Biomedical Engineering Reference
In-Depth Information
can decrease as
S
4
,
S
3
,or
S
2
depending on the other parameters' scaling.
S
4
corresponds to an electromagnetic system having the same current density in the
windings of both devices;
S
3
corresponds to a system that includes a permanent
magnet; and
S
2
corresponds to the case of equal operating temperature of the
windings. The electrostatic forces scale as
S
2
for the constant electric field and
S
when the electric field scales as
S
0.5
. Trimmer analyzed parameters such as
accelaration and time of part movements. Depending on the scaling force, these
parameters could scale as:
2
4
3
5
S
2
S
1
S
0
S
1
a
¼
;
(8.1)
2
4
3
5
S
1
;
5
S
1
S
0
;
5
S
0
t
¼
;
(8.2)
where
a
is the acceleration and
t
is the time of movement.
Trimmer also analyzed power generation and dissipation. If the force scales as
S
2
, then the power per unit volume scales as
S
1
. On the basis of this rule, Trimmer
concludes that electromagnetic motors will not be effective in microscale and
should be replaced by other types of micromotors. We will consider this problem
below.
Ishihara H., Arai F., and Fukuda T. [
41
] have analyzed the scaling of different
forces. They gave the following results (Table
8.1
). In defining the scaling effect for
an electrostatic force, H. Ishihara et al. assume that the voltage between the
electrodes does not change after the device size changes. In reality, the voltage
applied to the electrodes, as a rule, is reduced approximately linearly with a
reduction of device size. Taking this change into account, the scaling effect for
electrostatic force will be
S
2
, not
S
0
.
In defining the scaling effect for an inertial force, the authors of the article accept
the time of the displacement of some mass as constant. In real devices, the linear
velocity of device components is constant more often than not. We will discuss the
reasons for this phenomenon later. Let us consider the uniformly accelerated
movement of mass
m
over distance
d
. Let the initial velocity equal
v
1
and final
velocity equal
v
2
. Then, from the law of conservation of energy, the inertial force is:
m
v
2
m
v
1
F
i
d
¼
2
2
:
(8.3)
