# Machine Learning Based Surrogate Models for the Thermal Behavior of Multi-Plate Clutches
## 2 Methodology
### FE-Model and Use Cases  
The model developed and presented by [PERSON] et al. [20] was used as a basis for the research presented in this paper. The model is a parameterizable two-dimensional model of a multi-plate clutch in transient operation. The geometry of the illustrated clutch and the corresponding FE model are shown in Figure 2. The clutch pack consists of 6 steel plates and 5 carrier plates with linings on both sides and comprises 10 friction surfaces. Furthermore, the reaction and pressure plates are placed on the left and right. The simulation model can be divided into two distinct parts. In the first part, the mechanical aspects of the simulation are considered. The pressures and strains due to mechanical and thermal loads within the components are calculated based on the current axial force, speed and temperature distribution. The thermal aspects of the simulation are considered in the second part. Based on the pressure distribution calculated in the first part, the heat flows generated at the friction surfaces can be calculated. These are applied as loads for the thermal simulation. Subsequently, the transient thermal simulation is performed, and it provides the temperature distribution at the coupling as a result. After the two simulation stages have been carried out, the operating conditions of the clutch (pressure and temperature distribution) are updated. This procedure represents 1 time step. This procedure is performed for the defined number of time steps, each with the updated operating conditions as the initial condition. The complete process flow can be seen in Figure A1 in Appendix A. A time step size of 0.5 s and an element size of 0.0002 m were adopted. The simulation was carried out for 28 steps (14 s). The initial temperature of the clutch is 80 \({}^{\circ}\)C or 353.15 K.  
Figure 3 is a comparison of the experimentally determined data and the results of the FE simulation. The experimental temperatures were measured at a point inside the third steel plate. These were compared with the associated temperature determined by the simulation. Figure 3a shows that the FE simulation reproduced the temporal temperature variation with good precision. Figure 3b shows the measured and simulated temperature increases, along with the identity line. There was a strong correlation between the measured and the simulated data. The model enables the variation of a large number of parameters that influence the experienced load, the geometry of the clutch system and the material data of the installed components. Given that the study focused on creating a model suitable for operation, parameters that may vary during operation, such as load (axial force and speed) and lining thickness (due to wear of the lining), were considered. Other design and material parameters, such as the thickness of the steel plate or the Young's modulus, do not change  
Figure 2: (**a**) Geometrical dimensions and mechanical boundary conditions [20] and (**b**) FE model of the multi-plate clutch [20]. during operation and were therefore not considered in the modeling. Two different use cases were considered and are presented in Table 1.  
Use Case 1 only covered operations under varying loads. The axial force and the speed were varied. The profiles of the axial force applied and the differential rotational speed are shown by way of example in Figure 4. In this research, the clutch is analyzed in transient slip conditions. The axial force is applied and the differential force is increased and then reduced to zero again. In Use Case 2, the wear and tear of the lining during operation was taken into account in addition to the load parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Use Case** & **Description** & **Varied Parameters** \\ \hline \hline
1 & Load & Axial force \\ \hline \hline
2 & Load + lining wear & Radial speed \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of the two use cases with the corresponding examined parameters.