Computational stability analysis of chatter in turning

Machine tool chatter is one of the major constraints that limits productivity of the turning process. It is a self-excited vibration that is mainly caused by the interaction between the machine-tool/workpiece structure and the cutting process dynamics. This work introduces a general method which avoids lengthy algebraic (symbolic) manipulations in deriving, a characteristic equation. The solution scheme is simple and robust since the characteristic equation is numerically formulated as a single variable equation whose variable is well bounded rather than two nonlinear algebraic equations with unbounded variables. An asymptotic stability index is also introduced for a relative stability analysis. The method can be applied to other machining processes, as long as the system equations can be expressed as a set of linear time invariant difference-differential equations.