Tires play an extremely important role in the operation of a vehicle as they transmit forces between the ground and the vehicle. Consistent efforts have been made over the years towards modeling and simulation of tires and more recently, there has been an increasing need to understand the transient response of tires to various high-frequency events such as anti-lock braking and short-wavelength disturbances from the road. 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 objective of this research is to explain the development, implementation and validation of a simulation tool based on a dynamic tire model that would assist in the analysis of the effect of tire belt vibrations on the braking performance of a vehicle. A rigid ring tire model, tandem elliptical cam enveloping model and a rule-based ABS model have been developed for this purpose. These were combined together in a quarter vehicle model and implemented in Matlab-Simulink. These models were developed for adaptation with CarSim to provide a simulation tool that can be utilized in both tire and vehicle design processes. In addition to model implementation, a parameterization procedure was developed to estimate the parameters of the rigid ring tire and enveloping model based on experimental data for a given tire. Validation studies have also been performed to ensure the accuracy and validity of the tire model. Following this, the braking performance of ABS under different road surfaces were evaluated. Based on the simulation results, final conclusions were drawn with regards to the analysis and detailed recommendations for future work directed towards the improvement of the tool were provided. / Master of Science

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.

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.

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Obtaining the modal parameters of a deflected and rolling tire represents a challenge due to the complex vibration characteristics that cause the tire's symmetry distortion and the natural frequencies' bifurcation phenomena. The modal parameters are usually extracted using a detailed finite element model. The main issue with full modal models (FEA, for example) is the inability to integrate the tire modal model with the vehicle models to tune the suspension system for optimal ride comfort. An in-plane rigid–elastic-coupled tire model was used to examine the 200 DOF finite difference method (FDM) modal analysis accuracy under non-ground contact and non-rotating conditions. The discrete in-plane rigid–elastic-coupled tire model was modified to include the contact patch restriction, centrifugal force, Doppler, and Coriolis effects, covering a range of 0-300 Hz. As a result, the influence of the contact patch and the rotating tire conditions on the natural frequencies and modes were obtained through modal analysis. The in-plane rigid–elastic-coupled modal model with varying conditions was created that connects any two DOFs around the tire's tread or sidewall as inputs or outputs. The vertical movement of the wheel was incorporated into the in-plane rigid–elastic-coupled tire modal model to extract the transfer function (TF) that connects road irregularities as an input to the wheel's vertical movement as an output. The TF was utilized in a quasi-static manner to obtain the tire's enveloping characteristics rolling over short wavelength obstacles as a direct function of vertical wheel displacement under varying contact patch length constraints. The tire modal model was implemented with the quarter car model to obtain the vehicle response rolling over short wavelength obstacles. Finally, a sensitivity analysis was performed to examine the influence of tire parameters and pretension forces on natural frequencies. / Doctor of Philosophy / The goal of vehicle manufacturers is to predict the vehicle's behavior under various driving conditions using mathematical models and simulation. Automotive companies rely heavily on computational simulation tools instead of real-time tests to shorten the product development cycle and reduce costs. However, the interaction between the tire and the road is one of the most critical aspects to consider when evaluating automobile stability and performance. The tires are responsible for generating the forces and moments that drive and maneuver the vehicle. Tires are complex products due to their intricate design, and their characteristics are affected by many factors such as vertical load, inflation pressure, speed, and a road with an uneven surface profile. Consequently, this project aims to describe the influence of various driving circumstances and load conditions on tire properties, as well as to develop a model that can represent the vertical tire and vehicle behavior while traveling over a cleat under different vehicle loads.