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Файл:Моделирование и конструирование элементов летательных аппаратов. Учебное пособие
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ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɵ (2.124) ɢ (2.125), ɜɨɡɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɞɜɚ ɜɚɠɧɟɣ-
ɲɢɯ ɩɚɪɚɦɟɬɪɚ ɮɥɚɧɰɟɜɨɝɨ ɭɡɥɚ:
– ɩɨɬɪɟɛɧɵɣ ɞɢɚɦɟɬɪ ɲɩɢɥɶɤɢ d
– ɩɨɬɪɟɛɧɵɣ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢɡɝɢɛɭ ɮɥɚɧɰɚ W
ɉɨɬɪɟɛɧɵɣ ɞɢɚɦɟɬɪ ɲɩɢɥɶɤɢ d
;
ɲ
.
ɮɥ
, ɦɦ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɲ
4
1
k
ɲ
2
'
()
SV
ɤɒ
24
ɫ d
ɲȼ
d ɪ
Ɂɚ ɧɭɥɟɜɨɟ ɩɪɢɛɥɢɠɟɧɢɟ ɦɨɠɧɨ ɜɡɹɬɶ
Ɇ
ɢɡɝ
Qh
ɮ
()
ɤ
0,3 2
d ɪ
'
ɲ
ɛ
, ɦɦ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
d
ɲ
. (2.127)
3
ɛ
d Ɇɫ
ɲɢɡɝȼ
0,8 4
ɒ
SV
. (2.128)
Ɍɨɥɳɢɧɭ ɩɨɞɨɲɜɵ h
ɫɪɟɡɚ ɩɨɞɨɲɜɵ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ Ɋ
ɧɟɨɛɯɨɞɢɦɨ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢɡ ɭɫɥɨɜɢɹ
ɮ
. ɉɪɢ ɷɬɨɦ ɫɱɢɬɚɟɦ, ɱɬɨ ɫɪɟɡ ɩɨɞɨɲɜɵ
ɲ
ɩɪɨɢɫɯɨɞɢɬ ɩɨ ɨɛɟ ɫɬɨɪɨɧɵ ɝɚɣɤɢ, ɩɪɢɱɟɦ ɜ ɪɚɛɨɬɭ ɜɤɥɸɱɚɟɬɫɹ ɲɢɪɢɧɚ, ɪɚɜɧɚɹ
ɞɜɭɦ ɞɢɚɦɟɬɪɚɦ ɲɩɢɥɶɤɢ.
ɍɫɥɨɜɢɟ ɩɪɨɱɧɨɫɬɢ ɧɚ ɫɪɟɡ
Ʉ
, ɇ/ɦɦ2, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
0,7
V
ȼ
Ʉ
0,7 2 2
Ɋ hd
V
ȼɲ ɮɲ
. (2.129)
ɉɪɨɞɨɥɶɧɭɸ ɫɢɥɭ, ɞɟɣɫɬɜɭɸɳɭɸ ɧɚ ɲɩɢɥɶɤɭ
, ɇ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪ-
Ɋ
ɲ
ɦɭɥɟ
0,8
ɊɆɫ|
ɲɢɡɝ
. (2.130)
ȼ ɪɟɡɭɥɶɬɚɬɟ, ɩɨɫɥɟ ɭɩɪɨɳɟɧɢɣ ɬɨɥɳɢɧɭ ɩɨɞɨɲɜɵ h
, ɦɦ, ɜɵɱɢɫɥɹɸɬ ɩɨ
ɮ
ɮɨɪɦɭɥɟ
ɄɄ
h ɆɫɆɫ
ɮ ɢɡɝ ȼ ɢɡɝ ȼ
§·
3
VV
¨¸
©¹
. (2.131)
ɒɢɪɢɧɚ ɩɨɞɨɲɜɵ ɮɥɚɧɰɚ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɨɣ ɲɢɪɢɧɟ ɩɨɹɫɚ ɥɨɧɠɟɪɨɧɚ.
Ɂɚɞɚɱɚ ɪɚɛɨɬɵ
Ɋɚɫɫɱɢɬɚɬɶ ɢ ɫɤɨɧɫɬɪɭɢɪɨɜɚɬɶ ɮɥɚɧɰɟɜɵɟ ɫɨɟɞɢɧɟɧɢɹ ɤɪɵɥɚ ɢ ɤɨɪɩɭɫɚ ɫ
ɧɚɪɭɠɧɵɦɢ ɤɪɵɥɶɟɜɵɦɢ ɩɪɨɭɲɢɧɚɦɢ ɞɥɹ ɫɟɱɟɧɢɹ Ⱥ–Ⱥ. ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ
ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ 2.8 ɢ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.49.
81
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ
ɚɪ.
