Simplified 7 DOF Model of Car Vertical Vibrations for Small Pitch and Roll Angles

Abstract

This paper concerns a simplified 7 DOF model for car vertical vibrations. The classical 7 DOF of the considered 3D vertical model are: the vertical displacement of the gravity center of the car body, the roll and pitch angles of the car body and the four vertical displacements of the wheels centers. Using the x-y-z sequence of rotations parameterization, the Euler’s rotation equations concerning the roll and pitch angle are easily obtained. Small differences are observed between our car body rotation equations concerning the two pitch and roll angles and the same equations provided by Demić et al. [6]. For small pitch and roll angles, no differences were observed with respect with [6]. Also, no differences were observed concerning the other 5 dynamics equations of the 7 DOF model, the ones for the vertical displacements.The simplified 7 DOF car vertical dynamics model, comprising two rotation equations (for pitch and roll angles) and five dynamics equations concerning vertical displacements/accelerations, were integrated/simulated in Matlab. For small pitch and roll angles (a rather flat and smooth straight road profile was considered in our case study), the results obtained using the in-house 7 DOF model Matlab simulator are in very good agreement with the results provided by CARSIM.