Page 629 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 615
The design task of shaping a magnetic circuit is the design task of defining the
reluctance paths to the flow of magnetic field lines in the circuit. It is a function of material
and geometry. Series and parallel reluctances are added following the same rules for
electrical resistance. Iron and its various variations is the most commonly used material in
shaping a magnetic circuit, that is in design of electric actuators. The material and geometry
of the magnetic circuit determines the resistance paths to the flow of magnetic flux.
For instance, the magnetic flux in a coil (N turn coil with length l) can be determined
as follows. The magnetic field due to current i has been given above,
⋅ N ⋅ i
0
B = (8.48)
l
= ⋅ H (8.49)
0
N ⋅ i
H = (8.50)
l
MMF
= (8.51)
l
MMF = N ⋅ i (8.52)
The magnetic flux is defined as the integral of the magnetic flux density over a surface
perpendicular to the flux density vector (Figure 8.6c)
⋅ N ⋅ i
0
Φ = B ⋅ A = ⋅ A (8.53)
B
l
N ⋅ i
= (8.54)
[l∕( ⋅ A)]
0
MMF
= (8.55)
R B
For instance, a coil with N turns and current i, can be modeled in an electromagnetic
circuit as an MMF source (similar to voltage source) and magnetic reluctance R (similar
B
to electrical resistance) in series with the source (Figure 8.7),
MMF = N ⋅ i (8.56)
l
R = (8.57)
B
⋅ A
Then, the magnetic flux (analogous to current) through the coil is
MMF
Φ = (8.58)
B
R B

l
B
i
l
N

(a) (b)
FIGURE 8.7: (a) A coil winding, and (b) its magnetic model. Coil is modeled as having an
= l∕(μA)in
MMF = N ⋅ i, magnetomotive source, and magnetic resistance (reluctance) R B
series with the MMF.