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Rubber friction is an important aspect to tire engineers, material developers and pavement engineers because of its importance in the estimation of forces generated at the contact, which further helps in optimizing tire and vehicle performances, and to estimate tire wear. It mainly depends on the material properties, contact mechanics and operating condition. There are two major contributions to rubber friction, due to repeated viscoelastic deformation from undulations of surface called hysteresis and due to Vander Waals interaction of the molecules called adhesion. The study focuses on analytical modeling of friction for stationary sliding of rubber block on rough surfaces. Two novel approaches are discussed and compared. Frictional shear stress is obtained from the energy dissipated at the contact interface due to the elastic deformations of rubber block at different length scales. Contact mechanics theories based on continuity approach combined with stochastic processes to estimate the real contact area, mean penetration depth and true stresses at contact depending on operating conditions. Rubber properties are highly temperature dependent. Temperature model developed based on heat diffusion relation is integrated to consider the effects of temperature rise due to frictional heating. Model results are validated with theoretical results of literature. Simulation results of friction model is obtained for Compound A sliding on rough surface. Material properties are obtained using Dynamic Mechanical Analysis and Time temperature superposition. Influence of the friction models under different conditions are discussed. Model results are validated with experimental data from Dynamic friction tester on a 120-grit surface followed by future works. / Master of Science

The objective of this study is to develop a high-fidelity physics-based flexible tire model that can be fully integrated into multibody dynamics computer algorithms for use in on-road and off-road vehicle dynamics simulation without ad-hoc co-simulation techniques. Despite the fact detailed finite element tire models using explicit finite element software have been widely utilized for structural design of tires by tire manufactures, it is recognized in the tire industry that existing state-of-the-art explicit finite element tire models are not capable of predicting the transient tire force characteristics accurately under severe vehicle maneuvering conditions due to the numerical instability that is essentially inevitable for explicit finite element procedures for severe loading scenarios and the lack of transient (dynamic) tire friction model suited for FE tire models. Furthermore, to integrate the deformable tire models into multibody full vehicle simulation, co-simulation technique could be an option for commercial software. However, there exist various challenges in co-simulation for the transient vehicle maneuvering simulation in terms of numerical stability and computational efficiency. The transient tire dynamics involves rapid changes in contact forces due to the abrupt braking and steering input, thus use of co-simulation requires very small step size to ensure the numerical stability and energy balance between two separate simulation using different solvers. In order to address these essential and challenging issues on the high-fidelity flexible tire model suited for multibody vehicle dynamics simulation, a physics-based tire model using the flexible multibody dynamics approach is proposed in this study. To this end, a continuum mechanics based shear deformable laminated composite shell element is developed based on the finite element absolute nodal coordinate formulation for modeling the complex fiber reinforced rubber tire structure. The assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches are introduced for alleviating element lockings exhibited in the element. Use of the concept of the absolute nodal coordinate formulation leads to various advantages for tire dynamics simulation in that (1) constant mass matrix can be obtained for fully nonlinear dynamics simulation; (2) exact modeling of rigid body motion is ensured when strains are zero; and (3) non-incremental solution procedure utilized in the general multibody dynamics computer algorithm can be directly applied without specialized updating schemes for finite rotations. Using the proposed shear deformable laminated composite shell element, a physics-based flexible tire model is developed. To account for the transient tire friction characteristics including the friction-induced hysteresis that appears in severe maneuvering conditions, the distributed parameter LuGre tire friction model is integrated into the flexible tire model. To this end, the contact patch predicted by the structural tire model is discretized into small strips across the tire width, and then each strip is further discretized into small elements to convert the partial differential equations of the LuGre tire friction model to the set of first-order ordinary differential equations. By doing so, the structural deformation of the flexible tire model and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. Furthermore, a systematic and automated procedure for parameter identification of LuGre tire friction model is developed. Since several fitting parameters are introduced to account for the nonlinear friction characteristics, the correlation of the model parameters with physical quantities are not clear, making the parameter identification of the LuGre tire friction model difficult. In the procedure developed in this study, friction parameters in terms of slip-dependent friction characteristics and adhesion parameter are estimated separately, and then all the parameters are identified using the nonlinear least squares fitting. Furthermore, the modified friction characteristic curve function is proposed for wet road conditions, in which the linear decay in friction is exhibited in the large slip velocity range. It is shown that use of the proposed numerical procedure leads to an accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Furthermore, the fundamental tire properties including the load-deflection curve, the contact patch lengths, contact pressure distributions, and natural frequencies are validated against the test data. Several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physics-based flexible tire model developed in this study. Finally, the physics-based flexible tire model is further extended for application to off-road mobility simulation. To this end, a locking-free 9-node brick element with the curvature coordinates at the center node is developed and justified for use in modeling a continuum soil with the capped Drucker-Prager failure criterion. Multiplicative finite strain plasticity theory is utilized to consider the large soil deformation exhibited in the tire/soil interaction simulation. In order to identify soil parameters including cohesion and friction angle, the triaxial soil test is conducted. Using the soil parameters identified including the plastic hardening parameters by the compression soil test, the continuum soil model developed is validated against the test data. Use of the high-fidelity physics-based tire/soil simulation model in off-road mobility simulation, however, leads to a very large computational model to consider a wide area of terrains. Thus, the computational cost dramatically increases as the size of the soil model increases. To address this issue, the component soil model is proposed such that soil elements far behind the tire can be removed from the equations of motion sequentially, and then new soil elements are added to the portion that the tire is heading to. That is, the soil behavior only in the vicinity of the rolling tire is solved in order to reduce the overall model dimensionality associated with the finite element soil model. It is shown that use of the component soil model leads to a significant reduction in computational time while ensuring the accuracy, making the use of the physics-based deformable tire/soil simulation capability feasible in off-road mobility simulation.

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.