## 3 Results
### Stress Concentrations in Full-Chamfer Hubs (\(\beta=1\))
The SCF \(K_{\rm j}\) is defined [23; 27; 34] as the ratio between the maximum stress obtained by means of FEM simulations, \(\sigma_{\rm j,FEM-max}\), and the corresponding theoretical value, \(\sigma_{\rm j,th}\) (Equations (2) and (3)) as Equation (5) reflects, where subindexes \(j\equiv r\), \(t\), and \(vM\) refer to the radial, tangential, and von Mises stress, respectively:  
\[K_{\rm j}\ =\ \frac{\sigma_{\rm j,FEM-max}}{\sigma_{\rm j,th}} \tag{5}\]  
According to obtained results, a two-linear variation of the radial SCF, \(K_{\rm r}\), with the chamfer angle was obtained for all the dimensionless hub thicknesses, \(\gamma\), considered. The first linear variation (zone A) was extended from \(\alpha=0^{\circ}\) (conventional hub) to a certain angle (around \(13^{\circ}\)-\(15^{\circ}\)) that is denoted as the transition chamfer angle, \(\alpha^{\star}\). The second one (zone B) was extended from the transition angle \(\alpha^{\star}\) up to the maximum chamfer angle considered in this study, \(\alpha=30^{\circ}\). In this way, a high linear drop of \(K_{\rm r}\) with \(\alpha\) (high influence) was obtained for low chamfer angles within the interval \(0^{\circ}<\alpha<\alpha^{\star}\), and soft variations of \(K_{\rm r}\) (second-order influence) were observed for high chamfer angles, \(\alpha>\alpha^{\star}\). The influence of the hub thickness \(\gamma\) on the radial SCF was also revealed from the results plotted in Figure 10a. Regarding zone A (low chamfer angles), soft variations were observed for all the lines obtained for hub thickness \(\gamma>0.375\) and only the line corresponding to the lowest value of \(\gamma=0.250\) was clearly out of this band. However, at zone B (high chamfer angles), the slope of the lines progressively increased with \(\gamma\). In any case, it should be highlighted that the slope of lines in zone B was notably lower than the slope of lines in zone A and, consequently, a soft influence on the radial SCF can be considered for high chamfer angles \(\alpha>\alpha^{\star}\). These results can be understood by taking into account the aforesaid effects of the hub chamfer angle on the stress distributions previously shown in Figure 7. Thus, the high variation of \(K_{\rm r}\) for chamfer angles lower than \(\alpha^{\star}\) is linked to the progressive reduction of the stress at the hub edge surroundings (\(\zeta>0.8\) in Figure 7), reaching an almost plane distribution, i.e., without stress concentrations, for hub chamfer angles close to \(\alpha^{\star}\). Therefore, for such a case, the radial stress was similar to the theoretical value and, consequently, the value of the radial SCF was close to 1. For chamfer angles higher than \(\alpha^{\star}\), the radial stress at the hub edge (\(\zeta=1\)) was lower than the stress at the inner points (\(\zeta=0\)) and, consequently, the maximum value was placed at the hub center. In addition, a soft reduction of the radial stress at the inner points with regard to the theoretical value (given by Equation (2)) is observed in Figure 7 as the chamfer angle increased. Therefore, the radial SCF value given by Equation (5) is slightly lower than 1, as observed in Figure 10a, since the maximum radial stress at the hub center (\(\zeta=0\)) was lower than the value given by theory. This means that a loss of contact pressure (equal to radial stress) would appear if high chamfer angles were used. This is an undesirable scenario since a loss of contact pressure would lead to a loss of the maximum transmitted torque and the performance of the interference fits would be reduced. In Figure 10b the variations of radial SCF, \(K_{\rm r}\) (\(z\)-axis), with the chamfer angle, \(\alpha\) (\(x\)-axis) and hub thickness, \(\gamma\) (\(y\)-axis) are represented in a 3D plot. In this plot, the sections of the surface for a given value of hub thickness \(\gamma\) (\(y\)-axis) are the curves shown in Figure 10a.