Final report. T. Priruenrom 1), W. Sabuga 2) and T. Konczak 2) March 2013

Transcription

1 Final reort Results of the bilateral sulementary comarison on ressure measurements in the range (60 to 350) kpa of gauge ressure in gas media APMP.M.P-S4 T. Priruenrom 1), W. Sabuga 2) and T. Konczak 2) March ) 2) National Institute of Metrology (Thailand) (NIMT), Thailand Physikalisch-Technische Bundesanstalt (PTB), Germany

2 1. INTRODUCTION The objective of this bilateral sulementary comarison (SC) is to check equivalence of gas ressure standards of the two institutes, National Institute of Metrology (Thailand) (NIMT) and Physikalisch-Technische Bundesanstalt (PTB, Germany), in the ressure range 60 kpa to 350 kpa in gauge mode. The results of this comarison will be essential to suort the calibration and measurement caabilities (CMC) of NIMT. The ilot laboratory of this SC is NIMT, which has rovided a transfer standard (TS) for the SC. The TS was a iston-cylinder assembly (PCA) with a nominal effective area of 10 cm 2. The TS roerties are described in the Technical Protocol [1]. The measurements were started at NIMT during November The TS was brought to PTB from NIMT on 7 December 2012 and the measurements at PTB were carried out in the time December The TS was brought back to NIMT on 14 December 2012 and the measurements were done at NIMT again to control the transortation effect. All measurements were erformed in accordance with the Technical Protocol [1] at ressures (60, 100, 150, 200, 250, 300 and 350) kpa. This reort resents the results of NIMT and PTB. All uncertainties in this reort are standard ones (k = 1). 2. DESCRIPTION OF THE LABORATORY STANDARD 2.1 NIMT Laboratory Standard The NIMT laboratory standard (LS) used in this comarison was a ressure balance with a PCA of 10 cm 2 manufactured by Fluke Cororation, DH Instruments Division (DHI), USA, and identified by serial number The roerties of the NIMT LS are summarised in Tables 1 3. Table 1: Details of the ressure balance used for the comarison Base Piston-cylinder Weights Manufacturer Model / Serial Descrition DHI DHI DHI PG-7601 / serial no. 867 PC-7100/ TC / serial no MS / serial no. 2111, with carrying bell no Oeration mode #1 : Simle Pressure range [MPa]: 0.35 Thermometer DHI PG-7601 Serial No.: U856 #1 for examle: Simle or controlled-clearance, etc Total mass [kg]: 35 Tyical relative uncertainty of mass ieces (k=1) [m]: 2.5 2

3 Table 2: Details of the iston-cylinder Material Linear thermal exansion coefficient (α) [ C -1 ] Piston Tungsten carbide Cylinder Tungsten carbide Table 3: Details of the effective area of the iston-cylinder Zero-ressure effective area [cm 2 ] at ref. tem., A 0 #3 (Ref. tem.: t 0 ) Pressure distortion coefficient λ 1 #3 [kpa -1 ] Pressure distortion coefficient λ 2 #3 [kpa -2 ] (if alicable) Value Uncertainty [k=1] Traceability # (t 0 : 20 ) A 0 Dimensional measurement, Certificate No PTB Manufacturer #2 for examle: from PTB, Certificate number 1234, or mercury manometer, etc. #3 A = A 0 (1 +λ 1 + λ 2 2 ) Note: The zero-ressure effective area (A 0 ) was determined from dimensional measurements and from cross-float measurements against the other PCAs used as the rimary gas ressure standards at NIMT, described in [2]. The value of ressure distortion coefficient (λ 1 ) has been taken from the manufacturer and its uncertainty is assumed to be 35% (k = 2). 2.2 PTB Laboratory Standard The PTB LS used in this comarison was a ressure balance with a PCA of 10 cm 2 manufactured by Desgranges et Huot (DH) and identified by serial number 288. Its roerties are described in [3] and are summarised in Tables

