Abstract: A new method to describe the tire rolling kinematics and calculate the tire forces and moments is presented. The rolling contact is the core problem of tire/vehicle mechanics as well as wheel/track dynamics. It is extremely difficult to model rolling contact because of the rigid body rotation and the finite deformation occurred. The mixed Lagrange-Euler method is introduced to deal with the calculation of the velocity, acceleration, and contact deformation of rolling contact structure. By using Lagrange framework, the tire velocity and acceleration which include the rigid body rotation and elastic deformation can be obtained by treating the wheel position angles as Cardanic angles, while the Euler method is used to analyze the deformation and forces in the contact area. The dynamic analysis of the rolling structure is thus performed by transferring information between these two kinds of grids in the contact area. Not only can the presented principle be degenerated into Fiala tire model but it can explain the tire ply steer and ply camber phenomenon as well. The method to predict the tire forces and moments is built up by using the proposed kinematic theory and nonlinear finite element method. The detailed analysis of the slipping velocity, contact forces, contact areas, lateral forces of a radial tire have been performed. Study on the parametric sensitivity of the tire lateral forces and self-aligning torque on the tread stiffness and friction coefficient is also carried out. The results show that the tire cornering stiffness and self-aligning stiffness are mainly controlled by the structure stiffness, while the peak lateral force and peak self-aligning torque are mainly controlled by the friction coefficient. The effect of the belt structure to the cornering properties of the large radial tires will be studied by using related experiments and simulations, to verify the principles and methods mentioned above. The proposed methodology provides a new tool to predict tire forces and moments.

Key words: Ply camber, Ply steering, Radial tires, Rolling contact, Steady state kinematics, Tire forces and moments