PROBABILITY OF DETECTION OF FLAWS IN A GAS TURBINE ENGINE. Gary L. Burkhardt and R.E. Beissner

Transcription

1 PROBABILITY OF DETECTION OF FLAWS IN A GAS TURBINE ENGINE COMPONENT USING ELECTRIC CURRENT PERTURBATION Gary L. Burkhardt and R.E. Beissner Suthwest Research Institute 6220 CUlebra Rad San Antni, Texas INTRODUCTION In an explratry develpment prgram, the Electric CUrrent Perturbatin (ECP) methd was ptimized fr inspectin f typical F-100 gas turbine engine cmpnents (disks and seals).1,2 A primary bjective was t achieve high reliability fr the detectin f flaws (fatigue cracks) at the retirement-fr-cause (RFC) target flaw size f in. lng x in. deep. prbability f detectin (POD) data fr surface flaws in blade slts f an F-100 first stage fan disk were estimated frm experimentally determined prbability density functins (PDF's) fr backgrund and flaw signals. The POD as a functin f flaw size was estimated frm these data. EXPERIMENTAL SETUP Experimental data fr calculatin f POD were btained frm blade slts in an F-100 first stage fan disk. Factrs cnsidered in the selectin f blade slts included the availability f a statistically significant number f blade slts frm which backgrund signals culd be btained, as well as "wrst-case" inspectin cnditins due t backgrund nise frm the Ti material and peened surfaces. A cmputer-cntrlled, labratry breadbard scanning system was used t btain the ECP data. Figure 1 shws the F-100 first stage fan disk (Ti ) psitined in the scanning system. The ECP prbe was munted n an air bearing which allwed the prbe t be scanned withut physical cntact with the specimen surface and at a cntrlled liftff. The blade slt cnfiguratin and scan directin are shwn, schematically, in Figure 2. The flaws were lcated at the tangency pint f the in. radius, apprximately 0.50 in. frm the edge f the blade slt. Since equivalent ECP signals are btained frm fatigue cracks and EDM slts f the same size3, half-penny shaped EDM slts were used t simulate fatigue cracks. Dimensins f the tw EDM slts were in. lng x in. deep and in. lng x in. deep. 333

2 334 G. L. BURKHARDT AND R. E. BEISSNER Fig. 1. ECP labratry breadbard scanning system with F-100 first stage fan disk in place n. SCAN TRACK SPACING "::. SURFACE FLAW (at Rdn Tangency PInt) Fig. 2. Scan cnfiguratin fr blade slts. STATISTICAL ANALYSIS OF FLAW DETECTION Despite all effrts t insure repeatability, experimental measurements f flaw signal amplitudes are never exactly the same, in the strict mathematical sense, ver a set f repeated scans f the same flaw. Instead, the signal amplitudes thus btained frm a distributin f values ranging frm a minimum t a maximum and having sme mean, r average, value. If ne were t calculate the number f times a given amplitude was bserved divided by the ttal number f scans, and then plt the resulting data as a functin f signal amplitude, the curve btained wuld be the prbability density functin fr signal amplitudes frm that particular flaw size. A similar prbability density functin fr nise r backgrund signals can be defined in much the same way. Tw such prbability density functins, ne fr the flaw signal and the ther fr nise, are shwn schematically in Figure 3.

