Testing of a Magnetically Levitated Rocket Thrust Measurement System Demonstrator for NASA

Transcription

1 Testng f a Magnetcally Levtated Rcket Thrust Measurement System Demnstratr fr NASA Erc J. Blumber Thess submtted t the Faculty f the Vrgna Plytechnc Insttute and State Unversty n partal fulfllment f the requrements fr the degree f Master f Scence n Mechancal Engneerng Dr. Mary Kasarda, Charman Dr. Grdn Krk Dr. Al Wcks June 13, 00 Blacksburg, VA Keywrds: Frce Measurement, Actve Magnetc Bearngs, Thrust Measurement System Cpyrght 00, Erc Jseph Blumber

2 Testng f a Magnetcally Levtated Rcket Thrust Measurement System Demnstratr fr NASA Erc J. Blumber (ABSTRACT) Exstng thrust measurement systems (TMSs) at NASA Stenns Space Center use stran gauges and flux plates t measure frces prduced by a test artcle. Algnment and calbratn can take tw weeks r mre every tme a pece f hardware r test artcle s changed. Crss axs ladng s als prblematc because t s mpssble t perfectly algn the flex plates and stran gauges n the thrust drectn. In respnse t these prblems, a magnetcally levtated thrust measurement system has been prpsed and a 300lb capacty demnstratr has been desgned and bult. In ths desgn, the magnetc bearngs wrk cncurrently as supprt bearngs and frce measurement devces. The demnstratr cnssts f a flatng frame that s cmpletely levtated wthn a fxed frame by fur supprt bearngs carryng lads n the x- and y-drectn and seven thrust bearngs carryng lads n the z- r thrust drectn. Je Imlach f Imlach Cnsultng Engneerng desgned the demnstratr and magnetc bearng cmpnents, whle Vrgna Tech s rle has been the applcatn f the multpnt calbratn technque ncludng cde develpment, the mplementatn f a 18-channel data acqustn system, and the verall test verfcatn f the TMS demnstratr. A turnbuckle assembly and magnetstrctve actuatr are used n seres wth a cnventnal lad cell fr statc and dynamc testng, respectvely. Bth current based and flux based frce equatns were used t measure the reactn frces at the bearngs. The statc results usng the current based equatns ncludng the current based frngng equatns resulted n accuraces f 93% f full lad, whle the statc results usng the flux based equatns ncludng the flux based frngng equatns resulted n accuraces f 99.5% f full lad. These accuraces can be cmpared t accuraces f 83-90% seen n prevus wrk usng magnetc bearngs t measure frces by mntrng currents and t accuraces f abut 99% n prevus wrk usng magnetc bearngs t measure frces by mntrng fluxes. All f the mprved accuraces were made pssble thrugh the

3 mplementatn f a calbratn technque knwn as the multpnt methd and the mplementatn f a gap dependent frngng crrectn factr develped by Je Imlach. The demnstratr was nt utftted wth accelermeters s the nerta f the flatng frame culd nt be accunted fr, lmtng the scpe f dynamc testng. Hwever, the tests cnfrmed the ablty f the demnstratr t measure dynamc lads n general.

4 ACKNOWLEDGEMENTS Frst, I wuld lke t thank my advsr, Mary Kasarda, fr chsng me t wrk wth her n ths prject. I greatly value the freedm she gave me t wrk at my wn pace and the trust that she had n me t get the wrk dne. Just n case I dd get stuck, she always made sure I had a way t cntact her. I feel as thugh I am much mre prepared fr the wrkng wrld because f my pprtunty t wrk wth her. The next persn I wuld lke t recgnze s Je Imlach. Wthut hs plannng, hard wrk, and patence wth me, ths prject wuld nt have been pssble. He dd an utstandng jb desgnng the test rg and wrkng ut the snags alng the way. I wuld lke t thank hm fr hs nsghts and help n the near daly phne calls t Alaska that allwed me t fnsh n tme. I wuld als lke t thank my cmmttee members fr ther help alng the way. I had the prvlege f takng curses frm bth Dr. Wcks and Dr. Krk. Dr. Krk always used real wrld anecdtes t help emphasze pnts he wanted t make. Dr. Wcks made the class entertanng as well as humrus whle stll managng t teach the nfrmatn. Bth f them really helped t make my educatnal experence at Vrgna Tech the best t culd be. I als need t thank all the guys frm the lab. I always lked frward t ur hang ut tmes bth durng lunch and utsde the ffce. Travs Bash was always wllng t help ut n any way pssble. It always amazed me hw busy he was yet culd stll carve ut tme fr me. I culd always cunt n Erc Stasunas fr ff-the-wall humr and the latest mve crtque. Rb Prns helped me bth wth the test rg and n preparng me fr the real wrld. I greatly valued hs advce t me abut jbs, presentatns, and wrkng wth thers. He became nt nly an ffcemate, but als a gd frend. I wll mss the racquetball and tenns games we used t play. v

5 I cannt leave ut my parents, Je and Dane Blumber, wh have been s supprtve f everythng I have dne. I am very lucky t have such lvng and carng parents. I am mst grateful t them fr rasng me n a Chrstan hme and shwng me what t means t be a fllwer f Gd. I wuld lke t acknwledge the Natnal Aernautcs and Space Admnstratn (NASA) fr supprtng the wrk presented n ths paper under Cntract N. NAS I wuld als lke t acknwledge NASA Stenns Space Center fr ther supprt n ths prject. Last but certanly nt least I wuld lke t thank Chelsea McRaven. She s truly my ther half because we help t balance ne anther s extremes. Her heart fr thers mpresses me as well as her desre t serve Gd. I am s grateful fr her lve and supprt ver the years, and I lk frward t many mre years tgether. Blacksburg, VA June, 00 Erc J. Blumber v

6 TABLE OF CONTENTS Abstract... Acknwledgements... v Lst f Fgures... x Lst f Tables...x Nmenclature...x 1 Intrductn and Lterature Revew General Overvew Mtvatn fr Magnetcally Levtated Rcket TMS Lterature Revew... 5 Develpment f Frce Equatns Intrductn Flux Based Frce Equatns Current Based Frce Equatns Expermental Descrptn Overvew f TMS Demnstratr Data Acqustn System Data Acqustn Hardware Data Acqustn Sftware Statc Frce Acqustn Setup Prcedure Statc Frce Acqustn Prcedure Dynamc Frce Acqustn Setup Prcedure Dynamc Frce Acqustn Prcedure v

7 4 Calbratn Prcedure Intrductn The Multpnt Methd Usng the Multpnt Algrthm as a Calbratn Prcedure Calbratn Prcedure fr the TMS Demnstratr Setup Prcedure Calbratn Prcedure Thermal Testng Intrductn Prcedure Thermal Testng Results and Cnclusns Statc Frce Testng Intrductn Vertcal Weght Results and Cnclusns Axal Ladng Results and Cnclusns Dynamc Frce Testng Intrductn Dynamc Results and Cnclusns fr Orgnal System Dynamc Results and Cnclusns fr Stffer System Summary f Results and Recmmendatns Overvew f Wrk Cmpleted Summary f Results Recmmendatns fr Future Wrk References v

8 Appendx A Scale Drawngs fr TMS Demnstratr A.1 Frnt Vew A. Rear Vew A.3 Tp Vew f Tp Bearngs A.4Tp Vew f Bttm Bearngs Appendx B Uncertanty Analyss B.1 Intrductn B. Uncertanty Analyss fr Current Based Frce Equatns B.3 Uncertanty Analyss fr Flux Based Frce Equatns Appendx C FFT Analyss f Dynamc Data C.1 FFT Analyss fr Data frm Orgnal System C. FFT Analyss fr Data frm Stffer System v

9 LIST OF FIGURES Number Ttle Page 1.1 Requred cmpnents fr magnetc levtatn 1. Schematc f duble-actng AMB cnfguratn.1 Schematc f hrseshe electrmagnet and target 15. Schematc f a duble-actng magnetc bearng 17.3 Dagram f leakage lsses n a magnetc bearng 18.4 Dagram f frngng lsses n a magnetc bearng 18.5 Schematc f ferrmagnetc trd wth a cncentrated wndng Schematc f TMS Demnstratr 6 3. Pcture f TMS Demnstratr Schematc f Supprt Bearng (schematc prvded by Je Imlach) Schematc f Thrust Bearng (schematc prvded by Je Imlach) Supprt Bearng and Thrust Bearng Sample LabVIEW 6.1 Frnt Panel Sample LabVIEW 6.1 Blck Dagram Flwchart f three man grups f prgrams Turnbuckle Assembly fr Statc Testng Frnt Panel f FORCE MEASURE VI Magnetstrctve Actuatr Assembly fr Dynamc Testng Schematc f duble-actng sngle axs magnetc bearng Typcal B-H curve fr magnetc materal (Plnus, 1978) Flux Versus Temperature fr Bth Actuatrs f Bearng 3_ Current Versus Temperature Plts fr Bth Actuatrs f Bearng 3_ Pstn Versus Temperature Plts fr Bth Actuatrs f Bearng 3_ 60 x

10 LIST OF FIGURES Number Ttle Page 5.4 Flux Versus Temperature fr Bth Actuatrs f Bearng 37_ Current Versus Temperature Plts fr Bth Actuatrs f Bearng 37_ Pstn Versus Temperature Plts fr Bth Actuatrs f Bearng 37_ Least Squares Curve Fts fr Bth Axes f Bearng 3_ Flux Based Statc Results fr Pstve Pull wth Turnbuckle and Sx Thrust Bearngs Energzed Current Based Statc Results fr Pstve Pull wth Turnbuckle and Sx Thrust Bearngs Energzed Flux Based Statc Results fr Pstve Pull wth Turnbuckle and Fur Thrust Bearngs Energzed Current Based Statc Results fr Pstve Pull wth Turnbuckle and Fur Thrust Bearngs Energzed Flux Based Statc Results fr Negatve Pull wth Turnbuckle and Sx Thrust Bearngs Energzed Current Based Statc Results fr Negatve Pull wth Turnbuckle and Sx Thrust Bearngs Energzed Flux Based Statc Results fr Negatve Pull wth Turnbuckle and Fur Thrust Bearngs Energzed Current Based Statc Results fr Negatve Pull wth Turnbuckle and Fur Thrust Bearngs Energzed Typcal Plt f Calculated Axal Lad Versus Lad Cell Measurement Dynamc Results fr Input Frequency f 5Hz fr Orgnal System Dynamc Results fr Input Frequency f 10Hz fr Orgnal System Dynamc Results fr Input Frequency f 0Hz fr Orgnal System Dynamc Results fr Input Frequency f 30Hz fr Orgnal System Dynamc Results fr Input Frequency f 50Hz fr Orgnal System Tme Respnse wth Swept Sne Input fr Orgnal System 85 x

11 LIST OF FIGURES Number Ttle Page 7.7 Tme Respnse fr Lad Cell wth Swept Sne Input fr Orgnal System Dynamc Results fr Input Frequency f 5Hz fr Stffer System Dynamc Results fr Input Frequency f 10Hz fr Stffer System Dynamc Results fr Input Frequency f 0Hz fr Stffer System Dynamc Results fr Input Frequency f 30Hz fr Stffer System Dynamc Results fr Input Frequency f 50Hz fr Stffer System Tme Respnse wth Swept Sne Input fr Stffer System Tme Respnse fr Lad Cell wth Swept Sne Input fr Stffer System 94 x

12 LIST OF TABLES Number Ttle Page 3.1 Summary f Natnal Instruments Cmpnents Summary f PVF Cntrller Fles Used n the AUTOCAL VI Percent Errr Full Lad Results frm Indvdual Thrust Bearngs Summary f Quadratc Least Squares Ft n Flux and Temperature Data Estmatn f the Weght f the Flatng Frame Cmparsn f Axally Unladed Summed Flux and Current Based Y-Drectn Frces wth Estmated Flatng Frame Weght Summary f Prprtnal Gans Used fr Orgnal and Stffer Systems 88 x

13 NOMENCLATURE Symbl Metrc Unts Descrptn A m Crss Sectnal Area A t m Crss Sectnal Area f Trd A - Current Based MFEA Cnstant A b - Flux Based MFEA Cnstant A g m Ar Gap Area B T Magnetc Flux Densty B 1 T Tp Magnetc Flux Densty B max T Maxmum Flux Densty B mn T Mnmum Flux Densty B T Bttm Magnetc Flux Densty F N Frce F 1 N Frce Due t Tp Actuatr F N Frce Due t Bttm Actuatr F b N Flux Based Frce F est N Estmated Weght f the Flatng Frame F flux/current N Sum f the Y-drectn frces fr Flux r Current Based Methds F N Current Based Frce F LC N Frce Measured frm Lad Cell F net N Net Frce F result N Resultant Frce F DCx N Unladed Frce n the X-drectn F DCy N Unladed Frce n the Y-drectn F DCz N Unladed Frce n the Z-drectn F x N Frce n the X-drectn F y N Frce n the Y-drectn F z N Frce n the Z-drectn ff 1 - Tp Frngng Factr x

14 NOMENCLATURE Symbl Metrc Unts Descrptn ff - Bttm Frngng Factr g m Ar Gap Length g 1 m Tp Ar Gap g m Bttm Ar Gap g m Nmnal Ar Gap g 1 m Nmnal Ar Gap f Outer Legs g m Nmnal Ar Gap f Center Leg H A/m Magnetc Feld Strength I A Current I 1 A Tp Current I A Bttm Current K b - Flux Based MFEA Cnstant K - Current Based MFEA Cnstant L m Mean Irn Path Length l m Length m - Cuntng Varable N - Number f Cls, als Number f Energzed Thrust Bearngs R A/Wb Magnetc Reluctance R g A/Wb Magnetc Reluctance Thrugh Ar Gap R A/Wb Magnetc Reluctance Thrugh Irn V m 3 Vlume V DCLC V Unladed Vltage Measured frm Lad Cell V LC V Vltage Measured frm Lad Cell W - Flux Based MFEA Cnstant W mag J Magnetc Energy W mech J Mechancal Energy W 1 - Current Based MFEA Cnstant xv

15 NOMENCLATURE Symbl Metrc Unts Descrptn W - Current Based MFEA Cnstant W 3 - Current Based MFEA Cnstant W 4 - Current Based MFEA Cnstant x m Target Pstn x ptp m Abslute Target Pstn Predcted by Calbratn α b - Flux Based MFEA Cnstant α - Current Based MFEA Cnstant φ Wb Magnetc Flux φ g Wb Magnetc Flux Thrugh Ar Gap φ Wb Magnetc Flux Thrugh Irn Σ - Standard Devatn Matrx σ - Standard Devatn µ 0 Wb/A-m (N/A ) Magnetc Permeablty f Free Space µ Wb/A-m (N/A ) Magnetc Permeablty f Irn µ r - Relatve Magnetc Permeablty xv

16 Chapter 1 Intrductn and Lterature Revew 1.1 General Overvew Actve magnetc bearngs (AMBs) are electrmechancal devces that use a feedback cntrl system t keep a rtr, r target, levtated at a fxed pstn n a magnetc feld. Because there s n cntact between the electrmagnetc actuatr and the target and because f the feedback nature f AMBs, many new uses and applcatns that are mpssble wth cnventnal bearngs are beng develped. Ths thess dscusses the use f magnetc bearngs n a magnetcally levtated rcket Thrust Measurement System (TMS) fr NASA. The magnetc bearngs are used as bth supprt bearngs t levtate the test artcle as well as sensrs t measure the frces prduced by the test artcle. The gal f ths prject s t demnstrate the use f magnetc bearngs n a TMS prttype by calculatng accurate frces generated by a smulated test artcle n the TMS. A calbratn prcess knwn as the multpnt methd as well as equatns t accunt fr frngng lsses are ntrduced t measure appled frces wthn 0.5% errr full lad. There are fur man cmpnents requred by AMBs as shwn n Fgure 1.1. The fur man cmpnents are the actuatr, the rtr, the pstn sensr, and the cntrller and pwer amplfer. If the AMB s nt used n a rtatng applcatn, as s the case fr the rcket TMS, the rtr s called a target nstead because there are n rtatng parts. The AMB wrks by measurng the pstn f the target usng the pstn sensr and cmparng t t a predetermned desred lcatn set by the cntrller. The cntrller then adjusts the current thrugh the cl f the actuatr t keep the target levtated. The Intrductn and Lterature Revew 1

17 cl currents are adjusted thusands f tmes per secnd by the cntrller t keep the target accurately lcated n the desred pstn. Fgure 1.1: Requred cmpnents fr magnetc levtatn The mst cmmn arrangement fr AMBs s the duble-actng cnfguratn n whch there are tw electrmagnetc actuatrs arranged n ppsng drectns wth a target lcated between them. A schematc s shwn n Fgure 1.. Fr ths cnfguratn, Fgure 1.: Schematc f duble-actng AMB cnfguratn Intrductn and Lterature Revew

