## 4 Design Case
### Evaluation of Cornering Performance  
First, a global search for the optimal cornering performance with lateral torque vectoring under various driving conditions is carried out. For a given vehicle speed, \(v\), longitudi  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(l_{f}\) & 1.25 m & \(C_{a}\) & 0.28 & \(h  
nal acceleration, \(a_{x}\), and lateral torque vectoring ratio, \(\zeta_{lr}\), an algorithm for calculating the maximum lateral acceleration, \(a_{y\_max}\), is expressed as follows:  
1. The front-rear weight transfer, \(\Delta F_{zfr}\), is calculated by Equation (25) with known values of \(F_{frac}\) and \(F_{roll}\). 2. An initial value of \(a_{y}\), \(a_{y\_j}\), is guessed. 3. The left-right weight transfers of front and rear axle, \(\Delta F_{zf}\) and \(\Delta F_{zr}\), are calculated from Equations (34) and (35). 4. Having acquired the values of weight transfer of four wheels, the adhesive limits of lateral force of front and rear axle, \(F_{yf\_lim}\) and \(F_{yr\_lim}\), are calculated by \[F_{yf\_lim}=\left(F_{fl\_lim}^{2}-F_{xl}^{2}\right)^{\frac{1}{2}}+\left(F_{ fr\_lim}^{2}-F_{xx}^{2}\right)^{\frac{1}{2}}\] (45) \[F_{yr\_lim}=F_{rl\_lim}+F_{rr\_lim}\] (46) where \(F_{xl}=\left(\frac{1-\zeta_{lr}}{2\zeta_{lr}}\right)F_{frac}\) and \(F_{xr}=\left(\frac{1+\zeta_{lr}}{2\zeta_{lr}}\right)F_{frac}\). 5. Then, \(F_{yr\_lim}\) and \(F_{yr\_lim}\) are substituted into Equation (23) in turn to attain the correlated values of \(F_{yr}\) and \(F_{yf}\), respectively, that are subsequently checked whether the adhesive limits are exceeded or not. 6. The values of \(a_{y}\) are evaluated accordingly using Equation (24), and the higher one is selected as the adhesive limit of \(a_{y}\), \(a_{y\_lim}\). 7. Check whether \(\left|a_{y\_lim}-a_{y\_j}\right|\) is less than a preset tolerance or not. If not, guess a new value for \(a_{y\_i}\) and redo the step (3) to (6); if yes, treat the resulting value of \(a_{y\_lim}\) as that of the maximum lateral acceleration, \(a_{y\_max}\). Figure 14 shows the resulting variations in \(a_{y\_max}\) with \(\zeta_{lr}\) for \(v=60\) km/h, \(a_{x}=0\), and \(\mu_{p}=1.1\) or \(1.0\), indicating the existence of the optimal value of \(\zeta_{lr}\) denoted by superscript \"*\", i.e., \(\zeta_{lr}^{*}\), corresponding to the highest value of \(a_{y\_max}\), \(a_{y\_max}^{*}\). The optimal point for \(\mu_{p}\) = \(1.1\), as marked by point A in Figure 14, represents \(\zeta_{lr}^{*}\) = 0.604 and \(a_{y\_max}^{*}\) = 10.79 m/s\({}^{2}\), while that for \(\mu_{p}\) = 1.0 (point B) indicates \(\zeta_{lr}^{*}\) = 0.556 and \(a_{y\_max}^{*}\) = 9.81 m/s\({}^{2}\). Furthermore, it is observed in Figure 15a,b that both \(a_{y\_max}^{*}\) and \(\zeta_{lr}^{*}\) increase simultaneously by about 47% and 34%, respectively, as \(\mu_{p}\) increases by 32% from 0.75 to 1.1. Accordingly, applying lateral torque vectoring can significantly improve the cornering performance in view of \(a_{y\_max}\), offering more benefit at better gripping conditions. Since reducing vehicle mass, \(m\), has been a common and effective way to enhance energy efficiency as well as driving range for electric vehicles, it is of interest to assess how vehicle mass affect the cornering performance with or without lateral torque vectoring. For \(v=60\) km/h, \(a_{x}=0\), and \(\mu_{p}=1.1\), the cornering performance under neutral torque distribution, i.e., \(\zeta_{lr}=0\), will worsen, as seen in Figure 16a. However, adopting lateral torque vectoring can offer approximately a 0.6-0.7% improvement for \(a_{y,max}\) as illustrated by the optimal line in Figure 16a. In addition, exerting more efforts, i.e., higher \(\zeta_{lr}^{*}\), may compensate for the loss of \(a_{y,max}\) due to reduced vehicle mass and return to the same level of cornering performance as shown in Figure 16b.