The tire is one of the most important components of the vehicle. It has many functions, such as supporting the load of the vehicle, transmitting the forces which drive, brake and guide the vehicle, and acting as the secondary suspension to absorb the effect of road irregularities before transmitting the forces to the vehicle suspension. A tire is a complex reinforced rubber composite air container. The structure of the tire is very complex. It consists of several layers of synthetic polymer, many flexible filaments of high modulus cord, and glass fiber, which are bonded to a matrix of low modulus polymeric material. As the tire is the only component of the vehicle which makes contact with the road surface, almost all forces and moments acting on the vehicle must be transferred by the tire. To predict the dynamics of the vehicle, we need to know these forces and moments generated at the tire contact patch. Therefore, tire models that accurately describe this dynamic behavior are needed for vehicle dynamic simulation. Many researchers developed tire models for vehicle dynamic simulations; however, most of the development in tire modeling has been limited to deterministic steady-state on-road tire models. The research conducted in this study is concerned with the development of semi-empirical transient tire models for on-road and off-road vehicle simulations. The semi-empirical transient tire model is developed based on existed tire models, analytical tire structure mechanics analysis, and experimental data collected by various researchers. The tire models were developed for vehicle traction, handling and ride analysis. The theoretical mechanics analysis of the tire model focused on the determination of tire and terrain deformation. Then, the results are used together with empirical data to calculate the force response and the moment response. Moreover, the influence of parametric uncertainties in tire parameters on the tire-terrain interaction is investigated. The parametric uncertainties are quantified and propagated through the tire models using a polynomial chaos theory with a collocation approach. To illustrate the capabilities of the tire models developed, both deterministic and stochastic tire models are simulated for various scenarios and maneuvers. Numerically simulated results are analyzed from the perspective of vehicle dynamics. Such an analysis can be used in tire and vehicle development and design. / Ph. D.

The vertical force generated from terrain-tire interaction has long been of interest for vehicle dynamic simulations and chassis development. As the terrain serves as the main excitation to the suspension system through pneumatic tire, proper terrain and tire models are required to produce reliable vehicle response. Due to the high complexity of the tire structure and the immense size of a high fidelity terrain profile, it is not efficient to calculate the terrain-tire interaction at every location. The use of a simpler tire model (e.g. point follower tire model) and a pre-filtered terrain profile as equivalent input will considerably reduce the simulation time. The desired produced responses would be nearly identical to the ones using a complex tire model and unfiltered terrain, with a significant computational efficiency improvement. In this work, a terrain pre-filtering technique is developed to improve simulation efficiency while still providing reliable load prediction. The work is divided into three parts. First a stochastic gridding method is developed to include the measurement uncertainties in the gridded terrain profile used as input to the vehicle simulation. The obtained uniformly spaced terrain is considered probabilistic, with a series of gridding nodes with heights represented by random variables. Next, a constraint mode tire model is proposed to emulate the tire radial displacement and the corresponding force given the terrain excitation. Finally, based on the constraint mode tire model, the pre-filtering technique is developed. At each location along the tire's path, the tire center height is adjusted until the spindle load reaches a pre-designated constant load. The resultant tire center trajectory is the pre-filtered terrain profile and serves as an equivalent input to the simple tire model. The vehicle response produced by using the pre-filtered terrain profile and the simple tire model is analyzed for accuracy assessment. The computational efficiency improvement is also examined. The effectiveness of the pre-filtering technique is validated on probabilistic terrain by using different realizations of terrain profiles. It is shown through multiple profiles that the computational efficiency can be improved by three orders of magnitude with no statistically significant change in resulting loading. / Ph. D.

