.5 MPa/kg up to 200 MPa and 500 MPa, respectively). The FD piston-cylinder was used for the CCM.P-K7, and is traceable through a series of calibrations to larger PCUs whose effective areas have been evaluated by the NMIJ mercury manometer and/or dimensional measurements. The CC piston-cylinders have been originally developed in cooperation with Nagano Keiki Co., Ltd. The pressure dependence of the effective area of the CC piston-cylinders has been estimated experimentally based on the Heydemann-Welch model [9]. From the cross-float measurements, the effective area of the LS over the whole pressure range is expressed by a quadratic function of pressure: A = A0·(1 + λ1·p +λ2·p

2 ). The parameters are listed in the table above. The uncertainties of the parameters, u(A0), u(λ1), u(λ2), are determined so that the relative combined uncertainty of the effective area from the cross-float measurements, u(A), are approximated by the equation: u2(A) = (u(A0)/A0)

2 + (u(λ1)·p)2 + (u(λ2)·p

2)2 . Uncertainty of the pressure dependence of the effective area is estimated from the uncertainty of the parameters in the Heydemann-Welch model, zero clearance jacket pressure and jacket pressure coefficient, and of other influential factors in the characterization experiments [9]. The difference of the pressures generated by LS and TS was determined using high-resolution pressure transducers which were alternatively connected to the first and to the second pressure balance by the use of constant-volume valves [8].


- 12 -

2.7 LNE pressure balance and measurement method The standard used for the comparison was the LNE national standard balance Desgranges et Huot N°A equipped with a 1 GPa PCU # 2. The assembly was used in controlled-clearance mode, with a pressure jacket equal to 1/5 of the measurement pressure. The main characteristics and the uncertainties of the standard are given in Table 7. Table 7. LNE standard and measurement conditions Manufacturer Desgranges et Huot Measurement range in MPa 30 – 1000 Material of piston Tungsten carbide Material of cylinder Tungsten carbide + steel Operation mode, free-deformation (FD) or controlled-clearance (CC)

CC


9.804808

Relative uncertainty of A0 in 10-6 7.2 Pressure distortion coefficient (λ) in MPa-1 1.10·10-7 Uncertainty of λ in MPa-1 5.00·10-8 Relative uncertainty of mass pieces in 10-6 7.5 Linear thermal expansion coefficient of piston (αp) in °C-1

4.50·10-6


4.50·10-6


283.2

Uncertainty of h in mm 1 The high pressure standard consists of two pressure balances with a 1000 kg set of masses each. It allows mounting PCUs working in the ranges from 6 to 200 MPa [10], 30 to 1000 MPa, and more recently 1.5 to 50 MPa. All the configurations between the assemblies are allowed for comparison two by two. The pressure balances are controlled-clearance type ones: the jacket pressure is stabilised and measured using auxiliary pressure balances. The effective area at null pressure has been determined by comparison with the 50 MPa standard, itself traceable to the primary standard in the range 10 kPa to 1 MPa [11, 12]. The pressure distortion coefficient has been determined using the experimental method developed at the LNE. This method is based on fall rate measurements and cross-floating experiment under variable conditions of pressure jacket. It has been applied to 5 PCUs of the same geometry in order to demonstrate their consistency. The temperature of the transfer standard was measured using the same digital ohmmeter as for the laboratory standard, in order to eliminate any systematic error. The estimated standard uncertainty of the measurement of the temperature probe resistance is 2.5 mΩ. From this


- 13 -

value and the uncertainty of the temperature probe calibration the standard uncertainty of the temperature is estimated to be 7 mK. The observed temperature changes were less than 1 mK/min. The uncertainty of the PCU was estimated to be 29 mK which takes into account a probable gradient in the balance. The transfer standard arrived at LNE on January 26th 2010. The oil of the pressure balance was polluted and therefore was purged. Then, it was filled with clean oil. The measurements were performed in the period from 1 to 5 February 2010, according to the Technical protocol. It was not possible to measure the piston fall rate. The transfer standard was operating well. The observed sensitivity, leakage and temperature changes were well suitable for a good comparison. 3. TRANSFER STANDARD The transfer standard (TS) is described in detail in the Technical Protocol of the comparison. It was a piston-cylinder assembly of 1.96 mm2 nominal effective area with serial number 4603 manufactured by DH-Budenberg, France. It was mounted in a DH-Budenberg pressure balance model 5306 equipped with a mass carrier, a temperature probe, and all other parts required for the operation of the pressure balance and connecting it to the LS with the except of masses (Fig. 1).

Figure 1. Transfer standard Most of participants had to operate the TS pressure balance with their own 100 kg mass sets. NIM, which did not have masses suitable for operation with the TS pressure balance, was provided by a mass set from PTB. The pressure-transmitting medium in the TS was DHS. Its density as a function of pressure, and surface tension were provided by PTB.


- 14 -

According to the manufacturer information, the cylinder of the assembly is made of tungsten carbide, and the piston is made of steel with the following linear thermal expansion coefficient (α), Young’s modulus (E) and Poisson’s coefficient (µ): Table 8. Material properties of the transfer standard PCU Material α / °C E / GPa µ Piston Steel (1.00 ± 0.05)·10-5 200 0.3 Cylinder Tungsten carbide (0.45 ± 0.05)·10-5 620 0.218 The thermal expansion coefficient of the piston-cylinder unit can be taken as α’

p + α’ c = (1.45 ± 0.075)⋅10-5 °C-1. The piston cap is made of stainless steel. The piston, piston’s cap and carrying bell masses and densities were measured and provided to the participants by the pilot laboratory. The temperature probe - a platinum resistance thermometer - was calibrated at PTB, and the formula for the temperature-resistance dependence in the temperature range (18.5 to 24.5) °C was given. Each participant used their own electronics to measure the thermometer resistance. The piston working position and the pressure reference level were specified. The independency of the effective area of the TS when the piston deviates by ±1 mm from its working position was checked at PTB. Also the typical cross-float sensitivity and reproducibility, piston-cylinder temperature drift, and piston fall rates at different pressures were measured by the pilot laboratory and provided to the participants. These properties of the TS are as follows. Typical cross-float sensitivity and reproducibility: 20 mg at 50 MPa, 50 mg at 150 MPa and 100 mg at 350 MPa. This corresponds to the relative sensitivity in pressure of 2⋅10-6, 1.7⋅10-6 and 1.4⋅10-6 at (50, 150 and 350) MPa, respectively. The relative experimental standard deviations of single values of the effective areas, as measured by the pilot laboratory over the range (50 to 500) MPa, were typically between (3 and 7)⋅10-6. With the driving motor being switched on, the temperature of the piston-cylinder assembly increased at a typical rate between (0.05 and 0.15) K/h during first 4 h. The piston fall rates (vf) measured by the pilot laboratory as a function of pressure (p) at a temperature of 20 °C were:

p / MPa 50 100 150 200 250 300 350 400 450 500 vf / (mm/min) 0.06 0.12 0.19 0.27 0.32 0.38 0.41 0.46 0.50 0.49 It was assumed that the piston would be rotated by the motor. However, if any laboratory had discovered a disturbance of the measured pressure due to the motor drive, the pressure balance could be operated with the piston being rotating freely. For such cases the free rotation speed decay was measured by the pilot laboratory. At a pressure of 50 MPa and a temperature of 20 °C, the rotation speed decayed from 35 rpm to 30 rpm within 17 minutes. The piston-cylinder unit (PCU) of the TS was manufactured before 1992 and therefore was expected to be sufficiently old to have a stable value of its effective area in the period of the comparison. Numerous calibrations of the TS PCU performed in the period of time from 1992 to 2007 resulted in the maximum differences its zero pressure effective area (A0) and pressure distortion coefficient (λ) ∆A0/A0 = 2.5·10-5 and ∆λ = 0.083·10-6 MPa-1. Several measurements performed during 2007 showed maximum differences ∆A0/A0 = 1·10-5 and ∆λ = 0.041·10-6 MPa-1.