3 FLAWS IN AN ENGINE COMPONENT 335 z w c... c II: A. BACKGROUND SIGNAL DISTRIBUTION FLAW SIGNAL DISTRIBUTION PROBABILITY OF FALSE ALARM ECP SIGNAL AMPLITUDE Fig. 3. Schematic illustratin f prbability density functins fr signals and backgrund nise. In an inspectin situatin ne wuld hpe that the prbability density functin (PDF) fr flaw signals wuld lie well t the right (in the sense f Figure 3) f the PDF fr nise, s that a given signal amplitude culd be unambiguusly interpreted as either a flaw signal r nise. In such an ideal case all flaws wuld be detected and there wuld be n false alarms frm backgrund signals that appear t indicate the presence f a flaw. In practice this ideal situatin is realized nly fr very large flaws in the presence f very weak nise signals. Usually the PDF's fr flaw signals and nise verlap t sme extent, as indicated in Figure 3. It is the extent f verlap, r, mre precisely, the areas under the PDF curves in the verlap regin, that determine the reliability f the inspectin methd. This is because what ne usually des in a situatin where signal and nise PDF's verlap t a significant extent is decide, first f all, hw ften ne can tlerate false indicatins f the presence f a flaw. This decisin determines a threshld value fr signal amplitude, belw which signals will be interpreted as nise and abve which signals will be interpreted as flaw indicatins. The area under the nise PDF t the right f the threshld value is then the prbability that backgrund nise will give a false indicatin f the presence f a flaw. At the same time the chice f a threshld value als determines the prbability f flaw detectin, because the area under the flaw signal PDF t the right f the threshld is the prbability f detectin. It als determines the prbability that flaws will be missed, which is equal t the area under the signal PDF t the left f the threshld. Thus the extent f verlap f the flaw signal and nise PDF's, and the chice f a threshld amplitude fr flaw detectin, play a critical rle in determining the reliability f an NDE methd. SIGNAL AND NOISE DATA FOR BLADE SLOTS Fr the purpse f this analysis, signal and nise amplitudes are defined as peak-t-peak vltages as indicated in Figure 4. Flaw signal data was btained by recrding the amplitudes measured in 30 repeated

4 336 G. L. BURKHARDT AND R. E. BEISSNER scans directly ver the in. X in. flaw. The resulting PDF is shwn as a histgram n the right side f Figure 5. The smth curve is a Gaussian fit t the PDF determined frm the mean and standard deviatin f the data. Nise data were btained frm single scans in unflawed regins in each f 30 blade slts in the disk. The amplitude recrded fr each scan was the maximum nise signal bserved in a 1.0 in. scan length. The PDF resulting frm these data is shwn n the left side f Figure 5. Due t the relatively rugh, peened blade slt surface, the backgrund signals are larger than might be expected frm ther engine parts*, and the nise PDF is therefre shifted clser t the flaw signal PDF. Fig. 4. Definitin f flaw and backgrund signal amplitudes. The distributins shwn in Figure 5 represent the best pssible flaw detectin situatin because signal data were btained frm scans directly ver the flaw where the amplitude is greatest. In a practical situatin, f curse, ne des nt even knw if flaws exist, much less their exact lcatins. What is dne, therefre, is t scan the piece in a raster-like fashin, as in Figure 2, with the distance between scan tracks determined frm statistical data t give an acceptable prbability f detectin and false alarm rate. Under such cnditins the scan track-t-flaw distance can be assumed t be equally likely t be any distance frm zer (directly ver the flaw) t ne-half the spacing between scan tracks. *Althugh the surces f the backgrund signals are nt fully understd, a limited investigatin indicates that a higher backgrund is btained frm parts with peened surfaces than frm thse with smther surfaces. 2

5 FLAWS IN AN ENGINE COMPONENT FLAW SIGNAL DISTRIBUTION (0.0105In. X OOOS.ln.) > 0.35 I- W C 0.30 > 0.25 I- :::i 0.20 <I: I: G 0.10 BACKGROUND SIGNAL DISTRIBUTION ECP SIGNAL AMPLITUDE (mv) Fig. 5. Signal and backgrund prbability density functins fr blade slts. TO btain data representative f a practical inspectin prcedure, additinal flaw signal data were btained fr scan tracks displaced in in. increments frm 0.0 in. t in., each repeated 10 times. Data frm the displaced scans (0.001 in. t in.) were given twice the weight f data frm scans directly ver the flaw t accunt fr the fact that in an actual inspectin the flaw is equally likely t be n either side f the scan track. The full set f data thus apprximates the distributin f signal amplitudes btained frm an inspectin 1n which scan tracks are in. apart, because the flaw lcatin, which is equally likely t be anywhere in the scan pattern, can then be n mre than in. frm a scan track. The full set f data therefre determines a PDF crrespnding t an inspectin prcedure in which scan tracks are spaced in. apart. This PDF is shwn as a histgram in Figure 6, alng with the crrespnding Gaussian fit ' w c :::i 010 <I: I: G 0.05 FLAW SIE: In. x In ECP SIGNAL AMPLITUDE (mv) Fig. 6. Flaw signal prbability density functin fr a in. x in. flaw with in. scan track spacing.

