## 3 Case Studies
### Transmission Clutch  
#### 3.1.1 Task Clarification and Function Analysis  
The power train generally includes a transmission clutch or other means for interrupting the flow of power to the drive wheels. A clutch provides a means for the tractor operator to start a smooth delivery of power to the transmission, to interrupt power while the transmission gear ratio is being changed, and to interrupt power when the tractor is to be stopped [53]. Moreover, one (or more) separate clutch(es) can also be provided to interrupt the flow of power to the power take-off drive [53]. A transmission clutch is a knowledge intensive subsystem, with a complexity high enough for requiring a deep functional analysis, but manageable enough to be a feasible application for the DA development.  
First, the clutch design variants are analyzed by reviewing datasheets and transmission schemes for their function in the system, CAD models and drawings for dimensions and parts, design reports for simulations, dimensioning, company Product Lifecycle Management (PLM) on materials, manufacturing, and standards. The clutches are grouped as follows:  
1. **Power take-off (PTO)** Operation assisted by the control system, thus not prone to uneven and stressed actuation;
2. **Continuously variable transmission ranges (CVTR)** Comfort application with little disc slips, thus subject to low thermal stresses;
3. **Gear box (GB)** Used for gear shift but not for moving the tractor from standstill, thus with medium stresses;
4. **Power shift ranges (PSR)** Used to select ranges and start the tractor from standstill, thus very high load and heat stresses. A tractor transmission requires several clutches with specific functions and requirements:  
1. Geometry:  
* Layout, including shaft configuration;
* Nominal dimensions, including overall size, input and output shaft diameters, housing diameter.
2. Kinematics:
* Displacement of springs and piston;
* Gaps between discs and shafts.  
3. Loads:  
* Torque passed from input to output shafts;
* Safety factor as a dimensioning criterion;
* Maximum pressure on the discs;
* Engagement smoothness.  
4. Duration:  
* Dissipation of energy through friction.  
Therefore, due to a high number of parameters it was not possible to define a few concept models with continuously variable parameters. The design problem could be simplified by fixing a number of main parameters levels. This produced 54 possible solution concepts, with further possible adjustments in the detail design phase. An example of the clutch structure is shown in Figure 3.  
The functional FMEAs are fundamental tools for linking the subfunctions of each clutch component to the transmission requirements, as shown in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
\begin{tabular}{c} Life \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Clutch parts linked to the requirements through the subfunctions they deliver (extract).  
Figure 3: Parts of a transmission clutch with Belleville (diaphrag) spring and its functioning. (**a**) Single; (**b**) 5 clutch discs version.  
The main function of the subsystem is to engage or disengage two shafts, to transmit or not transmit the torque between them, as encased by the dotted box in Figure 4. Inside the box, all the subfunctions are drawn in relation to the structure of the subsystem. The subfunctions are connected by flows of material (double line), energy (solid), and information (dashed, but not used here). Then, these flows are described by equations between the fundamental parameters, or at least by a regression analysis model. These parameters are continuously variable numbers or tabulated in the catalogues of suppliers.