Biomedical Engineering Reference
In-Depth Information
3
3
2
3
3
2
Torsional - axial:
,
where γ
0
, γ
1,
γ
2,
γ
3
- coefficients of the characteristic
equation .
The results show that frequency domain solutions actually give a more
conservative stability estimate than the time domain model. By comparing the
model with the results from other researchers [3] it has been shown that the
values for critical depth of cut are less conservative in this particular model,
while the shape of stability lobes is different. The lateral chatter stability was
compared to a rotating coordinate approach, where the difference is in using
an average of time varying coefficients instead of time invariant cutting
coefficients. This comparison shows good agreement. The frequency domain
solutions have been compared with the experimental data to establish the
agreement and validity of the model used. Unfortunately, the stability lobes
obtained are both too small and too narrow to be used for selection of actual
cutting conditions. The experiments are not in agreement with the linear
stability prediction laws and show that if the spindle speed is below 2000 rpm
drilling is always stable and stability rises with decrease in spindle speed. It
has even been stated that stability increases with chisel edge engagement.
Although this paper has the most comprehensive model and covers the largest
number of influential parameters, it is not in agreement with the experimental
results and needs further work.
Present models of drilling motion do not include the gyroscopic moments
and rotary inertia effects and their influence on natural frequencies of the drills
[26]. Work conducted by Timoshenko et al. [27], showed that there is a slight
decrease in the value of the natural frequency calculated with the effect of
rotary inertia. The nonlinear equations of motion have been linearized,
including gyroscopic moments and rotary inertia:
..
.
..
..
..
.
2
2
2
2
2
2
m v
2
m
v
m
v
J v
J
v
J
v
J
v
J
v
J
v
EI v
1
2
1
zz
2
zz
1
1
0
0 1
1
p
0
2
0
2
0
0
p
0
0 2
z
1 0 1
zz
1 1
zzzz
2
3
4
2
2
E I
(
I
)
v
E
(2
I
4
I
)
v
2
E I
(
I
)
v
EI
v
Fz v
2
v
v
F
1
2
0 2
zzz
1
2
0 1
zz
1
2
0 2
z
1 0 1
1
zz
0 2
z
0 1
..
.
..
..
..
.
2
2
2
2
2
2
m v
2
m
v
m
v
J
v
J
v
J
v
J
v
J
v
J
v
EI v
2
zz
1
zz
2
2
2
2
p
0
1 0
1 0
0
p
0
0 1
z
2
0 2
zz
2 2
zzzz
2
3
4
2
2
E I
(
I
)
v
E
(4
I
2
I
)
v
2
E I
(
I
)
v
EI
v
Fz v
2
v
1
v
F
1
2
0 1
zzz
1
2
0 2
zz
1
2
0 1
z
2
0 2
2
zz
0
0 2
This paper confirms Timoshenko's statement showing that the effects of
the gyroscopic moment and rotary inertia are not significant if the rotational
