Integrating Certified Lengths to Strengthen Metrology Network Uncertainty

Transcription

1 Integratng Certfed engths t Strengthen Metrlgy Netwrk Uncertanty Authrs: Jseph Calkns, PhD New Rver Knematcs je@knematcs.cm Sctt Sandwth New Rver Knematcs sctt@knematcs.cm Abstract Calbrated and traceable scale lengths add sgnfcant value t 3D metrlgy netwrks. The prmary beneft s t prvde an bserved physcal standard wth a dcumented uncertanty wthn the measurement prcess. Ths leads t an assumptn that the bject measurements are generally nt mre precse than the net dfference between the calbrated and bserved scale bar lengths. A questn ften rased s: whle the bservatns f the calbrated scale bar are traceable hw d they relate t bject measurements? A methd fr uncertanty analyss f 3D metrlgy netwrks wth traceable scale standards s presented n ths paper. The effect f usng the bservatns n standards as cnstrants vs. just reprtng ther dfferences are studed wth an expanded versn f the Unfed Spatal Metrlgy Netwrk (USMN) measurement uncertanty analyss tl. A strnger netwrk slutn results when a length standard s appled n pprtunstc cnfguratns. A three step prcess s utlned whch prduces prpagated uncertanty estmates, 3D graphcal representatn, and hardcpy reprts f the results. Ths study shws the accuracy f calbrated length measurements n a survey d nt always relate t general bject measurements. Havng a methd t characterze the measurement prcess s crtcal t understandng prcess varatn and verall measurement qualty. The gemetrc dependences between nstruments, standards, and the pnt netwrk dmnate measurement uncertanty. Understandng the dependences and then usng them t yur advantage s key t successfully prducng qualty measurement results wth relable measurement uncertantes. Intrductn 3D metrlgy system users wrk t relably scale ther measurements f bjects and mantan a traceable lnk between ther results and dmensnal standards. One aspect f the scalng prcess cmpensates fr the effects f the bjects thermal expansn r cntractn. It s requred when bjects are measured at temperatures ther than the reference temperature. Accurate traceable thermal scalng has tradtnally been dependent n measurng the bject s actual temperature and usng a gd estmate fr the bject s Ceffcent f Thermal Expansn (CTE). Whle ths s cmmnly accepted practce, t ntrduces cnsderable uncertanty nt measurement results. Integratng calbrated length standards f lke materal type can mprve measurement results and reduce 3D metrlgy measurement uncertanty. 1

2 Thermal Cmpensatn Scalng fr 3D Metrlgy When buldng r verfyng bjects a reference temperature fr the prject s defned. It s typcally 2 C (68 F.) Hwever bjects are seldm measured n the shp at the reference temperature. A thermal cmpensatn scale factr s appled t the measurements t cmpensate the actual measurements t represent bject dmensns when t s at the reference temperature. Wth measurement results at the reference temperature they are cmpared aganst nmnal cnfguratns r ther measurements f matng assembly cmpnents. The prcess gal enables analyss f assembly cmpnents (e.g., fuselages and hull sectns) measured at dfferent temperatures t be cmpared. The accuracy r mre apprprately uncertanty f the thermal scalng prcess and ts effect n the measurement result can cnsume sgnfcant prtns f part tlerances. An errr n the scale factr s cnsdered a systematc errr and therefre can be cumulatve. It s drectly prprtnal t bject sze s a small errr n the thermal cmpensatn scale s magnfed when appled t a large part. Cnfdently and accurately cmpensatng fr thermal change s an mprtant element f sund metrlgy practce. Thermal ength Cmpensatn The dmensn change nduced by temperature dfference s sgnfcant. A functn t cmpute the expected dmensnal change uses nmnal bject length, the materal s CTE, and temperature delta frm the reference. The length f the bject ( ) at temperatures ther than the reference s mdeled wth the functn belw. = (1 αδt ) where : α = = actual length at temperature = calbrated length at reference temperature CTE fr scale bar materal (ppm/ ΔT = temperature delta between reference and actual and temperature ( C) The length f a 2-meter lng alumnum bject at dfferent temperatures s shwn n the graph belw. C) 2