ȼɚɪɢɚɧɬ
Ɍɨɥɳɢɧɚ
ɨɛɲɢɜɤɢ
,
ɦɦ
Ɋɚɫɱɟɬɧɚɹ
ɩɨɞɴɟɦɧɚɹ
ɫɢɥɚ
ɇ
10
Ɋɚɫɱɟɬɧɚɹ
ɬɟɦɩɟɪɚɬɭɪɚ
ɤɨɧɫɬɪɭɤɰɢɢ,
°ɋ
1
5
ɩɪɨɮɢɥɶ,
ɫɜɚɪɤɚ
0,8
0,9
60
120
150
150
6
9
Al
ɩɪɨɮɢɥɶ,
Ɍɉ-ɥɢɬɶɟ
1,2
1,2
135
180
180
180
10
11
12
13
14
ɩɪɨɮɢɥɶ,
ɫɜɚɪɤɚ
1
1
65
125
350
350
15
16
17
18
ɥɢɬɶɟ
1,3
1,3
140
185
370
370
Ɍɚɛɥɢɰɚ 2.8
75
90
105
150
165
80
95
110
155
170
ɤ
-2
150
150
150
180
180
350
350
350
370
370
ʋ
ɜ
2
3
4
7
8
ɈɄɌɊ
ɤɪɵɥɚ
ɥɢɫɬ ɢ
Ɍɉ-
ɥɢɫɬ ɢ
ɥɢɫɬ ɢ
Ɍɉ-
ɫɩɥɚɜ,
Ɍɉ-
Al
Ti
Ti
ɤɪɵɥɚ
0,8
0,9
0,9
1,2
1,2
1,3
1,3
G
ɨɛ
ɧɚ ɤɨɧɫɨɥɶ ɍ
1
1
1
Ɋɢɫɭɧɨɤ 2.49 – Ƚɟɨɦɟɬɪɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤɪɵɥɚ
ɫ ɥɭɱɟɜɨɣ ɫɢɥɨɜɨɣ ɫɯɟɦɨɣ
82
2.6. ɍɡɥɵ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ ɦɟɯɚɧɢɡɦɨɜ ɭɩɪɚɜɥɟɧɢɹ
Ɉɞɧɢɦɢ ɢɡ ɬɢɩɢɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɰɟɩɢ ɦɟɯɚɧɢɡɦɨɜ ɭɩɪɚɜɥɟɧɢɹ ɹɜɥɹɸɬɫɹ
ɨɞɧɨɩɪɨɥɟɬɧɵɟ ɬɹɝɢ ɬɪɭɛɱɚɬɨɝɨ ɫɟɱɟɧɢɹ, ɪɚɛɨɬɚɸɳɢɟ ɧɚ ɪɚɫɬɹɠɟɧɢɟ-ɫɠɚɬɢɟ.
ɋɱɢɬɚɸɬ, ɱɬɨ ɤɨɧɰɵ ɬɹɝɢ ɨɩɟɪɬɵ ɲɚɪɧɢɪɧɨ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.50.
Ɋɢɫɭɧɨɤ 2.50 – Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɨɞɧɨɩɪɨɥɟɬɧɨɣ ɬɹɝɢ,
ɪɚɛɨɬɚɸɳɟɣ ɧɚ ɫɠɚɬɢɟ
Ɉɩɪɟɞɟɥɹɸɳɟɣ ɮɨɪɦɨɣ ɪɚɡɪɭɲɟɧɢɹ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɹɜɥɹɟɬɫɹ ɩɨɬɟɪɹ
ɭɫɬɨɣɱɢɜɨɫɬɢ ɩɪɢ ɫɠɚɬɢɢ. Ʉɪɢɬɢɱɟɫɤɚɹ ɫɢɥɚ ɨɛɳɟɣ ɩɨɬɟɪɢ ɭɫɬɨɣɱɢɜɨɫɬɢ ɬɹɝɢ
ɩɨɫɬɨɹɧɧɚ ɩɨ ɞɥɢɧɟ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ
ɦɭɥɟ
Ɋ k Ɋ
ɝɞɟ
ɫɢɥɚ (ɩɪɢ ɪɚɛɨɬɟ ɜ ɩɪɟɞɟɥɚɯ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ), ɇ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
Ɋ
F – ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ, ɦɦ
ɝɨ ɦɚɬɟɪɢɚɥɚ, Ɇɉɚ;
ɥɚ, ɇ/ɦɦ
ɮɨɪɦɭɥɟ
ɊɊ LD ED
-GVS
ɩɪ ɤɪ B
– ɫɢɥɚ, ɪɚɡɪɭɲɚɸɳɚɹ ɦɚɬɟɪɢɚɥ, ɇ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɩɪ
2
; J – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɬɹɝɢ, ɦ4, ɜɵɱɢɫɥɹɸɬ ɩɨ
8
ɤɪ ɩɪ
3
223
– ɜɪɟɦɟɧɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɫɬɪɭɤɰɢɨɧɧɨɝɨ ɦɚɬɟɪɢɚ-
V
ȼ
11
ɊȿJL
S
ɤɪ
Ɋ FV
ɩɪ B
2
; ȿ – ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ɤɨɧɫɬɪɭɤɰɢɨɧɧɨ-
SG
, ɇ, ɤɨɬɨɪɭɸ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪ-
Ɋ
ɤɪ
---
; (2.134)
3
2
, (2.132)
; Ɋɤɪ – ɗɣɥɟɪɨɜɚ ɤɪɢɬɢɱɟɫɤɚɹ
2
; (2.133)
; (2.135)
8JD
83
– ɤɨɷɮɮɢɰɢɟɧɬ, ɭɱɢɬɵɜɚɸɳɢɣ ɨɫɥɚɛɥɟɧɢɟ ɬɹɝɢ ɡɚ ɫɱɟɬ ɦɟɧɶɲɟɣ ɠɟɫɬɤɨɫɬɢ
2
.
