Trabalho de Erros de Calibração

7/25/2019 Trabalho de Erros de Calibrao

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UNIVERSIDADE FEDERAL DO MARANHO UFMA

CENTRO DE CINCIAS EXATAS E TECNOLOGIA CCET

COORDENAO DO CURSO DE ENGENHARIA QUMICA COEQDOUGLAS FELIX SOUSA ROCHA

ERROS EM CALIBRAO DE TRANSDUTORES DE PRESSO

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UNIVERSIDADE FEDERAL DO MARANHO UFMA

DOUGLAS FELIX SOUSA ROCHA

ERROS EM CALIBRAO DE TRANSDUTORES DE PRESSO

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INTRODUO

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T21 A -+5*+%&-u%& .o &% 4o,./4/o,&.o +5 -o%,o .o 'u('o .o -+%55+-%o 7o1&(o% ./*o,1+(8@

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T41 A -+5*+%&-u%& u+ o &% -+%/& ,& +=&-& *o/6o .o 'u('o .o -+%55+-%o 4&o& /,-%u5+,-&6o ,o -/1++ *+%-u%'&.o & ./-%/'u/6o .+ -+5*+%&-u%& +1+(o4/.&.+ .o &% /,u9(&.o ,& &(& 7o 1&(o% 4o,4+/-u&(8;

*rros do Sistema de (edida

S+ T# 9o% -o5&.& 4o5o o 1&(o% 1+%.&.+/%o3 o5+,-+ o +%%o .o /-+5& .+5+./.& o (+1&.o +5 4o,/.+%&6o; Au/ +-o /,4(u.o -o.o o +%%o 9/=o +1&%/1+/ /,-%o.u2/.o *o% 4&.& 4o5*o,+,-+ .o /-+5& .+ 5+./.& -&/ 4o5o +%%o ,o?&,)o 79/=o83 9(u-u&6>+ ,& 9o,-+ .+ -+,o 7&(+&-%/o8 + o4/(&6>+ 4&u&.& *+(&

1&%/&6>+ .+ -+5*+%&-u%& ,o /,-%u5+,-o;


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E-+ +%%o *o.+5 +% +-/5&.o +=*+%/5+,-&(5+,-+ &-%&1 .+ u5& 4&(/'%&6o.o /-+5& .+ 5+./.&; O +%%o 9/=o +%o +1/.+,4/&.o *o% u5 .+1/o .o 1&(o% 5./o.& &.& 4o5 %+(&6o &o 1&(o% 4o,-&,-+ .& +,-%&.& +,u&,-o u+ o +%%o 1&%/1+/+%o +1/.+,4/&.o *o% 1&%/&6>+ .o 1&(o%+ /,./1/.u&/ .& &.&; C&'+ ,o-&% u+ +5u5& 4&(/'%&6o3 & 5+./.& .+1+5 +% %+&(/2&.& .u%&,-+ u5 /,-+%1&(o .+ -+5*o + +5

4o,./6>+ &5'/+,-+ %+*%++,-&-/1& .o -+-+ %+&(; C&o 4o,-%%/o3 o 4o5*o,+,-+1&%/1+/ 5& .+-+%5/,-/4o .o +%%o ?(o'&( ,o +%o +,-/.o;

*rros da Interao Sensor5(eio

S+ & -+5*+%&-u%& .o &% 7T!8 9o% -o5&.& 4o5o o 1&(o% 1+%.&.+/%o3 +-& .+1+ +%.+-+%5/,&.& & *&%-/% .o 1&(o% o'-/.o *&%& & -+5*+%&-u%& .& 0u,6o .o -+%5o*&%3 T #; A/,-+%&6o +,o%5+/o ,o%5&(5+,-+ .&.& *o% u5& +u&6o &,&(-/4& %+(&4/o,&,.o o1&(o% o'-/.o &o 1&(o% ./*o,1+(3 5& u+ +,1o(1+ *&%5+-%o 4u0o 1&(o%+ +-ou0+/-o & +%%o; Po% +=+5*(o3 o 'u('o .o -+%55+-%o -%o4& 4&(o% *o% 4o,.u6o 4o5 u&)&-+3 *o% %&./&6o 4o5 & *&%+.+ .& &(& + *o% 4o,1+46o 4o5 o &%; D+*%+2&,.o+ &

