# Investigation of Vehicle Stability with Consideration of
## 5 The Effect of Vehicle Suspensions on Stability
### Cornering Stability of the Vehicle
As already mentioned, changes in the camber angle of the wheel and the turning angle of the wheel about the vertical axis were evaluated by adjusting the kinematically obtained turning angle of the wheel, which was assumed to be the change in the angle of slip. Calculations were performed by estimating the limit turning radius \(R_{rib}\) for different speeds. This was calculated according to the grip conditions (turning radius limited by the car slip or camber) with nondeformable and deformable suspension (grip coefficient \(\mu=0.8\)). The results are presented in Table 3. The additional body rollover angle can be observed to undergo no significant change due to suspension deformations under these conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Speed, km/val**} & **Turning Radius at Slip, \(R_{ribs}\),** & \multicolumn{2}{c}{**Turning Radius at Rollover, \(R_{ribV}\), m**} \\  & **m** & **Deformable Suspension** & **Non-Deformable Suspension** \\ \hline
20 & 3.50 & 1.80 & 1.80 \\
40 & 13.98 & 7.20 & 7.21 \\
60 & 31.46 & 16.20 & 16.23 \\
80 & 55.93 & 28.81 & 28.86 \\
100 & 87.39 & 45.01 & 45.09 \\
120 & 125.85 & 64.82 & 64.92 \\
140 & 171.29 & 88.23 & 88.37 \\
160 & 223.73 & 115.23 & 115.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Vehicle boundary turning radius. Figure 27: Wheel load recalculation scheme when the vehicle is subjected to lateral force. In further investigations, a change of direction was noted to cause a transverse inertia force, which led to the redistribution of radial reactions. The kinematics of the suspension, in turn, led to possible changes in the spatial position of the wheels. Since the slip angle depends on the radial loads, in particular under boundary conditions, the redistribution of the radial loads must be evaluated when solving stability problems. For this, the algorithm provided the determination of the reaction \(R_{y}\) of each tire according to it load. The AUTOSTAB program was developed for the implementation of the model. The algorithm is shown in Figure 28.  
The simulation results show that in modeling the directional stability of the vehicle, it is necessary to evaluate the specifics of the suspension, the redistribution of radial loads under the action of lateral force and changes in the geometric position of the wheel due to the kinematic properties of the suspension. The results obtained by modeling the movement of the car under stabilized conditions are presented in Figure 29.  
Figure 28: Vehicle boundary turning radius calculation program AUTOSTAB algorithm. Figure 29 shows that by estimating the distribution of radial loads and changes in wheel position, the vehicle boundary turning radius increased up to 4.39 times at 120 km/h speed. The developed methodology enabled an evaluation of the influence of road condition on directional stability under vertical excitation, investigation of the sensitivity of individual suspension types to vertical excitation according to directional stability criteria, and an assessment of the technical condition of the vehicle if patterns of change in suspension parameters are available. The technical condition was assessed in the work by changing the stiffness of the suspension elements. Application of the numerical model to linear movement showed that this kind of modeling would not be effective without a driver's model. This was due to the fact that the vehicle would change direction under the action of random effects, and frequent correction would be required to simulate direction adjustment using the steering mechanism. Technical specifications for this kind of model were prepared in this work, and the excitation parameters when driving on roads of different quality may be established using this model.