# Investigation of Vehicle Stability with Consideration of
## 4 Experimental Investigations of Suspension Properties
### Analysis of Experimental Investigation Results  
During the tests, the characteristics of free oscillations of the suspension of the vehicle were determined by applying a load on the body using an additional mass and abruptly removing the load (Figure 15). The relative damping coefficient of the suspension was determined on the basis of these characteristics in relation to the theoretical relative damping coefficient corresponding to the front suspension of the VW Golf vehicle. Comparison of the relative damping coefficient of the suspension determined on the test bench with the theoretically calculated one showed that the actually measured coefficient was slightly (15%) higher. This change may have been determined by frictional forces in the suspension elements that had not been considered. Following measurement of the parameters describing the movement of the vehicle suspension elements, it was decided to use spectral records of oscillation displacement for the analysis of the results, as these records more accurately reflect the nature of low-frequency oscillations prevailing in the vehicle body and suspension elements. The spectral analysis of oscillations enabled a more accurate assessment of the components of oscillations of individual frequencies and the determination of their origin and the nature of the change. Investigation of vehicle body oscillations caused by wheel rotation (Figure 16) allowed the observation of the maximum values of the vertical displacements of the vehicle body corresponding to the wheel rotation speed. Figure 16: Spectrum of vehicle body displacements at different wheel rotational speeds: 1—gear I; 2—gear II; 3—gear III. Figure 15: The characteristic of the free oscillations of the vehicle suspension was determined on the car suspension test bench. The frequency of these values corresponded to the rotational speed of the wheel set by the respective gear. The spectral record showed an evident increase in the vertical displacement of the 1 Hz frequency, which corresponded to the lower natural frequency of the resonance oscillations of the sprung mass. The amplitudes of the body resonance oscillations increased with increasing wheel rotational speed. To verify the reality of the vertical displacements of the vehicle body measured on the test bench, real displacements of the vehicle body were measured when driving on a smooth asphalt pavement surface. Different low-frequency resonance displacements of the vehicle body were observed in the vertical displacement spectrum (Figure 17), and their amplitudes corresponded to the amplitudes measured on the test bench. During the vehicle suspension investigation, the excitation of a rolling wheel of different frequencies was investigated, thereby simulating the effect of the road surface. Different peak displacement values were observed in the vertical displacement spectrum of the vehicle body (Figure 18). The frequency of the peak displacement values corresponded to the excitation frequency. The value of the vertical displacement determined by an excitation frequency of 25 Hz was not distinct. This may be due to the slow action of the pneumatic chamber that  
Figure 17: Spectrum of vertical displacements of the real vehicle body at different speeds: 1—23 km/h; 2—31 km/h, 3—56 km/h. Figure 18: Spectrum of vertical displacements of the vehicle body determined by different excitation frequencies: 1—4.17 Hz; 2—5.55 Hz; 3—8.33 Hz; 4—25 Hz. simulates the effect of the road surface. Therefore, it can be concluded that it is reasonable to simulate only the low-frequency (<20 Hz) excitation effect of the road surface on the test bench. An experiment was performed to compare the vertical displacements of the suspension on the test bench and of the real vehicle body to verify the reliability of the test bench results. Spectral analysis of the vertical displacements (Figure 19) suggested that the values of the displacements and the nature of the change corresponded to each other.