- 15 -

During the initial investigation, the TS was compared with a nominally identical unit bearing serial number 6721, which was then stored for the whole period of the comparison as a backup unit in case of loss or damage to the TS. 4. ORGANIZATION, CHRONOLOGY AND PROBLEMS DURING THE

COMPARISON The measurements were performed in the order and times given in Table 9. Table 9. Chronology of measurements

Institute Measurement

start date Measurement

end date PTB, initial investigation of TS 4 Dec 2008 8 Dec 2008

NIST 29 Jan 2009 6 Feb 2009 CENAM 11 Mar 2009 18 Mar 2009

NPLI 2 May 2009 7 May 2009 NIM 2 Jul 2009 7 Jul 2009

KRISS 1 Aug 2009 20 Aug 2009 NMIJ 14 Oct 2009 23 Oct 2009

PTB, intermediate check of TS 16 Dec 2009 8 Jan 2010 LNE 1 Feb 2010 5 Feb 2010

PTB, final investigation of TS 4 Mar 2010 18 Mar 2010 There were different problems during the comparison. It was seriously delayed because of custom procedures when importing the TS to NPLI. In addition, there have been several technical problems. On the way from PTB to NIST, the hinges of the TS shipment box were detached and then were repaired by NIST. On the way from NIST to CENAM, the TS box was heavily damaged. Additional metal reinforcements were attached on all corners of the box (top, middle and bottom) by CENAM. NIST has reported that the variable volume changer occasionally leaked a small amount of oil at the shaft seal when the system pressure was above 200 MPa. Leaks in the mounting post, in the tubing below the balance in the variable volume screw press, and in the pump were reported by CENAM. The leaks in the mounting post and in the tubing were eliminated by CENAM. In spite of this repair, some laboratories reported increased piston fall rates which were attributed to a leak in the variable volume and the hand pump of the TS. In such cases, the measurements were performed by the participants without using the variable volume and the hand pump of the TS pressure balance, with all necessary pressure adjustments being done by the pressure generation systems of the laboratories standards. When the TS arrived at PTB in 2009 for the intermediate investigation, a complete repair and replacement of all damaged components of the pressure balance was carried out by DH-Budenberg. Some laboratories (NIM, NMIJ) reported that the TS arrived in inappropriate state with the pressure balance feet being removed or the rear panel of the pressure balance being detached. It seems that the TS was handled by unskilled persons, perhaps for custom or security reasons, when the transfer standard was outside the laboratories. In some cases, at NIM and LNE it was observed that the sebacate in the TS appeared blackened, which was assumed to be caused by a contamination from the laboratories standards. As a check in the laboratories proceeding NIM and LNE, which were NPLI and PTB, has shown their standards were operated with absolutely clean sebacate. It was finally concluded that the impurities may have been caused by the TS itself, e.g. by an abrasion in the movable sealing elements of the TS pressure balance. In spite of all the


- 16 -

difficulties and damages the KC could be successfully finished without indication of any changes in the main component of the TS – its piston-cylinder unit. 5. MEASUREMENT PROCEDURES The transfer standard was to be handled and the piston-cylinder assembly mounted in accordance with the instructions given in the User’s Manual Reference Pressure Balance, 5300 Series, Model 5306. Prior to making measurements, the magnetisation of the piston and cylinder was to be checked. The magnetic flow density at their surfaces was not to exceed 2⋅10-4 Tesla. If it was higher, the parts were to be demagnetised and the magnetisation to be checked again. Before mounting the PCU the piston and cylinder were to be cleaned according to the usual practice in the laboratory. The cylinder was to be installed in the mounting post and clamped with a torque of 5.5 Nm measured with a torque spanner sent with the TS. The TS pressure balance was operated with DHS as the working fluid. All NMIs with exception of NIST used DHS in their standards and thus could be connected to the TS directly. NIST standard working with another liquid was isolated from the TS. Nevertheless each laboratory receiving the TS was to check that the TS was filled with clean DHS, and, if it was contaminated, replace it and report about this. To check the tightness of TS, the piston fall rate was to be measured at pressures of (500, 250 and 50) MPa. The reference temperature of the comparison is 20 °C. For measurements performed at a temperature deviating from 20 °C, the effective area of the TS was to be referred to 20 °C using the piston-cylinder thermal expansion coefficient. In the equilibrium state, the TS piston was not to deviate from its working position by more than 0.5 mm. The direction and the rotation speed of the piston were predefined by the motor of the pressure balance model 5306. The rotation was counter clockwise with the speed 32 rpm. If a laboratory operated the TS with the motor being switched off, the piston was to be rotated by hand in the counter clockwise direction with the rotation speed ranging between 30 and 35 rpm. The time between a pressure level change and the acquisition of the data corresponding to the equilibrium of the laboratory standard and the TS was not to be shorter than 5 minutes. The measurements included five cycles each with nominal pressures generated in the following order (50, 100, 150, 200, 250, 300 350, 400, 450, 500, 500, 450, 400, 350, 300, 250, 200, 150, 100, 50) MPa. The generated pressures were not to deviate from these nominal values by more than 0.1 MPa. Thus, 100 measurements were performed in total. The wait time between two consecutive measurements at 500 MPa and between two measurement cycles was to be at least 15 minutes. The effective area of the TS determined for a particular measurement (Ap) referred to 20 °C was calculated by most participants with the equation

( )( )[ ]0cp

nom,0a

1

21

ttααp

πAσρ

ρgm

Ai

ii

p −++

+

−

=∑

, where (1)

mi are true masses of the piston, the weight carrier and the mass pieces placed on the weight carrier of TS;


- 17 -

ρi are densities of the parts with masses mi; ρa is air density; g is local gravity acceleration; σ is surface tension of the TS oil; A0,nom is nominal effective area of the TS; p is pressure determined with laboratory standard at the TS reference level; αp and αc are thermal expansion coefficients of the piston and cylinder materials, respectively; t is temperature of the TS; t0 is reference temperature, t0 = 20 °C. The values of p, ρa and t as well as the masses of the participating laboratory were calculated or measured by the laboratory. All other parameters were provided by the pilot laboratory. In the case of NIM, which used PTB masses, the mass values and densities were provided to NIM by PTB. Instead of equation (1), LNE applied an alternative equation:

( )( )[ ]0cp

nom,0aa0

0

a0

1

21

ttααp

πAσρ

ρρ

ρ

ρgm

Ai

ii

p −++

+

−+−=∑

, in which (2)

mi are conventional masses of the piston, the weight carrier and the mass pieces placed on the weight carrier of TS; ρ0a is conventional value of the air density, ρ0a = 1.2 kg/m3; ρ0 is conventional value of the mass density, ρ0 = 8000 kg/m3 and all other symbols are as specified for equation (1). For each measurement point the participants reported the ambient conditions (air temperature and pressure), temperatures of the LS and the TS, generated pressure, and Ap. Also, for each nominal pressure the participants reported summary results including the sensitivity of the transfer standard, uncertainties of t and p, average Ap, its standard deviation and combined standard uncertainty. Additionally, each participant calculated the zero-pressure effective area of the TS (A0) and its pressure distortion coefficient (λ) which satisfy the equation:

Ap = A0(1+λp) (3) and are based on the results of all 100 measurements. The combined standard uncertainties of A0 and λ as well as a description of how they had been calculated were included.