18 the pstn f the target s measured by the pstn sensr. The cntrller then adjusts bth the tp and bttm cl currents t mantan a predetermned fxed target pstn accurately. Fr nstance, f the pstn sensr measures that the target s t clse t the tp actuatr, the cntrller wll ncrease the current n the bttm cl and decrease the current n the tp cl t mve the target dwnward. The frce prduced by each magnetc actuatr n the target s prprtnal t the magnetc flux thrugh the ar gap between that actuatr and the target. Because flux sensrs are needed t measure the flux n the ar gap, t s ften desrable t calculate frces usng cl currents are ar gaps nstead. The general equatn relatng magnetc flux densty, B, t cl current, I, and ar gap, g, s shw n Equatn 1.1. µ NI B = (1.1) g In ths equatn, µ s the permeablty f free space and N s the number f turns n the cl. Due t the feedback system f the AMB, the cl currents and relatve target pstns are easly accessble frm the cntrller. The cl currents and ar gaps can then be used t nfer the magnetc flux thrugh the ar gaps. Therefre, gven ether the magnetc flux thrugh the ar gaps r the cls currents and physcal target pstn, the frces exerted by the actuatr n the target can be calculated. The equatns used fr frce calculatns wll be dscussed n mre detal n Chapter. 1. Mtvatn fr Magnetcally Levtated Rcket TMS Current rcket TMSs utlze stran gauges t measure thrust and ff-axs lads. Exstng test stands cnsst f a flatng frame n whch the test artcle s rgdly munted t a fxed frame va flex plates and data clumns. The data clumns and flex plates whch cnnect the flatng frame t the fxed frame must be algned and calbrated t accurately measure the frces exerted by the test artcle, r rcket engne. Intrductn and Lterature Revew 3

19 There are several weaknesses t ths desgn that can be slved usng a TMS wth actve magnetc bearngs. The frst s the amunt f tme needed fr calbratn and algnment f the flex plates and data clumns. The calbratn prcess alne currently takes upwards f tw weeks t perfrm and must be repeated every tme a new test artcle r pece f hardware s mplemented. Even after the test stand s calbrated, crss-axs frces can be supprted by the flex plates and data clumns because t s mpssble t acheve a perfect algnment. Wth a TMS ftted wth magnetc bearngs, the flex plates and data clumns are replaced by magnetc bearngs. In ths case, the flatng frame s cmpletely levtated n a magnetc feld s there s n cntact between the flatng and fxed frames. Fr a TMS usng magnetc bearngs, a calbratn prcess knwn as the multpnt methd can be perfrmed n the test stand. The multpnt methd calbratn technque determnes the physcal ar gaps fr all f the magnetc bearngs fr use n the frce equatns. Ths calbratn nly takes a cuple f hurs cmpared t a cuple f weeks fr cnventnal TMS setups. The calbratn prcess fr the TMS demnstratr s dscussed n mre detal n Chapter 4. Als, because the flatng frame s cmpletely slated frm the fxed frame and the targets have been verszed t mnmze crss-axs frces, algnment s n lnger prblematc. After the calbratn prcess s cmplete, the statc lads can be calculated and subtracted ut f subsequent frce measurements f desred. Anther ssue wth current thrust stands s the lmted thrust ranges that can be measured by a sngle stand. Current thrust stands cannt handle a large range f thrust lads whle keepng the accuracy needed fr a TMS. Therefre, multple thrust stands are needed t accurately measure frces fr rckets wth varus thrust utputs. The magnetcally levtated rcket TMS, hwever, can measure frces ver a range f mre than ten tmes the mnmum lad wthut a lss n accuracy. Ths s due t the fact that the magnetc bearngs that supprt frces n the thrust drectn, als knwn as thrust bearngs, are munted n parallel s dfferent numbers f thrust bearngs can be turned n r ff t cver a wder range f thrust lads. Intrductn and Lterature Revew 4

20 One fnal advantage f a magnetcally levtated rcket TMS ver cnventnal TMSs utlzng stran gauges s the ablty t mdfy the frequency respnse f the TMS usng the gan parameters f the magnetc bearngs. Because cnventnal TMSs utlze flex plates and data clumns, the dynamcs f the system are fxed nce the test stand has been assembled. Hwever, wth the magnetc bearng desgn, the dynamcs f the TMS can be changed nce the test stand s bult smply by varyng the gan parameters f the magnetc bearngs. Ths s helpful because the dynamcs f the TMS system are als a factr f the test artcle. A heaver test artcle may reduce the resnant frequency f the TMS enugh that t falls wthn the frequency range f frce measurements. In the case f cnventnal TMSs, the test stand wuld need t be redesgned; hwever, n the case f the magnetcally levtated TMS, the gan parameters f the magnetc bearngs can be changed t mve the resnant frequency f the TMS ut f the frequency range f nterest. Current TMSs must measure frces wth less than a 1% errr. T prve the capablty f the magnetcally levtated rcket TMS, t s desrable t demnstrate accurate frce measurements wthn 0.5% errr. Ths s accmplshed usng the multpnt calbratn prcedure as well as the mprved flux based frce equatns that accunt fr frngng lsses as a functn f ar gap. 1.3 Lterature Revew The cncept f magnetc bearngs has been arund fr decades (Imlach et al., 1990), but has nt been ecnmcally r techncally vable untl the advent f hgh-speed electrncs (Kasarda, 000). Tday magnetc bearngs are a prven technlgy n many cmmercal applcatns ncludng actve vbratn cntrl and rtatng applcatns where severe envrnments r lw mantenance are crtcal. Recently the use f actve magnetc bearngs cncurrently as supprt bearngs and nn-nvasve frce measurement devces has been nvestgated fr varus applcatns, and wth varyng degrees f success. Intrductn and Lterature Revew 5

21 AMBs have been used n labratry settngs t measure frces n prpulsn devces, seals, and bearngs. In these applcatns, the pump rtr s cmpletely supprted by magnetc bearngs. Thus, by drectly measurng the bearng reactn frces, t s pssble t determne the radal and axal hydraulc lads actng n the pump mpeller as well as btan nfrmatn abut the flw characterstcs that are therwse dffcult t btan (Gunzburg and Buse, 1994; Gunzburg and Buse, 1995; Baun and Flack, 1999). Prevus methds used ether stran measurements r pressure taps n the cmpressr shrud t measure frces. Baun and Flack (1999) used a current based frce equatn t calculate frces usng the magnetc bearngs n ther test stand. Ther test stand uses magnetc bearngs t measure radal and axal hydraulc frces n a centrfugal pump. The frce equatn used fr ths wrk s shwn n Equatn 1.. where ( ) ( ) 1 F th = kth (1.) g1 + bth g + bth k th = µ A g N (1.3) and b th L = (1.4) µ r Fr ths equatn, F th s the theretcal frce appled by the magnetc bearng n a dubleactng cnfguratn and k th and bth can be calculated based n actuatr gemetry and materal magnetc prpertes. The parameters n the k th equatn are the permeablty f free space, µ, the ar gap area, A g, and the number f turns n the cl, N. The b th equatn parameters are the mean path length f the rn, L, and the relatve permeablty f the rn, µ r. The actual frce relatnshp fr the thrust actuatr used n the pump test rg as well as any nnlnear effects due t materal hysteress, eddy currents, leakage, and frngng were determned by a calbratn apparatus and systematc calbratn develped by Baun. Ths calbratn apparatus and prcedure s dscussed n mre detal n (Baun et al., 1996). A statc calbratn prcedure was als cnducted t fnd the ptmzed values Intrductn and Lterature Revew 6

22 f k exp and b exp that mnmzed the rt-mean-square errr between the lad cell measurements and the frces calculated by the magnetc bearngs. Fttr et al. (1997) used a smlar mdel t calbrate an 8-ple planar radal magnetc actuatr. Three theretcal mdels f varyng degrees f cmplexty were used t predct frces. The frst mdel, deemed the full mdel, was develped usng magnetc crcut thery and assumng cnstant magnetc materal prpertes. The flux s fund by relatng t t the cl currents and ar gaps. Tw sets f lnearly ndependent equatns are generated usng ndal equatns as well as a cmplete set f ndependent lp equatns. These equatns are the cmpled n matrx frm t determne the frces n the X- and Y-drectns. The frm f these matrx equatns s shwn n Equatns 1.5 and 1.6. F F x y = εk = εk th th I I T T N N T T R R T T A A x y R R 1 1 NI NI (1.5) (1.6) where k th µ AN = (1.7) In these equatns, A x and A y are matrces that accunt fr the snes and csnes f the ple angles. The secnd mdel, deemed the reduced mdel, makes tw addtnal assumptns that reduce the number f flux denstes t be slved fr frm 4 dwn t 8. These assumptns are that the statr back rn and rtr have nfnte permeablty whle referrng ther actual reluctances back t the statr legs and that the jurnal fluxes are treated as f they rgnate frm a sngle ple at the center f the rtr. The thrd mdel, deemed the uncupled mdel, makes the assumptn that the actuatr s fully uncupled. Ths reduces the number f fluxes t be slved fr t 4. The system s then calbrated by recrdng the cl currents and rtr pstns as the magnetc actuatr s mved relatve t the statr and the cl currents are vared. An ptmzatn rutne based n Pwell s methd s then emplyed t mnmze the RMS Intrductn and Lterature Revew 7

23 errr between the expermental actuatr frce, as measured by a lad cell, and the frce calculated usng Equatns 1. thrugh 1.4. Ths results n an expermentally determned k exp and b exp as descrbed prevusly. The full mdel resulted n RMS errrs f apprxmately 0.19% whle the reduced mdel resulted n RMS errrs f abut 0.17%. The errr f the uncupled mdel was much hgher resultng n the cnclusn that the assumptn that the actuatr s fully uncupled s naccurate. Due t the accuracy and smplcty f the reduced mdel, t was chsen as the preferred mdel and used t generate the remander f the data. The ptmzed values f k exp and b exp are then used t calculate the frces n the actuatrs. These results are then cmpared t the measurements frm the lad cell. The resultng errrs were nrmally dstrbuted wth a mean f 1.04% wth a standard devatn f 3.69% and a maxmum errr f abut 10%. These are gd results frm a current based frce calculatn, hwever, the calbratn rutne nvlved applyng knwn lads, whch s nt practcal n a feld stuatn. Hysteress testng was als perfrmed n the test rg t determne the affect f ncreasng and decreasng currents n the calculated frces. The tests resulted n an average varatn between ncreasng and decreasng currents f abut.0%. Because the cmbned errrs frm the calbratn and the statc frce measurements are sgnfcantly hgher than the hysteress errrs, the hysteress errrs can be cnsdered nsgnfcant. Magnetc bearngs have als been used t determne the dynamc labyrnth ceffcents fr turb cmpressrs (Wagner and Steff, 1998). The peratnal relablty f turb cmpressrs wth very hgh pwer denstes depends n an accurate determnatn f flud frces rgnatng frm the nterstage seals and frm the balance pstn. Analytcal calculatns such as the cmputatnal flud dynamcs (CFD) methd and bulk-flw methd have been used t ad n the rtr-dynamc desgn f such turbmachnes. The results f these calculatns are hghly dependent n the selected bundary cndtns and parameters. Thus at lw speeds and pressures the calculated values shw an acceptable cncdence; hwever, at hgh speeds and hgh pressures, they Intrductn and Lterature Revew 8

24 may devate sharply frm the measured values. As a result, expermental verfcatn f the labyrnth stffness and dampng ceffcents remans ndspensable. In the test rg used by Wagner and Steff, magnetc bearngs are used t levtate the rtr as well as drectly measure the frces actng n the rtr. Wagner and Steff use a current based frce equatn that s lnearzed abut the equlbrum state t measure the frces n the magnetc bearng. The general frce equatn used s shwn n Equatn 1.8. F ~ = F + k ~ x + k (1.8) s q The ceffcents F, k s, and k q are functns f the equlbrum state (x brg =x and = ), the magnetc basng current, and bearng gemetry. Because the gas frces have a statc cmpnent due t unavdable rtr eccentrctes, k s and k q are als a functn f peratng pnt. T reduce these effects, a crrectn ceffcent fr each bearng s calculated based n the cndtn f statc equlbrum and n gas frces. The errrs n frce calculatn fr these tests are nt dscussed; hwever, the results prved successful n makng avalable relable data fr calculatng the stablty behavr f ndustral cmpressrs. Aens and Nrdmann (1999, 000) nvestgate the use f magnetc bearngs fr fault detectn n turbmachnes. Tday s mntrng systems are nt an ntegral cmpnent n turbmachnes, but must be purchased separately by the peratrs. Fr these falure detectn systems, the mtns f the rtr are measured as utput sgnals and cmpared t a faultless ntal state. The dagnss attempts t detect devatns frm the ntal state and prpse a cause. The prblem wth these systems s that the causes f the changes n the utput sgnal cannt be detected clearly because the devatn frm the ntal state culd be due t a change n the prcess r a mdfcatn f the system tself. Actve magnetc bearngs can be ntrduced t the system t mprve the dagnstc technque. Intrductn and Lterature Revew 9

25 The magnetc bearngs can be used t excte the rtatng shaft wthut cntact and measure smultaneusly the requred frces and dsplacements precsely. Frequency respnse functn can then be generated between the measured nput and utput sgnals. These frequency respnse functns can be cmpared t an ntal state t determne certan faults n turbmachnes. In rder t generate accurate frequency respnse functns, t s necessary t accurately measure the frces at the magnetc bearngs. Aens and Nrdmann cmpare three technques fr frce measurement fr use n ths applcatn. The frst equatn used t calculate magnetc bearng frces whle the bearngs are n dfferental mde s shwn n Equatn 1.9. F = k + k x x s s x (1.9) In ths equatn, F x s the frce n the x-drectn, x s the cntrl current n the x- drectn, s x s the rtr dsplacement n the x-drectn, and k and k s are lnearzatn cnstants that depend n the chsen desgn pnt f the magnetc bearng. Ths methd, called the -s methd, resulted n errrs f abut 17% n an peratng range f ±700N. A calbratn was used that perfrms a least-squares curve ft n the k -k s -plane t the measured data. Includng the calbratn, errrs were reduced t less than 9%. The secnd frce measurement methd used was based n a reluctance netwrk. Fr ths methd, the entre bearng s mdeled as a mult-nde netwrk f varable reluctances. The magnetc netwrk can be cmputed n a smlar way t electrcal netwrks. Gven cl current data and pstn data, the mdel calculates the magnetc flux and frm ths, the frce generated by the bearng. Because f the mathematcal cmplexty f ths methd, t culd nt be used t calculate real tme appled frces. Fr ths methd, errrs are abut 11% because the nn-lneartes f the magnetc materal are nt mdeled. Mre recent wrk by Aens and Nrdmann has prven errrs f abut 8% usng ths same methd, hwever detals were nt gven as t the calbratn prcedures used t mprve the results. Intrductn and Lterature Revew 10

26 The thrd and fnal frce measurement methd used by Aens and Nrdmann nvlves the use f Hall effect flux sensrs n the ar gap between the actuatr and rtr. Reprted errrs fr ths methd are abut 5% fr the entre wrkng range wth mst f the errr resultng frm an ffset dependng n the rtr pstn. If a rtr pstn dependent factr s ntrduced t accunt fr the ffset, errrs are reduced t.8%. If the rtr s nly perated n the nmnal center f the bearng, expected errrs are less than 1% fr ths methd. Flux sensrs are als used t calculate bearng frces n the test rg desgned by Knpf and Nrdmann (1998) fr the dentfcatn f the dynamc behavr f turbulent jurnal bearngs. The magnetc bearngs are used t levtate the rtr and t generate a relatve mtn between the rtatng and the statnary part f the jurnal bearng. The magnetc bearngs are used bth as actuatrs and frce measurement devces. The frce measurements were used n ths case t algn the rtr n the jurnal bearng and determne bearng clearances. T calculate accurate frces fr ths applcatn, knwn lads were appled t the rtr and frces were calculated usng the flux densty measurements frm the Hall effect prbes. Calbratn factrs were then chsen t mnmze the errr at maxmum magnetc frces. Ths methd results n errrs f less than 1% ver the entre peratng range f the bearngs. Hgher errrs result f eccentrc rtr pstns are cnsdered due t the change n flux dstrbutn n the ple surface wth the rtr pstn that cannt be measured by the Hall sensrs. In rder t ncrease the accuracy f frce measurement fr bth current based and flux based equatns, wrk has been dne t characterze effects such as frngng. Imlach et al. (000) fund that frngng was a strng functn f bth ar gap and magnetc bearng gemetry. The wrk presents a frngng mdel fr a planar E-cre actuatr gemetry that relates a frngng crrectn factr t the rat f ar gaps and actuatr ple wdths. As the target s mved relatve t the actuatr, the amunt f frngng changes, resultng n varyng crrectn factrs. Smaller ar gaps between the target and actuatr result n larger amunts f frngng. Frngng effects are dscussed n mre detal n Sectn.. The functn used t descrbe the pstn dependency f the frngng factr Intrductn and Lterature Revew 11