3 Thermal ength Cmpensatn (2 meter Alummum Scale Bar) ength (mm) Object Temperature (C) At the reference temperature the bar s 2-meters lng. At 3 C (86 F) the bar length s expected t be 2.47 mm ( nches) based n the Thermal ength Cmpensatn functn. Changng the bar s temperature by 1 C (18 F) the bar length changes.47 mm (.186 ). ength Thermal Cmpensatn Errrs The prcess and results usng the thermal cmpensatn functn are straght-frward t mplement n 3D metrlgy sftware. Understandng the surces f ptental errr n ths prcess and ther effects s sgnfcant. There are three cmpnents and ptental surces f errr n the thermal cmpensatn functn. The surces f errr nclude bject temperature delta frm the reference, a materal CTE and when usng a calbrated length standard fr cmparsn, t s publshed length uncertanty. Object temperature s typcally measured n ne r pssbly tw lcatns n the bject wth a thermcuple devce. The unt may r may nt be certfed dependng n measurement prcess cntrls. The measurements are generally dne n the surface f the bject. Gd practce suggests usng a certfed thermcuple r nfra-red temperature mntr t make the bject temperature measurements. There are several surces f temperature measurement errr n cmputng the expect length change wth thermal cmpensatn functn. Fr the delta temperature nput n the functn the cre/average temperature f the bject s needed t get accurate results. An bject s surface temperature s generally nt the same as ts cre r average temperature n shp envrnments. Surface temperatures wll typcally change faster than cre temperature. Shp envrnments generally have vertcal temperature gradents. Meanng the temperature at the flr level s nt the same at the tp f the part r tl. The 3

4 atmspherc temperature may vary by 5 C wthn 4 r 5 meters. It makes selectng the ptmal lcatn t measure an bject s average temperature dffcult t determne. Addtnal cmplcatns are apparent because the temperature gradent tends t nduce an expansn gradent n the bject beng measured. Cmpensatng fr a thermal expansn gradent acrss an bject s nt typcal n 3D metrlgy sftware. Typcal 3D metrlgy prcesses gnre ptental thermal expansn gradents. The cmmn practce s t make a sngle temperature measurement at a cnvenent lcatn n the part/tl surface and assume that t s representatve fr the entre bject. Certfcatn certfcates fr typcal shp bject temperature measurement equpment generally state ±.5 C (±1 F) uncertantes. The varably between temperature measurement unts s sgnfcant gven the amunt f dmensnal uncertanty that results when the bject temperature vary by ths amunt. Newer temperature sensrs are avalable wth certfcatns n the range f ±.4 C (reference: ScAlert specfcatn by 4G Metrlgy). Gettng an accurate estmate fr an bject s materal CTE prperty s mprtant when usng the thermal cmpensatn functn t adjust the actual measurements t the reference temperature. The publsh values fr partcular materal vary by ally and cndtn. A reprt by NIST ndcates the CTE materal prperty can vary sgnfcantly frm the publshed value. Materal prpertes references publsh average CTE values ver temperature ranges. The range f nterest fr 3D metrlgy applcatn s abut the typcal reference temperature f 2 C. Hwever the value at 2 C s seldm avalable. The average values are n general, averages ver the range -1 C, and the uncertanty f the publshed values s estmated t be 3-5 % (k = 2) ver ths temperature range. arge parts and tls are generally nt made frm a sngle materal type. Dfferent materals each wth dfferent CTE s are cmmnly measured metrlgy applcatns. Estmatng a CTE fr a structure made wth dfferent materal types can be a sgnfcant challenge. When large structures are munted r secured n the cncrete flr the cmbnatn becmes mre cmplex when usng the thermal cmpensatn functn. Certfed Scale ength Uncertanty When metrlgy labs certfy scale bars a pnt t pnt dstance s prvded. Alng wth the dstance an uncertanty statement fr the pnt t pnt dstance s prvded. The uncertanty s based n the calbratn prcess n the labratry. The measurement methd and precsn f the nstruments used t measure the dstance between the pnts are used t quantfy the certfcatn uncertanty. There are several characterstcs abut certfed scale bars that are f nterest. Specfcally the dstance between the pnts s nw a knwn quantty at the reference temperature. The scale bar materal type s als knwn. Typcally scale bars are prduced wth the same materal as the bject beng measured n the shp/factry. The uncertanty fr the dstance between these pnts s generally small when cmpared t the part tlerances. 4

