Investigations of the Nonlinear Dynamics of Machining

这笔赠款将促进私家侦探的自然变化他的研究重点是工业数学。她的研究重点从非线性动力学工业数学的转变既服务于个人的研究目标，也服务于培养就业数学学生的领导目标。工业数学作为一个领域仍处于早期阶段，在这一点上参与它可能会增加P.I.在应用数学界的影响力，并在未来增加领导角色的潜力。该研究涉及高速加工中颤振不稳定性的研究。颤振是机床与工件之间的一种自激振荡，它限制了加工作业的生产率，降低了产品的质量，缩短了机床的寿命。直到最近，模型主要是线性的，在再生颤振的情况下有延迟项。目前正在开发非线性模型，并在预测可能部分由低维系统描述的行为方面取得了一些成功。在飞机工业中，这个问题受到了密切关注，而私家侦探的工作他在波音公司（Boeing）的合作伙伴阿斯卡里（Abe Askari）博士一直致力于开发金属切削的有限元模型。大尺度数值模拟和低维模型这两种技术的结合是本课题研究的目标。

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.