Analysis of Non-Steady State Tire Cornering Properties Based on String-Concept Deformation and Geometric Relationship of Contact Patch

Vehicle handling and stability performances are greatly determined by non-steady state (NSS) tire cornering properties. Analytical derivation of NSS tire cornering models are presented in this paper based on Pacejka's string-concept assumption, in which carcass is assumed to be a stretched string with lateral deformation and lateral relaxation. The lateral inputs of the models are either displacement-based (lateral displacement and yaw angle) or slip-based (slip angle and turn slip). The transient deformations in spatial domain in both longitudinal and lateral directions are obtained directly from geometric relationship of contact patch. The additional self-aligning moment due to longitudinal deformation of contact patch after effect of tire width is considered is also achieved according to geometric relationship of contact patch in longitudinal direction and two transient geometric conditions of contact point. The presented analytical method is significantly different from and is regarded to be much simpler than that of Pacejka's although both derived models are consistent. The model derived by Pacejka is originally based on slip velocity of contact center and sliding velocity components (longitudinal and lateral) of contact point. Non-dimensional simplification of the NSS models and frequency responses (Bode plots) at different model parameters are presented in this paper.