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Метрология. Учебное пособие-1

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7%&  ' % 8",   ) +,7"35 ) "* 2 ($ ," 4", )!, " '38"  )!5 4 ) 0%9. +%" '%08 +4)"1+3,  ' "+5 4" '+'4%" $1" 1 '  ­,,  4 2 +,7"" ) "* 2 ($ ," 0)%"*")+3,  ) ­ 2 0$&6+3, "  )!5 4 ' 3)%3+3 '38", ' ' ­7" %&  +4)"10 '%08.
 "40,")!$ ' (# )%3$  +3+3 " $1" 0'­01" ' (# )%" ("+. 12, е), ) + )0 ,  !5 ' % 8 #)"+"$ +& $1" 2 ' "7$ +" ,  !5 $"% ) (8%# -$17) 1 +'%) " 4.)  0'01"5 4; $7"2.
" ) #42+)"" 0+"%"3 F  $1" ' ) 4 "#$"+3 )­%"*" 1 $1" 2 ' "7$ +" C ", +%4 )%& , $1­" 1 + ' ")%"3 0*+, $1" ' ) 4
R
= l /
CS, (18)
m
14 l " S – + )+) 4%" " '% :4& $1" ' ) 4.
 #0%& = 1 "#$"+3 "40,") +& ,06," " )­%"*" )!5 4 1 '38"3.
 +0,7"3 ' (# )%3 '4%3+3 4"'#  $ "#$3$ 1 '$:"3. ("! ' (# )%3 )!("­9 "+5 43 "#  (5 4"$ 2 $ : +" )!5 4 1 +"1%.
%3 "#$"3 )!5 4 1 '$ "40,")!5 ' (­# )%2 "( %&6 '"$" ' %0*"%" $ + )! () ­)+! " ) )+!) 7'",  ,8 , $'+7" 3 () )­ $"*+,"5 '"( 5) 7'& 4%3 4";;7"%&!5 +­; $ !5 ' (# )%2.
40,")! ' (# )%" "+' %  4%3 ' (# ­)"3 '$:"3 " 401"5 =%,"*+,"5 )%"*", ,  ! $ 10 (!& ' (# )! ) '$:" (0+"%", 4)%", $ $ " .4.).
40,")! ' (# )%", ' +)"9 + 401"$" ' (# )%3$" '$:"3, %"*9+3 #*"%&!$" ' $ : +" )!5 4!$" +"1%$", ' +  2 " 48 +&9 ) ( .
51
5 4 + , – (  ) #42+)" ' (# )%3  "++%40$!2 (<, () #42+)" =%, $1"  3, &) " )%"3" "7"" 3, 3  *+ ! 5,"+"," '"( .
Емкостные преобразователи. $, +! ' (# )%" + )!  #)"+"$ +" =%,"*+, 2 $, +" , 4+   #$ ), )#"$ 1 +' % 8"3 1 (,%4 , "  4"=%,­"*+, 2 ' "7$ +" +4! $840 "$".
%3 4)05 (,%4 * 1 '% +, 1 , 4+  =%,"*­+,3 $, +&
D0Ds / B, (19)
C =
14 D0 – =%,"*+,3 ' + 33;
D –  +"%&3 4"=%,"*+,3 ' "7$ +& +4!
$840 (,%4,$";
s –
,")3 '% :4& (,%4 ,;
B – ++ 3" $840 (,%4,$".
# )!8"3 (19) )"4 , * ' (# )%& $ 8 (!& ' +  + "+' %&# )"$ #)"+"$ +2 C = f
(D), C = f
1
(s),
2
C = f3 (B).
 "+. 13 +5$"*+," ' ,# 0+ 2+) #%"*!5 $, +!5 ' (# )%2.
 (# )%&  "+. 13, а '4+)%3 + ( 2 , 4­+ , 4 "# '%+" ,   1 '$:+3 ' 4 42+)"$ "#$3$ 2 )%"*"! x  +"%& ' 4)"8 2 '%+"!. "*+,3 5,"+", ' (# )"3 C = f3(B) %"2­. 0)+)"%& +& ' (# )%3 ) #+ + 0$&6"­$ ++ 3"3 B. ," ' (# )%" "+' %  4%3 "#$­"3 $%!5 '$:"2 ($ 1 $$).
