Biomedical Engineering Reference
In-Depth Information
S
4
F
A
r
A
¼
F
B
S
3
D
z
A
¼
r
B
¼
D
z
B
:
(8.77)
S
For case (8.50) we have:
S
3
F
A
r
A
¼
F
B
S
2
D
z
A
¼
r
B
¼
D
z
B
:
(8.78)
S
We can conclude that, in the majority of the considered examples, the errors
caused by elastic deformation decrease linearly (or faster) with the diminution of
the micromachine tool size. The exceptions are presented in the cases of equations
(8.54) and (8.62), where:
F
A
¼
S
F
B
(8.79)
and
F
A
r
A
¼
S
F
B
D
z
A
¼
r
B
¼ D
z
B
:
(8.80)
S
These cases correspond to the electrostatic force or capillary force. These forces
are of an order of magnitude lower than other forces until they reach a size of 1
m
m,
which is why it is possible not to take into account their influence.
8.3.10 Vibrations
Vibrations contribute a sufficiently large percentage of machine tool errors. To
calculate the deformations from vibrations, let us consider a disc fixed on a rotating
shaft (Fig.
8.13
). The center point of the disc is displaced relative to the center
point of the shaft. The displacement is
e
. The inertial force
F
i
of the disc can be
presented as:
2
F
i
¼
m
o
e;
(8.81)
where
m
is the mass of the disc, and
is the angular speed of disc rotation. The
shaft can be considered as a console beam loaded at the end by the inertial force,
F
i
(Fig.
8.14
).
The deflection,
o
D
z
, from beam bending is:
L
3
F
i
D
z
¼
C
D
4
;
(8.82)
E
