Analytical Research on Uncertainty of Calibration Equation Coefficient of

The build-up force standard machine, due to its simple and reliable structure as well as its appreciable precision, has found extensive industrial applications. Such machines typically consist of high-precision force transducers complemented by well-engineered structures. The system's output, defined by a force transfer standard calibrated by a deadweight force standard machine, is typically characterized using polynomial expressions. The choice of the calibration equation's order and the associated uncertainty in its coefficients are significant factors influencing the machine's accuracy. However, different countries' regulations and standards do not explicitly prescribe the equation's order. This study, therefore, explores the impact of the calibration equation on force transmission uncertainty. We demonstrate a negative correlation between the uncertainty in calibration equation coefficients and the number of calibration points. By carrying out numerical experiments with polynomial functions of different orders, we compute residuals and uncertainties for the linear coefficient. A comparison of the predicted values from the testing and training datasets suggests that a first-order polynomial function can be reliably used as the calibration equation for force sensors.