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ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ, ɫɨɜɩɚɞɚɸɳɢɦ ɫɨ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɟɣ
ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ ɞɥɹ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɧɟɣɬɪɨɧɨɜ, ɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ [14]:
'' ' '
'
3
0
2
'
'
'
2
'
4
,,
21
1
,,
22 1
sss s s ss
s
s
ss s s s
ss s
n
JJJ J J sJsJ
J
s
sqKc
s
K K sqK s qK qK
ss J J qK c
n
d
B
ddd
k
J
aab b h h f
I
k
SS
VS
H
H
TH
::{
::
{*
¦¦
Rr
Rr
rR
(69)
Ɇɟɬɨɞɵ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɞɚɥɢ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɴɹɫɧɢɬɶ
ɩɪɢɪɨɞɭ Ɍ-ɧɟɱɟɬɧɨɣ ɚɫɢɦɦɟɬɪɢɢ ɩɪɢ ɭɱɟɬɟ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ l ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫɨ ɫɩɢɧɨɦ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ.
Ƚɚɦɢɥɶɬɨɧɢɚɧ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
l
Cor
H ɞɥɹ ɫɥɭɱɚɹ
D
-
ɱɚɫɬɢɰɵ ɢɦɟɟɬ ɜɢɞ:
2
Cor
0
ˆ
2
H
Jl Jl
J
=
, (70)
ɝɞɟ ɨɩɟɪɚɬɨɪɵ J
r
ɢ l
r
ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɚɤ
'' ''
, ,
x
yxy
JJiJ llil
rr
r r
(71)
ɩɪɢɱɟɦ
'
x
J ,
'y
J – ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɫɩɢɧɚ J ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɨɫɢ '
x
ɢ 'y ɜ. ɫ., ɚɢ
'
x
l ,
'y
l – ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɬɪɟɬɶɟɣ
ɱɚɫɬɢɰɵ ɨɫɢ '
x
ɢ 'y ɜ. ɫ. Ⱦɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɨɜ (71) ɧɚ ɮɭɧɤɰɢɸ
J
MK
D
Z
ɢ
ɲɚɪɨɜɭɸ ɮɭɧɤɰɢɸ
'
l
lK
Y :
r
ɨɩɢɫɵɜɚɟɬɫɹ ɮɨɪɦɭɥɚɦɢ
12
1
1;
JJ
MK MK
JD J K J K D
ZZ
r
r ªº
¬¼
B
B (72)
12
''
1
1
l
l
lK l l
lK
lY l K l K Y
r
r
ªº
: r :
¬¼
rr
B . (73)
ɉɨɷɬɨɦɭ ɞɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɚ
Cor
ˆ
H ɧɚ
(70) ɧɚ ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ
s
s
J
M
qK
S
<
ɦɨɞɵ ɞɟɥɟɧɢɹ q ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɹɟɬ ɫɬɪɭɤɬɭɪɭ ɷɬɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ.
ȼ ɧɟɣ ɢɫɱɟɡɚɟɬ ɜɟɞɭɳɢɣ ɱɥɟɧ ɫ 0l
, ɚ ɨɫɧɨɜɧɭɸ ɪɨɥɶ ɧɚɱɢɧɚɸɬ ɢɝɪɚɬɶ
ɱɥɟɧɵ ɫ 0l
z . Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɚɦɩɥɢɬɭɞɵ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ
ɲɢɪɢɧɵ
Cor
s
s
J
qK
S
D
§·
*
¨¸
©¹
ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ Ʉɨɪɢɨɥɢɫɨɜɚ ɝɚɦɢɥɶɬɨɧɢɚɧɚ (70)
ɜɦɟɫɬɨ ɝɚɦɢɥɶɬɨɧɢɚɧɚ
A
H
ɜ ɮɨɪɦɭɥɟ (50) ɤɚɧɚɥɨɜɵɟ ɮɭɧɤɰɢɢ
s
J
M
U
S
D
(48)
ɧɟɨɛɯɨɞɢɦɨ ɡɚɦɟɧɢɬɶ ɧɚ ɧɨɜɵɟ ɤɚɧɚɥɨɜɵɟ ɮɭɧɤɰɢɢ
s
J
M
U
S
D
(
, 1mm
DD
{ r
), ɭɱɢɬɵɜɚɸɳɢɟ ɯɚɪɚɤɬɟɪ ɞɟɣɫɬɜɢɹ ɝɚɦɢɥɶɬɨɧɢɚɧɚ
Cor
ˆ
H ɧɚ
ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ
s
s
J
M
qK
S
<
. ɗɬɨ ɩɪɢɜɟɞɟɬ ɤ ɡɚɦɟɧɟ ɮɭɧɤɰɢɣ
ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɵ ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ, ɫɨɜɩɚɞɚɸɳɢɦ ɫɨ ɫɩɢɧɨɜɨɣ ɦɚɬɪɢɰɟɣ
ɩɥɨɬɧɨɫɬɢ ɹɞɪɚ ɞɥɹ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɵɯ ɧɟɣɬɪɨɧɨɜ, ɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ [14]:
d 3V 4S 0
B : R , :r , H {
d : R d :r d H kn2
1 J J J S Js J S J 2J s 1 sJ s ' J s '
{ ¦
kn2 ss ' J s J s 'qK s
aKs aKs ' bsqK
s
s b s'
s s ' qK hs hs '
s
s'
s 2 2I 1
¦ * qK s c f qKs
s
TrR , H ,
c
(69)
Ɇɟɬɨɞɵ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɟɥɟɧɢɹ ɞɚɥɢ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɴɹɫɧɢɬɶ
ɩɪɢɪɨɞɭ Ɍ-ɧɟɱɟɬɧɨɣ ɚɫɢɦɦɟɬɪɢɢ ɩɪɢ ɭɱɟɬɟ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ l ɬɪɟɬɶɟɣ ɱɚɫɬɢɰɵ ɫɨ ɫɩɢɧɨɦ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ.
