# Computerized Generation and Finite Element Stress Analysis of Endodontic Rotary Files
## 3 Results
### Parametric Study  
The developed procedure allows for a simple and fast generation of finite element models of endodontic files, and, in consequence, it is especially suitable for performing parametric and optimization studies. In this section, the performance of the proposed procedure is illustrated with three parametric studies, in which the pitch of the active part, the length of the active part and the diameter of the tip were varied. In each parametric study, only one parameter was varied and the rest were kept constant and equal to those shown in Table 1.  
Figure 11 shows the results obtained from the parametric study in which the pitch of the active part was varied. Four different magnitudes were considered for the pitch of the active part, which were between 1 mm and 4 mm. In each case, the endodontic file has been conveniently rotated so the orientation of the cross section at the encastre coincides with that shown in Figure 9. Figure 11a shows the results for the bending analysis. It can be observed that both the maximum von Mises stress and tip deflection reduced as the pitch of the active part increased. The maximum von Mises stress decreased from 517 MPa (when \(p_{z}=1\) mm) to 451 MPa (when \(p_{z}=4\) mm). The tip deflection decreased from 3.38 mm (when \(p_{z}=1\) mm) to 3.17 mm (when \(p_{z}=4\) mm). Figure 10: Stress results for bending analysis: (**a**) detail of the region where maximum von Mises stress takes place and (**b**) evolution of the von Mises stresses along the edge. On the other hand, Figure 11b shows the results for the torsional analysis. In this case, minor variations are observed for the maximum von Mises stress and the tip rotation, indicating that these parameters may be independent of the pitch of the active part (at least in the observed range). Figure 12 shows the results obtained from the parametric study in which the length of the active part was varied. Five different magnitudes were considered for the length of the active part, which were between 14 mm and 18 mm. Figure 12a shows the results for the bending analysis. It can be observed that both the maximum von Mises stress and tip deflection increased as the length of the active part increased. The maximum von Mises stress increased from 399 MPa (when \(L_{ap}=14\) mm) to 554 MPa (when \(L_{ap}=18\) mm). The tip deflection increased from 2.44 mm (when \(L_{ap}=14\) mm) to 4.05 mm (when \(L_{ap}=18\) mm). On the other hand, Figure 12b shows the results for the torsional analysis. As happened in the bending analysis, both the maximum von Mises stress and tip rotation increased as the length of the active part increased. The maximum von Mises stress increased from 690 MPa (when \(L_{ap}=14\) mm) to 960 MPa (when \(L_{ap}=18\) mm). The tip rotation increased from 0.30 rad (when \(L_{ap}=14\) mm) to 0.52 rad (when \(L_{ap}=18\) mm). Finally, Figure 13 shows the results obtained from the parametric study in which the diameter of the tip of the active part was varied. Four different magnitudes were considered for the diameter of the tip of the active part, which were between 0.20 mm and 0.35 mm. Figure 13a shows the results for the bending analysis. It can be observed that both the maximum von Mises stress and tip deflection decreased as the diameter of the tip of the active part increased. The maximum von Mises stress decreased from 630 MPa (when \(d_{ap}=0.20\) mm) to 295 MPa (when \(d_{ap}=0.35\) mm). The tip deflection decreased from 4.20 mm (when \(d_{ap}=0.20\) mm) to 2.01 mm (when \(d_{ap}=0.35\) mm). Figure 11: Results of the parametric study of the pitch of the active part: (**a**) bending analysis and (**b**) torsional analysis. Figure 12: Results of the parametric study of the length of the active part: (**a**) bending analysis and (**b**) torsional analysis. On the other hand, Figure 13b shows the results for the torsional analysis. As happened in the bending analysis, both the maximum von Mises stress and tip rotation decreased as the diameter of the tip of the active part increased.