GOALI: Friction as Anosov Flows on Hysteretic Manifolds

William Marsh Rice University, Houston TX

Investigators

Abstract

Friction and wear consume 23 percent of the world's total energy supply. One potential mechanism to reduce this loss of energy is to build predictive design optimization models for large structures with frictional interfaces (such as engines and aeroturbines), to allow new insight into the mechanisms of friction at interfaces. With a better understanding of the friction within jointed interfaces and how these interfaces transfer and dissipate energy, it would be possible to optimize design and significantly reduce the weight and emissions of aircraft, automobiles, and engines. One barrier to achieving this reduction is the lack of understanding of how friction behaves internally in a jointed structure. If a more accurate, predictive representation of friction within a jointed structure existed, then this would offer a new foundation to design more efficient structures, potentially saving more than $1 trillion annually and reducing annual emissions of carbon dioxide by more than 3 billion tons. This Grant Opportunity for Academic Liaison with Industry (GOALI) research project will address this challenge by creating a new mathematical understanding of friction. If successful, this will enable an order of magnitude reduction in computational time, making design optimization possible. Additionally, the experiments from this research will provide new insights into the fundamental physics of friction internal to jointed interfaces. The primary scientific goal of this GOALI research is to test the hypothesis that a hysteretic manifold can accurately represent the frictional interactions within an interface. The secondary goal is to merge the mathematics of Anosov flows with both hysteretic manifolds and structural dynamics to create a fundamentally new approach to simulating the nonlinear dynamics of hysteretic systems. The major technical outcome of this work will be to define the hysteretic manifolds mathematically, validate their existence experimentally, and exploit their structure to yield a new simulation paradigm for studying hysteretic systems and jointed structures. This research will utilize novel experiments on a custom-designed fretting rig to validate the concept of a hysteretic manifold. Unlike existing test rigs, the novelty of the proposed experiment is in accurately recreating the tribosystem (i.e., unique confluence of loads, geometry, materials, and environment that give rise to a specific set of wear mechanisms) of the motivating applications. This research will then use insights from these experiments to propose a new modeling framework for systems with frictional interfaces. With this novel framework, the mathematics of Anosov flows will be introduced to provide new opportunities for how friction can be modeled for frequency domain simulations. Preliminary work demonstrates that a reduction in computation time of an order of magnitude may be feasible for a new frequency domain solution method. This research thus addresses two major challenges: computational efficiency and accuracy for modeling assembled structures. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.