The Third Group of Spacial Distribution of Magnetic Leakage Field Yielded by A Rectangular Slot on The Workpiece Surface

Transcription

1 7th Word Conference on Nondestructive Testing, 5-8 Oct 8, Shanghai, China The Third Group of Spacia Distriution of Magnetic Leakage Fied Yieded y A Rectanguar Sot on The Workpiece Surface Astract Wei-Chang ZONG Nanjing Gas Turine Research Institute 47 Northern Centra Road,Nanjing 37, China Te: ,Fax: ,E-mai: zhong75wc@63.com The ojective of this study was to expain quantitativey a surprising phenomenon the magnetic poarity in a sot on the workpiece surface after discontinuation of ongitudina magnetization is opposite to it, when the specimen is eing magnetized, that is,the magnetic residua fied shows negative vaues. On the asis of uniform distriution of magnetic charges aong a edges of a cuoid magnetic medium in the stae condition of magnetization and the demagnetization aw of ferromagnetic materias( after remova of magnetizing fied the difficut degree of the returning of a magnetic dipoe ack to its origina orientation efore magnetization depends on the magnitude of the mechanica reacting force and mechanica moment affected y this magnetic dipoe in stae condition of magnetization,they are known that after discontinuation of ongitudina magnetization rear magnetic charges excited during the magnetization may e remained aong the ottom edges of the throughout rectanguar sot on a cuoid stee component,and that there wi appear unike magnetic charges opposite to those,which had existed at the magnetization aong the rest edges and over the atera surfaces of the sot. Therey this strange phenomenon was carified. The spacia distriution gragh of the magnetic eakage fied cacuated and potted aong the symmetrica axis of the sot asicay conformed to the third group of curves otained from Dr. F. Förster s experiment made in 985. Keywords: Magnetic eakage fied,spacia distriution, Rectanguar sot, Negative residua magnetism On the asis of magnetic dipoe theory the author deduced the approximate anaytic expression of magnetic eakage fied yieded y a rectanguar sot on the workpiece surface. Therey the first group ( Fig. [] and second group ( Fig., the part of x > [] of the spatia distriution of magnetic eakage fied in the cassica experiment made y Dr. F. Förster in 985 have een etter carified theoreticay [3,4]. In addition, the author aso expained quaitativey the reason, why the magnetic poarity in a sot on the workpiece surface after discontinuation of ongitudina magnetization is opposite to it, when the specimen is eing magnetized [5] from the demagnetizing aw of ferromagnetic materias. Now he is seeking again for the quantitative theory of the phenomenon of reversing of magnetic poes, which surprised Dr. Föster the anaytic expression for the third group of the spacia distriution of magnetic eakage fied ( Fig., the part of x < []. Cr STEEL C =.68 Oe a = Oe Active Fied Fig. First group of spacia distriution curves of magnetic eakage fied in Dr.Förster s experiment [] Fig. Second( X > and third ( X < groups of spacia distriution curves of magnetic eakage fied in Dr.Förster s experiment []

2 . Reuctant supposition Because in references [] and [] ony the depth (.5mm and different widths (.,.5,.8,. and mm of the sot are given, it has to e supposed that the testing ook used y Dr. Förster is a cuoid stee component with a rectanguar throughout sot on its surface, of which the shape, dimensions and coordinates seected are shown in Fig.3.a. And S=,,w,h are not known, so they may e aritrary. ( a ( Fig.3 Magnetic charges of the cuoid stee component with a rectanguar throughout sot on its surface (a at ongitudina magnetiztion ( most proay remained aong sot edges after discontinuation of magnetization. Known knowedge. Magnetie eakage fied yieded y a rectanguar sot magnetized ongitudinay ( Fig.3.a, X direction is (A/m [3,4]. = ( + ( + 3 ( s ( here ( magnetic eakage fied caused y the inear magnetic charges (W/m aong the apex edges and x vertica edges of the rectanguar sot, A/m. ( magnetic eakage fied caused y the inear magnetic charges (W/m aong the ottom edges of the sot, A/m. 3 ( s magnetic eakage fied caused y the equivaent uniform area magnetic charges s (W/m over the atera was of the sot, A/m And their X componets aong symmetrica axis of the sot Z are respectivey as foows. ( x= y= = πµ o - ( [ ( z w ] + ( (z + d + (z + d ( = [ - ] x πµ y x= = ( 3 o + (z + d w + (z + d ( = πµ [tg w(z + d s - - 3x s y x= = o + (z + d ( wz - tg ] ( 4 in which µ o permeaiity of the vacuum, µ o = 4π -7 /m. Magnetic charges distriution on cuoid stee componet with a rectanguar throughout sot after discontinuation of ongitudina magnetiztion According to the demagnetizing aw of ferromegnetic materias ( the difficut degree of destruction of a magnetic dipoe chain depends on the magnitude of its magnetic potentia energy, it was demonstrated that after discontinuation of ongitudina magnetization ony rare magnetic charges excited during the magnetization may e