27 s a cmpund expnental, wth three parameters used t tune the mdel (Kasarda et al., 000). Equatn 1.10 shws the general frm f the frngng equatn that fts the data fr ar gap t ple wdth rats f between 0.01 and Ths range cvers the desgn envelpe fr mst practcal systems. G γ Y ( G / W ) = α + β 1 + e W (1.10) In Equatn 1.10, G s the ar gap length, W s the wdth f the actuatr ple, and α, β, and γ are the three parameters used t tune the mdel. The accuracy f current based frce calculatns fr magnetc bearngs was mprved by a technque called the multpnt methd (Marshall, 000). In ths technque, several perturbatns are made t the magnetc bearng system usng bas currents. These perturbatns are then prcessed mathematcally t determne bth the frce and effectve gap at each bearng. The multpnt methd s dscussed n mre detal n Sectn 4.. Marshall uses a cnstant deratng factr, as des Baun et al. (1996), t accunt fr magnetc lsses. Errrs n frce calculatns usng the multpnt methd were less than 3% whereas errrs usng sngle pnt technques wth n system perturbatns led t errrs f mre than 6%. The multpnt methd prvdes mre accurate frce calculatns; hwever, at ths tme knwn frces must stll be appled t the bearngs t calculate the cnstant deratng factr. Usng Magnetc Fnte Element Analyss (MFEA) t calculate the deratng factr caused by effects such as frngng wuld add t the versatlty f the multpnt methd by allwng accurate frces t be calculated wthut applyng knwn lads. The multpnt methd has als been verfed usng MFEA (Kasarda et al., 000). The valdatn was perfrmed by tw grups f researchers. One grup perfrmed the MFEA analyss usng varus lads and ar gaps. The cl currents generated n the MFEA analyss were then gven t the secnd grup f researchers wh used them wth an AMB mdel that ncluded the frngng mdel t predct the frces and dsplacements Intrductn and Lterature Revew 1

28 used rgnally. The results shwed errrs f less than 0.1% fr bth the predcted frces and dsplacements. Ths wrk dd nt nclude expermental results t further valdate the technque. Imlach et al. (000) present a calbratn technque fr current based frce equatns utlzng the multpnt methd. Unlke the wrk dne by Marshall (000), the multpnt methd s presented as an n-stu calbratn methd rather than a statc frce measurement technque. Perturbatns are perfrmed t nfer addtnal nfrmatn abut the system. The result f the calbratn s the abslute actuatr/target gap fr each magnetc bearng n whch the multpnt methd s perfrmed. Ths calbratn technque slves the dffcult prblem f measurng physcal ar gaps, a necessary parameter fr accurate frce measurement. The multpnt methd calbratn s dscussed n mre detal n Sectn 4.3. The use f magnetc bearngs fr ndustral applcatns such as manufacturng scenars has als been examned. Kasarda (1999) addresses the beneft f usng magnetc bearngs fr mprved prcess cntrl. In these applcatns, magnetc bearngs can be used t mntr ndustral prcesses such as fber extrusn n whch the qualty f the prduct s drectly related t the ablty t hld a cnstant tensn between rllers. In a smlar applcatn, magnetc bearngs can be used t bserve peratng frces wthn machnery allwng mprved dagnstc nfrmatn fr health mntrng purpses. Ths wuld allw mantenance t be perfrmed when needed, nstead f accrdng t a schedule, resultng n lnger and safer prductn runs. Intrductn and Lterature Revew 13

29 Chapter Develpment f Frce Equatns.1 Intrductn In ths chapter, bth flux based and current based frce equatns are develped fr the magnetc bearngs. The flux based equatns lead t mre accurate frce calculatns (Aens and Nrdmann, 000); hwever, the need fr addtnal hardware and larger ar gaps fr the flux sensrs make current based frce equatn mre attractve n sme applcatns. The currents and relatve target pstns needed fr the current based frce equatns are readly avalable frm the magnetc bearng cntrller because f the feedback nature f the bearngs. A frngng factr s als appled t bth the flux and current based frce equatns t accunt fr frngng effects. Je Imlach, wh partcpated n the research fr ths prject, develped the frngng factr equatns usng Magnetc Fnte Element Analyss (MFEA). Frngng was fund t be a strng functn f ar gap length as well as bearng gemetry. Frngng factr equatns were develped fr bth the flux and current based frce equatns, and MFEA was used t verfy the valdty f these equatns fr the E- cre actuatrs used n the TMS demnstratr. Mre detals n the methds used t determne these equatns can be fund n [10].. Flux Based Frce Equatns The flux based frce equatn fr magnetc bearngs s derved frm smple magnetc crcut thery. A magnetc bearng can be mdeled as a basc hrseshe electrmagnet and target. Fgure.1 shws a schematc f ths basc setup. In ths Develpment f Frce Equatns 14

30 schematc, N s the number f cls arund the hrseshe, I s the current n the cls, A g s the area f the ar gap, and g s the ar gap between the hrseshe and the target. FIGURE.1: Schematc f hrseshe electrmagnet and target The current n the cls arund the hrseshe nduces a magnetc flux, φ, n the drectn shwn. All f the flux s assumed t be cnfned t the ferrmagnetc cre and the ar gap vlume defned by the prjectn f the ple face n the target. Neglectng edge effects such as frngng and leakage n ths dscussn allws scalar rather than vectr equatns t be used n the dervatns. Ths results n undrectnal frces perpendcular t the ple face and target. Edge effects wll be dscussed n mre detal n later dscussn. If we assume that the current s allwed t change s as t keep the magnetc flux cnstant, then a change n magnetc energy can nly ccur as a change n the energy stred n the ar gap. The energy stred n each ar gap s gven by: 1 Wmag = µ H V (.1) where µ s the permeablty f free space, H s the magnetc feld strength, and V s the vlume f the ar gap. The vlume f the ar gap s smply the area f the gap tmes the length f the gap, r A g *g. If the target s dsplaced an addtnal g, then the change n energy fr bth ar gaps s: Develpment f Frce Equatns 15

31 W mag 1 1 = µ H Ag ( g + g) µ H Ag g (.) r W mag = µ H A g g (.3) Due t cnservatn f energy, the change n magnetc energy s equal t the change n mechancal energy, s W = mech W mag (.4) where the change n mechancal energy fr bth gaps s *F* g and the change n magnetc energy s gven by Equatn.3. S, substtutng nt EQ. 4 gves F g = µ H A g g (.5) Slvng fr frce n the equatn abve yelds F µ H A g = (.6) Usng the defntn f the permeablty, B/µ can be substtuted fr H, resultng n the fllwng frce equatn: F B A g = (.7) µ where B s the magnetc flux densty, A g s the ple face area, and µ s the permeablty f free space. Develpment f Frce Equatns 16

32 Because f the feedback nature f magnetc bearngs, they are almst always arranged n an ppsng par cnfguratn, als called a duble-actng magnetc bearng cnfguratn. In ths cnfguratn, the electrmagnets pull aganst ne anther creatng a net frce. A schematc f a duble-actng cnfguratn s shwn n Fgure.. FIGURE.: Schematc f a duble-actng magnetc bearng The net frce n the target s the dfference between F 1 and F. S, the net frce s gven by: F net = F F 1 = A µ g ( B1 B ) (.8) where B 1 s the magnetc flux densty generated by I 1 and B s the magnetc flux densty generated by I. The frce equatn gven n Equatn.8 s based n smple magnetc crcut thery and des nt nclude lsses. Cmmn lsses n magnetc bearngs nclude leakage and frngng. Leakage ccurs when magnetc flux travels frm ne ple face t the ther ple face wthut travelng thrugh the target. Fgure.3 demnstrates leakage lsses. Develpment f Frce Equatns 17

33 FIGURE.3: Dagram f leakage lsses n a magnetc bearng Because the magnetc flux densty s measured drectly usng a Hall effect prbe and nt calculated usng the relatnshp between current and flux densty, leakage lsses can be gnred. Frngng lsses ccur when magnetc flux des nt travel drectly frm the ple face t the target, but frnges arund the edges. Ths results n a larger effectve ar gap area because the flux s dstrbuted thrughut a larger area. A dagram llustratng frngng lsses s shwn n Fgure.4. FIGURE.4: Dagram f frngng lsses n a magnetc bearng Develpment f Frce Equatns 18

34 Frngng lsses cannt be neglected because they are a strng functn f ar gap and bearng gemetry as shwn n the prevus sectn n the develpment f the frngng factr. Assumng the flux prbe s lcated n the center f the ple, the frngng factr crrects fr lsses due t frngng. S, ncludng the flux based frngng factr (develped by Je Imlach) n Equatn.8 t accunt fr frngng lsses yelds the fnal flux based frce equatn fr a magnetc bearng: F A = µ ) (.9) g ( ff1b1 ff B where ff 1 and ff are the flux based frngng factrs defned by the fllwng equatns: ff ff g x α b W 1 = Abe + K b (.10) g + x α b W = Ab e + K b (.11) and where g s the nmnal gap between the actuatr and target, x s the target pstn, and A b, α b, K b, and W are cnstants frm MFEA fr the partcular bearng gemetry. Accurate frces are calculated usng Equatn.9 n cnjunctn wth the flux based frngng factr equatns..3 Current Based Frce Equatns The current based frce equatn fr magnetc bearngs can be derved usng Krchhff s law fr magnetc crcuts and the flux based frce equatn derved n the prevus sectn. Krchhff s law states that fr any clsed lp electrcal crcut, the summatn f vltage rses equals the summatn f vltage drps; smlarly, fr a magnetc crcut, the summatn f the magnetmtve frce rses equals the summatn f magnetmtve frce drps. Ths can be wrtten as NI Rφ = 0 (.1) Develpment f Frce Equatns 19

35 where N s the number f turns n the cl, I s the current n the cl, R s the reluctance f the magnetc path, and φ s the magnetc flux. Fgure.5 shws a schematc f a smple magnetc crcut cnsstng f a ferrmagnetc trd wth a cncentrated wndng. FIGURE.5: Schematc f ferrmagnetc trd wth a cncentrated wndng The reluctance s defned as the rat f the magnetmtve frce t flux. Ths relatnshp s represented by the fllwng equatn: R = mmf flux = H dl B da (.13) where H s the magnetc feld strength, l s the path taken alng the trd, B s the magnetc flux densty, and A s the crss sectnal area f the trd. The ttal reluctance fr ths magnetc crcut s the summatn f the reluctance f the rn and the reluctance f the ar gap. Assumng the magnetc feld and crss-sectnal area are unfrm, the path length s the mean length alng the mddle f the rn, and the electrmagnet s peratng n the lnear prtn f the BH curve, the reluctance thrugh the rn s gven by: Develpment f Frce Equatns 0

36 L R = (.14) µ At where L s the mean rn path length, µ s the permeablty f the rn, and A t s the crss-sectnal area f the trd. Assumng the magnetc feld and crss-sectnal area are unfrm and the path length s the length f the ar gap, the reluctance thrugh the ar gap s gven by: g R g = (.15) µ A g where g s the gap length, µ s the permeablty f free space, and A g s the area f the gap. The result after substtutng the reluctance equatns nt Equatn.1 s NI L g = φ + φ g (.16) µ At µ Ag where N s the number f turns n the cl, I s the current thrugh the cl, φ s the magnetc flux thrugh the rn, and φ g s the magnetc flux thrugh the gap. If there s n leakage, the magnetc flux thrugh the rn s equal t the magnetc flux thrugh the gap; and f there s n frngng, the crss-sectnal area f the trd s equal t the area f the gap. After takng these assumptns nt accunt and defnng the relatve permeablty, µ r, as µ /µ, Equatn.16 smplfes t NI φ L = + g Aµ µ r (.17) Develpment f Frce Equatns 1

37 Magnetc flux densty, B, s defned as the magnetc flux dvded by the area t s dstrbuted ver. Makng ths substtutn and slvng fr magnetc flux densty yelds µ NI B = L + g µ r (.18) Fr tw ar gaps as n the case wth a magnetc bearng, Equatn.18 becmes µ NI B = L + g µ r (.19) Nw that the relatnshp between magnetc flux densty and current has been determned, t can be substtuted n the flux based frce equatn, Equatn.9, derved n the prevus sectn. S the net frce n an ppsng electrmagnet cnfguratn s gven by F net µ N g = A I1 L + g1 µ r I L + g µ r (.0) Ths equatn, lke the flux based frce equatn, s derved usng smple magnetc crcut thery and des nt nclude any lsses. The assumptns nherent n Equatn.0 are that the electrmagnet s peratng n the lnear prtn f the BH curve and that there s n leakage r frngng. In magnetc bearngs, a bas current r permanent magnet s used t ensure that the electrmagnet perates n the lnear prtn f the BH curve. Several desgn cnsderatn such as ver szng the target can be made t mnmze the effects f leakage; hwever, because frngng s a strng functn f ar gap and bearng gemetry, t s nt neglgble. S, ncludng the current based frngng factr (develped Develpment f Frce Equatns

38 by Je Imlach) n Equatn.0 t accunt fr frngng lsses yelds the fnal current based frce equatn fr a magnetc bearng yelds Equatn.1. The frngng factr equatns fr Equatn.1 are gven n Equatns. and = g L I ff g L I ff A N F r r g net µ µ µ (.1) = W x g W x g W x g W x g K A e K A e K A e K A e ff α α α α (.) = W x g W x g W x g W x g K A e K A e K A e K A e ff α α α α (.3) In Equatns. and.3, g 1 s the nmnal gap fr the uter legs f the actuatr; g s the nmnal gap fr the center leg f the actuatr; x s the target pstn; and A, α, K, W 1, W, W 3, and W 4 are cnstants frm MFEA fr the partcular bearng gemetry. The gaps g 1 and g n Equatn.1 are ften replaced by the nmnal gap, g, plus and mnus the target pstn, x. S Equatn.1 can be rewrtten as fllws: = 1 1 ) ( ) ( x g L I ff x g L I ff A N F r r g µ µ µ (.4) Develpment f Frce Equatns 3

39 In Equatn.4, g s the average f g 1 and g. Accurate frces can be calculated usng Equatn.4 n cnjunctn wth the current based frngng factr equatns gven n Equatns. and.3. Develpment f Frce Equatns 4

40 Chapter 3 Expermental Descrptn 3.1 Overvew f TMS Demnstratr A TMS demnstratr was desgned n rder t prve the capablty f usng magnetc bearngs n a magnetcally levtated thrust measurement system. Je Imlach desgned the test rg and magnetc bearng cmpnents, whle Vrgna Tech s rle has been the applcatn f the multpnt calbratn technque ncludng cde develpment, the mplementatn f a 18-channel data acqustn system, and the verall test verfcatn f the TMS demnstratr. There are sx man cmpnents t the TMS demnstratr: the fxed frame, the flatng frame, fur supprt bearngs, seven thrust bearngs, three cntrllers, and the data acqustn (DAQ) system. The frame fr the demnstratr s assembled frm cmmercally avalable precsn alumnum extruded structural elements (Mn-Tec Framng Systems, LLC; Canandagua, NY). Ths smplfed the desgn and cnstructn f the test rg and allws fr maxmum flexblty f future uses f the demnstratr fr actual testng. The fxed frame s essentally a rectangular bx (0.70 m x 0.70 m x 0.9 m) [7.5 n x 7.5 n x 36.4 n], wth three addtnal axal members n bth the tp and bttm plane. The flatng frame s lcated nsde the fxed frame and rests n blts that act as backup bearngs t supprt the weght f the flatng frame whle the frame s nt levtated. A schematc f the test rg s shwn n Fgure 3.1. Expermental Descrptn 5

41 Fgure 3.1: Schematc f TMS Demnstratr The fxed frame, flatng frame, supprt bearngs, and thrust bearngs can be seen n Fgure 3.1. The fxed frame s shwn n blue, the flatng frame s shwn n red, the supprt bearngs are shwn n green, and the thrust bearngs are shwn n grey. The numberng scheme fr the magnetc bearngs s als shwn n Fgure 3.1. The frnt supprt bearngs are numbered 10_ and 0_ and the back supprt bearngs are numbered 11_ and 1_. The tp thrust bearngs are numbered cunterclckwse startng wth 31_ n the left and gng arund t 34_ n the back. The rgnal number scheme fr the bttm thrust bearngs was 35_, 36_, 37_ (gng cunterclckwse frm the left); hwever, thrust bearng 35_ was unusable due t nstablty ssues. Thus, bearngs 35_ and 36_ were swtched t mantan symmetrc reactn frces n the flatng frame. The resultng number scheme fr the bttm thrust bearngs was 36_, 35_, 37_ (gng cunterclckwse frm the left) after the swap was made. A pcture f the TMS demnstratr s shwn n Fgure 3.. The demnstratr s shwn n the fregrund whle the cntrllers and data acqustn system are shwn n Expermental Descrptn 6

42 the backgrund. The ndvdual cmpnents f the TMS demnstratr wll nw be dscussed n mre detal. Fgure 3.: Pcture f TMS Demnstratr Fur supprt bearngs n the tp fur crners f the test rg levtate and measure frces appled n the x- and y-drectns. The weght f the rg as well as sde ladng s measured by the supprt bearngs. Each supprt bearng has tw axes, a hrzntal and a vertcal, as seen n the schematc n Fgure 3.3. Expermental Descrptn 7

