In industries large forces exceeding the range of available force standard machines should be measured with high accuracy. The build-up system, in which the force to be measured is shared by several force transducers arranged in parallel is an efficient method to measure the large forces. However the relative uncertainty of the build-up system is larger than the uncertainties of other force standard machines. In this study the build-up system was designed and tested to improve its accuracy.
The rotation effects of force transducers on the output of the build-up system were investigated to evaluate the test procedure of the build-up system. In order to deal with all variables simultaneously and reduce the total number of experiments efficiently, matrix experiments using the orthogonal array were carried out. A test procedure for the build-up system was proposed to reduce the systematic deviation from the indirect calibration of the build-up system. Based on the observation of the fluctuation of the force transducer signals, a model of the dynamics of the build-up system was proposed to predict the motion of the deadweight machine which increases random error in force measurement. The analysis of the force transducer signals as well as displacement signals shows the validity of the proposed model.
The setting position of the base platen on the force standard machine does not nearly affect the output of the build-up system, but the positions of force transducers mainly affect it irrespective of the parallelism condition of the build-up system and the bending moment compensations for force transducers. The calibration result of the build-up system from the conventional test procedure may show the large systematic deviation from the indirect calibration result. Therefore the test procedure is proposed in this study to reduce the systematic deviation. The systematic error could be significantly reduced by rotating the force transducers by 90˚ with respect to the fixed base platen. It has been confirmed that the build-up system may be used to measure the dynamic behavior of a deadweight force standard machine. In the force transducer signals of the build-up system the periodic oscillation of frequencies of about 0.23 Hz and 0.8~1.5 Hz were observed for the deadweight force standard machine. The 0.23 Hz component comes from the pendulum motion of the deadweight machine in which the length of the pendulum arm is the distance between the mass center and the geometrical center of the load button. The 0.8~1.5 Hz comes from the bounce-mode oscillation of the deadweight machine in which the combined stiffness of the loading frame and the force transducers corresponds to a spring of a single degree of freedom vibration system.