Calibración De Pesas Por Subdivisión

technique

WEIGHTS

Test procedures for Class E1 weights at the Romanian National Institute of Metrology: Calibration of mass standards by subdivision of the kilogram
ADRIANA VÂLCU, Romanian Bureau of Legal Metrology, National Institute of Metrology, Romania

500 g, 200 g, 200* g, 100 g 50 g, 20 g, 20* g, 10 g 5 g, 2 g, 2* g, 1 g The 1 kg reference standard, of known mass, is used forcalibration. Mass determinations are carried out by subdivision (to link standards having different nominal values up with a reference standard). Depending on the weighing scheme, this procedure requires a specific minimum number of standards. By the method of least squares adjustment, the mass departures and their standard deviations are calculated. Weighing is always carried out as substitutionweighing, i.e. single weights or combinations are always compared with another combination of the same nominal value. The difference between the balance indications has the symbol ∆m and it is necessary to apply air buoyancy corrections to the observed weighing differences. If “y” is the new corrected difference, this gives: y = ∆m + (ρa – ρo)(V1 – V2) where: y ∆m (1)

Abstract The provision of themass scale below one kilogram is achieved by subdivision. This paper describes one of the methods used by INM including details of the weighing techniques, weighing schemes, equipment used and the uncertainty of measurement of all the standards involved.

is the corrected indication; is the difference in balance readings calculated from one weighing cycle (RTTR, where R is the reference standardand T is the test weight); = 1.2 kg ⋅ m-3, the reference air density; ρo = air density at the time of the weighing; and ρa V1, V2 are the volumes of the standards (or the total volume of each group of weights) involved in the measurement. In designing the scheme, all the masses from 1 kg to 1 g are broken down into decades. A weighing scheme with 12 equations per decade is used in the calibration[1]. The first decade includes the 1 kg standard. For subsequent decades the role of the standard is taken by the “1” from the previous decade; thus the 100 g, 10 g masses become intermediate standards, whose uncertainty is propagated directly to masses in the decade they head and hence to those in subsequent decades. With the reference standard, the mass having nominal values: 500 g, 200 g, 200*g, 100 g, Σ100 g (the sum of 50 g, 20 g, 20* g and 10 g from the next decade) shall be calibrated using a 1 kg mass comparator. The observations are of the same accuracy (for all mass comparisons the same balance was used in the first decade). Once all the weighings have been completed, the first step consists in the formation of the design matrix. Matrix “X” contains the information about theequations used (the weighing scheme) and matrix “Y” contains the measured differences from these equations.

1 Introduction
INM is the custodian of the Prototype Kilogram No. 2. As such, it is INM’s task to propagate the Romanian mass scale by subdivision and multiplication of the kilogram. Class E1 weights ensure traceability to the national mass standard (the value of which is derived from theInternational Prototype of the kilogram, maintained by the BIPM) and weights of Class E2 and lower [1]. They are used as standards at the thirteen Romanian calibration laboratories.

2 Test procedures
The set (500...1) g of Class E1 weights usually has the following composition:

OIML

BULLETIN

VOLUME XLII

•

NUMBER 3

•

J U LY 2 0 0 1

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Denote: X = (xij);i = 1...n; j = 1...k; xij = 1, –1 or 0; β is (βj) vector of unknown departures; and Y is (yi) vector of measured values (including buoyancy corrections).
Σ100* g 0 1 0 –1 –1 –1 1 1 –1 –1 –1 –1

where XT is a transpose of X:
–1 –1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 –1 –1 1 1 –1 –1 –1 –1 –1 0 1 1 0 –1 –1 –1 0 0 0 0 1 1 –1 –1 –1 –1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 –1 –1 –1 –1 –1 –1 –1 –1...