Eigenvalue analysis of mode-coupling chatter for machine-tool stabilization

The mode-coupling chatter phenomenon, due to self-excited vibrations occurr ing during many machining operations, is studied in this paper. Although mo de-coupling chatter has been widely treated in the specialized literature, the authors propose here an approach that is rather different from the clas sical one, namely, an eigenvalue analysis of chatter based on system theory . A mathematical model of the workpiece tool system is established first, s o as to define the system equations. A closed-form equation, expressing the stability condition of the system as a function of the system parameters, and particularly of the angle between the feed direction and the piece surf ace, is then obtained from the eigenvalues of the system. Moreover, a study of the eigenvectors of the system enables one to analytically express the tool trajectories, both in the stable and in the unstable case. The model t hus formulated and the related considerations about the system stability ar e then employed in a real case. Namely, a wood-cutting machine subject to m ode-coupling chatter is considered, and a technique for stabilization, base d on the considerations made on the model, is presented. The authors believ e that the eigenvalue analysis of mode-coupling chatter presented in this p aper provides a more detailed and complete analysis of the phenomenon than what is currently present in the literature.