MEASUREMENT OF STRESS WTH AC MAGNETC BRDGES Otto H Zinke Department of Phyic Univerity of Arkana Fayetteville, AR 7271 William F Schmidt Department of Mechanical Engineering Univerity of Arkana Fayetteville, AR 7271 NTRODUCTON AC magnetic bridge have been ued to detect applied tre in teel and aluminum tet pecimen The data how effect of mechanical hyterei n the teel tet pecimen, change in real and imaqinary reluctance occur n aluminum ample only chanqe in imaginary reluctance are oberved From thee obervation it i concluded that AC magnetic bridge can be ued for the NDE of tre and could poibly be ued to determine reidual tre AC MAGNETC BRDGE For over a century, the phyical characteritic of material which can be detected through electrical change have been detected through the incorporation of thoe material in electrical circuit and particularly electrical bridge circuit Therefore, it i not trange that where magnetic propertie of material could be ued to determine phyical change in matter, the ame technique wa attempted, ie every effort wa made to meaure the change in magnetic propertie through the ue of electrical circuit The principal reaon for thi wa apparently the fact that electrical ignal were and are very convenient to proce However, uch technique have generally been unatifactory for magnetic meaurement except with very pecialized ample Thu, the permeability and the hyterei loop of toroid can be determined, although not eaily, through winding on toroid core Meauring the magnetic characteritic of teel part on a typical production line i difficult if not impoible with electrical mean A magnetic technique i decribed here which i more amenable for uch tet, and it i qualitatively hown that thi technique i reponive to tre in both ferritic and nonferritic ample The clue to the ucceful meaurement of magnetic characteritic of ferritic part can be found in the parallel to the hitoric examination of electrical characteritic of conducting material, ie the ferritic material can be placed in a magnetic circuit which i part of a magnetic bridge circuit f the magnetic flux driving the bridge 251
change periodically, eg if it i inuoidal, the ignal can be detected and analyzed with all the convenience of electrical circuitry Therefore, to realize the baic convenience of electrical bridge circuit, it only remain to be hown that magnetic flux can be conveniently manipulated in magnetic circuit through electrical mean n Fig l, a portion of a magnetic circuit i hown The cirtuit fragment conit of a ferriterod (which i hown a hatched), a gap in the rod, and a coil of N turn wound about the rod A parallel combination of capacitance C and reitance R i attached to the coil The ample to be examined would normally be placed within the gap jut a an electrical ample mut be placed in a gap in a conductor of an electrical circuit n the early day of working with electrical circuit, the coupling between the ample and the circuit caued coniderable difficultie At thi tage of development, magnetic circuit have the ame difficultie However, practice indicate that care in contructing jig which reproduce the poition of the ample in the gap (or with repect to the gap) with preciion available through normal machining capabilitie virtually eliminate problem with coupling The coupling reluctance will almot alway be high with repect to the ample reluctance, a problern not uually encountered in electrical circuit Another problern which mut receive coniderable attention with magnetic circuit i flux leakage from one part of the circuit to another, a problern imilar to operation an electrical circuit in a conducting olution Thi problern can uually be olved through deign The third problern i that magnetic circuit uually mut have a geometry which i pecific to the ample which i to be inpected to inure that the flux travel throughout the region of interet in the ample Since ferrite erve in a capacity in a magnetic circuit imilar to copper wire in an electrical circuit and ince ferrite i a ceramic, contruction of a magnetic circuit approache an art form Neverthele, magnetic bridge have been contructed with characteritic dimenion a mall a 38 inch and a large a three feet and have been adapted to a variety of ample Over and above the ability of bridge to detect magnetic characteritic of matter directly and electrical characteritic through eddy current induced in the ample, a primary advantage in the ue of uch bridge i the ability to adapt to ample geometry rather than having to interface through coil For thi advantage, the acrifice i that there will probably never be a univeral wand of the type available with eddy-current technique However, there i not the effective imitation on depth of penetration with ferritic material which exit with eddy current Fig 1 A portion of a magnetic circuit compoed of ferrite and having a gap g1 Fig 2 An AC magnetic bridge 252
