## 3 Results and Discussion
Furthermore, localized slip zones can occur at the hub edge. In conjunction with a preload, the slip zones can spread throughout the entire width of the hub (see Figure 9b) and lead to a slippage and may cause the fretting phenomena. Please note that an additional preloading increases the mode-dependent natural frequencies [17]. Those natural frequencies are above those from the studies of [25; 26; 27] but under those from [28] and it can be proven that frictional forces and the resulting contact pressures may reduce at varying frequencies. As also mentioned in [28], we can achieve only a rough qualitative agreement of the experimental and numerical work so far. Figure 10 shows the results of a simulation, in which a ball with a mass \(m=1.6\) kg falls with the velocity \(v=3000\) mm/s at an angular position \(\alpha=90^{\circ}\) on the shaft. The upper plot shows the contact pressure before the impulse is initiated. The application of the impact leads to a deformation of the shaft which results in a change in the contact pressure for a short period of time. At the edge zone, the pressure decreases at an angle of \(0^{\circ}\) to \(90^{\circ}\) and, at the angle \(90^{\circ}\) to \(300^{\circ}\), the pressure increases. The reduction in the pressure results in a slippage of the hub. While the hub is changing in thickness, the results from [26] can be confirmed: the tangential stiffness (which is dependent on the thickness) is very important for the friction force reduction. Figure 11 displays the average contact pressure and the reaction moment at virtual point RP2 in the simulation as a function of time. The torsional preload was measured with a value of 145 Nm. As described above, the deformation of the shaft caused by the impulse results in a change in the mean pressure. It also causes a vibration in the shaft, which can be seen in the wave-shaped mean pressure curve. After the vibration has stopped, the mean pressure returns to its initial state. This brief reduction in the frictional force due to the vibration [25; 26; 27; 28] is sufficient for the hub to slip, as evidenced by the reaction moment's progression. The torque drops from 146 Nm to 134 Nm. Figure 8: Results of the modal analysis exhibit a torsional natural frequency of 5578 Hz and a bending natural frequency of 8155 Hz. Figure 9: The determined natural frequencies are leading to a radial load at the torsional natural frequency (**a**) which may surpass the maximum of transmittable torque and may lead to a slippage. The resulting radial load due to the bend shape natural frequency is shown in (**b**). Figure 12 is showing the simulation result in which the impact (\(m=1.6\) kg, \(v=3000\) mm/s, \(E_{kin}=1.9\) J) was initiated three times at the same position during the captured time. Following the initiation of the first impulse, a significant reduction in the reaction moment is noticeable. The reaction moment drops from 144 Nm to 126 Nm. On triggering the second impulse, the reaction moment decreases only by 1 Nm. No shift in the reaction moment is apparent upon initiating the third impulse. In Figure 13, the influence of the distance between the hub and the point of impact (\(h\)) on the transmittable torque is shown. The results indicate that the biggest reduction in the torque (20 Nm) occurred at the smallest distance of \(h=10\) mm. As the distance (\(h\)) was increased, the effect of the impulse was diminished, with a barely noticeable drop in the reaction moment up to \(h=35\) mm. The results indicate that the closer the deformation field is to the hub due to the impulse, the greater the change in contact pressure and the associated drop in torque. In addition, the results may differ with different natural frequencies of the shaft or a different impact energy which causes different transverse vibrations and may arise in different locking mechanisms in the connection [30]. Figure 11: Simulation result of the impact behavior of the shaft–hub connection.