Título:  Force key comparison CCM.FK2.a.1 : 50 kN and 100 kN. Final report 
Fuente:  Metrología, 53 
Autor/es:  Savarin, Alejandro; Medina, Nieves; Knott, Andy 
Materias:  Metrología; Fuerza; Mediciones; Pesas; Transductores; Instrumentos de medición 
Editor/Edición:  IOP Publishing; 2016 
Licencia:  https://creativecommons.org/licenses/by/3.0/ 
Afiliaciones:  Savarin, Alejandro. Instituto Nacional de Tecnología Industrial (INTI); Argentina Medina, Nieves. (CEM); España Knott, Andy. National Physical Laboratory (NPL); Reino Unido 


Resumen:  This report describes CIPM key comparison CCM.FK2.a.1, a key comparison between force standard machines at the national measurement institutes of Argentina (INTI), Spain (CEM), and the United Kingdom (NPL), at generated forces of 50 kN and 100 kN, in the period from 2010 to 2012. Two transducers were used and the forcetime profile was strictly controlled, to minimise effects of creep. The final results are linked to the KCRV determined in CIPM Key Comparison CCM.FK2.a through the use of one common deadweight force standard machine (NPL's 120 kN machine) in the two comparison exercises. 
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Force Key Comparison CCM.FK2.a.1 (50 kN and 100 kN) Final Report 1 December 2015 Pilot: NPL, United Kingdom Coauthors: Alejandro Savarin (INTI, Argentina) Nieves Medina (CEM, Spain) Andy Knott (NPL, United Kingdom) CCM.FK2.a.1 Final Report, 01.12.2015 Page 1 of 15 Contents 1 Foreword ......................................................................................... 2 2 Background to the comparison................................................................ 2 3 Participants in the comparison ............................................................... 2 4 Principles of the comparison .................................................................. 2 5 Format of the comparison ..................................................................... 4 6 Limitations of the comparison ................................................................ 5 7 Instrumentation used in the comparison .................................................... 5 8 Stability of transducer sensitivity ............................................................ 6 9 Results obtained at participating laboratories ............................................ 10 10 Uncertainty analysis ........................................................................... 13 1 Foreword This report describes CIPM Key Comparison CCM.FK2.a.1, for force values of 50 kN and 100 kN. 2 Background to the comparison The CCM Force Working Group met in October 1998 in Sydney and made decisions about CIPM Key Comparisons for the unit of force. These were to cover four force ranges, with four different pilot laboratories: i) 5 kN – 10 kN ii) 50 kN – 100 kN iii) 500 kN – 1 MN iv) 2 MN – 4 MN Pilot: MIKESRaute, Finland Pilot: NPL, United Kingdom Pilot: PTB, Germany Pilot: NIST, USA Key Comparison ii), piloted by NPL, was officially designated CCM.FK2.a (Scheme A) and CCM.FK2.b (Scheme B) by BIPM. CCM.FK2.a.1 is a pair of subsequent bilateral key comparisons conducted to tie INTI and CEM into the results of CCM.FK2.a and, as such, it was also piloted by NPL using similar equipment and protocols. This report gives the results for CCM.FK2.a.1. 3 Participants in the comparison The three participants in the comparison were NPL (United Kingdom), who acted as the pilot, INTI (Argentina), and CEM (Spain). The work at NPL was performed in November 2010, March/April 2011, November 2011, and January 2012, the work at INTI in January 2011, and the work at CEM in December 2011. 4 Principles of the comparison The purpose of Key Comparisons is to compare the units of measurement as realised throughout the world. In the area of force, the way this is done is by the use of high quality CCM.FK2.a.1 Final Report, 01.12.2015 Page 2 of 15 force transducers subjected to similar loading profiles in national force standard machines, following a strict measurement protocol and using similar instrumentation. The loading scheme shown in Figure 1 was proposed by the CCM Force Working Group and used in both CCM.FK2.a and CCM.FK2.a.1. 