Biomedical Engineering Reference
In-Depth Information
The dynamic forces can therefore be expressed as:
k b dh
(
dh
) sin
t
k
k
(
dh
dh
) cos
t
Fx
tc
1
2
tc
rc
1
2
k b dh
(
dh
) cos
t
k
k
(
dh
dh
) sin
t
Fy
tc
1
2
tc
rc
1
2
k
k
b dh
dh
Fz
Tc
tc
ac
k b dh
(
dh
) (1
k
)
R
tc
rc
t
where: Fx, Fy, Fz - cutting forces acting on the tool tip, Tc - cutting torque
acting on the tool tip, Rt - torque arm - from tangential and radial forces, ktc -
tangential cutting stiffness , krc, kac - radial and axial force cutting stiffness
factors, b- radial depth of cut.
The dynamic cutting forces can be summarized as:
F t
( )
bk
B t
( )
r
tc
where, [B(t)] is the dynamic drilling coefficient matrix dependent on time and
contains the negative regenerative displacements.
In this paper, the frequency response method has been used and compared
with results from other models. The frequency response matrix at the tool tip
has been defined as:
(
i
) 0
0
0
xx
0
(
i
) 0
0
yy
()
i
0
0
(
)
(
)
zz
z
0
0
(
)
(
)
z
where: ʦaa (iω) is the direct frequency response function and ʦab (iω) is the
cross frequency response function.
After extensive computation the authors have expressed the eigenvalues
as:
1
1
0
1
1
0
Lateral:
,
