Comparing Weights According to Weighing Cycles with Nonlinear Drift of the Comparator

Cycle weighing is used by metrologists around the world to eliminate drift in comparator readings when comparing the mass of reference weights. Various types of cycles and their descriptions are given in the International Recommendation on legal metrology OIML R111-1-2004 adopted in the Russian Federation as a national standard. They consider cycles under the assumption of linear drift of comparator readings. The article discusses weighing cycles that eliminate nonlinear drift of the comparator. Drift models are proposed in the form of exponential and multinomial laws, which are characterized by a fast dependence of readings at the beginning of the cycle and a slower one at the end of the cycle. The derivation of formulas for the difference between the mass of the verified and the original standard according to four comparator readings at equal time intervals is given. The formulas consist of two components: the first coincides with the formula for linear drift, and the second plays the role of a correction for the drift deviation from linearity. The formulas are also correct for linear drift, since in this case the second components become zero. Estimates of the differences in the mass of the compared weights, taking into account the nonlinearity of the comparator drift, make it possible to estimate the measurement uncertainty for linear and nonlinear drift and become relevant with a constant increase in weighing accuracy, especially when comparing high-precision mass standards.