A Computer Simulation for Three-Dimensional Vehicle Dynamics

This paper describes a 14 degrees-of-freedom mathematical model that was developed to analyze and predict the handling dynamics of a 4-wheel vehicle. The system of nonlinear equations was programmed and numerically solved on the digital computer where the inputs are Ackerman steer angle to front and/or rear wheels and driving or braking torques on any or all wheels. The equations of motion for the sprung and unsprung masses were derived using Lagrange's equation. Constraints were included in the equations, which forced the sprung mass to roll about an inclined center roll axis.

The analysis also included nonlinear tire characteristics as well as suspension geometry and compliance parameters, such as roll steer, roll camber, auxiliary roll stiffness, and lateral force deflection steer. The results of computer simulations for J-turn maneuvers are compared with experimentally measured data for two different speeds and steering inputs.