  The actual research deals with determining by a new protocol the necessary
parameters considering a three-dimensional model to simulate in a realistic way
the turning process on machine tool. This paper is dedicated to the
experimental displacements analysis of the block tool / block workpiece with
self-excited vibrations. In connexion with turning process, the self-excited
vibrations domain is obtained starting from spectra of two accelerometers. The
existence of a displacements plane attached to the tool edge point is revealed.
This plane proves to be inclined compared to the machines tool axes. We
establish that the tool tip point describes an ellipse. This ellipse is very
small and can be considered as a small straight line segment for the stable
cutting process (without vibrations). In unstable mode (with vibrations) the
ellipse of displacements is really more visible. A difference in phase occurs
between the tool tip displacements on the radial direction and on the cutting
one. The feed motion direction and the cutting one are almost in phase. The
values of the long and small ellipse axes (and their ratio) shows that these
sizes are increasing with the feed rate value. The axis that goes through the
stiffness center and the tool tip represents the maximum stiffness direction.
The maximum (resp. minimum) stiffness axis of the tool is perpendicular to the
large (resp. small) ellipse displacements axis. FFT analysis of the
accelerometers signals allows to reach several important parameters and
establish coherent correlations between tool tip displacements and the static -
elastic characteristics of the machine tool components tested.
