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.

Extract from Thesis (Ph. D.)--Johns Hopkins University, 1938. / Vita. "Reprinted from ELH, a journal of English literary history, vol. 5. no. 2. June, 1938."

The in-plane phenomena of interaction between the tyre structural response and contact force generation are investigated in this work. The challenges of the physical tyre simulation are identified, primarily associated with the computational load imposed by the need to capture the space distributed mechanisms that prescribe the above interaction. The method of modal expansion and reduction is proposed for the moderation of this load. The theoretical framework for the transformation of a tyre modal representation into a transient contact and shear force generation model is developed. Various modelling approaches are examined with regards to their modal prediction characteristics. Linear and non linear structural features as well as the physical properties that define the broad range modal behaviour are identified. A discretised form of the ring model is derived and combined with a foundation of viscoelastic tread elements for simulating the transient contact behaviour of the tyre. The resulting pattern of the modes' excitation justifies the validity of the modal reduction method and reveals the relative importance of various mechanisms and physical properties in tyre contact behaviour. The interaction between the friction controlled shear slip of the tread, the belt compliance and the sidewall buckling is found to be reflected on the two-dimensional contact pressure distribution patterns. A method able to simulate the dynamic transient rolling and slipping operating conditions is developed, although the small displacement assumption of the modal approach is dropped. The method, which is based on the combined modal-time and space-time domain solutions, is applied on the study of the physical mechanism of the launch process. The examination of the model under steady state kinematic conditions reveals the saturation of the traction force for profound levels of slip, which highlights the contribution of the structural mechanisms on the macroscopically observed shear force performance of the tyre. The variation of the modes' level of excitation, as induced by the operating conditions, is proposed for the capture of the physical properties effect on tyre behaviour and performance.

The system for predicting tyre performance on sand, measuring sand strength with a cone penetrometer and using non-dimensional empirical curves developed by the Waterways Experiment Station (WES) of the U. S. Army was investigated. A series of tyre tests on dry Cresswell sand were carried out and the results were in complete disagreement with the WES system, in both its original and revised forms. It was therefore decided to try to discover the basic soil mechanics of such a system and modify it accordingly. Critical State Soil Mechanics describes two types of soil behaviour, dilating and weakening or compacting and strengthening. It was found that the first of these processes occurred in most situations likely to be found naturally, compaction occurring only in the loosest states obtainable under laboratory conditions. Under dilating conditions sand strength is described by the density, γ (Gamma). and the angle of internal friction, Ø. The angle of friction, for a single sand, was found to vary over a very wide range, depending on the state of compaction and the confining pressure. Density does not vary greatly. The cone penetrometer gradient, G, was found to be related to Ø at a low confining pressure, and the relationship was well described by the theory of Durgunoglu and Mitchell (1975). This lead to the idea that tractive performance would be dependent on Ø, which would be lower the higher the tyre contact pressure. A series of tyre tests on a single tyre on two sands showed clearly that performance depended on both tyre pressure and tyre load. The WES numeric only contains pressure. It was therefore decided to include both parameters by expressing performance by several curves depending on the tyre deflection. Deflection. being expressed as a ratio of tyre diameter rather than tyre section height. The new system was shown to describe all of the WES data better and more logically than their system. The reason why the system cannot describe performance in Yuma and Mortar sands with the same single curve as for Leighton Buzzard and Cresswell remains a mystery.

Inaug.-Dis.--Breslau. / Lebenslauf. Includes bibliographical references.

A successful model for off-road tyres must be reliable, efficient and capable of reproducing and predicting the main system phenomena. Mathematical models are proposed for longitudinal, lateral and combined lateral and longitudinal force generation characteristics of off-road tyres. For a better understanding of off-road tyre behaviour, the study of the interaction between the tyre forces and those generated by the deformed soil is very important. Details of the force system in the contact patch, therefore, are used as a basis for developing models for the prediction of the tractive performance and comering characteristics of off-road tyres. Previous work of the relevant literature pertaining to tyre behaviour is reviewed to provide the reader with background information on off-road tyre characteristics. Various models for off-road tyres of differing degrees of complexity but which all incorporate the key features of off-road tyre problems are then developed. Previous methods of analysing the combined lateral and longitudinal forces generated by off-road tyres on deformable surfaces are investigated. A modified version of a previous model is then proposed which is based on a different and original method for investigating tyre behaviour in the contact region. An entirely new model is then developed which is based on a modification of the "multi-spoke" tyre model used for road vehicle studies. Predicted results are compared with those obtained from other models and with reported experimental data. The usefulness of such models is in problems involving the steering, braking and handling behaviour of off-road vehicles. Hence, the models are formulated so that they can be applied to such vehicle problems by enabling lateral and longitudinal forces on the tyre to be predicted from any combined conditions of wheelslip, wheelskid and slip angle. The proposed models provide an improved qualitative description of behaviour in the contact region. Although slightly more complex than previous models, the computational load is nevertheless sufficiently small that the tyre models can conveniently be incorporated in off-road vehicle handling models. Suggestions for future recommendations are discussed with particular reference to improving the predictive models and for a possible extension of the study to generate more detailed practical results for tyre forces under controlled experimental conditions.