0,3 0,6
ɷ
ɤɪ ɦ cp
P ȿ R ȿ
GSG
k
3
ɤɨɧɰɟɜɵɯ ɱɚɫɬɟɣ, k
ɍɫɥɨɜɢɟ ɨɬɫɭɬɫɬɜɢɹ ɨɛɳɟɣ ɢ ɦɟɫɬɧɨɣ ɩɨɬɟɪɢ ɭɫɬɨɣɱɢɜɨɫɬɢ
ɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
Ɋ kD D D D
Ɍ B
– ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɬɹɝɭ ɫɠɢɦɚɸɳɚɹ ɪɚɫɱɟɬɧɚɹ ɫɢɥɚ, ɇ.
ɝɞɟ Ɋ
Ɍ
ɉɪɢ ɦɚɥɨɣ ɬɨɥɳɢɧɟ ɫɬɟɧɤɢ
ɦɟɫɬɧɚɹ ɩɨɬɟɪɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɫɬɟɧɨɤ. ɍɫɥɨɜɢɟ ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɢ ɬɹɝɢ ɩɪɢ ɷɬɨɦ
ɜɢɞɟ ɪɚɡɪɭɲɟɧɢɹ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
P
ɝɞɟ
ɜɨɫɬɢ ɫɬɟɧɤɢ, ɇ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɜɟɫɬɧɵɯ:
ɡɧɚɱɟɧɢɹ
ɡɧɚɱɟɧɢɹɦ D ɢ ɨɱɟɧɶ ɦɚɥɨɣ ɬɨɥɳɢɧɵ į, ɤɨɬɨɪɵɟ ɨɤɚɡɵɜɚɸɬɫɹ ɧɟɩɪɢɟɦɥɟɦɵɦɢ
ɧɢ ɩɨ ɜɧɭɬɪɟɧɧɟɣ ɤɨɦɩɨɧɨɜɤɟ ɅȺ, ɧɢ ɩɨ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦ ɨɝɪɚɧɢɱɟɧɢɹɦ ɧɚ
ɬɨɥɳɢɧɭ ɢɫɩɨɥɶɡɭɟɦɵɯ ɬɪɭɛ. ɉɨɷɬɨɦɭ, ɤɚɤ ɩɪɚɜɢɥɨ, ɞɢɚɦɟɬɪ ɬɹɝɢ, D ɡɚɞɚɟɬɫɹ ɫ
ɭɱɟɬɨɦ ɜɨɡɦɨɠɧɨɫɬɟɣ
ɥɹɟɬɫɹ ɪɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ (2.138). ȿɫɥɢ ɩɪɢ ɷɬɨɦ ɩɨɥɭɱɟɧɧɚɹ
ɦɟɧɶɲɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢ ɞɨɩɭɫɬɢɦɨɣ, ɬɨ ɦɨɠɧɨ ɭɦɟɧɶɲɢɬɶ D ɢ ɨɩɪɟɞɟɥɢɬɶ ɧɨɜɨɟ ɩɨɬɪɟɛɧɨɟ ɡɧɚɱɟɧɢɟ
ɛɨɬɚɸɳɟɣ ɧɚ ɪɚɫɬɹɠɟɧɢɟ ɢ ɫɠɚɬɢɟ (
ɧɨɣ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.50.
ɬɹɝɢ ɫ ɪɵɱɚɝɨɦ ɩɨɜɨɪɨɬɚ ɪɭɥɹ.
– ɗɣɥɟɪɨɜɚ ɤɪɢɬɢɱɟɫɤɚɹ ɫɢɥɚ, ɜɵɡɵɜɚɸɳɚɹ ɦɟɫɬɧɭɸ ɩɨɬɟɪɸ ɭɫɬɨɣɱɢ-
.ɷɤɪ ɦ
Ɏɨɪɦɭɥɵ (2.136) ɢ (2.137) ɫɨɫɬɚɜɥɹɸɬ ɫɢɫɬɟɦɭ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɜɭɯ ɧɟɢɡ-
ɢ D. Ɋɟɲɚɹ ɞɚɧɧɭɸ ɫɢɫɬɟɦɭ, ɜɨɡɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɨɩɬɢɦɚɥɶɧɵɟ
G
G
ɨɩɬ
Ʉɚɤ ɩɨɤɚɡɵɜɚɸɬ ɪɚɫɱɟɬɵ, ɬɚɤɢɟ ɪɟɲɟɧɢɹ ɨɛɵɱɧɨ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɛɨɥɶɲɢɦ
Ɂɚɞɚɱɚ ɪɚɛɨɬɵ
Ɋɚɫɫɱɢɬɚɬɶ ɩɨɬɪɟɛɧɵɟ ɪɚɡɦɟɪɵ ɬɪɭɛɵ
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ 2.9.