- 18 -

6. RESULTS 6.1 Stability of the transfer standard The TS stability was measured by the pilot laboratory at the beginning, in the middle, and at the end of the comparison. The results for the distortion-corrected effective areas in the three measurements are presented in Fig. 2 together with the data measured by PTB prior to the comparison in 2007. Results in the 2nd (16 Dec 2009) and 3rd (4 Mar 2010) measurements agree much better with each other than with the results in the 1st measurement (4 Dec 2008). Here it is necessary to note that the elapsed time between the 2nd and 3rd measurements was much less than the elapsed time between the 1st and 2nd measurement. Since 2007 a drift of the effective area to larger values is observed.

1.961006E-06

1.96094E-06

1.96096E-06

1.96098E-06

1.96100E-06

1.96102E-06

1.96104E-06

1.96106E-06

1.96108E-06

1.96110E-06

1.96112E-06

0 50 100 150 200 250 300 350 400 450 500 550

Ao

in m

2

p / MPa

PTB-2007, before KC

PTB-2007, mean Ao

PTB-2008

PTB-2009

PTB-2010

10 ppm

Figure 2. Stability of the transfer standard. Single values of the effective area

measured by PTB in 2008, 2009 and 2010 However all three measurements during the comparison fully agree within their uncertainties as shown for the averaged effective areas in Fig. 3.


- 19 -

1.961006E+00

1.96094

1.96096

1.96098

1.96100

1.96102

1.96104

1.96106

1.96108

1.96110

1.96112

1.96114

0 50 100 150 200 250 300 350 400 450 500 550

Ao

in m

m2

p / MPa

PTB-2007, before KC

PTB-2008

PTB-2009

PTB-2010

10 ppm

Figure 3. Stability of the transfer standard. Mean effective areas and their standard

uncertainties measured by PTB in 2008, 2009 and 2010 The drift rate of Ap with time (T), dAp/dT/Ap, was determined for each nominal pressure as the slope of a linear fit of the mean Ap values obtained by PTB at this pressure in 2008, 2009 and 2010. Choosing the end of the comparison 2010-03-11 – the middle of the final measurement at PTB – as a reference time point (T0), any effective area measured at time T (Ap,T) can be corrected to this reference time according to

Ap,To = Ap,T × [1 + dAp/dT/Ap × (T0–T)]. (4) The uncertainty of the drift correction (u(∆Ap,T)), u(∆Ap,T) = u(Ap,T × dAp/dT/Ap × (T0–T)), was determined as the standard deviation of the PTB values from 2008, 2009 and 2010 after having corrected them for the drift:

u(∆Ap,T) = StDevAp,To,PTB-2008; Ap,To,PTB-2009; Ap,To,PTB-2010 (5) The PTB values used for the drift correction calculation, the drift rate and the uncertainty for the drift correction are shown in Table 10.


- 20 -

Table 10. Effective areas measured by PTB in 2008, 2009 and 2010 (Ap,PTB), mean

drift rate (d Ap/dT/Ap) and relative standard uncertainty of the drift correction (u(∆∆∆∆Ap,T)/Ap)

Ap,PTB / mm2 dAp/dT/Ap u(∆Ap,T)/Ap

p / MPa 2008-12-06 2009-12-27 2010-03-11 day-1 × 106 50 1.961104 1.961143 1.961148 4.93·10-8 0.5 100 1.961248 1.961257 1.961261 1.44·10-8 0.5 150 1.961369 1.961378 1.961378 1.06·10-8 0.6 200 1.961474 1.961485 1.961486 1.35·10-8 0.2 250 1.961574 1.961588 1.961589 1.66·10-8 0.4 300 1.961669 1.961687 1.961685 1.96·10-8 1.2 350 1.961760 1.961780 1.961777 2.18·10-8 1.4 400 1.961847 1.961869 1.961866 2.37·10-8 1.6 450 1.961932 1.961957 1.961953 2.64·10-8 2.1 500 1.962015 1.962044 1.962040 3.19·10-8 2.2

Figure 4 presents the maximum drift of the effective area from 2008-12-06 to 2010-03-11 with the vertical bars showing the standard uncertainties of the drift correction.

0

5

10

15

20

25

0 50 100 150 200 250 300 350 400 450 500 550

dA

p/d

T/A

p * ∆∆ ∆∆

Tm

ax×× ××

106

p / MPa

Figure 4. Maximum drift of the effective area over the time of the comparison with the

vertical bars indicating the standard uncertainty of the drift correction The drift corrections for each participant at each pressure are given in Table 11.


- 21 -

Table 11. Relative drift corrections (∆∆∆∆Ap,T/Ap) to be applied to effective areas Ap,T

measured at pressure (p) and time (T) to transform them to reference time (T0) NMI PTB-1 NIST CENAM NPLI NIM NMIJ PTB-2 LNE PTB-3 Start date 2008-12-04 2009-01-292009-03-11 2009-05-02 2009-07-02 2009-10-14 2009-12-16 2010-02-01 2010-03-04 End date 2008-12-08 2009-02-062009-03-18 2009-05-07 2009-07-07 2009-10-23 2010-01-08 2010-02-05 2010-03-18 Middle 2008-12-06 2009-02-022009-03-14 2009-05-04 2009-07-04 2009-10-18 2009-12-27 2010-02-03 2010-03-11 (T0–T)/days 460 402 362 311 250 144 74 36 0

p/MPa ∆Ap,T/Ap × 106 50 22.7 19.8 17.8 15.3 12.3 7.1 3.6 1.8 0 100 6.6 5.8 5.2 4.5 3.6 2.1 1.1 0.5 0 150 4.9 4.3 3.8 3.3 2.7 1.5 0.8 0.4 0 200 6.2 5.4 4.9 4.2 3.4 1.9 1.0 0.5 0 250 7.6 6.7 6.0 5.2 4.1 2.4 1.2 0.6 0 300 9.0 7.9 7.1 6.1 4.9 2.8 1.4 0.7 0 350 10.0 8.8 7.9 6.8 5.4 3.1 1.6 0.8 0 400 10.9 9.5 8.6 7.3 5.9 3.4 1.7 0.9 0 450 12.1 10.6 9.5 8.2 6.6 3.8 1.9 0.9 0 500 14.7 12.8 11.5 9.9 8.0 4.6 2.3 1.1 0

As a PTB result in the comparison, the result obtained in 2010 (PTB-3) is used in the following analysis because only this measurement in its extent corresponded to the results of other participants. 6.2 Results of the participants The mean effective areas, the standard deviations of the effective areas at each pressure and the combined relative standard uncertainties of the effective areas reported by the participants (without drift correction) are presented in Table 12. It turns out that some participants have calculated the standard deviation of the mean and some the standard deviation of the distribution of the effective areas. To have a consistent comparison of the performance of each participant’s measurement the standard deviation of the distribution has uniformly been recalculated by the pilot and is additionally reported in Table 12.