No description available.

The aim of the research described in this thesis is to assess the technical feasibility of pneumatic tyres for passenger cars which have no directional reinforcement in their carcasses. Conventional tyres are constructed from composites of twisted textile or steel cords in a rubber matrix, a process which is both labour intensive and costly. If it were possible to injection mould or cast tyre carcasses in a single operation, and if the performance of the resulting tyres matched that of modern radial ply tyres, then the implications for the tyre industry would be of major proportions. After reviewing the history of pneumatic tyres and summarising their principal attributes, the design of unreinforced or fabricless tyres is investigated and methods developed for defining their meridional profiles. Materials suitable for their carcasses and treads are then considered, prior to describing the manufacture of two series of tyres designed to have section height to width ratios, or aspect ratios, of 0.9 and 0.7 respectively. To facilitate experimental work, two sizes of tyres were employed: half scale models for which testing procQdures had been developed previously; and a size suitable for small saloon cars. The results obtained on a range of tyre properties are presented and analysed to give a number of empirical relationships between the properties and the design variables: carcass material Young's modulus, carcass wall thickness and the inflation pressure. For the important property of radial stiffness which affects other tyre characteristics, an improved method of analysis is developed to allow the structural and pneumatic components to be quantified. Using the relationships established experimentally, consideration is given to optimising the design of a fabricless tyre. It is concluded that to approach the performance of a conventional tyre, a design with a low aspect ratio is preferred but, to restrict growth with inflation'pressure, limited directional reinforcement must be included as a circumferential-belt beneath the tread. Nevertheless, the discussion concludes that there are fundamental reasons why even the optimised tyre would be unacceptable for use on modern passenger cars, although less demanding applications may be identified.

This thesis introduces a versatile finite element package, which is tailored for the static and dynamic analysis of radial tyres. A new axisymmetric solid-of-revolution element which takes into consideration, large deformation, the influence of composite orthotropic material and the viscoelasticity and the nonlinearity of the material properties, has been developed for a general loaded tyre. The finite element package has been verified by comparing its results with available analytical, numerical and experimental results. A full static and dynamic investigation has been carried out for a commercial tyre 175 HR 14 and results obtained by using the package have been compared with available experimental results developed by DUNLOP or carried out at Cranfieid. The package has proved to be reliable, flexible, efficient, economic and accurate. The numerical instability problems which are prevalent in this type of analysis have been overcome by the derivation of a developed Newton-Raphson iterative scheme.

This work addresses the problem of tyre tread pattern design for optimum wet grip performance. A mathematical model of tyre behaviour on wet roads has been developed. This utilizes the finite element method in the representation of tread pattern geometry. The performance of a particular tread pattern is found in terms of the fluid pressures and film thicknesses existing within the contact patch, under wet conditions. Many modern tread patterns are based on 'blocks', and a computer model has been developed specifically to assist the tyre designer in the design of these blocks for improved wet grip. Numerical results are presented both for complete contact patches and for individual tread blocks. To allow the use of the computer models by the tyre designer, with no specialist knowledge of the finite element method, special purpose mesh generation and plotting programs have been developed. Experiments have been undertaken whereby the fluid pressures and film thicknesses existing in the tyre contact patch have been measured under high speed conditions in the wet. These measure- ments were made on an indoor testing machine, and the techniques developed can be used in the routine evaluation of tyre wet grip performance. Some results of experiments performed on plain and simple patterned tyres are presented. The main purpose of this work was the development of the mathematical models which can be used for future research into, and design of, tyres for improved wet grip. However, some conclusions are made as to possible features which could be utilized in future tyre designs.