-%o4& *o% 4o,.u6o3 & /,-+%&6o +,o%5+/o +%/& .&.& *+(o +?u/,-+ '&(&,6o .+ +,+%?/&74&(o% ?&,)o ,& -%o4& %&./&-/1& +,-%+ & *&%+.+ .& &(& + o -+%55+-%o /?u&( &o 4&(o%

*+%./.o *+(o -+%55+-%o *o% 4o,1+46o *&%& o &% &5'/+,-+8J

o,.+ & 4o,-&,-+ .+ S-+*)&,Bo(-25&,,3 & +5//1/.&.+ .o +,o%3 Tt &-+5*+%&-u%& .o -+%55+-%o o 1&(o% o'-/.o T13 Tpar& -+5*+%&-u%& .& *&%+.+3 Tar &

-+5*+%&-u%& .o &% ,& *o/6o .o 'u('o .o -+%55+-%o .+ 5+%4%/o ]o 1&(o%./*o,1+( T(2)^ + ) o 4o+9/4/+,-+ .+ *+(4u(& &%'u('o .o -+%55+-%o; H u&-%o 1&%/1+/ ,+-& +u&6o u0+/-& & +%%oJ h3 3 Tpar+ Tt; Po%-&,-o3 &o +u-/(/2&% +-& +u&6o o +%%o +5 h3 + Tpar3 u+ ,o o +%%o %+(&4/o,&.o &o/,-%u5+,-o u+ 5+.+ Tt3 -&5'5 &9+-&%o o 1&(o% 4&(4u(&.o 7u+ + +*+%& 1+%.&.+/%o8

*&%& Tar; E-& +u&6o *o.+ +,-o +% 1/-& 4o5o u5 *+u+,o _*%o?%&5& .+ -%&-&5+,-o.+ .&.o\ *&%& + 4&(4u(&% Tar & *&%-/% .+ Tt + & u& /,4+%-+2& .+1+ +% 4&(4u(&.&+*&%&.&5+,-+;

*rros de /erturbao do (eio

S+ o 1&(o% ,o *+%-u%'&.o 7T8 9o% -o5&.o 4o5o 1&(o% 1+%.&.+/%o3 -o.& &*+%-u%'&6>+ ,o 5+/o /,-%o.u2/.& *+(o /-+5& .+ 5+./6o .+1+5 +% (+1&.& +54o,/.+%&6o + & /,4+%-+2& ,o +u 4(4u(o +% u5& /,4+%-+2& %+/.u&( ,& 5+./.&%+&(/2&.&; Co5o %+?%& ?+%&(3 o +,o%+ u&.o .+1+5 +% -o *+u+,o u&,-o *o1+(& 9/5 .+ + 5/,/5/2&% & *+%-u%'&6o + & +-/5&-/1& .+-& .+1+ +% 9+/-& *o% 5+/o .+ u5&+u&6o /5*(+; Ou +,-o & 5+./6o .+1+ +% %+&(/2&.& 4o5 /,-%u5+,-o ,o/,-%u/1o;

No 4&o .o -+%55+-%o u+ 5+.+ & -+5*+%&-u%& .o &% ,& &(&3 & *+%-u%'&6o/,-%o.u2/.& .+*+,.+ .+ 1%/o 9&-o%+; A )&-+ .o -+%55+-%o 4o5*o%-&+ 4o5ou5& &(+-& + ) u5 4+%-o ?%&./+,-+ .+ -+5*+%&-u%& .o &% 4o,./4/o,&.o; E-+ u5 +9+/-o-*/4o .+ *+%-u%'&6o .o 5+/oJ & *%++,6& .o -+%55+-%o %+9%/&% ou &u+4+% 7.+*+,.+.o ?%&./+,-+ .+ -+5*+%&-u%&8 o &% +5 -o%,o .o 'u('o;

A.5/-/,.o+3 *o% /5*(/4/.&.+3 u+ ,o )&0& ou-%& 9o,-+ .+ +%%o3 & /,./4&6o.o -+%55+-%o 71&(o% o'-/.o8 *o.+ +% &.5/-/.& /?u&( `& -+5*+%&-u%& .o &% ,& *o/6o .o


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'u('o 71&(o% ./*o,1+(8; A -+5*+%&-u%& ,o *+%-u%'&.& .o 5+/o ,+-& 5+5& *o/6o*o.+ +,-o +% 4&(4u(&.& .+

