Air Rocket Thrust Experiment Involving Computerized Data Acquisition, Calibration, and Uncertainty Analysis

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1 Air Rocke Thrs Experimen Involving Comperized Daa Acqisiion, Calibraion, and Uncerainy Analysis Michael R. Kessler Deparmen o Mech. Eng., The Universiy o Tlsa Absrac The developmen and modiicaion o a laboraory experimen o deermine he hrs characerisics o an air propelled rocke is described. The experimen is sed in he jnior level Insrmenaions and Measremens corse in he Deparmen o Mechanical Engineering a he Universiy o Tlsa. I involves elemens o insrmen calibraion, comperized daa acqisiion, and ncerainy propagaion. The experimenal deails o he laboraory are described along wih he goals o he experimen and a descripion o he daa analysis procedre. Sden opinions o he lab experience as deermined by a srvey abo he lab are presened and ways o improve he lab based on sden commens are discssed. Inrodcion Three imporan conceps ha are covered in mos experimenal mehods corses are insrmen calibraion, comperized daa acqisiion, and propagaion o ncerainy ino a calclaed resl. While hese conceps are oen agh in he classroom, sdens benei more by acively learning abo hese conceps in he laboraory. This paper describes an experimen ha has been developed or he Insrmenaion and Measremens corse in he Universiy o Tlsa s Deparmen o Mechanical Engineering. This jnior level lecre-laboraory corse conains biweekly laboraory exercises where sden eams perorm hands on experimens and hen wrie p heir lab experience and resls in a ormal echnical lab repor. The lively laboraory is pariclarly well received by he sdens becase i involves he iring o an insrmened ballisic pendlm. The exciemen o iring a ballisic air rocke in he laboraory adds o sden moivaion and helps o reain heir aenion. An iniial version o he experimen was developed by Dr. Denis Zigrang a he Universiy o Tlsa and sbseqenly modiied [1]. The modiied experimen involves acqiring daa sing he comper and daa acqisiion soware and calibraing several sandard measremen ransdcers, e.g. acceleromeer, roary variable dierenial ransormer RVDT, and diaphragm pressre ransdcer. In he sbseqen lab wrie p, he sdens are reqired o calclae he experimenal ncerainy in he calclaed implse based on he elemenal ncerainies in he measred signals. Experimen Descripion The prpose o he experimen is o deermine he hrs characerisics o an air rocke. This experimen shold amiliarize sdens wih ypical insrmen calibraion procedres, comperized daa acqisiion, and he operaion o a roary variable dierenial ransormer RVDT, nbonded srain gage acceleromeer, and pressre ransdcer. Aer compleing he Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

2 experimen, he sden shold be able o calibrae linear insrmens sch as pressre ransdcers and acceleromeers. The sden shold also have gained enogh knowledge hrogh he experimen and discssion o explain he operaing principles o RVDTs, acceleromeers, and diaphragm pressre ransdcers and he componens o a daa acqisiion sysem. In he experimen, a modiied ire exingisher air rocke is moned o he end o a pendlm. An elecric solenoid valve is aached a he head o he air rocke. On he rocke is also moned a 1-D nbonded srain gage acceleromeer and a diaphragm pressre ransdcer. A RVDT is moned on he pivo o he pendlm o measre he anglar posiion o he pendlm arm. A PC based daa acqisiion sysem, consising o a PCI Bs Daa Acqisiion Board, screw erminal connecor, signal condiioning modles, and abview soware is sed o record he signals rom he ransdcers and o ire he rocke by opening he elecric valve a he head o rocke. The deails o he eqipmen sed in he experimen are lised in Table 1 below. Table 1. Eqipmen is. Iem Manacrer Model/Version 1. Modiied ire exingisher Waler Kidde and Company -4. Elecric solenoid valve Aomaic Swich Company 81C 3. 1-D nbonded srain gage acceleromeer Saham 6 A3 4. Diaphragm pressre ransdcer Borns 9. RVDT Schaeviz Sensors R3D 6. Dial op analog pressre gage Marsh PCI Bs Daa Acqisiion Board Keihley Insrmens, Inc. KPCI Screw erminal connecor Keihley Insrmens, Inc. STP Signal condiioning modles Omega Engineering, Inc. OM3 9. abview soware Naional Insrmens Version 6.1 The pendlm assembly is shown in igre 1. The air rocke shown in igre is moned o he end o he pendlm arm wih he iring nozzle oriened in he plane o he pendlm roaion. The pendlm roaes on a pair o ball bearings o minimize ricional losses in he sysem. The RVDT is conneced o he roaing axel and sis in a circlar mon on he op o he assembly. The pendlm arm can be locked in an arrangemen exacly 4 degrees rom he verical posiion by sliding a pin in he 4 degree posiioning slo. Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

