# Multi-Body Model of Agricultural Tractor for Vibration Transmission Investigation
## 3 Results and Discussion
### Modal Analysis  
A modal analysis of the whole tractor was performed to assess the contribution of different suspension elements to the overall movements of the tractor during the test track ride and to identify critical components to modify for better performance from the driving comfort point of view. The analysis was performed on the linearised model using Adams software. Table 6 presents the results of the modal analysis. Natural frequencies of corresponding modes are matched with corresponding frequency bands in the one-third octave analysis to observe the bands in which they contribute to vibration levels. Mode shapes are briefly characterised, and suspension elements in resonance are identified for each mode shape. It should be noted that the resonance of types is present in almost all shapes in the frequency bands from 1.6 Hz to 3.15 Hz. These modes also have low damping, from 13.7 % to 24.54 %. The contribution of these modes \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Frequency Band** & **Natural** & **Damping Ratio** & **Suspension Element in** & **Mode Shape Description** \\
**[Hz]** & **Frequency [Hz]** & **[\%]** & **Resonance** & **cabin pitch, driver seat have \\ \hline \multirow{3}{*}{1.25} & 1.17 & 73.87 & spring-dampers, driver seat suspension & cabin pitch, driver seat have \\ \cline{2-5}  & 1.24 & 15.94 & spring-dampers & cabin roll \\ \hline \multirow{3}{*}{1.6} & 1.53 & 31.33 & front tyres, spring-dampers & tractor body pitch, cabin pitch \\ \cline{2-5}  & 2.21 & 13.70 & tyres, spring-dampers, driver seat suspension & tractor body sway, cabin roll, driver seat have \\ \hline \multirow{3}{*}{2.5} & 2.52 & 24.54 & tyres, driver seat & tractor body heave, driver suspension & tractor body heave, driver seat heave \\ \cline{2-5}  & 3.18 & 41.74 & driver seat suspension & driver seat heave \\ \cline{2-5}  & 3.33 & 19.66 & tyres, driver & tractor body pitch, driver seat suspension & tractor body water, cabin heave \\ \hline \multirow{3}{*}{4} & 4.10 & 2.79 & front tyres, driver & tractor body sway, driver seat suspension & tractor body sway, driver seat heave \\ \cline{2-5}  & 4.14 & 40.89 & driver seat suspension & driver seat heave \\ \cline{2-5}  & 4.45 & 12.41 & tyres, front bushings, driver seat suspension & tractor body roll, cabin roll, driver seat heave \\ \hline \multirow{3}{*}{6.3} & 5.64 & 9.82 & tyres, front bushings & tractor body warp, cabin heave \\ \cline{2-5}  & 8 & 7.77 & 26.54 & front bushings & cabin roll \\ \hline \multirow{3}{*}{10} & 10.65 & 43.02 & front bushings & cabin pitch \\ \cline{2-5}  & 12.5 & 13.27 & 47.65 & front bushings & cabin sway \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The results of the modal analysis of the linearised model of the tractor with colour-coded areas of resonance of different suspension elements on the right. to the overall vibration level is significant. Since the tyres are suspension elements with specific stiffness and damping characteristics, reducing the vibration levels in these bands is difficult. The tyres' stiffness depends on the inflation pressure (see Figure 7), but it cannot be modified to reduce the vibration levels. The inflation pressure of tractor tyres is set based on the work conditions. Table 6 also shows natural frequencies in frequency bands from 6.3 Hz to 12.5 Hz, where the suspension elements in resonances are front bushings. These modal analysis results explain the significant increase in vibration levels on the cabin in these frequency bands. However, an increase in these frequency bands is also observable in the rear part of the cabin in Figure 15. This increase is significant even on the cabin floor and driver seat. Therefore, it is desirable to identify if the resonance of the front bushings also influences the vibration of the cabin in the rear part. Three modes with rear spring-dampers resonances are in frequency bands from 1.25 Hz to 2 Hz. It can be seen in Figure 15 that the vibration levels in frequency bands of 1.6 Hz and 2 Hz rose between the body and the cabin.