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Метрология. Учебное пособие-1

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14 Uc – '38"  #8"$5 , 4+ ; U0 – '38" 4 *% ' 7++; t – (C
)$3 "#$"3;
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0
 "+*"" )$" T, U0 0$&6+3 ) 1/e #, .. '"$  37% *%& 1 #*"3 U.  1"*") ) #$ 8 +" "+' %&# )"3 '&# ,"+%% ) ,  %$  %&, ,, )$!5 " (!+ $39:"5+3 ' 7++ ).
 16 +& '&# ' (# )%2 2–3%  )51 #­*"3.
"$0:+): 6" ,"2 4"'#  "#$"2, )!+ ,3 *0)­+)"%& +&.
4 +,":  (5 4"$ +& (+'*"3 *& )!+ , 1 + ' ")%"3 "# %37"", '"1 4 +& 4%3 +"*+,"5 "#$­"2.
Индукционные преобразователи. 40,7" ! ' (­# )%" + )!  "+' %&# )"" #,  =%, $1" 2 "40,7"", + 1%+ ,   $0 , "407" )3 ) ,06,,
"$9:2 ω )", ):
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ω
d
, 14
d
– +,  +& "#$"3
$1" 1 '  ,, +7'% 1 + ,06, 2.
40,7" ! ' (# )%" '"$39 4%3 "#$"3 +,  +" %"2!5 " 01% )!5 '$:"2. !5 4 2 +"1% ="5 ' (# )%2 $ 8 (!& ' "1" ) "%" ' -
41
4";;7" ) ) )$" + ' $ :&9 =%,"*+,"5 "1­"09:"5 "%" 4";;7"09:"5 0+ 2+).  +% ="5 '­ (# )"2 "; $")!2 '$ +"1% + )"+3 ' ­' 7" %&!$ + )+) '$:"9 "%" 0+, "9.  = $0 "40,7" ! ' (# )%" "+' %  ,8 4%3 "#$"3 %"2!5 " 01% )!5 '$:"2 " 0+, "2.
"( %&6 '"$" "40,7" ! ' (# )%" ' %0*"%" ) '"( 5 4%3 "#$"3 01% ) 2 +,  +" (5 $­5) " ) '"( 5 4%3 "#$"3 '$ ) )"(7"2.
40,7" ! ' (# )%" 4%3 5 $ ) '4+)­%39 + ( 2 ( %&6" (1–100 ) 1 ! ' + 3 1 "%" '$ 1  ,, (!* + #)"+"$!$ ) #(084"$  ' ­+ 3 1 $1",    ,  !5 $5"*+," +)3# + "+'!­0$!$ )% $. " "+' %&# )"" 1  ' + 3 1  , ( 01% ) 2 +,  +" +043 '  1 ,  ) +%0* '"­$"3 1  '$ 1  , 01% )09 +,  +& $ 8 '4%"& ' #*"9  "%"  *+ .
 "+. 9 ' ,# "40,7" !2 ' (# )%& 4%3 "#­$"3 $'%"04!, +,  +" " 0+, "3 ) #) -' +0'­%& 1 4)"8"3.  (# )%& '4+)%3 + ( 2 7"­%"4"*+,09 ,06,0 1, '$:9:09+3 ) , %&7) $ ##  $1" ' ) 4 2. ?"%"4"*+,"2 ' + 3!2 $1" 3 + #­4 ) , %&7) $ ##  ' + 3  4"%&  $1"  ' %. 06, '" '$:"" '+, +"% )! %""" $1"­ 1 ' %3, " ) 2 ) #", , ' ' 7" %&3 +,  +" '$:"3.
"+. 9. 40,7" !2 ' (# )%&
42
 16 +" "40,7" !5 ' (# )%2 '4%3­9+3 1%)!$ (# $ "#$"$ $1" 1 ' %3 ) )$" " '" "#$"" $'0!,  ,8 $'0!$" "#$­"3$" + ' ")%"3 ($ ,".
+ )! 4 + "+) "40,7" !5 ' (# )%2 #­,%9*9+3 ) +)"%& 2 ' +  , +0,7"", 48 +" ( ! " )!+ , 2 *0)+)"%& +". 4 + , – 1"*­!2 *+ !2 4"'#  "#$3$!5 )%"*".