6 338 G. L. BURKHARDT AND R. E. BEISSNER Mean signal amplitudes are pltted as a functin f distance frm the flaw in Figure 7. Frm this plt it can be seen that the signal amplitude decreases nly 10% ver distances frm 0.0 t in. frm the flaw. Thus, if scan tracks were taken t be in. apart, ne wuld expect the crrespnding PDF t clsely apprximate the ideal PDF btained frm scans directly ver the flaw. Fr this reasn a secnd PDF, based n the 5 scan tracks (each repeated 10 times) frm 0.0 t in. frm the flaw, was als generated. The result is shwn in Figure "ii ' - - J G. 0.02e s! UI M 0022 ::Ii FLAW SIE: In In POSITION FROM FLAW CENTERLINE (In.) Fig. 7. Mean signal amplitude fr a in. x in. flaw as a functin f flaw-t-scan track spacing. CALCULATIONS OF PROBABILITY OF DETECTION The PDF's shwn in Figures 6 and 8 crrespnd t tw different inspectin prcedures but nly ne flaw size. T extend the analysis t ther flaw sizes, the fllwing apprximatins were intrduced: (1) The standard deviatin is independent f flaw size. This means that the shape f the PDF is assumed t be the same regardless f the size f the flaw. (2) The mean signal amplitude is prprtinal t flaw area. This apprximatin shifts the PDF t the left r right by an amunt prprtinal t the area f the face f the flaw; it is based n a linear amplitude-area scaling relatinship which has been cnfirmed previusly.2,4 030 D 25 ffi 020 Q C a:i 0.10 f 005 FLAW SIE ECP SIGNAL AMPLITUDE (mv) Fig. 8. Flaw signal prbability density functin fr a in. x in. flaw with in. scan track spacing.

7 FLAWS IN AN ENGINE COMPONENT 339 Fr the calculatin f prbabilities f detectin, false alarm prbabilities f 10-6, 10-5, 10-4 and 10-3 were chsen as representative f the values ne might chse fr a blade slt inspectin. These numbers were then used t determine the fur crrespnding threshld amplitudes frm the nise PDF shwn in Figure 5. Prbabilities f detectin were then calculated as previusly described fr flaw lengths ranging frm in. t in. fr flaw signal PDF's crrespnding t bth the and in. scan track spacings. Because all detectin prbabilities were very clse t 1.0 fr in. flaws, there was n need t extend the analysis t larger flaws. 100 i= e () w tii 60 C If PROBABILITY OF FALSE ALARM 10 ' <t L e :L<a-<'':...Al''--C--::-,-L-::-----:0'""'.0:'-1-: :0-''.012 FLAW LENGTH (IN.) Fig. 9. prbability f detectin detail fr in. scan track spacing. Open symbls are based n the apprximatin discussed in the text: slid symbls are based n actual experimental data. I:;. 10 T simplify the cmputatins, Gaussian fits t the PDF's were used instead f actual PDF data fr mst f the estimates f prbability f detectin. As a check n the validity f this apprximatin, additinal calculatins were perfrmed fr the x in. flaw using the actual, experimentally determined PDF data. The results fr bth and in. scan track spacings are shwn in Figures 9 and 10, which are plts f all calculated prbabilities f detectin based n the Gaussian apprximatin, as a functin f flaw size. Data btained directly frm the PDF histgrams are als shwn in these figures.