3 igre 1. Pendlm Assembly igre. Phoograph o Rocke Assembly Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

4 The sdens irs calibrae he sysem by convering he volage signals rom he ransdcers ino pressre, acceleraion, and anglar posiion by applying known inps and adjsing he zeroose and saic sensiiviy in he soware. or he RVDT and acceleromeer, he known inps are deermined by examining he signal while he pendlm is in he verical posiion so ha he air rocke is horizonal and he 4 degree posiion sing he posiioning slo. The ser inerace rom he daa acqisiion soware is shown in igre 3. While he sdens do no wrie he daa acqisiion code or design he ron panel ser inerace, hey are shown he nderlying abview wiring diagram and given an explanaion o how he code works. When he rocke is a res in he horizonal posiion, he sdens adjs he zero ose volage rom he RVDT and acceleromeer signal so ha he eecive signals are zero. Then he sdens posiion he rocke a 4 degrees. The signal in degrees or acceleraion is eqal o he mv inp mliplied by he saic sensiiviy o he ransdcer. The sdens adjs he saic sensiiviy or he RVDT on he ron panel nil he signal reads 4 degrees. Then he sdens adjs he saic sensiiviy or he acceleromeer nil he signal reads g sin 9.87 sin m/s. The diaphragm pressre ransdcer is calibraed by comparing is op o a dial op pressre gage ha is conneced o he solenoid valve and adjsing is saic sensiiviy o mach he dial gage op. Hi o rn program Zero ose correcion, adjs so ha RVDT gives zero vols when a res Saic sensiiviy o RVDT, sed o calibrae a 4 deg. Zero ose correcion or Acceleromeer Saic sensiiviy o Acceleromeer. A 4 deg, acceleraion shold be m/s Adjs so ha Pressre reading maches dial on rocke Hi o sop program Daa Acqisiion Rae in ms. engh o ime o acqire daa Press o ire rocke and acqire daa igre 3. abview ron Panel Aer calibraion is complee, he sdens adjs he daa acqisiion rae, ener he amon o ime ha hey wan o collec daa, and send an op volage rom he comper o he valve Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

5 aached o he air rocke, opening he valve and allowing air o escape hrogh a nozzle. The sdens perorm or lanches o he air rocke assembly, wih iniial pressres o, 4, 6, and 8 psi. The sdens also deermine he naral period o oscillaion by raising and releasing he pendlm and recording he RVDT op. By recording and reviewing he RVDT op, he sdens can easily ind he period o oscillaion which is sed o calclae he polar momen o ineria in he analysis. Analysis Descripion The ollowing nomenclare is sed in he analysis o he daa T - Time period o oscillaions s g - Acceleraion de o graviy 9.87 m/s m - Toal mass m R m mass o rocke mass o leg kg - engh rom pivo o cener o graviy o rocke assembly m - Polar momen o ineria o rocke assembly kg-m - Polar momen o ineria o leg kg-m R - Polar momen o ineria o rocke kg-m 1 - engh o leg m - engh o weld illing m 3 - engh o rocke verical lengh exernal diameer o rocke, m - engh rom pivo o he cenral axis o rocke m - orce exered by he rocke by release o compressed air N - Angle beween he leg and he verical line a a pariclar insan deg. I - Implse N s a - Acceleraion experienced by he rocke a a pariclar insan m/s α - Anglar acceleraion experienced by he rocke a a pariclar insan rad/s 1 m g R Ay A igre 4. Geomery and ree Body Diagram R Ax In he analysis, he sdens irs compe he polar momen o ineria o he pendlm rocke assembly sing he period o oscillaion mehod and by direc calclaion. Compaion o Polar Momen o Ineria, Period o Oscillaion mehod: T m gt π eq. 1 gm 4π Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