Термоэлектрические преобразователи (термопары). " ' (# )%" + )!  $ =%,"*+, $ =;;,, ) #",9:$ ) 7'", + +)% 2 "# #  4!5 ' ) 4"­, ), '" )+) $'0 ) $+5 +'3. " # +" $'0  *, 1 " 2 + 4""3 4)05 #  4!5 ' ) 4­", ) A " B ("+. 10, а), (#09:"5 $ '0, ) 7'" $ ­'! ) #", $ . " "#$ 2 $'0, ­'"$,  *," + 4""3 2 (t2 = const), EAB = f(t1) – C = f1(t1), 14 t1 – $'0  *," + 4""3 1; C = f(t2). 0 #)"+"$ +& "+' %  ) $ =%,"*+,"5 ' (# )%35 4%3 "#$­"3 $'0!.
"+. 10. $ ' (а) " +' + ( ),%9*"3 '"(  ) 7'&
$ '! (б)
%3 "#$"3 $  =%, "#$"%&!2 '"( 
($"%%") %&$, , $'+ ) ),%9*9 ) 7'& $ '! (
"+. 10, б).  *,0 + 4""3 ' ) 4", ) (=%, 4 )) 1 -
43
#!)9 ( *"$ , 7 $ $ '!,  *," 2 " 2' – +) ( 4!$" , 7$".
 (! $  ) 7'" $ '! 4 #* '4%3­%+& $'0 2 ( *1 , 7, $'00 +) ( 4!5 , 7 ) $ '!  (5 4"$ ' 448")& 4", ) 2 " ­"#$ 2.
40" ),0 $ =%,"*+,"5 $ $ ) – '"(  ), "+' % :"5 $ '! 4%3 "#$"3 $'0!, (!* ' "#) 43 '" $'0 +) ( 4!5 , 7 ) 0 °C. 40" ­) *! (%"7! 4%3 +4!5 $ ' ,8 + +)%! '" 0+% )"" )+) $'0! +) ( 4!5 , 7 ) 0 °C.  $"%&! +"*+," 5,"+"," ' (# )"3 (1­40" ) *! 5,"+",") $ ' '")4! ) (%. 2. " ',"*+, $ '"$"" $ =%,"*+,"5 $ $­ ) $'0 +) ( 4!5 , 7 ) $ '! (!*  )
0 °C,
" ' = $0  (5 4"$ )) 4"& ' '),0.
%3 "#1  )%"3 $ ', '"$3$!5 ) + 3: )$3 4%3 "#$"3 $'0!, "+' %  ) + ) $ +'­7"%&! +'%)!.
 (%. 2 '")4! 5,"+"," $ '. %3 "#$­"3 )!+ ,"5 $'0 "+' %  $ '! "' ) ,  " . $ '! "# (%1  4!5 $%% ) ( " ) '"$39 '" "#$"35 + ' )!6 2  * +&9, $ '­! "# (%1  4!5 $%% ) (, ) – ) +%&!5 +%0­*35.
%3 #:"!  )6"5 ) #42+)"2 (4)%"3, 1++")­!5 1# ) " .4.) =%, 4! $ ' ' $:9 ) #:"09 $00.
7"  +& +4!5 $ ', 5,"#09:3 ' ,#%& '% ) 2 "7"", ) +, %&,"$ $"0$. #­)+! , +0,7"" $% "7" !5 $ ', 0 ,  !5 ' ­,#%& '% ) 2 "7"" + +)%3 5–20 °C.
44
ХАРАКТЕРИСТИКИ ТЕРМОПАР
(%"7 2
5"2 '4%
"#$3$ 2 $-
'0!, °C
4%"-
%&
,, ­)$-
1600 1800
"' -
$ -
'!


"%! =%, 4 )
$ '
%"  4"2 (10%  4"3) – '%"
%"  4"2 (30%  4"3) – '%"  4"2 (6%  4"3)
$ 
('"
t
= 100 °C,
р.к.
t
= 0 °C),
с.к.
