DOI: 10.1243/146441905X9908Abstract: An analysis of the mechanism of tyre contact force generation under transient conditions is presented. For this purpose, two different versions of a brush model are used, both with inertial and viscoelastic properties. The first model consists of independent bristles, while the second, with a more realistic scenario, introduces viscoelastic circumferential connections between the sequential bristles, which affect the lateral degrees of freedom. Friction between the tyre and the ground follows an experimentally verified stick -slip law. For the model with independent bristles, the state of each bristle at any instant of time depends only on the state of the same bristle at a previous time step. In the second model, the instantaneous state depends on the state of the same bristle at the preceding time step, as well as on the state of the two adjacent bristles at the same time. Simulation results reveal the differences between the two models and most importantly show how transient friction force generation may differ substantially from steady state predictions. The findings suggest that transient tyre behaviour should not be attributed solely to the contributions of the flexible belt and carcass. On the contrary, the observed transience in the neighbourhood of the contact patch should also be taken into account.

The paper presents a minimal parameter vehicle simulation model to predict the vertical suspension loads expected during abuse driving manoeuvres, such as a kerb strike event. This causes impulsive bump-stop loads. Since the aim is to specifically study impulsive bump-stop and tyre characteristics, an in-plane pitch model with 7 degrees of freedom suffices. Non-linear and hysteretic characteristics of the bump-stop elements are included by a parametric map concept, based on displacement and velocity dependent hysteresis. Furthermore, a static tyre model is described, tailored to predict the radial stiffness against penetration of an edge with a flat-type rigid body geometry. The tyre model is derived on the basis of classical shell theory and represented in terms of only a few input parameters. Model validation is supported through experiments at both component and system levels.

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 (...

The paper attempts to provide an integrated framework for the objective assessment of the transient handling responses of non-linear vehicles. The ultimate aim of the proposed framework is the characterization of such responses as neutral or under/over-steering. A new methodology is employed, which has previously been applied for the classification of the transient response of linear vehicles. The success of the proposed method is judged based on its robustness, the consistency of the results, and their practical implications. Furthermore, the results are compared with the findings of traditional approaches for the characterization of the steady-state and transient handling behaviour. The corresponding discussion reveals the agreement between the approaches, but also highlights the slightly different definition of the neutrally steering vehicle, as perceived by the proposed method.

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