Vibrations in milling processes may cause poor surface
properties and shortens the lifetime of the machine tool. There
are two types of these vibrations which are essential. The
first is the so-called “chatter” that is a kind of a self-
excited vibration caused by the regenerative effect of the
machined surface. The chip thickness depends on the current
position of the cutting edge and the past position of the
previous/neighbouring cutting edge of the mill. Consequently,
the governing equation of the model is a time delayed
differential equation. In order to avoid this type of
vibration, the so-called stability chart must be created as a
function of the technological parameters. The second type of
vibrations is caused by the periodic non-smooth cutting force.
This forced vibration can have large amplitudes at resonant
spindle speeds.
There are some regions of the technological parameters where
large material removal rates can be achieved, while
regenerative chatter is also avoided. However, in most cases,
forced vibrations can still occur at these parameters even
close to resonance. In case of helical tools, we found that
this kind of vibration can also be eliminated by using the
optimal axial immersion that depends on the helix pitch of the
tool and on the spindle speed. In this optimal case, the
appropriate component of the Fourier series of the cutting
force is zero, thus, resonance is excluded.
Measurements were carried out to prove the analytical
predictions. A test rig has been designed and manufactured that
can be modelled analytically. The work-piece is fixed on a
table, which is flexible in a direction perpendicular to the
feed motion. The signals of the accelerometers (B&K4397) were
detected by Pulse Front-end and Pulse Labshop v11.0 software.
To confirm our analytical results, we carried out a series of
measurements with constant spindle speeds and increasing axial
immersion, where the higher Fourier harmonics of the cutting
force excite the system just at its resonant frequency. Instead
of making numerous measurements with distinct spindle speeds,
we used wedge-shaped work-pieces to speed-up the lengthy
experiments. In this way, the axial immersion was increased
continuously during the cutting process. So the stability
boundary and the optimal axial immersions could be found with a
single test at each spindle speed. We found that the vibration
amplitudes were significantly reduced in case of the
theoretically predicted optimal axial immersions.