43 Fgure 3.3: Schematc f Supprt Bearng (schematc prvded by Je Imlach) There are als seven thrust bearngs lcated n the center f the test rg that levtate and measure frces appled n the z- r thrust drectn. Each thrust bearng has nly ne axs f supprt. Fgure 3.4 shws a schematc f ne f the thrust bearngs frm the TMS demnstratr. Fgure 3.4: Schematc f Thrust Bearng (schematc prvded by Je Imlach) The targets are attached t the flatng frame and the actuatrs are attached t the fxed frame s that the flatng frame s cmpletely levtated wthn the fxed frame by the Expermental Descrptn 8

44 magnetc bearngs. Thus the flatng frame s cmpletely supprted by 15 axes: fur n the x-drectn and fur n the y-drectn by the supprt bearngs, and seven n the z- drectn by the thrust bearngs. A magnetc bearng axs, r axs f supprt, cnssts f tw actuatrs, a target, and a dfferental prxmty sensr t measure the relatve pstn f the target. The prxmty sensrs prvde the hgh accuracy pstn measurements needed by the cntrllers t keep each target levtated wthn the actuatrs. Each actuatr s als equpped wth a thermstr t measure the cl temperature and a Hall effect flux sensr t measure the flux densty n the ar gap between the actuatr and target. Pctures f the supprt and thrust bearngs are shwn n Fgure 3.5. The target and actuatrs can be seen clearly n the pcture f the thrust bearng shwn n the rght whle the crcut bards that huse the electrncs fr the flux prbe and thermstrs as well as the eddy current pstn sensrs (wth yellw tps) can be seen n the pcture f the supprt bearng shwn n the left. These cmpnents are dscussed n mre detal n the hardware sectn f the DAQ system. Fgure 3.5: Supprt Bearng (left) and Thrust Bearng (rght) The wres prvdng current t the actuatrs as well as the prxmty sensr utputs are cnnected t three Revlve cntrllers. Each cntrller has the capablty f Expermental Descrptn 9

45 supprtng fve axes. Cntrller 1(A) cntrls the tw left supprt bearngs as well as the left center thrust bearng (bearngs 10_, 11_, and 31_ as seen n Fgure 3.1); Cntrller (B) cntrls the rght tw supprt bearngs as well as the rght center thrust bearng (bearngs 0_, 1_, and 33_ as seen n Fgure 3.1); and Cntrller 3(C) cntrls the remanng thrust bearngs (bearngs 3_, 34_, 35_, 36_, and 37_ as seen n Fgure 3.1). The cl currents and target pstns as well as the cl temperatures and flux prbe readngs are all nputs t the DAQ system. The DAQ system acqures and prcesses these sgnals t calculate accurate frces beng appled t the TMS demnstratr. 3. Data Acqustn (DAQ) System The man hardware cmpnents f the DAQ system are dscussed frst fllwed by an vervew f the DAQ sftware used t measure frces. Mst f the DAQ cmpnents ncludng the sftware package, LabVIEW 6.1, were purchased frm Natnal Instruments. The DAQ system has the capablty f samplng 18 channels, hwever nly 106 f thse channels are used fr the TMS demnstratr Data Acqustn Hardware J. Imlach and R. Kpp, n cnjunctn wth Natnal Instruments persnnel, desgned the DAQ system used fr the thrust measurement system. Table 3.1 summarzes the Natnal Instruments cmpnents that were purchased fr the DAQ system. Table 3.1: Summary f Natnal Instruments Cmpnents Item Number f Items Used n DAQ System PCI-603E data acqustn card fr PC 1 SCXI-1000 chasss 1 SCXI-110C mdule 4 SCXI-1300 cnnectr SH cables BNC-095 BNC cnnectr bxes Expermental Descrptn 30

46 There are 15 axes f cntrl, each cnsstng f tw ppsng electrmagnetc actuatrs, mntred by the DAC system. Each axs cnssts f tw flux measurements, ne fr each actuatr; tw temperature measurements; tw current measurements; and ne pstn measurement. The DAC system uses 106 f the 18 channels avalable: 30 fr flux denstes, 30 fr temperatures, 30 fr currents, 15 fr pstns, and ne channel fr lad cell measurements. FH-560 Hall effect flux prbes manufactured by F. W. Bell are used t measure flux densty n each actuatr. These sensrs are hgh gan (hgh senstvty) devces, and were each ndvdually calbrated usng a magnetc calbratn chamber. The Hall effect sensrs have an peratng range frm 55 t +100 C. The thermstrs are YSI mdel #4401 devces. Each thermstr package ncludes tw thermstrs (NTC and PTC) alng wth tw precsn resstrs that munt n a custm prnted crcut bard (PCB). The cmbnatn results n a lnear utput ver the range f 0 t 100 C. The thermstrs are munted between the cl and the center leg f the E-cre and are used t measure the temperature f the cl fr each actuatr. A custm PCB cntanng the drver and cndtnng crcuts fr the thermstrs and the Hall sensrs s munted by each electrmagnet. The current data s btaned thrugh utputs frm the Revlve MBResearch hardware suppled wth the cntrllers. Dfferental eddy current prxmty sensrs manufactured by Kaman Instrumentatn are used t measure the relatve target pstn. Ths pstn data s als btaned thrugh the utputs frm the MBResearch hardware. The flux and temperature utputs are wred frm the crcut bards lcated at each actuatr t the black termnal blck bx lcated n tp f the thrust measurement system. These wres are bundled and hardwred nt the SCXI-1300 cnnectr frm Natnal Instruments. The SCXI-1300 cnnectr plugs nt the SCXI-110C mdule munted t the SCXI-1000 chasss frm Natnal Instruments. The PC addresses the flux and temperature channels usng the PCI-603E data acqustn card. Expermental Descrptn 31

47 The current and pstn utputs frm the MBResearch hardware are cnnected t the BNC-095 usng BNC cables. The SH cables cnnect the BNC-095s t the SCXI-110C mdules munted t the SCXI-1000 chasss. The PC addresses the current and pstn channels usng the PCI-603E data acqustn card. LabVIEW 6.1 was used as a sftware nterface. In partcular, the Measurement and Autmatn Explrer suppled wth the LabVIEW 6.1 sftware prvdes fr smple channel cnfguratn. The channels have been set up t nclude all f the flux densty, temperature, current, and pstn measurements fr the 15 axes currently n the rg and extra channels fr measurements n anther axs f added n the future. The channels are named C1-C113: C1-C16 are pstn channels wth an utput range f ±.5V, C17-C48 are current channels wth an utput range f 0-10V, C49-C80 are flux densty channels wth an utput range f ±10V, C81-C11 are temperature channels wth an utput range f 0-10V, and C113 s the lad cell channel wth an utput range f ±10V. The LabVIEW sftware s used t cntrl the data acqustn f all the channels. 3.. Data Acqustn Sftware LabVIEW 6.1 s the sftware platfrm used fr cntrl f the data acqustn fr the thrust measurement system (TMS). LabVIEW s a graphcally based, user-frendly prgrammng language. Each prgram, called a Vrtual Instrument (VI) s cmpsed t tw man nterfaces: the frnt panel and the blck dagram. Prgram names n future sectns may have a VI fllwng the prgram name ntng t as a vrtual nstrument prgram. The frnt panel s the user nterface f the VI. Ths panel s desgned frst n the prgrammng prcess and ncludes any nputs needed by the user and utputs such as graphs, ndcatrs, r flenames fr savng data. A sample frnt panel s shwn n Fgure 3.6. Expermental Descrptn 3

48 Fgure 3.6: Sample LabVIEW 6.1 Frnt Panel Ths then generates blcks n the blck dagram that can be cnnected usng wres t cntrl data flw. The blck dagram shws the flw f data and all the data prcessng that s dne n the VI. VIs can be called as subrutnes n ther VIs t smplfy blck dagrams and wrng. A sample blck dagram s shwn n Fgure 3.7. Fgure 3.7: Sample LabVIEW 6.1 Blck Dagram The VIs wrtten fr the TMS are brken dwn nt three man grups: calbratn prgrams, statc frce acqustn prgrams, and dynamc frce acqustn prgrams. Expermental Descrptn 33

49 The three man grups are further brken dwn nt tw prcedures: the setup prcedure and the man prgram. The flwchart n Fgure 3.8 shws the step-by-step prcedure that the user perfrms fr ether statc r dynamc frce acqustn. Calbratn Prcedure All Prgrams Lcated In "TMS Cal - 15 Axes - Autcal" Flder Turn n Pwer Strp and Cntrllers; D Nt Levtate Run Calbratn Setup Prgram: "DC FLUX SAVE" Lad Calbratn Parameter Fles and Levtate Axes Run Calbratn Man Prgram: "AUTOCAL" Statc Frce Acqustn Prcedure All Fles Lcated In "TMS Cal - 15 Axes - Statc Frce Acqustn" Flder Delevtate Axes Dynamc Frce Acqustn Prcedure All Fles Lcated In "TMS Cal - 15 Axes - Dynamc Frce Acqustn" Flder Turn On TMO- Lad Cell Sgnal Cndtner Bx Turn On TMO- Lad Cell Sgnal Cndtner Bx Run the Statc Frce Acqustn Setup Prgram: "DC FLUX SAVE" Run the Dynamc Frce Acqustn Setup Prgram: "DC FLUX SAVE" Lad Frce Measure Parameter Fles nt Cntrllers and Levtate Axes Lad Frce Measure Parameter Fles nt Cntrllers and Levtate Axes Run Remanng Statc Frce Acqustn Setup Prgrams: "DC LOAD CELL SAVE" "DC POSITION SAVE" "DC THRUST SAVE" Run Remanng Dynamc Frce Acqustn Setup Prgrams: "DC LOAD CELL SAVE" "DC POSITION SAVE" "DC THRUST SAVE" Lad Flatng Frame Turn On Functn Generatr Then Frce Actuatr Pwer Amplfer; Input Desred Frequency and Ampltude Run Statc Frce Acqustn Man Prgram: "FORCE MEASURE" Run Dynamc Frce Acqustn Man Prgram: "FORCE MEASURE" Fgure 3.8: Flwchart f three man grups f prgrams Expermental Descrptn 34

50 The calbratn prgrams perfrm the multpnt methd n all 15 axes f the TMS and recrd the predcted target pstns f each axs fr use n subsequent statc and dynamc frce calculatns. The statc frce acqustn prgrams calculate, dsplay, and recrd statc frces appled t the flatng frame f the TMS. The dynamc frce acqustn prgrams calculate, dsplay, and recrd dynamc frces n real tme appled t the flatng frame. These three man grups f VIs are dscussed n mre detal n the next three chapters. 3.3 Statc Frce Acqustn The calbratn prcedure, descrbed n the next chapter, must be cmpleted prr t statc frce acqustn because the predcted target pstns are needed fr frce calculatns. The statc frce acqustn prgrams calculate, dsplay, and recrd statc frces appled t the flatng frame f the TMS. There are fur prgrams used n the setup prcedure fr statc frce acqustn: DC FLUX SAVE, DC LOAD CELL SAVE, DC POSITION SAVE, and DC THRUST SAVE. All f the fles fr these prgrams are fund n the TMS Cal 15 Axes Statc Frce Acqustn flder. After the setup prcedure, the FORCE MEASURE VI s used t calculate the statc frces appled t the flatng frame. FORCE MEASURE uses the fles created by the prgrams frm the setup prcedure alng wth the predcted target pstn results frm the calbratn prcedure t calculate accurate statc frces. Axal frces are appled t the test rg usng a turnbuckle assembly that cnnects the fxed frame t the flatng frame. Fgure 3.9 shws the turnbuckle assembly cnnectng the fxed and flatng frames. An MLP-300 lad cell manufactured by Transducer Technques s cnnected n seres wth the turnbuckle t measure the actual frce appled. The utput frm the lad cell, the actual frce appled, s then cmpared t the results frm the FORCE MEASURE VI, the measured frce appled. Expermental Descrptn 35

51 Fgure 3.9: Turnbuckle Assembly fr Statc Testng Statc frces measurements must have errrs less than 0.5% as determned by NASA STTR Phase II bjectves. The full lad s the maxmum lad f each bearng multpled by the ttal number f thrust bearngs used. Dfferent numbers f thrust bearngs can be turned n r ff t calculate accurate frces fr varus axal lads Setup Prcedure Several steps must be cmpleted prr t runnng the FORCE MEASURE VI fr determnatn f statc frces. Fr the labratry setup, the lad cell cndtner electrncs requre a 15-mnute warm-up tme befre lad measurements can be taken, s the TMO- lad cell sgnal cndtner shuld be turned n frst. The lad cell must be laded n tensn fr statc measurements because the turnbuckle assembly cannt guarantee prper ladng f the lad cell n cmpressn. Errrs may arse frm sde ladng f the lad cell f t s used n cmpressn. Fr that reasn, the lad cell assembly shuld be munted n the drectn the user desres t pull the flatng frame. Wth the crcut bards pwered and the flatng frame delevtated, the user must clck the Run arrw f the DC FLUX SAVE VI. Ths prgram recrds the flux densty vltage utputs frm the crcut bards when the flux n the actuatrs s zer. Expermental Descrptn 36

52 These vltages are subtracted frm subsequent flux densty measurements t fnd the actual flux densty thrugh each actuatr. If the calbratn prcedure was just cmpleted and the dcflux.dat fle s stll n the 15 Axes flder n the cmputer desktp, then t s nt necessary t run the DC FLUX SAVE VI. The crrect parameter fles must then be laded nt the Revlve cntrllers befre the flatng frame s levtated. Even f the calbratn prcedure was just cmpleted, new parameter fles usng a bas current f 1.1 amps must be laded nt the cntrllers. Cntrller 1(A) V0 Bas 1-1, Cntrller (B) V0 Bas 1-1, and Cntrller 3(C) V0 Bas Off frm the Frcemeasure PVF Fles flder shuld be laded nt cntrllers 1(A), (B), and 3(C), respectvely, usng the Parameter Lader prgram. The flatng frame s then levtated by pressng the green Start buttns lcated n the frnt panels f the Revlved cntrllers. The system must nw be allwed t reach a steady state n whch all the axes are levtated and centered. The MBScpe Snapshts sftware suppled by Revlve allws the user t vew the pstns f each axs fr the cntrller selected by the data swtch. The pstns f the axes are pltted n real tme by clckng n the Channels drp dwn menu and selectng Pstns. T vew the numercal values nstead f the plts f the pstns, the user can clck n the Vew drp dwn menu and select Statstcs. When all f the pstns f all three cntrllers are fluctuatng wthn the hundredths f a mcrn (µm) range, the system has reached steady state. It takes abut tw mnutes fr the system t reach steady state. Wth the flatng frame levtated but stll unladed, the user must run the DC LOAD CELL SAVE, DC POSITION SAVE, and DC THRUST SAVE VIs. DC LOAD CELL SAVE saves the utput vltage f the lad cell when the cell s unladed. Ths s typcally a small vltage; hwever, because f the accuracy needed n the frce measurements, t s nt neglgble. Ths vltage wll be subtracted frm future lad cell measurements cnverted t punds t fnd the actual frce beng appled t the lad cell. DC POSITION SAVE saves the DC pstn utput vltages fr all the actuatrs. Expermental Descrptn 37

53 These values wll be subtracted frm future pstn measurements and the result wll be cnverted t nches, yeldng the pstn f the target. These target pstns are added t the predcted target pstn and used n the frce calculatns f DC THRUST SAVE and FORCE MEASURE. DC THRUST SAVE saves the frces that all the actuatrs experence when the flatng frame s unladed (.e. the turnbuckle s nt tghtened). Ths allws the FORCE MEASURE VI t calculate the resultant frce appled t the flatng frame because the lad appled by the turnbuckle assembly s nt purely axal. The resultant s calculated usng Equatn 3.1 shwn belw. result ( F ) + ( ) + ( ) x FDCx Fy FDCy Fz F F (3.1) = DCz In ths equatn ΣF x, ΣF y, ΣF z are the sums f the frces n the x, y, and z drectns frm the FORCE MEASURE VI and ΣF DCx, ΣF DCy, ΣF DCz are the sums f the frces n the x, y, and z drectns frm the DC THRUST SAVE VI. The setup prcedure s nw fnshed and the TMS s ready fr statc frce acqustn Statc Frce Acqustn Prcedure When the Run arrw n the FORCE MEASURE VI s pressed, flux denstes, currents, and pstns are sampled at 104Hz and averaged ver 048 samples. Therefre data s beng taken fr a ttal f tw secnds. Ths means that the statc lad must reman cnstant fr the tw secnds durng data acqustn fr accurate frce measurements usng the FORCE MEASURE VI. The frce appled t the flatng frame by the turnbuckle assembly can be calculated usng Equatn 3.. F lb = ( VLC VDCLC )* (3.) V LC 30 In Equatn 3., V LC s the utput vltage frm the TMO- lad cell sgnal cndtnng bx, V DCLC s the DC lad cell value frm the DC LOAD CELL SAVE VI, and 30 lb/v s the cnversn factr fr the TMO- bx. The turnbuckle s tghtened t the desred axal lad accrdng t EQ. usng an 11/16 bx-end wrench n the shaft cmng frm Expermental Descrptn 38

