Biomedical Engineering Reference
In-Depth Information
FIGURE 3-2
Solenoid actuator.
(a) Schematic cross
section.
(b) Photograph.
3.2.1 Solenoids and Voice Coils
3.2.1.1 Solenoids
Solenoids consist of a fixed core and a movable plunger that complete a magnetic circuit
broken by a small gap, as shown in Figure 3-2. When the coil is energized by passing a
current through it, the core-plunger combination forms an electromagnet, and the plunger
is drawn downward to close the gap.
As a first-order approximation of how this works, a number of assumptions must be
made. It is assumed that all of the magnetic flux is constrained within the core and within
the gap and that all of the resistance to magnetic flux flow (magnetic reluctance) occurs
within the gap. The field is assumed to be uniform in the gap and zero everywhere else
and also that the core material does not saturate.
The magnetomotive force (
mmf
) set up by the coil is defined by the number of turns
on the coil,
N
, and the current
I
(A), flowing through it.
mmf
=
NI
=
H
ยท
dl
(3.7)
where
H
is the coercive force on the flux path, which is nonzero only in the gap.
Because the field is considered to be uniform and the gap length
l
g
(m) is constant,
then equation (3.7) can be simplified to
mmf
=
NI
=
Hl
g
(3.8)
Therefore the coercive force will be
NI
l
g
H
=
(3.9)
The energy
W
mag
(J) stored in the volume of space occupied by a magnetic field is
1
2
W
mag
=
BH dV
(3.10)
where
B
(weber/m
2
is the flux density and
V
(m
3
) is the volume.
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