George Mavros

Analysis of the transient handling properties of a tyre, based on the coupling of a flexible carcass—belt model with a separate tread incorporating transient viscoelastic frictional properties

The behaviour of tyres under transient handling manoeuvres is studied with the aid of a newly developed model. The model consists of a discretized flexible belt with damping and inertia, connected to the rim by viscoelastic elements representing the carcass. In the neighbourhood of the contact patch, the belt is connected to a separate discretized viscoelastic tread with inertia. A separate algorithm taking into account the radial deflection of the carcass elements is used for the calculation of the contact pressure distribution along the contact patch. Friction follows a stick—slip law taking into consideration the velocity of tread elements, the normal force and the unequal coefficients of friction in the lateral and longitudinal directions. The model seems capable of generating transient forces and moments including the phase lags observed under time-varying kinematic excitations.

Transient analysis of tyre friction generation using a brush model with interconnected viscoelastic bristles

Abstract 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.

Prediction of impulsive vehicle tyre-suspension response to abusive drive-over-kerb manoeuvres

This article presents a minimal parameter vehicle simulation model to predict the vertical suspension loads expected during abusive driving manoeuvres, such as a kerb strike event. Impulsive suspension loads are applied to tyre and suspension elements under such conditions. In particular, the aim is to specifically study the reactions of jounce bumper–rebound stop and tyre characteristics. For this purpose, a vehicle in-plane pitch dynamics model with 7 degrees of freedom suffices. Non-linear and hysteretic characteristics of the bump-stop elements are included through a new 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 membrane theory and represented in terms of only a few input parameters. Model validation is supported through experiments at both component and system levels.

Analysis of vehicle rollover dynamics using a high-fidelity model

Recent data show that 35% of fatal crashes in sport utility vehicles included vehicle rollover. At the same time, experimental testing to improve safety is expensive and dangerous. Therefore, multi-body simulation is used in this research to improve the understanding of rollover dynamics. The majority of previous work uses low-fidelity models. Here, a complex and highly nonlinear multi-body model with 165 degrees of freedom is correlated to vehicle kinematic and compliance (K&C) measurements. The Magic Formula tyre model is employed. Design of experiment methodology is used to identify tyre properties affecting vehicle rollover. A novel, statistical approach is used to link suspension K&C characteristics with rollover propensity. Research so far reveals that the tyre properties that have the greatest influence on vehicle rollover are friction coefficient, friction variation with load, camber stiffness and tyre vertical stiffness. Key K&C characteristics affecting rollover propensity are front and rear suspension rate, front roll stiffness, front camber gain, front and rear camber compliance and rear jacking force.

Influence of tyre transience on anti-lock braking:

Abstract Transient tyre characteristics can have significant influence in vehicle handling, particularly in anti-lock braking system (ABS), which involves wheel speed oscillations as a result of rapid changes in wheel brake pressure. Hitherto, ABS studies have been conducted mostly with straight-line motion. Relatively simple vehicle models have been used which cannot capture the interactions between non-linear handling dynamics and tyre behaviour. This article takes such interactions into account, using a non-linear 14-degrees-of-freedom vehicle model in combination with three different single-point contact tyre models with transient characteristics. They include a stretched-string-based model, a modified stretched-string model, and a contact mass model. The particularly demanding situation of combined cornering/ABS braking is investigated. It is shown that although all tyre models are of similar bandwidth (maximum frequency ≈ 15 Hz), the simple string tyre model fails to cope with the non-linearities involved in combined braking/cornering and predicts greater braking distances than the two more enhanced tyre models.

A study on the effect of road friction on driveline vibrations

Abstract The aim of this article is to assess the influence of the tyre/road contact interface on driveline vibrations. The mode shapes of a vehicle driveline are obtained and analysed, initially using three tyre models: a simple torsional spring, linear slip, and relaxation length-based models. Additionally, a fully transient load- and slip-dependent non-linear relaxation length model is incorporated into the driveline to determine the dynamic response on different surfaces. Simulations of pull-away manoeuvres on various surfaces are carried out. The halfshaft torque in each case is analysed and conclusions drawn on the effect of tyre dynamics on the frequency and intensity of driveline vibrations. In order to investigate the influence of higher-frequency tyre dynamics, a model incorporating tyre belt inertia is simulated for the same cases. It is found that the higher-order dynamics introduced by the tyre belt result in additional frequencies in the response, as well as differences in response amplitude. Using the non-linear relaxation length and belt inertia models it is observed that low-μ surfaces promote driveline vibrations at higher and more numerous frequencies compared with the typical shuffle response observed on a high-μ surface. It is shown that this frequency migration can be physically explained by considering the effect of decoupling between driveline and vehicle on low-μ surfaces. It is also shown that the observed frequencies can be predicted by appropriately modified linear models.

