# Conflict Resolution in Mechatronic Collaborative Design Using Category Theory
## 5 Case Study  
In order to demonstrate our approach, an Elector-Mechanical Actuator (EMA) of an aileron for a small aircraft is considered in this paper. The EMA is a mechatronic system used to actuate the aileron of the aircraft and replace the usual rod, lever and cables mechanisms [44; 45]. Several EMA architectures can be studied such as a direct drive, 3-bars or 4-bars architecture. In this work, our chosen structure is the 3-bars architecture as shown in Figure 8, adopted from [45]. The EMA is linked to the aileron and the wing through two spherical joints. It contains a DC motor controlled by a control unit, a gearbox and a ball screw-nut assembly aiming at transforming the motor rotation movement into the translation of the rod to push and pull the aileron. The EMA is considered as a multi-physical system since it encompasses mechanics, control, electrics, etc. Its multi-disciplinary aspect makes the EMA an interesting example to validate our approach. The different steps of our methodology described previously (see Figure 6) will be applied to the EMA system. Figure 8: EMA structure description adopted from [45]. Based on the multi-physical model another expert model is established (EM\({}_{\text{C}}\)). The existing commercial, off-the-shelf (COTS) components are chosen conforming within the simulation results. This model contains the characteristics of the chosen components (see Figure 10(a)). The final expert model is a 3D model (EM\({}_{\text{3D}}\)) using CATIA environment. This model is created in order to verify the integration of the whole mechanism in the aileron and the wing assembly (see Figure 10(b)). In our case study, a well-defined workflow while creating each expert model must be considered. This workflow starts with the requirement model (EM\({}_{\text{R}}\)). Then, the multi-physical model (EM\({}_{\text{MP}}\)) is provided. Once the simulation results are obtained from the multi-physical model (EM\({}_{\text{MP}}\)), the existing COTS components (EM\({}_{\text{C}}\)) will be found. The last model (EM\({}_{\text{3D}}\)) is used to verify the 3D integration of EMA mechanism in the assembly of the aileron and the wing. Once the expert models are created, the evolution of parameters used in the EMA design by different EMs will be illustrated through the P\({}_{\text{m}}\)CG. These categories contain only crucial parameters extracted from the EMs. To do so, we recommend an effective exchange between the stakeholders to extract the most important parameters. The crucial parameters of EMA system are listed in Table 2. For each parameter, a P\({}_{\text{m}}\)CG is created based on CT concepts. An excerpt of a PCG of the parameter P4 (maximal power for EMA system) is illustrated in Figure 12. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Unit** & **EM\({}_{\text{R}}\)** & **EM\({}_{\text{MP}}\)** & **EM\({}_{\text{C}}\)** & **EM\({}_{\text{3D}}\)** \\ \hline Response time (Rt) & ms & 600 & 535 & - & - \\ Static error (Se) & deg & 2 & 2.44 & - & - \\ Global Mass (Mass) & Kg & 3 & - & 31.43 & - \\ Maximal power (Pw) & W & 250 & 288 & 250 & - \\ Cost (Ct) & \(\mathbf{\epsilon}\) & 2000 & - & 1555.65 & - \\ Motor diameter (\(\mathcal{O}\)mot) & mm & 70 & - & 65 & 70 \\ Motor Length (Lgth\({}_{\text{mot}}\)) & mm & 145 & - & 131.4 & 145 \\ Motor resistance (Rm) & Ohm & - & 0.5 & 0.356 & - \\ Motor Inductance (Lm) & mH & - & 0.0039 & 0.000161 & - \\ Motor Inertia (Jm) & Kg.m\({}^{2}\) & - & \(10\times 10^{-7}\) & \(13.45\times 10^{-5}\) & - \\ Reducer diameter (\(\mathcal{O}\)red) & mm & 85 & - & 81 & 85 \\ Reducer Length (Lgth\({}_{\text{red}}\)) & mm & 95 & - & 91.9 & 95 \\ Reducer ratio (r\({}_{\text{red}}\)) & [] & - & 35 & 3.7 & - \\ Screw-nut diameter (\(\mathcal{O}\)sn) & mm & 25 & - & 22 & 25 \\ Screw-nut Length (Lgth\({}_{\text{sn}}\)) & mm & 60 & - & 58.4 & 60 \\ Screw-nut ratio (r\({}_{\text{sn}}\)) & [] & - & 330 & 333 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Crucial parameters for the EMA system and the values found by the EMs.