Tire parameters play a very important role in tire performance. Depending on the driving conditions for which a given tire is designed, its parameters must be chosen appropriately (e.g., the radius of the tire, the width of the tire, material properties of different sections). Among tire characteristics, the material properties of the rubber compounds have a vital role in tire behavior. Previous studies show that the material properties of the rubber are highly dependent on temperature. Thus, a comprehensive study on the effect of the material properties of the rubber on tire performance for different temperatures as well as different road conditions is required. In this study, a theoretical model has been developed for tire-ice interaction. The temperature changes obtained from the model are used to calculate the height of the water film created by the heat generated due to the friction force. Next, the viscous friction coefficient at the contact patch is obtained. By using the thermal balance equation at the contact patch, dry friction is obtained. Knowing the friction coefficients for the dry and wet regions, the equivalent friction coefficient is calculated. The model has been validated using experimental results for three similar tires with different rubber compounds properties. For the experimental part of this study, four tires have been selected for testing. Three of them have identical tire geometry and structure but different rubber tread compounds. Several tests were conducted for the chosen tires in three modes: free-rolling, braking, and traction. The tests were performed for two different normal loads (4 kN and 5.6 kN), two different inflation pressures (21 psi (144.8 kPa) and 28 psi (193 kPa)), and three tire temperatures levels (-10°C, -5°C, and -1 °C). The Terramechanics Rig at TMVS at Virginia Tech has been used for conducting the tests. The results from this study show the sensitivity of the magnitude of the tractive force with respect to parameters such as tire temperature, normal load, etc. The results also indicate that the tire with the lowest value of the Young modulus has the highest traction among all four tires used in this study. The model developed can be used to predict the temperature changes at the contact patch, the tire friction force, the areas of wet and dry regions, the height of the water film for different ice temperatures, different normal loads, etc. The results from this study coincide with the obtained results from the experiments. According to the data available, tire B with the smallest value of Young modulus and the smallest value of the specific heat parameter was shown to have the highest friction coefficient in both simulation and experiment. After validating the results using experimentally collected data, the model was used to perform a sensitivity analysis on the tire performance with respect to six material properties of the tread rubber: thermal conductivity, rubber density, Young's modulus, specific heat, roughness parameter of the rubber, and radii of spherical asperities of the rubber. The results from this study show the sensitivity of the magnitude of the friction coefficient to the rubber material properties. The friction coefficient has a direct relationship with the density of the rubber and has an inverse relationship with Young's modulus, specific heat, and roughness parameter. / Doctor of Philosophy / In order to decrease the number of deaths and injuries caused by driving on icy roads and increase the safety of the vehicle, it is important to improve the tire performance on ice. To this, understanding the effects of different tire and road parameters such as material properties of the rubber, loading condition, and temperature on the tire-ice performance is required. Tire parameters play a very important role in tire performance. Depending on the driving conditions for which a given tire is designed, its parameters must be chosen appropriately In this project, the effects of different tire and terrain parameters such as rubber material properties on tire performance on ice using an experimental and modeling approach have been studied. For the experimental part of this study, several tests were conducted for more than 30 tires with different material properties. The results of this study show what are the most important material properties of the rubber for designing a tire with the best performance on ice. For the modeling part of this study, a semi-analytical model was developed. The model was validated using collected experimental data and was used to predict the performance of the tire by having information about its material and physical properties. The developed model called ATIIM2.0 has several advantages. First, it is a unique model for a complete tire (not a rubber block) that can be used to predict the performance of the tire by using its material properties. In addition, this model can be connected to vehicle models to improve the performance of the vehicle in general. The model developed can be used to predict the temperature changes at the contact patch, the tire friction force, the areas of wet and dry regions, the height of the water film for different ice temperatures, different normal loads, etc. The results from this study coincide with the obtained results from the experiments.

