  Many studies simulates the machining process by using a single degree of
freedom spring-mass sytem to model the tool stiffness, or the workpiece
stiffness, or the unit tool-workpiece stiffness in modelings 2D. Others impose
the tool action, or use more or less complex modelings of the efforts applied
by the tool taking account the tool geometry. Thus, all these models remain
two-dimensional or sometimes partially three-dimensional. This paper aims at
developing an experimental method allowing to determine accurately the real
three-dimensional behaviour of a machining system (machine tool, cutting tool,
tool-holder and associated system of force metrology six-component
dynamometer). In the work-space model of machining, a new experimental
procedure is implemented to determine the machining system elastic behaviour.
An experimental study of machining system is presented. We propose a machining
system static characterization. A decomposition in two distinct blocks of the
system "Workpiece-Tool-Machine" is realized. The block Tool and the block
Workpiece are studied and characterized separately by matrix stiffness and
displacement (three translations and three rotations). The Castigliano's theory
allows us to calculate the total stiffness matrix and the total displacement
matrix. A stiffness center point and a plan of tool tip static displacement are
presented in agreement with the turning machining dynamic model and especially
during the self induced vibration. These results are necessary to have a good
three-dimensional machining system dynamic characterization.
