Page 631 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 617
F
i
S 1
F
i
B d
+ F
θ B i
N 2
v
l

(a) (b) (c)

FIGURE 8.8: Magnetic forces: (a) magnetic force acting on a moving charge in a magnetic
field, (b) magnetic force acting on a conductor with current in a magnetic field, and
(c) magnetic force between two current carrying conductors.

This relationship is convenient to derive the Tesla or T unit of ⃗ B,
N N
1Tesla = 1 = 1 (8.64)
C∕s ⋅ m A ⋅ m
This is the basic physical principle for the electromechanical power conversion for
motor action. Notice that the force is a vector function of the current and the magnetic flux
density. ⃗ B may be generated by a permanent magnet and/or electromagnet.
The force between two current carrying parallel conductors can be described as the
interaction of the current in one conductor with the electromagnetic field generated by the
current in the other conductor. Consider two conductors parallel to each other, carrying
currents i and i , separated from each other by a distance d and has length l.The force
2
1
acting between them (Figure 8.8c)
( l )
| ⃗ F| = ⋅ ⋅ i ⋅ i (8.65)
o 1 2
2 ⋅ d
where is the permeability of space between the two conductors. The force is attractive
o
if the two currents are in the same direction, and repulsive if they are opposite.
Generator Action: Similarly, there is a dual phenomenon called the generator action
which is a result of Faraday’s law of induction. Faraday’s law of induction states that an
electromotive force (EMF) voltage is induced on a circuit due to changing magnetic flux
and that the induced voltage opposes the change in the magnetic flux. We can think of this
as the relationship between magnetic and electric fields: a changing magnetic field induces
an electric field (induced voltage) where the induced electric field opposes the change in
the magnetic field (Figure 8.9a).
dΦ B
V =− (8.66)
induced
dt
Note that the time rate of change in magnetic flux can be due to the change in the magnetic
field source or due to the motion of a component inside a constant magnetic field strength
which results in change of effective reluctance or both (Figure 8.9a,b,c,d). If we consider
the induced voltage on a coil with N turns and the magnetic flux passing through each of
the turns is Φ , then
B
dΦ B d
V == −N ⋅ =− (8.67)
induced
dt dt
where = N ⋅ Φ is called the flux linkage, which is the amount of flux linking the N turns
B
of coil.