Friction-Induced Reverse Chatter in Rigid-Body Mechanisms with Impacts

Professor Harry Dankowicz

Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign (UIUC)

This talk reviews recent work on the possibility of formulating a consistent and unambiguous forward-simulation model of rigid-body mechanical systems with isolated points of intermittent or sustained frictional contact. The analysis considers paradoxical ambiguities associated with the coexistence of sustained contact and one or several alternative forward trajectories that include phases of free-flight motion. The presentation documents the original discovery of an apparently irresolvable, infinitely degenerate ambiguity known as reverse chatter – a transition to free flight through an infinite sequence of impacts with impact times accumulating from the right on a limit point and with impact velocities diverging exponentially away from the limit point, even where the contact-independent normal acceleration supports sustained contact. The conclusions of the theoretical analysis are illustrated through everyday examples of chattering contact.

Biosketch

Harry Dankowicz is Professor in the Department of Mechanical Science and Engineering at the University of Illinois at Urbana-Champaign (UIUC) and has held faculty positions in the Department of Engineering Science and Mechanics at Virginia Polytechnic Institute and State University and in the Department of Mechanics at the Royal Institute of Technology (KTH) in Stockholm, Sweden. He received his M.S. degree (1991) in Engineering Physics from KTH; and his Ph.D. degree (1995) in Theoretical and Applied Mechanics with minors in Mathematics and Astronomy from Cornell University. Prof. Dankowicz is the recipient of several prestigious awards, including a Junior Individual Grant from the Swedish Foundation for Strategic Research and a Presidential Early Career Award for Scientists and Engineers from NSF. He serves as Editor of Transactions of the ASME, Applied Mechanics Reviews and as General Conference Co-Chair for the 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. As director of the Applied Dynamics Laboratory at UIUC, he conducts dynamical systems research at the intersection of engineering, math and physics. This work involves studying a wide range of complex systems that are governed by differential equations and learning the behavior of those systems through theory and experiments. His research efforts further seek to make original and substantial contributions to the development and design of existing or novel devices that capitalize on system nonlinearities for improved system performance.