4 Table 4: Details of the ressure balance used for the comarison Manufacturer Model / Serial Descrition Base PTB - Piston-cylinder DH Serial no. 288 Weights DH Serial no Thermometer Greisinger Elektronic GTF 102 #1 for examle: Simle or controlled-clearance, etc Table 5: Details of the iston-cylinder Material Oeration mode #1 : Simle Pressure range [MPa]: Total mass [kg]: 100 Tyical relative uncertainty of mass ieces (k=1) [m]: 0.5 Linear thermal exansion coefficient (α) [ C -1 ] Piston tungsten carbide Cylinder tungsten carbide Table 6: Details of the effective area of the iston-cylinder Zero-ressure effective area [cm 2 ] at ref. tem., A 0 #3 (Ref. tem.: t 0 ) Value Uncertainty [k=1] Traceability # (t 0 : 20 C) A 0 PTB, dim. measurements and mercury manometer Pressure distortion PTB, elastic coefficient λ #3 1 [kpa -1 ] theory, dim. data, material roerties Pressure distortion coefficient λ 2 #3 [kpa -2 ] (if alicable) #2 for examle: from PTB, Certificate number 1234, or mercury manometer, etc. #3 A = A 0 (1 +λ 1 + λ 2 2 ) Note: The zero-ressure effective area (A 0 ) was determined from dimensional measurements and from measurements against a rimary mercury manometer [3], the latter being described in [4]. The ressure distortion coefficient (λ) of the PCA was determined from its dimensions and the elastic constants of its materials using equation R 2 + R1 R1 3r1 λ= + 4µ , (1) 2E R2 R1 R1 r1 4

5 in which E and µ are Young s modulus and Poisson s coefficient of the iston-cylinder material, R 1 and R 2 are inner and outer cylinder radii, and r 1 is radius of the bore in the iston. Additionally, λ was calculated by the finite element method taking into account the real dimensions of the ga between the iston and cylinder [5]. 3. DETAILS OF THE MEASUREMENT CONDITIONS Details of the measurement conditions are given in Tables 7 9. Table 7: Local gravity and height difference Value [m/s 2 ] NIMT Uncertainty (k=1) [mm] Value [m/s 2 ] PTB Uncertainty (k=1) [mm] Local gravity, g Height difference, h * * It will be ositive, if the level of the LS is higher Table 8: Piston rotation during measurement NIMT PTB LS Rotate by hand, with seed 15 rm Rotate by hand, with seed 20 rm TS Rotate by hand, with seed 15 rm Rotate by hand, with seed 20 rm Table 9: Instruments for measuring environmental condition NIMT PTB Parameter Manufacturer Model Uncertainty [k=1] Temerature 0.25 C Humidity Lufft % Ambient ressure 0.18 mbar Temerature 0.5 C Humidity Vaisala PTU % Ambient ressure mbar 4. CALIBRATION METHOD: TECHNICAL DETAILS 4.1 NIMT The TS PCA was oerated in a DHI latform PG 7601, serial no DHI mass carrying bell, serial no. 316, and DHI mass set, serial no. 2091, were used for oeration. The direct comarison method (also called the fall-rate method) was used in the measurements, according to EURAMET cg 3: Calibration of Pressure Balances, Version 1.0 (03/2011). The 5

6 ressure generated by LS at the reference level of TS and the effective area of TS were calculated with the formulas given in the Technical Protocol [1]. 4.2 PTB The TS PCA was oerated in a DHI latform PG 7601, serial no. 135, belonging to PTB. Also DHI mass carrying bell, serial no. 235, and DHI mass set, serial no. 2067, used for oeration of the TS are roerty of PTB. Pressure differences between TS and LS were measured using a differential ressure cell (DPC) MKS Baratron, tye 698A11TRC, serial no DPC readings measured over the time of 60 s were averaged and then used in the calculation. The absolute values of ressure differences between TS and LS were always smaller than 0.64 Pa. The standard uncertainty of the DPC in this ressure range is smaller than 0.08 Pa. The ressure generated by LS at the reference level of TS,, was calculated with the wellknown formula = g i m (1 ρ i A (1+ λ 0 a / ρ ) + ρ i nom N2 gv (1 ρ )[1+ 2α ( t t )] 0 a / ρ N2 ) + ρ N2 gh (1 ρ a / ρ N2 ) + (2) where: m i are masses of the iston, the weight carrier and the mass ieces laced on the weight carrier; ρ i are densities of the arts with masses m i ; ρ a is air density; ρ N2 is density of nitrogen at ressure and temerature t; g is local gravity acceleration; V is free volume in the iston above the ressure reference level; A 0 is zero-ressure effective area; λ is ressure distortion coefficient; nom is nominal ressure α is thermal exansion coefficient of the iston and cylinder material; t is temerature of the LS; t 0 is reference temerature, t 0 = 20 C; h is height difference between the reference levels of the LS and the TS; is ressure difference between the TS and LS measured with the differential ressure cell. The density of nitrogen was calculated by equations resented in [6]. The density of air that enters the calculation of the buoyancy effect was determined from the so-called BIPM formula [7] using values of room temerature and atmosheric ressure measured during the calibration rocess. The effective area of the TS at ressure and temerature 20 C (A' ) was calculated by formula A ' = g i ' m (1 ρ ' ' [1+ ( α + α c )( t i a ' ' ρ ) i t 0 )] (3) in which: 6