54 the lad cell t keep the lad cell frm turnng and a 5/8 bx-end wrench n the turnbuckle. Whle the desred lad s appled, the user must remve the wrenches and press the Run arrw n the FORCE MEASURE VI t begn the statc frce acqustn. The FORCE MEASURE VI dsplays the ttal frces and mments experenced by the flatng frame. Fgure 3.10 shws the sectn f the FORCE MEASURE VI frnt end that dsplays the frces calculated by the prgram. Fgure 3.10: Frnt Panel f FORCE MEASURE VI Ttal mments fr the flatng frame are summed abut the center f bearng 3_ as shwn n the schematc n Fgure 3.1. The fluxes, currents, and pstns used t calculate the frces alng wth the frces n each axs and resultant frces are saved t the 15axes flder n the cmputer desktp. The errr s calculated usng Equatn 3.3. % Errr Full Lad ( F F ) result LC = (3.3) N *37.77lb Expermental Descrptn 39

55 F result s ether the flux r current based resultant frce n punds, F LC s the crrected frce frm the lad cell, N s the number f energzed thrust bearngs, and 37.77lb s the lad capacty f each thrust bearng. After the setup prcedure s cmplete, FORCE MEASURE can be run any number f tmes wth dfferent lads whle levtated and the new data wll be appended t the utput fles. 3.4 Dynamc Frce Acqustn The calbratn prcedure, descrbed n the next chapter, must be cmpleted prr t dynamc frce acqustn because the predcted target pstns are needed fr frce calculatns. The dynamc frce acqustn prgrams calculate, dsplay, and recrd dynamc frces appled t the flatng frame n real tme. There are fur prgrams used n the setup prcedure fr dynamc frce acqustn: DC FLUX SAVE, DC LOAD CELL SAVE, DC POSITION SAVE, and DC THRUST SAVE. All f the fles fr these prgrams are fund n the TMS Cal 15 Axes Dynamc Frce Acqustn flder. After the setup prcedure, the FORCE MEASURE VI s used t calculate the dynamc frces appled t the flatng frame. Ths prgram uses the fles created by the prgrams frm the setup prcedure alng wth the predcted target pstn results frm the calbratn prcedure t calculate accurate frces. A magnetstrctve frce actuatr (Terfenl-D actuatr mdel #AA140J013-ES1; Etrema Prducts, Inc.) usng a functn generatr t prvde the nput sgnal s used t apply dynamc lads. An MLP-300 lad cell manufactured by Transducer Technques s cnnected n seres wth the frce actuatr t measure the actual frce appled. The utput frm the lad cell, the actual frce appled, s then cmpared t the results frm the FORCE MEASURE VI, the measured frce appled, t calculate the errr. Dynamc frces measurements must have full lad errrs less than 0.5% as determned by NASA STTR Phase II bjectves. The full lad s the maxmum lad f each bearng multpled by the ttal number f thrust bearngs used. Dfferent numbers f thrust bearngs can be turned n r ff t calculate accurate frces fr varus axal lads. Expermental Descrptn 40

56 3.4.1 Setup Prcedure The setup prcedure fr dynamc frce acqustn s smlar t that f the statc frce acqustn. The lad cell cndtner electrncs requre a 15-mnute warm-up tme befre lad measurements can be taken, s the TMO- lad cell sgnal cndtner shuld be turned n frst. Fr the dynamc ladng case, the magnetstrctve frce actuatr replaces the turnbuckle f the statc ladng case. Fgure 3.11 shws the dynamc testng setup usng the magnetstrctve frce actuatr. The lad cell must be preladed n tensn whle the flatng frame s levtated t ensure prper ladng. As wth the statc ladng case, errrs may arse frm sde ladng f the lad cell f t s used n cmpressn. Fgure 3.11: Magnetstrctve Actuatr Assembly fr Dynamc Testng Wth the crcut bards pwered and the flatng frame delevtated, the user must clck the Run arrw f the DC FLUX SAVE VI. Ths prgram saves the DC flux densty values fr all f the actuatrs. These values wll be subtracted frm future flux densty measurements t determne the actual flux densty. If the calbratn prcedure was just cmpleted and the dcflux.dat fle s stll n the 15 Axes flder n the cmputer desktp, then t s nt necessary t run the DC FLUX SAVE VI. Expermental Descrptn 41

57 The crrect parameter fles must then be laded nt the Revlve cntrllers befre the flatng frame s levtated. Even f the calbratn prcedure was just cmpleted, new parameter fles usng a bas current f 1.1 amps must be laded nt the cntrllers. Cntrller 1(A) V0 Bas 1-1 Thrust Off, Cntrller (B) V0 Bas 1-1 Thrust Off, and Cntrller 3(C) V0 Bas Off frm the Frcemeasure PVF Fles flder shuld be laded nt cntrllers 1(A), (B), and 3(C), respectvely, usng the Parameter Lader prgram. Then, nly Cntrllers 1(A) and (B) shuld be levtated by pressng the green Start buttn n the frnt panels f the cntrllers. The system must nw be allwed t reach a steady state n whch all the axes are levtated and centered. The MBScpe Snapshts sftware suppled by Revlve allws the user t vew the pstns f each axs fr the cntrller selected by the data swtch. The pstns f the axes are pltted n real tme by clckng n the Channels drp dwn menu and selectng Pstns. T vew the numercal values nstead f the plts f the pstns, the user can clck n the Vew drp dwn menu and select Statstcs. When all f the pstns f all three cntrllers are fluctuatng wthn the hundredths f a mcrn (µm) range, the system has reached steady state. It takes abut tw mnutes fr the system t reach steady state. Wth the flatng frame levtated but stll unladed, the user must run the DC LOAD CELL SAVE, DC POSITION FOR DC THRUST SAVE, and DC THRUST SAVE VIs. These prgrams save data fles needed by the FORCE MEASURE VI t calculate the frces n each axs. The thrust bearngs must be energzed befre runnng the next setup LabVIEW VI. Frst, the user must turn n Cntrller 3(C) by pressng the green Start buttn n the frnt panel f the cntrller. Then, new parameter fles must be laded nt Cntrllers 1(A) and (B). Cntrller 1(A) V0 Bas 1-1 and Cntrller (B) V0 Bas 1-1 frm the Frcemeasure PVF Fles flder shuld be laded nt Cntrllers 1(A) and (B), respectvely. All f the thrust bearngs are nw energzed. Expermental Descrptn 4

58 The system must agan be allwed t reach a steady state n whch all the axes are levtated and centered. The MBScpe Snapshts sftware, can be used as descrbed abve t determne when the system has reached steady state. When all f the pstns f all three cntrllers are fluctuatng wthn the hundredths f a mcrn (µm) range, steady state has been acheved. Ths takes apprxmately tw mnutes. The setup prcedure s nw fnshed and the TMS s ready fr dynamc frce acqustn Dynamc Frce Acqustn Prcedure A cuple f general prncples fr sgnal prcessng can be used t determne the samplng parameters that shuld be used fr dynamc frce acqustn. The hghest frequency cmpnent expected n a typcal rcket TMS s 30 Hz, but t be cnservatve, 50 Hz was used. Samplng at 10 t 0 tmes the frequency f the wavefrm results n a gd reprductn f the shape f the wavefrm. Thus, samplng a 50 Hz wavefrm at a rate f 1000 samples per secnd s suffcent. At least three cycles f wavefrm shuld be sampled, s at least 60 samples (3*0) shuld be taken f a wavefrm sampled at 0 tmes ts frequency. T ensure enugh cycles f the wavefrm are sampled, 300 samples were acqured n the FORCE MEASURE VI. Ths means that wth an nput wavefrm f 30 Hz takng 300 samples and samplng at a rate f 1000 Hz, nne cmplete cycles f 30*300 the wavefrm wll be captured Fr the labratry set up a magnetstrctve frce actuatr s used t lad the system fr testng. The functn generatr cnnected t the frce actuatr cntrls the magntude and frequency f the nput frce. The functn generatr shuld be turned n frst wth ampltude set t zer t prevent damage t the frce actuatr and magnetc bearngs. It s then safe t turn n the pwer amplfer f the frce actuatr. The ampltude and frequency f the nput sgnal can be adjusted t the desred values usng the functn generatr. Data acqustn begns when the Run buttn n the FORCE MEASURE VI s pressed. Three-tenths f a secnd f data s acqured 300samples and ttal frces and mments appled t the rg n that tme are 1000samples / sec Expermental Descrptn 43

59 pltted and saved. Ttal mments fr the flatng frame are summed abut the center f bearng 3_ as shwn n Fgure 3.1. The fluxes, currents, and pstns used t calculate the frces alng wth the frces n each axs and resultant frces are saved t the 15axes flder n the cmputer desktp. The purpse f these tests s t prve that the TMS demnstratr s capable f dynamc frce acqustn. Because f the nerta f the flatng frame, there s a tme lag as well as a magntude shft between the resultant frce frm the magnetc bearngs and the measured frce frm the lad cell. Ths tme lag s dependent n the mass f the flatng frame as well as the acceleratn f the flatng frame. The TMS demnstratr s nt equpped wth accelermeters, s the tme lag and magntude shft cannt be crrected n the frce data fr the TMS demnstratr. Hence, the cnclusns abut the dynamc results wll be mre qualtatve than quanttatve. Expermental Descrptn 44

60 Chapter 4 Calbratn f TMS Demnstratr 4.1 Intrductn Bth the current and flux based frce equatns fr magnetc bearngs nclude a physcal ar gap term. In the flux based methd, ths term s fund nly n the frngng factr equatns (see Equatns.9 thrugh.11). In the current based methd, the target pstn term s fund n bth the frce equatn and the frngng factr equatns (see Equatns. thrugh.4). Therefre, t s necessary t determne ar gaps fr accurate frce measurements wth ether methd. Pstn sensrs exst but they are nly able t determne a target pstn relatve t the pstn sensr and d nt ndcate a bearng/actuatr gap that may be a functn f temperature, algnment, and machnng tlerances. Prevus methds f dentfyng physcal ar gaps nvlve usng feeler gauges t physcally measure the gap between the actuatr and the target. Other calbratn methds nvlve applyng knw lads t the bearngs t calculate a crrectn factr. One gal f ths wrk s t develp a rbust calbratn that can be cmpletely autmated allwng t t be used n a feld stuatn. In rder t meet ths gal, a system dentfcatn methd, called the multpnt methd, has been develped. 4. The Multpnt Algrthm The multpnt methd was rgnally develped as a new current based frce measurement methdlgy that nherently accunts fr system uncertantes by utlzng multple sets f current pars n ppsng actuatrs, n cnjunctn wth a calculatn algrthm, t accurately determne the frce appled by the AMB. In the TMS scenar, the multpnt methd s used as a calbratn t determne ar gaps fr use n frngng Calbratn f TMS Demnstratr 45

61 mdels and frce equatns. The mult-pnt frce measurement technque takes advantage f the fact that an AMB feedback system wll keep the supprted target at a predetermned fxed lcatn between tw ppsng actuatrs wth great accuracy. The multple pnts requred by the technque are btaned by ncreasng the current nt ne sde f the duble-actng actuatr n small ncrements and recrdng the currents fr bth sdes f the actuatr fr each f these ncrements after ntal transents are dsspated and the target s re-centered wthn the actuatr. Ths s smply perfrmed by addng a perturbatn current t the cntrl effrt already levtatng the lad as shwn n Fgure 4.1. Alternatvely, the bas current n bth actuatrs can be mdfed s that the same perturbatn s acheved. Because f the cntrller and sftware used n the TMS test rg, the bas current perturbatn methd s used t perturb the thrust measurement system. Fgure 4.1: Schematc f duble-actng sngle axs magnetc bearng The ttal current n each cl s the summatn f the bas current and perturbatn current. The bas current s used t ensure that the actuatr s peratng n the lnear prtn f the B-H curve. The B-H curve fr a typcal magnetc materal s shwn n Fgure 4. where the extended lne ndcates the lnear prtn. The perturbatn current s njected by the cntrller t mantan the centered target pstn. Calbratn f TMS Demnstratr 46

62 Fgure 4.: Typcal B-H curve fr magnetc materal (Plnus, 1978) The perturbatn prcedure fr the TMS system cnssts f changng the nput bas current t bth actuatrs f an axs par. Fr each bas current, the ttal currents frm each f the ppsng actuatrs are recrded cmprsng a current par. Snce the cntrller mantans the same target pstn, the frce supprted by the axs and the pstn f the target are the same fr all f the recrded current pars. These current pars are then used t generate a vectr f pssble frces. Frst f all, a vectr f pssble target pstns s generated frm g t + g, the physcal bunds f the target wthn the actuatrs. The vectr s brken dwn nt dscrete steps by a user chsen step sze, x. Therefre, the target pstn vectr s f the frm shwn n Equatn 4.1. (4.1) + + = = g x g x g x g g x m g x m g x g x g g x M M 1) ( Calbratn f TMS Demnstratr 47

63 where m s defned as x g m = (4.) Fr the flux based frce equatn used n the TMS scenar, the target pstn vectr s substtuted nt the frngng factr equatns (see Equatns.10 and.11). alng wth the flux densty measurements t prduce a flux based frce vectr fr each pstn lsted n the vectr n Equatn 4.1. Once ths substtutn s cmplete fr all f the flux densty pars (.e. ne perturbatn cndtn), a matrx f pssble frces s prduced where each clumn represents a flux densty par frm an asscated perturbatn. The flux based frce matrx s f the frm (4.3) = ), ; ( ), ; ( ), ; ( ), ; ( ), ; ( ), ; ( n n n n n n b B B x m g F B B x m g F B B x g F B B x g F B B g F B B g F F L M O M L L Nte that fr the current based frce equatn, ths target pstn vectr s substtuted nt the frngng factr and frce equatns (see Equatns. thrugh.4) alng wth each current par t prduce a current based frce vectr. The current based frce matrx s f the frm (4.4) = ), ; ( ), ; ( ), ; ( ), ; ( ), ; ( ), ; ( n n n n n n I I x m g F I I x m g F I I x g F I I x g F I I g F I I g F F L M O M L L The frce matrces have the same number f clumns as perturbatns and the same number f rws as the target pstn vectr, x. Theretcally, the rw n whch the frces match exactly acrss all f the current r flux densty pars represents the actual Calbratn f TMS Demnstratr 48

64 physcally realzable target pstn and axs frce. Because the target pstn vectr s nt a cntnuus functn, but made up f dscrete target pstns, the actual frce and target pstn are determned by fndng the rw wth the lwest standard devatn. Thus, a standard devatn vectr s prduced frm each frce matrx as shwn n Equatn 4.5. σ[ F( g ; I σ[ F( g + x; I Σ = σ [ F( g + m x; I , I, I, I ), L, F( g ; I ), L, F( g M ), L, F( g 1n, I n + x; I ) 1n + m x; I, I 1n n, I ) n ) (4.5) The rw f the target pstn vectr that crrespnds t the rw wth the mnmum standard devatn s the mst lkely actual target pstn. Ths target pstn fund usng the multpnt methd s called the predcted target pstn. Ar gaps needed fr the frngng factr expressns are determned usng the predcted target pstn as well as the prxmty sensr utput. If used alne, the multpnt methd wuld use the average value f the frces n ths rw as the predcted frce. Hwever, fr the TMS scenar, the multpnt methd s utlzed nly as a calbratn technque as descrbed n the fllwng sectn. Increasng the number f perturbatns and ncreasng the number f steps used n the target pstn vectr mprves the accuracy f the results frm the multpnt methd. Fr the TMS calbratn prcedure, seven perturbatns and fve thusand steps between ±g have been determned as suffcent fr accurate frce and target pstn results. 4.3 Usng The Multpnt Algrthm as a Calbratn Prcedure The multpnt methd s used as an nlne calbratn fr the TMS prttype. The pstn sensrs utput a relatve pstn f the target, and the multpnt methd utputs the abslute physcal pstn f the target. Bth f these target pstns are used n subsequent frce calculatns. The predcted target pstn frm the multpnt methd s added t the pstn sensr measurements t gve the abslute target pstn at any tme. S, the flux based frce equatn ncludng the predcted target pstn term Calbratn f TMS Demnstratr 49

65 s shwn n Equatn 4.6 where the frngng factr equatn are gven n Equatns 4.7 and 4.8. ( 1 1 B ff B ff A F g = µ ) (4.6) b W x x g b K e A ff ptp b + = + ) ( 1 α (4.7) b W x x g b K A e ff ptp b + = + + ) ( α (4.8) where g s the nmnal gap between the actuatr and target; x s the relatve target pstn frm the pstn sensrs; x ptp s the abslute target pstn frm the multpnt methd; and A b, α b, K b, and W are cnstants frm MFEA fr the partcular bearng gemetry. Includng the predcted target pstn frm the multpnt methd n the current based frce equatn yelds Equatn 4.9 where the frngng factr equatn are gven n Equatns 4.10 and = 1 1 )) ( ( )) ( ( ptp r ptp r g x x g L I ff x x g L I ff A N F µ µ µ (4.9) = W x x g W x x g W x x g W x x g K Ae K Ae K Ae K Ae ff ptp ptp ptp ptp ) ( ) ( ) ( ) ( α α α α (4.10) = W x x g W x x g W x x g W x x g K Ae K Ae K Ae K Ae ff ptp ptp ptp ptp ) ( ) ( ) ( ) ( 1 1 α α α α (4.11) Calbratn f TMS Demnstratr 50