0 degree 0 degree 60 degree 3 preloads preload measurements preload measure 1. 2. 3. 1. 2. 3. ment F 2 F 1 0 6 12 18 24 30 60 90 120 150 time in min. Figure 1. Loading scheme with F1 = 50 kN and F2 = 100 kN The force transducer is rotated through a total of 720°. One preload and one measurement (as at 60° in Figure 1) is carried out at 120°, 180°, 240°, 300°, 360°/0°, 60°, 120°, 180°, 240°, 300°, and 360°. The relatively long reading period of six minutes was selected to minimise the influence of creep. The comparison was carried out using two transducers, both with nominal capacity 100 kN. The transducers are detailed in Table 1. Identification Code TrA TrB Manufacturer GTM Sensy Serial Number 42793 19994730004 Capacity 100 kN 100 kN Scheme A A Table 1. Transducers used in the comparison Prior to the comparison, the temperature sensitivities of the two transducers had been determined, to enable corrections to be made for the effect of calibration temperatures differing from the nominal value of 20 C. The results of these temperature tests are shown in Figures 2 and 3, and the assumption is made that the temperature sensitivity determined will be valid at any applied force. CCM.FK2.a.1 Final Report, 01.12.2015 Page 3 of 15 TrA (GTM 42793) : 1 000 kg applied 0.196 160 0.196 150 Deflection 0.196 140 / mV/V 0.196 130 y = 1.48E06x + 1.96E01 0.196 120 0.196 110 10 15 20 25 30 35 Temperature / degC Figure 2. Temperature sensitivity results for TrA at an applied load of 1 000 kg TrB (Sensy 19994730004) : 1 000 kg applied 0.196 120 0.196 110 Deflection 0.196 100 / mV/V 0.196 090 0.196 080 y = 1.41E06x + 1.96E01 0.196 070 10 15 20 25 30 35 Temperature / degC Figure 3. Temperature sensitivity results for TrB at an applied load of 1 000 kg From these test results, relative temperature sensitivities for TrA and TrB of 7.56 × 106 K1 and 7.17 × 106 K1 respectively were determined. The relative uncertainty estimates associated with these values were determined, from analysis of the linear fit results, to be 4.10 × 106 K1 and 1.99 × 106 K1 respectively, at a 95 % (k = 2) level of confidence. 5 Format of the comparison CCM.FK2.a.1 Final Report, 01.12.2015 Page 4 of 15 The comparison was made in a star format; the transducers came back to the pilot after each participating laboratory’s measurements. One complete measurement cycle (pilot – participating laboratory – pilot) is called a loop. The pilot’s first measurement is denoted the Ameasurement and its second, after the participating laboratory, is called the Bmeasurement. The change at the pilot (Bmeasurement – Ameasurement) is called the drift for that particular loop. The reference value for each loop is taken as the mean of the two pilot measurements – this is called the loop value. 6 Limitations of the comparison Due to the fact that there is no real reference value to circulate (as the sensitivity of the force transducers varies over time), the following conditions apply:  each measurement loop is independent of the others  numerical values of different loops are not easily comparable  only relative deviations can be compared  there is no absolute numerical reference value 7 Instrumentation used in the comparison In practice, it is not possible to calibrate the DMP40 measurement instruments used (one at each laboratory) against a single reference standard. The uniformity of the DMP40s used was confirmed by comparison against the same BN100 calibrator unit, circulated with the transducers. Each laboratory measured the indication of its DMP40 against the signal of the BN100 at a number of representative voltage ratios. The deflections obtained at each laboratory were adjusted using the assumption that the signal generated by the BN100 was absolutely correct. For example, if BN100 output settings of +0.0 mV/V and +2.0 mV/V resulted in DMP40 readings of +0.000 012 mV/V and +2.000 042 mV/V, giving a deflection