МЕРЕЊЕ И МЕРНИ ИНСТРУМЕНТИ
243
Универзитет „Гоце Делчев“ - Штип, Машински факултет доц. д-р Братица Темелкоска 2010 год.
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МЕРЕЊЕ И МЕРНИ ИНСТРУМЕНТИ
Transcript of МЕРЕЊЕ И МЕРНИ ИНСТРУМЕНТИ
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- ,
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2010 .
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CIP -
". ",
53.08:006.01]:681.2(075.8)
, / . - :
" ", , 2011. - 240 . : . ; 22
:.240
ISBN 978-608-4504-18-4
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COBISS.MK-ID 89639434
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. , , . . . , , . . . . , - , III .
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1. ........... 7 1.1. ................................................................................................. 8 1.2. ...................................................................... 8 1.3. ......................................................................... 9
1.3.1. ................................................................. 10 2. ............................................................................................... 11
2.1. 11
2.2. ................................................................ 12 2.3. ....................................................... 13
2.3.1. ....................................... 15
2.3.2. ............................................................................................ 15 2.3.3. 17
2.4. .................................................................... 24 3. ................................................................. 26
3.1 .................................................. 26 3.2 ...................... 27
3.2.1 ...................................................................... 27 3.2.2 ..................................................................... 28 3.2.3 ................................................. 28 3.2.4 ........................................................................ 29
3.3 .................................................................................... 29 4. .................................................................. 30
4.1. ............................................................................ 31 4.1.1 ......................................................................... 31 4.1.2 .................................................................. 34 4.1.3 . ..................................................... 35 4.1.4 ....................................................... 36 4.1.5 .................................... 39
4.2 .................................................................. 41 4.2.1 ................................................................ 41 4.2.2 ................................................................ 42 4.2.3 ................................................................................ 47
5. ..................................................................................... 52 5. 1 ................................................................ 52 5.2. ............................................................... 69 5.3 ................................................................ 71 5.4 .............................................................. 73
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6. ................................ 73 6.1 ................................................................. 74 6.2 ......................... 77
6.1.1 ..................................................................... 77 6.1.2 ................................................................ 79
6.1.3 779 6.1.4 .. 80 6.1.5 .......... 81 6.1.6 ............... 81 6.1.7 ...... 82
6.2 ........................................................................................ 82 6.3 ............................................................................................ 86
7. ................... 90 7.1. K ...................... 90 7.2. ...................................................................... 91 7.3. ....... 95
7.3.1. .................................................................... 95
7.4. .................................................................... 97 7.4.1. ............................ 97
7.4.2. ................................................................... 98
7.5. ....................................................................................................... 106
7.5.1. .. 106 8. ..................................................................... 108
8.1 .................................... 108 8.2 ........ 114
8.2.1 ...................................................................... 115 9. ....................................................................... 121
9.1 ............................................................................................. 121 9.1.1 .......................................................... 122 9.1.2 ....................................... 123
9.2 .............. 126 9.3 ................. 129
9.3.1 ........................ 129 9.3.2 ............................................................................. 131 9.3.3 ................................................................ 133
9.4 ................................. 133 9.4.1 - ................................... 135 9.4.2 .................................................... 136
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9.4.3 .................................................................... 137 9.4.4 3D Moire .............. 138 9.4.5 3D ........................................................... 140
9.5 ............................................................... 141 9.5.1 ......................................... 141 9.5.2 .......................................................... 142 9.5.3 ................................... 142
9.6 ................................................................................ 148 9.7 - .................................................................... 152
10. .......................................................... 155 10.1. ......................................................................................... 155
10.1.1. ................................... 156 10.1.2. .............. 160
10.2. ................................. 161 10.2.1. ............................................ 161 10.2.2. ...................................................... 168 10.2.3. .................................................. 169 10.2.4. ............................................... 171 10.2.5. ............................................................... 174
10.3. ............................................................. 178 10.3.1. ................................. 179
11. ................................................ 180 11.1. ...................... 180
11.1.1. ..................................................................................... 180 11.1.2. ............................. 181 11.1.3. ... 182 11.1.4. ............................. 182
11.2. ............................................................... 185 11.2.1. ....................................................... 186 11.2.2. ........................ 188 11.2.3. ............................................................. 188 11.2.4. .................................... 190 11.2.5. .................................. 192
11.3. ......................................................... 193 11.3.1. .................................................................. 194
12. E ........................ 197 12.1 ............................... 198
12.1.1 .......................................... 198 12.1.2 ......................................... 200 12.1.3 ......................................................... 201
12.2 ( ) ................. 202
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12.3 ().................................................................... 203
12.4 ( ) ................................................................................. 208
12.4.1 .......................................................................... 208 12.5 ................................... 209
12.5.1 () . 210
12.5.2 ................................. 210 12.6 .......................................................... 213
12.6.1 .............................................. 213 12.6.2 ................................................... 213
13. M ..................................................................... 215 13.1 ............................................................................................. 215 13.2 ............................... 216
13.2.1 ................................................. 216 13.2.2 ..................................... 218 13.2.3 ......... 222 13.2.4 .................................... 225 13.2.5 ............................................. 225 13.2.6 .................... 226
14. ........... 227 14.1 ............................................................ 227 14.2 .............................. 228
14.2.1 .................................................... 228 14.2.2 ( ) ............. 234
14.3 ( Wheatstonov ) ....... 240
1.
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1.1.
. . , , . . , . . , , . . , : , , . : , , . XVIII , - . , 20 1875 . , .
1.2.
. ( . , , , , , ) . . , ( , ). , ( .
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, , ). ( 63 kg), , . : , . : , . . : , , , , .
1.3.
, , . . : ( . kg, s,). : , ( . International System of Units (SI), CGS system of units).
, SI: General Conference on Weights and Measures (CGPM); SI 1.1. : . , . SI ( 1.2).
1.1 SI
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. - 10
m
kg
s
A
K
mol
cd
1.2
N
J
Pa
( . SI, , SI.
1.3.1.
, , , , , , . . : , , ; . : . . :
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. , . . , , . , , . , . .
2.
2.1.
. ( , - ). , , . . , , , , . . , . .
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2.2.
