This master‘s thesis describes problematics of mathematical models of tires for computer simulations. The goal of this thesis is to depict currently used models of tires and to compare them. Thesis describes brush type models, Fiala, Magic Formula (Pacejka), FTire, UA-Gim, 521 and DELFT. Those models are compared to each other by simulations carried out in software MSC ADAMS Car. The results are shown in figures with commentary and evaluation. This thesis serves as introduction to problematics of currently used mathematical models of tire in computer simulations.

This diploma thesis focuses on incorrect inflation and incorrect use of tires in extreme situations. In the first part, a search of previously created works is reported. This is followed by the elaboration of the basic theory, which describes the driving dynamics of the vehicle, braking and construction, marking, wear and inflation of tires. The next part is the measurement and evaluation of the effect of incorrect inflation and use of tires. Braking deceleration and evasive maneuvers were performed as tests. The third part is an evaluation and summary of the situation.

This thesis is focused on measuring the shape of loaded tire and finding dependencies between inner tire pressure, load and the influence of these parameters on the resulting shape of the tire. Data for these dependencies were obtained by using a constructed measuring stand and 3D optical technology. Found dependencies describe the change in shape of the tire in specific mathematical functions, and served the creation of a parametric model of the tire. The main finding of this thesis is that the tire is actually behaves according to dependencies described by varying degrees of polynomial function.

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Viscoelastic materials have been used widely in different applications, such as constructing tires, artificial joints, shoe heels, and soles. A study on the different characteristics of viscoelastic materials has always been a matter of interest in order to improve their properties for various applications. In the automotive industry, rubber, as a viscoelastic material, has been used in several subsystems, such as vehicle interior, suspension, steering joints, and tires. The tire and terrain's contact characteristics are among the essential factors for assessing the performance of the tire and the vehicle in general. Friction and tread wear are two of these contact characteristics. Considering the tire's functionality, for most applications, it is desired to have higher friction to have better traction and a lower wear rate to minimize the material loss of the tread. The friction coefficient and the rubber's wear rate depend on various parameters such as rubber material properties, terrain characteristics, temperature (tread and the environment), and the load. To obtain the wear rate and friction of a viscoelastic material, three approaches have been used for this study: Experimental, Analytical, and Numerical. The results obtained using these approaches have been compared and validated. Several test setups have been designed and implemented to study the wear and friction of the rubber experimentally. Also, a new linear friction tester has been designed and manufactured by the author to achieve this project's objectives. The new test setup has several advantages over existing test setups in this field, such as covering a higher range of velocities while maintaining high precision. The designed Linear Friction tester and the modified dynamic friction tester at the CenTiRe laboratory at Virginia Tech were used to measure the rubber's friction and wear for different testing conditions such as different normal loads, different velocities, and various surfaces such asphalt and sandpaper. The data collected by the experiment will later be used for the validation of the developed models. In order to obtain the wear rate of the rubber using the analytical approach, the real contact area and friction of the rubber were calculated using Persson's model. The simulation has created the surface to obtain the friction coefficient and the real contact area. After obtaining the friction coefficient and the real contact area, the rubber's wear rate was calculated using a novel approach by combining the Persson Powdery Rubber Wear model with the Crack Propagation model. The results from the improved model compare well with the results from the original model. For the last step of this project, a Finite Element approach was used for modeling a tread block and round rubber sample. A new semi-empirical model for wear was developed by improving the Archard wear model. The novel approach was implemented to Abaqus by using the Umeshmotion subroutine and adaptive mesh motion (ALE) and subroutine UFric and UFric_Coef in two categories: The Node base method and the Ribbon base method. For finite element modeling, the visco-hyper elastic material model has been used to define the rubber's material properties. / Doctor of Philosophy / Viscoelastic materials have been used widely in different applications, such as constructing tires, artificial joints, shoe heels, and soles. Therefore, studying the different characteristics of viscoelastic materials has always been a matter of interest in improving their properties for various applications. In the automotive industry, rubber, as a viscoelastic material, has been used in several subsystems, such as vehicle interior, suspension, steering joints, and tires. The tire and terrain's contact characteristics are among the essential factors for assessing the performance of the tire and the vehicle in general. Friction and tread wear are two of these contact characteristics. Considering the tire's functionality, for most applications, it is desired to have higher friction to have better traction and a lower wear rate to minimize the material loss of the tread. This study used different approaches such as experimental, analytical, and numerical methods to predict the friction and wear of the rubber sample in contact with different surfaces. For the experimental parts, the author designed and manufactured a linear friction test setup. For the numerical parts, a new semi-empirical model was created to predict rubber samples' wear accurately.

