Hard magnetic materials (permanent magnets) typically have a very wide magnetic hysteresis loop to maximize the operating magnetic field energy, as shown in Fig. 1.23. Permanent magnets are magnetized in quadrants I and III and are used in magnetic devices in quadrants II and IV. Since quadrants II and IV are identical, the properties and performance characteristics described here are based on quadrant II.
Both the normal and intrinsic hysteresis loops are shown in Fig. 1.23. Most permanent-magnet specification sheets show both curves, and both curves are required to fully determine the permanent-magnet performance at different temperatures. However, in general, only the normal curve is required to determine the performance of the permanent magnet and the system at constant temperature.
The intrinsic curve represents the added magnetic flux that the permanent-magnet material produces. The normal curve represents the total measurable or usable magnetic flux which is carried in combination by the air (free space) and by the permanent-magnet material. For example, imagine that a coil is placed in air with a flux meter located at one end of the coil axis. The magnetic flux measured by the meter is the flux carried by the air, and is called the air flux. When a magnetic material is placed in the center of the coil, the magnetic flux increases. The amount of the increase is called the intrinsic flux, and the total of the air flux plus the intrinsic flux is called the normal flux. The total or normal flux is the new flux-meter reading.
The quadrant II operating region generally lies on the normal curve between the remnant flux density Br and the coercive force Hc. As the external system acts to
FIGURE 1.22 Magnetic hysteresis loop and characteristic parameters.
TABLE 1.1 Soft Magnetic Material Properties
tizing flux density and field intensity. The product BdHd is called the energy product and represents the energy supplied to the system from the permanent magnet. The maximum energy product BHmax is a relative measure of the strength of a permanent magnet and is always listed on the material specification sheet.
Typical Properties of Permanent Magnets. Some typical properties of common permanent-magnet materials are listed in Table 1.2, and the quadrant II normal curves are plotted in Fig. 1.24. There are obvious design and performance tradeoffs involved in selecting a permanent-magnet material, including the shape of the normal curve, the energy product, and the operating temperature.
FIGURE 1.23 Hard magnetic material hysteresis loop and characteristic parameters.
Load Line. The permanent-magnet operating point must be determined before the size and the material of the permanent magnet can be finalized. The operating point is the intersection of the permanent-magnet recoil line (in this case the normal curve) and the system load lines, as shown in Fig. 1.25. Since the load line passes
FIGURE 1.24 Normal demagnetization curves for several common materials.
Solving Eq. (1.257) for the load-line slope results in the following definition of the load line. In some references, this slope is also called a permeance coefficient.
TABLE 1.2 Hard Magnetic Material (Permanent-Magnet) Properties
FIGURE 1.25 Quadrant II demagnetization curves for NdFeB at 20°C, showing the operating point and the load line with no coil.
When a coil is added to the system, as shown in Fig. 1.26, Eq. (1.256) is modified as follows to include the coil magnetizing force. In this case, it is assumed that the
coil magnetizing force is negative, or propagates in a direction that would demagnetize the permanent magnet.
FIGURE 1.26 Sketch of a permanent magnet in a simple system with a coil.
This load-line equation shows that the slope of the load line is independent of the coil. However, the denominator of
This shows that the H axis intercept is the magnetic field intensity of the coil as seen across the permanent magnet.This makes sense because Fig. 1.27 is a plot of the permanent-magnet material properties. Also, the slope of the load line represents the permeance of the system as seen across the permanent magnet.
FIGURE 1.27 Quadrant II demagnetization curves for NdFeB at 20°C, showing the operating point and the load line with a demagnetizing coil.
Permanent-Magnet Reluctance Model. Magnetic systems can be modeled using electric circuit analogies, as discussed in Secs. 1.2.1 and 1.2.2. In general, from Eq. (1.14), a coil is analogous to a voltage source, and the reluctance of each material and air gap in the system is analogous to a resistor. A permanent magnet can be modeled as a voltage source with a series resistance as follows.
1. The recoil line is the path of the operating point. The slope of the recoil line Urev defines the magnetic flux density change as a function of the magnetic field intensity change. Therefore, the permanent-magnet reluctance can be defined from
Eq. (1.29) as follows.
2. Extending the recoil line (beyond the normal and intrinsic curves if needed) to intersect with the H axis gives the effective coercive force of the recoil line HR,as shown in Fig. 1.28. The permanent-magnet magnetizing force provided at zero magnetic flux is then defined from Eq. (1.22) as follows.
FIGURE 1.28 Example of extending the recoil interest with the H axis.
