## 3 Validation of the Model with IPG CarMaker 8.0  
In order to secure that the optimisation results in this work are realistic, the model is validated using IPG/CarMaker 8.0 for the path illustrated in Figure 5b and the road profile of Class B assigned to it (Figure 5a).  
As mentioned above, the vehicle parameters selected for the model are extracted from the software demo vehicle to build its digital twin. The suspension and tyre parameters of the models are adjusted according to Tables 1 and 3. More specifically, the suspension parameters (Table 1) of the front wheels are adjusted into the section Car/VehicleDataSet/Suspensions of the software. Regarding the suspensions, for both the stiffness and the damping coefficient, a characteristic value option is selected, while the values of the buffer are set zero in the software, as the buffer is not included in the model. Then, regarding the tyres, the parameters related with them and considered in the vehicle and wear model (\(P\), \(d\), \(c\), \(r\), \(K_{T}\) and \(C_{T}\)), are adjusted according to section Tires/TireDataSet/GeneralandModelParameters of the software. The only parameters that are not provided are the crown thickness (\(b_{0}\)), the chordwise curvature (\(r_{w}\)) and the lateral shear elastic tread coefficient (\(C_{y}\)). Regarding the first two, its consideration is not possible, but \(C_{y}\) is extracted after evaluating it using the cornering stiffness obtained from the software simulation results. More specifically, the side force applied in the wheel for a rectangular contact area, as in this case, can be evaluated for small slip angles:  
\[F_{y}=\int_{0}^{b}f_{y}dx=C_{y}a\int_{0}^{b}Vdx=C_{y}a\int_{0}^{b}xadx=\frac{C _{y}ab^{2}}{2}\alpha \tag{23}\]  
Thus, according to Equation (23), the cornering stiffness \(C_{Fa}\) is equal to \(\frac{C_{y}ab^{2}}{2}\alpha\). Therefore, after fitting the simulation results (lateral slip angles and side forces) to a linear equation, as shown in Figure 6b, the value of \(C_{y}\) is extracted.  
Having created the digital twin of the demo vehicle (Figure 6), the wear energy (\(E_{y}\)[Nm/m2]) is selected for comparison in order to validate the simulation results. Therefore, the obtained measurements are used as follows for calculating the wear energy (\(E_{y_{corner}}^{w}\)):  
* The sliding distance (\(s_{d}\)) is calculated according to Equation (12).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Wear and Tread Model Parameters**} \\ \hline
**P[KPa]** & \(c\)**[m]** & \(d\)**[m]** & \(b_{0}\)**[m]** & \(r_{w}\)**[m]** \\ \hline
250 & 0.1950 & 0.3175 & 0.1660 & 0.1550 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Wear and tread model parameters.  
Figure 6: (**a**) The IPG/CarMaker demo vehicle used in this work and (**b**) the evaluation of its tyre cornering stiffness.  
The parameter (\(\phi\)) is calculated as follows: \[\phi=\frac{C_{Fa}|tana|}{\mu F_{z}}.\] (24)
* The sliding force is obtained by integrating the maximum possible frictional force distribution (\(uq_{z}\)) over the sliding region \(b_{h}\leq x<b\): \[F_{slid}=\int_{b}^{b_{h}}uq_{z}dx=\mu F_{z}\bigg{(}\frac{1}{3}\phi^{2}-\frac{2} {27}\phi^{3}\bigg{)}sign(a).\] (25)
* Finally, the wear energy per contact area according to Equation (26) is evaluated by multiplying the sliding force with the slipping distance (\(S_{y}\)) and dividing it by the contact area: \[E_{y_{camaker}}^{w}=\frac{F_{slid}S_{y}}{a*b}.\] (26)  
The comparison of \(E_{y_{camaker}}^{w}\) with \(E_{y}^{w}\) is illustrated in Figure 7, which proves a good convergence in the two simulation results. More specifically, Figure 7 illustrates high similarity in terms of the trend of the two curves. Slight differences occur in the magnitude with the model used in this work underestimating a few of the peaks. However, this underestimation is not an issue as the trend is accurately followed, and, given the simplicity of the model in comparison with IPG/CarMaker 8.0, the results should be considered valid.