Tires are the most influential component of the vehicle as they constitute the only contact between the vehicle and the road and have to generate and transmit forces necessary for the driver to control the vehicle. The demand for the tire models are increasing due to the need to study the variations of force generation mechanisms due to various variables such as load, pressure, speed, and road surface irregularities. Another need from the vehicle manufactures is the study of potential incompatibilities associated with safety systems such as Anti-lock Braking System (ABS) and Electronic Stability Control (ESC) and tires. For vehicle dynamic simulations pertaining to the design of safety systems such as ABS, ESC and ride controllers, an accurate and computationally efficient tire model is required. As these control algorithms become more advanced, they require accurate and extended validity in the range of frequencies required to cover dynamic response due to short wavelength road disturbances, braking and steering torque variations. Major thrust has been provided by the tire industry to develop simulation models that accurately predict the dynamic response of tires without the use of computationally intensive tools such as FEA. The objectives of this research are • To develop, implement and validate a rigid ring tire model and a simulation tool to assist both tire designers and the automotive industry in analyzing the effects of tire belt vibrations, road disturbances, and high frequency brake and steering torque variations on the handling, braking, and ride performances of the vehicle. • To further enhance the tire model by considering dynamic stiffness changes and temperature dependent friction properties. • To develop, and implement novel control algorithms for braking, stability, and ride performance improvements of the vehicle / Ph. D.

Lack of drivers knowledge about the abrupt changes in pavement friction and poor performance of the vehicle stability, traction and ABS controllers on the low friction surfaces are the most important factors affecting car crashes. Due to its direct relation to vehicle stability, accurate estimation of tire-road characteristics is of interest to all vehicle and tire companies. Many studies have been conducted in this field and researchers have used different tools and have proposed different algorithms. One such concept is the Intelligent Tire. The application of intelligent tire in tire-road characterization is investigated in this study. Three different test setups were used in this research to study the application of the intelligent tires to improve mobility; first, a wheeled ground robot was designed and built. A Fuzzy Logic algorithm was developed and validated using the robot for classifying different road surfaces such as asphalt, concrete, grass, and soil. The second test setup is a portable tire testing trailer, which is a quarter car test rig installed in a trailer and towed by a truck. The trailer was equipped with different sensors including an accelerometer attached to the center of the tire inner-liner. Using the trailer, acceleration data was collected under varying conditions and a Neural Network (NN) algorithm was developed and trained to estimate the contact patch length, effective tire rolling radius and tire normal load. The third test setup developed for this study was an instrumented Volkswagen Jetta. Different sensors were installed to measure vehicle dynamic response. Additionally, one front and one rear tire was instrumented with an accelerometer attached to their inner-liner. Two intelligent tire based algorithms, a tire pressure estimation algorithm and a road condition monitoring algorithm, were developed and trained using the experimental data from the instrumented VW Jetta. The two-step pressure monitoring algorithm uses the acceleration signal from the intelligent tire and the wheel angular velocity to monitor the tire pressure. Also, wet and dry surfaces are distinguished using the acceleration signal from the intelligent tire and the wheel angular velocity through the surface monitoring algorithm. Some of the model based tire-road friction estimation algorithms, which are widely used for tire-road friction estimation, were also introduced in this study and the performance of each algorithm was evaluated in high slip and low slip maneuvers. Finally a new friction estimation algorithm was developed, which is a combination of experiment based and vehicle dynamic based approaches and its performance was also investigated. / PHD

Tire testing has been one of the important aspects of the tire industry because it helps identify the tire behavior which further helps in improving the design of tires. It also helps automotive manufacturers choose the best tire for their automobiles. Indoor tire testing helps in relating the data better because of greater repeatability of the testing setup as compared to outdoor testing. This study focusses on modifying a rolling resistance machine to make it capable of force and moment and cleat testing along with the standard rolling resistance test. Additionally, the design of a mechanical loading mechanism (used to apply normal force on the tire) in place of the previous one using dead weights is also discussed. This study also talks about the structural and vibrational finite element analysis of a tire testing machine. Since the machine was designed to conduct different tire tests, different structural requirements of the tire positioning mechanism pertaining to each test were taken into consideration, and the structure was analyzed for maximum forces and moments acting on the assembly. Cleat testing subjects the tire as well as the structure to an impulse force which calls for the vibrational analysis of the assembly to avoid the structure from resonating. The design was modified to get it easily manufactured and assembled. These design changes and the aspects taken into consideration have also been discussed. / Master of Science