66 where g 1 s the nmnal gap fr the uter legs f the actuatr; g s the nmnal gap fr the center leg f the actuatr; x s the relatve target pstn frm the pstn prbes; x ptp s the abslute target pstn frm the multpnt methd; and A, α, K, W 1, W, W 3, and W 4 are cnstants frm MFEA fr the partcular bearng gemetry. By determnng physcal target pstns and asscated ar gaps, the multpnt methd allws fr accurate determnatn f frces. 4.4 Calbratn Prcedure fr the TMS Demnstratr The system calbratn prgrams use the multpnt methd t determne the predcted rtr pstns fr all the axes t be used n subsequent statc and dynamc frce calculatns. Tw LabVIEW Vrtual Instrument (VI) prgrams are used t calbrate the system: DC FLUX SAVE, used n the setup prcedure, and AUTOCAL, the man calbratn prgram. Bth system calbratn prgrams are lcated n the TMS Cal 15 Axes Autcal flder. Bas currents f 0.9 amps t 1.3 amps n 0.1 amp ncrements, frst ncreasng, then decreasng, are used n the AUTOCAL VI fr a ttal f nne perturbatns. The AUTOCAL VI must be run seven tmes wth a break between each test t allw the bearngs t cl, resultng n seven predcted rtr pstns fr each axs. Seven predcted rtr pstns are fund fr each axs because f the spread n results frm test t test. Fr each axs, the value that devates mst frm the average f these seven predcted rtr pstns s dscarded. The remanng sx predcted rtr pstn are then averaged and used n subsequent statc and dynamc frce calculatns. Ths has been determned t be the best prcedure fr fndng the predcted rtr pstn because f the lw standard devatn fr each average predcted rtr pstn. The TMS calbratn prcedure takes a lttle ver an hur, nt ncludng bearng cl dwn tme between tests. Includng a ten mnute cl dwn tme between tests ncreases the calbratn tme t abut tw and a half hurs. Calbratn f TMS Demnstratr 51

67 4.4.1 Setup Prcedure Several steps must be cmpleted prr t runnng the AUTOCAL VI. Wth the crcut bards pwered and the flatng frame delevtated, the user must frst press the Run arrw f the DC FLUX SAVE. Ths prgram recrds the flux densty vltage utputs frm the crcut bards when the flux n the actuatrs s zer. These vltages are subtracted frm subsequent flux densty measurements t fnd the actual flux densty thrugh each actuatr. Next, the crrect parameter fles must be laded nt the Revlve cntrllers befre the flatng frame s levtated. The parameter values fles (PVFs) wth a bas current f 0.9 amps must be laded frst. Ths s dne usng the MBScpe Parameter Lader sftware suppled by Revlve. The user must clck Brwse n the Parameter Lader wndw t select the Autcal PVF Fles flder. The cmputer can send and receve nfrmatn frm nly ne cntrller at a tme, s the data swtch s used t select the desred cntrller. There are fur pstns n the data swtch: A crrespnds t Cntrller 1(A), B crrespnds t Cntrller (B), C crrespnds t Cntrller 3(C), and D s unused. The user must then tggle the data swtch selectr t the A pstn selectng Cntrller 1(A), and pen the Cntrller 1(A) V0 Bas 0-9 fle. The parameter fles are sent t the cntrller by pressng the Send Fle t Cntrller buttn. Ths prcedure s repeated fr Cntrllers (B) and 3(C), usng the Cntrller (B) V0 Bas 0-9 and Cntrller 3(C) V0 Bas Off parameter fles, respectvely. Nte that the 35_ bearng, cntrller by Cntrller 3(C) s turned ff due t axs nstablty. The data swtch selectr must be tggled t send the fles t the crrect cntrller. Turnng n all three cntrllers levtates the flatng frame f the TMS. The system must nw be allwed t reach a steady state n whch all the axes are levtated and centered. The MBScpe Snapshts sftware suppled by Revlve allws the user t vew the pstns f each axs fr the cntrller selected by the data swtch. The pstns f the axes are pltted n real tme by clckng n the Channels drp dwn menu and selectng Pstns. T vew the numercal values nstead f the plts Calbratn f TMS Demnstratr 5

68 f the pstns, the user can clck n the Vew drp dwn menu and select Statstcs. When all f the pstns f all three cntrllers are fluctuatng wthn the hundredths f a mcrn (µm) range, the system has reached steady state. It takes abut tw mnutes fr the system t reach steady state. The calbratn prcess may nw begn Calbratn Prcedure The system s calbrated by determnng the rtr pstns usng the AUTOCAL VI. The user can enter the amunt f tme desred between tests by enterng the desred value n the Secnds Between Tests cntrl n the frnt panel. Ths s the amunt f tme the user s gven t change the parameter fles f all three cntrllers. The default value s 60 secnds. The Calculatng Test Number ndcatr shws the user whch perturbatn s beng prcessed by the prgram. Fluxes, currents, and pstns are sampled at 104 Hz and averaged ver 104 samples. Cnsequently, data s cllected fr ne secnd mmedately befre the number n the Calculatng Test Number ndcatr changes. Because the transent respnse takes a few secnds t decay when the bas current s changed, all f the parameter fles shuld be laded at least fve secnds befre the Calculatng Test Number changes. Thus, a value f 60 n the Secnds Between Tests really gves the user 55, nt 60, secnds t change the parameter fles f all three cntrllers. A summary f the parameter fles that must be laded n the cntrllers fr each test s shwn n Table 4.1. Table 4.1 shws the parameter fles that must be laded nt the cntrllers fr a gven number appearng n the Calculatng Test Number ndcatr. Fr example, mmedately after the Calculatng Test Number ndcatr changes frm 1 t, the user must begn ladng Cntrller 1(A) V0 1-1, Cntrller (B) V0 1-1, and Cntrller 3(C) V0 Bas Off nt Cntrllers 1(A), (B), and 3(C), respectvely. These fles shuld be laded at least fve secnds befre the Calculatng Test Number ndcatr changes t 3. Calbratn f TMS Demnstratr 53

69 Table 4.1: Summary f PVF Cntrller Fles Used n the AUTOCAL VI Number Value shwng n Calculatng Test Number ndcatr Bas Current (A) Cntrller 1(A) PVF Cntrller (B) PVF Cntrller 3(C) PVF Cntrller 1(A) V0 Bas 0-9 Cntrller (B) V0 Bas 0-9 Cntrller 3(C) V0 Bas Off Press the Run arrw n the AUTOCAL VI Cntrller 1(A) V0 Bas 1-0 Cntrller (B) V0 Bas 1-0 Cntrller 3(C) V0 Bas Off 1.1 Cntrller 1(A) V0 Bas 1-1 Cntrller (B) V0 Bas 1-1 Cntrller 3(C) V0 Bas Off 3 1. Cntrller 1(A) V0 Bas 1- Cntrller (B) V0 Bas 1- Cntrller 3(C) V0 Bas 1-35 Off Cntrller 1(A) V0 Bas 1-3 Cntrller (B) V0 Bas 1-3 Cntrller 3(C) V0 Bas Off 5 1. Cntrller 1(A) V0 Bas 1- Cntrller (B) V0 Bas 1- Cntrller 3(C) V0 Bas 1-35 Off Cntrller 1(A) V0 Bas 1-1 Cntrller (B) V0 Bas 1-1 Cntrller 3(C) V0 Bas Off Cntrller 1(A) V0 Bas 1-0 Cntrller (B) V0 Bas 1-0 Cntrller 3(C) V0 Bas Off Cntrller 1(A) V0 Bas 0-9 Cntrller (B) V0 Bas 0-9 Cntrller 3(C) V0 Bas Off 9 Wat fr the AUTOCAL VI t fnsh runnng After the last parameter fle s laded and the Calculatng Test Number ndcatr reads 9, the AUTOCAL VI calculates the predcted rtr pstns and predcted frces fr each f the axes usng the multpnt methd and saves these values t a fle. The AUTOCAL VI has cmpleted the calbratn when the Runnng arrws return t a sld Run arrw. The calbratn prcedure descrbed abve must be repeated sx tmes fr a ttal f seven calbratns. The same fle f DC flux denstes shuld be used fr all the calbratns, s the DC FLUX SAVE VI shuld nt be run agan. The utput flenames n the AUTOCAL VI must be ncremented every tme the calbratn prcedure s run. Calbratn f TMS Demnstratr 54

70 Fr example, after the frst run, fluxdat1.dat becmes fluxdat.dat, fluxrtpsdat1.dat becmes fluxrtpsdat.dat, etc. The default value s 1.dat. Runnng the AUTOCAL VI seven tmes results n furteen predcted rtr pstn vectrs: seven fr the current based methd and seven fr the flux based methd. These vectrs are used n bth the statc and dynamc frce acqustn prgrams t calculate accurate frces. Calbratn f TMS Demnstratr 55

71 Chapter 5 Thermal Testng 5.1 Intrductn Because the flux sensrs used n the unt are temperature senstve, and lcated n a pstn that s subject t heatng frm the AMB cls, thermal testng was perfrmed n the unts. Ths testng was ntally cnceved t prvde a thermal crrectn factr t subsequent statc and dynamc lad testng. Because the thermal effects f bearng 37_ culd nt be slated, t was mpssble t apply thermal crrectn factrs t all the bearngs. Crrectn factrs must be knwn fr all the bearngs because the ttal frces are a functn f the frces supprted by the ndvdual bearngs. Fr that reasn, subsequent testng s nt crrected fr thermal effects. Even wthut ths crrectn, hwever, the target accuracy f 99.5% was btaned. A mre sphstcated thermal testng prgram culd be develped t crrect fr thermal varatn n the flux sensrs, resultng n mprved accuracy. Such a prgram wuld be recmmended fr a full-scale system. Each actuatr s equpped wth thermstrs fr trackng electrmagnet cl temperatures. The cl and the Hall effect prbes fr ths demnstratr unt are nt desgned t wthstand mre than 180 C and 100 C, respectvely. Because f these thermal lmtatns, trackng the temperature t whch these cmpnents are expsed s essental n rder t prevent damage t the hardware. Addtnally, the Hall effect prbes that are used t measure the flux n the ar gaps are temperature senstve. Because f ths senstvty, t s desrable t have temperature data t crrect the utput, f a temperature Thermal Testng 56

72 crrectn crrelatn fr the prbes can be determned. It s nted that cls and Hall effect prbes are avalable that have a wder range f thermal peratns. The FH-560 flux sensrs used n ths test rg are manufactured by F. W. Bell and, accrdng t the specfcatns, have a maxmum thermal senstvty f 0.1% per degree Celsus. A mnmum thermal senstvty s nt specfed. If the thermal senstvty s near the maxmum value, t may be t hgh t gnre fr the flux accuracy needed n the frce calculatns. Hwever, t crrect fr thermal effects the actual, nt the maxmum, thermal senstvty must be determned fr each prbe. If the actual thermal senstvty s lw enugh, thermal effects may be gnred. The varatn f flux measurements due t thermal effects must reman at less than 0.5% errr t ensure less than 0.5% ttal full lad errr, because frce vares as the square f flux densty. 5. Prcedure Each electrmagnet actuatr n the test rg s equpped wth bth a Hall effect flux sensr fr measurng flux densty and a thermstr fr measurng temperature. Each par f actuatrs has a dfferental eddy current pstn sensr t measure the relatve pstn f the target. Fr each test, the supprt bearngs were energzed t levtate the flatng frame, and ne thrust bearng was energzed. The testng descrbed belw was then perfrmed n the energzed thrust bearng. Ths set-up ensured that changes n flux, current, and pstn were due slely t temperature changes and nt t the bearngs pullng aganst ne anther. Current, flux, pstn, and temperature measurements fr ndvdual actuatrs were recrded as the actuatrs heated up frm ambent (abut 5 C) t abut 75 C. Under lad, the bearngs naturally heat up ver tme due t resstance heatng n the cls. Larger lads, and thus larger currents, cause the actuatrs t heat up mre quckly, and als result n hgher actuatr temperatures. In addtn t flux measurements, current and pstn measurements were taken fr each bearng. If the trend n the flux measurements matched the trend n the current and pstn measurements, then the change n flux was mst lkely due t an actual change n flux and nt a change n Thermal Testng 57

73 measured flux due t temperature changes. Hwever, f the trend n the flux measurement dd nt match the trend n the current and pstn measurements, the trend culd be cnsdered due t thermal effects. The frst bjectve f the thermal testng was t determne f the temperature dependency f the flux measurements culd be gnred. The percent errr full lad fr the flux measurements s calculated usng Equatn 5.1. Bmax Bmn % Errr Full Lad = *100% 6kGauss (5.1) In Equatn 5.1, B max and B mn are the mnmum and maxmum magnetc flux densty ver the temperature range and 6 kgauss s the maxmum expected magnetc flux utput frm the actuatrs. As descrbed abve, f the flux errr s greater than 0.5% errr full lad, then a relatnshp between flux and temperature must be determned t crrect the temperature dependence f the flux measurements. Ths s accmplshed by perfrmng a quadratc least squares curve ft n the flux versus temperature data. An R-squared value s als calculated t determne hw well the curve ft matches the data. Bult-n functns n Mcrsft Excel are used t perfrm the quadratc least squares curve ft and calculate the R-squared value. In general, an R-squared value f greater than r equal t s cnsdered a gd ft f the data. 5.3 Thermal Testng Results and Cnclusns Bearngs 3_, 34_, and 37_ were tested t determne the temperature dependency f the flux measurements. Flux, current and pstn are pltted versus temperature fr bth actuatrs f each bearng. The flux versus temperature plts fr bth actuatrs f bearng 3_ are shwn n Fgure 5.1. These results are typcal f the data fr bth 3_ and 34_. Thermal Testng 58

74 Flux vs. Temp fr Cl 31 Flux vs. Temp fr Cl Flux (kgauss) Flux (kgauss) Temp (degrees C/10) Temp (degrees C/10) Fgure 5.1: Flux Versus Temperature fr Bth Actuatrs f Bearng 3_ There s a defnte trend n the flux versus temperature data fr bth actuatrs f bearng 3_. The flux ncreases slghtly then decreases mre dramatcally as the temperature ncreases. Ths trend culd be due t thermal effects because accrdng t the specfcatns fr the FH-560 prbes, the prbes have a negatve thermal senstvty. Ths means that the vltage utput decreases as the temperature ncreases. It s stll pssble that the trend s smply due t actual changes n flux; fr ths reasn t s necessary t cmpare the current versus temperature plts wth Fgure 5.1 t determne f the trend s due t the thermal senstvty f the prbes r actual changes n flux. Fgure 5. shws the current versus temperature plts fr bth actuatrs f bearng 3_. Current vs. Temp fr Cl 31 Current vs. Temp fr Cl 3 Current Readng (V) Current Readng (V) Temp (degrees C/10) Temp (degrees C/10) Fgure 5.: Current Versus Temperature Plts fr Bth Actuatrs f Bearng 3_ Thermal Testng 59

75 A slght decreasng trend can be seen n the current versus temperature plt fr actuatr 31; hwever, the ppste trend can be seen n the results fr actuatr 3. The slghtly ncreasng trend seen n actuatr 3 s prbably due t I R heatng f the cl wth hgher current. The slght decreasng trend n the current versus temperature plt fr actuatr 31 may be due t cnvectve clng due t the fact that ths actuatr s pstned tward the utsde f the test rg where t s mre susceptble t ar drafts. Despte the fact that there are slght trends n the current data, these trends d nt match the trends seen n the flux data shwn n Fgure 5.1, reteratng the hypthess made earler that the trend n the flux data s due t the thermal senstvty f the prbes rather than actual changes n flux. Because the changes n actual flux shwn n the current versus temperature plts are t small t accunt fr the changes n flux seen n Fgure 5.1, the change n flux s mst lkely due t the thermal senstvty f the flux prbes rather than the changes n actual flux. T further check ths hypthess, the pstn sensr utput s als pltted versus temperature fr bth actuatrs f bearng 3_. These plts can be seen belw n Fgure 5.3. Due t the fact that dfferental pstn sensrs are used n each axs, the pstn versus temperature plts fr actuatrs 31 and 3 are the same. Pstn vs. Temp fr Cls 31 and 3 Pstn Readng (V) Temp (degrees C/10) Fgure 5.3: Pstn Versus Temperature Plts fr Bth Actuatrs f Bearng 3_ Thermal Testng 60

