Biomedical Engineering Reference
In-Depth Information
2
02
where: and .
Further, Dilley et al., studied the effect of the chisel edge on the chatter
frequency in drilling in [18]. Owing to the problem of complex boundary
conditions of the margin and chisel edge, most researchers have been
dissuaded from studying such problems. A bending motion has been seen due
to the movement of the chisel and therefore it is proven to be wrong to use
fixed end conditions that would make the chisel stationary. This paper
considers a simplified model where a spring end condition, which represents
the chisel edge effect is used. In order to have proper frequency matching with
the experimental data, it is considered necessary to use a spring end condition
to represent the contact between the chisel edge and workpiece. A transverse
spring and axial thrust force were added to the simple fixed-free beam,
approximating the equation of motion using the Rayleigh-Ritz procedure to:
01
1
2
..
m q t
( )
k
q t
( )
0
L
m
(
z
)
(
z dz
)
ij
i
j
0
"
"
'
'
k
EI
(
z
)
(
z dz
)
K
(
L
)
(
L
)
F
(
z
)
(
z dz
)
ij
y
i
j
end
i
j
z
i
j
where: m - mass, k- stiffness, θ - trial function, q - generalized coordinates,
- dimensionless quantity.
After analyzing the effect of the chisel, Dilley at al., studied the problem
of margin engagement and its effect on the frequency shift in drilling [19].
This paper showed that there is a significant frequency shift in the case of
margin engagement.
The drill model has been presented in Figure 5:
2
(
F L
) / (
EI
)
Figure 5. Drill model diagrams: a. 2-DOF rotating single-mode system and .b.
simplified drill model with spring-end condition representing effects of margin
engagement. Tool fixed frame: ξ - η. Space fixed frame: x-y, where z is the depth into
the hole [19].
