APPLICATION OF EDDY CURRENT PRINCIPLES FOR MEASUREMENT OF TUBE CENTERLINE DEFLECTION E. J. Chern Martn Maretta Laboratores 1450 South Rollng Road Baltmore, MD 21227 INTRODUCTION Tubes are a vtal component of most structures, especally n the power, and ol and gas ndustres. Tube falure, especally n the nuclear and chemcal ndustres, can have catastrophc effects wth rreversble envronmental and ecologcal damage. The notable Chernobyl nuclear accdent n the Sovet Unon has made the publc extremely senstve and concerned about the safety of nuclear plant operaton. Tube falure s often caused by unntended, localzed deflectons, whch nduce undesrable stresses n the tube that accelerate corroson and crackng. Therefore, t s mperatve to measure deflecton to assess the tube's operatonal safety. However, tube deflecton cannot always be measured easly from outsde the tube. Furthermore, no off-the-shelf system exsts for measurng deflecton nsde the tube. In response to ths problem, we have developed an nnovatve system for measurng tube-centerlne deflecton based on eddy current prncples whch have been used for dmensonal measurements n many systems [1,2]. Ths method conssts of a devce that senses deflecton by followng tube contours and a mechancal delvery/postonng system. The eddy current sgnals are then nterpreted and ntegrated nto physcal tube-centerlne deflectons. In ths paper, we report on a study n whch the eddy current lft-off and edge effect prncples were appled to develop a measurng devce for sensng tube deflecton. We also present the sgnal reducton and nterpretaton methods used to process the eddy current sgnal nto true deflecton dmensons and the dervaton of a radus of curvature calculaton usng an arbtary set of three deflecton measurements. Fnally, the advantages and dsadvantages of usng ths eddy current mechancal devce for measurng tubecenterlne deflecton are dscussed. BACKGROUND AND ANALYSIS The prncple of the system s that eddy current effects [3], such as lft-off and edge effects, are senstve to dmensonal changes, and can thus be used to determne tube deflecton. Fgure 1 shows the ampltude response of an expermental eddy current sgnal versus deflecton angles due to the lft-off effect, and Fg. 2 shows the ampltude response due to the edge 1709
effect. Accordng to these results, the edge effect approach s more senstve and more lnear over the deflecton range of nterest. Fgure 3 shows a sketch of the mechancal measurng devce that was desgned usng the edge effect prncple. Here, c s the dstance between the sensng pont C and the pvot pont 0, b s the dstance between 0 and the frst contact pont B, and a s the dstance between B and the second contact pont A. The a10grthm dervaton and data analyss can be greatly smplfed by usng contact pont B as the effectve measurng poston. As shown n Fg. 4, the equaton for the deflecton, D(P), at an axal poston P can be expressed as D(P) D(P-b) + b tan [91(P)] (1) ' 0.6 ::J os 0.2 Sl E. -0.2 ::;) ;:j a. -0.6 :;; c( 1.0r------------------------------, Fgure 1. -1.0 L..--L.. ""---'...L.. L--L...L----'...L..--lI -10-6 -2 2 10 DEFLECTION ANGLE The eddy current ampltude response as a functon of the deflecton angle due to the lft-off effect. 1.0 :! 0.6 c ::J : 0.2 :e 0!!- w c -0.2 ::l ;:j a. :e -0.6 c( -1 10 10 Fgure 2. DEFLECTION ANGLE The eddy current ampltude response as a functon of the deflecton angle due to the edge effect. 1710
Fgure 3. a b c A B 0 C The mechancal devce desgned usng the eddy current edge effect prncple. A Fgure 4. A dagram of the sensng devce n relaton to the tube. where el(p)= e(p)+tan-1 [D(P-b)-D(P-b-a)]/a s the effectve deflecton angle at pont P, n whch e(p) = tan-l [c sn a / ( b + c cos a)] s the calculated deflecton angle at poston P wth the measured angle, a, wth respect to the pvot pont O. The deflecton angle a s converted from the eddy current sgnal, whch was obtaned wth reference to the calbraton curve, as shown n Fg. 2. The analyss algorthm can be further smplfed f the sensng pont C, the pvot pont 0, and frst contact pont B concde. In ths case, the deflecton D(P) at poston P s found to be D(P) = D[P - S (P)J + S(P) tan [el(p)] (2) where S(P) s the poston advanced at pont P by the axal delvery system, and el(p)= el[p-s(p)]+ e(p) s the effectve deflecton angle at poston P. We can obtan a two-dmensonal profle of the tube by correlatng the measurements of tube-centerlne deflecton wth ther axal coordnates. The radus of curvature (ROC) ndcates the degree of bendng. The ROC can be determned for an abtrary set of three deflecton measurements of the secton under consderaton. If X s the axal poston at pont P and D s the 1711
