## 2 Method and Modeling  
Figure 1 presents a flowchart of the research framework employed in the present study. The study commenced by collecting the design parameters of the suspension and steering systems of the target vehicle. Based on the hardpoint measurements of the vehicle, a half-vehicle model was constructed comprising the front and rear suspension systems and the steering system. The validity of the half-model was confirmed experimentally, and a full-vehicle analysis model was then constructed. Simulations were performed to investigate the steady-state and transient-state cornering handling performance of the vehicle under typical driving maneuvers. The simulation results were validated experimentally. The validated model was then used to investigate the effects of three main suspension design parameters on the cornering performance. As shown in Figure 2, the target vehicle was fitted with an SLA Strut front suspension system and a multi-link rear suspension system. Referring to the two degree-of-freedom (2-DOF) model shown in Figure 3, the equations of motion for the vehicle can be derived as Equation (1):  
\[ \begin{array}{l}m(\dot{V}_{x}-V_{y}\Omega_{2})=F_{xf}\cos\delta_{f}+F_{xr}-F_{ yf}\sin\delta_{f}\\ m(\dot{V}_{y}-V_{x}\Omega_{2})=F_{yf}\cos\delta_{f}+F_{yr}-F_{xf}\sin\delta_{f} \\ I_{z}\dot{\Omega}_{z}=l_{1}F_{yf}\cos\delta_{f}-l_{2}F_{yr}+l_{1}F_{xf}\sin \delta_{f}\end{array}  \tag{1}\]  
Figure 1: Research framework. Figure 2: Hardpoint positions in the front and rear suspension systems. **(a)** Hardpoint positions in the SLA strut suspension; **(b)** hardpoint positions in the multi-link suspension. For reasons of simplicity, the following assumptions are introduced: (1) the longitudinal acceleration of the whole vehicle is equal to zero, and (2) the longitudinal traction force is also equal to zero, i.e., \(F_{\forall t}\approx 0\). Furthermore, the steer angle (\(\delta\)) of the tire is small, i.e., \(\cos\delta_{f}\approx 1\). Consequently, the equations of motion can be simplified as:  
\[m(\dot{V}_{y}-V_{x}\Omega_{z})=F_{\forall t}+F_{\forall t}\] \[I_{z}\dot{\Omega}_{z}=I_{1}F_{\forall t}-l_{2}F_{\forall t}\]  
Notably, the two equations above describe the dynamic response of the vehicle under turning irrespective of the roll motion of the body or the angles of the various wheel alignments. Considering the tire forces developed at each wheel of the vehicle, the tire slip angles at the front and rear can be expressed respectively as:  
\[ \begin{array}{c}\alpha_{f}=\delta_{f}-\frac{I_{1}\Omega_{z}+V_{y}}{V_{x}}\\ \alpha_{r}=\frac{I_{0}\Omega_{z}-V_{y}}{V_{x}}\end{array} \]  
Let the front and rear cornering stiffnesses be denoted as \(C_{\alpha f}\) and \(C_{\alpha r}\), respectively. The tire forces at the front and rear can then be derived as:  
\[F_{\forall t}=2C_{\alpha f}\alpha_{f};\ F_{\forall t}=2C_{\alpha r}\alpha_{r}\]  
Let \(\tan\beta=\frac{V_{x}}{V_{y}}\cong\beta\), such that \(V_{y}\cong\beta V_{x}\) and \(\dot{V}_{y}\cong\beta\dot{V}_{x}+\dot{\beta}V_{x}\). Assuming that angle \(\beta\) is very small, then \(\tan\beta=\beta\), \(V_{x}\) is constant, \(\dot{V}_{x}\) is zero, and \(\dot{V}_{y}=\dot{\beta}V_{x}\). Furthermore, if the vehicle maintains a constant speed as it turns, the overall vehicle dynamic behavior can be expressed as:  
\[ \begin{array}{c}m\dot{V}_{y}+[mV_{x}+\frac{2I_{1}C_{\alpha f}-2I_{2}C_{ \alpha r}}{V_{x}}]\ \Omega_{z}+[\frac{2C_{\alpha f}+2C_{\alpha r}}{V_{x}}]V_{y}=2C_{ \alpha f}\delta_{f}\\ I_{z}\dot{\Omega}_{z}+[mV_{x}+\frac{2I_{2}C_{\alpha f}-2I_{2}^{2}C_{\alpha r} }{V_{x}}]\ \Omega_{z}+[\frac{2I_{1}C_{\alpha f}-2I_{2}C_{\alpha r}}{V_{x}}]\ V_{y}=2I_{ 1}C_{\alpha f}\delta_{f}\end{array} \]  
The tendency of a vehicle to steer less than the amount commanded by the driver during steady-state curve maneuvers can be evaluated using the understeer coefficient (\(K_{us}\)).