## 3 Case Studies
### Final Gear Reduction  
#### 3.2.1 Task Clarification and Functional Analysis  
The tractor transmission ends at the wheel axles with a final planetary reduction. The final drive lets the drive wheels run at a much slower speed and with a much higher torque than the earlier parts of the drive train [53]. A planetary gear set (Figure 8) is built into the axle of each drive wheel. The final drive shaft is attached to the sun gear on one end and it is spline connected on the other end to one of the side gears in the differential. The ring gear is held stationary in the axle housing, and the rear axle shaft is driven by the planet carrier. The rear axle shaft extends well beyond the axle housing. The drive wheels can be attached at different points along the rear axles to change the drive wheel spacing [53].  
Figure 7: CAD model of the clutch produced on the basis of the DA datasheet.  
High strength, fatigue resistance, and low noise are required for this demanding application [54]. All the actual final reductions are analyzed with the method described in Section 2. The component subfunctions are analyzed and linked to the transmission requirements, as shown in Table 3. The input requirements to the DA can be grouped as follows:  
1. Geometry:  
* Overall size;
* Meshing conditions for gears.  
2. Kinematics:  
* Speed reduction to deliver the expected final speed.  
3. Loads:  
* Torque capacity;
* Bending moment capacity.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Part** & **Subfunction** & **Requirement** \\ \hline \multirow{2}{*}{Planetary gear set} & transfer torque & transmissible torque \\ \cline{2-3}  & vary speed & output speed \\ \hline \multirow{2}{*}{Planet carrier} & transfer torque & transmissible torque \\ \cline{2-3}  & support/connect & geometry \\ \hline \multirow{2}{*}{Pin} & transfer torque & transmissible torque \\ \cline{2-3}  & support/connect & geometry \\ \cline{2-3}  & lubricate/cool & life \\ \hline \multirow{2}{*}{Needle bearing} & support/connect & geometry \\ \cline{2-3}  & support/connect & life \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parts of the final reduction linked to the requirements through their subfunctions (extract).  
Figure 8: Exploded view of the main components of the planetary gear set as a part of the final reduction.  
4. Duration:  
* Friction condition.
* Heat dissipation.  
The main function of the subsystem is to reduce the angular speed from an input shaft to the output one, as encased by the dotted box in Figure 9. Inside the box, all the subfunctions are investigated and connected in a functional analysis structure. The functional analysis flows are formalized with formulae, transforming the inputs into outputs. Fundamental relations are the gear transmission ratio, and the safety factors for the contact stress and for the bending moment.  
Because of the complexity of the system (Figure 10), the number of possible solutions was limited by fixing some of the driving parameters based on the company's best practices. The archetype suggests a preliminary solution that respects the company standards and that can be further optimized and detailed.  
After analyzing the design variants, reference values for the main parameters are defined. The experience of senior designers is fundamental for reviewing those parameter values in order to avoid conflicting effects and bias for maintaining those functions that somehow already worked.