; , . . . , . . . : ; ; . : ; ; , , , ; . : , ; , , , , , , , ; ; . : n , - :
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1
2
1
n
xx
s
n
i
i
(2.1)
xi i - , x
n ; s/ n
x ; ; ; : , , ; , . : , .
2.3.
(). , , . , , . , . . , ( ),
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. , :
)( xx (2.1)
x , x , ( ). , , . :
, , . , , .
- . .
- . ( ) , , .
. :
xxx ii (2.3)
, .
max
xxx i (2.4)
, .
%100
x
xx (2.5)
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2.3.1.
, . . , , , () . . , , n- , :
n
tT ,
g
lT 2 ,
2
22
2
2 44t
ln
T
lg
. . , .
2.3.2.
. , :
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( , )
, :
100
maxxkx
(2.7)
maxx
( ). . :
n
i
ixn
x1
1 (2.8)
n , xi . - :
xxx 11 , xxx 22 , ... xxx nn (2.9)
, :
maxxxx i (2.10)
: )( xx
,
cml 9,391 , cml 0,402 , cml 1,403
cmlll
l 0,403
321
:
cmcml
cmcml
cmcml
1,00,401,40
00,400,40
1,00,409,39
3
2
1
cmll 1,0max
: cml )1,00,40(
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, ( ).
2.3.3.
y ,
1x , 2x ,... nx , :
),...,( 21 nxxxfy
, :
i
n
i i
n
n
xx
yx
x
yx
x
yx
x
yy
1
2
2
1
1
... (2.11)
2.3.3.1 . :
2
224
t
lng
, g :
1. ln.
: tlng ln2lnln2ln24lnln
2. :
x
dxxd )(ln ,
, :
t
dt
l
dl
n
dndd
g
dg222
4
4
(2.12)
, :
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t
dt
l
dl
g
dg2 (2.13)
3.
, - . , . , . , ( ) , . , , . (2.11) - . :
t
t
l
l
g
g
2 (2.14)
, :
t
t
l
lgg 2 (2.15)
(2.11), , . 2.1.
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2.1.
. , , , . , . , - .
2.3.3.2 .
)(2 lfT
:
g
lT 22 4 kxy
kg
gk
22 4,
4
, ,
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, )(2 lfT
. .
2.3.3.3 )(xfy :
nkxy
, n - . , , , (. 2 ).
.2.1 :) , )
, . :
nykx , 1
n
y
k
n
x, 1
n
y
m
x
- knm / , - n. - , 2.2.
.2.2
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:
AB
AB
xx
yytgk
, , . . , , , , .2.3.
.2.3
. , . : . , . + -. , , .. .
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.2.4
- . , . :
lnAB
AB
xx
yyk
)ln()ln(ln ABAB xxyyk (I )
AB
AB
AB
AB
xx
xxd
yy
yyd
k
dk
)()( (II )
AB
BA
AB
BA
yy
yy
xx
xx
k
k
(III )
.
Ax , Bx , Ay By ,
:
- , ( ) - .
, ( ) ( ).
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, :
.
.. , . , .2.5.
.2.5
2.3.3.4
, . . , :
)002,0336,1( x
, 6, 1,33 . , , 1,33 . () . () .
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. , . , . : 6,45cm, 6 4 , 5 , 0,01cm. , , :
cmx )0004,04562,1( cmx )4(4562,1
2.4.
1. , :
- -
, . , , , . , . , (), .
2. . , . :
- - () .
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, , , . , : , . , . . : , , .. .
3. , :
- - .
. , . . , : , , . .
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3.
3.1
, . : 1. :
) , b) ,
c) /, d) , .
. (). / .
2. : ) b) .
: ) b) . , :
) , b) , c) d) .
3. : ) :
. .
b) : , . c) : .
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d) : . 4.
: ) , b) , c) , d) , e) f) .
) . . :
, ,
. b) . c) : . d) : - . ) a : - , o: - .
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. - 28
a) - :
- , - o .
b) :
- , - - .
c) ( ). d) . e) :
- , - () , - -
- . . , . ( ) () . . , . - .
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. . .
:
) - , :
- , - , - , - , - , - .
( ).
) - : - , - - .
( ).
: - ( ), -
, - ( ,
, ), - ( ,
).
: , . : , ( : , , , , ). : .
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. - 30
: . : ; , 100 200; , , 0-100V 100V. . ( -10V +10V 20V). : . / : ; .
4.
.. . :
) )
: ) , ) , ) , ) ) . - , :
) , ) , ) , ) ) .
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4.1. 4.1.1
, . ( ), () (), , .(.4.1).
. 4.1
: - , - , -
, , .
, , (.4.2) . , , . . l. 10mm 930mm, 10mm 935mm.
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.4. 2
( ) , 4.1.
4.1. K
0 ( 0,1 +210-3 l) ( 0,07 +0,1410-3 l)
1 ( 0,2 +3,510-3 l) ( 0,1 +210-3 l)
2 ( 0,5 +510-3 l) ( 0,26 +0,5210-3 l)
3 ( 1 +1010-3 l) ( 0,52 +1,0410-3 l)
l, , mm, m.
0 - ; 1 - ( ); 2 - ( , ); 3 - ( , ).
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(.4.3), 50 1-1,5mm.
.4.3.
. , , . = 460 N/cm2, 0,4m. , , , , , , , . () . , .. , . . = ( 11,51)10 -6 = ( 5,50,5)10 -6, 62 HRC. (.4.4)
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(.4.4) ( R=2
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.4. 7
.4.8 (
4.1.3
1 325mm .4.9. . 325mm 1mm, . . , 30-0,2 mm (.4.10 a) , 0,022 min. o - , 0,013 min.
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.4.9 :1 - 1-50mm,2 - 1-70mm, 3 - 1-180mm, 4 - 3-50mm, 5 - 3-100mm, 6 - 50-170mm, 7 - 100-325mm, 8 - 0-330mm
.4.10
4.1.4
: 100mm, 18-360mm, 250mm, 100mm . : 100mm, e , . 500-2500mm (.4.10). 1mm ( ) ( .4.10 ).
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)
)
.4.11
2-4 , .4.12.
