## 2 Fatigue Strength Assessment of Real Components
### Fatigue Assessment of the Motorcycle Transport Device  
#### 2.2.1 Background  
The second case study focuses on analysing a transportation system consisting of a motorcycle transport device, an automobile, and a motorcycle. This device is mounted on the car's hitch, as shown in Figure 14. During transportation, it is subjected to random vibrations originating from the road surface over which the movement takes place. While the S-N curves (fatigue strength) of the materials used in the device's construction are well-known, the exact loads and excitations acting on this device remain unknown. The Motorcycle Transport Device analysed in this study is a mechanical system subjected to complex loading conditions during vehicle towing operations. The fatigue analysis of this device was performed using both experimental and computational methods, with a focus on simplifying the power spectral density (PSD) function to reduce computational effort while maintaining accuracy in fatigue life predictions. In the context of the discussed system, which is related to the field of automotive engineering, there is an opportunity to reference the characteristics of excitations--standardized Power Spectral Density (PSD) functions that are commonly used in fatigue calculations within the automotive industry. However, the presented system is exposed to specific excitations resulting from interactions with the suspended mass on the car's hitch. To precisely analyse these excitations, real acceleration measurements were conducted directly on the device at the hitch mounting location (Figure 15). These measurements were conducted on two distinct road surfaces: asphalt roads and unpaved roads. The device underwent these measurements while being subjected to a full load during the transportation of a motorcycle (Figure 16). Figure 14: Transport device according to patent PL 224395 B1; 1. Mounting element (for tow hitch); 2. Wheel-base; 3. Stabilizing strap. Figure 15: Measurement point for acceleration in three axes. The power spectral density (PSD) function was obtained from real-world vibration measurements conducted on a Motorcycle Transport Device during vehicle operation and is presented on Figures 17 and 18. The PSD data represented the load history and dynamic response of the system, including random vibration inputs from road conditions. The PSD function served as the basis for the fatigue analysis, providing a frequency-domain representation of the loading conditions. Based on the measured accelerations, utilizing MATLAB tools, particularly the PWELCH function, the power spectral density function was determined for both the asphalt (Figure 17) and non-paved road (Figure 18) routes. The obtained PSD characteristics constitute significant input data for further analysis. To comprehensively assess the impact of these excitations on the device's behaviour, a numerical simulation was employed using the FEM within ANSYS 2020R1 software. The incorporation of PSD excitation characteristics in the computer simulation allowed for the replication of a realistic dynamic environment in which the analysed device operates. Such an approach facilitated a detailed assessment of stresses, deformations, and potential critical areas with regard to material fatigue. Comparing simulation results with previously known S-N curves of materials will enable an evaluation of safety and durability for the designed structure under real operating conditions. After constructing a simplified computer model of the analysed system, a detailed simulation was initiated using Ansys 2020R1 software. As part of the basic strength analysis, a node most susceptible to potential damage was identified (Figure 19). This pivotal node is located within a triangular support, where significant loads and stresses are present. Figure 16: The device with a motorcycle attached. Figure 17: Asphalt road: (a) raw recorded signal, (b) determined PSD function.