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PROJECT 2
By
Ramon Lopes de Arajo
ME438 Section 802_13858
Mec anica! En"ineerin" E#perimentation
$ni%ersity o& 'isconsin ( Mi!)a*+ee
,o!!e"e o& En"ineerin" App!ied Science
-. Bo# /84
Mi!)a*+ee 'isconsin 53201 0/84
Marc 28t 2014
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1.Introduction
is report e!on"s to t e second project o& t e co*rse ME, ECD
438 Mec anica! En"ineerin" E#perimentation &rom $ni%ersity o&
'isconsin Mi!)a*+ee6 e e#periments carried o*t are ca!i ration o&
&re9*ency !oad ce!! and air %e!ocity transd*cer6 e project is di%ided
into c apters ) ic t ey are denominated in !iterat*re re%ie)
met odo!o"y res*!ts disc*ssion o& res*!ts and conc!*sion6 >n !iterat*re
re%ie) contains in&ormations &rom oo+s artic!e or anot er so*rce) ic t ey e!p t e reader to *nderstand t e iss*es o& t e
e#perimenta! )or+ and interpretation o& t e data6 Met odo!o"y e#p!ains
o) t e e#periments )as cond*cted t e e9*ipment and so&t)are *sed
and t e settin"s o& t e e#periment6 Res*!ts s o) t e res*!ts o tained in
"rap s and ta !es6 isc*ssion o& res*!ts as a t eoretica! &o*ndation
t at aims to e#p!ain t e res*!ts e%en i& t e res*!ts are not consistent
)it t e !iterat*re6 ina!!y t e conc!*sion ) ic contains a c!ear
s*mmary a o*t ) o!e project6
,a!i ration is a set o& operations t at ens*res t at a meas*rin"
instr*ment operates )it in a "ood standard o& meas*rement6 >t can not
to ta!+ a o*t ca!i ration i& it not ta!+ a o*t statistica!6 *s statistica! is
a too! presents in t is project t at assists to *nderstand t e data6 An
important topic present in t is project is t e statistica! *ncertainty
ana!ysis6 >t is a )ay to interpret e#perimenta! data6
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2.Literature Review
e p*rpose o& t e !iterat*re re%ie) is to e#emp!i&y t e t eoretica!
&o*ndations and to "i%e s*pport &or a "ood *nderstandin" o& t e
e#periments done6 .&ten t e data are diFc*!t to *nderstand *t t ey
can e so!%ed )it t eoretica! &o*ndations6 e e#periments carried o*t
are ca!i ration o& &re9*ency !oad ce!! and air %e!ocity transd*cer6 A!on"
)it t is t e statistica! st*dy is %ery important to interpret and
*nderstand e#perimenta! data t e est )ay as possi !e6
o *nderstand a o*t ca!i ration process carried o*t in t e
e#periments one m*st 7rst *nderstand its de7nition6 ,a!i ration as
een de7ned y t e >nternationa! B*rea* o& 'ei" ts and Meas*res as
an .peration t at *nder speci7ed conditions in t e 7rst step
esta !is es a re!ation et)een t e 9*antity %a!*es )it meas*rement
*ncertainties pro%ided y t e meas*rement standards and
correspondin" indications )it associated meas*rement *ncertainties
?o& t e ca!i rated instr*ment or secondary standard and in t e second
step *ses t is in&ormation to esta !is a re!ation &or o tainin" a
meas*rement res*!t &rom an indication 6 Calibration is defined as an
association between measurements one of a scale or accuracy made or set
with one piece of equipment and another measurement made in as similar a way
as possible with a second piece of equipment. The piece of equipment or device
with the known or assigned accuracy is called the standard.
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ast o*rier rans&orm ? is a type o& discrete appro#imation o& a
o*rier trans&orm6 ,arr G Madan ?1=== ad t e &o!!o)in" to say a o*t
t is met odH I6667nd t at t e *se o& t e is considera !y &aster t an
most a%ai!a !e met ods and &*rt ermore t e traditiona! met od
descri ed in eston Bates Ba+s i and Madan and Scott can e ot
s!o) and inacc*rate666J6
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C> =1N2 $+*!e!e -o)er s*pp!y
Figure 1: NI9162 used in t e ex!eriment 1"
Speci7c data &rom t e acce!erometer ca!i rator is in 7"*re 26 >ts
main in&ormations areH &re9*ency e9*a! to 15=62 K ?O P 1 000 radQs 6
Acce!eration e9*a! to 10 ms < ?RMS 3@6 :e!ocity e9*a! to 10 ms
?RMS 3@6
Figure 2: a# $ccelerometer calibrator used in t e ex!eriment 1" b# %ata of t eaccelerometer
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Load ce!!H .me"a L,101 Stain!ess Stee! C> =21= -o)er s*pp!y
Figure ): Load cell calibration*s setu!"