.4. 12
.4.13
, , , . = (11,52)10-6, 56-64 HRC. , .
4. 2.
( ) 1-3mm
1-50mm
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6-50mm
30-100mm
18-100mm
5-300mm
50-150mm
150-360mm,
250-1000mm, 75-100mm.
1-18mm
18-100mm
100-325mm
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37-100mm
4.1.5
, o , , . : ; , .
4.3
/
/
-
: t : 0,05mm.
: t; : 0,05mm.
: t; : () 0,05mm.
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/
/
-
: t ; : 0,1mm.
()
: t ; : 0,1mm 150 .
-
: t ; : 0,1mm .
-
: t ; : 0,2mm .
: t, : 0,05mm .
: , t ; : 0,1mm .
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/
/
-
: t, ; : 0,05mm.
-
: t ; : , 0.05mm, .
4.2 4.2.1
. . , . : - , - - . . 1m , H,I,X. 3-7m. 10mm. . (0,2+0,03 L) m, L . . 2m (2525)mm (1515)mm. 20-40 m, (0,01+L/100000)mm. 040-065.
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10mm . 80-120m. ( 0,05+ L/50000)mm.
.4.14
4.2.2
. : , . , Pedro Nunez XVI . :
- . ( ) 1/10=0,1mm.
- . ( ) 1/20=0,05mm.
- . 1/50=0,02mm.
, c=1mm =c-i , 1,2 3; i . : 9 1, 1=1mm, 10 , 2 i2=0,1mm.
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. 4.15 0,05
2 :
1-c2= i2=0,1mm. :
L=n1c1+n2i2 (4.1) :
- n1 0- 0- .
- c1 ( mm) - n2
- i2 .
: -
2
12
i
cn (4.2)
- :
212 icc (4.3)
: - ( );
-
l=n2c2=n2(c1-i2)=c1(n2-1) (4.4)
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.4.16.
. : (1), (2), - (3) (4) . 4.16 0,1mm.
0,1mm;0,05mm; 0,02mm 0,001mm. .4.17 , 0,05mm.
.4.17 : 1 - , 2 - ; 3 - ; 4 - ; 5 - ; 6 - ; 7 - .
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.4.18
.4.19
.4.18 . 0,05mm 0,02mm, . , , , . , , .4.19. , , . 150mm 0,01mm. . . :
- 0,1mm ; ( 75+ L/20 )m, - 0,05mm; ( 50+ L/20 )m, - 0,02mm ; ( 20+ L/20 )m,
: L - mm.
(.4.20) , (.4.21).
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.4.20 : 1- , 2-; 3-; 4-; 5- ; 6-
.4.21 : 1- ; 2-;3-;4-;5-; 6- ;7- ; 8-
4.22. , . .
.4.22
(.4.23 .4.24) . . . .
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.4.23 ( 0,01)
.4.24 , 0,001
4.2.3
o . 25mm . 25mm , . , . 0,5mm 1,0mm. 0,5mm 50 , 1,0mm 100 . 0,01mm. , 50 , :
5000,050
1
40
1 .
, .
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.4.25
.4.26
(.4.26) , 1,0mm. , 0,01mm. , , . , : , . . 0,75mm 1,0mm. : n=c/i : - ; - ( 0,01mm 0,005mm).
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.4.27
(.4.27) (1) (2), (3). (4). (5), ( -) (6), (7). ( 5-10 N ), (8)-( D-D). 25mm, 0-25mm, 25mm 50mm, 50-75mm . 500mm. 500mm 1000mm 50mm. . , , . 0-25mm, 25-50mm, 50-75, 75-100,100-125mm ., 25mm, 500mm , 50mm 500-1000mm. 25mm , . , . , .
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.4.28
(.4.28) : (1 2), (3), , LCD (4), / (5), (6) (7). 0,001mm.
.4.29
4.29 (2) (1) (3) 0,1 0,01mm.
.4.30
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(.4.30) , , , , . (1), (2), (3) (4). (0-25)mm, (25-50)mm, (50-75)mm, (75-100)mm. 5-7 N, , , . , . 0-100mm. (.4.31) , ., 30-4000 mm, 0,01mm. 30-35mm; 40-50mm; 50-75mm; 75-100mm; 100-125mm, . , 4000mm.
.
.4.31 : - , b-, c- , d-
.4.32
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5.
. . . 0,01mm 0,0005mm, . , , o . : , , .
5. 1
, ( ) .
. 5.1 : - ; B- ; C- ; D- ; - ; F- ( );G- , , H- , I-
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1mm . , 1/100=0,01mm, , , . 1mm . 10mm, o 10mm. 0,005 0,002mm, 1m (1/1000=0,001mm), . . : , , , (.5.2).
) ) )
.5.2
. : . . . , , . ; ( ), ( ). ,
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, . , . :
1. : ( , ), : , , , .;
2. : ( ) , 0,01mm;
3. -: ( ), , - .
( ): , : 0,01 0,00001mm. , o, . , - ( ). .5.3a . . 0,01mm. 0 10mm 0 5mm. 0,002mm 0,001mm, . , , , .
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.5.3 : ) , ) ; 1-, 2- , 3,4 5 , 6- ,7- , 8- , 9- , 10-
- -, Zeiss, Carl Mahr, Pratt&Whituku, Tesa, LIZ, , . , . 0,01mm; 0,002mm 0,001mm, 0,01mm. , , .
:
f=s-s1 (5.1)
2sin2)cos1( 2
ssf (5.2)
sin :
242
22 ssf (5.3)
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.5.4
pupitas, (.5.5). , , . (.5.6) , , . . , , , , . , , , . (25-200)mm, ( 100-350) mm, ( 250-700) mm (600-1000) mm.
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.5.5
.5.6 -
.5.6 (6) (2) (3), (1).
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.5.7
. 5.8 - .
.5.8 -
.5.9 : 1-, 2- , 3-, 4-,5-, 6-
:
100051
10050
4
3
2
1
R
R
R
Ri (5.4)
1,0mm 0,001mm. 0,1mm, 0,001mm.
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, R4=5mm. . .8 . 0- 6, . .5.10 . 3 60 , . 0,3mm 0,01mm; 0,15mm 0,005mm, 0,03mm 0,001mm.
