Hardware Reference

In-Depth Information

It can be concluded from the above analysis that, for a given magnetic

circuit, the magnitude of the
fl
ux can be calculated using the MMF consumed

in the circuit and the reluctance of the circuit. If the MMF generated by the

winding current is
fi
xed, changing circuit reluctance by modifying the area of

cross section or the length of airgap or both alters the induced
fl
ux.

While equation 4.17 may look simple, it includes all the factors affecting

the magnetic
fi
eld, e.g., structure of the core, materials used, input current,

and number of turns in the winding. Using this magnetic circuit method, the

quantity of the magnetic
fi
eld obtained is
fl
ux, which is an integrated value, or

global value, of the magnetic
fi
eld. The
fl
ux density B and the
fi
eld intensity

H can be derived using equations 4.1, 4.3 and 4.9.

Structures of many EM systems are more complicated than the one shown

in Figure 4.5. But the magnetic circuit model which may include multiple

MMF sources and reluctances can still be used to describe these EM systems.

The reluctances may be connected in series or in parallel to form a complicated

network. Similarity between magnetic and electric circuits allows us to apply

methods used in analyzing electric circuits to the analysis of a magnetic cir-

cuit network. Non-linearity of ferromagnetic materials can also be taken into

consideration in the analysis [77].

It is evident from the above analysis that MMF can be linked directly to

the
fl
ux density in the airgap

µ

¶

g

µ
0

F
g
=

B
g
.

(4.19)

This implies that the waveform of the MMF on the airgap has the same shape

as the airgap
fl
ux density. This concept can be used to simplify the analysis

of the effects of airgap
fi
elds in EM devices.

Example-2: Magnetic circuit of a permanent magnet motor

Let us consider the EM device shown in Figure 4.6, which is a simpli
fi
ed

structure of motor. The stator core and rotor are made of steel, and their per-

meabilities are assumed in
fi
nite. The demagnetization curve of the permanent

magnet materials is shown in Figure 4.7.

If the airgap length g is much smaller than the radius of the rotor, the

surfaces of the stator core and the rotor on the two sides of the airgap can be

considered equal,

A
g
=rlθ
m
,

(4.20)

where, r is the average radius of the airgap, and l
m
is the thickness of the

motor core (Figure 4.6). Let us select the center line of the device (shown by

broken line in Figure 4.6) as the line of integration. There is no current in this

loop and the magnetic circuit is formed only by one magnet and two airgap.