Ƚɚɦɢɥɶɬɨɧɢɚɧ Ʉɨɪɢɨɥɢɫɨɜɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ H l Cor ɞɥɹ ɫɥɭɱɚɹ D -
ɱɚɫɬɢɰɵ ɢɦɟɟɬ ɜɢɞ:
=2
Hˆ Cor J l J l , (70)
2 J0
ɝɞɟ ɨɩɟɪɚɬɨɪɵ J r ɢ lr ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɚɤ
J r J x ' r iJ y ' , lr l x ' r il y ' , (71)
ɩɪɢɱɟɦ J x ' , J y ' – ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɫɩɢɧɚ J ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɧɚ ɨɫɢ x '
ɢ y ' ɜ. ɫ., ɚ ɢ l x ' , l y ' – ɩɪɨɟɤɰɢɢ ɨɩɟɪɚɬɨɪɚ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɬɪɟɬɶɟɣ
J
ɱɚɫɬɢɰɵ ɨɫɢ x ' ɢ y ' ɜ. ɫ. Ⱦɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɨɜ (71) ɧɚ ɮɭɧɤɰɢɸ DMK Z ɢ
ɲɚɪɨɜɭɸ ɮɭɧɤɰɢɸ YlKl :r' ɨɩɢɫɵɜɚɟɬɫɹ ɮɨɪɦɭɥɚɦɢ
J 12 J
J r DMK Z ª¬ J r K J B K 1 º¼ DMK B1 Z ; (72)
12
lrYlKl :r' ª¬ l B Kl l r Kl 1 º¼ Yl Kl r1 :r' . (73)
J SM
ɉɨɷɬɨɦɭ ɞɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɚ Ĥ Cor ɧɚ (70) ɧɚ ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ < qKs
s
ɦɨɞɵ ɞɟɥɟɧɢɹ q ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɹɟɬ ɫɬɪɭɤɬɭɪɭ ɷɬɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ.
ȼ ɧɟɣ ɢɫɱɟɡɚɟɬ ɜɟɞɭɳɢɣ ɱɥɟɧ ɫ l 0 , ɚ ɨɫɧɨɜɧɭɸ ɪɨɥɶ ɧɚɱɢɧɚɸɬ ɢɝɪɚɬɶ
ɱɥɟɧɵ ɫ l z 0 . Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɚɦɩɥɢɬɭɞɵ ɩɚɪɰɢɚɥɶɧɨɣ ɞɟɥɢɬɟɥɶɧɨɣ
Cor
ɲɢɪɢɧɵ §¨ * qKs D ·¸
J S
ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ Ʉɨɪɢɨɥɢɫɨɜɚ ɝɚɦɢɥɶɬɨɧɢɚɧɚ (70)
© s ¹
ɜɦɟɫɬɨ ɝɚɦɢɥɶɬɨɧɢɚɧɚ H A ɜ ɮɨɪɦɭɥɟ (50) ɤɚɧɚɥɨɜɵɟ ɮɭɧɤɰɢɢ UDJ sS M (48)
J SM
ɧɟɨɛɯɨɞɢɦɨ ɡɚɦɟɧɢɬɶ ɧɚ ɧɨɜɵɟ ɤɚɧɚɥɨɜɵɟ ɮɭɧɤɰɢɢ UD s
( D { D m, m r1 ), ɭɱɢɬɵɜɚɸɳɢɟ ɯɚɪɚɤɬɟɪ ɞɟɣɫɬɜɢɹ ɝɚɦɢɥɶɬɨɧɢɚɧɚ Ĥ Cor ɧɚ
J SM
ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ < qKs . ɗɬɨ ɩɪɢɜɟɞɟɬ ɤ ɡɚɦɟɧɟ ɮɭɧɤɰɢɣ
s
42
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