Operating Point, Load Line and Permeability Pc of Permanent Magnet

Operating Point, Load Line and Permeability Pc of Permanent Magnet

The permanent magnet works in the open circuit state. Since the magnet in the open circuit state is under the action of the demagnetization field, the magnetic induction intensity of the permanent magnet in the working state is not at the Br point in the closed circuit state, but at the demagnetization curve lower than Br A certain point on the magnet is called the working point of the permanent magnet, such as point D in the figure below.

Obviously, the working point is related to the shape of the demagnetization curve and the size of the demagnetization field of the magnet in the working state. BD and HD at the working point should satisfy the following two formulas:

BD=μ0(HD+MD)
HD=-NMD
Among them, MD is the magnetization intensity of the permanent magnet under the action of HD, and N is the demagnetization factor. Bring HD= -NMD into BD= μ0(HD +MD) to get BD= μ0HD (1-1/N), it can be seen that the slope of the straight line connecting the working point D and the origin O is μ0(1-1/N). This straight line, namely the OD line, is called the load line, and its slope is related to the demagnetization factor of the permanent magnet (click for related knowledge). The slope of the load line is also called the magnetic permeability, expressed in Pc:

Pc = BD/HD=μ0(1-1/N)

The figure below shows the relationship between two shapes of permanent magnets Pc and their size ratio

Explanation 1: Figure 1 is Joseph’s theoretical curve and SmCo and AlNiCo magnets, and Figure 2 is NdFeB magnets

Note 2: The above pictures are excerpted from “Sintered NdFeB Rare Earth Permanent Magnet Materials and Technology”, edited by Zhou Shouzeng and others, published in 2014

The shaded rectangular area of the working point P is the magnetic energy product (BH) [the absolute value of the product of B and H]. The right side of the above figure is the B-(BH) curve with (BH) as the abscissa and B as the ordinate. The maximum value of the upper abscissa is the maximum energy product (BH)max. The magnetic field energy generated by the magnet working at point P in the air gap is proportional to the product of (BH) and the volume of the magnet. In the application of the same magnetic field energy, work at the operating point corresponding to the maximum magnetic energy product, and the magnet volume is the smallest, or at the same In application, the magnet with larger (BH)max can provide larger magnetic field energy. Therefore, if conditions permit, in order to give full play to the role of permanent magnet materials, the magnet should be operated near the operating point corresponding to (BH)max, in other words, the product of B and H corresponding to the operating point D The closer the absolute value is to the (BH)max value, the better.
Operating Point, Load Line and Permeability Pc of Permanent Magnet

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