## 4 Validation with Automotive Production Equipment: Jig Structure
### Validation of Reconstructed Impact Load with Production Equipment  
The accuracy of the reconstructed impact load was investigated with the calculated and measured peak strains and the strain in the steady state at the validation points. The impact-induced peak strain and the strain in the steady state were measured at three validation points of the structure in both experiments and numerical simulation, as presented in Figure 10. The strains measured at Validation points 1 and 2 are the y-strain. The y-axis deformation of Validation points 1 and 2 is caused primarily by a bending force induced by the impact. Mainly tension is generated at Validation point 1, whereas compression is generated at Validation point 2. The error bars in the experimental data describe the deviation in the strain data measured during 11 consecutive impacts. The peak strain and the strain in the steady state measured in the experiments are listed in Tables 4 and 5. The error bars in the numerical simulation are presented to illustrate the uncertainty of the validation positions with respect to those in the experiments. Three elements selected at each validation point are shown in Figure 10a,b. The average peak strain and the strain in the steady state at each validation point are shown in Figure 10c. The average peak strain measured at each validation point for the loading velocity of \(246.8\) mm/s are \(45.09\) and \(-36.82\)\(\upmu\varepsilon\), respectively whereas the calculated values are \(30.47\) and \(-30.00\)\(\upmu\varepsilon\), respectively. The average peak strain measured at each validation point for the loading velocity of \(287.4\) mm/s are \(63.91\), \(-52.27\), and \(-209.63\)\(\upmu\varepsilon\), respectively, whereas the calculated values are \(41.97\), \(-40.27\), and \(-151.33\)\(\upmu\varepsilon\), respectively. The maximum difference between experimentally measured and numerically calculated peak strain is \(21.94\)\(\upmu\varepsilon\) which is at Validation point 1 for the loading velocity of \(287.4\) mm/s. The distribution of peak strains calculated for the validation points is consistent with those measured in the experiments. Although reasonable, the difference in magnitude of peak strain can be reduced by a more sophisticated simulation model of the jig structure with refined tightening bolts and complex features (these had been simplified in this study for computational efficiency).  
Figure 9: Finite element model of production equipment.  
The average strain in the steady state measured at each validation point for the loading velocity of 246.8 mm/s are 16.46 and \(-\)9.73 \(\mu\epsilon\), respectively, whereas the calculated values are 15.07 and \(-\)14.97 \(\mu\epsilon\), respectively. The average strain in the steady state measured at each validation point for the loading velocity of 287.4 mm/s are 14.73 and \(-\)9.18 \(\mu\epsilon\), respectively whereas the calculated values are 16.67 and \(-\)16.57 \(\mu\epsilon\), respectively. The strain in the steady state is caused mainly by the vehicle chassis weight and is consistent regardless of the loading velocity.  
The unknown external impact was determined and validated through experiments on the production equipment. Impact-induced structural strains were predicted with good accuracy by applying the reconstructed impact load in the numerical simulation. These results reveal that the proposed method for determining impact loads can be applied to predict the impact response of production equipment in various fields.  
Figure 10: Validation of reconstructed impact load with production equipment. (**a**) Contour representations of y-axis strain distribution with validation elements of Validation point 1; (**b**) contour representations of y-axis strain distribution with validation elements of Validation point 2; (**c**) comparison of experimentally measured and numerically calculated peak strain; (**d**) comparison of experimentally measured and numerically calculated strain in steady state.