"$39 ,8 4";;7"%&! ' (# )%"
(
"+. 13, б), 0 ,  !5 "$+3 4 ' 4)"83 " 4) ' 4)"8­! '%+"!. " ) #42+)"" "#$3$ 2 )%"*"! x 0 ="5 ' (# )%2 4 )$ "#$39+3 $, +" C1 " C2.  "+. 13, в ' ,# 4";;7"%&!2 $, + 2 ' (# ­)%& + '$ 2 ,") 2 '% :4&9 '%+". , 2 ' (­# )%& "+' %  4%3 "#$"3 +)"%& ( %&6"5 %"2!5 (( % 1 $$) " 01% )!5 '$:"2.  ="5 ' (-
52
# )%35 %1, ' %0*"& (0$09 5,"+",0 ' (­# )"3 '0$ ' ;"%" )"3 '%+".
"+. 13. $, +! ' (# )%" + "#$39:"$+3
++ 3"$ $840 '%+"$" (а), 4";;7"%&!2 (б), 4";;7"%&!2 + '$ 2 ,") 2 '% :4&9 '%+" (в) " + "#$39:2+3 4"=%,"*+, 2 ' "7$ +&9 +4! $-
840 '%+"$" (г)
 (# )%" + "+' %&# )"$ #)"+"$ +" C = f1(D) '"$39 4%3 "#$"3 0 )3 8"4, +2, )%8 +" )­:+),  %:"! "#4%"2 "# 4"=%,", ) " .'. %3 '"$
(
"+. 13, г) 4 0+ 2+) ' (# )%3 $, + 1 0 )­$. $, +& $840 =%, 4$", '0:!$" ) + +04, #­)"+"  0 )3 8"4, +", , ,, "#$" 0 )3 )4 , "#­$"9 +42 4"=%,"*+, 2 ' "7$ +" +4! $840 =%, 4$". #$"$ , ;"107"" '%+" $ 8 ' %0­*"& 8%$!2 5, #)"+"$ +" ' ,#"2 '"(   (<$ ($++!) 8"4, +".
%3 "#$"3 )!5 4 1 '$ $, +!5 ' (# ­)%2 '"$39 $ + )! 7'" " 7'" + "+' %&# )"$ ­# +!5 , 0 ).  +%4" ' #) %39 + #4)& '"( ! + )!+ , 2 *0)+)"%& +&9, +' + (! 1" )&  '­$:"3 ' 34, 10–7 $$. ?'" + $, +!$" ' (# )­%3$" (!* '"9  , $ ' )!6 2 *+ ! (4 4+3, ) $117), * )!#) 8%"$ 0)%"*"& +"1%, ' '49-
53
:"2 ) "#$"%&!2 '"( , "  (5 4"$ +&9 0$&6"& 60"09: 42+)" + ' ")%"3 "# %37"".
 + "+)$" $, +!5 ' (# )%2 3)%39+3 ' ­+  0+ 2+), )!+ ,3 *0)+)"%& +& " ) #$ 8 +& ' ­%0*"3 $% 2 "7"  +" ' (# )%3, 4 +,$" – )%"3" )6"5 =%,"*+,"5 ' %2, '#"!5 $, +2, $'0!, )%8 +",  +"%&3 +% 8 +& 7'2 ),%9­*"3 "  (5 4"$ +& ) +'7"%&!5 "+ *",5 '""3 ' ­)!6 2 *+ !.
Тензочувствительные преобразователи (тензорезисто­ры). + )0 ( ! ' (# )%2 ' % 8 # =;;,,
#,%9*9:"2+3 ) "#$"" ,") 1 + ' ")%"3 ' ) 4­", (' %0' ) 4",) ' 4 42+)"$ )!#!)$ 1 ) $ $5­"*+, 1 '38"3 " 4; $7"".
+%" ' ) % ,0 ' 4)10& $5"*+, $0 ) #42+)"9, '"$ +38"9,   + ' ")%" "#$"+3.  +"­%&  + ' ")%" ' ) % ,"
ER/R = SEl/l,
14 S – , =;;"7" # *0)+)"%& +";
El / l –  +"%&3 4; $7"3 ' ) % ,".
