Acta IMEKO, Title ACTA IMEKO ISSN: 2221-870X March 2018, Volume 7, Number 1, 86-88 ACTA IMEKO | www.imeko.org March 2018 | Volume 7 | Number 1 | 86 Cross-floating calibration study. Trim masses: on the standard balance or on the balance under calibration Francisco Flores, Jorge Torres Centro Nacional de Metrologia km 4.5 Carretera a los Cues, Mpio. El Marques, C:P. 76246 Queretaro, Mexico Section: TECHNICAL NOTE Keywords: pressure balances; cross-floating calibration; trim masses Citation: Francisco Flores, Jorge Torres, Cross-floating calibration study. Trim masses: on the standard balance or on the balance under calibration, Acta IMEKO, vol. 7, no. 1, article 17, March 2018, identifier: IMEKO-ACTA-07 (2018)-01-17 Section Editor: Paul Regtien, Measurement Science Consultancy, The Netherlands Received July 27, 2017; In final form November 22, 2017; Published March 2018 Copyright: © 2018 IMEKO. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited Corresponding author: Francisco Flores, e-mail: fflores@cenam.mx 1. INTRODUCTION The pressure balances are used as reference standards to calibrate secondary manometers and other balances. There are different types of pressure balances covering ranges from 3 kPa to 1 GPa. The pressure balances measure relative, absolute or differential pressure and some measure all types of pressure. This paper is a part of a project within Mexico to aid secondary calibration laboratories to better use their high accuracy pressure balances for calibration and internal traceability. The calibration of pressure balances or dead weight balances is of high importance in secondary laboratories, as well as in industry. This type of calibrations is performed by the cross- floating method. The method is for two pressure balances, connected together using a manometric fluid (i.e. gas or liquid) which transmits the pressure between them; the equilibrium must be achieved by adding or removing trim masses (small masses), either in the standard balance or in the balance under calibration. The piston-cylinder of each balance must be located at its floating level. In Mexico, more than 12 secondary laboratories have high accuracy pressure balances as calibration standards. This paper presents the results of a study of high accuracy pressure balances cross-floating calibration comparing the use of the trim masses on the standard balance or on the balance under calibration [1]-[3]. 2. STUDY Two piston-cylinder calibrations (DH Instruments, 5300 model, 8666 serial number, 20 MPa maximum range, CENAMs property) were made (Table 1). The reference standard used was a DH Instruments, 5300 model, 5716 serial number piston- cylinder, 100 MPa maximum range. On the first calibration, the trim masses were added on the pressure balance under Table 1. Standards used. Description Balance Under Calibration Standard Balance Manufacturer DH Instruments DH Instruments Model 5300 5300 Serial number 8666 5716 Range 0.04 MPa to 20 MPa 0.2 MPa to 100 MPa ABSTRACT The pressure balances are used as reference standards to calibrate secondary manometers and other balances. There are different types and models of pressure balances that cover measuring ranges from 3 kPa to 1 GPa. The pressure balances are designed to measure relative, absolute or differential pressure and some balances can measure all types of pressure. This paper presents the results of a study of high accuracy pressure balances cross-floating calibration comparing trim masses on the standard balance or on the balance under calibration. ACTA IMEKO | www.imeko.org March 2018 | Volume 7 | Number 1 | 87 Calibration (Table 2). In the second calibration, the trim masses were added on the standard pressure balance (Table 3). 3. RESULTS To evaluate the results obtained from the two calibrations the criteria used was the normalized error equation method. 𝐸n = 𝑥cal−𝑥ref �𝑈cal 2 −𝑈ref 2 (1) where: En is the normalized error; xcal is the area obtained by one method of calibration; xref is the area obtained by the other method of calibration; Ucal is the expanded uncertainty estimated for one method of calibration, (k = 2); Uref is the expanded uncertainty estimated for the other method of calibration, (k = 2). From the normalized error equation model, if: |En| ≤ 1 the results are compatible, |En| > 1 the results are not compatible. By means of the results included in Tables 2 and 3, we can obtain the effective area and its uncertainty, for each type of calibrations as shown in Tables 4 and 5. Figure 1 shows the results obtained in Tables 4 and 5 for the effective area Aeffe and its uncertainty. Normalized error equation method results can be calculated by means of the data in Tables 4 and 5, as presented in Table 6. Figure 2 graphs the results included in Table 6. Additionally to the calibrations made with the Mexican National Standard shown before (Figures 1 and 2), using the results from the original calibration made by the manufacturer for A0, we can compare the results from both calibrations for A0, as shown in Table 7, where A0 is the effective area at zero pressure. 