5 Checkng/Cnfrmng Thermal Cmpensatn Wth measurements f bject temperature and the materal s CTE prperty, metrlgy system users scale ther measurements f bjects at shp temperatures t match the reference temperature. T check r cnfrm that the scalng prcess was accurately appled ne r mre calbrated scale bar(s) f knwn materal are measured. When the calbrated bar s made frm the same materal as the bject the scaled measurements f ts length shuld match the publshed calbratn length. Cmmn metrlgy practce enfrces the cndtn that the measured pnt t pnt dstance must match the calbrated dstance wthn ±.5 mm (.2 ). When the measurements and bar length match wthn the tlerance the measurement results pass ths acceptance crtera. The pnt t pnt measurements f the certfed bar are used t cnfrm the thermal cmpensatn functn was crrectly appled. The prcess uses the certfed bar t check the bject temperature measurement and CTE value. Prpagatn f Uncertanty The prpagatn f uncertanty characterzes the prbablty and range f values wthn whch the true value les. It s used t relably mdel the dependence f varable uncertanty n the uncertanty f the functns utput. The varables n thermal cmpensatn are bject temperature, materal CTE and the pnt t pnt dstance measurement uncertanty. The uncertanty fr a dstance can be bunded by the abslute errr f the functns utput. In ths case the effect f the nput varable uncertantes (r errrs) n the thermal cmpensatn functn are studed. Ths uncertanty mdel s lmted t the effect f thermal cmpensatn. The thermal cmpensatn functn/mdel and assumptns fr an analyss example are shwn belw. = ( 1 αδt ) f (, α, ΔT ) = Uncertanty f Example : 2 meter = 2 mm σ =.2 mm ΔT = C σ =.5 C s a functn f, σ, α, σ, ΔT, σ Alum Scale Bar frm1 T αalum = 23.8 ppm/ C σ α = 5% α An equatn fr the varance between prducts by applyng the Prpagatn f Uncertanty technque s shwn belw; t cmbnes estmates frm ndvdual measurements. α T t 4 C 5

6 Mdel : [] U f ( 1 αδt ) = f ( ) [ ] = s = ( 1 αδt ) σ + ( ΔT ) σ + ( α ) σ U = s f = = δf 2 δf 2 δf 2 σ σ α σ T δ + + δα δδt 2 α 2 T 1 A graph f the scale bar length uncertanty verse a range f bject temperatures s shwn n the chart. 2-m Alum Object ength Uncertanty (2-sgma) vs. Object Temperatures ength Uncertanty (mm) Measured Scale Bar Temperature (C) +U (mm) -U (mm) Fr ths example a 2-meter (78.74 ) alumnum scale bar certfcatn certfcate reprts an uncertanty f.254 mm (±.1 ) wth k = 2. The uncertanty f the bar when used n the shp at the reference temperature s.35 mm (.14 ). Ths number s bgger than the certfcatn certfcate due t effects f the temperature measurement uncertanty. The uncertanty grws t.42 mm (.16 ) when the delta temperature s 1 C (18 F). At a delta temperature f 2 C (36 F) the bars uncertanty grws t.59 mm (.23 ). The dfference s due t the effects f temperature measurement and CTE uncertanty. Each f the ndvdual uncertanty cmpnents s cmpared by cmputng a unt vectr at each temperature. Each cmpnent s relatve cntrbute s shwn n the scale length uncertanty cmpnents chart belw. 1 e Gdman (196). "On the Exact Varance f Prducts" n Jurnal f the Amercan Statstcal Asscatn, December, 196, pp

