The paper suggests a new methodology for the objective assessment and quantification of the response of a vehicle subjected to transient handling manoeuvres. For this purpose, a non-dimensional measure is defined, namely the normalised yaw impulse.This measure appears in two variations. In its general or dynamic form, it represents the difference between the yaw moment due to the front tyre forces and the yaw moment due to the rear tyre forces, divided by the sum of the aforementioned yaw moments. By employing a linear, 2 degree-of-freedom bicycle model it is shown that the general form of the normalised yaw impulse can be written as a function of the steer angle and the forward, lateral and yaw velocities of the vehicle. This form is referred to as the kinematic yaw impulse. It is demonstrated that the combined application of the dynamic and kinematic expressions of the yaw impulse not only facilitates the explicit assessment and quantification of the transient behaviour of a vehicle, but also reveals the influence of parameters such as the yaw moment of inertia, which traditionally leave the steady-state behaviour unaffected. provides a rather informative image of a vehicle's handling qualities and can be also related to the transient response of the system, as is well known from basic dynamics and control theory [8]. For example, the inverse of a specified bandwidth frequency can be used as an equivalent time constant for the vehicle's yaw rate response to a step-steer input [7]. Furthermore, the existence of a resonance frequency indicates a system with sub-critical damping, which is related to under-steer [2], as opposed to over-steering vehicles which are characterised by an equivalent damping ratio greater than one [2].
KeywordsNevertheless, the general characterisation of a vehicle based on its frequency response should be attempted with caution. For instance, an observed resonance frequency which indicates under-steer, might be related to the roll frequency of the vehicle in conjunction with a suspension set-up which dictates severe lateral weight transfer at the front end only. Certainly, this condition would not apply on any manoeuvre and thus the overall characterisation of the vehicle proves to be a difficult mission.The frequency response of a vehicle has already been related to its transient response to zero. This is easily explained if one considers the fact that under steady-state conditions 7 the yaw acceleration and consequently the yaw moment (the numerator in equation (1)) converge to zero, while the denominator converges to a non-zero value.The behaviour of the dynamic normalised yaw impulse is investigated further by implementing a linear 2 degree-of-freedom bicycle model. Assuming a constant forward speed U , sufficiently small steer angles and linear tyres, the equations of motion for the lateral and yaw degrees of freedom of the model read:Further assuming a front-steered vehicle and relatively small slip angles f a and r a , the following relations apply [2]:Equations (2) and (...