Suppoe for the moment that no gap exit in the magnetic circuit fragment hown in Fig 1, AC magnetic circuit theory, predict that the complex flux - will have a relationhip to the magnetomotive force mmf and the complex reluctance given by 'V 'V - = mmf <:; (1) The eomplex reluctance i given by where Re i the real reluctance of the ferrite core and w=ztf where f i the frequency of the inuoidal mmf Thi theory aume that the magnetic material i linear, ie that it ha a coed and linear hyterei loop Yet, the theory hold reaonably well for actual magnetic circuit The real term in thi expreion i an energy torage term, and the imaginary term account for the diipation of energy in the circuit A a firt order approximation, a term r can be added to account for the energy diipation reulting from an open hyterei loop whether the open hyterei loop reult from the ferrite, the gap, or material placed within the gap Under thee circumtance, the complex reluctance then become From Eq 3, it i apparent that the real and the imaginary reluctance can be eparately manipulated electrically An AC magnetic bridge uch a the one depicted in Fig 2 i compoed of four arm contructed of the circuit fragment hown in Fig 1 and an input leg and an output leg The real and imaginary reluctance in the arm can be manipulated through technique uggeted by Eq3, or the change in reluctance of ample in the gap of thee arm can be meaured through uch technique The baic AC magnetic bridge circuit chematized in Fig 2 i, of coure, a copy of the electrical Wheattone bridge t i powered through an ocillator (oc) which produce a current in the coil N1 and, thu, a magnetomotive force which power the bridge The detector D, which can be anything from a imple amplifier to a wave analyzer, i chematized a earphone The four gap g1, gz, g3, and g4 erve in a capacity imilar to reactance in an AC electrical bridge Coil are hown on adjacent arm of the bridge with a parallel combination of reitance and capacitance on only one uch coil Thee will be called null coil here becaue they ait in nulling the bridge Only two uch et of coil are needed but they mut be on adjacent arm Uually only one capacitor and one reitor are needed to null the bridge with the capacitor and reitor ditributed in ome manner between the two coil The bridge can be operated in one of two mode: An offnull mode where the bridge i initially nulled and the voltage and the phae of the ignal at the detector are meaured The phae i uually compared to the phae of the input electrical ignal Or the bridge can be operated in the renull mode where the reitance and capacitance neceary to renull the bridqe a a reult of change in the ample are recorded From data obtained in the renull mode, the real and imaginary reluctance can be calculated throuqh Eq 3 above and bridge balance equation Both offnull and renull reult are preented here When inpecting ferritic material, adjuting the input mmf and inpecting amplitude and phae of the fundamental and everal barmonie frequencie yield clue to the nature of the hyterei loop (2) (3) 253
Such data are not preented here but have been ued to charactize type of flaw in pipe wall, for example From uch data it wa apparent that each type of flaw yielded a characteritic ignature through which the type of flaw could be identified A an indication of how the bridge wa modified to obtain the information to be preented here, Fig 3 i hown An extenion ha been placed on one arm of the bridge, and an inert (hown a a dotted legend) i placed between the modified arm The purpoe of the inert, which i uually copper, i to queeze the magnetic field out of the gap o that it will contact the ample The actual deign of the bridge i hown in Fig 4 Again, the inert i dotted and the ferrite i hatched n thi figure it can be een that the inert i andwiched between all four gap The extenion can be een on the left of the ide view The ample appear in both the front and ide view n thee experiment, the ditance between the face of the bridge and the ample wa 4 inche, the thickne of a commercially-available platic heet interpoed between the ample and the pole face of the bridge EXPERMENTAL RESULTS The bridge of Fig 4 wa mounted on tenile tet pecimen with a 18-inch thick and 12-inch wide tet ection on which were mounted two reitive train guage, deployed to compenate for any poible bending of the ample The ample were mounted in a tenile teter The reading of the train guage were recorded and correlated with the applied force reading of the tenile teter to produce the tre reading accompanying the reult A Hewlett Packard 3582A Waveanalyzer wa ued for detecting and analyzing the ignal at location D on Figure 4 A Hewlett Packard 6518 ocillator wa ued to drive the bridge through a Hewlett Packard Model 467A Power Amplifier The inuoidal driving ignal wa at 1 kilohertz in thee experiment Bridge have been operated in other context anywhere from everal Hertz to everal megahertz 5CAl( Fig 3 An AC magnetic bridge with an extenion added to one arm An inert i placed in the gap which ha the effect of puhing the magnetic field out of the gap front Fig 4 The AC magnetic bridge a built The hatched area i ferrite and the dottea area i the inert 254
