Hardware Reference
In-Depth Information
Therefore,
m
Φ
m
+2
g
Φ
g
=0, (4.21)
where, the subscripts m and g represent the magnet and airgap, respectively.
As Φ
m
= Φ
g
, the equation 4.21 is reduced to,
m
= −2
g
.
(4.22)
From Example-1 shown earlier, the airgap reluctance
g
is positive. Therefore,
the reluctance of the magnet
m
is negative implying that the magnet has the
capability of providing magnetic energy to external magnetic circuit. The
following results can be deduced using the de
fi
nition of reluctance introduced
earlier,
g
µ
0
A
g
=
g
µ
0
rθl
m
g
=
(4.23)
and
h
m
µ
m
A
m
=
h
m
µ
m
l
c
l
m
,
m
=
(4.24)
where, θ, A
m
and µ
m
are the angle of the rotor facing the stator core, the cross
section area of the magnet, and the permeability of the magnet, respectively.
From equations 4.22 - 4.24, it can be shown that
µ
m
= −
rθh
m
2gl
c
µ
0
.
(4.25)
As the relationship between B
m
and H
m
can also be expressed as
B
m
= µ
m
H
m
,
(4.26)
we can use a straight line with slope µ
m
to describe equation 4.26 on the
demagnetization curve of the magnet, see Figure 4.8. This straight line is
known as the load line in the PM device design. In the system operation,
the magnetic performance of the magnet must meet both the relationships
determined by the demagnetization curve of Figure 4.8 and the load line given
by equation 4.26. The point of intersection between the load line and the
demagnetization curve is the operating point from which the
fl
ux density B
m
can be found. Consequently, the
fl
ux in the magnetic circuit can be calculated,
Φ
m
= Φ
g
= A
m
B
m
.
(4.27)
And the
fl
ux density in the airgap is,
b
g
=
Φ
g
A
g
=
A
m
A
g
B
m
.
(4.28)
It can be easily concluded from equation 4.25 and Figure 4.8 that the para-
meters like airgap length g and magnet length l
m
affect the capability of the
permanent magnet to generate magnetic
fi
eld. In the design of the EM system,
these parameters should be adjusted so that the permanent magnet is utilized
effectively, and the system possesses the required magnetic characteristics.
