Cutting Stability Of A Workpiece Of UnsymmetricalStiffness

In this article we propose to study the dynamic stability of a rotating flexible workpiece of non circular section. The solution of the non uniform equilibrium equation of motion of the workpiece yielded a characteristic equation in a form of a fourth order polynomial with complexes and variable coefficients. The stability of this complex polynome is based on the Nyquist criterion. This allowed us to draw polar graphs which indicated clearly that the orientation of the principal axis of the workpiece in respect to the cutting tool edge has a decisive influence on the generation of chatter vibrations leading to the instability of the cutting.