Biomedical Engineering Reference
In-Depth Information
chatter vibrations, and combined lateral and torsional-axial vibrations. The
presented model was used for prediction of lateral chatter and prediction of the
combination of lateral and torsional-axial vibrations.
The general equation of motion for the dynamic drilling system in the
stationary frame are:
..
.
x t
( )
x t
( )
F
xt
()
x
..
.
F
y t
( )
y t
( )
y t
( )
()
y
M
C
K
..
.
zt
F
z
z t
( )
z t
( )
()
t
T
c
..
.
( )
( )
where: x, y - lateral, z - axial, θ - torsional deflection of the drill, matrices M,
C, K - mass, damping and stiffness characteristics at the drill tip, Fx, Fy lateral
forces, thrust Fz force, and Tc - torque.
The total displacement in any direction can be calculated by summing
vibrations in all natural modes in a chosen direction, giving the overall effect:
k
m
q t
( )
q t
( )
i
1
These deflections will influence the chip thickness, changing the force
distribution and effecting the vibrations in all directions, therefore the cutting
force system has to be coupled through the dynamic chip thickness distribution
along the cutting edges.
The influence of pilot hole size, spindle speed, torsional-axial chatter on
lateral forces was experimentally observed and compared with simulated
results. As the authors point out, this paper has a fundamental contribution to
the investigation of drilling by creating a complex numerical model that
incorporates cutting force models, rigid body motion as well as vibrations that
occur in the process of drilling. Apart from combining these effects, the
authors include both grinding errors and tool misalignment effects. From the
data collected from the experiments, it has been shown that the coupling of
lateral and torsional vibrations does not happen; torsional-axial chatter is seen
as dominant, while lateral chatter is absent. The lateral chatter could be
become more important in longer, slender drills. On the contrary to the