.5.10 : 1- , 2 3- , 4-,5-
.5.11 : 1- ,2- , 3-, 4-, 5-
.5.12 - : 1- , 2- ,3- ,4-
1 5 2 3 4. .5.11 - . 1 2,
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3 4 .
.5.13 : 1- , 2- , 3-
.5.13.1
.5.12 - . 0,01mm . 1 0, 2 . 1 , 3, 4. . 5.13 - . . . . , 0,2-0,3mm 0,004 -0,012mm.
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, . , . 1 . 0,005mm; 0,002mm; 0,001mm; 0,0005mm; 0,0002mm 0,0001mm 0,15mm; 0,06mm; 0,03mm; 0,006mm; 0,003mm. 2 N. .5.14a - , , , .5.14- .
.5.14 :1- , 2-, 3-, 4-, 5-, 6- , 7-
.5.14
(.5.14) . , , 1 2; 3 4 5 2. . 0- ,
-
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. . 0,0001mm; 0,0002mm; 0,0005mm, 0,024mm; 0,05mm 0,100mm. 100 , 100 . 1,5 N. . , , . .5.15 , . . , . . 100mm 80m, 2m. 100 mm 150m 5m.
.5.15 : 1-, 2-, 3- , 5- , 6- 5, 7-
.5.16 , . , (3) (4) (2). , , , .
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. 5.16
, , . . .5.17 . 1, 2 3. 4 , . .5.17 . , (.5.18).
.5.17 : 1- ,
2- , 3-, 4-
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.5.18 : ) 1 2 3 4; ) 1 2 3; ) 3
.5.19 : 1- , 2-
. . , . , . , , , 0,01mm. , , .. , .. . , . , .
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.5.20
18mm ( Zeiss, Tesa, Mahr, Kalibar) . .21-) (3) . (1) (2). . .21 -) Mahr, .
.5.21 : - , -
-
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- 90, . . (1) (2) (3). (4) . (5) .
.5.22.
. , . , ( I), ( II), (2), (2), (1) . , , ( ), , (1), .
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.5.23 : 1- , 2- , 3-, 4-, 5 6-, 7-, 8- .
5.23 . 11-18mm, 19-30mm, 32-50mm, 52-80mm, 85-120mm.
70m, 140m. 5-6 N. (1) . , , ,
:
ADABBEx 2
2cos
22cos
2
dd
BCACAB
1
2cos
222cos
221
ddddddx
:
=d-d` :
1
2cos
21
x
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. - 68
, (3), (5), (6) (7). (8) , (4), , . , , , . , , . .5.24 . , , . .5.24 .
. 5.24
-
____________________________________________________________
. - 69
5.2.
f G .
, ),( fpG ,
. G, , . , , . , . , . , :
- - .
: - 0,12 10 5N/cm2 - (0,5-2) 10 5N/cm2.
e .5.25.
. 5.25
f1 , f2 . h, , :
-
____________________________________________________________
. - 70
212 /1 ddH
h
(5.1)
d1, d2 . z , , . z, . z . .5.25. . , 1 2. . .
.5.26 solex: 1. , 2. , 3. , 4.
.5.26 , solex. 35 50 N/cm2 2, 1 . . , , , f1 . f1 3 f2 z . 5.27 . , . 2, .
-
____________________________________________________________
. - 71
(.5.28), . 5.29 . .
.5.27. :1- ; 2-
.5.28 : 1- ; 2-
.5.29
5.3
, . -, -, -, - . - - . . 5.30 - . , . . 1 2, 3, 4. 5. , , 6,
-
____________________________________________________________
. - 72
. 8, 9 . . , , 7. 1-2 N, 0,001mm. 5.30 . 1 2 3, 5. . , . , , 6. : 0,010mm; 0,020mm; 0,050mm; ,10mm, 0,001mm 0,0001mm. 0,5 4 N.
. 5.30 E : 1- ;2- ; 3-; 4- ;5- ; 6- ; 7- ;8- ;9-
.5.31 : 1- ; 2-; 3-; 4-; 5-; 6-; 7-
-
____________________________________________________________
. - 73
5.4
. .32 1 , 2 .
.5.32
D h ( ). 1- , 2- , - , C- , , D- . : , , , , , , .
6.
: , . . : , , .
-
____________________________________________________________
. - 74
. . . , . .
6.1
, , . , 0-180, 1` 5`. 12 . 6.1 14 , : 6- 1, 3, 5, 15, 30, 45, 6- 1, 3, 5, 10, 25 , 40 2- 20 , 30 . 150 mm 20mm, . , (.6.2). , ( 90), :
0- : ( 0,002 mm + / 100 000 )mm, 1- : ( 0,005 mm + / 50 000 )mm, 2- :. ( 0,01 mm + / 20 000 )mm, 3- : ( 0,02 mm + / 10 000 )mm,
mm.
-
____________________________________________________________
. - 75
: +15 +5=30=2030
: +15-5-30=930
.6. 1
.6.2
:
H
h
31085,4 (6.1)
h - , mm, - , mm. =100mm, 0- h=0,003mm, (6.1) =6. - , .6.3. .
.6.3
-
____________________________________________________________
. - 76
.6.3
(.6.5)
.6.5 : 1-, 2- , 3- 4-, 5- , 6- , 7- , 8- , 9- , 10-
1, 2. 3 4 1 . 3 5, 4 6 7. 5 6 7 2.
-
____________________________________________________________
. - 77
, 8 9 1, 2. 5 6, 7 , . , 10 7 . .
6.2
, , . , .
6.1.1 6.6.
.6.6
h , , 100mm ( 200, 300 500mm). :
xL
hsin = arcsin x (6.2)
, . (.6.7). , . 10-15.
-
____________________________________________________________
. - 78
.6.7
, C.Mahr, .6.8. . , . (3) , (4) 0,001mm, . . 7 8.
.6.8 C.Mahr
-
____________________________________________________________
. - 79
6.1.2 , .6.9, . ( m n), . :
ll
hHtg
(6.3)
h , L,l , 6.9.
.6.9
6.1.3
, l1, , l2 (.6.10).