- 22 -

Table 12. Effective areas (Ap), their relative standard deviations (s(Ap)/Ap) and combined uncertainties (u(Ap)/Ap) as reported by participants (without drift correction) as well as relative standard deviations (ss(Ap)/Ap) of single effective areas calculated by pilot laboratory

p / M

Pa

NIST CENAM NPLI NIM NMIJ LNE PTB

Ap / mm2

s(A

p)/A

p ×

106

u(A

p)/A

p ×

106

s s(A

p)/A

p ×

106

Ap / mm2

s(A

p)/A

p ×

106

u(A

p)/A

p ×

106

s s(A

p)/A

p ×

106

Ap / mm2

s(A

p)/A

p ×

106

u(A

p)/A

p ×

106

s s(A

p)/A

p ×

106

Ap / mm2

s(A

p)/A

p ×

106

u(A

p)/A

p ×

106

s s(A

p)/A

p ×

106

Ap / mm2

s(A

p)/A

p ×

106

u(A

p)/A

p ×

106

s s(A

p)/A

p ×

106

Ap / mm2

s(A

p)/A

p ×

106

u(A

p)/A

p ×

106

s s(A

p)/A

p ×

106

Ap / mm2

s(A

p)/A

p ×

106

u(A

p)/A

p ×

106

s s(A

p)/A

p ×

106

50 1.961148 1.7 17 5.5 1.961140 2.7 85 4.2 1.961074 12.0 40 12.0 1.961074 0.8 17 2.6 1.961138 2.8 17 2.8 1.961188 1.1 11 3.4 1.961148 3.6 15 3.6

100 1.961274 1.0 17 3.2 1.961250 2.2 85 3.4 1.961235 5.6 40 5.6 1.961168 1.5 17 4.9 1.961265 2.5 17 2.5 1.961272 1.1 13 3.5 1.961261 3.0 15 3.0

150 1.961400 0.6 17 2.0 1.961360 1.6 85 2.5 1.961370 7.4 40 7.4 1.961275 1.4 17 4.4 1.961383 1.6 19 1.6 1.961373 1.6 16 5.2 1.961378 4.0 16 4.0

200 1.961509 0.8 17 2.5 1.961470 2.1 85 3.3 1.961485 8.1 40 8.1 1.961374 1.3 18 4.2 1.961491 1.3 20 1.4 1.961473 2.0 18 6.5 1.961486 2.9 17 2.9

250 1.961594 0.2 17 0.7 1.961580 1.7 85 2.8 1.961593 6.3 40 6.3 1.961469 0.8 19 2.5 1.961592 0.9 22 0.9 1.961573 2.1 20 6.6 1.961589 2.1 18 2.1

300 1.961690 1.8 85 2.8 1.961694 8.7 40 8.6 1.961554 0.9 20 2.9 1.961686 1.0 24 1.1 1.961669 2.1 23 6.7 1.961685 1.5 20 1.5

350 1.961790 1.5 85 2.3 1.961789 7.3 40 7.3 1.961636 0.8 21 2.5 1.961776 1.0 27 0.9 1.961764 2.1 25 6.5 1.961777 1.5 22 1.5

400 1.961890 2.1 85 3.1 1.961873 5.9 40 5.9 1.961718 0.8 22 2.4 1.961864 1.2 30 1.1 1.961854 1.7 28 5.4 1.961866 1.6 24 1.6

450 1.961990 1.8 85 2.7 1.961971 8.1 40 8.1 1.961761 1.6 23 5.1 1.961949 1.5 33 1.6 1.961944 1.4 30 4.4 1.961953 1.8 26 1.8

500 1.962100 1.5 85 2.3 1.962073 8.4 40 8.4 1.961837 2.2 25 7.0 1.962032 0.6 36 0.5 1.962038 1.6 33 4.9 1.962040 1.6 28 1.6


- 23 -

The mean effective areas corrected for the transfer standard drift given by eq. (4) with the coefficients given in Table 10 are presented in Table 13. In the following analysis, the drift-corrected effective areas as given in Table 13 with the standard uncertainties as given in Tables 10 and 12 are used. Based on the data in Table 13, the following mean zero pressure effective area <A0> and the distortion coefficient <λ> were obtained by a linear fit to the data of all participants:

<A0> = 1.961065 mm2 and <λλλλ> = 1.018·10-6 MPa-1. (6) Table 13. Effective areas (Ap) corrected for the transfer standard drift

p / M

Pa (Ap + ∆Ap,T) / mm2


50 1.961187 1.961171 1.961104 1.961098 1.961152 1.961191 1.961148

100 1.961285 1.961258 1.961244 1.961175 1.961269 1.961273 1.961261

150 1.961409 1.961367 1.961376 1.961280 1.961386 1.961373 1.961378

200 1.961519 1.961481 1.961493 1.961381 1.961495 1.961474 1.961486

250 1.961607 1.961589 1.961603 1.961477 1.961597 1.961574 1.961589

300 1.961699 1.961705 1.961564 1.961692 1.961671 1.961685

350 1.961802 1.961802 1.961646 1.961782 1.961766 1.961777

400 1.961905 1.961887 1.961729 1.961871 1.961856 1.961866

450 1.962013 1.961987 1.961774 1.961956 1.961945 1.961953

500 1.962120 1.962093 1.961853 1.962041 1.962040 1.962040

Table 14 presents the uncertainties of A0 and λ for the laboratories standards; values for A0 of the TS with their associated standard deviations, standard uncertainties and deviations from the mean zero-pressure effective area, <A0>; and λ of the TS with its associated standard deviation, standard uncertainty, and deviation from the mean pressure distortion coefficient.


- 24 -

Table 14. Relative standard uncertainties of zero-pressure effective areas (u(A0,LS)/A0,LS) and standard uncertainties of distortion coefficients (u(λλλλLS)) of the laboratory standards; zero-pressure effective areas of TS (A0), their relative standard deviations (s(A0)/A0), standard uncertainties (u(A0)/A0) and relative deviations from the average zero-pressure effective area ((A0-<A0>)/<A0>); pressure distortion coefficient of TS (λλλλ), its standard deviation (s(λλλλ)), standard uncertainty (u(λλλλ)) and deviation from the average pressure distortion coefficient (λλλλ-<λλλλ>).

Property NIST CENAM NPLI NIM NMIJ LNE PTB

u(A0,LS) / A0,LS × 106 16 85 9.2 15 16 7.2 13 u(λLS) × (106 MPa) 0 0.12 0.0083 0.037 0.064 0.05 0.05

A0 / mm2 1.961047 1.961079 *)

1.961054 *)

1.961040 *)

1.961016 1.961027 *)

1.961078 1.961084 *)

1.961088 1.961092 *)

1.961076 1.961076 *)

s(A0)/A0·106 2.4 17 *)

8.5 *)

30 *)

8.9 24 *)

2.3 20 *)

13 *)

18 18 *)

u(A0)/A0·106 17 26 17 10 23 (A0-<A0>)/<A0>·106 *) 7.5 -5.3 -12.7 -19.1 9.9 14.0 5.6

λ × (106 MPa) *) 1.095 1.088 1.094 0.872 1.001 0.972 1.006

s(λ) × (106 MPa) 0.014 0.11 *)

0.027 *)

0.096 *)

0.077 *)

0.007 0.064 *)

0.045 0.041 *)

0.059 0.059 *)

u(λ) × (106 MPa) 0.014 0.084 0.064 0.045 0.078 (λ-<λ>) × (106 MPa) *) 0.077 0.069 0.075 -0.146 -0.017 -0.046 -0.012 *) These values have been calculated by the pilot laboratory after applying the drift correction to the participants’

results obtained in individual cycles. The laboratories have calculated the standard deviations of A0 and λ in some cases as those of mean and in some cases as those of distribution. For comparison purposes all standard deviations of A0 and λ have been recalculated by the pilot as standard deviations of their distributions after applying the drift correction and are included additionally to the values reported by the participants. This recalculation was performed using equations (7-10). Standard deviation of the pressure-dependent effective area:

