Dynamics of High-Speed Machining

这项资助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合作研究钻井中的颤振不稳定性。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。由于切削表面的复杂几何形状，钻孔本身是最不容易理解的加工过程之一，简单的线性钻孔模型取得了有限的成功。我们正在开发非线性模型，该模型结合了金属切削的有限元模型信息以及钻头的振动模式信息。所得到的模型采用延迟微分方程的形式。我们结合了传统工程技术和非线性动力学技术（如中心流形缩减）来分析这些系统。我们将利用大规模仿真软件的新功能，并在波音公司先前的理论工作基础上进行动态稳定性分析。该奖项由工程理事会的动态系统与控制计划和与工业的学术联络拨款机会（GOALI）计划共同资助，并由GOALI计划通过数学和物理科学理事会的多学科活动办公室共同资助。在飞机制造中，钻孔是一个至关重要的加工过程：在一架商用飞机的制造过程中，可能会钻出超过一百万个孔，而导致超公差孔的生产误差可能会造成极其昂贵的代价。提高钻孔精度取决于对颤振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。与波音公司的合作是犹他州立大学工业数学项目的核心部分，该项目通过让学生接触实际应用、鼓励团队合作和磨练沟通技巧，为数学专业的学生提供强化训练。该项目的另一个方面是发展波音-西雅图和斯通博士的研究人员与波音- st的研究人员之间的积极合作。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相结合，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叉推进。该基金支持的项目是该合作的一部分，该合作结合了两个团队的专业知识和设施，并将产生能够增强高速钻井实践的最先进的结果。

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.