7 m' i are masses of the iston, the weight carrier and the mass ieces laced on the weight carrier on the TS; ρ' i are densities of the arts with masses m' i ; α' and α' c are thermal exansion coefficients of the iston and cylinder materials of the TS; t' is temerature of the TS. The zero-ressure effective area and the ressure distortion coefficient of the TS, A' 0 and λ', were calculated by a linear fit of (A' ; ) data using the model equation A ' ' ' = A (1+ λ ). (4) 0 5. MEASUREMENTS RESULTS The effective area results obtained in individual comlete measuring series of each institute are resented in Table NIMT Results Table 10: Measurement results of NIMT for series 1 of 3 Date: 26 Nov Meas. Local No. Time Nom. R.H. [%] [bar] t t' Pressure Effective area A [cm 2 ] : : : : : : : : : : : : : : t is temerature of the institute s standard; t' is temerature of the TS; ' is the ressure measured with the institute standard at the local gravity g and the local air density ρ a and calculated at the reference level of the TS; A is the effective area of TS at the reference temerature 20 C. 7

8 Table 11: Measurement results of NIMT for series 2 of 3 Date: 27 Nov Meas. Local No. Time Nom. R.H. [%] [bar] t t' Pressure Effective area A [cm 2 ] : : : : : : : : : : : : : : Table 12: Measurement results of NIMT for series 3 of 3 Date: 28 Nov Meas. Local No. Time Nom. R.H. [%] [bar] t t' Pressure Effective area A [cm 2 ] : : : : : : : : : : : : : :

9 5.2 PTB Results Table 13: Measurement results of PTB for series 1 of 3 Date: 10 Dec Meas. Local No. Time Nom. R.H. [%] [bar] t t' Pressure Effective area A [cm 2 ] : : : : : : : : : : : : : : Table 14: Measurement results of PTB for series 2 of 3 Date: 11 Dec Meas. Local No. Time Nom. R.H. [%] [bar] t t' Pressure Effective area A [cm 2 ] :37: :51: :06: :21: :36: :52: :07: :24: :40: :55: :10: :27: :42: :57:

10 Table 15: Measurement results of PTB for series 3 of 3 Date: 12 Dec Meas. Local No. Time Nom. R.H. [%] [bar] t t' Pressure Effective area A [cm 2 ] :31: :46: :01: :17: :32: :48: :01: :13: :29: :44: :59: :14: :29: :41: The results for all of three measuring series are lotted in Figure 1, in which S1, S2 and S3 reresent the result from series 1, 2 and 3, resectively. Effective area of TS (PCU 1671) NIMT_S-1 NIMT_S-2 NIMT_S-3 PTB_S-1 PTB_S-2 PTB_S-3 1 m A' (cm 2 ) (kpa) Figure 1: Distorted effective area results for all of the measuring oints, NIMT and PTB 10