( ) ( )

5.02

,2

,

1

−

−

=∑∑

nn

AAn

Asj

jpj

jp

p

ii

i (7)

Zero-pressure effective area and distortion coefficient:

−= ∑∑

ii

jijp pbnA

mnA

i,

,0

1,

0A

b=λ (8)


- 25 -

Standard deviations of the zero-pressure effective area and the distortion coefficient:

( )( )

5.0

2

2

,

20,

2

0 2

−

−−×

−=

∑ ∑

∑∑

i iii

jiijp

ii

ppm

bpAA

mn

pmAs

i

, ( )( )

5.0

2

2

,

20,2

0 2

1

−

−−×

−=

∑ ∑

∑

i iii

jiijp

ppm

bpAA

mn

m

As

i

λ (9)

Slope of dependence Ap(p):

∑∑

∑∑∑

−

−=

ii

ii

jijpi

jijp

ii

pmnpn

ApmAp

bii

2

2

,,

,,

(10)

Here jpi

A , are Ap-values at p = pi; n is number of points at pi, n = 10; m is number of different

pressures, m = 10; i = 1,…,m; j = 1,…,n. Figure 5 shows relative deviations of the participants’ effective areas from the linear fit equation (3) with A0 and λ given in (6).

-120

-100

-80

-60

-40

-20

0

20

40

0 100 200 300 400 500

[Ap

-<A

o>*(

1+<

λλ λλ>p

)]/<

Ao>

×10

6

p / MPaNIST CENAM NPLI NIM NMIJ LNE PTB

Figure 5. Relative deviations of the participants’ results from the linear fit Figures 6 and 7 show the same data with indication of the reported standard and expanded uncertainties (k = 2), respectively. For better readability the results of the participants are slightly shifted from the pressure nominal values.


- 26 -

-150

-100

-50

0

50

100

150

0 100 200 300 400 500

[Ap

-<A

o>*

(1+<

λλ λλ>p

)]/<

Ao>

×10

6

p / MPa


Figure 6. Relative deviations of the participants’ results from the linear fit. Vertical

bars are standard uncertainties of the participants.

-200

-150

-100

-50

0

50

100

150

200

250

0 100 200 300 400 500

[Ap

-<A

o>*

(1+<

λλ λλ>p

)]/<

Ao>

×10

6

p / MPa


Figure 7. Relative deviations of the participants’ results from the linear fit. Vertical

bars are expanded uncertainties (k = 2) of the participants.


- 27 -

6.3 Reference value calculation The key comparison reference value (KCRV) can be calculated in different ways which are considered in the following. First, the reference effective area (Ap,ref) can be defined by the linear fit (Ap,ref,lin.fit) applying eq. (3) to the participants’ results corrected for the transfer standard drift (Ap,i), i indicating the laboratory number, with the coefficients given in (6). With this approach Ap,ref,lin.fit is a linear function of pressure as expected for most pressure balances and does not suffer from random physically irrelevant changes which are usually observed when Ap,ref is calculated as a mean or median value. The disadvantage of this approach lies in the expression of the uncertainty of Ap,ref,lin.fit, because this expression in terms of parameter errors for A0 and λ does not reflect the uncertainty of Ap,ref as observed in the participants’ results. In addition, the linear fit appears less suitable for the particular results of this KC showing a relatively strong non-linearity of the TS effective area with pressure (Fig. 5). Finally, the use of the linear fit was not practised in the past KCs with pressure balances as TS, would not be advantageous in this KC is not considered in the following. Second Ap,ref is calculated at each pressure point of the KC as a non-weighted mean (Ap,ref,mean) using (11), where N is the number of the participants, N = 7. Its standard uncertainty u(Ap,ref,mean) can be calculated as the standard deviation (12).

NAAN

iipp ∑

=

=1

,meanref,, (11)

( ) ( ) ( )5.0

1

2meanref,,,meanref,, 1

−−= ∑=

NAAAuN

ipipp (12)

Third, Ap,ref can be calculated as the weighted mean (Ap,ref,w.mean). This method is recommended in [13] and has been used for evaluation of numerous KCs. Ap,ref,w.mean and u(Ap,ref,w.mean) are calculated by equations (13) and (14). The weighted mean method is applicable only when the results of the participants pass the consistency check based on the chi-squared test. Results are considered as consistent if the observed chi-squared value χ2

obs calculated by (15) is smaller than the value of chi-square distribution calculated for degree of freedom ν = N – 1 at probability Pr = 0.05, χ2(ν, Pr).

( ) ( )∑∑==

=N

i ip

N

i ip

ipp AuAu

AA

1 ,2

1 ,2

,w.meanref,,

1 (13)

( ) ( )5.0

1 ,2w.meanref,,

1−

=

= ∑

N

i ipp Au

Au (14)

( )( )∑

=

−=

N

i ip

pip

Au

AA

1 ,2

2w.meanref,,,2

obsχ (15)

Fourth, Ap,ref can be calculated as a median (16), Ap,ref,med. This is a robust and a preferable method in the case of outlining results [13, 14]. For the median values, the uncertainties can be calculated by (17).


- 28 -

( )p,ip AA medmedref,, = (16)

( ) medref,medref,, med1

858.1p,p,ip AA

NAu −

−= (17)

Results of the KCRV evaluation as mean, weighted mean and median are summarised in Table 15. Table 15. Relative deviations from the linear fit of the KCRV ([ Ap,ref-Ap,lin.fit ]/Ap,ref);

relative standard uncertainties of the KCRV (u(Ap,ref)/Ap,ref) calculated as mean, weighted mean and median; observed chi-squared value (χχχχ2

obs) and value of the chi-square distribution calculated for degree of freedom νννν at probability Pr = 0.05 (χχχχ2

νννν)

p / M

Pa

Mean Weighted mean Weighted mean without NIM

Median

(Ap,

ref,m

ean -

Ap

,lin

.fit)

/ A

p,r

ef,m

ean ×

106

u(A

p,re

f,mea

n) / A

p,re

f,mea

n ×

106

(Ap,

ref,w

.me

an -

Ap

,lin

.fit)

/ A

p,r

ef,w

.me

an ×

106

u(A

p,re

f,w.m

ean)

/ A

p,re

f,w.m

ean ×

106

χ2 obs

χ2 ν, ν

= 7

(Ap,

ref,w

.me

an -

Ap

,lin

.fit)

/ A

p,r

ef,w

.me

an ×

106

u(A

p,re

f,w.m

ean)

/ A

p,re

f,w.m

ean ×

106

χ2 obs

(Ap,

ref,m

ed -

Ap,

lin.fi

t) /

Ap

,re

f,me

d × 1

06

u(A

p,re

f,med)

/ Ap,

ref,m

ed ×

10

6

50 -7.4 19.0 -2.1 6.5 6.7 12.6 3.4 7.1 2.6 -6.4 13.5 100 -6.1 18.5 -4.6 6.9 7.3 12.6 3.4 7.5 0.4 -1.5 4.6 150 1.5 20.7 0.8 7.3 8.8 12.6 10.7 8.1 0.7 6.1 3.4 200 5.9 22.5 4.4 7.8 9.3 12.6 15.3 8.7 1.0 11.2 3.4 250 6.4 23.1 3.5 8.3 8.3 12.6 15.0 9.3 0.4 13.1 5.4 300 2.8 27.1 -6.0 10.4 7.1 11.1 10.6 12.2 0.2 12.6 5.9 350 -0.4 29.9 -11.8 11.2 7.5 11.1 7.5 13.3 0.2 8.3 7.7 400 -5.6 32.0 -19.0 12.1 7.3 11.1 2.2 14.4 0.2 2.5 6.7 450 -12.8 43.0 -32.2 12.9 11.7 11.1 -2.7 15.6 0.3 -4.5 8.8 500 -16.3 47.7 -37.2 13.9 11.8 11.1 -6.1 16.6 0.5 -11.4 11.1

The KCRV calculated from the mean has the highest uncertainty. The weighted mean based on the results of all 7 NMIs fails the consistency check at pressures of 450 MPa and 500 MPa. Following to the recommendation of [13], the consistency check was performed with the weighted mean from which the extremes in this KC, results of NIM (Fig. 5), were withdrawn. In this case, the KCRVs pass the consistency check at all pressures. Therefore, three calculations of the KCRV as the mean, the weighted mean without NIM and the median are principally possible. The results of these three evaluations are shown in Figure 8.