Ⱥɥɝɨɪɢɬɦ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɬɪɟɛɧɵɯ ɪɚɡɦɟɪɨɜ ɞɟɬɚɥɟɣ ɭɡɥɚ ɫɨɟɞɢɧɟɧɢɹ
= 0,95; L – ɞɥɢɧɚ ɬɹɝɢ, ɦɦ.
3
, ɇ, ɜɵɱɢɫ-
Ɋ
Ɍ
S GGV -- --- G
3
ɊɊ DDD
Ɍɩɪ ɦ ɦ ɦ
-G GV G
ɦɩɪɤɪɦ B
ɢ D
ɨɩɬ
1,1, ,
(,) 0,6
D ɊɊ DE
, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɦɢɧɢɦɭɦ ɦɚɫɫɵ ɬɪɭɛɱɚɬɨɣ ɱɚɫɬɢ ɬɹɝɢ.
ɜɧɭɬɪɟɧɧɟɣ ɤɨɦɩɨɧɨɜɤɢ, ɚ ɩɨɬɪɟɛɧɚɹ ɬɨɥɳɢɧɚ G ɨɩɪɟɞɟ-
ɢ ɬ. ɞ.
G
1,1, ,
ɢ ɛɨɥɶɲɢɯ ɞɢɚɦɟɬɪɚɯ D ɦɨɠɟɬ ɜɨɡɧɢɤɚɬɶ
G
-G -G-G
ɷ
.
G
) ɢɡ ɭɫɥɨɜɢɹ ɪɚɜɟɧɫɬɜɚ ɨɛɳɟɣ ɢ ɦɟɫɬ-
Ɋr
Ɍ
ɢ D ɞɥɹ ɨɞɧɨɩɪɨɥɟɬɧɨɣ ɬɹɝɢ, ɪɚ-
2
2
, (2.137)
, (2.138)
. (2.139)
G
ɨɤɚɡɵɜɚɟɬɫɹ
, (2.136)
84
Ɍɚɛɥɢɰɚ 2.9
ʋ
ɜɚɪɢɚɧɬɚ
L,
ɦɦ
ɊɌ,
ɇ
10
-2
Ʉɨɧɫɬɪɭɤɰɢɨɧɧɵɣ ɦɚɬɟɪɢɚɥ
ɢ ɟɝɨ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
1
6
500
500
500
500
500
500
90
100
110
120
130
140
7
10
11
12
750
750
750
750
750
750
90
100
110
120
130
140
13
14
15
16
17
18
1000
1000
1000
1000
1000
1000
90
100
110
120
130
140
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ
2
3
4
5
8
9
1. ɉɨɬɪɟɛɧɵɦɢ ɪɚɡɦɟɪɚɦɢ ɞɟɬɚɥɟɣ ɭɡɥɚ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.51
ɹɜɥɹɸɬɫɹ:
– ɞɢɚɦɟɬɪ ɛɨɥɬɚ d
– ɧɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɩɨɞɲɢɩɧɢɤɚ D
– ɲɢɪɢɧɚ ɭɡɥɚ ɬɹɝɢ D
– ɬɨɥɳɢɧɚ ɭɲɤɚ ɬɹɝɢ
– ɧɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɭɲɤɚ ɪɵɱɚɝɚ D
– ɬɨɥɳɢɧɚ ɭɲɤɚ ɪɵɱɚɝɚ
2. ȼɨɡɦɨɠɧɵɟ ɮɨɪɦɵ ɪɚɡɪɭɲɟɧɢɹ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ, ɫɥɟɞɭɸɳɢɟ:
– ɫɪɟɡ ɛɨɥɬɚ (ɧɚɩɪɹɠɟɧɢɟ
– ɫɦɹɬɢɟ ɦɚɬɟɪɢɚɥɚ ɛɨɥɬɚ ɩɨɞ ɭɲɤɨɦ ɬɹɝɢ (ɧɚɩɪɹɠɟɧɢɟ
– ɫɦɹɬɢɟ ɦɚɬɟɪɢɚɥɚ ɭɲɤɚ ɬɹɝɢ ɩɨɞ ɛɨɥɬɨɦ (ɧɚɩɪɹɠɟɧɢɟ
– ɪɚɡɪɵɜ ɭɲɤɚ ɬɹɝɢ ɩɨ ɩɟɪɟɦɵɱɤɟ ɚ
– ɫɪɟɡ ɩɟɪɟɦɵɱɤɢ ɭɲɤɚ ɬɹɝɢ S
– ɪɚɡɪɵɜ ɭɲɤɚ ɪɵɱɚɝɚ (ɧɚɩɪɹɠɟɧɢɟ
– ɫɪɟɡ ɩɟɪɟɦɵɱɤɢ ɭɲɤɚ ɪɵɱɚɝɚ (ɧɚɩɪɹɠɟɧɢɟ
Al ɫɩɥɚɜ
ı
= 420 ɇ/ɦɦ
ȼ
2
ȿ = 0,7·107 ɇ/ɦɦ2
Ɍɢɬɚɧ
ı
= 110 ɇ/ɦɦ
ȼ
2
ȿ = 1·107 ɇ/ɦɦ2
ɋɬɚɥɶ
ı
= 900 ɇ/ɦɦ
ȼ
2
ȿ = 2·107 ɇ/ɦɦ2
;
ɛ
;
ɩ
;
ɬ
G
;
ɬ
;
ɪ
.
