Page 697 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 683
Steel (flux return path)
Permanent
magnet (tubular)

Coil
holder

Fixed
working gap
Tubular
coil
FIGURE 8.58: Voice coil actuator operating principle and components.

determined by the solution of FEA based software instead of analytical solutions which are
only possible for simple and idealized motor geometries.
A voice coil actuator (also called a moving coil actuator) is made of a tubular
permanent magnet (PM) and a coil winding (Figure 8.58). The interaction between the
current carrying coil assembly and PM generates the linear force. In principle, this is
identical to the brush-type DC motors. At any given instant in time, both motor action
(force generation) and generator action (back EMF voltage) are in effect,

F = k ⋅ l ⋅ N ⋅ B ⋅ i = K ⋅ i (8.284)
F
V bemf = k ⋅ l ⋅ N ⋅ B ⋅ ̇ x = K ⋅ ̇ x (8.285)
E
where F is linear force, V bemf is the back EMF voltage, l is the length of the winding and N
is the number of turns of the coil, B is the magnetic field strength across the air gap between
the rotor and stator, i is the current in the coil, and ̇ x is the linear speed of the rotor. As long
as the geometric overlap between the rotor and stator (coil and PM) is the same, the force is
essentially independent of the displacement of the rotor and only a function of the current.
In order to provide such a force–current–displacement relationship, the axial length of the
PM and the coil must be different (one longer than the other). The current in the coil winding
is non-commutated. There are no commutator-brush components. Only the direction and
magnitude of the current is controlled, that is using an H-bridge amplifier which is the
same type used for a brush-type DC motor. Moving coil actuators are precision motion
versions of the solenoid-plunger or audio-speaker designs. Voice coil actuators typically
have a small travel range (i.e., microns to a few inches range) and very high bandwidth.

8.8 DC MOTOR: ELECTROMECHANICAL DYNAMIC MODEL

The most commonly used model for a direct current (DC) electric motor is shown in
Figure 8.59. This dynamic model includes electrical, electrical to mechanical power con-
version, and mechanical dynamic relations.
The electrical relation between terminal voltage, current, and rotor speed is

di(t)
̇
V (t) = L a + R i(t) + k (t)
e
t
a
dt