# The Influence of Fatigue Loading on the Durability of the Conveyor Belt
## 5 Results and Discussion
By introducing this number into the Equation (6), the maximum force required for specimen fracture after 10,000,000 cycles would be 8311.5 N, i.e., 63,5% in relation to the breaking strength of the belt specimen:  
\[F_{MAX}=-451.2\ln(10,000,000)+15,584=8311.5\ \mathrm{N} \tag{7}\]  
Figure 8: Graphically presented results and F-N curve. Figure 9: Some of the fractured specimens after fatigue tests. In order to verify the obtained experimental results, a FEM model of the belt specimen was created. The results are shown in Figure 10.  
As for the FEM model, first the idealization was done. The belt specimen was formed as a solid model and was prepared by removing the rubber protective layers that would only distort the results. The model was defined based on the material of the belt carcass. The multi-axial fatigue module was activated in the Autodesk Inventor Nastran 2022 software to perform the fatigue test. Second, boundary conditions were applied. Fixed constraint was applied at the top surface of the specimen, while the loading was applied at the bottom surface of the specimen. In order to simulate the sinusoidal loading cycle, loading history table data were created. Loading scale factor in the range of 0.6 \(\div\) 1 was entered for 1 s in order to achieve 1 Hz test frequency. After that, mesh was applied. Local mesh control was applied on the edges of the specimen. Finally, the simulation was started. During the first iteration of the simulation of the first specimen, analysis was done with default mesh size. After that, the simulation was done with the half of the default mesh size. It took several iterations to achieve result convergence. The final mesh size was 2 mm. The number of finite elements was 61,244. Numerical simulations were carried out on the formed belt specimen model in an identical manner to the physical experiment described in the previous part of the paper. The obtained results of the FEM analysis were compared with the average values of the experimentally obtained results, and both are shown in Table 3.  
Figure 10: Results of FEM fatigue analysis. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Loading Level**} \\ \cline{2-5}  & **1** & **II** & **III** & **IV** & **V** \\ \hline Average no. of cycles & & & & & \\ until break during physical experiments & & & & & \\ No. of cycles & & & & & \\ \multicolumn{5}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ No. of cycles & & & & & \\ until fracture according to FEM & & & & & \\ Percentage of result difference [\%] & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of comparative analysis of experimental and FEM results. The obtained value of the average number of cycles until the belt breaks at the maximum loading of 95.6% of the nominal breaking strength, only 823 cycles, indicates that the damage occurs at the first loading cycles. This is due to the fiber damage mechanisms explained previously. In metals, molecular bonds enable homogeneity of the structure, and such material can withstand a greater number of cycles at a maximum loading close to the nominal ultimate tensile strength than is the case with textile composites such as conveyor belts. At the maximum loading level of 91.7% of the nominal belt-breaking strength, the number of cycles did increase (823 \(\rightarrow\) 3168), but that number still does not ensure an economically profitable and acceptable lifetime of the belt. Moving to the maximum loading levels of 82.6% and 81%, there was a significant increase in the number of cycles to fracture. It should be noted here that the higher number of cycles to fracture (39,180-82,472) with a slight decrease in the loading level (82.6-81%) indicates the sensitivity of the considered influence, which requires further and more detailed analysis.