Abstract

In the present study, a new two-dimensional hybrid quarter-car model has been developed. The hybrid model takes into account the inertia of the discrete vehicle body mounted on suspension and the dynamics of the rotating tire modeled as a continuous ring. The contact force between the tire and road is defined as a function of the bounce vibration of the vehicle as well as a function of the radial and tangential displacements and accelerations of the tire. The effects of the vibrating system on the contact force are investigated. Three different types of solution are presented: the Galerkin method, the finite element method, and the exact analytical method. Different solutions are used to validate the accuracy of the results. The mode shapes of the center-fixed rotating ring are used as admissible functions in the Galerkin method. In the finite element method, a curved beam is used as the element. The equations are derived in a non-rotating coordinate system. In other words, the nodes do not rotate. However, the material of the ring does rotate by flowing through the non-rotating nodes. The analytical study presents the closed-form solutions of the horizontal displacement and of the vertical displacement of the center of the tire (unsprung mass) as well as the displacement of the vehicle body (sprung mass). This method also provides the radial displacement and the tangential displacement of the rotating ring in the non-rotating coordinate system, all the displacements of the ring being measured with respect to the center of the ring. The results obtained by the different methods are compared and discussed. The natural frequencies of this hybrid system are compared with those obtained for a center-fixed ring. Also the damped frequencies of the system are obtained for different velocities of the vehicle. The mode shapes of the hybrid model are complex because of the rotating tire. Moreover, the response of the hybrid model to the random excitation caused by the road is studied. Results show that the rotation of the tire and the bounce vibration of the vehicle body affect the dynamic forces at the contact point. These results are compared with those of the conventional 2-DOF quarter-car model.