n thee experiment, the tre cycle wa carried out at leat ten time before data were recorded n the offnull mode, difference were found between data of ucceive tre cycle even when the ample had been cycled ten time Thee difference gradually decreaed a the number of tre cycle wa increaed Typical offnull data for a tre cycle i hown in Fig 5 The ordinate i in millivolt which i meaured at No The abcia i tre in unit of 1, pi The croe repreent increaing load and the boxe repreent decreaing load Problem were encountered with the tenile teter at the point where the mall peak appear in the acending curve The peak een i probably a reult of the lippage in the teter at thi point The experimental error i too mall to how When thi curve wa replicated in the renull mode, the value of reitance and capacitance required to renull the bridge were converted to real and imaginary reluctance through Eq 3 and bridge equation The reult are hown in Fig 6 and 7 The abcia i in the ame unit a thoe of Fig 5 The reluctance value repreented by the ordinate are in megas unit The real reluctance (Fig 6) i directly related to the permeability of the ample while the imaginary reluctance i related to the conductance Note that the tre-hyterei loop for the real reluctance i more open than that for the imaginary reluctance The dicontinuitie produced by lippage in the tenile teter eem more pronounced for the imaginary reluctance than for real reluctance n Fig 8, two ucceive real reluctance curve have been plotted one over the other to demootrate the reproducibility of thi technique of meauring applied tre While the tre here wa externally applied, thee experiment were timulated by a erie of experiment in which ferritic plate were canned for flaw n the coure of thoe can, ignal developed which were unrelated to the flaw, and it wa upected that thoe ignal aroe from reidual tre Later experiment found a correlation between variation of real reluctance and the reult of Rockwell hardne tet The experiment here were deigned for qualitative confirmation of the relation between bridge reading and applied tre 2 ---------+----------+----------4------------------ 15 1 unloading!) 5 oading St r e * 1 p o l Fig 5 Output of the AC magnetic bridge a a reult of loadi ng and unloading a 18 x 12 teel ample 255
- * e a: a: 3 unloading 2 ',, r, li',f - _-1 _,,, 5 15 2 2 5 St r e 1 p Fiq 6 Change of real reluctance in a 18 x 12 inch teel tenile pecimen 256
4- ----- ; 3 * t:r: 2 unloadin_p,- ' l oading (' 5 1 1 5 Slrea 1 p l 2 2 5 Fig 7 Change of imaginary reluctance in a 18 x 12 inch tell tenile pecimen ; - * c t:r: t:r: 3 2 5 e two cycl e unlo adin g$ ff c yc l e 1 5 Stre1 1 pl, -- Fig 8 Change of real reluctance in a teel tenile pecimen 2 e 2 5 257
12-------------------+--------+------------------- i: 9 3 ',( - - unloading 1!1 t o+---------2+---------4----------------e--------1 Stre *1, p1l Fig 9 Output of the AC magnetic bridge a a reult a loading and unloading a 18 x 12 inch aluminum tenile peciman : ' - o 3 1 1t,' ( j ' - -- --- - _ --- i t i j o----------------,--------+-----------------1 Strooo 1 ' Fig 1 Change of imaginary reluctance in a 18 x 12 inch aluminum tenile peciman 258
DSCUSSON A qualitative tet of thi technique which would further confirm the relationhip between bridge reading and tre would reult from making imilar meaurement on nonferritic material where a correlation hould be found between applied tre and imaginary reluctance and not between applied tre and real reluctance Therefore, tet were run on an aluminum ample The offnull reult appear in Fig 9 While thee reult were not a reproducible a the reult with the teel ample, the preented curve i fairly typical of the data obtained The abcia i in unit of 1 lbq inch and the ordinate i in microvolt The croe repreent data obtained with increaing load, and the boxe repreent the data obtained with decreaing load Again, the dicontinuitie in the curve occurred imultaneouly with lippage in the tenile teter Thi lippage may have been the primary reaon for difficultie in replicating the data The renull curve obtained in the next data erie i hown in Fig 1 Only the reitance required for renull changed in thee experiment The value for capacitance required for renull did not change indicating, conitent with expectation, that the real reluctance did not change Here, the reitance data have been again converted to imaginary reluctance While it i till too oon to draw quantitative concluion from thee experiment, it i clear that the AC magnetic bridge repreent a new technique for finding applied and poibly reidual tre in both ferritic and nonferritic metal 259