Hardware Reference
In-Depth Information
where, the coefficient µ
0
is the permeability in vacuum whose value is 4π×10
−7
in units of Henrys per meter (H/m).
Different materials show different behaviors when the magnetic
fi
eld passes
through them. But the concept of permeability can still be used to describe the
relationship between B and H. For a given material, the relationship between
the
fi
eld strength and
fl
ux density can be described by
B = µH,
(4.3)
where µ is permeability of the material. Permeability of any material de
fi
nes
its ability to allow transmission of magnetic
fi
eld through it. Permeability is
also described as
µ = µ
r
µ
0
(4.4)
where µ
r
is known as the relative permeability of the material. For most of the
materials, the value of µ
r
is close to 1. If a material shows linear relationship
between B and H when the magnetic
fi
eldvariesinaverywiderange,then
the material is called linear material in the context of electro-magnetic (EM)
analysis.
4.1.4 Energy in Magnetic Field
The magnetic
fi
eld contains energy, and its energy density is expressed as
w
m
=
1
2
B · H.
(4.5)
The SI unit of the energy density (w
m
)isJoule per cubic meter (J/m
3
).
MGOe is also used as the unit where 1MGOe=10
5
/4π J/m
3
.IftheEMper-
formance of the material is homogeneousanditsB-Hcurveismonotonic,then
the expression for energy density can be simpli
fi
ed by substituting equation 4.3
into equation 4.5,
w
m
=
1
2
B.H =
1
2µ
B
2
=
µ
2
H
2
.
(4.6)
Tak ing V as the volume of the whole system, the magnetic energy in the system
is
Z
Z
B
2
2µ
dv =
µH
2
2
W
m
=
dv.
(4.7)
V
V
Operation of an electric motor depends on the conversion between the mag-
netic and mechanical energy. However, the EM structure of the motor is
normally complicated and the magnetic material used in the motor normally
operates in non-linear state. As a result, it is generally difficult to calculate
the local magnetic energy density and the total magnetic energy of the motor.
But it is important in the design and analysis of any electric machine.