$
0,64 1300 1600
13,81 ('"
= 1800 °C)
t
р.к.
 $%& (90% Ni + 10% Cr) –

%9$%& (94,83% Ni + 2% Al +
4,10 1000 1300
+ 2% Mn + 1% Si + 0,17% Fe)


 $%& – , '%& (56% Cu +
+ 44% Ni)
 %&;$"2 (5% "3) – ) %&;$"2 (20% "3)
Примечание. t
– $'0 ( *1 , 7; t
р.к.
6,90 600 800
1,33 2200 2500
– $'0
с.к.
+) ( 4!5 , 7 ).
) ( 4! , 7! $ '! +' %19 ) 1 % ), ­$ '!. 4, #4+& "#$"& $'00,  $ ( % ­$ +" )&  *& 04 . $'0 1 % )," (!) )!+ , 2 "  ++3 ' + 3 2, "#$33 +) 9 )%"*"0.  ­= $0 ' ) 4, "40:"  $ '! , "#$"%& $0 '"( ­0, (!*  '"+ 4"39 '3$ , 1 % ),,  )!) 43  ­,    ++ 3" ) # 0 ( % "#, 2,  1%)  – ( % ' ­+ 3 2 $'0!. %3 04%""3 =%, 4 ) $ '! '"$39 , #!)$!2 , $'+7" !2 ' ) 4.  '4­+)%3 + ( 2 1"(,"2 "# %" )!2 ' ) 4 + 4)0$3 8"%$", "#1  )%!$" "# 5 8 +'%) ), * " =%, 4! $ '!, "%" "# $"% ), ,  ! ) ' + $"% $ $ '! ) '4%5 0–100 °C "$9 ,09 8 #)"+"$ +& $   $'0!, ,, " 0 + ) 2 $ '!.
45
8.2. Параметрические измерительные преобразователи
$ *0)+)"%&!
40,")!
$, +!
# #"+ !
 '$"*+,"5 "#$"%&!5 ' (# )%35 )!­5 4 2 )%"*" 2 3)%3+3 '$ =%,"*+, 2 7'" (R, L, C, M, f). " "+' %&# )"" '$"*+,"5 ' (# )%2  (5 4"$ 4 ' %"%&!2 "+ *", '""3, =1"3 ,   ­1 "+' %�+3 4%3 (# )"3 )!5 4 1 +"1% ' (# ­)%3.
Термочувствительные преобразователи (терморезисто­ры). "7"' 42+)"3 ' (# )%2 + )  #)"+"$ -
+" =%,"*+, 1 + ' ")%"3 ' ) 4", ) "%" ' %0' ­) 4", )  $'0!.
840 $ #"+  $ " "++%40$ 2 +4 2 ) ' 7++ "#$"3 ' "+5 4" '% ($. , ,, $ #"+  '" = $ ),%9* ) =%,"*+,09 7'&, + ' $ :&9 ,   2 ' "#­) 43 "#$" 1 + ' ")%"3,  ' $0 ' ,  ,, )!4%39:"2 ) $ '% 0. '% ($ $ #"+  + +4 2 ' "+5 4" "#-# '% ' ) 4 +" +4! " , ),7"" ) 2, '% ' ) 4 +" +$ 1 $ #"+  " $0!, , ,   2  ,'"+3. +") +& '% ($,  +%4 )­%& , " $'0 $ #"+  #)"+3  1 1 $"­*+,"5 #$ ) " ; $!,  , +0,7"" #:" 2 $0!,  + +), '%  +", '% ' ) 4 +" " 401"5 ;"#"*+,"5 +) 2+) +4!, ,089:2 $ #"+ .
,"$ (# $, #)"+"$ +& $'0!,  +%4 )%& , " + ' ")%"3 $ #"+   '*"+%!5 )!6 ;,­  ) $ 8 (!& "+' %&# ) 4%3 "#$"3 #%"*!5 ­=%,"*+,"5 )%"*". " , +0" )"" ' (# )%3 +$3+3 ,  $0, * (! '% ($ $ #"+  + +4 2 ) + ) $ '4%3%+3 "#$3$ 2 =%,"*+, 2 )%"*" 2.
