Page 630 - Mechatronics with Experiments

616 MECHATRONICS
TABLE 8.1: Analogy between electrical and
electromagnetic circuits.

Electric circuits Magnetic circuits
V MMF or H
i Φ B or B
1
R R or
B m
V MMF
i = Φ = or B = ⋅ H
m
B
R R B

By analogy to electrical circuits, there are three main principles used in analyzing
magnetic circuits as follows (Table 8.1):
1. The sum of the MMF drop across a closed path is zero. This is similar to Kirchoff’s
law for voltages, which says the sum of voltages over a closed path is zero.
∑
MMF = 0; over a closed path, (8.59)
i
i
2. The sum of flux at any cross-section in a magnetic circuit is equal to zero (that is,
the sum of incoming and outgoing flux through a cross-section). This is similar to
Kirchoff’s law for currents which says that at a node, the algebraic sum of currents
is zero (sum of incoming and outgoing currents).
∑
Φ Bi = 0; at a cross-section, (8.60)
i
3. Flux and MMF are related by the reluctance of the path of the magnetic medium,
similar to the voltage, current and resistance relationship,
MMF = R ⋅ Φ (8.61)
B B
Magnetic circuits typically have:
1. current carrying conductors in coil form which act as the source of the magnetic field,
2. permanent magnets (or a second current carrying coil),
3. iron based material to guide the magnetic flux, and
4. air.
The geometry and material of the medium uniquely determines the reluctance distribution
in space. Current carrying coils and magnets determine the magnetic source. Interaction
between the two (magnetic source and reluctance) determines the magnetic flux.
Motor Action: Force ( ⃗ F) in a magnetic field ( ⃗ B) and a moving charge (q) has vector
relationship (Figure 8.8a),
⃗ F = q ⃗ v × ⃗ B (8.62)

where ⃗ v is the speed vector of the moving charge. This relationship can be extended for a
current carrying conductor instead of a single charge. The force acting on a conductor of
over length l due to the current i and magnetic field ⃗ B interaction is (Figure 8.8b)
⃗
⃗ F = l ⋅ i × ⃗ B (8.63)