Obtaining relations between the Magic Formula coefficients and tire physical properties

This paper introduces a technique that relates the coefficients of the Magic Formula tire model to the physical properties of the tire. For this purpose, the tire model is developed by ABAQUS commercial software. The output of this model for the lateral tire force is validated by available tire information and then used to identify the tire force properties. The Magic Formula coefficients are obtained from the validated model by using nonlinear least square curve fitting and Genetic Algorithm techniques. The loading and physical properties of the tire such as the internal pressure, vertical load and tire rim diameter are changed and tire lateral forces for each case are obtained. These values are then used to fit to the magic formula tire model and the coefficients for each case are derived. Results show the existing relationships between the Magic Formula coefficients and the loading and the physical properties of the tire. In order to investigate the effectiveness of the method, different parameter values are selected and the lateral force for each case are obtained by using the estimated coefficients as well as with the simulation and the results of the two methods are shown to be very close. This proves the effectiveness and the accuracy of the proposed method.