4. DISCUSSION During the calibrations, all considerations for effective area pressure balance procedure were taken into account. From the two calibrations made, there are only one point bigger than one, En, with not compatible results. The form to realize the Table 4. Results adding trim masses to the balance under calibration. Pressure / kPa Aeffe (20 °C) / m2 Uncertainty / m2 Relative uncertainty / Aeffe Pressure due to the trim masses / kPa 1 995.560 4.902 72 E-05 ± 1.8 E-09 ± 37 E-06 0.835 3 990.331 4.902 82 E-05 ± 1.7 E-09 ± 35 E-06 1.343 5 985.121 4.902 81 E-05 ± 1.7 E-09 ± 35 E-06 1.700 9 974.638 4.902 78 E-05 ± 1.7 E-09 ± 35 E-06 0.880 13 964.110 4.902 79 E-05 ± 1.7 E-09 ± 35 E-06 1.131 17 953.648 4.902 82 E-05 ± 1.7 E-09 ± 35 E-06 1.134 19 948.393 4.902 85 E-05 ± 1.7 E-09 ± 35 E-06 1.413 Table 5. Results adding trim masses to the standard balance. Pressure / kPa Aeffe (20 °C) / m2 Uncertainty / m2 Relative uncertainty / Aeffe Pressure due to the trim masses / kPa 1 994.499 4.903 35 E-05 ± 1.8 E-09 ± 37 E-06 1.473 3 989.208 4.903 08 E-05 ± 1.7 E-09 ± 35 E-06 1.658 5 984.078 4.902 86 E-05 ± 1.7 E-09 ± 35 E-06 1.733 9 973.585 4.902 80 E-05 ± 1.7 E-09 ± 35 E-06 1.718 13 962.929 4.902 83 E-05 ± 1.7 E-09 ± 35 E-06 1.575 17 952.378 4.902 82 E-05 ± 1.7 E-09 ± 35 E-06 1.548 19 947.078 4.902 82 E-05 ± 1.7 E-09 ± 35 E-06 1.523 Figure 1. Results of effective area and its uncertainty for both calibrations made. Table 6. Results adding trim masses to the standard balance. Pressure / kPa Trim masses on the standard balance Aeffe (20 °C) / m2 Trim masses on the balance under calibration Aeffe (20 °C) / m 2 En 1 994.499 4.903 35 E-05 4.902 72 E-05 2.5 3 989.208 4.903 08 E-05 4.902 82 E-05 1.1 5 984.078 4.902 86 E-05 4.902 81 E-05 0.22 9 973.585 4.902 80 E-05 4.902 78 E-05 0.08 13 962.929 4.902 83 E-05 4.902 79 E-05 0.16 17 952.378 4.902 82 E-05 4.902 82 E-05 0.02 19 947.078 4.902 82 E-05 4.902 85 E-05 0.14 Table 2. Adding trim masses to the balance under calibration. Nominal pressure / MPa Masses, Standard balance / kg Masses, Balance under calibration / kg 2.0 2.0 10.004 050 4.0 4.0 20.004 570 6.0 6.0 30.004 910 10.0 10.0 50.005 100 14.0 14.0 70.005 060 18.0 18.0 90.006 250 20.0 20.0 100.007 120 Table 3. Adding trim masses to the standard balance. Nominal pressure / MPa Masses, Standard balance / kg Masses, Balance under calibration / kg 2.0 1.998 900 10.0 4.0 3.998 870 20.0 6.0 5.998 940 30.0 10.0 9.998 930 50.0 14.0 13.998 770 70.0 18.0 17.998 750 90.0 20.0 19.998 730 100.0 ACTA IMEKO | www.imeko.org March 2018 | Volume 7 | Number 1 | 88 adjustment with trim masses is compatible using one or the other method for most of the target points calibrated. As shown in Figures 1 and 2, comparing both results, the most significant difference for high accuracy pressure balances is in the low range of the calibration. On the other hand, the pressure generated by the trim masses, as shown in Tables 4 and 5, is in the order of 1.7 kPa, which is less than 0.009 % of the minimum range measured. 5. CONCLUSIONS When comparing the A0 results between the two methods with the Mexican national standard and alternatively with the results from the original calibration made by the manufacturer, both methods are compatible. Although, slightly better results were obtained by the method using the trim masses on the standard balance. There is still more experiments to be carried out to discriminate other possible effects (i. e. different ranges, uncertainties, etc.). As general recommendation, it is better to use the minimum possible number of masses and trim masses. REFERENCES [1] Sabuga W., Bergoglio M., Rabault T., Waller B., Torres Guzman J. C., Olson D. A., Agarwal A., Kobata T., Bandyopadhyay A.K. [PTB, IMGC, BNM-LNE, NPL, CENAM, NIST, INMS/NRC, NMIJ/AIST, NPLI], Final Report on Key Comparison CCM.P- K7 in the range 10 MPa to 100 MPa of Hydraulic gauge pressure. Metrologia 2005, 42, Tech. Suppl., 07005. [2] Torres-Guzman J. C., Olvera-Arana P., Olson D., Hydraulic gauge pressure SIM comparison for a range up to 100 MPa. The 4th CCM International Conference on Pressure Metrology from Ultra-High Vacuum to very high pressure. England, 2005. [3] Torres Guzmán J. C., Guía y Lineamientos Generales para Comparaciones de Patrones de Medición, Memorias del Segundo Congreso Internacional Metrocal. Concepción, Chile. April 2001. Figure 2. Normalized error equation results for the two calibrations. Table 7. Normalized error equation results of the two calibrations using the manufacturer’s first calibration information as reference. Description A0 (20 °C) / m2 Uncertainty / m2 Relative uncertainty / m2 En Manufacturer 4.902 67 E-05 ± 3.9 E-09 ± 80 E-06 --- Trim masses on the Standard Balance 4.903 17 E-05 ± 2.1 E-09 ± 42 E-06 1.1 Trim masses on the Balance Under Calibration 4.902 76 E-05 ± 1.8 E-09 ± 37 E-06 0.20 -2 -1 0 1 2 3 0 5 000 10 000 15 000 20 000 25 000 N or m al iz ed E rr or Pressure / kPa Normalized Error, comparison between adding trim masses on the Standard Balance and on the Balance Under Calibration Cross-floating calibration study. 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