Page 638 - Mechatronics with Experiments

624 MECHATRONICS
The susceptibility
1. is positive but small (i.e., 10 −4 to 10 −5 range) for paramagnetic materials,
2. is negative but small (i.e., −10 −5 to −10 −10 range) for diamagnetic materials, and
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3
3. is positive and several thousand times larger than 1 (i.e., in the range of 10 to 10 )
for ferromagnetic materials. Furthermore, the effective in the ⃗ B and ⃗ H relation-
m
ship is not linear, but exhibits hysteresis nonlinearity. Ferromagnetic materials are
categorized into two groups based on the size of the hysteresis:
(a) materials that exhibit small hysteresis in their B-H curves are called soft
ferromagnetic materials (Figure 8.13a),
(b) materials that exhibit large hysteresis in their B-H curves are called hard
ferromagnetic materials (Figure 8.13b).
In the case of soft ferromagnetic materials, the material goes though the full cycle of
magnetization and demagnetization at the same frequency of the external magnetic field.
For instance, the stator and rotor material in an electric motor are made of soft ferromagnetic
material. As the stator current changes direction in a cyclic way, the B-H curve for the steel
goes through the hysteresis loop. The energy in the hysteresis loop is lost as heat. Hysteresis
loss is proportional to the maximum value of magnetic field intensity magnitude and its
frequency. Therefore, in order to minimize the energy loss in motor and transformer cores,
lamination material is chosen among the soft ferromagnetic materials. Soft ferromagentic
materials have less hysteresis losses. But, as a result of the same property, they have a
small residual magnetization when the external magnetic field is removed. Therefore, we
can think of them temporarily magnetized materials.
Hard ferromagnetic materials have a large residual magnetization, which means they
maintain a strong magnetic flux density even when the external field is removed, hence the
name permanent magnets. But, as a result of the same property, they have large hysteresis
losses if they operate in a full cycle of external magnetic field variation. The maximum
value of the product of B ⋅ H on the hysteresis curve indicates the magnetic strength of the
material. It is easy to confirm that the BH term has energy units as follows,
Nt Nt Nt ⋅ m
Tesla ⋅ A∕m = A∕m = = (8.94)
Am m 2 m 3
Joule
= (8.95)
m 3
1 3 3
or in CGS units, BH has units of Gauss ⋅ Oerstead GOe = × 10 Joule∕m .
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The residual magnetization (B ) left after the external magnetic field is removed,
r
which is a result of the magnetic hysteresis, is used as a way to permanently magnetize
ferromagnetic materials. This permanent magnetization property is called remanent mag-
netization or remanence (B ) of the material, which means the “remaining magnetization.”
r
As the magnitude of the residual magnetic flux density (B ) increases, the capability of
r
the material to act as a permanent magnet (PM) increases. Such materials are called “hard
ferromagnetic materials” compared to the “soft ferromagnetic materials” which have small
residual magnetization. The value of the external magnetic field strength (H ) necessary
c
to remove the residual magnetism (to totally demagnetize it) is called the coercivity of
the material. It is a measure of how hard the material must be “coerced” by the external
magnetic field to give up its magnetization. Notice that the area inside the hysteresis curve
is the energy lost during each cycle of the magnetization between ⃗ H and ⃗ B. This is called
the hysteresis loss. This energy is converted to heat in the material. In electromagnetic
actuator applications such as electric motors, a permanent magnet (PM) usually operates in
the second quadrant of B-H curve. As long as the external field is below the H , the magnet
c