.6.10-
-
____________________________________________________________
. - 80
2cos
2
,2
cos2
2
2
2
22
11
121212
222
111
dx
dx
abxxddll
bxdl
axdl
22
2
ACtg
ab
;
2sin
222sin
22
1122 ddddAC
: 22
sin12
cos 12121212
tgddddddll
:
1
2cos
2sin1
22sin1
2cos1
12
12
tgdd
llk
:
2cos11
2cos)1( 2
k
1)1(
)1(2
2cos
2
k
k
6.1.4
.6.11 . , , l1, l2. :
h
lltg
22
12
(6.4)
-
____________________________________________________________
. - 81
.6.11
6.1.5
l2, l1, d1, d2 ( .6.12 ).
: )(22 12
12
ll
ddtg
.6.12
6.1.6
. .6.13 :
)(22 123
12
lll
ddtg
(6.5)
-
____________________________________________________________
. - 82
.6.13 ()
6.1.7
d1 , d2, , h4, h5 (.6.13). (h) , h1, h2, :
x
ddhh
dd
ddhh
dd
1212
12
1254
12
2
1
1
2
2
1
1
22sin
(6.6)
=2arcsin x , 11 15 .
6.2
. : .
0 360. , . .6.14 . 0 360 , 5'.
-
____________________________________________________________
. - 83
.6.14 5': 1-, 2-, 3-
, 4-
. .
.6.15
-
____________________________________________________________
. - 84
.6.15 . (1) ( -) (2) (3) 0-60'. . 6.15 . 5'. (3) 40- . (8), (5). (4) (3) (1). (3) 5 (2), 1. .6.16 .
.6.16
, , , . . , , . 5-15, , .
-
____________________________________________________________
. - 85
. 6.17 , .6.17 . , (6) (1) (2) , .
. 6.17 : ) , ) , 1- ,2- ,3- ,4-,5- ,6-, 7-,8-
, 9- ,10- , 11-,12-,13-
(3) . 2', 10''. 41 6' 40''. (11) (9), (12). , .
-
____________________________________________________________
. - 86
.6.18 W.Jahnet
.6.18 W.Jahnet (1) (2) (3). , .
6.3
, . . , . 6.19 , , . R , L, : =L/R , : =206,265L/R.
-
____________________________________________________________
. - 87
.6.19
. 2 2', 2mm. , mm/m. . , (.6.20)
.6.20
-
____________________________________________________________
. - 88
200200mm, 250250mm 300300mm. 0,02-0,03mm/m.
6.21 Zeiss. . (1) (2) (3). 120 , (+), (-).
.6.21. Zeiss
(4), . (5), (7), . (6) .
6.22 , . Zeiss.
-
____________________________________________________________
. - 89
.6.22
(1) (2) (3) (). (.6.22). (4) , , .6.22 . , (.6.22), mm/m, 0,01mm/m.(.6.22). 10mm/m(34'), 0,01mm/m, 1mm/m, 0,02mm/m, . :
b
a
lZ
hc
1000
h- mm; Z-
; b- ; l- . h=0,5mm, Z=100, a=18mm, b=100 mm i l=90 mm, :
01,0100
18
90100
5,01000
c mm/ m
-
____________________________________________________________
. - 90
Niveltronic Tesa , , 1000 ( .6.23).
.6.23 Niveltronic Tesa
. , . , . I:0,75mm/m(150 sec) II: 0,15mm/m(30sec). 0,001 mm/m(0,2 sec) 0,005 mm/m (1sec).
7. 7.1. K
: . , : , . - , (). ().
-
____________________________________________________________
. - 91
(.7.1) :
- D,d - D1,d1 - D2,d2 - h - /2
.7.1
7.2.
, : , , . . , . (.7.2 ). , . 45. .7.2 ) . , , . : d2.
-
____________________________________________________________
. - 92
) ) .7.2 ) : )
:
a) , b) , c) d)
.7.3
) . . , , . ) , , 7.4.
-
____________________________________________________________
. - 93
.7.4
, d2.
d2=M-2AC, : AC=AD-CD , AD :
)
2sin
11(
2
2sin
22
zz
z dd
dADABAD (1)
CD=bt/2, 2
cot2
g
hbt (2)
2cot
4
g
hCD (3)
AD CD AC :
2cot
4)
2sin
11(
2
ghd
AC z (4)
d2 :
2cot
2)1
2sin
1(2
gh
dMd z (5)
:
2
42
coszd
h
2cos2
h
d z (6)
-
____________________________________________________________
. - 94
)
2sin
11(
. (5) =60, 3m. , 1m . .7.5 . .
.7.5 : 1-, 2- , 3- , 4- , 5-
) : () . . 7.5.1 d2 o . BG=L.
7.5.1 :
2sin
2cot
24
22
2 zdg
hhLd (7.7)
: , ,
. .
.7.5.1
-
____________________________________________________________
. - 95
.7.6 . 1 ( 0,005mm), 2 . 2 .
.7.6 : 1- , 2-
.7.7
, . , .7.7. . , . zh, z , h- .
7.3. 7.3.1.
. .8 , :
- db;
-
____________________________________________________________
. - 96
- d0 z m. m=t/;
- : dk df . , db=d0cos;
- .
:
- t0, ;
- tb, ;
- S ;
.7.8
.7.9
- ;
- () ;
- W (.7.9) .
-
____________________________________________________________
. - 97
7.4.
. , .
7.4.1.
. -, . , - .
7.4.1.1.
, - , . .7.10 .
.7.10 : 1,2,3,4-, 5- , 6--, 7- , 8- , 9-, 10-, 11 12-, 13-,14-, 15-,16-, 17-
-
____________________________________________________________
. - 98
7.4.1.2.
, -, . . . . .7.11 .
.7.11 : 1-, 2-
, 3- , 4- ,5- , 6-, 7-, 8-9-, 10-, 11-12-13-
,14-
7.4.2.
7.4.2.1.
. , . .7.12 . .7.13. .7.14.
-
____________________________________________________________
. - 99
.7.12 : 1-, 2-3- , 4- ,5-, 6-7- ,8-
.7.13 Zeiss
.7.14 Zeiss: 1-, 2-3- , 4-, 5-,6-
. . .7.15 g- . 1 2 . , 3 4 , 5 . 0,001. (.7.15), .7.16.
