Improved Constraint Mode Tire Model with Analytical Derivations and Numerical Approximations

Abstract

Tires are of particular significance in vehicle studies, as they are the interface between the vehicle and the terrain. They are responsible for the load generation in vehicle handling, dynamics, vehicle-terrain interactions, hydroplaning, etc. Numerous studies have been conducted in the field of tire modeling techniques. Existent empirical, semi-empirical and analytical tire models are studied in this study, accompanied by discussions of their individual pros and cons. A 2-D tire model and its expansion to 3-D are proposed in this study. Both the 2-D and 3-D models are analytically derived and constructed based on principles and theorems of solid mechanics, solved using numerical methods to yield approximate solutions. In both models, a tire is treated as an elastic component mounted onto an elastic foundation. Contributions from different components of a tire to the tire stiffness are included with justifications, therefore the mechanics and structure of a tire are reflected in the models, creating strong correlation among the model parameters and tire properties. The equations of forces and deformation are derived with the energy method. Some issues with applying the energy method in a previous study are also identified and improved. The proposed models are capable of providing quick and accurate estimations of a tire in terms of spindle force, pressure distribution and deformation profile. The models are calibrated using experimental data, then used to predict tire performances under a variety of situations. The predictions by the proposed models show good alignment with experimental data. The models also demonstrate much potential for future improvements.