of +2.000 030 mV/V instead of the nominal +2.000 000 mV/V, the assumption was made that the DMP40 was reading 1.5 × 105 too high and the measured deflection was reduced by this relative amount. Figures 4 and 5 show the DMP40 readings at the participating laboratories, at two different BN100 settings, corresponding to the different transducer deflection levels. The values obtained at the pilot vary over the period of the comparison by less than 5 × 106 – this indicates that the instability of the BN100 throughout the comparison is no greater than this value. CCM.FK2.a.1 Final Report, 01.12.2015 Page 5 of 15 BN100 Setting : +2.0 mV/V 2.000 030 2.000 020 Deflection / mV/V 2.000 010 NPL 2.000 000 INTI CEM 1.999 990 Aug 10 Nov 10 Feb 11 Jun 11 Sep 11 Dec 11 Apr 12 Figure 4. BN100 check results for a setting of +2.0 mV/V BN100 Setting : +1.0 mV/V 1.000 015 1.000 010 Deflection / mV/V 1.000 005 NPL 1.000 000 INTI CEM 0.999 995 Aug 10 Nov 10 Feb 11 Jun 11 Sep 11 Dec 11 Apr 12 Figure 5. BN100 check results for a setting of +1.0 mV/V 8 Stability of transducer sensitivity Because the quality of the comparison is dependent upon the three measurements made during each loop, the stability of each transducer’s sensitivity is critical. Tables 2 to 5 detail the results obtained at the pilot and Figures 6 to 9 plot each transducer’s mean deflection over the period of the comparison – these graphs also show the individual data points (at the twelve orientations) from which the mean deflection is calculated. For comparison purposes, in each graph, the yaxis gridline separation is approximately equal to a relative value of 5 × 105. As TrA was also used during the CIPM and subsequent CCM.FK2.a.1 Final Report, 01.12.2015 Page 6 of 15 EURAMET Key Comparisons, and TrB was used during the EURAMET Key Comparison, their results during these periods are also plotted in the relevant figures to show their longterm stability. The adjusted deflections take into account the results of the BN100 checks and also the difference in calibration temperature from the nominal 20 C, using the temperature sensitivity values described earlier. Date 17 Nov 2010 31 Mar 2011 17 Nov 2011 30 Jan 2012 TrA (GTM 42793) – 50 kN Deflection Adjusted Deflection mV/V mV/V 0.999 827 0.999 838 0.999 822 0.999 832 0.999 847 0.999 843 0.999 843 0.999 838 Loop Value mV/V 0.999 827 0.999 840 Table 2. Results obtained from TrA (50 kN) at pilot laboratory Date 17 Nov 2010 31 Mar 2011 17 Nov 2011 30 Jan 2012 TrA (GTM 42793) – 100 kN Deflection Adjusted Deflection mV/V mV/V 1.999 959 1.999 948 1.999 981 1.999 968 1.999 993 1.999 985 1.999 991 1.999 978 Loop Value mV/V 1.999 958 1.999 982 Table 3. Results obtained from TrA (100 kN) at pilot laboratory CCM.FK2.a.1 Final Report, 01.12.2015 Page 7 of 15 Date 16 Nov 2010 1 Apr 2011 18 Nov 2011 31 Jan 2012 TrB (Sensy 19994730004) – 50 kN Deflection Adjusted Deflection mV/V mV/V 0.999 953 0.999 969 0.999 983 0.999 981 0.999 946 0.999 964 0.999 979 0.999 975 Loop Value mV/V 0.999 955 0.999 977 Table 4. Results obtained from TrB (50 kN) at pilot laboratory Date 16 Nov 2010 1 Apr 2011 18 Nov 2011 31 Jan 2012 TrB (Sensy 19994730004) – 100 kN Deflection Adjusted Deflection mV/V mV/V 1.999 841 1.999 848 1.999 827 1.999 836 1.999 876 1.999 865 1.999 867 1.999 854 Loop Value mV/V 1.999 831 1.999 861 Table 5. Results obtained from TrB (100 kN) at pilot laboratory TrA (GTM 42793) : 50 kN 0.999 90 0.999 85 Deflection / mV/V 0.999 80 CCM.FK2.a EURAMET KC CCM.FK2.a.1 0.999 75 01/05 01/07 01/09 01/11 01/13 Figure 6. Stability of TrA at 50 kN throughout the comparison CCM.FK2.a.1 Final Report, 01.12.2015 Page 8 of 15 2.000 1 2.000 0 Deflection / mV/V 1.999 9 TrA (GTM 42793) : 100 kN CCM.FK2.a EURAMET KC CCM.FK2.a.1 1.999 8 01/05 01/07 01/09 01/11 01/13 Figure 7. Stability of TrA at 100 kN throughout the comparison TrB (Sensy 19994730004) : 50 kN 1.000 00 0.999 95 0.999 90 Deflection 0.999 85 / mV/V 0.999 80 0.999 75 0.999 70 0.999 65 0.999 60 07/07 07/08 07/09 EURAMET KC CCM.FK2.a.1 07/10 07/11 07/12 Figure 8. Stability of