-
____________________________________________________________
. - 100
.7.15 g: 1-2-, 3-4- , 5-
.7.16 Zeiss: 1-2- ,3- , 4- , 5-, 6-
7.4.2.2.
. .7.17 , 90. , q, 1 2 . q 3 4. 5 . , 6 . 3.
.7.17 : 1-2- , 3-, 4-5-, 6- ,7-
-
____________________________________________________________
. - 101
(.7.18), 7.19 Zeiss.
.7.18 : 1-, 2-4-, 3- , 5-, 6-8-, 7- , 9--, 10-
.7.19 Zeiss
, , . , . , :
2
cos1
m
d m - , - .
, m . , , (.7.20). , M=d1+d0,
d0 - , d1-
. :
1
0
0
90cos d
zdM
-
____________________________________________________________
. - 102
.7.20 : )-
, )-
7.4.2.3.
(. 7.21). .
.7.21 : 1- , 2-
, 3-
7.4.2.4.
. :
- -
. 7.22 Maag.
-
____________________________________________________________
. - 103
.7.22 Maag: 1- ,
2- , 3- , 4-, 5-, 6- , 7-
7.4.2.5.
, . .7.23 - .
.7.23 - : 1- , 2-, 3-, 4-
-
____________________________________________________________
. - 104
7.4.2.6.
. . .7.24 .
.7.24 : 1-
, 2- , 3- -4- , 5- , 6- , 7- , 8- , 9- , 10-
(9) (10), . . . Zeiss. .7.25 . .
.7.25 Zeiss
7.4.2.7.
.
-
____________________________________________________________
. - 105
. . ( ).
.7.26 : 1- , 2-
, 3-, 4- , 5- , 6- , 7- , 8- ,
9-
.7.26 . , 5, 6 .
7.4.2.8.
, - . .7.27 . - .7.28.
-
____________________________________________________________
. - 106
.7.27 : 1--, 2- , 3--
.7.28 : 1-, 2- , 3--
7.5.
7.5.1.
, . . . . , (.7.29 ). . . , ( ), .
-
____________________________________________________________
. - 107
.7.29
(.7.30). .
.7.30
, , (.7.31).
) ) ) ) .7.31.
.7.32 . , , . .
-
____________________________________________________________
. - 108
.7.32 : 1- , 2-
, 3- , 4-, 5-
8.
. , , , . . . , , . . :
- - .
8.1
.8.1 . 10 12, . 12 11 100mm. ,
-
____________________________________________________________
. - 109
13, 2 100mm. 5 6. 3, 4, 5 6 11 7. 7 100mm 0,1mm.
.8.1 , Karl Zeis: 1-, 2- , 3-, 4-, 5- , 6-, 7- , 8- , 9-, 10-, 11- , 12- , 13- , 14-
9. 8 9 10 1 .14. 5 6. 8 7 11, 2 8 . 10 . . . 8.2 .
-
____________________________________________________________
. - 110
.8.2 : )- , )-
450,200-0,002=450,198mm. , . : 0 1000mm, 0-3000mm, 0-6000mm. :
- 100mm, = (0,5 + L/200) m, - 100mm, = (0,5 + L/100) m, - : L- mm.
20 1 ea 0,5. 2N. . 8.3 .
.8.3 : 1- , 2- , 3- , 4- , 5-
, 100mm 0,1mm .
-
____________________________________________________________
. - 111
.8.4 . , . -1 . 2 3 . 2 4 . 3 6, 5 7 . 8, , . .
.8.4 : 1-, 2 3 , 4 , 5- , 6- , 7- , 8- , 9-, 10- , 11- , 12-
5. . 8.5 . , . ( 0,012mm). 11 0,1 mm, : , 0,1mm , .
-
____________________________________________________________
. - 112
.8.5
. 0,1 mm. 6. 100 mm, 100 , 1,0 mm. 10 . . 0,001 mm. , , 5, 12,272 (4) mm. . , . : , 1,0 50 mm, . .8.6 .
-
____________________________________________________________
. - 113
.8.6 :
1- , 2- , 3- , 4- , 5- , 6- , 7-
1 3, 2. .8.7 . 1 6 . , 3 4, . 5. 3 6 . 2 7.
.8.7
,
-
____________________________________________________________
. - 114
. . :
1. : - : (1,5 + L/100) m,
(0,5 + L/100) m,
- : (1,8 + L/100) m, ,
(0,7 + L/100) m,
2. : (2 + L/100) m,
(1+ L/100) m,
2N, . , . . .
8.2
, . . () ( .8.8-). . , . (.8.12). /2 , .
-
____________________________________________________________
. - 115
( .8.8-),
22
K (8.1)
: - , . ( .8- ),
2
)12(
K (8.2)
.
) )
)
.8.8 : )- , , )- . , )- /2.
, . . 0,1 , 0,1 . , =0,55m, 0,550,1=0,05m. 3-5mm.
8.2.1
. 8.10 , o . .8.9. 1 2 3 4 7.
-
____________________________________________________________
. - 116
7, 6 5. 6 7. 7, 11, 7 , ( ) . 8 . 9, 10. 11 12 , . 12 11 . 6 7 . 6 : . 6 7. 6 7 , . 5 , . 11, . . . : /n, - n . /2 4. , /2, :
n
Ki
2
(8.3)
/2 () . () n :
-
____________________________________________________________
. - 117
n
Ki
2
(8.4)
.8.9 : 1- , 2-, 3-, 4-,5- , 6- ,7- , 8- , 9- ,10-,11-,12- ,13-
.8.10 : 1- 7, 2- , 3- , 4-, 5- , 6- , 7-
,
i(m) 0,05 8 0,1 16
0,2 32
: i = 0,2 m = 32, = 0,559 m, :
442,02
32550,0
n
, 4 5 , 32 44 .