7 CTE Scalng Cmpnents f Unt Vectr.9.6 Cmpnent Uncertanty (Unt Vectr) Ttal Scale Uncertanty (mm) Materal Temperature (C) Base ength Uncertanty Temperature Uncertanty CTE Uncertanty Base ength Uncertanty Temperature Uncertanty CTE Uncertanty +U (mm) The chart shws that the CTE cmpnent has mnmal effect when the bject temperature s clse t the reference temperature. Hwever ts cntrbutn grws cnsderably as the bject temperature devates frm the reference. The CTE cmpnent becmes the dmnate uncertanty cntrbutr past a delta f 1 C (18 F). Cmmn metrlgy systems (e.g., aser Trackers) are able t make measurements n 2- meter lng bjects wth uncertantes that are less than the thermal cmpensatn uncertantes shwn n the charts abve. The mplcatn s usng the thermal cmpensatn functn t set the survey scale can add sgnfcant amunts f varablty t measurement results. Varablty ncreases as the bject temperature devates frm the reference. Thermal Cmpensatn Uncertanty Example When the scale factr frm thermal cmpensatn prcess s appled t larger bjects an the errr gets magnfed. The chart belw shws the thermal cmpensatn uncertanty fr a 9.78-m (32-ft) alumnum bject. At a delta temperature f 1 C (18 F) the uncertanty s.165 mm (.65 ) wth k=2. 7

8 9.78-m Alum Object ength Uncertanty due t Thermal Cmp (2-sgma) vs. Object Temperature ength Uncertanty (mm) Measured Scale Bar Temperature (C) +U (mm) -U (mm) These thermal cmpensatn uncertantes are seen n the shp flr. The varatn n measurement results are perceved as nstrument r setup repeatablty ssues. The underlyng prperty s related t precsely measurng the bject s cre temperature relatve t the reference and CTE varablty. CTE Scalng Cmpnent Uncertanty Percentle (Alumnum Object 9.74 m) Percentle f Uncertanty (%) 12% 1% 8% 6% 4% 2% % Materal Temperature (C) Base ength Uncertanty Temperature Uncertanty CTE Uncertanty Base ength Uncertanty Temperature Uncertanty CTE Uncertanty +U (mm) The calbrated scale bar length uncertanty s a small cmpnent when the measurng larger bjects. Ths result s apparent because an bject temperature measurement errr and CTE varatn are multpled nt a lnger dstance. 8

9 Slutn Better Metrlgy Practce A better chce when measurng large bjects s t use a lke-knd materal calbrated scale bar(s) t scale the measurements. A functn t cmpute a scale factr that mnmzes the dfferences between a seres f measured scale bar dstances (between the pnts and calbrated length) s straght-frward t mplement. Applng the scale factr t the nstrument results n temperature cmpensated measurement results wthut measurng the temperature r estmatng the materal s CTE. Errr prpagatn analyss shws the bject temperature measurement and CTE are sgnfcant uncertanty cntrbutrs. Calbrated bar uncertantes are generally less than half the thermal cmpensatn uncertanty n larger bjects based n the errr prpagatn mdel analyss. Reducng measurement prcess uncertanty by scalng wth calbrated scale bars has ther benefts. Scalng wth calbrated lengths ntegrates the traceable artfact nt the measurement prcess. Current practces may use a traceable length t check thermal cmpensatn results. Addng multple bar pstns enables dfferent scalng at dfferent vertcal lcatns n the bject. When measured nt dfferent grups r by dfferent nstrument statns a slutn fr lcal a scale factrs wuld allw a cnsstent methd t adjust fr thermal cmpensatn gradents. Dfferent calbrated scale bar materals surveyed nt dfferent grups r by dfferent nstrument statns means a methd t cmpensate fr dfferent thermal ceffcents f expansns wthn the same survey. Temperature measurement n the bject can be used as a check/valdatn fr the scalng wth calbrated bars. In ths case the methd wth lwer uncertanty s used t set the scale factr whle the less-precse methd s used t check t. Scale engths n USMN Scale lengths wth uncertanty estmates can effectvely be cnsdered nstruments wthn the netwrk. Pnt t pnt dstance resduals between bservatns and the calbrated dstance are added as crrectns t the netwrk durng the ptmzatn. When weghted wth ther publshed uncertanty statement they cnstran the resultng Cmpste Pnt grup wth apprprate weghts. Ths methd adds physcal traceable length(s) t the netwrk. Reprts and nstrument uncertanty analyss nclude drect cmparsn aganst these traceable standards. The USMN slutn ntegrates scale lengths as ether Reprt Only r as Cnstrants n ts ptmzatn and target uncertanty analyss prcesses. As Reprt Only the scale bar d nt add crrectns t the netwrk. The Reprt Only cnfguratn s the default setup. In a Reprt Only cnfguratn users can check r cnfrm the netwrk s present thermal cmpensatn. The fgure belw shws an example Measured Scale Bar reprt dalg when n Reprt Only mde. 9

