A nonlinear kinematic and dynamic modeling of Macpherson suspension systems with a magneto-rheological damper

It is well known that Macpherson strut suspension systems are widely used in light and medium weight vehicles. The performance of these suspension systems can be enriched by incorporating magneto-rheological (MR) dampers and an appropriate dynamic model is required in order to find out the ride comfort and other performances properly in the sense of practical environment conditions. Therefore, in this work the kinematic and dynamic modeling of Macpherson strut suspension system with MR damper is presented and its responses are evaluated. The governing equations are formulated using the kinematic properties of the suspension system and adopting Lagrange's equation. In the formulation of the model, both the rotation of the wheel assembly and the lateral stiffness of the tire are considered to represent the nonlinear characteristic of Macpherson type suspension system. The formulated mathematical model is then compared with equivalent conventional quarter car suspension model and the different dynamic responses such as the displacement of the sprung mass are compared to emphasize the effectiveness of the proposed model. Additionally, in this work the important kinematic properties of suspension system such as camber angle, king-pin angle and track width alteration, which cannot be obtained from conventional quarter car suspension model, are evaluated in time and frequency domains. Finally, vibration control responses of the proposed suspension system are presented in time and frequency domains which are achieved from the semi-active sky-hook controller.