-
____________________________________________________________
. - 118
:
mni
5,103,0( , (8.5)
: n- 0- . - m, i- m, - m. : . , , . I- , II- , I- . . 8.11, , /2, l, 1 () 2, :
2)( nXl (8.6)
.8.11
-
____________________________________________________________
. - 119
: X- , n- , - . .8.12 . , . . 8.12 l 1 : l=l1-l2 (8.7)
l1 l2 : l1 1 n1- , /2, (8.6) :
2)( 111 nXl (8.8)
:
2)( 222 nXl (8.9)
l1 l2 (7) :
)(2
2211 nXnXl
(8.10 )
l n, :
(X+n)=(X1+n1)-(X2+n2) (8.11)
1 2 . , l , 1 2 n1 n2. . , 1mm, 4000, 10mm 35000. , . , , .
-
____________________________________________________________
. - 120
.8.12
ni . , . .8.13 Kester, 8.14 . . 8.14 : , .
.8.13 : 1- , 2-, 3-, 4- , 5- , 6- , 7- , 8- , 9- , 10 - , 11-
-
____________________________________________________________
. - 121
.8.14 : 1- , 2-, 3-, 4- , 5- , 6- , 7- , 8-, 9- , 10- , 11-, 12- , 13-, 14- , 15- , 16- 17- , 18- , 19- , 20-
9.
o . , , . , - . , .
-
____________________________________________________________
. - 122
.9.1 ,
to (.9.1). , . a : , , , , , . : , , , .
9.1.1 :
- -
.9.2
, , . . , .9.3.
-
____________________________________________________________
. - 123
.9.3
() () .9.4.
a) b) c)
.9.4 : ) n1
-
____________________________________________________________
. - 124
.9.5
. . . . , . . .9.3 . .9.6 .
.9.6
-
____________________________________________________________
. - 125
) ) ) ) .9.7 ,)- , )-
. . . . . . , (), . . . ( ), . ( ). . . . , . . . , 45
2/
-
____________________________________________________________
. - 126
. 90. . . . .
9.2
. :
- , - , - Moire , - , - , - .
, :
- , - , - , - , - , - .
) - ; 1010m10m
-
____________________________________________________________
. - 127
) , 9000
) ; 0,1m
. 9.8
. . , .. , . :
1. , 2. , 3. ,
-
____________________________________________________________
. - 128
4. , 5.
.
, - . : , , , . , .
.9.9
, , . .9.9 ( 200200m) 50mm x 50mm. , ( .9.10).
-
____________________________________________________________
. - 129
.9.10
5 10 -7 ( .9.10 ).
.9.11
9.3 9.3.1
. . . , . .9.12.
-
____________________________________________________________
. - 130
, , . . . . . .
.9.12
, , . . .9.13. 180. . L1 ( ),
-
____________________________________________________________
. - 131
. L2, . .
.9.13
. . , . , . . (.9.12). .
9.3.2 . .9.14. . .
-
____________________________________________________________
. - 132
. . . . , . . . , . . , . . .
.9.14 .
,
-
____________________________________________________________
. - 133
. :
)/( bLay m.
9.3.3 .9.14. , . , . .
.9.15
9.4
.
-
____________________________________________________________
. - 134
:
- - , - , - , - .
.9.16 CCD ( charge couple camera)
CCD 9.17.
.9.17 CCD
9.17 :
- , - , - , - , - .
CCD (charge coupled device) . . .
-
____________________________________________________________
. - 135
CCD . - , CCD CCD . CCD . CCD . CCD image processing. . - CCD . , . CCD , .
9.4.1
, , , . CCD , , -. . 2D . , CCD . . , . . . CCD , . .
-
____________________________________________________________
. - 136
9.4.2
. , . , , , . ( .-triangulum) (.9.18).
.9.18
, CD . (.9.19) , , . , , , CCD e. . , . CCD
-
____________________________________________________________
. - 137
. . (.9.20).
.9.19
.9.20
9.4.3
. , (zerodur). , .
-
____________________________________________________________
. - 138
, - . , , , , .(.9.21).
.9.21
9.4.4 3D Moire
. . . . (. 9.22).
-
____________________________________________________________
. - 139
.9.22 CCD
.9.23
-
____________________________________________________________
. - 140
, , a . . . , . . .
9.4.5 3D
. 3D . . , . 3D . , . . 9.24 .
.9.24
. 3D . .
-
____________________________________________________________
. - 141
, . 1 m3 1: 15 000 . .
9.5 9.5.1
(Light Amplification by Stimulated Emission of Radiation).
: , . . . . , : , (.9.25).
.9.25
, , , . , . , , .
-
____________________________________________________________
. - 142
, . .
9.5.2
: - , - - .
: - - .
:
- , - - .
: - , - - .
9.5.3
: - ; - , , ,
; -
; - ; - ; - ; - ; - ; - ; -
. .
-
____________________________________________________________
. - 143
85-95%. , . , :
- ;
-
- . . .
9.5.3.1
, . . . .9.26 , , , .
.9.26
9.5.3.2
-
____________________________________________________________
. - 144
. . , . CCD . CNC . . . . , . . .
.9.27
90 . .
-
____________________________________________________________
. - 145
.9.28
9.5.3.3
. (.9.29) , . Michael . , . . . . .
-
____________________________________________________________
. - 146
.9.29 Michael-
, . , . .
.9.29
-
____________________________________________________________
. - 147
9.5.3.4
. . . 9.30.
.9.30
, . , . . . , . . . . , . , , :
-
____________________________________________________________
. - 148
- , . ;
- . 90 60. , .
1m. 400 .
9.6
- . . . . , , , , . 9.31 -. 1 4, 14 10. 7 6 5 . 10. 14 11 13 . 0-25mm. 14 0 150 mm. 10 12. . 7 3. 9. . 2.
-
____________________________________________________________
. - 149
6.3W. 3, 8. .9.31.
.9.31. :
1-, 2-, 3-, 4-, 5-, 6- , 7-, 8-, 9-, 10 - , 11-
, 12-, 13- , 14-
:
32
1K
LH
K
LK m
: L- mm, mm, 1,2,3 . : , . . , . , .
-
____________________________________________________________
. - 150
.
.9.32 .9.33 .
.9.34
-
____________________________________________________________
. - 151
.9.35
.9.36
.9.37 ( )
.9.38
-
____________________________________________________________
. - 152
9.7 -
-, , , . , , - . - : - , ; - . - . . 9.39 - .
