Factors Affecting Inhomogeneous External Magnetic Field of Rectangular Magnet

The macroscopic inhomogeneity of the external magnetic field of the permanent magnet is closely related to the spatial distance and the shape design of the permanent magnet. Permanent magnet technology such as powder particles, degree of orientation, sintering and solidification, mechanical processing, etc. will affect the non-uniformity of the external magnetic field of the permanent magnet, such as magnetization deflection, symmetry, and smoothness. The main permanent magnets used in the market are cast permanent magnets, ferrite permanent magnets, rare earth permanent magnets and so on.

Shape design, demagnetization, craftsmanship, etc., and there are basic laws in common. In this paper, taking anisotropic rectangular neodymium iron boron and samarium cobalt permanent magnets for synchrotron radiation undulators as examples, the theoretical analysis of various factors that affect the inhomogeneity of the external magnetic field of the permanent magnets is carried out, so as to provide high-precision permanent magnets for undulators and other high-precision permanent magnets. The physical design of the magnetic device and the development of high-uniform permanent magnets provide a certain reference basis.

What is the non-uniformity of the external magnetic field?

The inhomogeneity of the external magnetic field of a rectangular magnet generally refers to the uniformity and relative size of the area of the main magnetic field, the three-dimensional remanence distribution (magnetization deflection angle), the symmetry of the N/S pole space magnetic field, and the smoothness of the magnetic field. The uniformity of the good field area of the main magnetic field is generally expressed by the fluctuation of the magnetic field value B0 of the cross-sectional area in the orientation direction. The fluctuation value depends on the physical design and engineering development requirements of different permanent magnet devices, and the indicators are also different. The so-called "smoothness" of the external magnetic field of permanent magnets means that there is no large "sawtooth" magnetic field distribution.

[Spatial distribution of the main magnetic field Bz of a rectangular permanent magnet]

Under ideal uniform magnetization conditions, the distribution of the good field area of the main magnetization field Bz is closely related to the relative area size and the spatial distance. As the distance increases: (a) → (b) → (c) → (d), the central area The intensity of the main magnetic field Bz gradually decreases, and the area of the good field first increases and then decreases (the maximum in Figure 1(c)), while the main magnetic field Bz in the edge area decreases rapidly with the increase of distance. This phenomenon also indicates that under the same conditions Next, as the magnetic gap of the permanent magnet device decreases, the uniformity of the magnetic field has an optimized optimal magnetic gap value. This also shows that under the condition of a small gap magnetic circuit, if the magnetic field is to achieve high-quality requirements, the shape of the permanent magnet Design, magnetic field uniformity, permanent magnet device system design, etc. put forward higher requirements. The good field distribution of the permanent magnet's main magnetic field is closely related to the shape design of the permanent magnet. The molecular current method can be used to calculate the external magnetic field of the permanent magnet of any shape Spatial distribution pattern.

Factors Affecting Inhomogeneous External Magnetic Field of Rectangular Neodymium Magnet

Demagnetization field

The demagnetizing field has a complex effect on the micro-inhomogeneity of the external magnetic field of the permanent magnet.

In engineering, permanent magnets are used in an open circuit, and there is a demagnetizing field, which is one of the significant differences between permanent magnets and electromagnets. When the permanent magnet is magnetized under its action, the internal magnetic field is not equal to the external magnetic field. The size and distribution of the demagnetizing field are mainly determined by the geometry and size of the permanent magnet. When a demagnetizing field exists, even if it is magnetized in a uniform external magnetic field, since the magnetic field generated inside the permanent magnet is not uniform, the permanent magnet cannot be guaranteed in most cases. Absolutely uniform magnetization of the magnet. The theory proves that only ellipsoidal permanent magnets can meet the requirements of uniform magnetization.

Due to the uneven magnetization caused by the demagnetization field, according to the ampere molecular current point of view, the internal molecular current of the permanent magnet cannot be completely offset, and the permanent magnet has only the surface macromolecular current. Under non-ideal conditions, the internal molecular current of the permanent magnet cannot be completely offset. The remaining part of the micro current, they also generate a magnetic field, which is equivalent to countless "small permanent magnets". Macroscopically, the magnetic field generated by the "small permanent magnet" and the overall external magnetic field of the permanent magnet under non-ideal conditions are vectorially superimposed, which affects the remanence Distribution such as magnetization deflection angle produces complex systemic microscopic effects.

