# Modal Analysis and Optimization of Tractor Exhaust System
## 3 Results and Discussion
### Modal Analysis of the Exhaust  
To improve the reliability of the tractor exhaust system, a modal analysis method was used. The first ten natural frequencies were determined for both the current and modified designs using ANSYS 2022 R2 (Tables 3 and 4). The results presented in Tables 3 and 4 illustrate the vibration modes and amplitudes of the exhaust system at different frequencies. This enables us to determine at which frequencies the system is more sensitive and how design changes affect this sensitivity. Comparisons made across different frequency ranges demonstrate how the system's vibration behavior changes with frequency, allowing for a more comprehensive analysis. This has enabled us to more clearly identify the system's weak points. Excessive vibrations observed in the exhaust system were caused by resonance, which occurred when the forces generated during engine operation and external influences from road conditions were close to the system's natural frequencies. This condition resulted in excessive deformations and potential fractures in certain areas of the exhaust system. Design modifications made to solve the problem increased the system's natural frequencies, reducing the likelihood of resonance. As a result, the exhaust system became more resistant to external forces. The modal analysis results presented in Tables 3 and 4 and Figure 8 demonstrate the successful implementation of the design changes and significant improvements in the system's vibration behavior. These comparisons at different frequency ranges have contributed to a better understanding of the exhaust system's dynamic behavior and enabled the development of more effective solutions for future designs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Mode & 1. Mode & 2. Mode & 3. Mode & 4. Mode & 5. Mode \\ \hline Frequency (Hz) & 31.971 & 31.978 & 256.25 & 262.69 & 363.6 \\ \hline Mode & 6. Mode & 7. Mode & 8. Mode & 9. Mode & 10. Mode \\ \hline Frequency (Hz) & 486.96 & 514.96 & 570.82 & 570.83 & 792.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Natural frequencies obtained after changes made to the exhaust system. Figure 7: Mesh structure of vertical exhaust. Figure 9 clearly demonstrates how the design modifications have affected the vibration behavior of the exhaust system. This graph clearly demonstrates how the design modifications have affected the vibration behavior of the exhaust system by comparing the natural frequencies before and after the changes. The most significant finding is that the design changes have significantly altered the natural frequencies of the system. As a result of these changes, the natural frequencies have generally shifted to higher values. This has moved the system further away from the operating frequencies of the engine, reducing the likelihood of resonance. In other words, the exhaust system is now less prone to vibration while the engine is running. The primary objective of our study was to adjust the exhaust system's natural frequencies to the desired level and thereby eliminate vibration-related problems. Figure 10 visually presents the first ten vibration modes of the exhaust system according to the modal analysis results. Deformations shown in different colors reveal different levels of deformation in different parts of the system. Red areas represent maximum deformation, while blue areas represent minimum deformation. These visualizations have been valuable tools both in diagnosing the problem and in making design improvements. Figure 8: Modified exhaust system modal analysis, ten mod. Figure 9: Modal frequency graph for existing and modified exhaust. the exhaust pipe and adding additional supports, an increase in the natural frequency of the fifth mode was observed, and the total deformation in the fracture area was reduced by approximately 92% (Figure 12). Geometric modifications are design changes implemented to enhance system performance. However, these enhancements typically lead to increased system weight and cost.