# Investigation of Vehicle Stability with Consideration of
## 7 Conclusions  
1. A comprehensive analysis of vehicle-road interactions shoed that in order to determine the stability of vehicle movement it is necessary to accurately assess the characteristics of the interacting subsystems. Factors influencing vehicle-road interactions were specified during the investigation, including road surface characteristics; nature of road surface, tire contact area and compared properties of the tire, suspension design; kinematic and dynamic models of the suspension, all of which affect stability of the vehicle movement. 2. A revised model of tire equalizing function was developed. The coordinates of relative measures were found to cause no essential differences in the assessment of tire deformations of different vehicle tires. This means that the number of tire groups may be reduced to evaluate their impact on stability. 3. A dynamic quarter-car model was developed for a comprehensive integrated assessment of suspension characteristics, suspension kinematics, and road surface condition. The model enabled the development of a methodology for the determination of the safe speed of the car on roads of known quality using numerical models. 4. Analysis of the revised quarter-car model showed that the nonlinearity of the suspension elements could be ignored only with examination of movement on a good quality asphalt pavement, because the suspension elements work in the linear part of the suspension characteristic. The effects of nonlinear elements occurred when driving on low quality roads and in case of severe, random damage to the road surface. During large suspension movements, it was necessary to account for friction forces in the damper frame; therefore, methodology for formalizing friction force was considered. 5. The adequacy of the theoretical characteristics of the quarter-car model in relation to the real characteristics was investigated using an experimental test bench. The relative damping coefficient of the vehicle suspension measured on the test bench was approximately 15% higher than the calculated coefficient. The frequency characteristics of the vertical displacements of the real vehicle and vehicle body measured on the test bench were similar to those predicted by the quarter-car model in terms of the magnitude and nature of the change. The developed model is appropriate for further investigations and improvement of vehicle suspension properties. 6. The revised kinematic model of suspension confirmed that the relative real camber changes by up to 2\({}^{\circ}\) when modeling an asphalt road surface compared to an ideally horizontal road surface. This causes the alignment angle of the wheel to change by up to 1.5\({}^{\circ}\). 7. The results of the experiment on the asphalt pavement road surface were compared with the model. Certain issues were observed in the analysis of experimental results due to additional oscillations and vibrations occurring in the body and suspension elements, which could be avoided by modeling movement after recording the road microprofile with a profilograph. The parameters that had the greatest impact on the stability of the direction--the difference between the displacement of the sprung and unsprung masses in the model versus the field experiment--did not exceed 15%. 8. Changes in car behavior at changing speeds are related not only to the slip effect but also to changes in wheel spatial position due to suspension kinematics and suspension incompatibility with the steering mechanism. This effect can be particularly pronounced when road defects (pits, ruts) lead to an increase in suspension movement. **Author Contributions:** Conceptualization, V.L., R.M., A.R., R.K., A.D. and R.S. ; methodology, V.L., R.M., A.R., R.K., A.D. and R.S. ; software, V.L., R.M., A.R., R.K., A.D. and R.S. ; validation, V.L., R.M., A.R., R.K., A.D. and R.S. ; formal analysis, V.L., R.M., A.R., R.K., A.D. and R.S. ; investigation, V.L., R.M., A.R., R.K., A.D. and R.S. ; resources, V.L., R.M., A.R., R.K., A.D. and R.S. ; data curation, V.L., R.M., A.R., R.K., A.D. and R.S.