Page 659 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 645
i
View from top View from bottom
B B B
+

Straight i (out) i (in)
conductor

B
Magnetic flux
i
B
i
One turn coil
Solenoid coil (multiple turns)
(a) Current carrying conductors and electromagnetic fields

N S N S

(b) Magnetic field of permanent magnets
FIGURE 8.25: Basic principles of electromagnetism: (a) a current carrying conductor
generates a magnetic field around it, (b) the magnetic field generated by permanent magnets.

the current flow, a force is generated on the conductor as a result of the interaction between
the “stator magnetic field” and the “rotor magnetic field” (Figures 8.26a, 8.27).
⃗
⃗
⃗ F = l i x B (8.172)
Next, let us consider that we place a loop of conductor into the magnetic field and feed
DC current to it using a pair of brushes (Figure 8.27). Since the current directions in the
two opposite sides of the conductor are in opposite directions, the exerted force on each
leg of the conductor loop is in opposite directions. The force pair creates a torque on the
conductor.

T = F ⋅ d (8.173)
m
Considering the fact that ⃗ B, l, d are constant, we can deduce that
T = K ⋅ i (8.174)
t
m
where K (B, l, d), the torque constant, is a function of the magnetic field strength and size
t
of the motor. For a practical motor, the conductor loop would contain multiple turns, not
just one pair. As a result, the K constant is also a function of the number of conductor turns
t
(n) or equivalently the surface area (A ) over which flux density acts on the conductors,
c
K (B, l, d, n) = K (B, l, d, A ). This is the main operating principle of a DC motor where
t
c
t