The tire is one of the most complex subsystems of the vehicle. It is, however, the least understood of all the components of a car. Without a good tire model, the vehicle simulation handling response will not be realistic, especially for maneuvers that require a combination of braking/traction and cornering. Most of the simplified theoretical developments in tire modeling, however, have been limited to on-road tire models. With the availability of powerful computers, it can be noted that majority of the work done in the development of off-road tire models have mostly been focused on creating better Finite Element, Discrete Element, or Boundary Element models. The research conducted in this study deals with the development of a simplified tire brush-based tire model for on-road simulation, together with a simplified off-road wheel/tire model that has the capability to revert back to on-road trend of behavior on firmer soils. The on-road tire model is developed based on observations and insight of empirical data collected by NHSTA throughout the years, while the off-road tire model is developed based on observations of experimental data and photographic evidence collected by various terramechanics researchers within the last few decades. The tire model was developed to be used in vehicle dynamics simulations for engineering mobility analysis. Vehicle-terrain interaction is a complex phenomena governed by soil mechanical behavior and tire deformation. The theoretical analysis involved in the development of the wheel/ tire model relies on application of existing soil mechanics theories based on strip loads to determine the tangential and radial stresses on the soil-wheel interface. Using theoretical analysis and empirical data, the tire deformation geometry is determined to establish the tractive forces in off-road operation. To illustrate the capabilities of the models developed, a rigid wheel and a flexible tire on deformable terrain is implemented and output of the model was computed for different types of soils; a very loose and deformable sandy terrain and a very firm and cohesive Yolo loam terrain. The behavior of the wheel/tire model on the two types of soil is discussed. The outcome of this work shows results that correlate well with the insight from experimental data collected by various terramechanics researchers throughout the years, which is an indication that the model presented can be used as a subsystem in the modeling of vehicle-terrain interaction to acquire more insight into the coupling between the tire and the terrain. / Ph. D.

Sensor-embedded tires, known as intelligent tires, have been widely studied because they are believed to provide reliable and crucial information on tire-road contact characteristics e.g., slip, forces and deformation of tires. Vehicle control systems such as ABS and VSP (Vehicle Stability Program) can be enhanced by leveraging this information since control algorithms can be updated based on directly measured parameters from intelligent tire rather than estimated parameters based on complex vehicle dynamics and on-board sensor measurements. Moreover, it is also expected that intelligent tires can be utilized for the purpose of the analysis of tire characteristics, taking into consideration that the measurements from the sensors inside the tire would contain considerable information on tire behavior in the real driving scenarios. In this study, estimation methods for the tire-road contact features by utilizing intelligent tires are investigated. Also, it was discussed how to identify key tire parameters based on the fusion technology of intelligent tire and tire modeling. To achieve goals, extensive literature reviews on the estimation methods using the intelligent tire system was conducted at first. Strain-based intelligent tires were introduced and tested in the laboratory for this research. Based on the literature review and test results, estimation methods for diverse tire-road contact characteristics such as slippages and contact forces have been proposed. These estimation methods can be grouped into two categories: statistical regressions and model based methods. For statistical regressions, synthetic regressors were proposed for the estimation of contact parameters such as contact lengths, rough contact shapes, test loads and slip angles. In the model-based method, the brush type tire model was incorporated into the estimation process to predict lateral forces. Estimated parameters using suggested methods agreed well with measured values in the laboratory environment. By utilizing sensor measurements from intelligent tires, the tire physical characteristics related to in-plane dynamics of the tire, such as stiffness of the belt and sidewall, contact pressure distribution and internal damping, were identified based on the combination of strain measurements and a flexible ring tire model. The radial deformation of the tread band was directly obtained from strain measurements based on the strain-deformation relationship. Tire parameters were identified by fitting the radial deformations from the flexible ring model to those derived from strain measurements. This approach removed the complex and repeated procedure to satisfy the contact3 constraints between the tread and the road surface in the traditional ring model. For tires with different specifications, identification using the suggested method was conducted and their results are compared with results from conventional methods and tests, which shows good agreements. This approach is available for the tire standing still or rolling at low speeds. For tires rolling at high speeds, advanced tire model was implemented and associated with strain measurements to estimate dynamic stiffness, internal damping effects as well as dynamic pressure distributions. Strains were measured for a specific tire under various test conditions to be used in suggested identification methods. After estimating key tire parameters step by step, dynamic pressure distributions was finally estimated and used to update the estimation algorithm for lateral forces. This updated estimation method predicted lateral forces more accurately than the conventional method. Overall, this research will serve as a stepping stone for developing a new generation of intelligent tire capable of monitoring physical tire characteristics as well as providing parameters for enhanced vehicle controls. / PHD