76 It can be seen n Fgure 5.3 that there s n real trend n the pstn data. The gan fr the prxmty sensrs s 0.008n/V, s the changes n pstn seen n Fgure 5.3 are small wth n apparent trend. Because these plts and the current versus temperature plts seen n Fgure 5. lead t the same cnclusn, the trend n flux wth ncreasng temperature fr bearng 3_ s mst lkely due t the thermal senstvty f the flux prbes rather than any actual change n flux. Because the results fr bearng 3_ are typcal fr bearng 34_ as well, ths same cnclusn can be made abut the results frm bearng 34_. The same trends n flux versus temperature are nt seen n bearng 37_, hwever; these results are shwn belw n Fgure 5.4. The trend n flux s nt the same fr bth actuatrs f bearng 37_. Flux vs. Temp fr Cl 371 Flux vs. Temp fr Cl 37 Flux (kgauss) Temp (degrees C/10) Flux (kgauss) Temp (degrees C/10) Fgure 5.4: Flux Versus Temperature Plts fr Bth Actuatrs f Bearng 37_ The flux thrugh actuatr 371 decreases then ncreases wth ncreasng temperature, whle the flux thrugh actuatr 37 ncreases slghtly then decreases. Because the flux prbes have a negatve thermal senstvty, the trend seen n actuatr 371 s mst lkely due t actual changes n flux rather than the thermal senstvty f the flux prbes. The trend n flux seen n actuatr 37 s very smlar t the trend seen n bth actuatrs f bearng 3_ and culd be due t thermal effects. Agan, t s necessary t nvestgate the current versus temperature data as well t check these hyptheses. Thermal Testng 61

77 The current versus temperature plts fr bth actuatrs f bearng 37_ are shwn n Fgure 5.5. Fr actuatr 371, the trend n current matches the trend n flux almst exactly. The current frst decreases, then after abut 55 C starts t ncrease. Current vs. Temp fr Cl 371 Current vs. Temp fr Cl 37 Current Readng (V) Temp (degrees C/10) Current Readng (V) Temp (degrees C/10) Fgure 5.5: Current Versus Temperature Plts fr Bth Actuatrs f Bearng 37_ Therefre, the trend n flux fr actuatr 371 s mst lkely due t actual changes n flux rather than the thermal senstvty f the flux prbe. The trend n current fr actuatr 37 s als smlar t the trend seen n the flux data; hwever, the ntal ncrease at lwer temperature s mre drastc n the current data than the flux data. Ths makes t dffcult t determne the cause f the flux changes fr actuatr 37. The pstn data may allw a cnclusn t be made. The pstn data fr bth actuatrs f bearng 37_ s pltted n Fgure 5.6. Agan, due t the fact that dfferental sensrs are used fr each axs, the pstn data s the same fr actuatrs 371 and 37. As temperature ncreases, the pstn data frst ncreases, then begns decreasng at abut 55 C. Ths fllws the same trend as the flux and current data fr actuatr 37. Ths culd mean that the trend n flux fr actuatr 37 s als a results f actual changes n flux rather than the thermal senstvty f the flux prbe. Thermal Testng 6

78 Pstn vs. Temp fr Cls 371 and 37 Pstn Readng (V) Temp (degrees C/10) Fgure 5.6: Pstn Versus Temperature fr Bth Actuatrs f Bearng 37_ It has been determned that a thermal senstvty can be seen n the flux data at least fr bearngs 3_ and 34_. Therefre, the percent errrs full lad were calculated usng Equatn 5.1 fr bearngs 3_, 34_, and 37_ t determne whether the spread seen n the flux data ver the temperature range was wthn an acceptable range. The results fr the three bearngs tested are summarzed n Table 5.1. Table 5.1: Percent Errr Full Lad Results frm Indvdual Thrust Bearngs % Errr Full Actuatr Lad Ths table shws that nne f the results fall wthn the 0.5% maxmum errr full lad. Ths means that the temperature senstvty f the flux prbe cannt be gnred and must be crrected fr f pssble. In can als be seen that the errrs fr bearng 37_ are much hgher than the ther tw bearngs. Ths s prbably due t the fact that the trends n the flux data fr bearng 37_ are due t actual changes n flux rather than the thermal senstvty f the flux prbes. Because there are actual changes n flux as evdenced n Thermal Testng 63

79 the current data, these changes are larger than changes that wuld result frm the thermal senstvty f the flux prbes therefre leadng t hgher errrs. Because the flux varatns are t large t gnre, a least squares curve ft was appled t the flux versus temperature plts fr bth actuatrs f all three bearngs. Fgure 5.7 shws the results f the curve ft fr bth actuatrs f bearng 3_. Flux vs. Temp fr Cl 31 Flux vs. Temp fr Cl Flux (kgauss) y = x x R = Flux (kgauss) y = x x R = Temp (degrees C/10) Temp (degrees C/10) Fgure 5.7: Least Squares Curve Fts fr Bth Actuatrs f Bearng 3_ The least squares curve fts are shw as a thck black lne whereas the flux data tself s shwn as a sld blue lne wth damnds. The equatns descrbng the curve fts as well as the R-squared values are als shwn n each plt f Fgure 5.7. Fgure 5.7 s meant as an example t shw hw the least squares curve ft was perfrmed usng Excel fr each actuatr f bearngs 3_, 34_, and 37_. Table 5. summarzes the curve ft results fr bth actuatrs f all three bearngs. Table 5.: Summary f Quadratc Least Squares Ft n Flux and Temperature Data Actuatr B = at^ + bt + C; Flux n kg, Temp n C/10 A b c R-squared Value Thermal Testng 64

80 It s frst nted that the ceffcents fr bearngs 3_ and 34_, whle f smlar sgn and magntude, have sgnfcant dfferences. Ths ndcates that a separate thermal crrectn factr wll need t be appled t each flux sensr. It s als nted that the ceffcents fr bearng 37_ are dfferent n bth sgn and magntude, further demnstratng the nn-thermal effects present n ths bearng. Addtnally, all f the R- squared values are belw wth the nly R-squared value abve beng that f actuatr 31. Ths ndcates that quadratc curve may nt be suffcent t ft the data. Effrts were made t elmnate the dscrepances between bearngs 3_ and 34_ versus 37_. Hwever, the cause f the behavr seen n bearng 37_ s stll unknwn. Fr ths reasn a vald thermal crrectn factr fr ths bearng culd nt be derved. Ths nablty t develp a crrectn factr fr 37_ n the current testng, hwever, precludes the pssblty f usng ndvdual crrectn factrs fr each actuatr. The thermal testng results prve that the temperature senstvty f the flux prbes cannt be gnred. The percent errrs full lad fr all f the actuatrs tested were hgher than the 0.5% errr full lad maxmum set by the accuracy needed fr the frce calculatns. The varatn n quadratc least squares curve ft results, hwever, make t mpssble t accurately determne a sngle relatnshp relatng flux and temperature fr all flux sensrs. A separate thermal calbratn curve shuld be develped fr each Hall sensr. Whle ths wuld be pssble f the testng were cnducted prr t system assembly, the nablty t establsh an ndvdual crrectn factr fr bearng 37_ n ths demnstratr unt makes t mpssble t apply ndvdual crrectn factrs fr each bearng. The ablty t develp ths type f testng n a full scale TMS utlzng magnetc bearngs wll mprve the accuracy f that unt ver the results fr the demnstratr. The TMS demnstratr stll has the capacty t make temperature measurements at each actuatr. Ths temperature data s useful n preventng hardware damage t the actuatr cls and Hall effect flux prbes. Thermal Testng 65

81 Chapter 6 Statc Frce Testng 6.1 Intrductn After the calbratn prcedure was cmpleted, fur ladng cases were perfrmed t determne the statc frce measurement capablty f the TMS prttype. The fur statc ladng cases used t test the TMS were cmpleted usng a pstve pull wth the turnbuckle and sx thrust bearngs energzed, a pstve pull wth the turnbuckle and fur thrust bearngs energzed, a negatve pull wth the turnbuckle and sx thrust bearngs energzed, and a negatve pull wth the turnbuckle and fur thrust bearngs energzed. As descrbed n the Statc Frce Acqustn sectn, an axal ladng that results n pullng the flatng frame n the pstve z-drectn s called a pstve pull, and an axal ladng resultng n pullng the flatng frame n the negatve z-drectn s called a negatve pull. Due t tme lmtatns, nly three trals were perfrmed fr each f these cases; hwever, an ndcatn f repeatablty s acheved. Fr each tral, the turnbuckle s tghtened frm n lad t full lad n ten steps. The capacty f each bearng s 37.77lb, s wth sx thrust bearngs energzed, full lad s 6.6lb, and wth fur thrust bearngs energzed, full lad s lb. Thus, fr the ladng cases wth sx thrust bearngs, each step frm n lad t full lad s apprxmately.5lb, and fr the lad cases wth fur thrust bearngs, each step frm n lad t full lad s apprxmately 15lb. 6. Vertcal Weght Results and Cnclusns As descrbed n Sectn 3.3, every tme a new tral s run, t s necessary t run the LabVIEW VI DC THRUST SAVE t calculate the unladed frces n the test rg. Statc Frce Testng 66

82 When the flatng frame s unladed, the nly frce appled t the bearngs n the y- drectn s the weght f the flatng frame, s the sum f the frces fr each bearng n the y-drectn crrespnds t the weght f the flatng frame. Because the flatng frame was nt weghed after fabrcatn, an estmate f the weght f the flatng frame was determned n rder t cmpare t t the flux and current based weght calculatns frm the DC THRUST SAVE VI. The estmatn f the flatng frame weght s based n prduct specfcatns fr sme cmpnents and dgtal scale measurements fr ther cmpnents. The estmated flatng frame weght s 63.66lb. The breakdwn f the frame weght estmatn s shwn n Table 6.1. Cmpnent Thrust Bearng Target Radal Bearng Target Alumnum Framng and Cnnectrs Table 6.1: Estmatn f the Weght f the Flatng Frame Cmpnent Weght Number f Each Ttal Cmpnent (lb) Cmpnent Weght (lb) TOTAL WEIGHT Ths estmated frame weght was then cmpared t the sum f the frces n the y- drectn fr bth the flux and current based frce calculatns frm the DC THRUST SAVE VI. The percent errr full lad was determned usng Equatn 3.3. % Errr Full Lad ( Fflux / current Fest ) = (3.3) N* 3777lb. where F flux/current s the sum f the frces n the y-drectn fr ether the flux r current based frce calculatns, F est s the estmated weght f the flatng frame, N s equal t fur because there are fur bearngs supprtng the flatng frame n the y-drectn, and 37.77lb s the maxmum capacty f each bearng. The weght f the flatng frame s calculated by DC THRUST SAVE befre the turnbuckle s tghtened fr all three trals Statc Frce Testng 67

83 f every ladng case. A summary table cmparng the flux and current based weght calculatns wth the estmated weght s shwn n Table. Table 6.: Cmparsn f Axally Unladed Summed Flux and Current Based Y- Drectn Frces wth Estmated Flatng Frame Weght Case Test Number Flux Based Result (lb) Pstve Pull, 6 Bearngs Pstve Pull, 4 Bearngs Negatve Pull, 6 Bearngs Negatve Pull, 4 Bearngs 1 Estmated Weght (lb) Percent Errr Full Lad Flux Current Based Result (lb) Percent Errr Full Lad Current The flux based frce calculatn prvdes a mre accurate flatng frame weght than the current based frce calculatn. The current based apprach resulted n errrs belw 4.%, and all but ne f the full lad errrs fr the flux based methd are belw 0.50%, the target maxmum errr fr the TMS. 6.3 Axal Ladng Results and Cnclusns Fr each tral f the fur ladng cases, ten data pnts between n lad and full lad were taken. Because the capacty f each bearng s 37.77lb, full lad s 6.6lb fr cases n whch sx thrust bearngs are energzed and lb fr cases n whch fur Statc Frce Testng 68

84 thrust bearngs are energzed. The results fr all fur statc ladng cases are shwn n Fgures 6.1 thrugh 6.8. Each plt shws percent errr versus percent full lad fr all three trals f that ladng case. Fgure 6.1 presents the flux based results fr a pstve pull wth sx thrust bearngs energzed. Flux Based Results fr Flatng Frame Pulled n Pstve Z-Drectn wth 6 Thrust Bearngs On 0.6 Percent Errr Full Lad Flux Based - Tral 1 Flux Based - Tral Flux Based - Tral 3 0.5% Errr Bund -0.5% Errr Bund Percent Full Lad Fgure 6.1: Flux Based Results fr Pstve Pull wth Turnbuckle and Sx Thrust Bearngs Energzed The maxmum errr seen n the flux based results fr ths ladng case s a lttle mre than 4%. All f the errrs fr the flux based methd are belw the maxmum target errr f 0.50%. At lwer lads, the errrs are clse t ne anther; hwever, at hgher lads the spread n the errr ncreases. Beynd ths, there s really n apparent trend n the flux errrs. Statc Frce Testng 69

85 Current Based Results fr Flatng Frame Pulled n Pstve Z-Drectn wth 6 Thrust Bearngs On 1 Percent Errr Full Lad Current Based - Tral 1 Current Based - Tral Current Based - Tral 3 0.5% Errr Bund -0.5% Errr Bund Percent Full Lad Fgure 6.: Current Based Results fr Pstve Pull wth Turnbuckle and Sx Thrust Bearngs Energzed Fr the current based methd results shwn n Fgure 6., hwever, the errr appears t vary lnearly wth lad. Because f the determnstc nature f the errrs n the current based methd, a calbratn culd be determned that wuld decrease these errrs dramatcally. Hwever, ne f the gals f ths wrk s t present a calbratn prcedure that can be perfrmed n a feld stuatn and des nt requre applyng knwn lads. Crrectng fr ths determnstc errr wuld, therefre, negate the benefts f ths calbratn prcedure. The maxmum errr fr ths lad case seen n the current based data s abut 6%. Even thugh the errrs fr the current based methd are hgher than the flux based methd, the multpnt calbratn technque used t prduce ths data has stll prved successful at predctng frces mre accurately ver a large range f lads. Calbratn prcedures that requre applyng knwn lads and, thus, are mpractcal a feld stuatn are prducng errrs f abut 10% (Fttr et al., 1997; Aens, 000) usng a current based frce equatn. Ths ladng case prduces errrs f less than 6% ver the full range f ladng, makng ths frce acqustn technque mre accurate as well as mre versatle. It shuld als be nted that all f the current based errrs are negatve, Statc Frce Testng 70

86 whch means that the current based frce equatn s cnsstently under predctng the frce appled. Fgures 6.3 and 6.4 present the results fr the secnd ladng case wth a pstve pull and fur thrust bearngs energzed fr the flux and current based methds, respectvely. A smlar trend s shwn n the results fr ths ladng case as the ladng case wth a pstve pull and sx thrust bearngs energzed. Flux Based Results fr Flatng Frame Pulled n Pstve Z-Drectn wth 4 Thrust Bearngs On 0.6 Percent Errr Full Lad Flux Based - Tral 1 Flux Based - Tral Flux Based - Tral 3 0.5% Errr Bund -0.5% Errr Bund Percent Full Lad Fgure 6.3: Flux Based Results fr Pstve Pull wth Turnbuckle and Fur Thrust Bearngs Energzed The errrs n the flux based results fr ths ladng case are slghtly hgher wth fur data pnts lyng abve the maxmum target errr f 0.50%. Even s, the largest errr seen fr ths ladng case s 0.54%, whch s nly slghtly abve the maxmum target errr. It s evdent that the fewer number f bearngs runnng des affect the accuracy f results, but nly slghtly. Wth a pstve pull and fur thrust bearngs energzed, all f the flux errrs are pstve, whch means that the flux based frce equatn s cnsstently ver predctng the frce appled. Ths s just the ppste trend as the current based results. Statc Frce Testng 71

87 Current Based Results fr Flatng Frame Pulled n Pstve Z-Drectn wth 4 Thrust Bearngs On Percent Errr Full Lad Percent Full Lad Current Based - Tral 1 Current Based - Tral Current Based - Tral 3 0.5% Errr Bund -0.5% Errr Bund Fgure 6.4: Current Based Results fr Pstve Pull wth Turnbuckle and Fur Thrust Bearngs Energzed The same lnear ncrease wth lad n the current based errrs s seen n ths ladng case as the prevus wth a slghtly hgher maxmum errr. In ths ladng case wth nly fur thrust bearngs energzed, the maxmum errr s clse t 7.5%. Agan, the accuracy f the frce predctns usng the current based frce equatns s slghtly affected by the number f thrust bearngs that are energzed. All f the current based errrs are nce agan negatve, meanng that the current based frce equatn s cnsstently under predctng the appled frces. The flux based results fr the thrd ladng case wth a negatve pull and sx thrust bearngs energzed are shwn n Fgure 6.5. Wth sx thrust bearngs energzed, the errrs n the flux based methd are nce agan all belw the maxmum target errr f 0.50%. Statc Frce Testng 7