G
ɪ
);
W
Ȼ
Ɍ
(ɧɚɩɪɹɠɟɧɢɟ
Ɍ
(ɧɚɩɪɹɠɟɧɢɟ
Ɍ
W
);
ɫɪ
Ɋ
W
ɫɪ
ɪ
G
ɪ
V
);
).
Ȼ
);
V
ɫɦ
Ɍ
);
V
ɫɦ
Ɍ
);
ɪ
85
Ɋɢɫɭɧɨɤ 2.51 – Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɫɨɟɞɢɧɟɧɢɹ ɬɹɝɢ ɫ ɪɵɱɚɝɨɦ
3. ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɭɫɥɨɜɢɹ ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɢ ɜɯɨɞɹɳɢɯ ɞɟɬɚɥɟɣ ɜɵ-
ɱɢɫɥɹɸɬ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ
ȻȻ
WW
d
ȻȻ
VV
ɫɦ ɞ ɫɦ ɪ
ɌɌ
VV
ɫɦ ɞ ɫɦ ɪ
ɌɌ
WW
ɫɪ ɞ ɫɪ ɪ
ɌɊ
VV
ɪɞ ɪ ɪ
ɊɊ
VV
ɪɞ ɪ ɪ
ɊɊ
WW
ɫɪ ɞ ɫɪ ɪ
, (2.140)
ɞɪ
d
..
..
..
..
..
..
, (2.141)
d
, (2.142)
d
, (2.143)
d
, (2.144)
d
, (2.145)
d
. (2.146)
Ⱦɥɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɷɬɨɣ ɫɢɫɬɟɦɵ ɧɟɪɚɜɟɧɫɬɜ ɩɪɨɜɟɞɟɦ ɚɧɚɥɢɡ, ɩɨɡɜɨɥɹɸɳɢɣ ɫɨɫɬɚɜɢɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɭɪɚɜɧɟɧɢɹ, ɢɡ ɤɨɬɨɪɵɯ ɦɨɝɭɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɵ ɭɤɚɡɚɧɧɵɟ ɜɵɲɟ ɧɟɢɡɜɟɫɬɧɵɟ ɪɚɡɦɟɪɵ. ɐɟɥɶɸ ɬɚɤɨɝɨ ɚɧɚɥɢɡɚ ɹɜɥɹɟɬɫɹ
ɜɵɹɫɧɟɧɢɟ ɜɨɡɦɨɠɧɨɫɬɢ ɡɚɦɟɧɵ ɧɟɪɚɜɟɧɫɬɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɪɚɜɟɧɫɬɜɚɦɢ.
ɉɪɟɠɞɟ ɜɫɟɝɨ ɦɨɠɧɨ ɢ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɜɵɞɟɥɢɬɶ ɧɟɪɚɜɟɧɫɬɜɨ (2.140), ɬ. ɤ.
ɨɧɨ ɫɨɞɟɪɠɢɬ ɨɞɧɨ ɧɟɢɡɜɟɫɬɧɨɟ d
. ɉɨɞɫɬɚɜɢɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɵɪɚɠɟɧɢɹ ɜ
ɛ
86
Ȼ
ɩɪɚɜɭɸ ɢ ɥɟɜɭɸ ɱɚɫɬɢ, ɩɪɟɞɟɥ ɩɪɨɱɧɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ɛɨɥɬɚ
, ɇ/ɦɦ2, ɜɵɱɢɫ-
0, 7
V
ȼ
ɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
Ȼ
0,7 4
Ɋ d ɩ
VS
ȼɌ Ȼ
2
, (2.147)
ɝɞɟ ɩ – ɱɢɫɥɨ ɩɥɨɫɤɨɫɬɟɣ ɫɪɟɡɚ ɛɨɥɬɚ, ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɪɚɜɧɨ ɞɜɭɦ.
ɂɡ ɮɨɪɦɭɥɵ (2.149) ɞɢɚɦɟɬɪ ɛɨɥɬɚ
, ɦɦ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
d
Ȼ
0,95
d Ɋɩ
ȻɌȼ
Ȼ
V
. (2.148)
ɉɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɹ ɞɢɚɦɟɬɪɚ ɛɨɥɬɚ ɩɨ ɮɨɪɦɭɥɟ (2.150) ɨɤɪɭɝɥɹɸɬ ɞɨ
ɛɥɢɠɚɣɲɟɝɨ ɛɨɥɶɲɟɝɨ ɫɬɚɧɞɚɪɬɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɤɨɬɨɪɨɟ ɢ ɩɪɢɧɢɦɚɟɬɫɹ.
