Sensitivity study and optimization of magic formula tire parameters for vehicle handling and steering targets

Abstract

Vehicle handling and steering is one of the most important attribute which defines the overall performance and driving dynamics for a car. The factors which primarily define the handling and steering performance are its chassis, suspension and tire characteristics. There are multiple Multi Body Dynamics (MBD) tools currently used in order to better understand and develop the chassis and suspension performance of a car respectively. But the tire development is currently dependent on physical prototyping and testing. This makes the whole process of understanding the tire attributes and its impact on the dynamics of the car difficult and expensive. This calls for further development of tire models and tire simulation tools to aid virtual development of tires. This thesis mainly focuses on developing a tool which optimizes Magic Formula tire parameters to meet the desired vehicle dynamic targets using Magic formula tire 5.2 (PAC2002) which is an empirical tool which defines the forces and moments developed by a tire under the influence of load and slip accurately.Thereby aiding the development and understanding of impact of tire parameters on vehicle handling and steering targets. This thesis looks into the Magic Formula Tire model 5.2, which is widely used to study vehicle dynamic handling and steering attributes of a car. It is an empirical formula which efficiently captures the physical dynamics of a tire and its impact on a car. This study looks at Magic Formula pure lateral force parameters and their influence on lateral force characteristics of a tire under various load and slip conditions. Simulation software VI-CarRealTime was used in this study in order to integrate Magic Formula tire properties to a vehicle model and to analyse the effect of Magic Formula tire parameters on handling and steering performance of a car. The first part of the study includes the parameter analysis and identification of the most influential Magic Formula tire parameters. Then the study includes identification of suitable maneuvers and vehicle dynamic performance metrics in order to study the influence of Magic Formula tire parameters on handling and steering targets. Once the vehicle dynamic metrics and most influential Magic Formula Tire parameters are identified, a sensitivity study is carried out with Magic Formula Tire parameters varied in equal steps over a fixed range. During the sensitivity run, respective vehicle dynamic metrics and the influence of Magic Formula Tire parameters on these vehicle dynamic metrics are recorded in the form of a objective sensitivity matrix for a reference vehicle used for this study. The objective sensitivity matrix was also developed based on the sensitivity of Magic Formula tire parameters on the axles of a car. Using the objective sensitivity matrix and the weights assigned to the vehicle dynamic metrics by the attribute leaders, an objective function was set up. The minimum value of this objective function will then provide a reference vehicle equipped with the optimized set of tires which will satisfy as many handling and steering targets as possible, including the possibility to optimize a set of tires for individual axles.