## 4 Results
### Fatigue Life Evaluation Based on Simulation Model  
The fatigue life of the spiral bevel gear was evaluated for each agricultural operation, using the developed simulation model. Figure 9a shows the accumulated damage sum for each operation acting on the spiral bevel gear, respectively. It can be seen that subsoiler tillage exceeded a damage sum of 1 (which is the criterion for fatigue failure based on the Miner cumulative damage rule) and, thus, leads to a shorter life than the service life. In addition, the damage sum in the other three operations are less than 1, indicating that the fatigue life is longer than the service life. Figure 9b shows the fatigue life for each agricultural operation. This is the value of the service life divided by the damage sum, which shows the opposite tendency to the sum of the damage. Subsoiler tillage, with the harshest load conditions, had a fatigue life of less than 1000 h. Table 7 shows the results of damage sum and fatigue life under the four operations. As a result, the damage sums for moldboard plow tillage, subsoiler tillage, rotary tillage, and baler operation were 0.2012, 9.6000, 0.0098, and 0.0052, respectively. The fatigue life for moldboard plow tillage, subsoiler tillage, rotary tillage, and baler operation were 13,599, 285, 278,884, and 525,977 h, respectively.  
Figure 8: Load spectra for the spiral bevel gear by field operations: (**a**) moldboard plow tillage, (**b**) subsoiler tillage, (**c**) rotary tillage, and (**d**) baler operation.  
Figure 10a shows the ratio of fatigue life (obtained through simulation) to service life (2736 h). The ratio of fatigue life for each agricultural operation ranged from 0.104 to 192. In subsoiler tillage, with the most severe load conditions, the fatigue life ratio was 0.104, indicating it was lower than the service life. This means that, when working with the subsoiler during the entire life cycle of the tractor, the life of the tractor can be guaranteed at about 10.4% of its service life. The fatigue life ratio of plow tillage, rotary tillage, and baler operation were 4.97, 101, and 192, respectively, indicating that tractor may be used longer than the service life. In particular, the fatigue life during rotary tillage and baler operation was shown to last 100 times longer than the service life. This was considered to be due to the fact that, as these operations are performed by driving the PTO, a rather low load is applied to the spiral bevel gear to drive the tractor. Figure 10b shows the relative fatigue life obtained by dividing the fatigue life value of each agricultural operation based on the subsoiler tillage, which had the lowest fatigue life. The results of the Relative Fatigue Life Analysis indicate that the tractor during moldboard plow, rotary tillage, and baler operations can be used 48, 979, and 1846 times longer than subsoiler tillage, respectively. Consequently, as the life of the tractor is differently affected by the frequency of use of various implements, the designer needs to design and develop tractors taking into consideration the frequency and characteristics of use of the attached implements.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Field Operations** & **Damage Sum** & **Fatigue Life (h)** \\ \hline Moldboard plow tillage & 0.2012 & 13,599 \\ Subsoiler tillage & 9.6000 & 285 \\ Rotary tillage & 0.0098 & 278,884 \\ Baler operation & 0.0052 & 525,977 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Damage sum and fatigue life of the spiral bevel gear by each agricultural operation based on our simulation model.  
Figure 9: Results of fatigue analysis of spiral bevel gears based on simulation model: (**a**) damage sum and (**b**) fatigue life.