Extending the Magic Formula Tire Model for Large Inflation Pressure Changes by Using Measurement Data from a Corner Module Test Rig

Since the tire inflation pressure has a significant influence on safety, comfort and environmental behavior of a vehicle, the choice of the optimal inflation pressure is always a conflict of aims. The development of a highly dynamic Tire Pressure Control System (TPCS) can reduce the conflict of minimal rolling resistance and maximal traction. To study the influence of the tire inflation pressure on longitudinal tire characteristics under laboratory conditions, an experimental sensitivity analysis is performed using a multivalent usable Corner Module Test Rig (CMTR) developed by the Automotive Engineering Group at Technische Universität Ilmenau. The test rig is designed to analyze suspension system and tire characteristics on a roller of the recently installed 4 chassis roller dynamometer. Camber angle, toe angle and wheel load can be adjusted continuously. In addition, it is possible to control the temperature of the test environment between −20 °C and +45 °C. The results of the experimental study that covers a wide range of different wheel loads and inflation pressures for three different tire variations show a significant influence of the inflation pressure on longitudinal tire characteristics as slip stiffness or maximum traction force. To simulate the influence of a TCPS on vehicle dynamics with a numerical simulation tool, it is essential to describe the influence of the inflation pressure on tire characteristics correctly with a tire model. Consequently, the well-known semi-empirical Magic Formula tire model adapted from Pacejka is extended for large inflation pressure changes. The parameters of the tire model are identified with a method of least squares which is implemented in an automatic MATLAB analysis tool. A comparison of the standard and respectively the enhanced tire model show an obvious improvement of the model accuracy.