46
%3 "#$"3 $'0! "( % +' +! $ #"+ !, )!' %! "# '%" ) 2 "%" $4 2 ' ­) % ,". 4! '%" )! $ #"+ ! '"$39 4%3 "#$"3 $'0! ) 4"'#   –260 4 +1100 °C, $4! – ) 4"'#   –200 4 +200 °C. "#, $'0! '%" )! $ #"+ ! '"$39 4%3 "#$"3 $'­0! ) '4%5  –261 4 –183 °C.
 "+. 11, а ' ,# 0+ 2+) '%" ) 1 $ #"­+ .  ,%5 ,$"*+, 2 0(," 2 +' % 8! 4) ("%" *!) +,7"" +'"%" 3 "# '%" ) 2 ' ) % ,", + 4"­! $840 + ( 2 ' +%4 )%& .  , 7$ +'"%" '"'"­)9 )!) 4! 4, "+' %�$! 4%3 ),%9*"3 $ #"+  ) "#$"%&09 7'&. '%" )!) 4 ) " 1$"#7"9 ,­$"*+, 2 0(," ' "#) 43 1%#0&9 1. %! 0(," #+!­'9 '  6, $ (#) 4 1 ,+"4 %9$""3, )!' %39:"$  %& "# %3  " ;",+  +'"%".   6 , (#) 4 1 ,­+"4 %9$""3, "$9:"2 )!+ ,09 '% ' ) 4 +& " $%09 '% $, +&, (+'*") 5  609 '4*0 '% ! " $­%09 "7"  +& $ #"+ . %3 #:"! $ #"+ ­  $5"*+,"5 " 5"$"*+,"5 ) #42+)"2 )62 +4! 1 ' $:9 ) #:"09 $00 ("+. 11, б) "# 8)9­:2 +%".
"+. 11. + 2+) (а) " )6"2 )"4 $0! (б)
'%" ) 1 $ #"+ 
47
*%&! + ' ")%"3 ('" 0 °C) '%" )!5 +4­!5 $ #"+  ) )! 1, 5, 10, 46, 50, 100 " 500 $, $4­!5 – 10, 50, 53 " 100 $.
 '0+"$  #*"  ,, ' ,9:1 ' $ #"­+ 0 '" ),%9*"" 1 ) "#$"%&09 7'&, 4 %8 (!& ,"$, * (! "#$" + ' ")%"3 $ #"+  '" ­1)  ')!6% 0,1% *%& 1 + ' ")%"3.
"*+," 5,"+"," ' (# )"3 ) )"4 (%"7
140" ) *!5) " 4 '0+,$! ,% "3 ="5 5,"+",
(
4%3 +4!5 $ #"+  ) '")4! )  6651-78.
%""*+," #)"+"$ +& + ' ")%"3  $'0! 4%3 '%" )!5 $ #"+  ) )!89 +%409:"$" 0)­"3$":
Rt = R0 [1 + At + B
= R0 (1 + At + B
R
t
14 R0 – + ' ")%" '" t = 0 °C;
A = 3,968·10
B = 5,847·10
C = –4,22·10
%3 $4 1 $ #"+ :
–3 –1 –7 –2
–12 –4
2
t
3
+ C
(t – 100)] '" –200 °C A t A 0 °C; (14)
t
2
) '" 0 °C A t A +650 °C,
t
; ;
.
Rt = R0 (1 + αt) '" –50 °C A t A +180 °C, (15)
14 α = 4,26·10
–3 –1
.
 $"$ '%"! " $4", " 14 4%3 "#1  )%"3 $ ­#"+  ) "+' %  ",%&.
%3 "#$"3 $'0! '"$39 ,8 ' %0' ) 4­", )! $ #"+ ! ($"+ !) #%"*!5 "' ), ,  ­! 5,"#09+3 ( %&62 *0)+)"%& +&9 " "$9 ( ­% )!+ ," + ' ")%"3 (4 1 $) '" )+&$ $%!5 #­$5. 4 + , $"+  ) – '% 53 ) +' "#) 4"$ +& " %"2 +& 5,"+"," ' (# )"3:
R
= R0 exp [B (1/T – 1/T0)], (16)
T
14 RT " R0 – + ' ")%"3 $"+  '" $'05 T " T0;
48
T0 – *%&3 $'0 ( *1 4"'# ; B –
, =;;"7".
