## 3 Results
### Stress Concentrations in Partial-Chamfer Hubs (0 \(<\beta<1\))
This plot is a useful tool for designing interference fits with partial-chamfer hubs since it allows obtaining the chamfer angle, \(\alpha\), and the chamfer height, \(\beta\), that reduce the radial SCF for a given hub thickness \(\gamma\). According to the results, a decrease of the transition chamfer angle with the chamfer height was observed up to \(\beta\) = 0.5 and, afterward, a uniform value was obtained up to the full-chamfer hub case (\(\beta\) = 1). The variations were sharper for low values of the hub thickness \(\gamma<\) 0.25 and for hub thicknesses higher than 0.5, the variation of the transition chamfer angle, \(\alpha^{\star}\), was the same for all the hub thicknesses considered. Low hub chamfer heights can be discarded since the radial SCFs at zone B (Figure 13a-e) were higher than 1. Taking these results into account, the use of partial-chamfer hubs with hub thicknesses \(\gamma\) = 0.5 and hub chamfer heights \(\beta\) = 0.5 would cause the same effects in terms of reducing the radial and von Mises SCF observed in full-chamfer hubs. Therefore, the design of partial-chamfer hubs is straightforward; the optimal chamfer angle is \(\alpha=\) 15\({}^{\circ}\) considering chamfer heights \(\beta\) higher than 0.5 when using hub thickness \(\gamma\) = 0.5. In this way, the SCFwould be as low as 1, which means that the SCF would be reduced at the interface and, consequently, the design equations could be used for predicting the real stress state of an interference fit. Figure 13: (**a–e**): Radial stress concentration factors as a function of \(\beta\) for different hub thicknesses and (**f**): variation of the transition chamfer angle with the chamfer height for diverse hub thicknesses. Additional simulations were considered to check the validity of the proposed design parameters for different shaft/hub dimensions, diverse interference fits, or different materials. Thus, six different shaft dimensions were considered (two lower and three higher than the reference case) with the same interference fit H7s6 and the same length ratio \(l/L=4\). For all shaft dimensions, the design conditions previously proposed for full chamfer (\(\alpha=15^{\circ}\), \(\gamma=0.5\)) and partial-chamfer hubs (\(\alpha=15^{\circ}\), \(\beta=0.5\), \(\gamma=0.5\)) were analyzed. Thus, the cases considered are the following: (i) 30H7s6; (ii) 40 H7s6; (iii) 50 H7s6 the reference case; (iv) 65 H7s6; (v) 80 H7s6, and, finally, (vi) 100H7s6. The results showed that the radial stress at the hub edge was lower than the radial stress at the hub center for all cases analyzed in a similar way as observed, in Figure 7, for the reference case. Consequently, the SCF reduction was the same for all the cases analyzed, and, hence, the proposed geometry led to the same reduction for any shaft diameter (Figure 14a). Regarding the second analysis, five interference fits recommended by the ISO standard for fits and tolerances [12] were tested for a shaft diameter of 50 mm as follows: (i) 50H7x6 (\(\delta=56.5\)\(\upmu\)m); (ii) 50H7u6 (\(\delta=43\)\(\upmu\)m); (iii) 50H7t6 (\(\delta=35\)\(\upmu\)m); (iv) the reference case, 50H7s6 (\(\delta=29.5\)\(\upmu\)m); and (v) 50H7r6 (\(\delta=24\)\(\upmu\)m). In a similar way as previously discussed, the same SCF reduction was achieved for all the cases of study (Figure 14b) and, hence, the proposed geometry led to similar values for any interference fit selected from the ISO standard recommendation. Figure 14: Variation of the radial, tangential, and von Mises SCFs for full–chamfer (blank symbols) and partial–chamfer hubs (full symbols) with (**a**) diverse shaft dimensions, (**b**) different interference fits, and (**c**) diverse materials. Finally, four different metallic materials were selected for the reference case 50H7s6 as follows: AISI 1080 steel (reference case); (ii) stainless steel 316L (\(E\) = 190 GPa, \(\
u\) = 0.27); (ii) titanium (\(E\) = 95 GPa, \(\
u\) = 0.36); (iii) aluminum (\(E\) = 75 GPa, \(\
u\) = 0.33); and finally a (iv) a magnesium-aluminum alloy (\(E\) = 55 GPa, \(\
u\) = 0.30).