Biomedical Engineering Reference
In-Depth Information
ω
Fig. 8.8 Rotation of the disc
V
A
S
3
V
B
m
A
m
B
S
2
F
A
¼
R
A
¼
R
B
¼
F
B
:
(8.47)
D
S
D
With condition
t
=
const
we will have:
2
A
S
3
2
B
S
4
F
A
¼
m
A
o
D
R
A
¼
m
B
o
S
D
R
B
¼
F
B
(8.48)
8.3.4 Magnetic Forces
W. S. N. Trimmer [
4
,
48
] investigated the scaling of magnetic, electrostatic forces
and power generation and dissipation. For magnetic forces, there are different
scaling conditions. If, for example, devices
A
and
B
are electromagnetic motors
and current density in the windings of these motors is constant, the forces in motors
A
and
B
scale as:
S
4
F
A
¼
F
B
:
(8.49)
If these motors have permanent magnet rotors, the force scaling will be:
S
3
F
A
¼
F
B
:
(8.50)
However, a small motor has better conditions for refrigeration; therefore, it is
possible to increase the current density in motor
B
until the temperature of its
windings is equal to the temperature of motor
A
's windings. In this case, Trimmer
obtained the formula:
S
2
F
A
¼
F
B
:
(8.51)
8.3.5 Electrostatic Forces
In conventional mechanics, electrostatic actuators are not used in the motors
because the electrostatic forces are weak. In [
4
,
48
] it is shown that scaling of