Frictional contact behaviour of the tyre: the effect of tread slip on the in-plane structural deformation and stress field development

The analysis of the in-plane deformation of the tyre in relation to the frictional contact between the road and the tread is a crucial first step in the understanding of its contribution to the longitudinal dynamics of a vehicle. In this work, the physical mechanism of the generation of the two-dimensional contact pressure distribution for a non-rolling tyre is studied. Towards this aim, a physical tyre model is constructed, consisting of an analytical ring under pretension, a non-linear sidewall foundation, and a discretised foundation of viscoelastic elements representing the tread. Tread behaviour is examined first, with focus on the development of shear micro-slip. The tread simulation is enhanced with the combination of radial and tangential tread elements and the benefits of such an approach are identified. Subsequently, the contact of the complete model is examined by implementing an algorithm for transient simulations in the time domain. The effects of the imposed vertical load and sidewall non-linearity on the contact stress and strain fields are identified. The modelling approach is validated by comparison with published experimental results. The physical mechanism that couples the torsional and horizontal/vertical deformations of the carcass with the frictional forces at the tread is identified and discussed in detail. The proposed modelling approach is found appropriate for the description of the development of the two-dimensional contact pressure field as a function of the frictional potential of the contact.

The simulation of in-plane tyre modal behaviour: a broad modal range comparison between analytical and discretised modelling approaches

In-plane tyre modal behaviour determines the response of tyres to ride excitations and braking/traction manoeuvres. In many studies, the interest is limited to relatively low frequencies and a detailed investigation into the ability of models to accurately simulate higher-order responses is unnecessary. In cases where an in-plane model is to be used for the generation of the contact deformation and stresses, or where modal reduction methods are implemented, a detailed knowledge of the modal response is desirable. The present work forms a study on the ability of a number of frequently used modelling approaches to generate realistic modal data throughout a wide frequency range. The analytical ring on elastic foundation model is used as a benchmark throughout the paper. Its predictions are compared with those of two discretised models, namely a truss- and a beam-based model. The sensitivity of the ring’s response to a number of physical parameters is discussed. The results are used to inform the comparison between the analytical ring and the discretised models, providing explanations for any discrepancies observed. The limited applicability of the truss model is pointed out, while the accuracy of the beam-based model is enhanced by a circumferential inextensible string element. Both the ring and the enhanced beam models are further improved with the addition of a nonlinear string-based sidewall that accounts for the change in sidewall stiffness with inflation pressure. The findings may offer a reference when setting up in-plane models, including the stage of planning modal tests for parameter identification.

A study on the influences of tyre lags and suspension damping on the instantaneous response of a vehicle

Abstract The paper aims to quantify the influences of non-steady state tyre behaviour and suspension damping on the instantaneous response of a vehicle to handling manoeuvres. The influences of such parameters cannot be determined using steady state tests. In the present work, a recently developed methodology is employed, which has been applied in the past to simple transient handling studies. Here, the approach is applied to more demanding situations and the effects of tyre lags and suspension damping are directly related to the under-steer, over-steer, or neutral-steer character of the vehicle under test. To distinguish between the effects of tyre force lags, tyre non-linearities, and combined tyre—vehicle non-linearities, an increasingly complex approach is adopted, which involves the implementation of a linear bicycle model, a non-linear bicycle model, and a ten-degrees-of-freedom (10DOF) non-linear vehicle model. In all cases, tyre-force lags are simulated using the relaxation length concept. The 10DOF vehicle model is validated against experimental measurements and forms the basis for fully non-linear studies. It is shown that even inherently under-steering vehicles may initially over-steer as a result of the delayed response of tyres. Finally, it is demonstrated that the proposed approach captures the effect of suspension damping and some problems are discussed regarding its application.

Optimisation of AWD off-road vehicle performance using visco-lock devices

A comprehensive computer model is devised for the simulation of AWD off-road vehicle dynamics. Particular attention has been paid to the modelling of various visco-lock devices, including the viscous couplings and visco-lock limited-slip differentials. These devices are represented by fully parameterised physical models which capture the torque transmission mechanism represented by various thermodynamic, hydrodynamic, structural and mechanical modules. The characteristics of these devices can easily be altered so that comparisons can be made between different types. In addition, the influence of a wide range operating conditions, vehicle design parameters and tyre characteristics can also be made over various deformable soils.