As vehicle dynamics research delves deeper into better insights in performance, modeling, and vehicle controls, one area remains of utmost importance: tire and road friction forces. The vehicle???s interaction with the road remains the dominant mean of vehicle control. Ultimately, the tire-road interaction will determine the majority of the vehicle???s capabilities and as the understanding of the interface improves, so too can the performance. With more computationally intensive systems being instrumented into modern vehicle systems, one is able to observe a great deal of important vehicle states directly for the remaining vehicle information; excellent estimation techniques are providing the rest of the insights. This study looks at the possible improvements that can be observed by implementing an adaptive dynamic tire model that is physical and flexible enough to permit time varying tire performance. The tire model selected is the Average Lumped LuGre Friction Tire Model, which was originally developed from physical properties of friction and tire systems. The material presented here examines the possibility of an adaptive tire model, which can be implemented on a real-time vehicle platform. The adaptive tire model is just one section of an entire control strategy that is being developed by General Motors in partnership with the University of Waterloo. The approach allows for estimated and measured vehicle information to provide input excitation for the tire model when driven with real-world conditions that enabling tire estimations. The tire model would then provide the controller information indicating the expected tire capacity and compares it with the instantaneous loading. The adaptive tire model has been tested with flat road experimental cases and the results provided reasonable estimates. The experimentation was performed with a fully instrumented research vehicle that used in-wheel force transducers, and later repeated with a completely different non-instrumented fully electric vehicle. The concepts and investigation presented here has initiated the ground work for a real-time implementation of a full adaptive tire model. Further work is still required to evaluate the influence of a range of operating conditions, tire pressure, and of different tire types. However, the findings indicate that this approach can produce reasonable results for the specified conditions examined.

A significant number of studies address various aspects related to tire modeling; most are dedicated to the development of tire models for on-road conditions. Such models cover a wide range of resolutions and approaches, as required for specific applications. At one end of the spectrum are the very simple tire models, such as those employed in real-time vehicle dynamic simulations. At the other end of the spectrum are the very complex finite element models, such as those used in tire design. In between these extremes, various other models have been developed, at different levels of compromise between accuracy and computational efficiency. Existing tire models for off-road applications lag behind the on-road models. The main reason is the complexity added to the modeling due to the interaction with the soft soil. In such situations, one must account for the soil dynamics and its impact on the tire forces, in addition to those aspects considered for an on-road tire. The goal of this project is to develop an accurate and comprehensive, while also efficient, off-road tire model for soft soil applications. The types of applications we target are traction, handling, and vehicle durability, as needed to support current army mobility goals. Thus, the proposed approach is to develop a detailed semi-analytical tire model for soft soil that utilizes the tire construction details and parallels existing commercially available on-road tire models. The novelty of this project relies in developing a three-dimensional three-layer tire model employing discrete lumped masses and in improving the tire-soil interface model. This will be achieved by enhancing the resolution of the tire model at the contact patch and by accounting for effects and phenomena not considered in existing models. / Master of Science

Automotive and Tire companies spend extensive amounts of time and money to tune their products through prototype testing at dedicated test facilities. This is mainly due to the limitations in the simulation capabilities that exist today. With greater competence in simulation, comes more control over designs in the initial stages, which in turn lowers the demand on the expensive stage of tuning. The work presented, aims at taking today's simulation capabilities a step forward by integrating models that are best developed in different software interfaces. An in-plane rigid ring model is used to understand the transient response of tires to various high frequency events such as Anti-Lock Braking and short wavelength road disturbances. A rule based ABS model performs the high frequency braking operation. The tire and ABS models have been created in the Matlab-Simulink environment. The vehicle model has been developed in CarSim. The models developed in Simulink have been integrated with the vehicle model in CarSim, in the form of a design tool that can be used by tire as well as vehicle designers for further tuning of the vehicle functional performances as they relate to in-line braking scenarios. Outdoor validation tests were performed to obtain data from a vehicle that was measured on a suspension parameter measuring machine (SPMM) in order to complement this design tool. The results of the objective tests performed have been discussed and the correlations and variations with respect to the simulation results have been analyzed. / Master of Science

Accurate and efficient tire models for deformable terrain operations are essential for performing vehicle simulations. Assessment of the forces and moments that occur at the tire-terrain interface, and the effect of the tire motion on properties of the terrain are crucial in understanding the performance of a vehicle. In order to model the dynamic behavior of the tire on different terrains, a lumped mass discretized tire model using Kelvin-Voigt elements is developed. To optimize the computational time of the code, different techniques were used in memory allocation, parameter initialization, code sequence, and multi-processing. This has resulted in significant improvements in efficiency of the code that can now run close to real time and therefore it is suitable for use by commercially available vehicle simulation packages. Model parameters are obtained using a validated finite element tire model, modal analysis, and other experimental test procedures. Experimental tests were performed on the Terramechanics rig at Virginia Tech. The tests were performed on different terrains; tire forces and moments, soil sinkage, and tire deformation data were collected for various case studies based on a design of experiment matrix. This data, in addition to modal analysis data were used to validate the tire model. Furthermore, to study the validity of the tire model, simulations at conditions similar to the test conditions were performed on a quarter car model. The results have indicated the superiority of this model as compared to other lumped parameter models currently available. / Ph. D.

