A New Analytical Tire Model for Cornering Simulation. Part I: Cornering Power and Self-Aligning Torque Power

A new analytical tire model for cornering power (CP) and self-aligning torque power (SATP) is proposed on the basis of the Fiala model. In a pneumatic tire, the self-deformation by the transmission of force and torque is so large to influence recursively the force and torque generation during cornering. Then CP and SATP have negative feedback loops: As CP and SATP increase, the steering transmission loss by the tire self-deformation also increases to depress further increments of CP and SATP. The present model, the CP/SATP system model, analytically describes the force and torque transmission with feedback loops by taking into account not only (i) the shear deformation of the tread rubber and (ii) the in-plane belt deflection, but also (iii) the out-of-plane sidewall rotation. As well as other practical systems with a negative feedback loop, the CP and SATP feedback stabilize the CP and SATP output level at a higher vertical load, and approximates the measured load dependence of CP and SATP with high accuracy. Although the sidewall rotation feedback by SATP has not been considered in conventional cornering studies, its contribution in recent radial tires is shown to be larger than that of belt deflection by CP. The model is applicable to not only the numerical simulation for tire design but also the inverse data analysis of the cornering test. Nonlinear least-squares fittings of the measured data to the model are excellent and give the dynamic estimates of tire-part stiffness.