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Comparison between matrix method, equation method and full air-buoyancy correction method for dissemination of microgram weights

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Abstract

Over the past 9 years since 2007, there has been growing interest in the field of small weight measurement, like determination of sensitivity property of microbalance. This drives the requirement for more accurate small weight measurement down to microgram level. NMIs researched on the microgram from manufacture, material and shape, storage and holding method, measurement equipment and weighing scheme. Subdivision comparison is commonly adopted and matrix method (MM) is used to solve the measurement Eq.. In this paper, the density of test and standard weight rather than the volume were adopted in MM. Details on how to use this method based on Matlab software were presented. Then the comparison between MM, Eqution method (EM) and full air-buoyancy correction method (FACM) were made. Differences between these three methods were analyzed and evaluation results were given out. Experiment showed that EM and FACM were of the same relative uncertainty, but MM had lower measurement uncertainty than EM and FACM.

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Abbreviations

MM:

Matrix method

EM:

Equation method

FACM:

Full air-buoyancy correction

References

  1. Kim, M.-S. and Pratt, J. R., “Si Traceability: Current Status and Future Trends for Forces Below 10 Micronewtons,” Measurement, Vol. 43, No. 2, pp. 169–182, 2010.

    Article  Google Scholar 

  2. Newell, D. B., Kramar, J. A., Pratt, J. R., Smith, D. T., and Williams, E. R., “The Nist Microforce Realization and Measurement Project,” IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 2, pp. 508–511, 2003.

    Article  Google Scholar 

  3. Madec, T., Mann, G., Meury, P.-A., and Rabault, T., “Micro-Mass Standards to Calibrate the Sensitivity of Mass Comparators,” Metrologia, Vol. 44, No. 5, pp. 266–274, 2007.

    Article  Google Scholar 

  4. Wang, J., Ren, X., Changing, C., and Yang, N., “Research on Uncertainty Evaluation for Matrix Method of Mass Measurement from 500 µg To 50 µg,” Proc. of 21st IMEKO World Congress, 2015.

    Google Scholar 

  5. Jones, C. W., Kramar, J. A., Davidson, S., Leach, R. K., and Pratt, J. R., “Comparison of NIST SIForce Scale to NPL SI Mass Scale,” Proc. of ASPE Annual Meeting, 2008.

    Google Scholar 

  6. Kim, M.-S., Choi, J.-H., Kim, J.-H., and Park, Y.-K., “Si-Traceable Determination of Spring Constants of Various Atomic Force Microscope Cantilevers with a Small Uncertainty of 1%,” Measurement Science and Technology, Vol. 18, No. 11, pp. 3351–3358, 2007.

    Article  Google Scholar 

  7. Chung, J. W., Lee, S. J., and Kim, K. P., “Establishment of Mass Standards from 1 mg to 50 µg,” Proc. of Asia-Pacific Symposium on Measurement of Mass, Force and Torque, pp. 66–70, 2009.

    Google Scholar 

  8. Hu, M. H., Wang, J., Zhang, Y., Cai, C. Q., Zhong, R. L., et al., “Research on Micro-Gram Weight Standards Below 1 mg in NIM,” Proc. of 20th IMEKO World Congress on Metrology for Green Growth, pp. 374–377, 2012.

    Google Scholar 

  9. Ren, X. P., Wang, J., Dong, L., and Wilson, O., “Dissemination of Micro-Gram Weights from 500 µg To 50µg Based on Automatic Mass Measuring System,” Key Engineering Materials, Vols. 645-646, pp. 693–697, 2015.

    Article  Google Scholar 

  10. Wang, J., Fuchs, P., Russi, S., Ren, X., Cai, C., and Yang, N., “Uncertainty Evaluation for a System of Weighing Equations for the Determination of Microgram Weights,” IEEE Transactions on Instrumentation and Measurement, Vol. 64, No. 8, pp. 2272–2279, 2015.

    Article  Google Scholar 

  11. Ren, X. P., Wang, J., Zhang, Y., and Ombati, W., “Calibration of Weights and Weight Sets Based on Micro-Mass Standard Measurement System,” Key Engineering Materials, Vols. 609-610, pp. 1473–1477, 2014.

    Article  Google Scholar 

  12. Kim, M. S., Choi, J. H., and Park, Y. K., “Test of A Microbalance Below 1 mg Using the Electrostatic Load and Micro Weights,” Proc. of Asia-Pacific Symposium on Mass, Force and Torque, pp. 142–146, 2007.

    Google Scholar 

  13. Davidson, S., “Report on EURAMET. MM-S2: Supplementary Comparison of 100 Gram, 10 Gram, 500 Microgram, 200 Microgram and 100 Microgram Weights,” Metrologia, Vol. 48, No. 1A, Paper No. 07005, 2011.

    Article  Google Scholar 

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Correspondence to Xiao-Ping Ren.

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Ren, XP., Wang, J., Cai, CQ. et al. Comparison between matrix method, equation method and full air-buoyancy correction method for dissemination of microgram weights. Int. J. Precis. Eng. Manuf. 18, 1213–1220 (2017). https://doi.org/10.1007/s12541-017-0142-0

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  • DOI: https://doi.org/10.1007/s12541-017-0142-0

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