Self-excited nonlinear vibrations occurring in the machining \nprocesses are investigated
in this paper. Our treatment applies \nanalytical techniques to a one degree of freedom
but strongly \nnonlinear mechanical model of the turning process. This tool \nenable
us to describe and analyse the highly nonlinear dynamics \nof the appearing periodic
and more complicated motions. Using \nnormal form calculations for the delay-differential
equation \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. Zones of bi-stability are presented in the \ntraditional
stability lobe diagram.
