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Non-Relevant Indications Along the Base Apex Lines of Work Pieces Magnetized CircumferentiallyWei-Chang Zhong
Nanjing Gas Turbine Research Institute, 47 Northern Central Road,
Nanjiing, 210037, People's Republic of China
According to magnetic dipole theory for the absorption of magnetic particles along the edges of a square steel's lateral faces after longitudinal magnetization, this paper proves that after circumferential magnetization of the work pieces ( including cylinder, cuboid, parallelepiped and triangular prism etc.) same linear magnetic charges will uniformly distribute along not only the edges of the lateral faces, but also the base apex lines, so both the former and the latter must adsorb magnetic particles and non-relevant indications may also be formed along the base apex lines of work pieces .
Keywords: Non-relevant indication, Base apex lines, Circumferential magnetization
The author explained the reason, why the non-relevant (stray) magnetic particle indication appears along the lateral edges of a cuboid steel magnetized longitudinally by the magnetic charge ( magnetic dipole ) theory in reference . And in books of magnetic particle inspection there is still following content : "On a work piece of simple square steel as shown in Fig.1.appears non - relevant magnetic particle indication after circumferential magnetization, due to the excessive magnetization ". Truly, as the reference  states:"As circunferential magnetization by the method, that electric current flows directly through the specimen, magnetic induction strength reaches the maximum on the specimen surface . If the electric current is too much, the magnetic induction strength becomes so large, that the magnetic lines of force is compelled to leave the specimen from the sharp edges ." Though this explains the reason, why the magnetic particle piles appear along the cuboid work piece lateral edges, which is parallel to the magnetizing electrical current . Why magnetic pattern also is piled along the base apex edges, which are perpendicular to the magnetizing electric current, similar to that being piled along lateral edges? Because the magnetic lines of force, excited by the magnetizing electric current (dotted lines in Fig.2.a ) are all parallel to the base apex edges of the cuboid, they force the (molecular) magnetic dipoles  in the work piece to form a series of "closed hoop" heads by tails along these magnetic lines of force (Fig.2.b). Thus the effects of positive magnetic poles and negative magnetic poles are counteracted each other, so they don't appear magnetism externally . Even if the magnetizing electric current is still larger, any non-offset magnetic charge ought not to appear along the base apex edges . And then how this difficult problem is solved?
|Fig 1: Non-relevant indication on a square steel magnetized circumferentially.|
a. Magnetic lines of force b."Closed hoop" of molecular magnetic dipoles|
Fig.2 Circumferential magnetization of a square steel .
The author's conclusion in reference - magnetic charges must uniformly distribute along all edges of a cuboid magnetic medium magnetized longitudinally, and the magnetic charge density along each edge is equal - is just the theoretical basis to solve this difficult problem . Of course, some necessary extension must be further carried out .
Besides, the author in reference [6,7] proved that when a part as shown in Fig.3 was magnetized, there was relation :
|smq = smo . cosq||(1)|
in which,smo-linear (or areal ) magnetic charge density along edges (or in cross sections ) of the part, perpendicular to the magnetizing field .
smq - the corresponding magnetic charge density along edges (or in cross sections ), tilting the magnetizing electric current with an angle q.
|Fig 3: Magnetization of work piece and magnetic particle.|
It isn't difficult to extend expression (1) to cuboid, parallelepiped and triangular prism (Fig.4) .
|sma = smo . sina||(2)|
here, smo - magnetic charge density along the base apex edges of cuboid, perpendicular to the magnetizing field .
sma - magnetic charge density along the base apex edges of parallelepiped or triangular prism, tilting the magnetizing field with an angle a.
|Fig 4: Magnetic charge linear density along all edges of a cuboid, parallelepiped and triangular prism magnetized longitudinally.|
After circumferential magnetization of a cuboid, through which an electric current directly flows, the distribution of the magnetic lines of force is shown as Fig.2.a. Obviously, they can be divided roughly into four regions :
Just the two conditions 1 and 2 mentioned above are directly related to this difficult problem, so in the two regions a, b of Fig.2.a imaginally take a cuboid, a parallelpiped and a triangular prism as shown in Fig.5.a,b,c . If the magnetic field through them is regarded as uniform (it can be proved that non-uniform magnetizing field is the same ), according to reference  and the 2nd paragraph of this paper, it can be known that magnetized positive and negative magnetic charges distribute uniformly along all the edges of cuboid, parallelepiped and triangular prism, as shown in Fig .5.a,b,c . And a cuboid can be regarded to be composed of infinite three types of volume element mentioned above, and the typical compositions are nothing more than the two types as shown in Fig.5.d,e . It isn't difficult to see that the linear magnetic charges along edges of two adjacent volume elements on the lateral surfaces of the cuboid and in the cuboid all offset to each other due to the opposite magnetic polarities, only the positive and negative magnetic charges along the edges of the base surfaces can not completely cancel each other out, that is, only along the base apex edges of cuboid appear magnetic poles in positive and negative check as shown in Fig.5.f . So, after circumferential magnetization the base apex edges will adsorb magnetic particle to form abnormal stray ( non-relevant ) indication, as shown in Fig. 1. Thus, this principled difficult problem in magnetic particle inspection is solved theoretically .
|Fig 5: Magnetic charges along all edge lines of three types of volume elements and their macroscopic effect.|
Everyone knows that when a direct electric current flows through a long cylinder the magnetic lines of force are a group of concentric circles, whose centres are along the cylinder axis, and the magnetic field strength, where is r from the cylinder axis is
Besides, a cylinder can be regarded to be composed of infinite elemental triangular prisms, whose vertex angle is dq and the two sides of the triangle are both R (Fig.6.) . As H is perpendicular to both sides of the triangle, according to the 3rd paragraph of this paper, uniformly distributing linear magnetic charges will appear along all edges of these triangular prisms magnetized by H, as shown in Fig.6.b . But the linear magnetic charges along axial edges on the cylindrical surface and along radial edges on the end surfaces of two adjacent elemental triangular prisms all offset each other by positive and negative, only the magnetic charges along the intersecting lines of the cylindrical surface and the two end surfaces ( circular edges ) are left and remained as shown in Fig.6.c .
|Fig 6: Elemental triangular prisms composing a cylinder.|
In summary, when cylinder magnetic medium is magnetized circumferentially, only non -offset positive and negative magnetic charges ( poles ) are remained along the two end edges ( circles ), they present interlocking arrangement ( Fig.6.a ). So the base apex edges of a cylinder must adsorb magnetic particle to form non-relevant ( stray ) indication .
The author gratefully acknowledges the financial support of this research by The National Natural Science Foundation of China under Grant No.59271060 .
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