#$" + ' ")%"3 ' ) 4", (' %0' ) 4",) '" $5"*+, $ ) #42+)""   (<3+3+3 "#$"$ 1 $"*+,"5 #$ ) (4%"!, 4"$) " 04%& 1 + ' ­")%"3 $"%.
0)+)"%&! =%$! # #"+  ) $ 10 (!& )!­' %! ) )"4 '% (# 2 6," "#  , 2 ' ) % ,"
"+. 14, а) "%" ; %&1" ("+. 14, б), ) )"4 '%+"," $  ,"-
(
+%% "# ' %0' ) 4", ) 1 $"%. 0)+)"%&! =%­$! $ 10 (!& ,8 (# )! '!%"$ ) ),00$ ' ­%0' ) 4", ) 2 '%," " 401"$" +' + ($".
54
а)
б)
"+. 14. # #"+ !:
а) + ' ) % *!$ *0)+)"%&!$ =%$ $;
б) + *0)+)"%&!$ =%$ $ "# ; %&1"
0)+)"%&!2 =%$ 4 (!* '",'%39 , + ) 2 "# "# %37"  1 $"% ("# (0$1", %, ) 2 '%,", ," " 4.) + ' $ :&9 +)3#09:1 3 (,%3, 7$), ,  ! '­49 4; $7"9  + )! , *0)+)"%& $0 =%$0.  (<, "++%4 )"3 + )0 ,8 #,'%39 ' +4+) $ +)3#09:1 .  (# )%& ),%9*9 ) 7'& + ' $ :&9 '"­)")$!5 "%" '"'")$!5 )!) 4 ) 1.  (# )%& ­,%")9  ' )5 +& "++%40$ 2 4%" ,, * (! ­')%" 8"4$ 2 4; $7"" + )'4% + ' 4 %& 2 +&9 ' ) % * 2 6,".
%3 "#1  )%"3 ' (# )%2 '"$39 1%)!$ (# $ , + )09 ' ) % ,0 4"$ $ 0,02–0,05 $$ (S = 1,9 ÷ 2,1).  + (%4 $%!$ $'0!$ , ­=;;"7" $ =%,"*+, 1 + ' ")%"3, * *& )8 , , ,, "#$" + ' ")%"3 ' (# )%2 '" 4; ­$7"35, '"$, +%&!5 4%2 + "#$"$ + "#$"$ + ' ")%"3 ' (# )%3 '" "#$"" $'0!.
# #"+ ! )!' %39 #%"*!5 #$ ) ) #)"+"­$ +"  #*"3. "( % *+ "+' %  ' (# )-
55
%" + 4%" 2 6," ((# 2)  5 4 50 $$, "$9:" + ' ­")%" 30–500 $.
#$" $'0! )!#!) "#$" 5,"­+"," ' (# )"3 # #"+  ), * (<3+3+3 $'­0 2 #)"+"$ +&9 + ' ")%"3 ' (# )%3 " #­%"*"$ $'0!5 , =;;"7" ) %"2 1 +6""3 $"% # #"+  " "++%40$ 2 4%". %"3" $­'0! 0+3+3 (!* '0$ '"$"3 + )+­)09:"5 $ 4 ) $'0 2 , $'+7"".
,%!2 # *0)+)"%&!2 ' (# )%& ) #­$ 8 +3& + 4 2 4%" " ,%"&  40109.  = $0 4%3 '4%"3 5,"+", ' (# )"3 (, =;;"7" S) '"(19 , )!(  * 2 140" ), ' (# )%2, * 4­ #*" , =;;"7" S + ' 16 +&9 ±1%.  4! '­4%"3 5,"+", # #"+  ) 1%$" )! +4 $.  + "+) ="5 ' (# )%2 – %"2 +& +"*+, 2 5,"+"," ' (# )"3, $%! 1("! " $++, ' +  , +0,7"", 4 + , – $%3 *0)+)"%&­ +&.
