With an increasing need for accurate full vehicle models, a sensitivity analysis of the modelling of tyres depending on their age and wear was conducted. This included a sensitivity analysis into the accuracy of acquiring the tyre stiffnesses on a static test setup. An FTire model is developed with the aim to update this model with basic tests to give a more accurate representation of the aged or worn tyre. A well-researched and documented method is used to artificially age the tyres. During the aging process the tyre was statically tested to monitor the potential changes in characteristics. Tyres were also worn on a dynamic test setup and periodically tested to monitor the property changes. These tests included both static and dynamic measurements. The results indicate that the vertical and longitudinal stiffnesses of the tyre have convincing dependencies on the age and wear of the tyre. While the aging process was a trustworthy method, the wear process created irregular wear across and around the tyre subsequently skewing the results. Simple methods of updating the FTire tyre model without re-parameterising the model completely, was found to be effective in accounting for age and wear. / Dissertation (MEng)--University of Pretoria, 2017. / Mechanical and Aeronautical Engineering / MEng / Unrestricted

The work presented in this thesis is dedicated to the study of transient tyre dynamics and how these influence the dynamic behaviour of the vehicle and its driveline, with the main focus being on low-to-zero speed manoeuvres such as pull-away events. The bulk of the work focuses on the amalgamation of the hitherto disparate fields of driveline modelling and detailed tyre modelling. Several tyre models are employed and their relative advantages and disadvantages analysed. The observed dynamic behaviour is correlated to the inherent structure of each tyre model in order for the most appropriate for driveline studies to be identified. The main simulation studies are split into two parts: the first comprises a study into isolated driveline dynamics; where the yaw, pitch and roll behaviours of the vehicle body are neglected. A relatively detailed driveline model with an open differential is used with tyre models of increasing complexity with the aim of determining when increased model detail fails to increase the accuracy of the results. The second part is concerned with the study of how the dynamics of the vehicle body and suspension affect tyre model performance and associated effects on the driveline behaviour. For this, the driveline and tyre models are incorporated into a full six degree-of-freedom vehicle model with full suspension effects. Frequency migration on low-μ surfaces is successfully explained via the decoupling of the vehicle and driveline inertias. Frequencies observed in FFT analyses of the simulation results correspond to those obtained through eigen-analysis of appropriately modified state-space models with varying degrees of coupling that reflect the vehicle travelling on uniform low- or split-μ surfaces. The main finding of the thesis is that this decoupling theory can also be applied to high-speed take-off manoeuvres, as it is the position along the tyre slip-force curve that dictates decoupling; i.e. if the curve has saturated. This leads to the effective traction stiffness being zero, which modifies the equations of motion and subsequently the system eigenvalues. A series of measurements are taken in order to verify the findings from the simulation work. Manoeuvres analogous to those simulated are carried out. It is found that only the simulation of split-μ conditions is necessary, as the results from the low-μ test show a similar pattern to those seen on the split-μ surface.