N& +u&6o &4/5&3 ) +/ 1&%/1+/ u0+/-& & +%%o 7h, D, kar, kt, Tar+T28 + &/,4+%-+2& +,1o(1/.& ,o uo .+-& +u&6o .+1+ +% +-/5&.& &o + 4&(4u(&% T;A&'o%.&?+5 &,(o?& :u+(& u&.& ,o 4&o .o +%%o ,& /,-+%&6o +,o%5+/o;

*rros Conceituais

S+ & -+5*+%&-u%& .+ 5/-u%& 7T8 9o% -o5&.& 4o5o & -+5*+%&-u%& 1+%.&.+/%&3 o

+9+/-o .& ./-%/'u/6>+ .+ -+5*+%&-u%& + 1+(o4/.&.+ ,& +6o -%&,1+%&( .+1+5 +%(+1&.o +5 4o,-& *o% 5+/o .& &*(/4&6o .+ 4o%%+6>+ *+%-/,+,-+; M&/ u5& 1+23 &/,4+%-+2& ,+-& 4o%%+6>+ .+1+5 +% +-/5&.& u&,.o .o 4(4u(o .o 1&(o% 1+%.&.+/%o3T; Co5o +1/.+,-+3 o *%o4+o .+ .+-+%5/,&6o .o 1&(o% Y1+%.&.+/%oY .& -+5*+%&-u%&.o &% -o%,&+ 4&.& 1+2 5&/ 4o5*(+=o; C&'+ +,9&-/2&% u+ +5 5u/-& /-u&6>+ o +%%o4o,4+/-u&/ o 5u/-o 5&/o%+ u+ o .+5&/; A/53 *o.++ 4o,4(u/% u+3&*&%+,-+5+,-+3 ,o ) (/5/-+ *&%& & /,-+%*%+-&6>+ +%%,+& u+ u5& *+o& *o.+ .&%&o %+u(-&.o .& 5+./6o .+ u5& 4+%-& ?%&,.+2&;

E5 5u/-o 4&o o +=*+%/5+,-&(/-& ,o 4o,/.+%&5 & /,9(u+ *&%& & .+9/,/6o .o 1&(o% 1+%.&.+/%o3 .+1+ + *+%?u,-&%J _Qu&( +%& u-/(/2&6o 9/,&( .+-& 5+./.&a Qu&( o +u /?,/9/4&.o 9/4o ,& +u&6>+ u+.+4%+1+5 o 9+,5+,o +5 +-u.oa\ O 'o5 +=*+%/5+,-&(/-& .+1+ +-&% 4/+,-+3 ,o+,-&,-o3 .+ u+ o +%%o .& /,-+%&6o /-+5&5+/o3 o +%%o .+ *+%-u%'&6o .o 5+/o + o+%%o 4o,4+/-u&/ o ?+%&(5+,-+ 5&/o%+ .o u+ o +%%o .o /-+5& .+ 5+./6o; E-&&9/%5&6o 1(/.& *%/,4/*&(5+,-+ *&%& +=*+%/5+,-o +,1o(1+,.o -%&,9+%


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.&.o 4o5 1&(o%+ *%=/5o .& 5./&; O'+%1&+3 +,-o3 u+ & 5./& u5& 5+./.& .+(o4&(/2&6o .o .&.o +=*+%/5+,-&/;

M&3 &(5 .& (o4&(/2&6o .o .&.o3 ,+4+%/o 4o,)+4+% 4o5o +-+ .&.o+-o +*&()&.o; I,9o%5&% o'%+ o +*&()&5+,-o .o .&.o 5+./.o +% o *&*+(

.& 9&/=& .+ 1&(o%+ 5+./.o3 .& 1&%/,4/&3 .o .+1/o *&.%o3 .& ./-%/'u/6>++-&--/4& + u& 4&%&4-+%-/4&;

A 9&/=& .o 1&(o%+ 5+./.o 7& ./9+%+,6& +,-%+ o 5&/o% + o 5+,o% 1&(o% 5+./.o8 /5*o%-&,-+3 +1/.+,-+5+,-+3 *&%& o 1&(o%+ ,o -o*o + ,& '&+ .o 4o,0u,-o .+ .&.o;Po% +=+5*(o3 *o.++ u+-/o,&% + o %+*%++,-&-/1o 9%+,-+ &o 4o,0u,-o .+ .&.o + &o+=*+%/5+,-o +5 u+-oJ

F8( 9 :m! 5 :m;n

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29 #


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Figura 3. A PDF (funo densidade de probabilidade) de uma distribuio Gaussiana