 5 +%0*35, , 14 (0+3 )!+ ,3 *0)+)"%& +&, 5 43 '"$" # *0)+)"%&! ' (# )%", )!­' %! ) )"4 ' % + , "# ' %0' ) 4", ) 1 $"%.  =;;"7" S 0 ,"5 ' (# )%2 4 +"1 +, %&,"5 + . 4, ) +' "#) 4"$ +& 5,"+", ' %0' ) 4­", )!5 ' (# )%2 '% 53.  + 3: )$3 +"2 )!'0+,9 "1%&! ' %0' ) 4", )! # #"+ !, (#09:" $ + "%" ' %0$ + + =%$$" $ , $'+7"".
 ,*+) "#$"%&!5 7'2 4%3 # #"+  ) "+­' %  ) )+! " ) )+! $ +!.
" )+$ $ 1 (#"" #4*, 6$!5 + ' $ :&9 # ­#"+  ), $ 8 )!4%"& 4) + )! (%+" "5 "+' %&­# )"3.
 ') 2 (%+"  +3+3 "++%4 )"3 ;"#"*+,"5 +) 2+) $"% ), 4; $7"2 " '38"2 ) 4%35 " , -
56
+0,7"35. %3 ="5 #4* 5,! #*"%&  *"+%  *, "#$"2, 6" ," 4"'# ! "#$"3 '$ ) ,0­89:2 +4!,  ,8 ) #$ 8 +& 140" )," "#$"­%&!5 ,% ). + ) 2 '"*" 2 ' 16 +" ) ="5 +%0­*35 3)%3+3 #( + '$ ) # #"+  ) ) ,01 +4­"5 4%3 4 2 '"" #*"2; ' 16 +& "#$"3 + ­+)%3 2–10%.
 3 (%+& – '"$" # #"+  ) 4%3 "#$­"3 $5"*+,"5 )%"*", ' (#0$!5 ) 4; $7"9 0'0­1 1 =%$.  = $ +%0* ' (# )%" 140"09+3 ' "#$3$ 2 )%"*"; ' 16 +" %8 ) 4"'#  0,05–
0,5%.
57
9. ПОГРЕШНОСТИ СРЕДСТВ ИЗМЕРЕНИЙ
 4"*+,3, "+0$%&3, %"*3 ' 16 +"
+ )3 " 4 ' %"%&3 ' 16 +"
(+ %93,  +"%&3, '")43 ' 16 +"
2+)"%&  #*" ;"#"*+, 2 )%"*"!
"+$"*+," " +%0*2! ' 16 +"
5 4"$ +& " ')"%& +& "#$"2
 16 +& ,) )"3
 16 +&9 "#$"3 #!)+3 ,% " #0%&­ "#$"3  "+" 1 #*"3 "#$3$ 2 )%"*"!.  $ 8 (!& )!*"+% ' ; $0%
∆ = Х – Хи , (20)
14 Х – ' ,#"3 ;
Х
– "+"  #*" "#$3$ 2 )%"*"!.
и
4, '")4  +  6" % "+' %&# )& 4%3 5 84"3 ' 16 +" "#$"3 '  2 ' + 2 '"*", * "+"  #*" "#$3$ 2 )%"*"! )+14 "#)+ , +%" 8 1 $ 8 +*"& "#)+!$,  "#$"  08 .  = $0 ' 16 +" "#$"2 '"5 4"+3 7")& + "+­' %&# )"$ , +)!5 4!5.
(3#%&!$" , $' $" )+3, 1 "#$"3 3)%3+3 $ 4 "#$"3 " , *& *+ "#$"3 )!' %39+3 + 0*+"$ *% ),.  = $0 ) (:$ )"4
∆ = εм + εи + ε
, (21)
л
14 εм – ' 16 +& $ 4"*+,3;
ε
– ' 16 +& "+0$%&3;
и
ε
– ' 16 +& %"*3.
