Coupled Vertical-Lateral Dynamics of a Pneumatic Tired Vehicle: Part I—A Mathematical Model

A method is presented which permits the simulation of the coupled vertical and lateral rigid body vibration response of an automobile to roadway roughness inputs. A set of equations in matrix form is obtained for an assumed ten degree-of-freedom mathematical model of the vehicle-tire system using generalized linear and Euler angle coordinates. Kinematic relations for a rolling tire which treat it as an elastically supported string under tension are incorporated into the overall system model. Forces and moments that act in the tire-roadway contact interface are represented mathematically as a function of the parameters and response variables of the vehicle system. The nonlinear system equations are subsequently simplified in order to apply them to a vehicle moving along a straight roadway. The formulated model is shown to be adequate for predicting acceleration response in a frequency range of 0.1–10 Hz for the set of roadway test roadway sections considered in the present study.