Taheri, S. and Wei, T., "A New Semi-Empirical Method for Estimating Tire Combined Slip Forces and Moments during Handling Maneuvers," SAE Int. J. Passeng. Cars - Mech. Syst. 8(2):797-815, 2015, doi:10.4271/2015-01-9112.
Modeling the tire forces and moments (F&M) generation, during combined slip maneuvers, which involves cornering and braking/driving at the same time, is essential for the predictive vehicle performance analysis. In this study, a new semi-empirical method is introduced to estimate the tire combined slip F&M characteristics based on flat belt testing machine measurement data. This model is intended to be used in the virtual tire design optimization process. Therefore, it should include high accuracy, ease of parameterization, and fast computational time.Regression is used to convert measured F&M into pure slip multi-dimensional interpolant functions modified by weighting functions. Accurate combined slip F&M predictions are created by modifying pure slip F&M with empirically determined shape functions. Transient effects are reproduced using standard relaxation length equations. The model calculates F&M at the center of the contact patch.The developed methodology is implemented as an external tire module for the vehicle simulation software CarSim. The validation studies are conducted using the data sets from a flat belt testing machine and outdoor handling tests. The model demonstrated a high correlation with experimental results, while featuring an improved performance in parameterization and F&M estimation routines, compared to the commercially available Magic Formula tire model.