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## The device for contactless circular magnetization of cylindrical articles

Matyuk V.F.
Gorbash V.G.
Institute of Applied Physics of National Academy of Sciences of Belarus
Minsk, Republic Belarus
Contact

### Definition of a problem

For solution of some problems of nondestructive testing (for instant for testing the lengthwise weld of pipes) the creating of circular magnetic field is required. The use of known methods of circular magnetization based on the passing through the article or through the conductor inside it of current for solution of some problems, for instant, for magnetization the article in motion impossible is. The experimental investigations and analysis of known magnetizing devices show that for creating the circular fields in local regions distant from the symmetry axis of body with axial symmetry (body of revolution) the coil in the form of tore or the section of tore that represents the cylindrical framework what on the rectangular turns of magnetizing coil are placed, can be used (Figure 1).

 Fig 1: The arrangement of coil turns relative the coordinate system

### The computation of circular field of doughnut coil

In the base of computation of the doughnut coil the formula is putted determining the value of magnetic field strength of portion of conductor what through the current is flowing

 (1)

where r0 is the distance from the observation point M0 up to the portion of the conductor, α1 and α2 are the angles, that the radii-vectors form drawn to the point from the start and from the end of the portion of conductor, I is the value of current.

At computation the circular component of the field of doughnut coil it is to be taken into account that its turns in the space different placed are. Every turn consists from four portions of conductor with current (two of them axial are and two radial are)having their own dimensions and angles. The computation was curried out in coordinate system from Figure 1. The axis OX lies in the plane of the first turn. The angle between the plane of the kth turn and the axis OX denote φk.

The corresponding expression for circular component of field of kth turn and the resultant circular components of magnetic field of one-layer and multilayer doughnut coil in the point inside the tore were received. The contribution of every kth turn in the resultant field was considered. That approach allow to compute the coils with periodically repeated groups of turns (sectors) used in the magnetization coils for receiving the scattering fields of sufficient high value. To receive the more uniform distribution of circular component of field in the local region was suggested to shift the turns in the neighbouring layers of coil for one and the same angle θ. This angle between the planes of turns in the next layers by the ratio

 (2)
determined is, where N the quantuty of turns in layer is, M the number of layer in a coil is.

The distinction of the multilayer coil consists in that for different layers the relative coordinate of fixed observation point change, what in the circular field is determined. As the computations show it is possible to receive in some points at corresponding conditions sufficient value of circular field that by the next expression can be determined

 (3)
where

The next unit symbols are used: δ = d/a1, d is the diameter of magnet wire, a1 and a2 are the inside and the outside radii of upper layer, α = a/a1, α2 = a2/a1, β = b/a1, ξ = z/a1, a is the radius of observation point, z is the coordinate of observation point, m is the number of corresponding layer (starting the count from the external one).

### Analysis of the circular field of doughnut coil

The analysis of the change of the circular component of field around the circle in the region of doughnut coil that meets the requirement a<a1 with the change of quantity of turns in a layer and quantity of layers in the wide region of change of turns quantity N and layers quantity M for different diameters of magnet wire d was curried out. It shows that increase of turns quantity in one layer takes to amplitude decrease of circular component of magnetic field although the quantity of points with maximum value increases. It can not take to the magnetization of article as in some points this component clockwise directed is and in others counterclockwise directed is. The increase of layers in the coil increases the amplitude of circular field not sufficiently. The distribution of circular component of field of coil having N = 50 turns is in the Figure 2a for the one layer and in the Figure 2b for four layers are done.

 a) b) Fig 2: The distribution of circular component of doughnut coil inside it around the radius α = 0,9; α2 = 1,7; β = 1; ξ = 0; δ = 0,03; N = 50: a) M = 1; b) M = 4.

Thus the construction of magnetizing system of toroidal type for receiving the circular component of sufficient amplitude in the region of doughnut coil that satisfy the condition a/a1 using the direct current questionable is. In the local region (point) it is possible to receive the circular component of field using the small quantity of turns in layer or due to increase the quantity of layers with some turns in one layer. But the extent of that region small is. To rise the component of field is possible using the pulse current in the magnetizing coil.

As it is known the circulation in that case will be proportional to the value dE/dt (to the change of strength of electromagnetic field with the time). Concerning the creating the circular component of magnetic field by direct current it exists one more method. It is necessary to construct such winding of doughnut coil that the scattering fields of its turns maximum will be. It is possible to divide the magnetizing winding for periodically repeated regions with uniform distribution of turns in each of them. For instant using instead the coil with N = 160 and M = 4 the coil with four layers each having 80 turns distributed on four regions with identical density takes to sufficient increase of circular component in the inside region (for hundreds times). The results of computation of such coil in the Figure 3a in Cartesian coordinates and the Figure 3b in polar coordinates are done.

 Fig 3: The distribution of circular component of doughnut coil with four cyclic repeated regions inside it around the radius α = 0,9 a) in Cartesian coordinates; b) in polar coordinates (α2 = 1,7; β = 1; ξ = 0; δ = 0,03; N = 160; M = 4).

The analysis of dependence of circular component on the outside radius a2 and on the length 2b shows that the optimum value of the length exists, as its outside radius can be changed in wide region don't influence the distribution and value of field.

### Conclusion

For receiving the circular component of sufficient magnetic field the use of pulse excitation in doughnut coil having small quantity of turns and layers or at direct current to construct the windings consisting from cyclic repeated regions is necessary.

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