Evaluation of balance measurement uncertainty based on standard error of calibration coefficients

The measurement uncertainty of strain gauge balance is one of the important sources of uncertainty in aircraft wind tunnel test data. The conventional methodology obtains the balance calibration formula through the comprehensive loading residual method. The measurement uncertainty introduced by this approach tends to cause an overestimation of the combined measurement uncertainty in the low-load range during wind tunnel test data processing. To this end, a new methodology for evaluating the measurement uncertainty of a balance was proposed. The core idea lay in leveraging the calibration raw data through least-squares regression analysis to quantify the mathematical modeling uncertainty. Specifically, the methodology derived both the standard error of the calibration formula coefficients and residual standard deviation of the calibration formula, thereby systematically assessing the propagated uncertainty components introduced by the mathematical modeling of the balance calibration formula. To verify the effectiveness of this methodology, static calibration, comprehensive loading, loading before wind tunnel testing, and wind tunnel testing were carried out on a 100E balance. The results are as follows: 1) The comprehensive loading results from five different temperature conditions show that the new methodology agrees with the conventional methodology, with a slight difference of –0.017%～0.029% for the normal force (F_Y ), –0.018%～–0.002% for the pitching moment ( Mz ), and –0.006%～0.058% for the axial force (F_X); 2) The loading before wind tunnel testing results show that with the expanded uncertainty factor k = 2, the uncertainty calculated by the new methodology can objectively quantify the measurement uncertainty, while that by the conventional methodology is relatively conservative; 3) The measurement results of the axial force (F_X ) of the balance during the wind tunnel test demonstrate that when compared to the measurement uncertainty characterized by the repeatability standard deviation of the balance, the conventional methodology introduces an additional 3.41 N to 4.42 N of synthetic standard uncertainty through its calibration mathematical model, whereas the proposed methodology exhibits a negligible increment of 0 N to 0.40 N. The proposed methodology evaluates the measurement uncertainty introduced by the mathematical model of the calibration formula, which is objectively reliable without relying on comprehensive loading. It can not only be used to verify the comprehensive loading during the calibration process, but also effectively evaluate loading results before wind tunnel testing. At the same time, it provides a reliable basis for the uncertainty source of the balance calibration mathematical model in wind tunnel test data processing, significantly improving the accuracy of aircraft aerodynamic data evaluation and having important engineering application value.