6 Compaion o Polar Momen o Ineria, Direc Calclaion: R eq. 1 m m 1 x dx eq m eq. 4 R R m 1 mr eq. 3 Compaion o hrs,, as a ncion o ime and Implse, I: Nex hey compe he hrs as a ncion o ime in erms o he measred acceleraion and anglar posiion. They begin by smming he momens abo he pivo o he pendlm, poin A. a g sin ΣM m g sin α where α eq. 6 A m g sin a g sin eq. 7 sin sin a g m g eq. 8 is implicily dependen on ime. Nex he sdens calclae he oal implse o he rocke or each iniial pressre by solving I d sing nmerical inegraion. Experimenal Error Analysis: inally, he sdens calclae he ncerainy in he implse and hrs by propagaing he ncerainy rom he individal ransdcer and dimensional measremens ino he resls. The propagaion o ncerainy in he variables o he resl yields an ncerainy esimae by n. x 9% eq. 9 i X i 1 i where each Xi is a variable sed o calclae he hrs,, and x, is he esimaed 9% ncerainy in each o hese variables []. Assming negligible ncerainy in he graviaion consan, g, here are six variables ha conribe o he hrs in eqaion 8. Combining eqaion 8 and 9 yields Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

7 Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion m a m a eq. 1. The ncerainy in he polar momen o ineria,, and ncerainy in he lengh rom he pivo o he hrs line,, are given below. T m T m eq eq. 1 The parial derivaives in eqaion 1 1 are deermined rom eqaion 8 and lised below: sin g a eq. 13 m g sin eq. 14 a eq. 1 sin g m eq. 16 sin sin 3 m g g a eq. 17 m g g cos cos eq. 18 The ncerainy in he orce and implse are wrien in erms o percenage below: %U U / *1% eq. 19 %U I %U Ignoring U eq.

8 Going rom eqaion 19 o eqaion is no enirely correc becase he ncerainy in is no a consan vale, b changes wih ime, while he ncerainy in implse shold be a ixed vale. Sdens can choose o se he percen ncerainy in a he maximm hrs o esimae he percen ncerainy in implse rom eqaion, or se more deailed ncerainy analysis o propagae he ncerainy hrogh he nmerical inegraion. Typical Resls Aer iring he rocke a he or dieren pressre levels and recording he daa, he sdens plo he measred variables anglar posiion, pressre, and acceleraion verss ime sing Excel. Then wih heir Excel daa hey calclae he hrs verss ime sing eqaion 8. Typical resls a an iniial pressre o 8 psi are shown in igre. a 4 AngleDeg b PressrePsi Time sec Acceleraionm/s Thrs N Time sec igre. Typical resls rom he experimen a Anglar displacemen and pressre verss ime or iniial pressre o 8 psi. b Acceleraion and calclaed hrs verss ime or iniial pressre o 8 psi. Nex, he sdens calclae he implse and associaed ncerainy in he orce and implse as a ncion o ime. Typical resls or he or dieren iniial pressres are shown in igre 6. The error bars in igre 6 represen he U 9 ncerainy esimaed wih eqaion. Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

9 8 7 6 Implse N sec Iniial Pressre psi igre 6. Typical resls o calclaed implse and associaed ncerainy or or dieren iniial pressres. Sden Assessmen Aer he sdens rned in heir laboraory repors wo weeks aer perorming he experimens a shor srvey was given in order o assess he eeciveness o and sden aides owards his laboraory exercise. The srvey conained nine qesions/commens. The irs seven commens sed a six poin iker scale o indicae i hey srongly disagree, disagree, slighly disagree, slighly agree, agree, or srongly agree wih each saemen. A nmber rom 1 or srongly disagree o 6 or srongly agree was assigned o each selecion. The las wo qesions were open ended shor answer qesions asking he sdens o lis srenghs o he Rocke Engine Thrs Experimen and commen on how he experimen cold be improved. A oal o 31 sdens responded o he srvey. The irs seven qesions rom he srvey are lised in Table below. Hisograms, showing he disribion o iker scale responses or each qesion, are shown in igre 7. Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