deflecton obtaned at pont P, the expresson for the ROC for ponts Pl(Xl,Dl), P2(X2,D2), and P3(X3,D3) can be wrtten as 2 2 2 2 2lh ROC = [X3' D2' + (X2' +D2' -X2'X3') ) /2D2' (3) where X2'.. (X2-Xl) cos a + (D2-Dl) sn a, D2' = -(!-Xl) a, X3'.. (X3-Xl) cos a + (D3-Dl) sn a, and B - tan [(D3-Dl)/(X3-Xl»). If sn a + (D2-Dl) cos the deflecton s downward, the ROC s postve. If the deflecton s upward, the ROC s negatve. The ROC s nfnte f the tube s straght. SYSTEM CONFIGURATION AND EXPERIMENTS A dagram for the deflecton measurement system s shown n Fg. 5. The system can be dvded nto three functonal segments: the devces (sensng devce and delvery devce), nstrumentaton, and analyss. The sensng devce houses the eddy current cols and follows the contour of the nner wall of the tube. The delvery/postonng devce, consstng of a motor and gear box and wheel assembles, drves the sensng devce nto the tube. As shown n Fg. 3, wheel assembles at A and B ensure that the devce mantans the proper contact wth the tube wall. Wheel assembly at C follows the profle of the tube, wth the pvot pont 0 correspondng to the degree of bendng. The hardware must be desgned to measure not only the smallest deflecton, but also negotate the largest bend that may occur n the tube beng nspected. The eddy current cols are housed n each sde of a statonary base and are confgured n a dfferental mode to average out the nherent nose. The mechancal bar cuts across dfferent col surface areas as the sensng devce follows a bend n the tube. The devce s desgned such that the sensng mechansm measures tube deflecton wthout beng nfluenced by of the tube materals. The nstrumentaton conssts of a mechancal controller and the eddy current test nstrument. The mechancal controller advances the delvery/postonng devce nto the tube and drects t to feed back postonal nformaton. The eddy current nstrument s calbrated usng the gan adjustment so that the range of the eddy current output corresponds to the range of the deflectng angles desred. The vertcal channel sgnal provdes the deflectng sgnal output. The horzontal channel sgnal s mnmzed durng operaton. The axal postonal nformaton and the eddy current voltage readng are sent to a data acquston devce (e.g., a strp-chart recorder) for data reducton and analyss. The eddy current sgnal s converted nto the true tube deflecton value usng Eq. (l). DEVICES INSTRUMENTATION ANALYSIS - TUBE CONTOUR EDDY CURRENT EDDY CURRENT FOLLOWING DEVICE SIGNAL AND INSTRUMENT f---- EDDY CURRENT AXIAL POSITION COILS... ACQUISITION I + TUBE AXIAL MECHANICAL SIGNAL/DATA POSITIONING ENCODER PROCESSING AND SYSTEM CONTROLLER PRESENTATION Fgure 5. System dagram for the measurement of tube-centerlne deflecton. 1712
Computer-smulated experments were conducted to test the algorthms appled n the analyss functon usng a set of a and b values. For these experments, we assumed an arbtrary test tube whose centerlne s shown n Fg. 6. Data sets were then obtaned from trgonometrc calculatons. A known set of ROC data was used to test the ROC algorthm. 1.0 c ;:, 0.6 :s 0.2 z 0 = 0 IlJ..J "- IlJ Q -0.2-0.6-1.0 0 100 Fgure 6. TUBE AXIAL POSITION (arbtrary unts) Results of computer-smulated experments. We also conducted laboratory experments to demonstrate the operatng concept. Eddy current and postonng sgnals were generated by a Zetec MIZ- 12 eddy current nstrument, operated at 400 khz, and output to a Gould 2400 strp-chart recorder. The angle of deflecton taken from the chart was processed on an IBM PC to calculate the true deflecton and ROC. Data acquston and sgnal analyss can be fully automated by usng a computer to control the measurng and analyzng processes. RESULTS AND DISCUSSION Results from the computer-smulated experments ndcated that the mathematcal algorthms were correct. The data obtaned wth gven sets of a and b values corresponded to those shown n Fg. 6, usng ether Eq. (1) or (2) and the calculated ROC results agreed wth known ROC data. The results of the laboratory experments are shown n Fg. 7. The sold lne shows the true deflecton along the axs of the tube, and the dashed lne shows the data obtaned from our prototype system usng the algorthms tested n the computer-smulated experments. The prototype data set s generally n good agreement wth the true data set. Dscrepances result from errors n measurements of the axal poston. As expressed n Eqs. (1) and (2), the deflecton calculaton depends not only on the axal poston, but also on prevous deflectons, so that errors are propagated durng the calculaton. 1713
2.0 1.2 g z 0.41 0 j: U 1&1... 1&1 C -0.4-1.2 Measured Tube Dellectlon -2.0 0 125 250 375 500 625 Fgure 7. TUBE AXIAL POSITION (n.). Results of laboratory experments. These errors can be mnmzed by desgnng a sensng devce that refers to unversal reference felds such as gravty and earth magnetcs. However, gravty and earth magnetcs cannot be used to measure the tube deflecton at an arbtrary orentaton. Although ths deflecton sensng system was developed prmarly for nuclear applcatons, t can be used n the ol and gas, ppng, and other ndustres. ACKNOWLEDGEMENT The author would lke to thank Dr. B. B. Djordjevc for hs valuable comments. The ntal work was performed at Combuston Engneerng, Inc., Wndsor, Connectcut. REFERENCES 1. E.J. Chern, Mat. Eval. (13), 1644 (1985). 2. P.L. Blue, Mat. Eval., (5), 100 (1974). 3. H.L. Lbby, Introducton to Electromagnetc Nondestructve Test Methods, (Robert E. Kreger Publshng, Huntngton, N.Y. 1979). 1714