# On the Influence of Suspension Geometry on Steering Feedback
## Materials and Methods
### Torque Vectoring and Its Effects  
A description of the strategy adopted for typical torque vectoring (TV) control in itself is beyond the scope of this paper, and so is the related impact on vehicle balance, handling dynamics, and stability. Therefore, an over-simplified open-loop TV logic was purposely built within MATLAB-Simulink(r) and simulated through co-simulation. The TV action in terms of torque difference, left to right, is proportional to the steering wheel angle and is directed at reducing understeer. That means the outer wheel torque is higher than the inner wheel torque, so the torque at wheel is:  
\[\text{C}[\text{Nm}]=\text{k}[\text{Nm/rad}]\cdot\text{SW}_{\text{angle}}[ \text{rad}] \tag{19}\]  
Figure 12, obtained by a sine sweep steer test, shows the torque delivered to the left-hand and right-hand side wheels being strongly differentiated to achieve a yaw moment by means of the torque vectoring action.  
Figure 11: Steering wheel angle for both vehicles (continuous blue line) and steering torque for passive vehicle with original (dotted blue line) and EB0 (dotted red line) suspension.  
Figure 10: Schematic front view (yz plane) of the EB0 suspension, KO (Kingpin Offset) is halved.  
Two values of coefficient k (300 and 600 Nm/rad) were tested. The vehicle balance change in terms of the understeer reduction is shown in Figure 13 for a 90\({}^{\circ}\) step steer test at 80 km/h. A higher value of k results in less understeer and a smaller cornering radius as expected.  
Figure 14 compares the steering wheel torque required with the passive vehicle (dotted green line) and with torque vectoring (k = 300 dotted blue line, k = 600 dotted red line), with the standard geometry in all cases.  
Figure 12: Front wheel torque at the ground on left (red) and right (blue) sides for vehicle with TV (Torque Vectoring), k = 600.  
Figure 13: Trajectory after a 90\({}^{\circ}\) step steer for passive vehicle (green), TV k = 300 (blue), TV k = 600 (red).  
It shows that the disequilibrium in terms of torques and longitudinal forces Fx at the ground affects the shape, linearity and phase of the steering effort required. The adverse effects are even more evident in the driver-in-the-loop simulator: the TV coefficient k = 600 Nm, in particular, results in a surprising and confusing feedback, and in the onset of steering instability, with the phase shift inducing an undesirable self-steering effect and jeopardising the driving feeling; the vehicle model becomes literally undriveable. From now on, all simulations will be performed with k = 600 because this appeared as the most critical case.  
Figure 15 shows the steering effort required with torque vectoring applied to the EB0 modified geometry. The reaction is similar to the standard geometry with TV and k = 300, so the negative effects affecting steering feedback are somehow mitigated; the phase shift is reduced, but the response is still very far from the desirable curve obtained with the passive vehicle, as it can also be perceived in the driving simulator.  
Figure 14: Steering wheel: angle and torque for passive vehicle (green) and TV vehicle (blue k = 300, red k = 600).  
Figure 15: The EB0 sine steer (blue line) compared with TV original (red) and passive vehicle (green).