No-+ u+ & G&u/&,& u5& 4u%1& /5-%/4& 4o5 & 9o%5& .+ /,o; O Y+/=o .+/5+-%/&Y .& 4u%1& /,./4& & 5./&3 [ X c K !; Quo &4)&-&.& ou +-/4&.& ou Y5&?%& ou?o%.&Y & G&u/&,&3 o 1&(o%+ .o .+1/o *&.%o 1o +-&'+(+4+%; D+1++ o'+%1&%u+ o /5*(+ 9&-o .& 4u%1& -+% & 9o%5& .+ /,o ,o /,./4&.o% .+ ./-%/'u/6o No%5&(;E,-%+-&,-o3 +-& u5& ./-%/'u/6o 5u/-o 4o5u5 ,& %+& .+ +,?+,)&%/& + .+1+ +%4o,/.+%&.&; A o%.+,&.& b .& G&u/&,&3 *&%& u5 4+%-o 1&(o% X J

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Co,+u+,-+5+,-+3 + & 5./& + o .+1/o *&.%o .+ u5 4o,0u,-o .+ .&.o+=*+%/5+,-&/ o 4o,)+4/.o3 *o.++ o'-+% /,9o%5&6>+ -+/ 4o5 4(4u(o &%/-5-/4o/5*(+; Co(o4&,.o #3 ! ou SD &4/5& + &'&/=o .& 5./& X3 *o.++ o'-+% & 9&/=& .+1&(o%+ u+ /,4(u/3 %+*+4-/1&5+,-+3 $Z3 dZ + dd3Z .o .&.o +=*+%/5+,-&/;


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Concluso

O -%&'&()o &*%++,-&.o -+1+ 4o5o 9o4o *%/,4/*&( /(u-%&% o +%%o u+ +=/-+5

.u%&,-+ *%o4+o3 4o5o ,o 4&o3 +5 5+./.o%+ .+ *%+o; Ou-%o .+-&()+ *&%&?&%&,-/% & u&(/.&.+ .& 4&(/'%&6o3 u+ o *&.%o .+1+ +% 1+2+ 5+()o% u&,-o :4(&+ .+ +=&-/.o +5 %+(&6o &o -+-+3 *o.+,.o +% &,&(/&.o +-+ 1&(o% ,o ?%9/4o .++%%o3 ,o u&( o &.o-&.o *&%5+-%o +5 9u,6o .o 1&(o% .+ /,./4&6o3 1&(o%1+%.&.+/%o + & 5./& .o 1&(o%+ .+ +%%o + 5+/& ./1/o .o 1&(o% .& %+o(u6o .o-%&,.u-o%; Qu&,-o &o (+1&,-&5+,-o .& 4u%1& .+ 4&(/'%&6o + *+(& %+?%+o (/,+&% .o/,-%u5+,-o-+-+3 .+ o .+-&()&5+,-o .& u&(/.&.+ ,& +9/44/& .o %+u(-&.o .&5+./6o; Po%-&,-o3 o 5&/ /5*o%-&,-+ *&%& u5 %+u(-&.o &-/9&-%/o +5 -+%5o .&9u,6>+ 5+-%o(?/4&3 u+ o o*+%&.o% +0& &-/9&-%/o .u%&,-+ & 4&(/'%&6o; P&%& u+/o &4o,-+6& 4o5 +9/44/&3 ,+4+%/o )&1+% u5& /-+5-/4& .+ *+%/o./4/.&.+ .+

-%+/,&5+,-o .o o*+%&.o%+ ,& 4&(/'%&6>+3 ,& u&( ++ %+u(-&.o *o.+5 +%&,&(/&.o 4o5 -4,/4& +*+49/4& 4o5o 7%+*+-/-/1/.&.+ + %+*%o.u-/'/(/.&.+8?&%&,-/,.o &/53 ,o -o-&(3 & u&(/.&.+ ,& 5+./6>+;


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Re.erencias

ALBERTAI3 A; G; e%; Fu,.&5+,-o .+ M+-%o(o?/& C/+,-9/4& + I,.u-%/&(;#f+.; B&%u+%/J M&,o(+3 !"";

FIALHO3 A; B; I,-%u5+,-&6o I,.u-%/&(J Co,4+/-o3 A*(/4&6>+ + A,(/+; $f+.; So P&u(oJ W%/4&3 !"";

NBR ISOIEC #"!J R+u//-o G+%&/ *&%& & Co5*+-

Trabalho de Erros de Calibração

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