e e#perimenta! desi"n o& t e e#periment 261 )as or"aniKed as
&o!!o)sH
-er&orm t e sensor e#periment in ascendin" and
descendin" increments &or 4 cyc!es ?0! T 1! T 3! T N! T
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8! T N! T 3! T 1! T 0! 6 Record a!! t e data )it t e
LabView" Statistica! ana!yses6 Meas*re &o*r *n+no)n %aria !es *sin" a*tomatic
con%ersion &*nction in LabView 6 ,ompare t e res*!ts o& e#periments )it t e t eoretica!
prediction6
3.3 E !eri"ent 2.2# 'ir (elocity
Tran)ducer Cali&ration
or t e rea!iKation o& t e e#periment ca!!ed !oad ce!! t e
e9*ipment t at a%e een *sed areH
Air %e!ocity ransd*cer C> =21= -o)er s*pp!y
Air %e!ocity transd*cerJs in&ormations can e &o*nd in t e 7"*re
56
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Figure +: $ir ,elocit- transducer*s informations"
e e#perimenta! desi"n o& t e e#perimente 262 )as or"aniKed
as &o!!o)sH
-er&orm t e sensor e#periment in ascendin" and
descendin" increments &or 4 cyc!es ?5 : T / : T = : T 11 :
T 13 :T 11 : T = : T / : T 5 : 6 Record a!! t e data )itt e LabView"
Statistica! ana!yses6 Meas*re &o*r *n+no)n %aria !es *sin" a*tomatic
con%ersion &*nction in LabView 6 ,ompare t e res*!ts o& e#periments )it t e t eoretica!
prediction6
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Figure 6 . /etu! of t e ex!eriment 2"2"
*.Re)ult)
e c apter 4 contains res*!ts &rom t e e#periments 1 261 and
2626 e res*!ts are s o)n in "rap s and ta !es6
*.1 E !eri"ent 1# $re%uency Cali&ration
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E#periment 1 as t)o partsH ca!i ratin" t ro*" ce!!p one is t e
7rst part and t e anot er is ca!i ratin" *sin" $+*!e!e6 e ne#t t)o
&o!!o)in" "rap s are &rom ca!i ration *sin" t e ce!p one6
N604=============NE 4
15
10
5
05
10
15
20
ata ,e!!p one
ime
Amp!it*de Acce!eration ?RMS
Figure 0: %ata from cell! one"
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N604=============NE 4
062
0
062
064
06N
068
1
162
ata $+*!e!e
ime
Amp!it*de Acce!eration ?RMS
Figure 9: %ata from '(ulele"
00605
0610615
0620625
0630635
0640645065
$+*!e!e
re9*ency Acce!eration ?RMS
Amp!it*de Acce!eration ?RMS
Figure 14: FF 5 '(ulele
e disc*ssion o& res*!ts is in t e topic 56 e "rap s amp!it*de
%s time amp!it*de %s &re9*ency and t e statistica! ana!yses are
more t an eno*" to e%a!*ate a!! o& data6
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*.2 E !eri"ent 2.1# Load Cell
e topic 462 as t e res*!ts o& e#periment 2616 e &o!!o)in"ta !e contains t e %a!*e meas*red in %o!ts accordin" to t e )ei" t6
able 1: %ata from load cell"
+eight
,l&-
$ir)t Run,'-
$ir)t Run, -
/econdRun,'-
/econd Run, -
Third Run,'-
Third Run, -
'verage
0 0 0315/ 0 0315=5=3N
0 031N 0 031N 0 031N 0 031N 0 0315=4323
1 0 032043 0 031/4N15/ 0 031/4830= 0 031/5031= 0 031/5024N 0 031/5028/ 0 031/=80533 0 0324=N1
480 0320302
=N0 032052=2
=0 032053/85 0 032053N
380 03251048
/0 0321==5
4/0 032/==/
=0 031/214
N/0 0325103N
/0 032511303 0 0325102
N0 03251048
/0 03242/2
/=0 0324=1N
N=0 0325 0 03281521
30 0328 0 032814/
=10 032814/=
10 032/0N0
//
0 1 2 ! " # $ % &0.0
0.0
0.0
0.0
0.0
0.0
f'() * 0( + 0.0,- * 0."#
f'() * 0( + 0.0,- * 0.#"
irst ,un
/scendinginear '/scending)escendinginear ' escending)
eight 'lb)
3utput '4)
Figure 11: First run of calibration of t e load cell"
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0 1 2 ! " # $ % &
0.0
0.0
0.0
0.0
0.0
0.0
f'() * 0( + 0.0,- * 1f'() * 0( + 0.0,- * 1
5econd ,un
/scendinginear '/scending)escendinginear ' escending)
eight 'lb)
3utput '4)
Figure 12: /econd run of calibration of t e load cell"
0 1 2 ! " # $ % &0.0
0.0
0.0
0.0
0.0
0.0
f'() * 0( + 0.0,- * 0.%"f'() * 0( + 0.0,- * 1
Third ,un
/scending
inear '/scending)escendinginear ' escending)
eight'lb)
3utput '4)
Figure 1&: ird run of calibration of t e load cell"
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0 1 2 3 4 5 N / 8 =
0603
0603
0603
0603
0603
0603
0603
0603
0603
0603&?# P 0# U 0603R< P 06=/
ina! ,a!i ration ,*r%e E#periment 261
A%era"eLinear ?A%era"e
'ei" t ?!
