Coupled analysis of tire slip and longitudinal vehicle response using a parameterized tire model under different torque conditions

Abstract

This study presents a computational investigation of longitudinal tire slip dynamics and their influence on vehicle motion using a parameterized tire model within an integrated four-wheel vehicle framework. Existing analytical, reduced-order, and experimental studies frequently treat the governing sub-systems in a decoupled or simplified manner, imposing load transfer quasi-statically, assuming a constant rolling radius, or computing slip from a rigid kinematic relationship. The contribution of this work is a closed, self-consistent formulation, in which four independently parameterized Magic Formula tires are dynamically coupled with the vehicle body, wheel rotational dynamics, dynamic axle load transfer, and braking dynamics, and solved simultaneously as a single differential-algebraic system. In this coupling, the instantaneous slip determines the tire force, which drives wheel rotation and longitudinal load transfer, which in turn updates the normal load and the speed- and load-dependent effective rolling radius governing the subsequent slip. The model incorporates drive torque, braking inputs, road inclination, and aerodynamic drag, and simulates a complete driving cycle consisting of acceleration, steady-state motion, and braking. Key performance parameters, including the longitudinal slip ratio of the front and rear tires, vehicle velocity, travel distance, and axle normal loads, are evaluated under varying torque inputs. The results reveal distinct slip characteristics between the front and rear wheels during transient acceleration and braking, a pronounced increase in negative slip during braking corresponding to potential wheel-lock tendencies, and a braking-phase rear-axle slip that converges to a nearly constant value independent of the initial drive torque. The coupled analysis of vehicle speed, travel distance, and dynamic load transfer further establishes the relationship between slip dynamics and vehicle kinematics. The findings provide insight into vehicle stability and the design of traction and braking control strategies, particularly for electric vehicles characterized by rapid torque delivery.