Page 37 - June

METALWORKING EQUIPMENT AND TOOLS

This is because vibration modes with higher natural
frequencies, despite smaller vibration amplitudes, can have
higher vibration velocities and accelerations, which allows them
to manifest themselves at the slightest imbalance caused by
shifts of chip elements or changes in the relative position of
the tool and workpiece due to low-frequency vibrations [12].
Processes similar to the passage of the groove also occur when
the chip elements shift. However, these time shifts are much
shorter, and the release from bonds is not as complete as when
entering the groove. This is especially true for drain chips, where

a shears occur, but the chips do not completely lose their elastic
properties, partially restraining the "rebound" of the tool from
the cutting surface. This leads to the fact that the attractor,
to which the tool tip trajectories gravitate during cutting, is
usually elongated along the cutting speed vector, its contour
has a relatively stable ellipse shape in two-dimensional space
and an ellipsoid shape in three-dimensional space. The paths
themselves are far from the shape of an ellipse, are chaotic,
but elongated in the direction of the cutting speed.
The trajectory of oscillation of the tool tip is determined by
many parameters, some of which have a random component.
It is not only the dynamic stiffness of the elastic system of the
machine, which includes the dynamic characteristics of the tool
and the workpiece and is a complex function of the working
b space of technological equipment. It is not only the cutting

Fig. 4. Diagram of the torsional mode modes and the heterogeneity of the properties of the processed
of vibration of the cutter and the
direction of movement after release material, which determine the load, experience shows, it is
from ties (a); section of the conical also the geometry of the tool changing with wear, the state of
surface after boring with traces of self- its cutting edges, the nature of the formed chips, especially
oscillations (b).
the degree of its differentiation, etc. Complex processes in the
cutting zone lead to the fact that at each moment of time the conditions of interaction of the
surfaces of the tool with the chips, the processed surface and the cutting surface change.
The moments of shear of the chip elements lead to abrupt changes in the load, the very
polycrystalline structure of the processed material makes it impossible to describe the resulting
reactions, changing contact stiffness and damping in the frictional contact zone and in the
dynamic system. All this suggests that cutting is accompanied by chaotic or quasi-attractors,
which are more complexly arranged in comparison with strange attractors [4, 13, 14].
The trajectories of such attractors are called Poisson stable, since they do not go beyond
the bounds of a bounded region. If the boundaries of this area meet the requirements for
surface cleanliness and quality of the surface layer, then the cutting process can be considered

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