This project addresses challenging aspects in modeling complex nonlinear mechanical systems, such as terrain vehicles and pneumatic tires, in the context of their operating environment. Within the scope of this study we will develop an analytical and computational framework to efficiently model such systems in the presence of parametric and external uncertainty. Specifically, we will develop methods to accurately represent the operating environment and the vehicle-terrain interaction. Moreover, we will conduct experimental studies using high-end technology to analyze the physical phenomena at the tire-terrain contact, and to validate the modeling techniques developed. For realistic performance predictions multibody dynamic models must account for uncertainties resulting from poorly-known environment parameters and rapidly-changing forcing functions. This project will employ the polynomial chaos expansion to simulate multibody dynamic systems with parametric and external uncertainties. This method is applicable to highly nonlinear systems, is computationally efficient, and can handle large uncertainties. Off-road vehicles represent a rich test-bed for the theoretical and experimental work proposed. Their performance prediction requires accurate models of the vehicle, the tire, and the terrain, all of which are affected by uncertainties. This project will model the soil from the standpoint of its dynamic interaction with a running vehicle, and will develop stochastic models for hard-to-predict soil characteristics. We will also employ a multi-step stochastic technique to simulate a rough terrain profile which does not impose unrealistic assumptions, and can be seamlessly incorporated in the vehicle-operating environment model. Further, the study will investigate innovative analytical methods to develop computationally efficient off-road tire models. The theoretical and the computational tools developed will significantly advance the field of multibody dynamics beyond the current deterministic paradigm, and will enable the development of appropriate control strategies. These tools are not domain specific and can also be applied to autonomous vehicles, industrial manipulators, actuators, and human body modeling.
The main focus of this study was to investigate challenging aspects in modeling complex nonlinear mechanical systems, such as terrain vehicles and pneumatic tires, in the context of their operating environment. Such mechanical systems are affected by a variety of uncertainties, related for example with their design parameters, or operating environment parameters. The computational challenges associated with modeling multibody dynamic systems under uncertainty stem from the dimensionality of the system with parameterized uncertainty and from the nonlinear coupling terms which require the evaluation of multiple statistical integrals. Incorporating large uncertainties in nonlinear systems also precludes the use of Taylor series. Moreover, the non-Gaussian and non-stationary nature of unprepared terrain profiles renders traditional stochastic methods not directly applicable. As part of this study we employed the polynomial chaos theory to simulate multibody dynamic systems with parametric and external uncertainties. The methodology thus developed has been applied to various tire parameters. Thorough investigations were conducted to also model the uncertainty in critical soil parameters and to accurately model their impact on the vehicle traction performance. Furthermore, we developed stochastic models for rough terrain profile. The forces developed at the tire-terrain interface are responsible for the dynamic behavior of a ground vehicle. Vehicle traction depends on the thrust, the compaction resistance, the driving torque, the soil compaction, and the slope resistance. Steering maneuvers are contingent upon the lateral force developed at the tire-terrain interaction. The suspension design must account for the vehicle sinkage and soil shearing, and their influence on the ride quality of the vehicle. Thus, a thorough understanding of the physical phenomena in the contact patch is of paramount importance, since the entire vehicle performance hinges upon them. As part of this study we developed computationally efficient, two dimensional and three dimensional quasi steady-state and transient semi-analytical tire models for on-road and off-road vehicle dynamics applications. The off-road tire models developed are capable of operating in soft soil and on rough rigid terrain. Moreover, we also conducted experimental work to study the traction capabilities of tires on ice. The main contributions of this project are thus in the area of uncertainty quantification for mechanical systems and in the area of tire modeling, especially for off-road environments. The project outcomes have been disseminated through numerous journal and conference proceedings papers, posters, and presentations. Invited presentations given by the PI also acknowledged the support of NSF for this research. Overall, this project had a substantial impact on the education, training, and development of all the students involved; it also provided the PI the opportunity to explore very interesting research directions. The project contributed to the education of a diverse group of students: three PhD students have been partially supported on the award; one African-American MS student, and two undergraduate students (one female and one Hispanic) participated on this project.
