# Optimization of Damping in a Semi-Active Car Suspension System with Various Locations of Masses
## 3 Results and Discussion  
Initially, the road profiles with various waviness \(w_{1}\) values of 1, 2, 4, and 6; \(w_{2}\) values of 0.5, 1, 2, and 3; and displacement PSD value \(G_{\text{d}}(\Omega_{0})=4\times 10^{-6}\) m\({}^{3}\)[62] (ISO road class B) were generated. The length of the artificial road profile was 200 m. Finally, our dynamic full-car model simulated a vehicle passing these profiles at speeds \(v\) = 20, 50, 70, 90, and 130 km/h. Damping coefficient values can vary in the range from 1000 Ns/m up to 15,000 Ns/m. Most research authors studying suspension system optimization highlight three basic assessment touchstones related to minimization of the crew ride discomfort and changes in the tire contact with the road: (1) minimization of the standard deviation of sprung mass (body) acceleration, (2) minimization of the standard deviation of the normal reaction at the tire/road contact, and (3) reduction in the displacements of the suspension system [49; 66; 67]. In order to evaluate the ride comfort, statistics such as the suspension travel and sprung mass (body) acceleration [68], the standard deviation (RMS) of vertical acceleration [69; 70], and the vertical jerk [71; 72] are considered. The intuitive relationship between safety and comfort is contradictory [3], and a concurrent enhancement of both of them is not viable. In ref. [48] it is showed that the dependence of these parameters in some ranges of damping consistently grows and shrinks. In addition, a combined performance index with different weighting for each performance measure was used. The weightings depend on the intent of the design; for example, in the case of a luxury car, the highest weight is given to ride comfort. Thus, in this work, we considered only the vertical acceleration of the driver as a criterion for evaluation of the ride comfort, as in ref. [54]. All these optimizations were repeated for the seven masses: (1) \(m_{1}=m_{2}=m_{3}=m_{4}=80\) kg; (2) \(m_{1}=80\) kg; (3) \(m_{1}=m_{2}=80\) kg; (4) \(m_{1}=m_{3}=80\) kg; (5) \(m_{1}=m_{4}=80\) kg; (6) \(m_{1}=160\) kg; and (7) \(m_{1}=100\) kg, \(m_{2}=60\) kg, \(m_{3}=50\) kg, and \(m_{4}=40\) kg. The optimized suspension's damping coefficient \(h_{\text{s}}\) values for generated profiles and for all masses 80 kg are shown in Table 2, Figure 1a. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & \(h_{s_{s}}\)**N/m** & & \\
**Waviness** & **20 km/h** & **50 km/h** & **70 km/h** & **90 km/h** & **130 km/h** \\ \hline \(w_{1}=1\); \(w_{2}=0.5\) & 1131 & 1153 & 1141 & 1106 & 1291 \\ \(w_{1}=2\); \(w_{2}=0.5\) & 1129 & 1191 & 1410 & 1378 & 1658 \\ \(w_{1}=4\); \(w_{2}=0.5\) & 1122 & 1390 & 2433 & 2687 & 2701 \\ \(w_{1}=6\); \(w_{2}=0.5\) & 1116 & 1953 & 4729 & 5739 & 4148 \\ \hline \(w_{1}=1\); \(w_{2}=1\) & 1326 & 1351 & 1280 & 1170 & 1319 \\ \(w_{1}=2\); \(w_{2}=1\) & 1319 & 1408 & 1598 & 1478 & 1690 \\ \(w_{1}=4\); \(w_{2}=1\) & 1312 & 1688 & 2735 & 2881 & 2726 \\ \(w_{1}=6\); \(w_{2}=1\) & 1299 & 2382 & 5267 & 5944 & 4160 \\ \hline \(w_{1}=1\); \(w_{2}=2\) & 1856 & 1844 & 1581 & 1295 & 1357 \\ \(w_{1}=2\); \(w_{2}=2\) & 1839 & 1941 & 1973 & 1663 & 1725 \\ \(w_{1}=4\); \(w_{2}=2\) & 1808 & 2375 & 3324 & 3197 & 2752 \\ \(w_{1}=6\); \(w_{2}=2\) & 1776 & 3375 & 6297 & 6272 & 4175 \\ \hline \(w_{1}=1\); \(w_{2}=3\) & 2747 & 2412 & 1858 & 1402 & 1378 \\ \(w_{1}=2\); \(w_{2}=3\) & 2689 & 2565 & 2317 & 1811 & 1748 \\ \(w_{1}=4\); \(w_{2}=3\) & 2596 & 3170 & 3867 & 3422 & 2767 \\ \(w_{1}=6\); \(w_{2}=3\) & 2512 & 4585 & 7280 & 6508 & 4180 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The optimized damping coefficients when all masses \(m_{1}=m_{2}=m_{3}=m_{4}=80\) kg.