ɂɡ ɭɫɥɨɜɢɣ (2.141) ɢ (2.142) ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɧɢɯ ɜɯɨɞɢɬ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɧɟɢɡɜɟɫɬɧɵɣ ɪɚɡɦɟɪ
. ȿɫɥɢ ɭɱɟɫɬɶ, ɱɬɨ ɦɚɬɟɪɢɚɥ ɛɨɥɬɚ, ɤɚɤ ɩɪɚɜɢɥɨ, ɩɪɨɱɧɟɟ
G
ɬ
ɱɟɦ ɦɚɬɟɪɢɚɥ ɭɲɤɚ ɬɹɝɢ, ɬɨ ɜɨɡɦɨɠɧɨ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ
(2.142) ɡɚɜɟɞɨɦɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ (2.141). ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ,
ɭɫɥɨɜɢɟ (2.141) ɦɨɠɧɨ ɢɫɤɥɸɱɢɬɶ ɢɡ ɪɚɫɫɦɨɬɪɟɧɢɹ, ɚ ɭɫɥɨɜɢɟ (2.142) ɡɚɦɟɧɢɬɶ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɭɪɚɜɧɟɧɢɟɦ
Ɍ
k Ɋ d ɩ
VG
ɫɦ ȼ Ɍ Ȼ Ɍ
, (2.149)
– ɤɨɷɮɮɢɰɢɟɧɬ ɞɨɩɭɫɬɢɦɨɝɨ ɫɦɹɬɢɹ, ɞɥɹ ɧɟɩɨɞɜɢɠɧɵɯ ɫɨɟɞɢɧɟɧɢɣ
ɝɞɟ k
ɫɦ
k
= 1–1,5, ɞɥɹ ɦɚɥɨɩɨɞɜɢɠɧɵɯ k
ɫɦ
ɉɪɢɧɢɦɚɹ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ k
ɜɵɱɢɫɥɹɸɬ ɬɨɥɳɢɧɭ ɭɲɤɚ ɬɹɝɢ
= 0,5–0,65, ɞɥɹ ɩɨɞɜɢɠɧɵɯ k
ɫɦ
= 0,4, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɮɨɪɦɭɥɨɣ (2.149)
ɫɦ
, ɦɦ, ɩɨ ɮɨɪɦɭɥɟ
G
Ɍ
= 0,2–0,4.
ɫɦ
1, 2 5
GV
ɌɌȻȼ
Ɋ d
Ɍ
. (2.150)
Ɂɚɦɟɧɢɜ ɭɫɥɨɜɢɟ (2.144) ɪɚɜɟɧɫɬɜɨɦ, ɩɨɥɭɱɚɸɬ ɭɪɚɜɧɟɧɢɟ ɫ ɨɞɧɢɦ ɧɟɢɡɜɟɫɬɧɵɦ D
, ɩɪɟɞɟɥ ɩɪɨɱɧɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ɬɹɝɢ
ɬ
Ɍ
, ɇ/ɦɦ2, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪ-
V
ȼ
ɦɭɥɟ
Ɍ
kDd
VG
ȼ KTȻɌ
, (2.151)
ɝɞɟ k
– ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɧɚɩɪɹɠɟɧɢɣ, ɞɥɹ ɩɟɪɟɦɟɧɧɨɣ ɰɢɤɥɢɱɟɫɤɨɣ
Ʉ
ɧɚɝɪɭɡɤɢ k
= 2,5.
Ʉ
ɂɡ ɜɵɪɚɠɟɧɢɹ (2.151) ɲɢɪɢɧɭ ɭɡɥɚ ɬɹɝɢ
Dd Ɋ
T ȻɌɌȼ
2,5
, ɦɦ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
D
T
Ɍ
GV
. (2.152)
87
Ɂɚɦɟɧɢɜ ɭɫɥɨɜɢɟ (2.146) ɪɚɜɟɧɫɬɜɨɦ, ɩɨɥɭɱɚɸɬ ɭɪɚɜɧɟɧɢɟ ɫ ɨɞɧɢɦ ɧɟɢɡ-
0,7
Ɍ
ȼ
V
0,7 2
Ɋ
ȼɌ ɪ pn
Ɋ DD
VG
2
ɜɟɫɬɧɵɦ S
, ɩɪɟɞɟɥ ɩɪɨɱɧɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ɬɹɝɢ 0
Ɍ
, ɇ/ɦɦ2 ɜɵɱɢɫɥɹɸɬ ɩɨ
ɮɨɪɦɭɥɟ
Ɍ
0,7 2
kP S
VG
ȼ KT TɌ
1, 8
S Ɋ
T ɌɌȼ
, (2.153)
Ɍ
GV
. (2.154)
ȼ ɪɟɡɭɥɶɬɚɬɟ, ɜɫɟ ɪɚɡɦɟɪɵ ɭɲɤɨɜ ɬɹɝɢ ɨɩɪɟɞɟɥɟɧɵ, ɢ ɜɨɡɦɨɠɧɨ ɩɟɪɟɣɬɢ ɤ
ɨɩɪɟɞɟɥɟɧɢɸ ɪɚɡɦɟɪɨɜ ɭɲɤɚ ɪɵɱɚɝɚ.