Process factors

From the analysis of the principles of magnetism and magnetic materials science, the inhomogeneity of the external magnetic field of a permanent magnet is essentially caused by the inhomogeneity of its magnetic structure. For anisotropic permanent magnets, the quality of the powder particles is to ensure that the permanent magnet has a good microscopic magnetic structure And the primary condition of orientation. The ideal magnetic powder particles are:

1. The powder particle size is small and the distribution is narrow, all powder particles are single crystals.

2. The powder particles are elliptical.

3. Few crystal defects of powder particles.

4. Less impurities and gas adsorbed on the surface of powder particles.

For NdFeB permanent magnets, using the fast scale (SC) + hydrogen crushing (HD) + jet mill (JM) process, the technical results of the manufactured powder particles are somewhat close to the ideal state, but the process also needs to be optimized. Improvements can produce powder particles close to the ideal model. For samarium-cobalt permanent magnets, due to the difference in alloy properties, it is impossible to simply apply the advanced powdering process of neodymium iron boron permanent magnets such as jet milling in actual production. The elliptical shape close to the ideal model can be manufactured through processes such as oxidation-reduction diffusion. Powder particles. If the traditional powder metallurgy process is adopted, the main problem is that the powder particle size distribution range is relatively wide, the shape is diverse, and the crystal defects are many.

【(a) Ideal powder particle model; (b) Irregular magnetic phase crystal grain shape】

The degree of orientation has an extremely important influence on a number of technical parameters of anisotropic permanent magnets, and restricts the uniformity of the permanent magnet's macroscopic external magnetic field (magnetization deflection angle, microscopic smoothness, symmetry, etc.). Under the same design and process The degree of orientation indicates the degree of anisotropy of the permanent magnet. The higher the degree of orientation, the higher the remanence Bz in the orientation direction of the permanent magnet, and the smaller the remanence Bx, By in other directions, that is, the higher the degree of orientation, the smaller the magnetization deflection angle. However, the high degree of orientation does not mean that the microscopic smoothness and symmetry of the magnetic field are good, and their relationship is more complicated. The degree of orientation is affected by many factors, mainly including orientation field strength, powder particle shape and size, and molding method , Powder loose packing density, etc.

Powder particles close to the ideal model and suitable loose packing density will improve the fluidity during magnetic field orientation molding, thereby greatly increasing the degree of orientation. The strong magnetic field orientation molding process of powder particles is essential to obtain high-oriented permanent magnets For example, the typical domestic molding methods include parallel molding (ADP), vertical molding isostatic (TDP), rubber mold isostatic (RIP), and the orientation degrees obtained by these three molding methods are significantly different.

ADP is generally used in the design of the moulding process of low-to-medium magnetic permanent magnets, which will damage the orientation degree; TDP is a moulding technology used for high-performance permanent magnets, which also has a certain degree of damage to the orientation degree.

Sintering and solidification

The practice has proved that the influence of gravity and other factors in the sintering and solidification of permanent magnets will cause varying degrees of density unevenness and orientation distortion, which will also deteriorate the smoothness, magnetization deflection angle, and symmetry of the permanent magnet's external magnetic field.

Obtaining a uniformly oriented permanent magnet blank is the primary condition to ensure that the permanent magnet has a good external magnetic field uniformity. During moulding, the process should be optimized so that the loose powder particle assembly in the mould is in the centre of the magnetic field and distributed symmetrically. The sintered permanent magnet must undergo slicing, preliminary grinding, finishing and other processes to obtain permanent magnet components that meet the size requirements. For permanent magnets with high uniformity requirements, the machining process also has an important impact on the uniformity of the magnetic field. 

In fact, for cylindrical, tile-shaped, ring-shaped, and other special-shaped permanent magnets, for cast permanent magnets and ferrites, the law and idea of the inhomogeneity of the external magnetic field of permanent magnets are basically the same as the above, but in actual engineering, the combination The shape design of permanent magnets and the non-uniform technical requirements of the external magnetic field require certain adjustments in the development process.