- 29 -

-80

-60

-40

-20

0

20

40

0 100 200 300 400 500

(Ap,

ref-A

p,lin

.fit)

/ Ap,

ref

×10

6

p / MPa

Non-weighted mean

Median

Weighted mean without NIM

Figure 8. Relative deviations of the KCRV calculated as mean, weighted mean without

NIM results and median from the linear fit. Vertical bars are standard uncertainties

From the analysis of these results the median appears as the best choice for the KCRV, because 1) it provides the smallest uncertainty, 2) no discrimination of any participant result is necessary. Therefore, the median and its uncertainty are used as the KCRV and its uncertainty in this KC, Ap,ref = Ap,ref,med, u(Ap,ref) = u(Ap,ref,med), which are shown in Table 16. Table 16. Key comparison reference values (Ap,ref) and their relative standard

uncertainties (u(Ap,ref)/Ap,ref)

p / MPa Ap,ref / mm2 u(Ap,ref) / Ap,ref × 106

50 1.961152 13.5 100 1.961261 4.6 150 1.961376 3.4 200 1.961486 3.4 250 1.961589 5.4 300 1.961688 5.9 350 1.961780 7.7 400 1.961868 6.7 450 1.961955 8.8 500 1.962041 11.1


- 30 -

6.4 Degree of equivalence The degrees of equivalence of the laboratories are expressed by the relative differences of the laboratories’ results from the KCRVs (∆Ap,i/Ap,ref) and the expanded (k = 2) relative uncertainties of these differences (U(∆Ap,i/Ap,ref)) were calculated by:

( ) ref,ref,,,,ref,, ppiTpippip AAAAAA −∆+=∆ and (18)

( ) ( ) ( ) ( )[ ] ref,

21

ref,2

,2

,2

ref,, 2 ppTpippip AAuAuAuAAU +∆+⋅=∆ , (19)

where ∆Ap,T,i and u(∆Ap,T) are the drift corrections and their uncertainties as given in Tables 11 and 10, respectively. The deviations of the participants’ results from the reference values are shown graphically in Figure 9.

-120

-100

-80

-60

-40

-20

0

20

40

60

0 100 200 300 400 500

(Api

-Ap,

ref)

/ Ap,

ref×

106

p / MPa


Figure 9. Relative deviations of the participants' results from the reference values The degrees of equivalence at individual pressures are shown in the figures in Annex A. The error bars in that figures present the expanded (k = 2) relative uncertainties of these deviations calculated according to eq. (19). Numerical data for the deviations and the uncertainties at all pressures are given in Table 17.


- 31 -

Table 17. Relative deviations of the participants’ results from the reference values (∆∆∆∆Ap/Ap) and their expanded uncertainties (U(∆∆∆∆Ap/Ap))

p in MPa

NIST CENAM NPLI NIM NMIJ LNE PTB ∆A

p /A

p ×

106

U(∆

Ap/

Ap)

×

106

∆Ap

/Ap

× 10

6 U

(∆A

p/A

p)

× 10

6

∆Ap

/Ap

× 10

6 U

(∆A

p/A

p)

× 10

6 ∆A

p /A

p ×

106

U(∆

Ap/

Ap)

×

106

∆Ap

/Ap

× 10

6 U

(∆A

p/A

p)

× 10

6 ∆A

p /A

p ×

106

U(∆

Ap/

Ap)

×

106

∆Ap

/Ap

× 10

6 U

(∆A

p/A

p)

× 10

6

50 17.8 44 9.6 173 -24.5 92 -27.6 43 0.0 43 20.1 35 -2.0 40 100 12.3 35 -1.8 169 -9.1 88 -43.8 35 3.9 36 6.1 28 0.0 31 150 16.6 34 -4.5 169 0.0 88 -48.9 35 5.0 38 -1.4 32 0.7 33 200 17.1 34 -2.3 169 3.5 88 -53.6 37 4.5 41 -6.0 37 0.0 35 250 8.8 35 0.0 170 7.1 89 -57.5 40 3.7 45 -7.9 42 -0.4 38 300 5.4 170 8.8 89 -63.6 42 1.6 49 -9.1 47 -1.6 42 350 11.4 170 11.6 89 -68.0 45 1.2 56 -7.2 53 -1.2 47 400 18.9 170 9.7 89 -70.8 46 1.2 62 -6.4 57 -1.2 50 450 30.0 170 16.7 90 -92.1 49 1.0 68 -4.6 63 -1.0 55 500 40.4 171 26.6 91 -95.7 55 0.2 75 -0.2 69 -0.2 61

The degrees of equivalence between the laboratories are presented in the tables in Annex B by the relative differences between the participants’ results (di,j) corrected for the TS drift and their expanded uncertainties (U(di,j)) which were calculated as

( ) ref,,,,,,, pjTpjpiTpipij AAAAAd ∆−−∆+= and (20)

( ) ( ) ( ) ( )[ ] ref,

21

,2

,2

,22 pTpjpipij AAuAuAudU ∆++= . (21)

Note: In eq. (21), the drift uncertainty contribution u2(∆Ap,T) is applied only one time because ∆Ap,T,i and ∆Ap,T,j are correlated. The absolute total drift correction is maximum when laboratory i measured at Tmin and laboratory j at Tmax. In this case, the squared uncertainty contribution due to the drift correction will be maximum and equal to u2(∆Ap,T). 7. DISCUSSION From Tables 10 and 11, the performance of the TS can be considered as acceptable. The typical relative standard deviations of Ap range from 0.5·10-6 to 12·10-6 with most values being around 4·10-6. A comparison of s(Ap) with u(Ap) clearly shows that almost the entire uncertainty of Ap is contributed by the uncertainty of the laboratory standards. The changes of typical s(Ap)/Ap values from laboratory to laboratory demonstrate different performances of pressure measurements. As it is seen in Table 14, the participants claim rather different uncertainties for A0,LS and λLS of their standards. For A0,LS the relative standard uncertainty lies between 7.2·10-6 and 85·10-6, and the standard uncertainty of λLS ranges from 0 to 0.12·10-6 MPa-1. In dependence on the claimed u(A0,LS) and u(λLS), the resulting relative standard uncertainty of Ap of the TS is pressure dependent and ranges from 11·10-6 to 85·10-6 (Table 12). The highest and the lowest uncertainties reported for the same pressure differ by a factor of eight. An analysis of the comparison results in terms of the zero-pressure effective area and pressure distortion coefficient is of interest because these quantities are frequently reported in calibration certificates (Table 14). For all participants, the standard deviation of A0 obtained


