This grant supports collaboration between a mathematician at Utah State University and an engineer at The Boeing Company to investigate chatter instability in drilling. Chatter is a self-excited oscillation between the machining tool and the work piece that limits productivity of machining operations, reduces the quality of the product, and shortens machine tool life. Drilling itself is one of the least well understood machining processes due to the complex geometry of the cutting surface, and simple linear models of drilling have had limited success. We are developing nonlinear models that incorporate information from finite element models for metal cutting as well as information about vibrational modes of the drill. The resulting models take the form of delay differential equations. We use a combination of conventional engineering techniques and techniques from nonlinear dynamics (e.g. center manifold reduction) to analyze these systems. We will utilize new capabilities in large-scale simulation software and build on previous theoretical work done at Boeing to perform dynamic stability analysis. The award is co-funded by the Dynamic Systems and Control Program and Grant Opportunities for Academic Liaison with Industry (GOALI) Program in the Directorate for Engineering and by the GOALI program through the Office of Multidisciplinary Activities of the Mathematical & Physical Sciences Directorate.

Drilling is a crucial machining process in aircraft manufacture: over a million holes may be drilled during the construction of a commercial airplane, and production errors resulting in out-of-tolerance holes can be extremely costly. Improving the precision with which holes may be drilled depends on a detailed understanding of instabilities such as chatter. Beyond the technological importance of this work is the synergy it promotes by supporting collaboration between academic mathematicians and industry engineers. The connection with The Boeing Company is a central part of Utah State University's industrial mathematics program, which provides mathematics students with enhanced training by exposing them to real applications, encouraging group work, and honing communication skills. Another aspect of this project is the development of an active collaboration between researchers at Boeing-Seattle and Dr. Stone and those at Boeing-St. Louis and Dr. Philip Bayly of Washington University. The capabilities of these two groups mesh in a unique way, providing a strong research environment with interlacing thrusts of theory, experiment, and direct numerical simulation. The projects supported by this grant are part of this collaboration, which combines the expertise and facilities of both groups, and will lead to state-of-the-art results capable of enhancing high-speed drilling practices.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Henry A. Warchall
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Utah State University
United States
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