Development of a generalised equivalent estimation approach for multi-axle vehicle handling dynamics

This paper devotes analytical effort in developing the 2M equivalent approach to analyse both the effect of vehicle body roll and n-axle handling on vehicle dynamics. The 1M equivalent vehicle 2DOF equation including an equivalent roll effect was derived from the conventional two-axle 3DOF vehicle model. And the 1M equivalent dynamics concepts were calculated to evaluate the steady-state steering, frequency characteristics, and root locus of the two-axle vehicle with only the effect of body roll. This 1M equivalent approach is extended to a three-axle 3DOF model to derive similar 1M equivalent mathematical identities including an equivalent roll effect. The 1M equivalent wheelbases and stability factor with the effect of the third axle or body roll, and 2M equivalent wheelbase and stability factor including both the effect of body roll and the third-axle handling were derived to evaluate the steady-state steering, frequency characteristics, and root locus of the three-axle vehicle. By using the recursive method, the generalised 1M equivalent wheelbase and stability factor with the effect of n-axle handling and 2M equivalent generalised wheelbase and stability factor including both the effect of body roll and n-axle handling were derived to evaluate the steady-state steering, frequency characteristics, and root locus of the n-axle vehicle. The 2M equivalent approach and developed generalised mathematical handling concepts were validated to be useful and could serve as an important tool for estimating both the effect of vehicle body roll and n-axle handling on multi-axle vehicle dynamics.