11 The summary of all three measuring series of each institute are given in Tables Table 16: Summary results of NIMT Period: 26 Nov Nov Nom. Tyical min. adjusted mass [mg] 1) Average of A, < A > [cm 2 ] 2) Rel. standard deviation of < A > [10-6 ] 3) Rel. standard uncertainty of ' [10-6 ] 4) Standard uncertainty of t' 5) Rel. standard uncertainty of < A > [10-6 ] 6) Table 17: Summary results of PTB Period: 10 Dec Dec Nom. Tyical standard uncert. of 1) Average of A, < A > [cm 2 ] 2) Rel. standard deviation of < A > [10-6 ] 3) Rel. standard uncertainty of ' [10-6 ] 4) Standard uncertainty of t' 5) Rel. standard uncertainty of < A > [10-6 ] 6) ) the smallest mass adjusted on the iston of the TS to reach the equilibrium between it and the institute s standard, if the classical fall rate method is used. If a differential ressure cell was alied to measure the ressure difference between the laboratory and transfer standard, the tyical uncertainty of the ressure difference between the reference standard and TS due to this method should be given. In this case the heading of this column shall be changed to "Tyical uncertainty of "; 2) average of the A' values measured at the same nominal ressure; 3) standard deviation of the mean value; 4) tye B uncertainty of the ressure at the reference level of TS, which includes uncertainty of ressure generated by the institute s standard, of the height difference between the institute standard and TS, of the density of the ressure transmitting medium, etc.; 5) tye B uncertainty of the temerature measurement on TS; 6) combined uncertainty of the mean value in 2). All the uncertainties are exressed as the standard ones. 11

12 The average of effective area values measured at the same nominal ressure with its uncertainty for each nominal ressure is lotted in Figure 2. In this figure the scale of ressure (in x-axis) has been slightly shifted for a better resolution of the NIMT and PTB mean values. Effective area of TS (PCU 1671) m NIMT PTB NIMT_ave PTB_ave A' (cm 2 ) Figure 2: Average values of the effective areas measured at the same nominal ressure with their exanded uncertainties (k = 2), NIMT and PTB Table 18 shows the relative difference of the effective area values between NIMT and PTB, using the data from Tables 16 and 17, the exanded uncertainties of A' (U) and the normalized error (E n ) that was calculated by the equation below. [ < A' > NIMT < A' > PTB ] / < A' > PTB E n = (5) [ U ( < A' > ) + U ( < A' > )] NIMT PTB Uncertainty at k = (kpa) Table 18: Relative difference of the effective areas and E n Nom. Rel. difference of <A' >, [< A' > NIMT - < A' > PTB]/ < A' > PTB [10-6 ] Rel. uncertainty of <A' > (k=2) U(< A' > NIMT) [10-6 ] U(< A' > PTB) E n 12

13 The maximum difference of the effective area values between NIMT and PTB occurs at the minimum ressure. It is about 4.3 m, which corresonds to E n = At higher ressure the difference becomes smaller. At ressure 350 kpa, the difference is only 1.7 m, which corresonds to E n = The uncertainty claimed by NIMT is almost the same for all nominal ressures, whereas that by PTB decreases with increasing ressure. By a linear fit of (A' ; ) data using the model equation A' = A' 0 (1+λ' ), the zero-ressure effective area and the ressure distortion coefficient of the TS, A' 0 and λ', can be obtained as given in Table 19. Table 19: Zero-ressure effective area (A' 0 ) and ressure distortion coefficient (λ ) of TS with their uncertainties A' 0 [cm 2 ] at ref. tem., 20 C Value NIMT Uncertainty [k=1] ( A' 0 ) Value PTB Uncertainty [k=1] ( A' 0 ) λ' [kpa -1 ] Note: The value of ressure distortion coefficient (λ ) reorted by NIMT was taken from the manufacturer certificate and its uncertainty was assumed to be 35% (k = 2). PTB exlains that the result for λ' cannot be considered as a realistic distortion coefficient because the ressure range of the measurement was too short for an exerimental determination of λ'. This is exressed by the rather big uncertainty of λ'. The distorted effective areas A' from all measurements, the zero-ressure effective areas A' 0, which were calculated using the model equation A' 0 = A' / (1+λ' ) with λ given in Table 19, and the average values of A' 0 with their uncertainties are lotted in Figure 3. 13

