Self-excited non-linear vibrations occurring in the machining \nprocesses are investigated
in this paper. Our treatment applies \nanalytical techniques to a one Degree of Freedom
(DOF) but \nstrongly non-linear mechanical model of the turning process. \nThis tool
enables us to describe and analyse the highly non- \nlinear dynamics of the appearing
periodic motions. Using normal \nform calculations for the Delay-Differential Equation
(DDE) \nmodel, we prove that the low-amplitude vibrations are unstable \nall along
the stability lobes due to the subcriticality of Hopf \nbifurcations. This means that
self-excited vibrations of the \nmachine tool may occur below the stability boundaries
predicted \nby the linear theory. Consequently, stable stationary cutting \nmay not
be robust enough for external perturbations close to the \nlinear stability limits
determined during the parameter \noptimisation of turning processes. Robustness is
characterised \nby the amplitude of unstable oscillations along the stability \nlobes
for non-linear cutting force characteristics having \nessential inflection points
against chip thickness.
