Environmental Engineering Reference
In-Depth Information
The temperature capability of REs is now of the order of 180
C when trace
amounts of dysprosium are added to the alloy mix.
●
Table 5.2 summarizes some of the shock and bending moment characteristics
of the more popular permanent magnets.
Table 5.2 Mechanical properties of common permanent magnets
Type of permanent
magnet
Shock resistance
Bending moment
resistance
Alnico
Strong, but brittle
55-206 MPa
Ferrite
Chips or fractures easily
Brittle
SmCo
Chips or fractures
35-42 MPa
NdFeB
Chips or fractures
69-97 MPa
Bonded types
Resists chipping
20-82 MPa
The rare earth PMs are the most widely used magnets and should be under-
stood before elaborating more on electric machines. A generally useful method to
understand the differences between normal and intrinsic flux density is to consider
a gapped toroid with a PM inserted into the physical gap and a current carrying
winding on this toroid that produces a flux in the same direction as the PM. A
simple calculation of Ampere's circuital law around the closed contour of the flux
path resolves to (5.1), where
L
m
is the magnet length,
L
g
the airgap length,
I
arm
the
total armature winding current (i.e. the coil of
N
arm
turns) and
I
0
the coil current:
X
I
arm
¼
N
arm
I
0
H
m
L
m
þ
2
B
g
m
0
L
g
¼
ð
5
:
1
Þ
A straightforward calculation shows that (5.1) reduces to (5.2), assuming no
fringe flux at the physical airgaps, which, in this case, are assumed to be very small
relative to the magnet length (i.e. the dimension aligned with its magnetization
vector). The normal flux density is therefore given by
P
I
arm
L
m
H
m
L
m
2
L
g
B
m
¼ m
0
¼
ð
5
:
2
Þ
The intrinsic flux density,
B
i
, accounts for flux density that would exist in vacuum
for the same applied magnetic field strength,
H
, and is given as
B
i
¼
B
m
0
H
.
The intrinsic flux density is normally displayed in permanent magnet characteristic
curves and is given by (5.3), which is
B
m
m
0
H
m
:
P
I
arm
L
m
þ
2
L
g
H
m
L
m
2
L
g
þ
1
B
m
m
0
H
m
¼ m
0
ð
5
:
3
Þ