14 Effective area of TS (PCU 1671) A'_NIMT A'_PTB A'o_NIMT A'o_PTB A'o_NIMT_ave A'o_PTB_ave A'o+/-U_NIMT A'o+/-U_PTB 5 m Effective area (cm 2 ) (kpa) Uncertainty at k = 2 Figure 3: Plot of the effective areas, A' and A' 0, and the average values of A' 0 with their uncertainties (k = 2) The difference in the zero-ressure effective area of NIMT and PTB is cm 2 or 5.5 m, whereas the value of NIMT is lower than of PTB. The exanded uncertainty (k = 2) of A' 0 claimed by NIMT is 13 m and by PTB is 8 m. Due to the fact that the ressure range of the measurement is too short for an exerimental determination of λ'; the result for λ' cannot be considered as a realistic value. Therefore, its value should not be comared. 6. UNCERTAINTY ESTIMATION 6.1 NIMT The measurement uncertainty of <A' > is determined in accordance with EURAMET cg 3 [8] and the ISO GUM [9]. The uncertainty budget of the <A' > calculated at the minimum and the maximum ressure range, 60 and 350 kpa, are shown in Tables

15 Table 20: Uncertainty budget of the <A' > at 60 kpa Symbol Source of Uncertainties Value Prob. Dist. Divisor Sensitivity Standard Uncer. (m 2 ) DOF const. 1/ u_a 0,std Uncertainty of A 0 standard (m 2 ) 9.8E-09 N 2 1.0E E-09 u_m,std Uncertainty of STD mass (kg) 3.0E-05 N 2 1.6E E-09 u_ρ m,std Uncertainty of STD mass density (kg m -3 ) 5.0E+01 R 3 6.1E E-10 u_t,std Uncertainty of STD tem. ( o C) 2.5E-01 R 3 8.8E E-09 u_m,uuc Uncertainty of UUC mass (kg) 3.0E-05 N 2 1.6E E-09 u_ρ m,uuc Uncertainty of UUC mass density (kg m -3 ) 5.0E+01 R 3 6.1E E-10 u_t,uuc Uncertainty of UUC tem. ( o C) 2.5E-01 R 3 8.8E E-09 u_(α +α c ) Uncertainty of thermal ex. ( o C -1 ) 9.0E-07 R 3 2.3E E-09 u_ρ a Uncertainty of air density (kg m -3 ) 5.9E-03 N 2 1.2E E-10 u_ h Uncertainty of head corr. (m) 2.0E-03 R 3 6.3E E-06 u_ρ f Uncertainty of fluid density (kg m -3 ) 3.7E-03 N 2 0.0E E+00 u_θ Uncertainty of verticality (mm/m) 4.0E-01 R 3 3.9E E-11 u_v Uncertainty of volume UUC (m 3 ) 1.0E-06 R 3 6.4E E-06 u_sens Uncertainty of sensitivity of UUC (kg) 5.0E-06 R 3 1.6E E-10 u_λ,std Uncertainty of STD distortion coeff. (Pa -1 ) 1.5E-12 N 2 9.8E E-16 u B Tye B uncertainty 7.2E E E-06 u A Tye A uncertainty 5.9E-10 u c Combined uncertainty 7.2E E E-06 m 2 m Standard uncertainty (k=1) 6.4E

16 Table 21: Uncertainty budget of the <A' > at 350 kpa Symbol Source of Uncertainties Value Prob. Dist. Divisor Sensitivity Standard Uncer. (m 2 ) DOF const. 1/ u_a 0,std Uncertainty of A 0 standard (m 2 ) 9.8E-09 N 2 1.0E E-09 u_m,std Uncertainty of STD mass (kg) 1.8E-04 N 2 2.8E E-09 u_ρ m,std Uncertainty of STD mass density (kg m -3 ) 5.0E+01 R 3 6.1E E-10 u_t,std Uncertainty of STD tem. ( o C) 2.5E-01 R 3 8.8E E-09 u_m,uuc Uncertainty of UUC mass (kg) 1.8E-04 N 2 2.8E E-09 u_ρ m,uuc Uncertainty of UUC mass density (kg m -3 ) 5.0E+01 R 3 6.1E E-10 u_t,uuc Uncertainty of UUC tem. ( o C) 2.5E-01 R 3 8.8E E-09 u_(α +α c ) Uncertainty of thermal ex. ( o C -1 ) 9.0E-07 R 3 2.3E E-09 u_ρ a Uncertainty of air density (kg m -3 ) 5.9E-03 N 2 1.2E E-10 u_ h Uncertainty of head corr. (m) 2.0E-03 R 3 3.8E E-05 u_ρ f Uncertainty of fluid density (kg m -3 ) 1.0E-02 N 2 0.0E E+00 u_θ Uncertainty of verticality (mm/m) 4.0E-01 R 3 3.9E E-11 u_v Uncertainty of volume UUC (m 3 ) 1.0E-06 R 3 3.9E E-05 u_sens Uncertainty of sensitivity of UUC (kg) 1.0E-05 R 3 2.8E E-10 u_λ,std Uncertainty of STD distortion coeff. (Pa -1 ) 1.5E-12 N 2 9.8E E-16 u B Tye B uncertainty 7.2E E E-05 u A Tye A uncertainty 5.9E-10 u c Combined uncertainty 7.2E E E-05 m 2 m Standard uncertainty (k=1) 6.4E

