Stability and Nonlinear Dynamics of Variable Speed Milling

颤振是加工过程中普遍存在的问题，它是指刀具与工件之间的自激相对振动。它的不利影响包括噪音、表面光洁度差、尺寸精度降低和缩短机床寿命。震颤的出现限制了材料的去除速度和生产率。本项目的目的是阐明通过连续调节主轴转速来抑制颤振的机理。该项目采用分析、数值和实验相结合的方法来解决这一问题，弥补了从单自由度车削模型到高速铣削过程的现实模型之间的差距。工作中统一的主题是对控制刀具运动的非线性延迟微分方程的研究。计划将项目中开发的创新理论和模拟转化为行业创新理论和模拟，使各种材料去除过程得到改进的设计和更好的性能。该项目将开发基于网络的模拟器，用于高级本科生和研究生课程，并为工业设计师提供预测工具，以避免不需要的机器行为。这些图形工具将增强对噪声和波动时滞对实际工程问题的影响的理解。该项目通过研究应用数学和工程的接口，为学生教育提供了一个很好的环境。

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.