10 Measured Scale Bar Reprt Analyss aganst Certfed engths (Reprt Only) When the USMN uses measurements f scale length as cnstrants the netwrk s adjusted alng the cmpnents t mnmze the delta between the length nputs. Each nstrument statn can be setup t allw ts scale factr t be ncluded n the netwrk ptmzatn. The fgure abve ndcates Statn 3 measurements have nt been thermal cmpensated. Nte the red utlned deltas fr statn 3 are hgher. When nstrument scale factrs are ncluded the result balances the netwrk s thermal cmpensatn durng the ptmzatn. Reprts f all the scale bar lengths shw the resultng measurement deltas aganst the traceable standards. The fgure belw shws the Measured Scale Bar reprt after the multple scale bars pstns have been used as Cnstrants n the ptmzatn. Measured Scale Bar Reprt Analyss aganst Certfed engths (Cnstrants) An example jb usng multple pstns f a certfed alumnum scale bar s shwn n the fgure belw. There were 4 tracker statns n ths survey. The bar was made f Alumnum and was 2.44 m (96-nches) n length. Temperature measurements f the bar shwed t was between 23 C and 25 C durng the measurement prcess. The bar was measured n dfferent 1 pstns. 1

11 Tw gage these effects bservatns were made n tw pnts that were 9.87-m (32 ft) apart. The uncertanty wth the thermal cmpensatn functn was at 22.5 C ±.13 mm and at 23.5 C ±.13 mm. In ths case the publshed certfed length standard was 2.44 m (96 nches) lng wth an uncertanty f ±.2 mm (.1 nches). The survey was scaled wth thermal cmpensatn functn and then scaled usng the scale bars. The 9.87 m pnt t pnt deltas were evaluated n bth cases. The net dfference between the results was.1 mm n the 9.87 m ( ±.5 n 386 ). Survey Scaled n USMN 4 statns 1 scale bar pstns Cnclusn Metrlgy systems n use n factry envrnments make accurate measurements n bjects. A challenge fr users s t relably scale thse measurements back t a reference temperature t cmpensate fr bject thermal expansn/cntractn. The Prpagatn f Uncertanty analyss shws usng the thermal cmpensatn functn t set the survey scale can add sgnfcant amunts f varablty t measurement results. The varablty ncreases as the bject temperature devates frm the reference. Scalng 3D metrlgy surveys wth the thermal cmpensatn functn usng bject temperature and CTE estmates ncreases uncertanty. Scalng the same measurement netwrks wth certfed lengths reduces measurement uncertanty and enhances traceablty reprtng. Scale bar cnstrants shuld be weghted by ther relatve publshed uncertantes n the netwrk ptmzatn. Measurement uncertanty analyss s enhanced when traceable length standards are ncluded n the analyss and subsequent reprt. Target Uncertanty Feld Analyss s mprved by ncludng traceable length standards. The cnclusn frm these results ndcates usng calbrated scale lengths as nstruments prduces better measurement results. 11

12 References 1. Gudelnes fr Evaluatng and Expressng Uncertanty f NIST Measurement Results - NIST Techncal Nte 1297, Gude t the Expressn f Uncertanty n Measurement, ISO, Frst Edtn Thedre D. Drn, Temperature and Dmensnal Measurement, NIST reprt n CTE materal prperty, NIST, Gathersburg, MD, Web Ste: 4. Calkns, Jseph, Dssertatn, 22, Quantfyng Crdnate Uncertanty Felds n Cupled Spatal Measurement Systems, etd , 5. Sandwth, S. C., Scale Artfact ength Dependence f Vdegrammetry System Uncertanty, SPIE 324-4, Nv Phllps, Eberhardt, and Parry, Gudelnes fr Expressng the Uncertanty f Measurement Results Cntanng Uncrrected Bas, Jurnal Research f NIST, Vl. 12, N. 4, July-August Wlf, P. R., Elements f Phtgrammetry, McGraw-Hll, e Gdman (196). "On the Exact Varance f Prducts" n Jurnal f the Amercan Statstcal Asscatn, December, 196, pp