Biomedical Engineering Reference
In-Depth Information
where
C
is a constant,
s
T
is the specific tension of the compression of raw material,
t
1
is the height of the squashed area (Fig.
8.11b
), and
p
is the cutting depth
(Fig.
8.11a
). When the cutter moves forward,
the additional force increases
(Fig.
8.11c
) and reaches the maximum value
D
F
in the position presented in
Fig.
8.11d
:
D
F
¼
C
s
T
t
3
p
:
(8.70)
We can describe the scaling of this force as:
S
2
D
F
A
¼
C
s
T
t
3
A
p
A
¼
C
s
T
S
t
3
B
S
p
B
¼
D
F
B
:
(8.71)
8.3.9 Elastic Deformations
Elastic deformations are one of the more important causes of error in mechanical
device production with the help of machine tools. From formula (8.21) we obtain
the elastic deformation:
F
r
;
D
z
¼
(8.72)
where
r
is the machine tool rigidity, and
F
is the force. From equations (8.27),
(8.31), (8.34), and (8.40) we have:
r
A
¼
S
r
B
:
(8.73)
For the many cases presented in equations (8.44), (8.47), (8.51), (8.52), (8.56),
and (8.71), the force is:
S
2
F
A
¼
F
B
:
(8.74)
For these cases, the deformation scaling is:
S
2
F
A
r
A
¼
F
B
D
z
A
¼
r
B
¼
S
D
z
B
:
(8.75)
S
In other cases [equations (8.45), (8.48), (8.49)] we have:
S
4
F
A
¼
F
B
;
(8.76)
and
