Theoretical insights on the influence of the experimental plan in the calibration of multicomponent force and moment transducers

Calibration of multicomponent force and moment transducers using uniaxial force standard machines integrated with tilted plates

“…The time duration of a whole measurement campaign is around 24 h, in particular due to the long alignment operations. However, in the future, the possibility to decrease the number of calibration combinations will be investigated as preliminary shown at theoretical level in [22].…”

“…The whole experimental plan for each couple of components is shown in figure 7. Correlation values between each couple of generated forces and moments range from −0.37 to 0.32, thus guarantee minimized uncertainty levels [21,22]. It is also worth noting that, since a high but unavoidable number of combinations has side forces and torsion moments close to zero, the uncertainties associated with their cross-talk effects are expected to be higher compared to the others, as detailed in section 4.2.…”

“…Avoiding correlations between variables is also important to satisfy some assumptions behind the calculation and propagation of uncertainty. Since a full factorial experimental plan is not applicable with this calibration system since each component cannot be independently applied, the starting point is the definition of the values for each independent parameter in order to have, at the same time, a feasible number of measurements to be performed and a wide number of combinations to minimize the correlation between the applied components [22]. The idea of the proposed experimental plan is to locate the transducer into 4 positions, given by different dx and dy misalignment combinations (dx=0 mm dy=0 mm; dx=8 mm dy=0 mm; dx=0 mm dy=16 mm; dx=16 mm dy=8 mm) and at 4 different tilt angles α (0°, 1°, 2° and 3°) and 7 rotations ω (0°, 45°, 90°, 135°, 180°, 270°, 360°), and to apply 4 different load levels F (10 %, 50 %, 80 % and 100 % of the maximum applied force).…”

“…A comprehensive uncertainty evaluation of Aij terms can be performed according to GUM [18,22]. The i×k (6×6) matrix of the variances referred to the single terms of the exploitation matrix, u 2 (A), is given by the general rule of uncertainty propagation, according to equation (6),…”