.*tp*t ?:
Figure 1) . Final calibration cur,e of t e ex!eriment 2"1
,a!c*!*sH
Acc*racy !imits
bound = upper lower2
a 0 =0.03187066 0.03146402
2
a 0 = 0.00040664
a 1 =0.00017605 0.000089351
2
a 1 = 0.000086699
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*.3 E !eri"ent 2.2# 'ir (elocity
Tran)ducer
e topic 463 as t e res*!ts o& e#periment 2626 e &o!!o)in"
ta !e contains t e %a!*e meas*red in %o!ts accordin" to t e )ei" t6
! " # $ % & 10 11 12 1 1!
6".00760"
6 .00760"
61.00760"
1.00760"
.00760"
".00760"
$.00760"
&.00760"
1.10760!
f'() * 0( 6 0,- * 0.1&f'() * 0( + 0,- * 0.12
irst ,un
/scendinginear '/scending)escending
inear ' escending)
8nput '4)
3utput '4)
Figure 1+ . First run of t e ex!eriment 2"1"
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! " # $ % & 10 11 12 1 1!
6".00760"
6 .00760"
61.00760"
1.00760"
.00760"
".00760"
$.00760"&.00760"
1.10760!
f'() * 0( 6 0,- * 0."$f'() * 0( 6 0,- * 0.12
5econd ,un
/scendinginear '/scending)escendinginear ' escending)
8nput '4)
3utput '4)
Figure 16 . /econd run of t e ex!eriment 2"2"
! # % 10 12 1!
6".00760"
6 .00760"
61.00760"
1.00760"
.00760"
".00760"
$.00760"
&.00760"
1.10760!
f'() * 0( + 0,- * 0
inal Calibration Curve 6 7(periment 2.2
/verageinear '/verage)
8nput '4)
3utput '4)
Figure 10 . Final calibration cur,e of t e ex!eriment "
1=
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A&ter to "enerate t e t ree r*n o& t e e#periment 262 it )as
created t e re"ression ana!ysis t ro*" E#ce! 6
able &: egression anal-sis . Ex!eriment 2"2
/ MM'R4 O TP T
Regression StatisticsMulti!le
R0 05=0N4
R /%uare 0 00348='d5u)ted
R /%uare
0 328N8
/tandardError
1 /=E 05
O&)ervation)
5
'6O('df // M/ F /igni7cance F
Regre))ion
1 3 3NE12
3 3NE12
0 010502
0 =24841
Re)idual 3 = N1E10
3 2E10
Total 4 = N4E10
3oe8cients
/tandard
Error
t /tat 5,alue
9+inferiores
9+su!erior
esInter)e89o 2 05E 05 2 N/E
050 /NN5
8/0 4==1
28N 4E 05 0 000105
(ari:vel 71
2 =E 0/ 2 83E0N
0 102481
0 =24841
8 /E 0N = 3E 0N
,a!c*!*sH
Acc*racy !imits
bound = upper lower2
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a 0 =0.000105 0.000064
2
a 0 = 0.000002055
a1
=0.0000093 0.0000087
2
a 1 = 0.0000006
;. i)cu))ion o< Re)ult)
' en it comes to ca!i ration e#pected res*!t )it a !inear "ro)t 6
e project 2 )as di%ided in t ree i" parts ca!!ed e#periment 1 as
&re9*ency ca!i ration ) ere it )as *sed a ce!!p one and an *+*!e!e to
per&orm samp!e meas*rement6 e e#periment 261 is ca!!ed !oad ce!!