Induced vibrations due to tire-pavement interaction are one of the main sources of vehicle exterior noise, especially near highways and main roads where traveling speeds are above 50 kph. Its dominant spectral content is approximately within 500-1500 Hz. However, accurate prediction tools within this frequency range are not available. Current methods rely on structural modeling of the complete tire using finite elements and modal expansion approaches that are accurate only at low frequencies. Therefore, alternative physically-based models need to be developed. This work proposes a new approach that incorporates wave behavior along the tire's circumferential direction, while modes are assumed along its transversal direction. The formulation for new infinite plate and cylindrical shell structural models of a tire is presented. These are capable of accounting for orthotropic material properties, different structural parameters between the belt and sidewalls, inflation pressure, and rotation of the tire. In addition, a new contact model between the pavement and the tire is developed presented. The excitation of the tire due to the impact of the tread-pattern blocks in the contact patch region is characterized and coupled to the structure of the tire. Finally, a Boundary Element Method is implemented in order to compute the vibration-induced noise produced by the tire. All the modeling components are combined in a single prediction tool named Wave Pro Tire. Lastly, simulated responses and validation cases are presented in terms of harmonic responses, Frequency Response Functions (FRF), and produced noise. / Doctor of Philosophy / Induced vibrations due to tire-pavement interaction are one of the main sources of vehicle exterior noise, especially near highways and main roads where traveling speeds are above 50 kph. Accurate prediction tools are not currently available. Therefore, new physically based models need to be developed. This work proposes a new approach to model the tire’s structure with a formulation that accounts for multiple physical phenomena. In addition, a model that simulates the contact between the pavement and the tire’s tread is presented. Finally, the vibrations are coupled to the produced noise in a single prediction tool named Wave Pro Tire. This work also includes simulated responses and validation cases.

The suspension system of a vehicle is conventionally designed such that the spring-damper element is configured in the vertical direction, and the longitudinal connection between the vehicle chassis and wheels is always very stiff compared to the vertical one. This mechanism can isolate vibrations and absorb shocks efficiently in the vertical direction but cannot attenuate the longitudinal impacts caused by road obstacles. In order to overcome such a limitation, a planar suspension system (PSS) is proposed. This novel vehicle suspension system has a longitudinal spring-damper strut between the vehicle chassis and wheel. The dynamic performance, including ride comfort, pitch dynamics, handling characteristics and total dynamic behaviour, of a mid-size passenger vehicle equipped with such planar suspension systems is thoroughly investigated and compared with those of a conventional vehicle. To facilitate this investigation, various number of vehicle models are developed considering the relative longitudinal motions of wheels with respect to the chassis. A 4-DOF quarter-car model is used to conduct a preliminary study of the ride quality, and a pitch plane half-car model is employed to investigate the pitch dynamics in both the frequency and time domain. A 5-DOF yaw plane single-track half-car model along with a pitch plane half-car model is proposed to carry out the handling performance study, and also an 18-DOF full-car model is used to perform total dynamics study. In addition to these mathematical models, virtual full-car models are constructed in Adams/car to validate the proposed mathematical models. For the sake of prediction of the tire-ground interaction force, a radial-spring tire model is modified by adding the tire damping to generate the road excitation forces due to road disturbances in the vertical and longitudinal directions. A dynamic 2D tire friction model based on the LuGre friction theory is modified to simulate the dynamic frictional interaction in the tire-ground contact pitch. The ride quality of a PSS vehicle is evaluated in accordance with the ISO 2631 and compared with that of a conventional vehicle. It is shown that the PSS system exhibits good potential to attenuate the impact and isolate the vibration due to road excitations in both the vertical and longitudinal directions, resulting in improved vehicles’ ride and comfort quality. The relatively soft longitudinal strut can absorb the longitudinal impact and, therefore, can protect the components. The investigation of handling performance including the steady-state handling characteristics, transient and frequency responses in various scenarios demonstrates that the PSS vehicle is directionally stable and generally has comparable handling behaviour to a similar conventional vehicle. The application of PSS in vehicles can enhance the understeer trend, i.e. the understeer becomes more understeer, neutral steer becomes slightly understeer, and oversteer becomes less oversteer. The total dynamic behaviour combining the bounce, pitch, roll and the longitudinal dynamics under various scenarios such as differential brake-in-turn and asymmetric obstacle traversing was thoroughly investigated. Simulation results illustrate that the PSS vehicle has a relatively small roll angle in a turning manoeuvre. In some cases such as passing road potholes, the PSS vehicle has a better directional stability.