3 remained aong the ottom edges of the throughout rectanguar sot on a cuoid stee component ( Fig.3.. Because the ottom edges are extreme narrow (, the magnetic charges remained aong them are very sma, so the opposite residua magnetic fied strength over the sot must e very ow [5]..3 Uniform distriution of magnetic charges aong a edges of a cuoid magnetic medium magnetized ongitudinay It has een proved that [6,7] : x y z ( 5 in which x, y, z inear magnetic charge densities aong X,Y,Z axes through one same point, W/m 3. New conception recenty-otained 3. From paragraphs. and.3, after discontinuation of ongitudina magnetization if there were rare magnetic charges remained aong the ottom edges of a rectanguar throughout sot on the cuoid stee component, which had een excited at magnetization ( Fig.3. [5], that is, ( 6 << ( 7 here, and are respectivey the magnetic charges densities at magnetization and after discontinuation of magnetization aong the ottom edges of the sot ( W/m. The same inear density of magnetic charges shoud aso appear aong the other edges of the sot ( Fig.4.a. ( a ( Fig.4 Magnetic charges distriution of the cuoid stee component with a rectanguar throughout sot on its surface after discontinuation of magnetization a inear magnetic charges aong every edge area magnetic charges over the atera was 3. After remova of magnetizing fied a ( A/m the part of magnetic dipoes ( the simpest magnetic domains, which had een forced to orient to a intensey at magnetization, is reouned ack suddeny, ecause of the tremendous reaction of eastic moment. And the opposite magnetic poarity wi appear in the sot to it, when a is eing appied, that is, area magnetic charges density st ( W/m, of which poarity is opposite to it, when the specimen is eing magneticzed, wi appear over the atera was of the sot ( Fig.4. [8,9]. st =-k s ( 8 here, s area magnetic charges density over the atera was of the sot at magnetization, W/m. k a positive constant, and k<<. And st wi decrease graduay with the passage of the time [8,9]. 4. Anaysis and cacuation It is known from paragraph 3 that after discontinuation of ongitudina magnetization of a workpiece the magnetic poaraty of the inear magnetic charges aong the apex and vertica edges of a rectanguar throughout sot ( Fig.4.a and the area magnetic charges over the atera was of the sot ( Fig.4. are a just opposite to them, when the specimen is eing magnetized ( Fig.3.a [9]. Either the inear magnetic charges density t or area magnetic charges density st are a smaer than the reevant quantities and s at magnetization. The 3

4 anaytic expression for the third group of magnetic eakage fied shoud e as foows. x =- x ( t + x ( t - 3x ( st ( 9 x ( t << x ( t ( x ( t << 3x ( st ( So as the first approximation the third group of the spatia distriution for magnetic eakage fied yieded y the rectanguar throughout sot on a cuoid stee component can e otained from the resut at magnetization ony reduce them severa times as much and add a minus symo. For exampe, if d=.5, w=3, =.,, α= s / =9 γ= st / s = /4 δ= t/ =/4 The charateristic x x= y= - Z can e cacuated and potted according to expressions ( ~ (4 as shown in Fig.5, in which the part of x > is the first group of the spatia distriution for magnetic eakage fied and the part of x < is just the third group of the curves. Oviousy the characteristics for the part of x < in Fig.5 asicay conform to the curves of the part of x < in Fig.. 5. Concusion Fig.5 The third group ( x < and first group ( x > of spacia distriution curves of magnetic eakage fied yieded y a rectanguar throughout sot on the cuoid stee component surface. 5. After discontinuation of ongitudina magnetization the magnetic dipoe chains excited in cuoid stee component aong the direction of magnetizing fied at magnetization immediatey coapse every magnetic dipoe a attemps to return ack to its origina spacia orietation efore magnetization under the reaction of eastic moment ( anti the moment yieded y magnetizing fied. Because of the mechanica resistance of the adjacent magnetic domaims, ony the magnetic domains, which otained higher magnetic energy at magnetization, can accompish this process. The magnetic dipoes with ower magnetic energy sti keep the orientation in the magnetization condition. And the magnetic domains with extremey high magnetic energy continue rotate forward after returned ack to their origina ocation, so a new construction of magnetic domains, of which magnetic poarity is opposite to when the specimen is eing magnetized wi e formed. 5. After discontinuation of ongitudina magnetization, rare part of magnetic charges excited at magnetization may e remained proay aong the ottom edges of the rectanguar throughout sot on a cuoid stee component surface. Therey there wi appear the same inear magnetic charges t (W/m aong the apex and vertica edges as the ottom edges of the sot. But t magnetic charges aong apex and vertica edges t and must e smaer than at magnetization. And the poartities of the 4 are opposite each other. 5.3 After discontinuation of ongitudina magnetization there must appear area magnetic charges st (W/m over the atera was of the rectanguar throughout sot on the surface of a cuoid stee comporent. The magnetic poarity of st is opposite to s (W/m, when the specimen is eing magnetized, and st is much weaker

