A new approach based on response surface methodology to take into account the effects of interaction between components in a force measurement balance

Effects of the interaction between components have been studied and modeled for a five-component internal strain gauge balance which is extensively used for force and moment measurement in wind tunnels. The calibration matrix has been constructed using a central composite design, designed experiment with additional axial points on the factorial faces and dead-weight loading scheme was developed for simultaneous application of moments and forces. A run efficient test matrix along with star points and replications was included to the scenario. The calibration results were then used to construct a response surface model (RSM), to relate the output voltages and the loads applied to the components. The RSM model obtained for each component revealed mutual couplings between them. Such interactions play a vital role in the measurement accuracy of balances. The interactions between some components may be insignificant and just increase the random errors in a regression model. In this paper, using proper statistical metrics, the significant interactions have been identified and retained in the RSM model while the others were removed. The models obtained by RSM in which the interaction terms have been intellectually selected and considered based on their degree of interaction were then compared with the conventional second-order regression model including all possible interaction terms. The comparisons show a smaller lack of fit error and a better agreement with actual loadings for the present partial interaction method, than that in which all interactions have been taken into account.