A two-dimensional suspension-Tire system is modeled to investigate the dynamic interaction between the suspension and the tire of an automotive system. A double A-arm suspension system is used in the model. Lagrange equation for a constrained set of generalized coordinates is employed to derive a lumped-mass model of the system. The effects of friction and mechanical characteristics of the tire-road interface in both lateral and vertical directions is modeled and utilized in the system’s dynamics using the Magic Formula for tire. The utilization of Lagrange equation along with the Magic Formula provided a means of prediction of the system’s dynamic response to different initial sprung mass load conditions and the alteration and optimization of the suspension system geometry to achieve minimum sprung mass and tire vibration. The model is used to illustrate tire slip angle variation as a result of induced vibration due to a step load along the vertical and lateral direction. Albeit the response is a damped nonlinear vibration response, the system shows relatively large variation in slip angle in the transient regime of the system response.

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