Parameter Identification of mathematical-empirical Tire Models using Measurement Data of a Wheel Force Transducer

"In research and development, the use of model-based methods has been established widely. In spite of the required costs and time for modelling and parameterization, the models become applicable in many steps of the design process from concept studies until parameter optimization. Particularly, during the early phase of the development of products or functions, it is necessary to keep time and cost efforts as low as possible without significantly reducing the quality of the simulation results. For the development of vehicle dynamic controls, the quality of the used models depends highly on the modelling of the wheel-road contact. Due to the reduced parameterization and calculation effort, mathematical-empirical or semi-physical approaches as well as flexible belt-ring models are preferred to simulate severe driving manoeuvres such as full braking with ABS intervention or the ISO 3888 double lane-change. The determination of the model parameters is carried out using special tire test rigs in which the tire and rim are clamped. Due to the complex experimental setup and the required infrastructure, these tests are very cost-intensive. In driving tests with real vehicle, commercially available wheel force transducers are used today. By means of force measuring elements, which are usually attached to an especially manufactured and split rim body, the transmitted forces and moments are determined while driving. A high-resolution angle sensor detects the rotation angle and the angular velocity of the wheel in order to transform the measured quantities (forces and torque at the wheel) from the rotating to the vehicle related coordinate system. At the beginning of the paper, established concepts of tire test rigs for determining the parameters of mathematical-empirical tire models will be summarized and compared with the proposed usage of a wheel force transducer in real-driving tests. This will include an estimation of the boundary conditions and the reproducibility of the measurements as well as influencing factors on the force transmission. Subsequently, the test equipment and driving manoeuvres that were carried out with the test vehicle are presented. In addition to the wheel force transducer, a 2-axis optical speed sensor is added to the test setup. Using the measured vehicle velocity and the measured wheel speed the tire slip can be calculated now. The measurement data is partly used for parameter identification of two simplified tire models according to PACEJKA and BURCKHARDT, which describe the steady-state friction coefficient slip characteristic. Since these are nonlinear tire models, a non-linear least squares algorithm is used as the mathematical optimization method. The measurement data, which was not used for the parameterization, are applied in the subsequent validation of the tire model. On the basis of the obtained results a statement about the usability of a parameterized tire model based on measurements with a wheel force transducer is made and possible extensions and suggestions for improvement are derived."