## 2 Models and Methods  
In this study, the base material of the shaft is a low-alloyed construction steel, 1.0580, according to [33]. The base material of the hub is a heat-treated medium alloy cold work tool steel, 1.3505, according to [34]. A detailed microstructural material analysis as in [35] is not performed in this paper but might be the content of future work. The hollow shaft and hub were thermally joined. There is a smooth connection between the joining parts. The interference fit of the shaft-hub connection is approximately 21 \(\upmu\)m.  
In order to investigate the possible phenomena during the impact load, a test rig was developed, which is shown in Figure 1. The torque is applied in the shaft by a bolt, which introduces a force on a lever of a defined length. The rotation forces the hub to press against a part of the frame. This leads to a preload torque of the shaft-hub connection. In order to determine the preloaded torque, the force is measured via a load cell (5 kN, A. S. T. GmbH, Dresden, Germany). By multiplying the measured force with the length of the lever, the preloaded torque can be calculated. It is important to note that the preload torque must not reach the static transmittable torque of the connection. A mass is then dropped from a height at a defined position. The mass falls perpendicularly to the frame on the shaft (not the hub) to minimize any further torque load on the shaft-hub connection that may arise from the introduced impulse. Please note that the test rig also obtains a bearing frame to stabilize the shaft-hub connection and avoid effects from the bending of the shaft. A marker is placed on the shaft and hub to detect any slippage of the hub. The slippage of the hub is indicated by the markers moving in relation to each other. The impact of the mass induces an oscillation which then leads to the stimulation of the connection at a specific frequency. As a result, the frictional force and the contact pressure in the connection is reduced locally [23; 26; 27; 31] and the transmittable torque of the shaft-hub connection is temporarily reduced. Simulative investigations were conducted alongside the experimental tests to verify this assumption. The simulations were performed with the software Abaqus(tm) 2019 (Co. Simulia, Velizy-Villacoublay, France) and the general work of [36] was taken into account. Linear hexahedral elements of type C3D8R with reduced integration were used in all simulations. Modal analyses were conducted to determine the natural frequencies and mode shapes. As contacts are unaccountable, the shaft-hub connection is modelled as a monolithic structure in the simulation model. Subsequently, the identified natural frequencies were employed in a frequency response analysis. In order to simulate contact pressure accurately, the shaft and the hub are defined as two distinct parts with different material properties. Depending on the stimulated eigenmodes, the radial stress between the shaft and the hub can be reduced. These radial stress reductions indicate the changing of the real contact pressure in a shaft-hub connection. Figure 1: Experimental setup for the impact testing of the preloaded hubs. With the help of the bolt, the lever is turned (the length of the lever is known). The force, generated by pressing the bolt onto the load cell, exerts a torque \(M_{t}\), because the hub is locked. A specific mass is dropped from a defined height via another hollow shaft. That results in different impact energies depending on the height of dropping. In addition to the modal analysis, the experimental test setup is numerically evaluated. The geometry and boundary conditions in the simulation are based on the test setup, which is shown in Figure 2.  
The impact of the mass on the shaft can produce a slip zone in the contact, in addition to the vibration modes. This slip zone temporarily reduces the transmittable torque. To test this phenomenon, the given geometry data and parameters were used to simulate the test sequence in Abaqus(tm).