## 3 Results
### Influence of the Mechanical Properties of the Material of the Contact Ring  
To reveal the influence of the mechanical properties of the contact ring on the stress distribution of an interference fit, diverse shrink fits were modeled and simulated by FEM considering different values of stiffness (varying the material Young modulus) with a similar or higher strength (yield strength) than the material used (steel AISI 1085) in the conventional shrink fit for the shaft and the hub. As was previously discussed, it is well known that this method for reducing the stress at the shaft/hub interface is effective when the material of the contact ring exhibits more flexibility than the one used for the hub, or in other words, the Young modulus of the contact ring must be lower than the one used for the hub. For these reasons, all the materials with a Young modulus higher than AISI 1085 (\(E\) = 200 GPa) were excluded. Another requirement was the working temperature since during the manufacturing process, the shrink fit can undergo temperatures higher than 200 \({}^{\circ}\)C. Taking into account these requirements, 14 different materials were selected, whose material properties are collected in Table 1. The materials were numbered in such an order decreasing with their Young modulus.  
All the cases simulated correspond to the reference shrink fit 200H7/s6. A total of 28 simulations were carried out; 14 of them correspond to a hub with a contact ring thickness ratio of \(\gamma\) = 0.125, manufactured with each one of the 14 materials listed in Table 1, and on the other hand, the remaining 14 simulations correspond to a contact ring thickness ratio of \(\gamma\) = 0.250 in a similar way. The axial distributions of the radial, tangential, and von Mises stresses were obtained at the interface for each case of study (Figure 12).  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Id.** & **Material** & **Commercial Code** & **E\({}_{\textbf{0}}\) (GPa)** & \(\textbf{v}_{\textbf{0}}\) & \(\boldsymbol{\sigma}_{\textbf{Y}}\) (GPa)** \\ \hline
1 & Stainless steel & 316L & 190 & 0.27 & 310 \\
2 & Cr–Ni & 50 Cr-50 Ni & 190 & 0.20 & 340 \\
3 & NI–Be & 440 & 190 & 0.30 & 1030 \\
4 & Ni–Cu (Monel) & Monel 400 & 180 & 0.32 & 630 \\
5 & NI–Fe & K950S & 160 & 0.29 & 290 \\
6 & Cu–Ni & CuNi2 Si & 150 & 0.34 & 450 \\
7 & Ni low alloy & N03260 & 140 & 0.31 & 295 \\
8 & Cu–Be & TH04 & 124 & 0.28 & 965 \\
9 & Cu–Al & Cu4110 & 120 & 0.34 & 320 \\
10 & Cu–Mn & C67500 & 110 & 0.34 & 310 \\
11 & Ti & Ti24 Al11 Nb & 95 & 0.36 & 581 \\
12 & Zn & Z35841 & 80 & 0.32 & 345 \\
13 & Al–Cu & A9 2618 & 75 & 0.33 & 266 \\
14 & Mg–Al & Electron2C71 & 55 & 0.30 & 310 \\ \hline \end{tabular}
\end{table}
Table 1: Mechanical properties of the materials selected for the contact ring.  
As was observed in the axial distribution of the radial component (Figure 12a), the stress concentration at the hub edge surroundings (45 mm \(<z<\) 50 mm) decreases in a progressive way when materials with a lower Young modulus are used. However, this influence disappears far from the stress concentrator (hub edge) with the stress distribution being very similar for all the materials selected. This supposes that the maximum transmitted torque will undergo slight variations when a contact ring with a lower stiffness were used. In the case of the axial distribution of the tangential stress, the contact ring markedly modifies the magnitude of the stress distribution causing a progressive reduction as the Young modulus is reduced at both the hub edge vicinity and the inner points. As a consequence, the von Mises stress distribution also exhibits similar behavior, decreasing the magnitude throughout the interface as the Young modulus of the contact ring is decreased.