Analysis of compliance between the cutting tool and the workpiece on the stability of a turning process

Chatter is a common vibration problem that limits productivity of machining processes, since its large amplitude vibrations causes poor surface finishing, premature damage and breakage of cutting tools, as well as mechanical system deterioration. This phenomenon is a condition of instability that has been classified as a self-excited vibration problem, which shows a nonlinear behavior characterized by the presence of limit cycles and jump phenomenon. In addition, subcritical Hopf and flip bifurcations are mathematical interpretations for loss of stability. Regeneration theory and linear time delay models are the most widely accepted explanations for the onset of chatter vibrations. On the other hand, models based on nonlinearities from structure and cutting process have been also proposed and studied under nonlinear dynamics and chaos theory. However, on both linear and nonlinear formulations usually the compliance between the workpiece and cutting tool has been ignored. In this work, a multiple degree of freedom model for chatter prediction in turning, based on compliance between the cutting tool and the workpiece, is presented. Hence, a better approach to the physical phenomenon is expected, since the effect of the dynamic characteristics of the cutting tool is also taken into account. In this study, a linear stability analysis of the model in the frequency domain is performed and a method to construct typical stability charts is obtained. The effect of the dynamics of the cutting tool on the stability of the process is analyzed as well.