Dynamic simulation and active vibration control design of an ultra-precision fly-cutting machine tool

As an intermittent cutting process, fly-cutting machining often results in unwanted and non-negligible vibrations, which adversely affect the surface quality of the machined workpiece. This work presents a dynamic simulation and active vibration control approach for the ultra-precision fly-cutting machine tool based on the transfer matrix method for multibody systems (MSTMM) and the independent modal space control method. The dynamic model of the ultra-precision fly-cutting machine tool system, incorporating rigid body elements, beam elements, flexible body elements, and hinge elements is established. The dynamic equations of the system are derived by directly combining the body dynamic equations of all body elements and decoupling them using augmented eigenvectors. Further, the state-space representation of the system is obtained and expressed within each independent modal space. The structure of the active vibration control system, including the modal filter and controller, has been meticulously designed. The controlled modes are selected based on H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{2}$$\end{document} norm of each mode, while the optimization of actuator positions is performed using the controllability Gramian. Finally, numerical simulations are conducted to verify the efficacy of the proposed modal space control approach in effectively reducing the tool-tip vibration and improving the machining accuracy.