TrB at 50 kN throughout the comparison CCM.FK2.a.1 Final Report, 01.12.2015 Page 9 of 15 TrB (Sensy 19994730004) : 100 kN 1.999 9 1.999 8 1.999 7 Deflection 1.999 6 / mV/V 1.999 5 1.999 4 1.999 3 1.999 2 07/07 07/08 07/09 EURAMET KC CCM.FK2.a.1 07/10 07/11 07/12 Figure 9. Stability of TrB at 100 kN throughout the comparison 9 Results obtained at INTI and CEM Tables 6 to 9 detail the results obtained at INTI and CEM and give the difference from each loop’s reference value (given in Tables 3 to 6) in both absolute and relative terms. As with the calibrations at the pilot laboratory, the adjusted deflections compensate both for the BN100 values and for the calibrations not being performed at 20 C. TrA (GTM 42793) – 50 kN Date (Lab) 6 Jan 2011 (INTI) 20 Dec 2011 (CEM) Deflection mV/V 0.999 810 0.999 778 Adjusted Deflection mV/V 0.999 807 0.999 776 Loop Value mV/V 0.999 827 0.999 840 Difference mV/V 0.000 020 Relative 1.98E05 0.000 065 6.48E05 Table 6. Results obtained from TrA (50 kN) at INTI and CEM CCM.FK2.a.1 Final Report, 01.12.2015 Page 10 of 15 TrA (GTM 42793) – 100 kN Date (Lab) 6 Jan 2011 (INTI) 20 Dec 2011 (CEM) Deflection mV/V 1.999 943 1.999 888 Adjusted Deflection mV/V 1.999 939 1.999 883 Loop Value mV/V 1.999 958 1.999 982 Difference mV/V Relative 0.000 019 0.93E05 0.000 099 4.94E05 Table 7. Results obtained from TrA (100 kN) at INTI and CEM TrB (Sensy 19994730004) – 50 kN Date (Lab) 12 Jan 2011 (INTI) 15 Dec 2011 (CEM) Deflection mV/V 0.999 954 0.999 935 Adjusted Deflection mV/V 0.999 951 0.999 932 Loop Value mV/V 0.999 955 Difference mV/V 0.000 004 Relative 0.39E05 0.999 977 0.000 045 4.47E05 Table 8. Results obtained from TrB (50 kN) at INTI and CEM TrB (Sensy 19994730004) – 100 kN Date (Lab) 12 Jan 2011 (INTI) 15 Dec 2011 (CEM) Deflection mV/V 1.999 801 1.999 801 Adjusted Deflection mV/V 1.999 798 1.999 796 Loop Value mV/V 1.999 831 Difference mV/V 0.000 033 Relative 1.64E05 1.999 861 0.000 064 3.22E05 Table 9. Results obtained from TrB (100 kN) at INTI and CEM Figure 10 summarises these results, expressed as differences from the loop value, and Figure 11 shows the unweighted mean relative differences from the loop value obtained at forces of 50 kN and 100 kN. Note that weighted mean differences cannot be calculated until estimates of uncertainty have been made. CCM.FK2.a.1 Final Report, 01.12.2015 Page 11 of 15 5.0E05 INTI CEM 0.0E+00 Relative Difference 5.0E05 1.0E04 TrA  50 kN TrA  100 kN TrB  50 kN TrB  100 kN Transducer Figure 10. Summary of results 5.0E05 0.0E+00 Relative Difference 5.0E05 1.0E04 INTI CEM 50 kN 100 kN Applied Force Figure 11. Mean differences obtained from both transducers CCM.FK2.a.1 Final Report, 01.12.2015 Page 12 of 15 10 Uncertainty analysis Table 10 calculates, for each mean deflection obtained in each participating laboratory, an expanded relative uncertainty value. Each uncertainty value is calculated in the same way, with contributions due to the applied force, the reproducibility of the readings (calculated as the standard deviation of the mean), and the resolution of the DMP40. No allowance is made yet for the BN100 checks or temperature corrections – these will be dealt with in conjunction with the effect of drift of the transducer at a later stage. Relative Standard Uncertainty Relative Lab Transducer / Force Expanded Uncertainty Force Reproducibility Resolution (k=2) TrA / 50 kN 5.0E06 TrA / 100 kN 5.0E06 NPL TrB / 50 kN 5.0E06 TrB / 100 kN 5.0E06 TrA / 50 kN 5.0E05 TrA / 100 kN 5.0E05 INTI TrB / 50 kN 5.0E05 TrB / 100 kN 5.0E05 TrA / 50 kN 1.0E05 TrA / 100 kN 1.0E05 CEM TrB / 50 kN 1.0E05 TrB / 100 kN 1.0E05 5.0E06 5.4E06 3.6E06 3.8E06 6.4E06 4.4E06 1.2E06 2.1E06 2.0E06 1.6E06 3.8E06 3.3E06 4.1E07 2.0E07 4.1E07 2.0E07 4.1E07 2.0E07 4.1E07 2.0E07 4.1E07 2.0E07 4.1E07 2.0E07 1.4E05 1.5E05 1.2E05 1.3E05 1.0E04 1.0E04 1.0E04 1.0E04 2.0E05 2.0E05 2.1E05 2.1E05 Table 10. Relative expanded uncertainty value for each mean deflection For each deflection value obtained by INTI or CEM, the difference between it and the loop value is calculated. The