Biomedical Engineering Reference
In-Depth Information
1
b
,
C
2 Re
Gp
(
)
1
where: Re[Gp(ω)] is the real part of the frequency response function for the p
th
mode.
The consequence of the obtained derivations is that unlike the onset of
chatter in turning and milling, it is required for the chatter frequency to be
slightly below the natural frequency of the corresponding mode, not slightly
above, for the chatter episodes to occur. This has also been experimentally
confirmed by cutting tests. In their experiment, Bayly et al. have used a
symmetric ―winged‖ steel collar, attached 25mm from the tip of the drill. The
collar was designed symmetrically to avoid inertial coupling between bending
and torsion. However, the added inertia of the collar lowered the natural
frequencies of the drill so that the phenomena usually apparent at high speeds
would be observed at lower speeds. This causes the natural frequencies in the
test to be much lower than the frequencies that actual drills have. Apart from
the collar effect, the authors pointed out that they have neglected to include
some effects which influence the model: burnishing, plowing, rubbing and
process damping due to the clearance face of the tool interfering with the cut
surface. The process damping should be especially significant at lower speeds.
Owing to the fact that this paper deals with the existing piloted hole, the
phenomenon of damping was neglected. Further, there is the inevitable effect
of the friction between the rake face and the chip as well as the margin effect
when the margin of the drill interacts with the sides of the hole. The effect of
the axial loading of the drill during drilling has been neglected even though it
would cause some change in the torsional natural frequency. The fact that the
workpiece deforms during the drilling process has been neglected, even
though it will influence the surface and therefore the chip load. Other possible
causes of torsional vibration in drilling that have not been covered are
considered to be: stick slip interaction between tool and wall of the hole, built-
up edge, etc.
Stone and Askari continued on Bayly's work in 2002 in [15] developing a
model which incorporated the friction effect into the axial-torsional vibrational
model by studying the stick - slip interaction mode between the tool and
workpiece material. The stick-slip mode provides non-linear process damping
to the system. By interacting with the vibrational mode it produces instability
in the non-regenerative chatter case.