17 6.2 PTB The calculation of the measurement uncertainty of <A' > is based on the ISO GUM [9]. The list of the main uncertainty quantities, X, their standard uncertainties, u(x), and their contributions to relative uncertainties of <A' >, u(<a' >)/<A' >, at the minimum and maximum ressures are given in Table 22. The contributions of smaller than are omitted. The values of the oututs were calculated by a numerical method (variation of arameters). A comuter rogram calculated the uncertainty in the values of the outut quantities (effective areas) from the uncertainty in the inut quantities. Table 22: List of rincial uncertainty comonents (u) for the effective area <A' > determined at ressures of 60 kpa and 350 kpa Quantity (X) u(x) u(<a' >)/<A' > 60 kpa 350 kpa Gravity acceleration change in 0.5 m X Height difference 0.37 mm Temerature of LS 0.1 C Temerature of TS 0.1 C Thermal exansion coefficient of LS K Thermal exansion coefficient of TS K DPC reading 0.08 Pa Standard deviation of DPC 0.26 Pa Pressure distortion coefficient of LS MPa Free volume in iston of LS 3 cm Non-verticality of NPS 1 mm/m Non-verticality of TS 1 mm/m Const. mass arts (iston, etc.) on LS 7.5 mg Const. mass arts (iston, etc.) on TS 3.8 mg Density of const. mass arts on LS 54 kg/m Density of const. mass arts on TS 51 kg/m Additional mass (deadweights) on LS max. 17 mg Additional mass (deadweights) on TS max. 28 mg Density of additional mass on LS 25 kg/m Density of additional mass on TS 20 kg/m Effective area of LS X Tye B relative uncertainty of <A' > Tye A relative uncertainty of <A' > Combined relative uncertainty of <A' >

18 7. CONCLUSION The relative difference of A' in this bilateral sulementary comarison varies from 1.7 m to 4.3 m, which corresonds to E n = 0.12 to 0.26, resectively. Therefore, it confirms that the gas ressure standards maintained by the two institutes, NIMT and PTB, in the ressure range 60 kpa to 350 kpa in gauge mode are equivalent. The results of this bilateral sulementary comarison suort the calibration and measurement caabilities (CMC) of NIMT in the ressure range 60 kpa to 350 kpa. 8. REFERENCES 1. Sulementary comarison of NIMT and PTB ressure standards in the range 60 kpa to 350 kpa of gas gauge ressure. Technical Protocol, Priruenrom T., Changan T. The rimary gas ressure standards at NIMT, Proceedings of the 6th APMP Pressure & Vacuum Worksho, Wellington, New Zealand, 2012, Klingenberg G., Lüdicke F. Characterization of a ressure balance from dimensional measurements and from ressure comarison exeriments, PTB-Mitteilungen, 1991, 101, Jäger, J.: Use of a recision mercury manometer with caacitance sensing of the menisci, Metrologia, 1993/94, 30, Sabuga W., Priruenrom T., Molinar G., Buonanno G., Rabault T., Wongthe P., Pražák D. FEA calculation of ressure distortion coefficients of gas-oerated ressure balances EURAMET roject 1039, Measurement, 2012, 45, Wagner W., San R. Secial equations of state for methane, argon and nitrogen for the temerature range from 270 to 350 K at ressures u to 30 MPa, Int. J. Thermohysics, 1993, 14, No. 4, Giacomo P. Equation for the determination of the density of moist air (1981), Metrologia, 1982, 18, Calibration of ressure balances, EURAMET cg 3, Version 1.0 (03/2011). 9. Guide to the Exression of Uncertainty in Measurement, ISO GUIDE, Geneva,