$"+ ! "+' %  ) 4"'#  $'0  –60 4 +120 °C.
 +0,") $"+ ! $ 10 (!& +$ 2 # (#­ 2 ; $!: +8)!, 4"+, )!, (0+", )!.
Индуктивные преобразователи. "7"' 42+)"3 ' (­# )%2 + )  #)"+"$ +" "40,") +" ($  ,  $1" ' ) 4  ' % 8"3, 1 $"*+,"5 #$ ) " $1­" 1 + + 3"3 =%$ ) "5 $1" 2 7'".
 "+. 12 +5$"*+," ' ,#! #%"*! "'! "40,­")!5 ' (# )%2.
"+. 12. 40,")! ' (# )%" + "#$39:2+3 4%" 2
##  (а), + "#$39:"$+3 +*"$ ##  (б),
4";;7"%&!2 (в), 4";;7"%&!2 +; $ !2 (г),
4";;7"%&!2 +; $ !2 + # $,0 2
$1" 2 7'&9 (д) " $1" 0'01"2 (е)
40,")!2 ' (# )%& ("+. 12, а) + '$ 2 4%" 2 ) #406 1 ##  B 5,"#0+3 %"2 2 #)"­+"$ +&9 L = f(B). , 2 ' (# )%& (!* '"$39 '" '$:"35 3, 3  0,01–5 $$. *"%& $&62
49
*0)+)"%& +&9,  %"2 2 #)"+"$ +&9 L = f(s) %"*­9+3 ' (# )%" + '$!$ +*"$ ) #406 1 #­#  ("+. 12, б). " ' (# )%" "+' %  '" '$­:"35 4 10–15 $$.
, & ) "40,") $ ' (# )% "+'!!) 0+"%"
(
8%%& ) '"38"3 + +  ! =%, $1"
F =
dWm /dB = d/dB (LI
2
/2), (17)
14 Wm – =1"3 $1" 1 ' %3;
L – "40,") +& ' (# )%3;
I –
 ,, ' 5 43:"2 *# ($ ,0 ' (# )%3.
" , +' +! "40,")! 4";;7"%&! ' (# )%" ("+. 12, в), ) ,  !5 ' 4 ) #42+)"$ "#$­3$ 2 )%"*"! 4 )$ " '" $ + #!$" #,$" "#$39+3 4) ##  =%, $1" ). ";;7"%&! ' (# )%" ) + *"" + + )+)09:2 "#$"%& 2 7'&9 ( (!* $ + ) 2) "$9 ( % )!+ ,09 *0)+)"%&­ +&, $&609 %"2 +& 5,"+"," ' (# )"3, "+'!!)9 $&6 )%"3" )6"5 ;,  ) " +"8  #0%&"09: 0+"%"  3, & + +  ! =%, $1", *$ 4";;7"%&! ' (# )%".
 "+. 12, г ' ,# +5$ ),%9*"3 4";;7"%& 1 "40,") 1 ' (# )%3, 0 ,   1 )!5 4!$" )%"*"­$" 3)%39+3 )#"$! "40,") +". ," ' (# )­%" #!)9 )#"$ -"40,")!$" "%" +; $ !$". " '""" ')"* 2 ($ ," '$!$  , $ " '" +"$­$"* $ ' % 8"" 3, 3  +"%& =%, $1" )   )!5 4!5 #8"$5 ) 0%9. " '$:"" 3, ­3  )!5 4!5 #8"$5 ' 3)%3+3 .
%3 ' (# )"3 +)"%& ( %&6"5 '$:"2 (4 50–100 $$) '"$39 +; $ ! ' (# )%" + #$,0 2 $1" 2 7'&9 ("+. 12, д). " "$9 " (­$ ,", +' % 8!  (:$ $1" ' ) 4, '"*$ ) ­"*3 ($ , + + " "# 4)05 4", )!5 +,7"2, ),%9*­!5 )+*0 401 4010. +%" '%08 (+4*",) #"$
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