# Semi-Active System of Vehicle Vibration Damping
## 5 Simulation Research of Vehicle Vibration
The changes in pressure on the road surface on the front axle is shown in Figure 15, and the vertical acceleration on the front axle is shown in Figure 11.0  
The third simulation was analogous to the second, but the forces in the dampers were determined in accordance with the first criterial function \(\mathcal{K}^{\text{sky}}\). Figure 17 shows the change in the vertical acceleration over the front axle with control. Figure 11.1 The change in vertical acceleration over the front axle with control by criterial function \(\mathcal{K}^{(1)}\). Figure 11.2 The change in vertical accelerations over the front axle without control. Figure 11.3 Change in the wheels’ pressure on the road surface on the front axle with control by criterial function \(\mathcal{K}^{(1)}\). in the wheels' pressure on the road surface on the front axle, and Figure 18 shows the change in vertical acceleration over the front axle. The purpose of this simulation research was the effectiveness comparison of reduction in the vehicle vibration in the three situations described above. Evaluation of this effectiveness was performed based on indicators W\({}_{1}\) and W\({}_{2}\), which characterize the intensity of the vibration. At the same time, the smaller the value of the indicator, the greater the efficiency of the vibration reduction. Table 1 presents the values of the considered indicators. The results obtained show that the values of indicators W\({}_{1}\)--characterizing the vibration intensity with regard to comfort--are significantly smaller for a vehicle equipped with the MR dampers than for a vehicle with classic dampers. In the \(\mathcal{K}^{(1)}\) system, the W\({}_{1}\) indicator has shown an improvement of 51.6%, compared to the classic suspension, and in the \(\mathcal{K}^{(\mathrm{sky})}\) system, one of 42.5%. However, the influence of the form of the criteria function used in the control system on the value W\({}_{1}\) is insignificant. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Criterion** & \(\mathcal{K}^{(1)}\) & \(\mathcal{K}^{(\mathrm{sky})}\) & **Classic** & \(\mathcal{K}^{(1)}\)/\(\mathcal{C}\)**[\%]** & \(\mathcal{K}^{(\mathrm{sky})}\)/\(\mathcal{C}\)**[\%]** \\ \hline W\({}_{1}\) & 2.2362 & 2.6568 & 4.6212 & 51.6 & 42.5 \\ \hline W\({}_{2}\) & 0.3250 & 0.6523 & 0.3418 & 4.9 & \(-\)90.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Indicator values. Figure 17: Change in the wheels’ pressure on the road surface on the front axle with control by arterial function \(\mathcal{K}^{\mathrm{sky}}\). Figure 18: The change in vertical accelerations over the front axle with control by arterial function \(\mathcal{K}^{\mathrm{sky}}\). In the case of indicator W\({}_{2}\)--determining changes in the wheel vertical forces--the impact of the MR dampers controlled in accordance with the criterion \(\mathcal{K}^{(1)}\), is little (4.9% reduction). However, as a result of the control according to the \(\mathcal{K}^{\text{sky}}\) criterion, there was a 90.8% increase in the W\({}_{2}\) value, which indicates that the conditions of impact of the wheels on the road surface deteriorated.