- 32 -

by the linear regression is noticeably higher than s(Ap), which expresses the fact of the Ap nonlinearity with pressure. This nonlinearity produces a significant contribution to the uncertainties of A0 and λ of the TS. The relative difference between the maximum and minimum zero-pressure effective areas is equal to 33·10-6 and between the maximum and minimum pressure distortion coefficients to 0.22·10-6 MPa-1. These differences are for most NMIs larger and for some laboratories significantly larger than the expanded uncertainties which are ascribed to the laboratory standards. The maximum difference in λ of 0.22·10-6 MPa-1 is also higher than 0.1·10-6 MPa-1, the value which is currently assumed to be a reasonable uncertainty of the pressure distortion coefficient of pressure balances and is used by many NMIs in their Calibration and Measurement Capabilities (CMC) tables in the BIPM KCDB. This observation may require a re-evaluation of the smallest acceptable uncertainty when it is calculated by the so called “simple theory” i.e. Lamé equations for perfect cylindrical shapes of the piston and cylinder bore and elastic constants provided by pressure balance manufacturers. Among the laboratories reported combined uncertainties for A0 and λ of the TS, all A0 and λ values agree within their expanded uncertainties (k=2). All NMIs with exception of NIM agree with the KCRV within their expanded uncertainties (k = 2), (Table 17 and Annex A). NIM disagrees with the KCRV at pressures from 100 MPa to 500 MPa. Most results agree with the KCRV even within their standard uncertainties (k = 1). A comparison in pairs demonstrates that results of all participants except NIM agree with each other within their expanded uncertainties (k = 2) at all pressures (Annex B). NIM shows disagreement with NIST, NPLI, NMIJ, LNE and PTB at several pressures. Within 180 compared pairs of results, in 26 cases there is disagreement on the level of the expanded uncertainties (k = 2) and in 47 cases on the level of the standard uncertainties (k = 1). 8. SUPPLEMENTARY RESULTS After distribution of the Draft B report LNE informed the pilot laboratory about a mistake in their pressure reference level of 2.5 cm, which occurred from a movement of the laboratory standard to another room shortly before the KC measurements. LNE submitted new results, recalculated with a corrected height difference between the TS and LS. The majority of the participants voted to keep the original LNE result and all related KC calculations, but agreed the corrected LNE result to be additionally reported. Figure 9a shows deviations of the participants’ results from the reference values in the same way as Figure 9 but additionally presents the LNE corrected result.


- 33 -

-120

-100

-80

-60

-40

-20

0

20

40

60

0 100 200 300 400 500

(Ap

i-A

p,r

ef)

/ Ap,

ref×

106

p / MPa

NIST CENAM NPLI NIM NMIJ LNE LNE corrected PTB

Figure 9a. Relative deviations of the participants' results from the reference values with

the addition of the LNE corrected result Numbers of the corrected results' deviations are given in Table 17a. Table 17a. Relative deviations of the LNE corrected results from the reference values

(∆∆∆∆Ap/Ap) and their expanded uncertainties (U(∆∆∆∆Ap/Ap))

p in MPa

LNE corrected

∆Ap

/Ap

× 10

6

U(∆

Ap/

Ap)

×

106

50 15.5 35 100 3.6 28 150 -3.1 32 200 -7.4 37 250 -9.0 42 300 -10.0 47 350 -8.0 53 400 -7.0 57 450 -5.2 63 500 -0.7 69

The use of the LNE corrected results would not produce any change in the equivalence statements drown above.


- 34 -

9. CONCLUSIONS The transfer standard's pressure dependent effective area was stable within (5 to 23)·10-6 in the period of the comparison. For laboratories which have reported the zero-pressure effective area and the pressure distortion coefficient of the transfer standard with their combined standard uncertainties (NIST, NIM, NMIJ, LNE and PTB for A0, and NIM, NMIJ, LNE and PTB for λ) all the results are equivalent within the expanded uncertainties (k = 2). For NMIJ, LNE and PTB the agreement is within the standard uncertainties. For the NMIs’ results compared in pairs, 154 of totally 180 pairs show agreement within the expanded (k = 2) and 133 pairs within the standard uncertainties. Compared on the expanded uncertainty (k = 2) level, only disagreements between the NIM results on one side and the NIST, NPLI, NMIJ, LNE and PTB results on the other side are observed. The uncertainties claimed by the participants for the transfer standard calibrated in the range 50 MPa to 500 MPa (NIST up to 250 MPa) agree with the results of the comparison for all participants with exception of NIM. With the results of this comparison LNE, PTB, NPLI, NMIJ, NIST have supported their measurement capabilities stated in the KCDB of BIPM. The NIM uncertainties claimed in this comparison appear too optimistic. NIM has currently KCDB CMC records for pressures up to 100 MPa. The NIM results in the actual KC agree with the KCDB CMC uncertainties up to 100 MPa, which herewith are supported. For a potential extension of the CMC in the range 100 MPa to 500 MPa, evidently higher uncertainties must be claimed than those claimed by NIM in this KC. KRISS KCDB CMC could not be supported because, after a damage of the KRISS standard, KRISS considered their results, which were analysed within the draft A report and appeared reasonable, as meaningless and withdrew them. VNIIFTRI has currently KCDB CMC records for the pressure range 250 MPa to 1.6 GPa. VNIIFTRI could not support its CMC in this KC because the VNIIFTRI standard was damaged and measurements were not possible. 10. ACKNOWLEDGMENTS The authors thank R.G. Driver (NIST), S.A. Gelany (NIS, Egypt, participated in the NIST measurements), J. Aranzolo-Suárez (CENAM), A.K. Bandyopadhyay (NPLI), L. Yanhua (NIM), H. Kajikawa (NMIJ), T. Rabault (LNE) and T. Konczak (PTB), who have significantly contributed to this comparison either by its organisation, analysing and discussing the results as well as a critical reading of the manuscript or by characterising the transfer standard, carrying out pressure measurements and taking other responsibilities at different stages of this project. 11. REFERENCES 1. Legras J.C., Jäger J., Molinar G.F., Palomino S., Quintas J., White M.R. EUROMET

Intercomparison in the Pressure Range 100 MPa to 700 (1000) MPa, Metrologia, 30 (1994) 721-725

2. 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

3. 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, Metrologia, 36 (1999) 541-544


- 35 -

4. 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, Proceedings of International Symposium on Pressure and Vacuum, IMEKO TC16, Beijing, September 22-24, 2003, Acta Metrologica Sinica Press, 92-104

5. 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, Metrologia, 43 (2006) 311-325

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

7. Kobata T., Olson, D.A., Automating the calibration of two piston gage pressure balances, Proceedings of the National Conference of Standards Laboratories International, 2002

8. Kobata T., Olson D.A., Accurate determination of equilibrium state between two pressure balances using a pressure transducer, Metrologia, 42 (2005) 231-234

9. Kajikawa H., Ide K., Kobata T. Precise determination of the pressure distortion coefficient of new controlled-clearance piston-cylinders based on the Heydemann-Welch model, Rev. Sci. Instrum. 80 (2009) 095101

10. Legras J.C., Huot A., Delajoud P. La référence nationale de pression du BNM dans le domaine de 5 à 200 MPa, Bull. d'Information du BNM, N° 48, Avril 1982, 9-33

11. Legras J.C. Piston gage used as high accuracy standards in the range 0.01 - 1000 MPa. BIPM, Monographie 89/1 (1989) 41-52

12. Le Guinio J., Legras J.C., El-Tawil A. The new standard of BNM-LNE for absolute pressure measurements up to 1 MPa, Metrologia, 36 (1999) 535-539

13. Cox M.G., The evaluation of key comparison data, Metrologia, 2002, 39, 589-595 14. Müller J.W., Possible advantages of a robust evaluation of comparisons, J. Res. Natl.