5 than s in vaue. 5.4 After discontinuation of ongitudina magnetization the magnetie eakage fied measured in the sot xt is overapped y them yieded from t ( inear magnetic charges aong apex and vertica edges of the sot, t ( inear magnetic charges aong ottom edges of the sot and st ( area magntic charges over the atera surfaces of the sot. Oviousy its direction is opposite to it of xo caused y, and s at magnetization. The former is presented y the third group of Dr. Förster s experimenta curves, and the atter is presented y the first or second group of spacia distriution characteristics of the experiment. 5.5 The three groups of spatia distriution characteristics of magnetic eakage fied in the cassica experiment made y Dr. F. Förster in 985 can e presented y an unified anaytica expression. The differences etween them ony ie in the posstive or negative symos of the magnetic eakage fied caused y the magnetic charges aong sot edges and over atera was of the sot as we as the proportiona coefficient of area density to inear density of magnetic charges (α and the proportiona coefficients of remained magnetic charges to tota excited magnetic charges(γ,δ. Acknowedgment The author gratefuy acknowedges the financia support of this work y The Nationa Natura Science Foundation of China under Grant No Referenees [] Föster F., On the way from the know-how to the know-why in the magnetic eakage fied method of nondestructive testing ( Part [J]. Materias Evauation, 985, 4(9: [] Iidem ( Part. 985, 4(: [3] Zhong W.C. Magnetic eakage fied caused y a rectanguar sot on the workpiece surface [J]. ( Chinese Journa of NDT, 4, 6(7: ; [C]. 6th Word Conference on Nondestructive Testing. Augast 3~Septemer 3, 4. Montrea, Canada [CD]. [4] Zhong W.C. The second group of spatia distriution curves of magnetic eakage fied yieded y a rectanguar sot on the workpiece surface Principe of Magnetic Partice Inspection, Part [C]; Proceedings of 9th Chinese Conference on MT, PT Techniques. Octoer 4~7, 5. Xian, China: [5] Zhong W.C. Reversing of magnetic poes in a sot on the workpiece surface after discontinuation of ongitudina magnetization [C]. 5th Word Conference on Non-Destructive Testing. Octoer,.Rome, Itay [CD]; [J]. Materias Evauation,, 6(5: [6] Zhong W.C. Theoretica fundamenta of magnetic dipoe for ongitudina magnetizationg of a square stee [J]. (CJ NDT, 997, 9(4: 95-98; [C]. 9th Asia-Pacifie Conference on Nondestructive Testing in Conjunction with ASNT s 998 Spring Conference and 7th Annua Research Symposium. March 3~7, 998. Anaheim, Caifornia, USA: [7] Zhong W.C.Theoretica fundamentas of magnetic dipoe for ongitudina magnetization of a square stee component [J], Materias Evauation, 999, 57(9: [8] Zhong W.C. Demagnetization of a 3 MW gas turine rotor [J]. (Chinese Jouna of Testing and Evauation, 983, (3: 6-8. [9] Zhong W.C. Magnetization and demagnetization of ferromagnetic materias staying in static state in geomagnetic fied [C]. Proceedings of 7th Word Conference on Non-Destructive Testing, August 7~3, 8. Shanghai, China [CD]. 5