Page 639 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 625
state moves back and forth along the curve on the second quadrant. In this case, there is a
very small hysteresis loss (Figure 8.13c).
The power of a permanent magnet is measured in terms of the magnetic flux and
MMF it can support,
Φ = B ⋅ A (8.96)
B m
MMF = H ⋅ l m (8.97)
where l is the length of the magnet in the direction of magnetization, and A is the cross-
m m
section of the magnet perpendicular to the magnetization direction. In order to increase the
MMF for a given PM with a specific B-H characteristics, it must have a large thickness in
the direction of magnetization (l ). Similarly, in order to increase the flux, it must have a
m
large surface area that is perpendicular to its magnetization (A ).
m
If a permanent magnet is placed in an infinitely permeable medium, no MMF would
be lost and the magnetic field intensity coming out of the magnet would be B = B , H = 0.0
r
(Figure 8.13c). If, on the other hand, the permanent magnet is placed in a medium with
zero permeability, no magnetic flux can exit it. The operating point of the magnet would be
B = 0 and H =−H .
c
In a real application, the effective permeability of the surrounding medium is finite.
Hence, the permanent magnet operates somewhere along the curve between the two extreme
points in the second quadrant of the B-H curve. The nominal location of the operating point
is determined by the permeance of the surrounding medium. The absolute value of the slope
of the line connecting the nominal operating point to the origin is called the permeance
coefficient, P and the line is called the load line. The applied coil current shifts the
c
net MMF (or H), and hence the operating point of the magnet along the H-axis. It is
important that the applied coil current should not be large enough to force the magnet
into the demagnetization zone. In permanent magnet motors, the electromagnetic circuit
of the motor generally results in a load line that is P = 4 to 6 range. In magnetic circuits
c
where the closed path of the flux is made of an air gap, highly permeable material, and a
permanent magnet, it can be shown that
l m
P ≈ (8.98)
c
l g
where l is the permanent magnet thickness in the direction of magnetization, and l is the
g
m
effective air gap length.
The B-H curve of a permanent magnet is strongly a function of the operating tem-
perature. Consider a permanent magnet in an electromagnetic circuit. We will consider two
◦
◦
operating temperature conditions 20 C and 140 C. Figure 8.13d shows the B-H demag-
netization curves in the second quadrant for a particular permanent magnet for these two
◦
temperatures. On the figure on the left of Figure 8.13d, B-H curve A is for 20 C, and
◦
B-H curve B is for 140 C. Notice the drop in the magnetic strength as the temperature
increases. In particular we want to focus on the “knee point” effect. Let us assume that
the current operating condition is defined by the load line P and its intersection with the
1
◦
B-H curve. At 20 C temperature, the nominal flux density is B . Now, assume that under
a
◦
this operating condition, the temperature has risen to 140 C. Then, the nominal operating
◦
point is now the intersection between the load line P and the B-H curve for the 140 C
1
temperature. Under this condition, the nominal magnetic flux density is B . Then, let us
b
◦
assume that the operating temperature returns to 20 C. The nominal magnetic flux density
will return to the B value. Under this operating condition, temperature variation did not
a
result in permanent demagnetization. When the temperature increases, the magnetic field
strength reduces. But when the temperature returns to its original lower value, the original