Inst. Stand. Technol. 105, 551-555, 2000


- 36 -

12. ANNEX A: Relative deviations of the participants results’ from the reference value and the expanded uncertainties (k = 2) of these deviations at pressures 50 MPa to 500 MPa

-200

-150

-100

-50

0

50

100

150

200N

IST

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106

Relative deviations and their expanded uncertaintie s at 50 MPa

-200

-150

-100

-50

0

50

100

150

200

NIS

T

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106



- 37 -

-200

-150

-100

-50

0

50

100

150

200

NIS

T

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106


-200

-150

-100

-50

0

50

100

150

200

NIS

T

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106



- 38 -

-200

-150

-100

-50

0

50

100

150

200

NIS

T

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106


-200

-150

-100

-50

0

50

100

150

200

NIS

T

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106



- 39 -

-200

-150

-100

-50

0

50

100

150

200

NIS

T

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106


-200

-150

-100

-50

0

50

100

150

200

NIS

T

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106



- 40 -

-200

-150

-100

-50

0

50

100

150

200

NIS

T

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106


-200

-150

-100

-50

0

50

100

150

200

NIS

T

CE

NA

M

NP

LI

NIM

NM

IJ

LNE

PT

B

(Api

-Ap,

ref)

/ Ap,

ref×

106



- 41 -

13. ANNEX B: Relative differences between the participants’ results (dij) and their

expanded uncertainties (U(dij)) (k = 2) at pressures 50 MPa to 500 MPa

j

p = 50 MPa

NIST CENAM NPLI NIM NMIJ LNE PTB d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST 8 174 42 94 45 48 18 48 -2 41 20 45 CENAM -8 174 34 192 37 174 10 174 -10 172 12 173

NPLI -42 94 -34 192 3 94 -24 94 -45 91 -22 93 NIM -45 48 -37 174 -3 94 -28 48 -48 41 -26 45 NMIJ -18 48 -10 174 24 94 28 48 -20 41 2 45 LNE 2 41 10 172 45 91 48 41 20 41 22 37 PTB -20 45 -12 173 22 93 26 45 -2 45 -22 37

j

p = 100 MPa


d ij

× 10

6 U

(dij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST 14 173 21 94 56 48 8 48 6 43 12 45 CENAM -14 173 7 191 42 173 -6 173 -8 171 -2 172

NPLI -21 94 -7 191 35 94 -13 95 -15 92 -9 93 NIM -56 48 -42 173 -35 94 -48 49 -50 43 -44 45 NMIJ -8 48 6 173 13 95 48 49 -2 44 4 46 LNE -6 43 8 171 15 92 50 43 2 44 6 40 PTB -12 45 2 172 9 93 44 45 -4 46 -6 40

j

p = 150 MPa


d ij

× 10

6 U

(dij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST 21 173 17 94 66 48 12 50 18 46 16 46 CENAM -21 173 -4 191 44 173 -9 173 -3 172 -5 172

NPLI -17 94 4 191 49 94 -5 96 1 93 -1 94 NIM -66 48 -44 173 -49 94 -54 50 -47 46 -50 47 NMIJ -12 50 9 173 5 96 54 50 6 49 4 49 LNE -18 46 3 172 -1 93 47 46 -6 49 -2 45 PTB -16 46 5 172 1 94 50 47 -4 49 2 45


- 42 -

j

p = 200 MPa


d ij

× 10

6 U

(dij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST 19 172 14 94 71 49 13 52 23 49 17 48 CENAM -19 172 -6 191 51 173 -7 174 4 173 -2 173

NPLI -14 94 6 191 57 95 -1 97 10 95 3 94 NIM -71 49 -51 173 -57 95 -58 54 -48 51 -54 50 NMIJ -13 52 7 174 1 97 58 54 11 54 5 52 LNE -23 49 -4 173 -10 95 48 51 -11 54 -6 49 PTB -17 48 2 173 -3 94 54 50 -5 52 6 49

j

p = 250 MPa


d ij

× 10

6 U

(dij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST 9 172 2 94 66 51 5 55 17 53 9 50 CENAM -9 172 -7 191 58 173 -4 175 8 174 0 173

NPLI -2 94 7 191 65 96 3 98 15 97 8 95 NIM -66 51 -58 173 -65 96 -61 58 -50 56 -57 53 NMIJ -5 55 4 175 -3 98 61 58 12 60 4 57 LNE -17 53 -8 174 -15 97 50 56 -12 60 -8 55 PTB -9 50 0 173 -8 95 57 53 -4 57 8 55

j

p = 300 MPa


d ij

× 10

6 U

(dij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST CENAM -3 191 69 174 4 176 15 175 7 174

NPLI 3 191 72 97 7 100 18 99 10 97 NIM -69 174 -72 97 -65 63 -55 61 -62 57 NMIJ -4 176 -7 100 65 63 11 66 3 63 LNE -15 175 -18 99 55 61 -11 66 -7 61 PTB -7 174 -10 97 62 57 -3 63 7 61


- 43 -

j

p = 350 MPa


d ij

× 10

6 U

(dij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST CENAM 0 191 79 175 10 178 19 177 13 175

NPLI 0 191 80 98 10 103 19 102 13 98 NIM -79 175 -80 98 -69 68 -61 66 -67 61 NMIJ -10 178 -10 103 69 68 8 74 2 70 LNE -19 177 -19 102 61 66 -8 74 -6 67 PTB -13 175 -13 98 67 61 -2 70 6 67

j

p = 400 MPa


d ij

× 10

6 U

(dij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST CENAM 9 191 90 175 18 180 25 178 20 176

NPLI -9 191 81 98 9 107 16 104 11 100 NIM -90 175 -81 98 -72 74 -64 71 -70 65 NMIJ -18 180 -9 107 72 74 8 82 2 77 LNE -25 178 -16 104 64 71 -8 82 -5 74 PTB -20 176 -11 100 70 65 -2 77 5 74

j

p = 450 MPa


d ij

× 10

6 U

(dij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST CENAM 13 191 122 176 29 182 35 180 31 177

NPLI -13 191 109 99 16 110 21 107 18 102 NIM -122 176 -109 99 -93 81 -87 76 -91 70 NMIJ -29 182 -16 110 93 81 6 90 2 84 LNE -35 180 -21 107 87 76 -6 90 -4 80 PTB -31 177 -18 102 91 70 -2 84 4 80


- 44 -

j

p = 500 MPa


d ij

× 10

6 U

(dij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6 d i

j ×

106

U(d

ij)

× 10

6

i

NIST CENAM 14 191 136 177 40 184 41 182 41 179

NPLI -14 191 122 101 26 114 27 110 27 105 NIM -136 177 -122 101 -96 88 -96 82 -96 76 NMIJ -40 184 -26 114 96 88 0 97 0 92 LNE -41 182 -27 110 96 82 0 97 0 87 PTB -41 179 -27 105 96 76 0 92 0 87

Documents

CCM.P-K13 final report - BIPMFinal Report on CCM.P-K13, Version 4 of 2012-04-10 - 4 - - in Oct. 2008 in the range (100 to 500) MPa against 5 mm 2 PCU no. 10; - in Jan. 2009 in the