uncertainty associated with this difference is a combination of INTI or CEM’s measurement uncertainty, the uncertainty of the loop value, and the uncertainty associated with the temperature corrections. The uncertainty of the loop value includes contributions due to the drift of the transducer, the effect of the BN100 corrections, and any change in the force applied at the pilot laboratory (note that this is smaller than the uncertainty of generated force, as the same masses are used for each pilot calibration – the main contribution will be a change in buoyancy force due to air pressure variation, and it is evident that this effect is negligible when compared to the magnitudes of the drift and BN100 effects). Considering both Figures 4 and 5, and also previous experience, an estimate of a relative standard uncertainty associated with the BN100 corrections of 5 × 106 would not seem unreasonable, and the uncertainty associated with the temperature corrections is simply taken as the difference between calibration temperatures at the pilot and the participating laboratory multiplied by the standard uncertainty associated with the sensitivity value. Drift of each transducer is dealt with by considering the changes between the two deflections measured at the pilot laboratory as the extremes of a CCM.FK2.a.1 Final Report, 01.12.2015 Page 13 of 15 rectangular distribution – this approach does have the danger of possibly underestimating the drift’s magnitude, but the values resulting from this approach do not appear unreasonable when compared with the known history of each device. When the drift, BN100, and temperature uncertainty contributions are incorporated with the uncertainty associated with the deflection at each laboratory, the results are as shown in Figure 12. 1.0E04 INTI 5.0E05 CEM Relative 0.0E+00 Difference 5.0E05 1.0E04 1.5E04 TrA  50 kN TrA  100 kN TrB  50 kN TrB  100 kN Transducer Figure 12. Differences from the loop value together with associated expanded uncertainties The next step is to combine the results from each laboratory at each force and this is done as a weighted mean of each laboratory’s results, giving more weight to the values with lower associated uncertainties. Results are given in Table 11. Lab Force Relative Mean Deviation From Loop Value 50 kN INTI 100 kN 1.0E05 1.4E05 50 kN CEM 100 kN 5.6E05 4.2E05 Relative Expanded Uncertainty (k=2) 1.0E04 1.0E04 2.2E05 2.2E05 Table 11. Relative mean deviation and expanded uncertainty at each force level CCM.FK2.a.1 Final Report, 01.12.2015 Page 14 of 15 Appendix – Key Comparison Reference Values In order to link the results of this comparison to the KCRVs determined in CIPM Key Comparison CCM.FK2.a, the assumption is made that the forces generated by the machine at NPL have not changed significantly. The results of CCM.FK2.a indicate that the 50 kN and 100 kN forces generated by NPL are both 0.5 × 105 smaller than the KCRV, with expanded uncertainty values of 1.6 × 105 and 1.7 × 105 respectively. In order to determine degrees of equivalence for INTI and CEM, their deviations from the loop value need adjusting by the deviation between NPL and the KCRV, and the uncertainties increasing to incorporate the uncertainty in this deviation. When this is done, the figures in Table 12 are calculated and plotted in Figure 13. The conclusions to be drawn from these results, at both force values, are that the INTI results are consistent with their uncertainty claims but the results at CEM are inconsistent with their CMCs. 50 kN 100 kN Laboratory Deviation from KCRV Expanded Uncertainty of Deviation Deviation from KCRV Expanded Uncertainty of Deviation INTI 1.5 10.2 1.9 10.2 CEM 6.1 2.7 4.7 2.8 Table 12. Degrees of equivalence of individual laboratories, all relative figures × 105 1.0E04 5.0E05 Relative 0.0E+00 Difference from 5.0E05 KCRV 1.0E04 1.5E04 INTI: 50 kN INTI: 100 kN CEM: 50 kN CEM: 100 kN Laboratory / Force Figure 13. Deviations from KCRV with associated expanded uncertainties CCM.FK2.a.1 Final Report, 01.12.2015 Page 15 of 15Ver+/ 