Investigations of the Nonlinear Dynamics of Machining

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This grant will facilitate a natural change in the P.I.'s research emphasis to Industrial Mathematics. The shift in her research emphasis from nonlinear dynamics Industrial Mathematics serves both a personal research objective and a leadership objective in the training of employable mathematics students. Industrial Mathematics is still in its early stages as a field and participation in it at this point could increase the P.I.'s influence in the applied mathematics community, with increased potential for leadership roles in future. The research proposed involves investigations of chatter instability in high-speed machining. 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. Up until recently, models have been primarily linear, with delay terms in the case of regenerative chatter. Nonlinear models are currently being developed, and have had some success in predicting behavior that may be described in part by low dimensional systems. In the aircraft industry this problem has received intense scrutiny, andthe work of the P.I.'s collaborator at Boeing (Dr. Abe Askari) has been in the development of finite element models for metal cutting. A union of the two techniques, large scale numerical simulation and low dimensional models, is the goal of the research in this proposal.