State-space analysis of mode-coupling in orthogonal metal cutting under wave regeneration

In this paper, mode-coupling in orthogonal metal cutting is analyzed in the state-space domain. Closed-form equations are obtained for eigenvalues and eigenvectors of the joint system formed by the cutting process and the mechanical structure, as a function of cutting conditions and structure modal parameters. System stability is analyzed and variations of the joint system natural frequencies are proposed for monitoring stability, forces and indirectly tool condition. Finally, experimental tests are presented to validate theoretical formulations in orthogonal aluminium cutting. By means of a state-space domain analysis of the joint system, formed by the cutting process and the machine structure, it is possible to obtain mathematical formulations that quantitatively relate joint system natural frequencies to system stability. Therefore, it is possible to detect chatter vibrations before work piece quality is affected by monitoring vibrations during machining. These formulations facilitate the development of robust active vibration control system which will improve machine tool stability in the future.