ɉɨɞ ɞɢɚɦɟɬɪ ɛɨɥɬɚ d
ɢ ɫɢɥɭ ɊɌ ɫɥɟɞɭɟɬ ɩɨɞɨɛɪɚɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ
ɛ
ɫɬɚɧɞɚɪɬɧɵɣ ɩɨɞɲɢɩɧɢɤ. ɒɢɪɢɧɚ ɧɚɪɭɠɧɨɣ ɨɛɨɣɦɵ ɷɬɨɝɨ ɩɨɞɲɢɩɧɢɤɚ ɨɩɪɟɞɟɥɢɬ ɢ ɲɢɪɢɧɭ ɭɲɤɚ ɪɵɱɚɝɚ į
ɱɚɝɚ ɜ ɩɥɚɧɟ ɫɥɟɞɭɟɬ ɭɱɟɫɬɶ, ɱɬɨ ɧɚɩɪɚɜɥɟɧɢɟ ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɧɟɝɨ ɫɢɥɵ Ɋ
. ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɪɚɡɦɟɪɨɜ ɢ ɮɨɪɦɵ ɭɲɤɚ ɪɵ-
ɪ
ɩɪɢ
Ɍ
ɨɬɤɥɨɧɟɧɢɹɯ ɪɭɥɹ ɢɡɦɟɧɹɟɬɫɹ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɭɫɥɨɜɢɟ ɩɪɨɱɧɨɫɬɢ ɩɨ ɫɪɟɡɭ
ɩɟɪɟɦɵɱɤɢ ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɞɥɹ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɭɝɥɨɜ ɨɬɤɥɨɧɟɧɢɹ ɪɭɥɹ.
Ɉɛɟɫɩɟɱɢɬɶ ɷɬɨ ɫ ɧɟɤɨɬɨɪɵɦ ɡɚɩɚɫɨɦ ɩɪɨɱɧɨɫɬɢ ɦɨɠɧɨ ɫ ɩɨɦɨɳɶɸ ɤɨɧɰɟɧɬɪɢɱɟɫɤɨɝɨ ɨɛɜɨɞɚ ɫ ɩɟɪɟɦɵɱɤɨɣ, ɪɚɛɨɬɚɸɳɟɣ ɧɚ ɫɪɟɡ, ɪɚɡɦɟɪɵ ɤɨɬɨɪɨɣ ɨɩɪɟɞɟɥɹɸɬɫɹ ɢɡ ɭɫɥɨɜɢɹ (2.147). ȼ ɫɜɹɡɢ ɫ ɜɵɲɟɢɡɥɨɠɟɧɧɵɦ, ɩɪɟɞɟɥ
ɪɢɚɥɚ ɪɵɱɚɝɚ
Ɋ
, ɇ/ɦɦ2, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
0,7
V
ȼ
ɩɪɨɱɧɨɫɬɢ ɦɚɬɟ-
, (2.155)
DD Ɋ
pn Ɍɪȼ
0,7
Ɋ
GV
, (2.156)
– ɧɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɩɨɞɲɢɩɧɢɤɚ, ɦɦ.
ɝɞɟ D
n
Ɂɚɞɚɱɚ ɪɚɛɨɬɵ
Ɋɚɫɫɱɢɬɚɬɶ ɢ ɫɤɨɧɫɬɪɭɢɪɨɜɚɬɶ ɫɨɟɞɢɧɟɧɢɹ ɬɹɝɢ ɫ ɪɵɱɚɝɨɦ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ
ɫ ɪɢɫɭɧɤɨɦ 2.51, ɩɨ ɢɫɯɨɞɧɵɦ ɞɚɧɧɵɦ ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥɢɰɟɣ 2.9 ɧɚɪɭɠɧɵɣ ɞɢɚɦɟɬɪ ɩɨɞɲɢɩɧɢɤɚ D
= 20 ɦɦ. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɦɚɬɟɪɢɚɥɚ
n
ɞɥɹ ɡɚɤɨɧɰɨɜɤɢ ɬɹɝɢ ɢ ɪɵɱɚɝɚ ɬɟ ɠɟ, ɱɬɨ ɢ ɞɥɹ ɦɚɬɟɪɢɚɥɚ ɬɪɭɛɵ. Ɇɚɬɟɪɢɚɥ ɫɨ-
ߪ
ɟɞɢɧɢɬɟɥɶɧɨɝɨ ɛɨɥɬɚ – 30ɏȽɋȺ (
= 1200 ± 10 ɇ/ɦɦ2).