л
843 + +)%39:3 ' 16 +" "#$"3 $ 8 )!­#!)&+3 34 $ '"*". ,, методическая погрешность $ ­8 ) #",0& "#-# 1"* 2  * +" ; $0%, '"$­3$!5 4%3 '"+"3 3)%"2, ,  ! ' % 8! ) + )0 "#-
58
$"2.  ,*+) '"$ '")4$ *"+% )  #*" 1 ­$"*+,"5 01% ) ) 01 %&",.  1%+ ' +0%0 ),%"­4 ) 2 1 $"", +0$$ 01% ) ) 01 %&", ) 180°. 4­, ) 1 $""  (*)+, 1 +0$$ )0"5 01% ) ­01 %&", $&6,  ) =%%"'"*+, 2 1 $"" "$ – ( %&6 180°.  ) ),%"4 ) 2 1 $"" "#$"$ % 4 ­,#&, * +0$$ 01% ) 5 & ,, 1 - 01 %&",  +$ $ 4% ) 180°, , ,, '" %9( $ "#$"" $! (3#%& 0+ )"$ ( %&6 "%" $&6 ,% "  = 1  "­*+," #4 1 #*"3.
Инструментальные погрешности "#$"3 – ' 16 ­+" "#-# + )6+) +4+) "#$"2. (!* #%"*­9 основную ' 16 +&  – ' 16 +& ) 0+% )"35, '"­3!5 #  $%&!, " дополнительные ' 16 +", (0­+% )%! ,% "$ )%"39:"5 )%"*"  "5  $%&!5 #*"2.
 ; $ *"+% ) 1 )!8"3 ' 16 +" ' 4#4%3­9+3  (+ %9!,  +"%&! " '")4!.
 4 абсолютной погрешностью ' "$9 %1("*­+,09 # +& $840 ' ,#"3$"  " 42+)"%&!$ #­*"$.  4 42+)"%&!$ #*"$ ;"#"*+, 2 )%"*"! ' "$+3  #*", 24  =,+'"$%& " ­+ %&, '"(%"89:+3 , "+" $0, * 4%3 4 2 7%"  $ 8 (!& "+' %&# ) )$+ 1 . (!* # 42+)"­%&  #*" '""$9 #*", '4%   *!$ $ 4 $.
(+ %93 ' 16 +& )!8+3 ) 4""75 "#$3­$ 2 ;"#"*+, 2 )%"*"! " $ 8 (!& #4:
) 4"$ *"+% $ (%""3 1  "+. 15): ∆х = ± а;
() ) )"4 %"2 2 #)"+"$ +" (%""" 2 " 3): ∆х = ±bx;
)) ) )"4 ;0,7"" Fх = f(x) "%" 1;",, (%"7!.
+%" #*" ' 16 +"  "#$3+3 ) )+$ 4"'­#  "#$"3 (%""3 1), '"$ "#-# "3 ) ' 5,  ,3 ' 16 +& #!)+3 аддитивной ("%" ' 16 +&9 0%3).
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"+. 15. / $" )" 44"") 2 " $0%&"'%",") 2
+ +)%39:"5 ' 16 +"
+%" ' 16 +& "#$3+3 ' ' 7" %& "#$­ 2 )%"*" (%""3 2),   #!)9 мультипликативной.
 ( %&6"+) +%0*) 44"")3 " $0%&"'%",")3 + +)%39:" '"+0+)09 4 )$ (%""3 3).
*+) #0%& ) "#$"2 04 ( 5,"# )&  (+ %9 2 ' 16 +&9,   +"%& 2. Относительная погрешность  )!8+3  6"$ (+ %9 2 ' 16­ +" , "#$3$ 2 )%"*" ( (!* ) ' 75):
ε = (∆х / х) · 100%, (22)
14 ∆х – (+ %93 ' 16 +&;
х – ' ,#" .
4 (+) , 1 '4+)%"3 *+" (0+% )% $, * + )%*!$" *"+%$" ' : "$& 4% , *$ + "$ ­)!$",  1%)!$ (# $ '"$"  +"%& 2 ' ­16 +" +)3# + $ (+ 3%&+) $, * 0,#" (+ ­%9 2 ' 16 +" $% 1 ) " 42+)"%& 2  * +", +%"  + ' +)"& )%"*"0 ' 16 +" + +$ 2 "#$3$ 2 )%"*" 2. 2+)"%& , +%" $! "#$3$ +  * +&9 1 +$ ,,09-%"( 4%"0,  )  $ +%0*, , 14 *& "4 ( '4­%"" 4%"! ,46, = (04 *& "#,3  * +& ( , %
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