Biomedical Engineering Reference
In-Depth Information
experimental work, the model actually predicts a small value for the coupling
of vibrations and actually predicts both torsional-axial and lateral chatter
vibrations. Therefore, it can be seen that the model does not actually agree
with the experimental results. The predicted values for stiffness and damping
are not in agreement with the obtained experimental data, and issues like the
rubbing of the cutting lips against the bottom of the hole which is wavy in the
first place, hole wall contact with drill flutes, the change in the contact
boundaries as the drill penetrates deeper in the hole, the friction effect all add
to the complexity of accurate prediction of chatter vibrations.
The second part of the two-part paper [25] presents a general solution of
drilling chatter stability in the frequency domain. In order to determine the
regenerative chip thickness, the drill's flexibility in torsional, axial and lateral
directions has been analyzed.
All the mentioned vibrations have an influence on the regenerative chip
thickness. Mathematically, the change in chip thickness due to regenerative
displacements can be defined as:
dx
cos
t
dy
sin
t
dh
1
tan
cos
t
dx
t
dy
sin
t
dh
2
tan
t
where: κt is the tip angle of the drill and Ωt is the tool rotation angle.
The effect of the torsional vibrations on the chip thickness can be defined
as:
, where f
r
is feed per revolution.
1
2
dh
dh
d
f
r
The effect of the axial vibrations on the chip thickness can be defined as:
dh
dh
dz
When all the vibrations are taken into consideration, the effect of the
whole system on the change in chip thickness is:
f
1
r
(
dx
cos
t
dy
sin
t
)
dz
d
dh
dh
tan
2
1
2
t
1
f
r
(
dx
cos
t
dy
sin
t
)
dz
d
tan
2
t
