Page 31 - June

METALWORKING EQUIPMENT AND TOOLS
Cutting stability

When assessing the quality of manufacture and the very design of metal-cutting machines,
much attention is paid to the ability of the machine to carry out a stable cutting process. In
this case, stability, more often called vibration resistance, is understood as the possibility of
obtaining surfaces of parts with permissible parameters waviness and roughness in a fairly wide
range of cutting conditions. Vibration resistance testing is carried out either experimentally
or using approximate analytical methods or using computer simulation. In modeling, the
elastic system of the machine tool and the cutting process are represented in the form of a
system of differential equations, which is studied for stability. Wherein stability is assessed in
accordance with the definition given by Lyapunov [1]. In a simplified form, this definition can
be formulated as follows: stability is a property of a system in the process of motion, as late
as desired, to return as close as desired to its initial state in the phase space. With regard to
the cutting process, this means that the violation of the relative position of the cutter and the
workpiece during cutting under the influence of external disturbances after some time after the
disappearance of the disturbing influence will be eliminated. These processes are considered
in the phase space defined by generalized coordinates and corresponding velocities. Even if
we assume the adequacy of the mathematical model to the real cutting process, the presence
of such stability upon closer examination is neither a necessary nor a sufficient condition for

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