The thesis presents an intermediate modelling approach to study transient behaviour of vehicle systems, with emphasis put on simplified yet accurate representation of important system elements. A representative non-linear vehicle model is developed in MA TLAB/Simulink environment, where non-linear characteristics of tyre, suspension and braking system are included to capture the dynamic behaviour of a vehicle under transient conditions. The novel aspect of this work is the application of a representative full vehicle-tyre-ABS integrated set-up to study the complicated interaction between tyre and anti-lock braking, under a range of demanding operating conditions, including combined cornering and braking. The modelling methodology involves development of low end vehicle models, based on the Newton-Euler formulation. Subsequently, an intermediate vehicle model is devised, where more details are incorporated such as additional DOF to capture the sprung mass motion in space, along with its non-linear interactions with the un-sprung masses, large angle effects, kinematics of steering/wheels and an appropriate tyre model suitable for transient manoeuvres. Particular attention is paid to the suspension system modelling, through inclusion of non-linear effects in springs, dampers, bump-stops, and anti-roll bars, along with the jacking and anti-dive effects using the virtual work method. The model also incorporates a hydraulic brake model, based on the reduced order brake system dynamics for realistic simulation of the braking manoeuvres. A complex multi-body ADAMS/Chassis model, with much greater level of detail, has also been established to extensively compare and enhance the realistic behaviour of the intermediate vehicle model. During the simulation exercise, the intermediate vehicle model has shown good agreement with the complex ADAMS model, thus justifying the accurate representation of vehicle.non-linear characteristics, particularly the suspension system. The realistic behaviour of the vehicle model is further ascertained with a reliable GPS enabled test vehicle, by performing number of manoeuvres on test tracks, including combined cornering and braking. A representative 4-channel conventional ABS system is modelled and integrated in the intermediate vehicle model. The ABS adopts generic peak seeking approach, employing wheel deceleration and brake slip as control variables. External braking inputs, in form of stepped pressure pulses, are also separately used to represent the transient braking system dynamics. In the current work, different transient tyre models based on the single point contact approach and using Magic Formula steady-state characteristics are applied, while studying the influence of their dynamic behaviour on the ABS system. By employing a representative ABS system in a multi-body vehicle model and considering the particularly demanding situation of combined braking I cornering, it is shown that the models which are adequate for pure braking might struggle when the complicated full vehicle dynamics are excited. It is shown that the first order relaxation length approach may not be sufficient to fully satisfy the requirements of an ABS braking, especially if the relaxation length is not modelled as a variable dependent on tyre slip. In comparison, the modelling approach, where the carcass compliances and contact patch properties are explicitly represented, can handle the oscillatory tyre behaviour associated with ABS braking, in a far more accurate manner. In comparison to the earlier studies, which were mostly conducted for straight-line braking, this thesis stresses the fact that the tyre behaviour can be influenced by the complex interaction of handling and braking, and hence the effect should be captured while investigating or evaluating the performance of a tyre model in relation with ABS simulation.

The current state-of-the-art tyre models tend to be demanding in parameterisation terms, typically requiring extensive and expensive testing, and computational power. Consequently, an alternative parameterisation approach, which also allows for the separation of model fidelity from computational demand, is essential. Based on the above, a tyre model is introduced in this work. Tyre motion is separated into two components, the first being the non-linear global motion of the tyre as a rigid body and the second being the linear local deformation of each node. The resulting system of differential equations of motion consists of a reduced number of equations, depending on the number of rigid and elastic modes considered rather than the degrees of freedom. These equations are populated by the eigenvectors and the eigenvalues of the elastic tyre modes, the eigenvectors corresponding to the rigid tyre modes and the inertia properties of the tyre. The contact sub-model consists of bristles attached to each belt node. Shear forces generated in the contact area are calculated by a distributed LuGre friction model while vertical tread dynamics are obtained by the vertical motion of the contact nodes and the corresponding bristle stiffness and damping characteristics. To populate the abovementioned system of differential equations, the modal properties of the rigid and the elastic belt modes are required. In the context of the present work, rigid belt modes are calculated analytically, while in-plane and out-of-plane elastic belt modes are identified experimentally by performing modal testing on the physical tyre. To this end, the eigenvalue of any particular mode is obtained by fitting a rational fraction polynomial expression to frequency response data surrounding that mode. The eigenvector calculation requires a different approach as typically modes located in the vicinity of the examined mode have an effect on the apparent residue. Consequently, an alternative method has been developed which takes into account the out-of-band modes leading to identified residues representing only the modes of interest. The validation of the proposed modelling approach is performed by comparing simulation results to experimental data and trends found in the literature. In terms of vertical stiffness, correlation with experimental data is achieved for a limited vertical load range, due to the nature of the identified modal properties. Moreover, the tyre model response to transient lateral slip is investigated for a range of longitudinal speeds and vertical loads, and the resulting relaxation length trends are compared with the relevant literature.

Arbetets syfte var att göra ett motiverat val av däck till bilen som KTH Formula Student planerar att utveckla till 2025. Detta gjordes genom att använda däckdata från FSAE TTC och utifrån den modellera alla däck med däckmodellen Magic Formula TNO MFTyre/MF-Swift 6.1. Denna modell innehåller variationer i däcktryck, camber och vertikal last. Därefter simulerades varvtid vid olika grenar som skidpad, autocross och endurance för att jämföra alla däcks prestanda. Dessutom kunde flera andra värden värda att jämföras beräknas utifrån däckmodellen och datan från FSAE TTC. Dessa var hållbarhet, däcktemperatur, däckens massa, sidkraftskoefficient, camberkänslighet och däckens fjäderkonstant. Alla dessa värden jämfördes till sist där varvtid och hållbarhet prioriterades. Tre däck fanns kvar i slutet vilka rekommenderades.