Dynamics of High-Speed Machining

美国国家科学基金会奖数学科学奖-DMS-0104818数学科学：高速加工动力学摘要DMS-0104818石头这笔赠款支持犹他州立大学的一名数学家和波音公司的一名工程师之间的合作，以研究钻井中的颤振不稳定性。颤振是加工工具和工件之间的一种自激振荡，它限制了加工操作的生产率，降低了产品质量，缩短了机床寿命。由于切削面的复杂几何形状，钻削本身是最不被了解的加工过程之一，简单的线性钻削模型取得的成功有限。我们正在开发非线性模型，其中包括金属切割有限元模型的信息以及钻头振动模式的信息。所得到的模型采用时滞微分方程组的形式。我们结合了传统的工程技术和非线性动力学的技术(例如中心流形简化)来分析这些系统。我们将利用大型仿真软件中的新功能，并在波音公司之前所做的理论工作的基础上进行动态稳定性分析。该奖项由工程局的动态系统和控制计划和与工业的学术联系机会(GOALI)计划以及通过数学和物理科学局多学科活动办公室的GOALI计划共同资助。钻孔是飞机制造中的关键加工过程：在制造商用飞机的过程中，可能会钻出100多万个孔，而导致超公差孔的生产错误可能代价极其高昂。提高钻孔的精度取决于对抖动等不稳定性的详细了解。除了这项工作的技术重要性之外，它还通过支持学术数学家和工业工程师之间的合作来促进协同作用。与波音公司的联系是犹他州立大学工业数学项目的核心部分，该项目通过让数学学生接触实际应用程序、鼓励团队合作和磨练沟通技能，为他们提供增强的培训。该项目的另一个方面是在波音-西雅图的研究人员和斯通博士与波音-圣彼得堡的研究人员之间开展积极的合作。路易斯和华盛顿大学的菲利普·贝利博士。这两个小组的能力以一种独特的方式结合在一起，提供了一个强大的研究环境，理论、实验和直接的数值模拟交错推进。这笔赠款支持的项目是这一合作的一部分，合作结合了两个团队的专业知识和设施，将产生能够增强高速钻井实践的最先进成果。

NSF Award Abstract - DMS-0104818 Mathematical Sciences: Dynamics of High-Speed Machining Abstract DMS-0104818 Stone 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.