An overview of existing and alternative forms of vehicle understeer/oversteer expressions is presented. New forms are derived consistent with conceptual extensions to the configurations of the vehicle's steering system, the driving mode - steady-state or transient, and the responses - path curvature or yaw velocity. Derivation of all understeer expressions is presented with a consistent use of the Ackermann reference case and the related “Ackermann vehicle” construct. The vehicle is otherwise represented in a traditional manner as a bicycle model operating in the linear range consistent with small angle approximations.
The vehicle's steering system is assumed to be more generally configured with four-wheel steer and active or steer-by-wire actuation at both axles. The actuation is assumed to allow the introduction of significant speed sensitivity to the effective overall steering ratios. Discussion is devoted to the significance of this speed sensitivity on test results and the determination of the mean reference steer angles. Expressions for understeer gradient associated with this generally configured vehicle are simplified for the more familiar case of a front-wheel steer vehicle with a passive steering system having a fixed overall steering ratio.
The driving mode can be either steady-state, as is traditionally assumed, or transient. The transients are assumed to be the result of steering transients or speed changes.
Understeer expressions are presented using traditional variables, included reference steer angle and included Ackermann steer angle, and less frequently used variables, axle reference sideslip angles and cornering compliances.
Context is given with a brief history of the development of understeer concepts, both traditional steady-state and transient, and usage of the terms “understeer” and “oversteer”.
