Machine tool chatter is one of the major constraints that limits produ
ctivity of the turning process. It is a self-excited vibration that is
mainly caused by the interaction between the machine-tool/workpiece s
tructure and the cutting process dynamics. This work introduces a gene
ral 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 asympt
otic stability index is also introduced for a relative stability analy
sis. The method can be applied to other machining processes, as long a
s the system equations can be expressed as a set of linear time invari
ant difference-differential equations.