# Assessment of Tire Features for Modeling Vehicle Stability in Case of Vertical Road Excitation
## 3 Vehicle Excitation by Road Unevenness
### Experimental Investigation  
In an investigation of a car stability, the characteristics of the road microprofile must be available. To measure the road microprofile, a measuring device consisting of the Volkswagen Transporter with DYNATEST road profile measuring equipment and laser sensors mounted on the front of the car were used (Figure 23). Measurement equipment: VAS-21 vibration analysis and processing system [59], PicoScope 3424 signal converter (Table 7), two low-frequency (WILCOXON Model 793L SN7688) and two medium-frequency (WILCOXON Model 784A SN12040) sensors (Table 8). The data were registered real-time on a PC, recorded, and processed using PICOSCOPE 5.13.7 software. Measurements were performed in the city and on the highway. Road unevenness was measured using the Lithuanian Transport Safety Administration and Transport Competence Agency a VW Transporter car equipped with the measuring devices. The driving speeds in the city were and on the highway: 50, 60, 70, and 80 km/h. Measurement duration: 50 s.  
To determine the frequency characteristics of the sprung and unsprung mass, compact car was selected for the study (Table 9). The measurement sensors for compact city car unsprung mass vibrations were mounted on the suspension arms (Figure 24a,b), while the sensors for measuring sprung mass vibrations were mounted on the front fender and car roof (Figure 24c,d). During the experimental studies, the driving speed down the road of the investigated profile was different during the 50 s drive and the accelerations of the sprung (body) and unsprung (suspension) masses of the cars. The test results for the compact car are shown in Figures 25 and 26. High-intensity noise and the nonlinear reaction of the car suspension to excitation made the result analysis more complex. While the movements of the unsprung mass show relatively little variation at the speeds of 50 and 70 km/h, the reaction of the sprung mass was very different at the same speeds, as individual unevenness may excite considerable body displacements without causing any significant suspension deformations. Figure 24: Mounting of sensors for measuring vibrations of unsprung mass: (**a**)—front suspension, (**b**)—rear suspension; and sprung mass: (**c**)—on the front fender, and (**d**)—on the roof. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{3}{c}{**Overall Dimensions, mm**} & \multicolumn{3}{c}{**Mass, kg**} & \multirow{2}{*}{**Tire Dimensions**} & \multirow{2}{*}{**Static Radius, mm**} & \multirow{2}{*}{**Tire Diameter, mm**} \\ \cline{1-2} \cline{5-8}
**Length** & & & & & & **mm** & **mm** \\ \hline
3985 & 1665 & 1415 & 2475 & 870 & 1400 & 175/70R13 & 261 & 293 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Compact car data. Frequencies close to the frequency of own oscillations of the suspension (for passenger cars 0.8-1.3 Hz) and own oscillation frequency of unsprung masses (for passenger cars 8-13 Hz) were of particular interest in terms of the stability characteristic. It was the travel of the suspension that was defined as the difference between the displacements of the sprung and unsprung masses that had the greatest influence on the changes in the spatial position of the wheel. The equipment registered the peaks of the lowest frequencies in the range of 5-7 Hz (Figure 27), i.e., the frequencies characteristic of own oscillation frequency of the suspensions. In addition, the vibration sensors registered additional vibrations caused by the vibrations of the suspension elements (Figure 27a). Their frequencies exceeded the characteristic vibration frequencies of the tire (80-100 Hz). The oscillations were transmitted to the body (Figure 27b); however, comparing the frequency spectra of sprung and unsprung masses, the oscillations in the body were observed to be influenced by the structure of elements selected as sensor mounting points, namely, the wing at the suspension fixing point was less sensitive to high-frequency vibrations than the roof panel.