Tire, or in its primitive form, Wheel, an important invention for the transportation sector, has evolved from a circular block of hard and durable material to one of the most complex and influential components of an automobile. It is the only means of contact between the vehicle and the road and is responsible for generating forces and moments that impact vehicle performance, stability, and control. Tire tribology is the study of interacting surfaces in relative motion which includes friction and wear. Tire friction is an essential concept for estimating the tractive effort/ traction at the tire-road interface that further helps to determine the control and stability of the vehicle. In contrary, it also results in rolling resistance and wear. Tire and vehicle engineers are henceforth interested in a robust and efficient approach towards estimation of friction and wear. Past experimental observations using tread compound samples have revealed the different factors influencing the friction at the contacting interface. In addition, different mechanisms or components resulting in frictional losses, being Hysteretic, Adhesive and Viscous, and wear being abrasive, fatigue, adhesive and corrosive were also observed. Although experimental and empirical observations have provided us with an accurate estimation of friction and wear parameters, it is very tedious and expensive approach. Recent developments in the computational power encouraged researchers and engineers towards evolution of analytical and numerical models considering the underlying physical mechanisms at the contact interface. Past research studies developed multiscale techniques for estimation of friction coefficient due to hysteretic losses from internal damping of the rubber material because of oscillation from surface undulations. Later, contact mechanics models developed using Hertzian technique or stochastic approach were considered in conjunction with frictional losses to obtain the hysteretic component of friction to consider the effect of surface roughness. Previous studies at CenTiRe focused on surface characterization techniques and estimation of friction for dry surfaces using Persson and Klüppel's approach. Comparative studies unveiled the importance of considering pressure/ normal load towards friction estimation. In addition, it was found that effect of adhesion for estimation of contact mechanics parameters must be considered. The present work focusses on obtaining a conceptual framework to model a comprehensive friction model considering the effect of surface roughness, substrate condition and asperity interaction. A finite element simulation of rubber block sliding on a rough substrate is performed using a multiscale technique for estimation of friction and contact mechanics under dry condition. The estimated contact mechanics and friction is compared with analytical models and experimental measurements obtained using Linear sliding friction tester developed in collaboration with other members of the group. In addition, a FE model is developed to measure the wear properties of rubber material based on continuum damage mechanics and further obtain the wear profile of a rubber block sliding on a rough substrate. / Doctor of Philosophy / Tribology, a recent terminology for an age-old concept of friction, wear, and lubrication. the study of interacting surfaces in relative motion which includes friction and wear. Friction is the resisting force at the contact interface leading to heat build-up and material loss at the contact interface which is known as flash temperature and wear respectively. Tire is one of the most complex and influential components of a vehicle that helps in optimizing its performance for better stability and control. Knowledge of tire friction and wear is important for tire engineering and vehicle dynamics engineers as it helps in characterizing the handling characteristics of the vehicle, characterizing the tire material compounds to understand the tire durability. Rubber is a viscoelastic material, the friction and wear in rubber is intricate as opposed to other elastic materials. Based on experimental observations in the past, friction and wear are influenced by factors like material properties, normal load/ pressure, sliding velocity, temperature, surface characteristics, and environmental conditions. In addition, the frictional losses at the contact interface are considered to compose of adhesion, hysteresis and viscous components and wear is categorized as – adhesive, abrasive, fatigue, corrosive and erosive. Recent developments in computational power encouraged researchers and engineers in developing analytical and computational models that consider the physical mechanisms occurring at the contact interface. The present research focuses on obtaining a comprehensive friction and contact mechanics model considering the effect of surface roughness at different length scales, surface condition (dry/ wet) and asperity interaction. In addition, the developed model in conjunction with a brush model is considered for estimating the tire traction characteristics such as the forces and moments. A finite element simulation of rubber block sliding on a rough substrate is performed using a multiscale technique for estimation of friction, contact mechanics and abrasion parameters under dry condition. The results thus obtained are compared with the analytical model that is developed for wet conditions. Experimental validation of the friction estimated using the analytical and numerical methods will be performed using a linear sliding friction tester developed in collaboration with other members of the group.

Στο πρώτο μέρος της διατριβής περιγράφεται η "στρατηγική του μιγαδικού επιπέδου" (cxps) και εξηγείται ο λόγος για τον οποίο προκρίνεται αυτή. με την cxps συνεργάζεται στενά η "τεχνική της πολλαπλής διαμερισης" (MTP), η οποία χρησιμοποιείται στους σχετικούς υπολογισμούς. κατασκευάζεται το μοντέλο ενός διαφορικά περιστρεφόμενου πολυτρόπου αστέρα υπό την επίδραση τυροειδούς μαγνητικού πεδίου. εισάγεται η ποσότητα h σαν παράμετρος διαταραχής και u παράμετρος διαφορικής περιστροφής. αναπτύσσεται η θεωρία που περιλαμβάνει όρους μέχρι και πρώτης τάξης στις παραμέτρους διαταραχής u, h και ευρίσκονται οι διαφορικές εξισώσεις, στις οποίες, υπακούουν οι συναρτήσεις του προβλήματος. ακολούθως γίνεται αριθμητική εφαρμογή των προηγούμενων για όλες τις ενδιαφέρουσες καταστάσεις περιστροφής. το δεύτερο μέρος της διατριβής διαπραγματεύεται μοντέλα, στα οποία η διαφορική περιστροφή προκύπτει από το ιξώδες υλικό του αστέρα με επίλυση της λεγόμενης "εξισώσεως ζεύξης", η οποία είναι συνέπεια της εξισώσεως Navier-Stokes για ιξωδοπολυτροπικούς αστέρες. παρουσιάζονται αριθμητικά αποτελέσματα για τη δομή διαφόρων μοντέλων με ασθενές, μέτριο και ισχυρό μαγνητικό πεδίο. δίνεται έμφαση στον υπολογισμό της "ενεργειακής απώλειας" λογω ιξώδους τριβής. ακολουθει σχολιασμός των αριθμητικών αποτελεσμάτων με έμφαση στο γεγονός ότι η ύπαρξη του μαγνητικού πεδίου περιορίζει δραστικά την ενεργειακή απώλεια. στην περίπτωση αυτή το μαγνητικό πεδίο δρα ως "λιπαντικό" και προστατεύει τον αστέρα από την υπερβολική απώλεια ενέργειας λογά ιξώδους τριβής των διαφορικώς περιστρεφόμενων φλοιών του. / In the first part, it has primarily been described the "complex plane strategy"(cxps) and has also been explained the reason of implementing this method in the present investigation. With the cxps collaborates the "multiple partition technique" (MTP) which is involved in the corresponding computations. In particular, the model of a differentially rotating polytropic star is constructed, which is under the cooperating influence of a toroidal magnetic field. To this purpose, perturbation theory is used on the basis of the fundamental magnetic perturbation parameter h. the theory including terms up to the first order in both the perturbation parameters u (rotation) and h (magnetic field),is developed and the corresponding differential equations are set up. Our computation concerns mainly critical rotations. In the second part of the thesis, we consider models with differential rotation owing to the viscous material of the star, on the basis of the so called "coupling equation" that is consequence of the Navier-Stokes equation for viscous polytropic stars. Emphasis is given on the study of dissipative effects due to viscous friction, as they are determined by the combined action of rotation and magnetic field. The computations show that a toroidal magnetic field can play the role of an efficient "lubricant" injected into the material of the particular magnetic model, thus reducing drastically the energy dissipated due to viscous friction.

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