and t e e#periment 262 is ca!!ed air %e!ocity transd*cer 6
e e#periment 1 treats a o*t ca!i rate i" &re9*ency data *sin"
6 Rea!iKes t at t e res*!ts o tained &rom ce!!p one compared )it
t e res*!ts o tained &rom *+*!e!e a%e a di;erence et)een di;erent
types o& so*nds at a p ysica! !e%e!6 ' i!e t e ce!!p one as t e i" est
&re9*ency ( acce!eration ?RMS aro*nd 1N0 and t e i" est meas*re o&
amp!it*de ( acce!eration ?RMS aro*nd = t e *+*!e!e as t emeas*rement !o)er t an ce!!p one6 >t as t e i" est &re9*ency
aro*nd 0645 and t e i" est meas*re o& amp!it*de ( acce!eration ?RMS
aro*nd 36
e e#periment 261 ad t e meas*rement as e#pected6 e second
r*n )as a!most per&ect a%in" t e R< a!most e9*a! 16 Amon" t reee#periments t e e#periment 261 Load ,e!! presented t e res*!ts in a
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more consistent ca!i ration )it t e !iterat*re6 >n addition t e res*!ts
o tained represent a 9*ite re"*!ar series o& data and 7t )it in a sma!!
con7dence and6 R< o& t e 7na! ca!i ration c*r%e is 06=/ ) at means
t at it )as a satis&actory ca!i ration
e e#periment 262 s o)ed )e!! dispersed and *nconnected
meas*res6 >t )as attempted to ma+e t e e#periment c an"in" t e
position o& t e sensor *t it did not a%e e;ect and t e error persisted6
>n t e 7na! ca!i ration c*r%e t e R< is 0600356 is means t at t e
meas*rements are &ar &rom t e e#pected6 Co one +no)s &or s*re ) y
*t a possi i!ity o& t is error is t e settin" o& t e sensor6 is pro !em
can e inV*enced y t*r *!ence6 e transd*cer )as attac ed to a
pipe and t is pipe can e may a%e mas+ed t e rea! %a!*e ?meas*res
o& t e e#periment6 Anot er possi i!ity can e t e sensiti%ity o& t e
sensor ) ere it )as not in a"reement )it t e ade9*ate sca!e6
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.Conclu)ion)
e e#periments attained t e e#pectations "enerated y !iterary
st*dy )it t e e#ception o& t e e#periment 262 Air :e!ocity ransd*cer 6 e statistica! ana!yses )as made )it con7dence !e%e! o&
=5@ a "ood option et)een a!! o& ot er con7dence !e%e!6 e
e#periment 1 and 261 con7rmed t e e#pects in t e !iterat*re re%ie)6
e app!ication o& transd*cers depends direct!y on t e acc*racy at
) ic t ey can ta+e meas*rements and t e ease at ) ic t ese
res*!ts are ana!yKed )it re!ation to t e inp*t and o*tp*t6
e t*r *!ence can e a &actor t at )i!! inV*ence in t e 7na! res*!t
in t is case it is t e ca!i ration6
e e#perience o& ma+in" a ca!i ration is an e#ce!!ent tas+ &or
en"ineerin" st*dent6 >t is tota!!y di;erent ) en t e data are ready and
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it is necessary on!y do t e ana!yses6 e project 2 contri *ted &or t e
&ormation o& t e st*dents since ca!i ration o& sensors is e!p&*! and
common in t e ind*stry6
=.Re!;@es %e %Alar ?aseado No Modelo %e
Volatilidade EstocBstica %e Ceston 6 issertation ?Masters *ndaZ[o
Det!io :ar"as S[o -a*!o BR 20106
W2X ' ee!er A6 \6 Introduction to Engineering Ex!erimentationD
?-rentice a!! $pper Sadd!e Ri%er Ce) \ersey 2010 t ird edition6
W3X empcon6 - is 3alibration /o Im!ortant
? ttpHQQ)))6tempcon6co6*+Qca!i ration@20ser%icesQ' at@20is
@20,a!i ration]6$K5 SVd:8E accessed Marc 22 t 2014 6
W4X 3alibration Exciter 5 -!e )29) 6
24
http://www.tempcon.co.uk/calibration%20services/What%20is%20Calibration#.Uz5-SfldV8Ehttp://www.tempcon.co.uk/calibration%20services/What%20is%20Calibration#.Uz5-SfldV8Ehttp://www.tempcon.co.uk/calibration%20services/What%20is%20Calibration#.Uz5-SfldV8Ehttp://www.tempcon.co.uk/calibration%20services/What%20is%20Calibration#.Uz5-SfldV8E8/11/2019 Engineering Experimentation - Calibration of Sensors
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? ttpHQQ)))6 r*e!6 *Qdo+si+QreK"es+a!i rator6pd& accessed Marc 22 t
2014 6
W4X -orta! Action egress
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Figure 1 . Instructions of t e roGect 2"