## 3 Results
### Stress Concentrations in Partial-Chamfer Hubs (0 \(<\beta<1\))
In addition, the sections of the surface for different chamfer angles are the curves shown in Figure 12e. Moreover, the section of the 3D surface for \(\beta=1\)  
(full-chamfer hub case) revealed a two-linear variation with the chamfer angle but in this case with softer changes than in the variations observed in radial SCF. In a similar manner to the radial SCF 3D plot (Figure 12b), an almost flat surface of minimum von Mises SCF appeared for values of the chamfer height (0.4 \(<\beta<\) 1) and chamfer angles (\(\alpha<\) 15\({}^{\circ}\)). Consequently, partial-chamfer hubs with a chamfer height higher than 0.5 and chamfer angles between 13\({}^{\circ}\) and 15\({}^{\circ}\) will exhibit the optimal behavior, a huge reduction of radial SCF, a reduction of von Mises SCF, and a soft increment of the tangential SCF. To go deeper into the analysis, the variation of the radial SCF with the chamfer angle for a given hub thickness is represented in Figure 13 for different values of the chamfer height \(\beta\). Notice that the curves included in this figure are sections of the 3D surface shown in Figure 12b discussed above. A two-linear variation of the radial SCF with the chamfer angle was obtained in partial-chamfer hubs similar to the one previously observed in full-chamfer hubs (Figure 10a). Thus, the maximum value of SCF was located at \(\alpha=0^{\circ}\) (conventional hub) and it progressively decreased as the chamfer angle increased (zone A) until reaching a certain value where the SCF was uniform (zone B). For low hub thicknesses (\(\gamma\) = 0.125) and low chamfer heights (\(\beta<\) 0.1), the transition chamfer angle appeared at high chamfer angles, \(\alpha=\) 45\({}^{\circ}\). However, as the chamfer height increased, the transition chamfer angle progressively reduced until reaching \(\alpha^{\star}=\) 13\({}^{\circ}\) for a chamfer height \(\beta\) = 0.5. For higher chamfer heights \(\beta>\) 0.5, the curves were quite similar. In addition, for low hub heights (\(\beta<\) 0.1), the SCFs at zone B were higher than 1 and they progressively decreased until reaching a value close to 1 for chamfer heights \(\beta>\) 0.5. A similar trend was observed for higher hub thicknesses \(\gamma\) (Figure 13b-e), but in these cases, the transition chamfer angle \(\alpha^{\star}\) for the lowest chamfer height considered (\(\beta\) = 0.05) was progressively lower than the one observed in \(\gamma\) = 0.125 as the hub thickness increased. Differences were only noticeable for low chamfer heights since curves for \(\gamma>\) 0.50 only exhibited slight differences. In addition, the minimum radial SCF (zone B) was always 1 for hub thicknesses lower than 0.5. For \(\gamma>\) 0.5, the minimum \(K_{\rm r}\) decreased as the chamfer height increased, always reaching the lowest value for the full-chamfer hub case (\(\beta=\) 1). Furthermore, it is noticeable that from hub thickness \(\gamma>\) 0.5, zone B is not a horizontal line and a slight decrease of \(K_{\rm r}\) with the chamfer angle was observed, reaching values below 1. The slope of zone B increased with the chamfer height and, hence, values of radial SCF as low as 0.82 were obtained for full-chamfer hubs (\(\beta=\) 1) with high chamfer angles. Note that the decrease of radial SCF below 1 is not adequate, since it means a loss of the contact pressure and consequently a loss of the maximum transmitted torque. Therefore, it can be concluded that high values of \(\gamma\) are not adequate. Therefore, the recommendation is clear: hub thicknesses, \(\gamma\) higher than 0.5 are not recommended due to the loss of contact pressure and hubs with chamfer heights \(\beta\) lower than 0.5 are also not recommended; the optimal chamfer angle, \(\alpha\), is within the range 13\({}^{\circ}<\alpha<\) 15\({}^{\circ}\). Finally, the transition chamfer angle, \(\alpha^{\star}\), was obtained from curves plotted in Figure 13a-e and the variation of such a parameter with the chamfer height \(\beta\) for different values of the hub thickness \(\gamma\) is represented in Figure 13f.