Stability and Nonlinear Dynamics of Variable Speed Milling

颤振是工件与刀具之间的自激相对振动，是机械加工过程中普遍存在的问题。 其不利影响包括噪音、表面光洁度差、尺寸精度降低和机床寿命缩短。 颤振的发生限制了材料去除率和生产率。 本课题的目的是阐明通过连续调节主轴转速来抑制颤振的机理。 该项目解决了这个问题，使用分析，数值和实验的努力相结合，弥合差距从一个自由度的车削模型，以现实的模型，高速铣削过程。 该项目的统一主题是研究控制刀具运动的非线性延迟微分方程，计划将该项目开发的创新理论和模拟转移到工业领域，从而改进各种材料去除工艺的设计并提高其性能。 该项目将开发基于网络的模拟器，用于高年级本科生和研究生课程，并为工业设计师提供预测工具，以避免不必要的机器行为。 这些图形工具将增强对噪声和波动时间延迟对真实的工程问题的影响的理解。 该项目通过应用数学和工程接口的研究为学生教育提供了一个良好的环境。

Chatter, the self-excited relative vibration between workpiece and cutting tool, is a common problem in the machining process. Its adverse effects include noise, poor surface finish, reduced dimensional accuracy, and shortened machine tool life. The onset of chatter limits material-removal rates and productivity. The purpose of this project is to clarify the mechanism of suppression of chatter through continuous modulation of spindle speed. The project addresses this issue using a combination of analytical, numerical, and experimental efforts, bridging the gap from the one-degree-of-freedom turning model to realistic models for high-speed milling processes. The unifying theme in the work is a study of the nonlinear delay differential equations that govern the tool motion.It is planned to transfer to industry innovative theory and simulations developed in the project, allowing improved design and greater performance of various material removal processes. The project will develop web-based simulators to be used in senior undergraduate and graduate courses and to provide industrial designers with a predictive tool to avoid unwanted machine behavior. These graphical tools will enhance understanding of the effect of noise and fluctuating time delay on real engineering problems. The project provides an excellent environment for student education through research at the interface of applied mathematics and engineering.