.9.39 -: 1- , 2-
.9.40 : 1- , 2-, 3- , 4- ()
-
____________________________________________________________
. - 153
.9.41 -
.9.42
-
____________________________________________________________
. - 154
.9.43 -
.44 -
.9.45
.9.46 ()
-
____________________________________________________________
. - 155
10. 10.1.
, . . . . . , ( ). , , , . :
. .
, . pt.
.10.1 () ()
, SI Pascal. 1 N(Newton) . , 1 bar 105 . 1= 1 N/m2 1bar=105N/m2=105Pa
-
____________________________________________________________
. - 156
1mbar=102N/m2
: 1. :
a. ( ), b. (
), c. , d. ( );
2. : a. , b. , c. , d. ;
3. : a. , b. , c. .
:
, 100.
.
.
. . .
10.1.1.
. ,
-
____________________________________________________________
. - 157
. . :
- - Prandtlova .
. 10.2 10.3.
.10.2
.10.3 Prandtlova
10.1.1.1. -
:
r
c
dn
dp 2 (10.1)
r = , p=const., , ( ), . . , . . , . 4-8 (.10.2) . , . Prandtl (.10.3).
-
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10.1.1.2.
, . . Rayleingh Re- , , (Machov ), Machov . d=2-5mm, , . . .
10.1.1.3. Machov
=0,8, , . , 0,8
-
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10.1.1.4.
Pitotova , .. , , .10.5. , 0,2% =1 . , .
.10.5
. .10.5, . , . . .
10.1.1.5.
, . (.10.6)
-
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. - 160
.10.6
10.1.2.
, , , , 0,5mm. , , , . , , . , . , , . d V . .10.7 P0 1. , , 1. , 99% 1-0, tb, .
-
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ta, 0 1 .
.10.7
10.2.
. . :
- , - - .
, , . . . :
- , - - .
.
10.2.1.
.
-
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. - 162
h e , F=mg=hAg, p=hg, . , hk. . , , hk=K/d mm. , : 11mm2, 14mm2.
: - U- , - U- , - U- , - , - , - U- , - , - .
10.2.1.1. U-
. 1 2, .10.8. p :
ghppp fm )(21 (10.2)
: m- , f . U- . , .
-
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. - 163
.10.8 U-
.10. 9 U-
10.2.1.2. U-
, , .10.9. m
-
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. - 164
ghhl
lpp MVaps 2
0
00
(10.5)
.10.10 U
.10.11
10.2.1.4.
10.11 . U 0. , 0 . 2 , 2 .
10.2.1.5. -
.10.12. :
ghp M (10.6)
:
-
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. - 165
constA
Axhhh )(sin
2
121 (10.7)
, 0 , , .
.10.12
10.2.1.6. U-
U- . . U- . . . ,
-
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. - 166
.10.13
:
RAmgrppp /sin21 (10.8)
: m - , A - =d2/4, r - , R - .
10.2.1.8.
. . , . . .
.10.14
-
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, 1=2, . 2 , 2>1, . () . , . , :
Mp = - Mm (10.9)
:
Mp= r x Fp ; Fp=( p2-p1)S (10.10)
: r- - .
Ft F. .
Ft=Fsin , F=Mg, (p2-p1)Sr =MgSsin (10.11)
:
RgM
rSPP 12arcsin (10.12)
, . .
10.2.1.9. ( Betz)
(.10.15). G S R
-
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. - 168
. ( 20 ) mm . 300-800mm, , . 0,5.
.10.15 ( Betz)
10.2.2.
: - , - - .
10.2.2.1.
Bourdonova (.10.16) ( ) , ( ). , . . 0,6-2%.
-
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, 1 .
.10.16 : ) , )
10.2.2.2.
.10.16., . 2 . , . 2% .
10.2.2.3.
10.17 , . . 2% .
.10.17
10.2.3.
, , .
-
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U- .
10.2.3.1.
:
- , - , - -, - , - , - .
. , , , , . - . , , . 1 2% . , , . . .
10.2.3.2.
, .10.18. =0,9806cm2 , , 0,5kg, 1 kg, . 1 kg , :
P=mg/A=105 N/m2 (10.13)
-
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.10. 18
, 1/2. V , R , .. , . . (1):
10.1
0,6 1,0 2,0
0,4 0,8 1,6%
0,6 1,0 2,0%
10.2.4.
. :
- , - - .
. , . ()
-
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. - 172
. , . - .
=(1-0) (10.15)
.10.19
. (0 1 ), (0 100). , .
.10.20 : ) ( ) 0-1, 0-50 , 3%; ) , 0-1,
0-100 , 0,25%, 4-20 mA
- (.10.21). .22 . .
-
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.10.21 : ) , ) ()
() , . , , e 4-20 mA.
.10.22
, (.10.23), . . , .
-
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.10.23 : ) , )
10.2.5.
, (100 000 ). , 0 ( ), 1 , . , :
- 100 000-100 , - 100 -10-1 , - 10-1- 10-4(10-6) , - 10-6- 10-8 .
, . . : . - . . : . : , - , .
-
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10.2.5.1. - Mc Leod -
, . . .
.10.24 Mc Leod-
. (1) (2). . (1) (3) (4). , , (1) . (5) (6) (7). . (8) (2). (2) (8) . - . .
-
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10.2.5.2. -
10-3 , , 10-4 mmHg. , .. , , .. .
10.2.5.3. .
.10.25
(). , (R). (). . (100-250 V), (2-50 V). . , , . . , . , , , .
-
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10-3 10-8 mmHg. 10-3 mmHg , . 10-8 mmHg .
10.2.5.4. e . N-S. 2000-3000V. . , . , , , . 10-3 10-6 mmHg, 500- 1500 .
.10.26
. 3%, .
10.2.5.5. - , . . .10.27. (3) (4). 10-1010-13 ,
-
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. 107-108 , . 103 10-3 torr.
.10.27
, . 1,5%.
10.3.
, . 1-3 , . :
- ( 2 ms), - , - , - - .
, . , , . , . .10.24, 1 , 2 -.
-
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3 .10.24 , / .
