Page 640 - Mechatronics with Experiments

626 MECHATRONICS
TABLE 8.2: Temperature dependence of the magnetic
properties of various permanent magnetic materials.

Material B ∕ T H ∕ T
r
c
Neodymium −0.10 −0.60
Samarium −0.04 −0.30
Alnico −0.02 +0.01
Ferrite −0.18 +0.30

magnetic field strength (and magnetic flux density) is recovered. This is called reversible
loss in magnetization. The loss on B value as a function of temperature is defined as tem-
perature sensitivity constant for a permanent magnet material. For instance, Neodymium
magnets lose about 10% of their magnetic strength when the temperature rises from room
◦
◦
temperature 20 C to 120 C, whereas samarium cobalt loses only 4%.
There are also non-reversible losses due to temperature and operating condition
variations, such as knee point, Curie temperature (Table 8.2). Next, let us consider the
◦
◦
◦
same temperature cycling between 20 C and 140 C and back to 20 C while operating
on the load line P (i.e., the same magnet is used in a slightly different circuit, such as
2
◦
the air gap in this circuit is larger). When the temperature is 20 C, the nominal magnetic
◦
flux density is B . When the temperature is 140 C, the nominal flux density is B .Itis
c d
important to note that this operating condition falls below the “knee point.” Some of the
◦
magnetic strength will be permanently lost. When the temperature returns to 20 C, the
nominal magnetic flux density will be a value B between B and B . The original B value
e c d c
will not be recovered. This means that if the operating conditions (such as a combination of
load line and temperature) bring the magnet to a point below the “knee point,” there is some
permanent loss of magnetic strength. In electromechanical actuators, the electromagnetic
circuit should be designed such that PM never reaches the knee point, that is the point of
permanently losing some of its magnetization. The lost magnetization can only be recovered
by re-magnetizing the magnet.
In an electromagnetic circuit, a permanent magnet can be modeled as a flux source
Φ and a reluctance R in parallel with it (Figure 8.14)
r
m
Φ = B ⋅ A m (8.99)
r
r
l m
R = (8.100)
m
⋅ ⋅ A m
r
o
where l is the length along the magnetization direction, and A is the cross-section area
m
m
perpendicular to the magnetization direction, is the recoil permeability of the magnet
r
material.
In short, remanence B , coercivity H , and (BH) max maximum energy are three
c
r
nominal parameters which characterize the magnetic properties of a ferromagnetic material.
Φ
r
Φ = B A m
r
FIGURE 8.14: Magnetic model of a
permanent magnet. The permanent
magnet acts like a flux source and a
parallel reluctance. The actual flux, Φ,
which leaves the magnet is determined
by the rest of the load circuit.