88 Flux Based Results fr Flatng Frame Pulled n Negatve Z-Drectn wth 6 Thrust Bearngs On 0.6 Percent Errr Full Lad Flux Based - Tral 1 Flux Based - Tral Flux Based - Tral 3 0.5% Errr Bund -0.5% Errr Bund Percent Full Lad Fgure 6.5: Flux Based Statc Results fr Negatve Pull wth Turnbuckle and Sx Thrust Bearngs Energzed Fr ths ladng case, hwever, there appears t be mre f a trend n the flux based errrs. The errrs are hgher at lwer lads, then decrease t a mnmum at abut 50% full lad, and ncrease agan clse t full lad. Ths culd be explaned n the develpment f the frngng factr equatn whch s a curve ft frmed frm the average f many curve fts ver a large range f lads. Ths wuld lead t lwer errrs at medum ladngs and hgher errrs at ether extreme. Statc Frce Testng 73

89 Current Based Results fr Flatng Frame Pulled n Negatve Z-Drectn wth 6 Thrust Bearngs On 1 Percent Errr Full Lad Current Based - Tral 1 Current Based - Tral Current Based - Tral 3 0.5% Errr Bund -0.5% Errr Bund Percent Full Lad Fgure 6.6: Current Based Statc Results fr Negatve Pull wth Turnbuckle and Sx Thrust Bearngs Energzed The current based methd results shwn n Fgure 6.6 shw the same lnearly ncreasng trend n errr wth respect t lad. Once agan, wth sx thrust bearngs energzed, the maxmum errr s less than 6%. The errr tends t start levelng ff at lads clse t full lad. Ths s mst lkely due t saturatn effects. As the actuatrs apprach saturatn, mre current s needed t prduce nly small changes n flux. Because the current based methd s cnsstently under predctng the appled frce, these larger currents that result frm saturatn lead t smaller errrs. Fgure 6.7 shws the flux based results fr the furth and fnal ladng case wth negatve pull and fur thrust bearngs energzed. There s n apparent trend n the flux based data shwn n Fgure 6.7. Statc Frce Testng 74

90 Flux Based Results fr Flatng Frame Pulled n Negatve Z-Drectn wth 4 Thrust Bearngs On 0.8 Percent Errr Full Lad Flux Based - Tral 1 Flux Based - Tral Flux Based - Tral 3 0.5% Errr Bund -0.5% Errr Bund Percent Full Lad Fgure 6.7: Flux Based Statc Results fr Negatve Pull wth Turnbuckle and Fur Thrust Bearngs Energzed Fr ths ladng case wth a negatve pull and fur thrust bearngs energzed, nly tw data pnts le utsde the maxmum target errr, wth the largest errr beng 0.66%. Ths s a larger maxmum errr than the ladng case wth a pstve pull and fur thrust bearngs energzed, hwever, the number f data pnts that le utsde the maxmum target errr s fewer. Als, as seen n Fgure 6.7, nly ne f the tests resulted n errrs utsde the maxmum target area. Ths means that an errr culd have ccurred durng testng whch led t the hgher errrs fr the ne test. Statc Frce Testng 75

91 Current Based Results fr Flatng Frame Pulled n Negatve Z-Drectn wth 4 Thrust Bearngs On Percent Errr Full Lad Percent Full Lad Current Based - Tral 1 Current Based - Tral Current Based - Tral 3 0.5% Errr Bund -0.5% Errr Bund Fgure 6.8: Current Based Statc Results fr Negatve Pull wth Turnbuckle and Fur Thrust Bearngs Energzed The results frm the current based methd shwn n Fgure 6.8 nce agan shw a lnearly ncreasng trend n errr wth lad fr the fnal ladng case. The maxmum errr fr ths ladng case s abut 6%. Ths shws nce mre that the number f thrust bearngs energzed has nly a small effect n the resultng errrs. Thus far, the lad cell measurements have been assumed t be free f errr, whch s nt true f any measurement. The specfcatns ncluded wth the MLP-300 lad cell state that the accuracy f the lad cell measurements s better than 99.9% full lad. Ths means that the lad cell culd have errrs as large as 0.3 lb (0.1% f full lad) because the full lad f the lad cell s 300 lb. When ths s substtuted nt Equatn 6.1 (a varatn f Equatn 3.3), ths crrespnds t abut a 0.% errr. % Errr Full Lad F = (6.1) N *37.77lb Statc Frce Testng 76

92 Because the largest errr seen n the flux based results s 0.66%, t s pssble that the flux based methd dd n fact measure frces wthn 0.50% errr full lad. Ths s due t the fact that f 0.% errr bars are placed n the largest flux based errr f 0.66%, the bttm bar falls wthn the maxmum target errr f 0.50%. T shw the relatnshp between the flux based and current based results, a plt f calculated axal lad versus lad cell measurement was cnstructed. Fgure 6.9 shws the results frm the frst tral f the pstve pull, sx thrust bearngs energzed ladng case. Ths plt s typcal f all trals f all ladng cases and s desgned t shw the relatve errrs between the flux and current based methds. Calculated Axal Lad vs. Lad Cell Measurement Calculated Axal Lad (lb) Lad Cell Measurement (lb) Flux Based Methd Current Based Methd Lne f Equalty Fgure 6.9: Typcal Plt f Calculated Axal Lad Versus Lad Cell Measurement In Fgure 6.9, the lne f equalty represents the pnts at whch the calculated lad s equal t the lad cell measurements fr axal lads. Because the errrs n the flux based methd are s small, the flux based methd results are hardly dstngushable frm the lne f equalty n ths chart. Ths plt, typcal fr all ladng cases, shws that the Statc Frce Testng 77

93 flux based methd calculates frces mre accurately than the current based methd ver the full range f lads. The results frm statc testng shw that the flux based methd, wth maxmum errrs f abut 0.66% full lad, calculates mre accurate frces than the current based methd, wth maxmum errrs f abut 7.5% full lad. Ths can be cmpared t errrs f abut 1% as seen n prevus wrk nvlvng flux based frce equatns and t errrs f abut 10% as seen n prevus wrk nvlvng current based frce equatns (Aens, 000). Furthermre, f the accuracy f the lad cell s cnsdered, t s pssble that all f the flux based errrs fall wthn the maxmum target errr f 0.50%. There s n trend n the flux based errrs wth respect t percent full lad that apply t all fur lad cases. Fr sme cases the errr decreases wth lad; fr thers, t decreases then ncreases. The current based errrs, hwever, ncrease lnearly wth lad. Thus the technques develped here have mprved the state f the art n bth flux and current based frce measurement. Ths frce measurement technque als has the added advantage that, when the frngng expressns are knw frm MFEA, the calbratn des nt nvlve applyng knwn lads t calculate accurate frces, allwng ths technque t be used n a feld stuatn. The calbratn fr the TMS demnstratr s a prcess that can be cmpletely autmated and results n smaller errrs n the frce calculatns than ther methds. The statc results als prve that the number f thrust bearngs energzed has nly a small effect n the accuracy f the frce measurements. Ths means that a large range f thrusts can be measured n the same test stand smply by energzng dfferent numbers f thrust bearngs. Ths ncreases the versatlty f the TMS beynd exstng technlges allwng ne test stand utlzng magnetc bearngs t replace several test stands utlzng stran gauges wth lwer ranges f thrust capablty. Statc Frce Testng 78

94 Chapter 7 Dynamc Frce Testng 7.1 Intrductn Dynamc testng was als perfrmed n the rcket TMS. Accrdng t results frm prevus TMS tests at NASA, the maxmum frequency cmpnent expected fr a rcket TMS s abut 30Hz. In rder demnstrate the capablty f dynamc frce acqustn beynd ths expected maxmum frequency, the magnetcally levtated rcket TMS prttype was tested up t 50Hz. Recall that the flatng frame s nt equpped wth accelermeters; therefre, t s nt pssble t crrect fr the ampltude and phase shfts asscated wth the nerta f the flatng frame. The magnetstrctve frce actuatr was used t nput varus frequences nt the TMS. Frce data was recrded fr nput sne waves f 5, 10, 0, 30, and 50Hz wth zer t peak ampltude f half a vlt resultng n peak lad cell frces frm abut 4lb at 5Hz t abut 55lb at 50Hz. The dynamc acqustn VI FORCE MEASURE was used t recrd the lad cell measurement and the flux and current based frce resultants. The prgram was set up wth a samplng rate f 1000Hz acqurng 300 samples per channel. Cnsequently, frces are calculated ver a tme perd f three tenths f a secnd. An advantage f a magnetcally levtated rcket TMS ver current stran gauge desgns s that the dynamcs, ncludng the lcatn f system resnant frequences, f the TMS can be cntrlled by changng the gan parameters f the magnetc bearngs. T prve ths capablty wth the TMS demnstratr, a swept sne wave frm 5 t 50Hz, n ffteen steps, wth a zer t peak magntude f a half a vlt was nput nt bth the Dynamc Frce Testng 79

95 rgnal system and the stffer system. The stffer system was acheved by dublng the prprtnal gan f the magnetc bearngs. Fr the swept sne wave nput, the FORCE MEASURE VI was set up wth a samplng rate f 500Hz acqurng 7500 samples per channel. Thus frces are calculated ver a tme perd f ffteen secnds. 7. Dynamc Results and Cnclusns fr Orgnal System In Fgure 7.1, the frces fr the flux and current based methds as well as the lad cell measurements are pltted versus tme fr an nput frequency f 5Hz. Fgure 7.1: Dynamc Results fr Input Frequency f 5Hz fr Orgnal System The phase and AC cmpnent f the current based resultant are almst exactly the same as the lad cell measurement; hwever, the flux based resultant s mre accurate at calculatng the DC cmpnent f the nput frce. Ths s unexpected because the flux based methd shuld predct bth the AC and DC cmpnents f frces mre accurately than the current based methd due t the fact that the flux s measured drectly rather than nferred frm cl currents and target pstns. Even thugh the TMS demnstratr s nt equpped wth accelermeters t crrect fr nertal effects f the flatng frame, at lw frequences where the system dynamcs are mnmal, a gd crrelatn between the nput frce as measured by the lad cell and the reactn frce as measured by the flux Dynamc Frce Testng 80

96 and current based frce calculatns s expected. Nevertheless, at an nput frequency f 5Hz, all three methds f frce measurement are farly clse n bth phase and ampltude. Fgure 7. shws the dynamc results fr an nput frequency f 10Hz. At ths nput frequency, the current based methd agan predcts bth the AC cmpnent and phase f the lad cell measurement mre accurately; hwever, the flux based methd predcts the DC cmpnent mre accurately. Fgure 7.: Dynamc Results fr Input Frequency f 10Hz fr Orgnal System As n the prevus case wth an nput frequency f 5Hz, the peak t peak ampltude f the lad cell and current based measurements s abut 8lb, whereas the peak t peak ampltude f the flux based measurement s abut 10lb. Ths agreement wth the 5Hz nput frequency results shws that the effects f system dynamcs are stll qute mnmal at 10Hz. In ther wrds, the flux and current based resultants at nput frequences f 5Hz and 10Hz that have nt been crrected fr the nerta f the flatng frame shuld be clse n bth ampltude and phase t the actual reactn frces at the bearngs. The dynamc results fr an nput frequency f 0Hz are shwn n Fgure 7.3. At ths nput frequency, t s the flux based methd rather than the current based methd that calculates the AC cmpnent f the lad cell mre accurately. Dynamc Frce Testng 81

97 Fgure 7.3: Dynamc Results fr Input Frequency f 0Hz fr Orgnal System S, fr an nput frequency f 0Hz, the flux based methd predcts bth the AC and DC cmpnents f the nput frce mre accurately than the current based methd. The peak t peak ampltude f the lad cell measurement s abut 8lb whch s clse t 7lb, the peak t peak ampltude f the flux based methd. It shuld be nted that the peak t peak ampltude f the current based methd s 10lb fr an nput frequency f 0Hz, whch s qute a large ncrease frm the 8lb peak t peak ampltude frm the 10Hz case. The man frequency cmpnent f all three frce measurements s 0Hz; hwever, there s a 60Hz cmpnent supermpsed n the lad cell measurement. Ths s prbably nt due t nse because t des nt appear n any f the prevus results; hwever, t shuld be nted. Fgure 7.4 shws the dynamc results fr an nput frequency f 30Hz. Once agan, the flux based methd predcts bth the AC and DC cmpnents f the lad cell measurement mre accurately than the current based methd. Bth the lad cell measurement and flux based resultant have a peak t peak ampltude f abut 6lb. The current based AC ampltude s very hgh whch s prbably due t hysteress and eddy current effects. At the nput frequency ncreases, the currents n the cls must als Dynamc Frce Testng 8

98 change mre quckly t keep the flatng frame levtated. These quckly changng currents lead t resdual currents that must be vercme by the nput current frm the cntrller. Ths means that a large current s needed fr nly a small change n flux because sme f the current s beng used t vercme the resdual currents and hysteress effects. Ths wuld lead t ver predctns n the frces calculated by the current based methd. The flux based methd wuld be unaffected by hysteress and eddy current effects because the flux s beng measured drectly, nt nferred frm current and target pstn data. Fgure 7.4: Dynamc Results fr Input Frequency f 30Hz fr Orgnal System The 60Hz frequency cmpnent n the lad cell measurement s a bt strnger at an nput frequency f 30Hz than an nput frequency f 0Hz. Ths cmpnent s prbably due t harmncs wthn the lad cell nstead f nse because t s nly seen when the frame s frced at 0Hz and 30Hz. When the frame s frced at 0Hz, the secnd harmnc s 60Hz; whereas when the frame s frced at 30Hz, the frst harmnc s 60Hz. Ths explans the fact that the 60Hz cmpnent s strnger when the frame s frced at 30Hz than when the frame s frced at 0Hz because harmncs drp ff n ampltude wth ncreasng frequences. There are n 60Hz cmpnents n ether the flux r current based frce resultants. Dynamc Frce Testng 83

99 The fnal nput frequency t the TMS demnstratr was 50Hz. These results are shwn n Fgure 7.5. At ths frequency, the lad cell measurement data shws nput frces that are beynd the capablty f the magnetstrctve frce actuatr. Ths prbably means that there s a system resnance clse t 50Hz. The flux based resultant s nly 5lb peak t peak whch shws that the dynamcs f the system are begnnng t becme sgnfcant. Ths means that the flux and current based resultants must nclude the nertal cmpnent f the flatng frame t gve accurate frce and phase nfrmatn. The current based methd s als predctng frces that are ncapable f beng generated by the frce actuatr. Ths s prbably due t the hysteress and eddy current effects dscussed prevusly. Fgure 7.5: Dynamc Results fr Input Frequency f 50Hz fr Orgnal System Frm the dynamc results f the rgnal system as a whle, several bservatns can be made. As the frequency s ncreased, bth the magntude and phase f the flux and current based frce calculatns devate mre. The larger devatns n magntude f the flux based methd at hgher frequences culd be due t the fact that the effects f the system dynamcs are strnger at hgher frequences. Therefre, the lwer the nput frequency, the better the results f they are nt crrected fr system dynamcs. At hgher nput frequences, the current based resultant ncreases n magntude. Ths s prbably Dynamc Frce Testng 84

100 due t hysteress and eddy current effects and cannt be crrected fr. It shuld als be nted, that the lad cell measurements are als much larger than the capablty f the frce actuatr at 50Hz. Ths culd be evdence f a system resnant frequency clse t 50Hz. T check ths hypthess and prve that varyng the gan parameters f the magnetc bearngs can change the dynamcs f the system, a swept sne wave nput frm 5Hz t 50Hz was nput nt the flatng frame. The FORCE MEASURE VI was set up wth a samplng rate f 500Hz acqurng 7500 samples per channel. Fgure 7.6 shws the tme respnse fr flux and current based frce calculatns as well as the lad cell measurement fr the rgnal system. In ths plt, the frequency starts at 5Hz and ncreases 3Hz every secnd untl t fnally reaches 50Hz at 15 secnds. Thus, every secnd n the x-axs represents a 3Hz ncrease n frequency. Fgure 7.6: Tme Respnse wth Swept Sne Input fr Orgnal System The measurement frm the lad cell shws a decreasng trend untl abut 11 secnds, r abut 35Hz, fllwed by an ncreasng trend beynd the mnmum at 11 secnds. Ths s evdence that the system s apprachng a resnance at abut 35Hz. Dynamc Frce Testng 85

101 Fgure 7.7: Tme Respnse fr Lad Cell wth Swept Sne Input fr Orgnal System The trend can be seen mre clearly n Fgure 7.7 where the lad cell data s pltted by tself. As the system appraches the resnance, the structure becmes very plable leadng t a smaller nput frce needed t mve the frame a gven dstance. Then, after the system passes thrugh the resnant frequency, t appears as thugh the flatng frame s mvng 180 ut f phase wth the nput frm the magnetstrctve frce actuatr causng the respnse t ncrease as the frequency ncreases. In rder t cmpletely determne whether r nt the system s gng thrugh a resnance at abut 35Hz, a plt f phase versus frequency s needed. Ths culd be accmplshed by determnng the transfer functn between frce and pstn and plttng the phase fr ths transfer functn versus frequency. A phase shft f 180 wuld desgnate a system resnance. Unfrtunately, tme restrctns dd nt allw ths t be nvestgated. The tme respnse fr the flux based measurement des nt fllw the same ncreasng trend as the lad cell measurements. Instead, the tme respnse fr the flux based methd cntnues t decrease as the frequency ncreases. Ths s due t the fact Dynamc Frce Testng 86