## 3 Results
### Stress Concentrations in Partial-Chamfer Hubs (0 \(<\beta<1\))
The variation with the chamfer height, \(\beta\), was nonlinear with a sharp increase for low chamfer heights until reaching a horizontal uniformity similar to that obtained for full-chamfer hubs (\(\beta=1\)). The effect of the chamfer angle on tangential SCF was the opposite of the one observed in the radial SCF. Therefore, the value at which the stable value was reached (transition chamfer height, \(\beta^{\star}\)) increased as the hub chamfer angle increased. By using high chamfer angles, tangential SCFs as high as 1.3 were obtained; however, if intermediate chamfer angles (\(13^{\circ}<\alpha<15^{\circ}\)) were selected, the tangential SCF was slightly incremented. Figure 12d shows the 3D plot of the variations of tangential SCF, \(K_{\rm t}\) (z-axis) with chamfer height, \(\beta\) (\(x\)-axis) and chamfer angle, \(\alpha\) (\(y\)-axis). Notice that the curves shown in Figure 12c are sections for different values of the hub chamfer angle. Thus, the lowest values of tangential SCF were obtained for the conventional case (either line at the plane \(\beta=0\) or line at the plane \(\alpha=0^{\circ}\)). In addition, the curve included within the plane \(\beta=1\) (full-chamfer hub) showed a progressive increment of the \(K_{\rm t}\) with the chamfer angle. In this way, the highest tangential SCF was reached for full-chamfer hubs (\(\beta=1\)) and the highest chamfer angle (\(\alpha=30^{\circ}\)). In fact, this is just the opposite trend of radial SCF. However, for values of \(\alpha\) and \(\beta\) within the recommended range (\(13^{\circ}<\alpha<15^{\circ}\) and \(\beta>0.5\)) previously established for the radial SCF, the increments of the tangential SCF were not so significant. In any case, the effect of the chamfer geometry is clear: a redistribution of stress that reduces radial stress and increases tangential stress. Therefore, cases causing a high reduction of radial stress will exhibit a high increment of tangential stress and vice versa. Finally, regarding the von Mises SCF, the variation was quite similar to the one observed in the radial SCF. Thus, the highest SCF, as high as 1.3, was obtained for the conventional hub case (either \(\beta=0\) or \(\alpha=0^{\circ}\)). As the chamfer height \(\beta\) increased, the von Mises SCF decreased until reaching a uniform value equivalent to the one obtained for full-chamfer hubs (\(\beta=1\)). As the chamfer angle increased, the SCF decrease became sharper and the value of the transition chamfer height, \(\beta^{\star}\) (for which the stable value is reached) was obtained for lower values of the hub thickness in a similar way to that of the radial SCF trend shown in Figure 12a. This supposes that the lowest value of von Mises SCF corresponding to full-chamfer hubs (\(\beta=1\)) is also obtained for partial-chamfer hubs with hub thickness higher than the transition chamfer height. This parameter is dependent on the chamfer angle \(\alpha\). Thus, for intermediate angles (\(\alpha<15^{\circ}\)), \(\beta^{\star}\) was higher than 0.5, and for high chamfer angles \(\beta^{\star}\) was as low as 0.25. It should be highlighted that chamfer angles that significantly reduce the radial SCF also reduce the von Mises SCF. Therefore, the effect of the radial SCF and tangential SCF on the von Mises SCF is clear. The high reduction of the radial SCF compensates for the increment of the tangential SCF, obtaining a reduction of the von Mises SCF. Therefore, the use of the chamfer hubs with the proposed values allows the reduction of the maximum von Mises stress in the shaft-hub interface. In this way, plasticity is less likely to occur at the hub interface. Figure 12f shows the 3D plot of the variations of von Mises SCF, \(K_{\rm vM}\) (z-axis) with chamfer height, \(\beta\) (\(x\)-axis), and chamfer angle, \(\alpha\) (\(y\)-axis). A similar trend to the one previously discussed for the radial SCF was observed but with softer variations. In a similar way, the edges for planes \(\beta=0\) and \(\alpha=0^{\circ}\) represent the conventional hub reaching the maximum \(K_{\rm vM}\).