10 Table. iker scale qesions rom srvey. Qesion/Commen Average Response 1. The experimen did a good job o amiliarizing me wih ypical insrmen 4.4 calibraion procedres.. The laboraory did a good job o amiliarizing me wih comperized daa 4.6 acqisiion and abview. 3. The laboraory did a good job o amiliarizing me wih he operaion o a roary 4.9 variable dierenial ransormer RVDT, acceleromeer, and pressre ransdcer. 4. Deailed ncerainy analysis became more clear as a resl o he experimen and 4.4 lab wrie-p.. The lab and sbseqen lab repor cased me o hink criically abo sorces o 4.48 experimenal error ha conribe o ncerainy in he rocke engine hrs. 6. Overall he lab was a posiive experience Overall he lab wrie-p was a posiive experience. 3.9 Qesion 1 Qesion Qesion 3 Qesion Con Qesion Qesion 6 Qesion Con igre 7. Hisogram resls or iker scale resls or commens 1 hrogh 7. Srongly Disagree 1, Srongly Agree 6. Some o he commens rom he irs open ended qesion abo he srenghs o he experimen are lised below. I was n o see how he se p worked The ncerainy analysis calclaions become more clear, and were a good complimen o he maerial sdied in Ch.. Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

11 Being able o see how he calibraion o pressre had o be adjsed really helped me see how error changes hrogh he measremen I enjoyed learning abo he daa acqisiion sysem Good se o daa colleced, airly easy o analyze Calibraion, daa acqisiion, and abview ndersanding I go exposed o parial derivaive and ncerainy more Perorming he ncerainy analysis in he lab wrie p helped me ndersand how ncerainy propagaes Clariy in how o inerpre he daa, calclae hrs and implse, and ind varios ncerainies. Helped me beer ndersand he eec o ncerainies in measremen I was cool. I made yo hink o error ha occrred. I also made yo realize how imporan calibraion hrogh an experimen is. One o he greaes srenghs o he experimen was ha we were orced o ind ncerainy as a ncion o changing variables and hereore saw exacly how ncerainy can change wih ime or an experience. I was n. Examples o commens abo how he lab cold be improved inclde he ollowing. I hogh he lab was grea. The only problem I had was wih he wrie p. I gess i he calclaions in he wrie p cold have been rher explained ha wold improve he lab. I ond he amon o daa colleced and p in excel was very cmbersome and edios. I we cold learn how o se he program prior o sing i in he lab. Sep hrogh an example o calclaing he ncerainy analysis. oose he annoying TA, more sden involvemen. None, good as i is. Don' really have any problem wih i I was los when abview was being explained since i was he irs ime I saw i. rher explanaion o he program and componens RVDT, randcer, acceleromeer sed o gaher he daa. More backgrond on how he pressre ransdcer acally works. No sre i can. I seemed very edios earn more abo abview I wold like o have programmed abview on my own o calibrae he ransdcers. Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion

12 Conclsions Improvemens o he laboraory can cerainly be made based on some o hese sden commens. One sggesion is o lenghen he lab by having he sdens program he daa acqisiion code hemselves. Also, by spending more ime or more class ime beore he lab discssing he operaing principles o RVDTs, acceleromeers, and diaphragm pressre ransdcers he lab experience wold be srenghened. However, or he mos par, his laboraory exercise worked well o amiliarize he sdens wih ypical insrmen calibraion procedres, comperized daa acqisiion, and deailed ncerainy analysis. Over 9% o he sdens a leas parially agreed ha he laboraory was a posiive experience based on he pos experimen srvey. Appendix The ollowing vales and ncerainies were sed in he calclaions Toal Mass m 391.4g ±.1g Mass o eg m 164g ±.1g Cener o Graviy : 7.mm± mm±.mm 4.97mm±.mm 3 11.mm±.mm 1 3 / Graviaional acceleraion g 9.87 m/s assme exac. 3 a ±.3m/s ±. T ±. sec. Reerences igre 8. Deiniion o 1, and 3 [1] Zigrang, Denis. Elemens o Engineering Measremens, Revision 6, College o Engineering, Universiy o Tlsa. Ags, [] igliola, Richard S. and Beasley, Donald E. Theory and Design or Mechanical Measremens, 3 rd ed. New York: ohn Wiley & Sons, Inc., MICHAE R. KESSER Michael Kessler is an Assisan Proessor o Mechanical Engineering a The Universiy o Tlsa. His research ineress inclde he mechanics and processing o polymers and polymer marix composies, hermal analysis, racre mechanics, and biologically inspired maerials. He is a member o ASME and ASEE. Proceedings o he American Sociey or Engineering Edcaion Annal Conerence & Exposiion Copyrigh, American Sociey or Engineering Edcaion