8 340 G. L. BURKHARDT AND R. E. BEISSNER! 100 i= 80 U w I > 40 I :::; 20 <I: O L Q. FLAW LENGTH (in.) Fig. 10. prbability f detectin detail fr in. scan track spacing. Open symbls are based n the apprximatin discussed in the text; slid symbls are based n actual experimental data. The very sharp rise in the prbability f detectin data pltted in Figures 9 and 10 means that virtually all flaws with areas slightly greater than that f x in. target flaw size will be detected with either the t the in. scan spacing. Fr flaw lengths in the t in. range, Figures 9 and 10 shw the sensitivity f the prbability f detectin t the chice f false alarm prbability and, cmparing the tw figures, t the chice f scan track spacing. These figures als shw that the use f the Gaussian apprximatin t PDF's, which was largely a matter f cnvenience, tends t give detectin prbabilities that are smewhat greater than ne wuld btain frm experimentally determined PDF data. Althugh differences are significant, it was decided that the data set was t limited t warrant further study. Thus, these data shuld be regarded as preliminary estimates, with the differences between prbabilities f detectin as calculated frm actual PDF data and Gaussian fits t the data giving sme indicatin f the uncertainty in the estimates. Clearly, much mre data are needed fr a mre accurate assessment f prbability f detectin. In spite f such uncertainties, the high POD values btained frm the study are very encuraging (see Figures 9 and 10). It is particularly gratifying t nte that the experiments were perfrmed under what was cnsidered t be a "wrst case" cnditin in which backgrund nise frm the rather rugh blade s l surface t is greater than might be expected with ther engine cmpnents. It is clear that much better detectability can be achieved in cmpnents with backgrund nise lwer than that f these blade slts.

9 FLAWS IN AN ENGINE COMPONENT 341 CONCLUSIONS 1. Depending n the scan track spacing, the POD is apprximately 100% fr flaw lengths f abut in. t in. 2. A higher POD fr smaller flaws wuld be btained in parts with backgrund nise lwer than btained in the F-100 first stage fan disk blade slts. ACKNOWLEDGMENTS The authrs wish t thank Mr. Flyd Balter fr fabricatin f ECP prbes and Mr. Thmas Dss fr assistance with data acquisitin. Supprt f this wrk was prvided by the Air Frce Wright Aernautical Labratries, Materials Labratry. REFERENCES 1. Gary L. Burkhardt, Felix N. Kusenberger, and R.E. Beissner, "Electric CUrrent Perturbatin Inspectin f Selected Retirementfr-Cause Turbine Engine COmpnents," Review f Prgress in Quantitative Nndestructive Evaluatin, 3B, Dnald O. Thmpsn and Dale E. Chimenti, Eds., Plenum Publishing COrp., pp , R.E. Beissner, Gary L. Burkhardt, and Felix N. Kusenberger, "EXplratry Develpment n Advanced SUrface Flaw Detectin Methds, Final Reprt, COntract N. F C-5020, Air Frce Systems Cmmand, June C.M. Teller and Gary L. Burkhardt, "Applicatin f the Electric CUrrent Perturbatin Methd t the Detectin f Fatigue Cracks in a Cmplex Gemetry Titanium Part," Review f Prgress in Quantitative Nndestructive Evaluatin, 2B, Dnald O. Thmpsn and Dale E. Chimenti, Eds., Plenum Publishing COrp., pp , R.E. Beissner, M.J. Sablik, and C.M. Teller, "Electric CUrrent Perturbatin calculatins fr Half-penny Cracks," Review f Prgress in Quantative Nndestructive Evaluatin, 2B, Dnald O. Thmpsn and Dale E. Chimenti, Eds., Plenum Publishing Crp., pp