A Combined-Slip Physical Tire Model Based on the Vector Distribution Considering Tire Anisotropic Stiffness

The tire mechanics characteristics exert significant influence on vehicle dynamics and control, especially under the combined cornering/braking/driving conditions. In general, tire steady-state mechanics models can be divided into three categories: empirical models, semi-empirical models, and physical models. Compared with empirical model and semi-empirical model, the physical model is more suitable for theoretical derivation and analytical solution in vehicle dynamics research, especially under the extreme conditions of large slip, such as drift cornering. Therefore, a physical predictive tire model with high accuracy and simplified expression has been proposed in the paper, which avoids the complex tire testing for the combined-slip conditions. The Exact Unified Combine Brush (EUCB for short) model proposed is based on the brush model and the vector distribution principle considering anisotropic tire stiffness. The brush model, as a theoretical basis of many tire models, could analytically and qualitatively explain many tire mechanics phenomena. The vector distribution could accurately describe the magnitude and direction of the shear forces from the physical sense under the combined lateral and longitudinal slip conditions. In the paper, the derivation process of the proposed model is introduced firstly from pure and combined slip conditions. Then, comparison between the brush physical models based on three assumptions about the direction of resultant shear force and the proposed model is separately conducted. Lastly, the proposed model is compared with the COMBINATOR model, Magic Formula (MF for short) model and Modified Dugoff model, and validated by the test data under different conditions. The result shows that the proposed model has good accuracy and predictive ability.