Page 34 - June

METALWORKING EQUIPMENT AND TOOLS

formula (1) the potential energy is expressed as a function of cij for the principal axes of rigidity
in the vicinity of the tip of the cutter, then expression (1) will take a simple form: , (2)

where qi are the values of deformations along the principal axes of rigidity. If, for example,
a cutting force of a certain value is required to implement the turning process under specified
conditions, then the stored potential energy will depend on the location of the main axes of the
tool stiffness relative to the direction of the cutting force vector (P) and the values of cij. The
closer this direction is to the axis with the greatest rigidity, the lower the potential energy in the
elastic system. It follows from the fact that the displacement of the tip of the cutter from the
equilibrium position can be expanded along the principal axes of rigidity, then the displacement
along each of the axes qi = Picii-1. Now expression (2) can be represented as:
(3)

From expression (3) it follows that when the force vector coincides with the axis of
greatest rigidity, the value of P will be minimal. You can also make the obvious conclusion
that with increasing rigidity along all axes, the potential energy in the mechanical system will
decrease. This determines the recommendations for increasing the stiffness of elastic system of
technological equipment and a rational arrangement of the main axes of rigidity [1, 5]. However,
during cutting, the position of the elastic system remains non-equilibrium even with a reduced
amount of potential energy. In this case, the stability of the disturbed equilibrium position is
ensured by the constancy restraining forces, which are external influences on the cutting tool,
including detached chips. If we consider the position of the cutter in the section perpendicular
to the cutting surface (Fig. 2), then the reaction from the side of the cutting surface acts on the
rear face of the tool, and from the side of the front surface, which is distorted by the stagnant
zone, the reaction from the side of the coming off chips acts.
These forces are counterbalanced by the elastic reaction that occurs when the tool is
deformed. The chips and stagnation zone are not constant, so they do not provide absolute
process stability.

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