ȼ
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɫɱɟɬɧɵɯ ɧɚɝɪɭɡɨɤ ɧɚ ɪɭɥɶ ɩɪɢ ɡɚɞɚɧɧɨɣ ɭɩɪɚɜɥɹɸɳɟɣ
ɫɢɥɟ Y
ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɩɪɟɞɩɨɥɨɠɟɧɢɟɦ ɨ ɬɨɦ, ɱɬɨ ɫɢɥɚ Yp ɦɨɠɟɬ ɛɵɬɶ ɪɟɚɥɢɡɨ-
p
ɜɚɧɚ ɧɚ ɥɸɛɨɣ ɫɤɨɪɨɫɬɢ ɩɨɥɟɬɚ ɜ ɡɚɞɚɧɧɨɦ ɞɢɚɩɚɡɨɧɟ ɨɬ ɞɨɡɜɭɤɨɜɨɣ ɞɨ ɫɜɟɪɯɡɜɭɤɨɜɨɣ (
ɧɢɪɧɵɣ ɦɨɦɟɧɬ
) ɡɚ ɫɱɟɬ ɭɝɥɚ ɨɬɤɥɨɧɟɧɢɹ ɪɭɥɹ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɷɬɢɦ ɲɚɪ-
2Ɇ
f
, ɇɦ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
Ɇ
ɲ
Ɇ Yxd xk
ɲ pipɞɢɧ
, (2.157)
88
– ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɧɨɫɤɚ ɫɪɟɞɧɟɣ ɯɨɪɞɵ ɪɭɥɹ ɞɨ ɰɟɧɬɪɚ ɞɚɜɥɟɧɢɹ (ɩɪɢ ɞɨ-
2
ɝɞɟ xd
i
ɡɜɭɤɨɜɨɣ ɫɤɨɪɨɫɬɢ ɩɨɥɟɬɚ i = 1 ɢ ɫɜɟɪɯɡɜɭɤɨɜɨɣ ɫɤɨɪɨɫɬɢ ɩɨɥɟɬɚ i = 2), ɦɦ, ɜ
ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.52; ɯ
ɨɫɢ ɩɨɜɨɪɨɬɚ ɪɭɥɹ, ɦɦ; k
ɞɢɧ
– ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɧɨɫɤɚ ɫɪɟɞɧɟɣ ɯɨɪɞɵ ɪɭɥɹ ɞɨ
ɪ
– ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɧɚɦɢɱɧɨɫɬɢ ɪɭɥɹ, ɭɱɢɬɵɜɚɸɳɢɣ
ɧɟɨɛɯɨɞɢɦɭɸ ɫɤɨɪɨɫɬɶ ɩɟɪɟɤɥɚɞɤɢ, ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɩɨɬɪɟɛɧɨɝɨ ɛɵɫɬɪɨɞɟɣɫɬɜɢɹ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ (k
= 1,5–3).
ɞɢɧ
Ɋɢɫɭɧɨɤ 2.52 – Ɇɨɞɟɥɶ ɧɚɝɪɭɠɟɧɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɭɥɹ:
1, 2 – ɰɟɧɬɪɵ ɞɚɜɥɟɧɢɹ ɪɭɥɹ ɩɪɢ
ɢ
1Ɇfd
; 3 – ɨɫɶ ɜɪɚɳɟɧɢɹ ɪɭɥɹ;
2Ɇ
f
4 – ɫɪɟɞɧɹɹ ɯɨɪɞɚ ɪɭɥɹ
ɒɚɪɧɢɪɧɵɣ ɦɨɦɟɧɬ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ (2.157) ɞɥɹ i = 1 ɢ i = 2, ɢ
ɩɪɢɧɢɦɚɟɬɫɹ ɛɨɥɶɲɟɟ ɩɨ ɚɛɫɨɥɸɬɧɨɣ ɜɟɥɢɱɢɧɟ ɡɧɚɱɟɧɢɟ. ɋɯɟɦɚ ɧɚɝɪɭɠɟɧɢɹ
ɪɭɥɟɜɨɝɨ ɲɩɚɧɝɨɭɬɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɚɦɢ 2.53 ɢ 2.54.
ȿɫɥɢ Ɇ
ɩɟɪɟɞɚɟɬɫɹ ɨɬ ɜɚɥɚ ɪɭɥɹ ɱɟɪɟɡ ɪɵɱɚɝ, ɩɪɢɫɨɟɞɢɧɹɟɦɵɣ ɤ ɜɚɥɭ
ɲ
ɫɤɜɨɡɧɵɦ ɛɨɥɬɨɦ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.55, ɬɨ ɷɬɨɬ ɦɨɦɟɧɬ ɜɨɫɩɪɢɧɢɦɚɟɬɫɹ ɪɵɱɚɝɨɦ ɜ ɜɢɞɟ ɩɚɪɵ ɫɢɥ
, ɇ, ɜɵɱɢɫɥɹɟɦɨɣ ɩɨ ɮɨɪɦɭɥɟ
ɊɆ
ɊɆ Ɇ ɪ '
, (2.158)
ɲ
ɝɞɟ ɪ'– ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɰɟɧɬɪɚɦɢ ɩɥɨɳɚɞɨɤ ɨɩɨɪɵ ɪɵɱɚɝɚ ɧɚ ɛɨɥɬ, ɦɦ, ɚ
ɭɪɚɜɧɨɜɟɲɢɜɚɟɬɫɹ ɩɚɪɨɣ ɫɢɥ
, ɇ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɮɨɪɦɭɥɨɣ
Ɋ
Ɍ
ɊɆl
Ɍɲp
, (2.159)
ɝɞɟ lp – ɩɥɟɱɨ ɪɵɱɚɝɚ, ɦɦ.
89
ɚ – ɅȺ ɫɯɟɦɵ «+»
ɛ – ɅȺ ɫɯɟɦɵ «ɯ»
Ɋɢɫɭɧɨɤ 2.53 – ɋɯɟɦɚ ɧɚɝɪɭɠɟɧɢɹ ɪɭɥɟɜɨɝɨ ɲɩɚɧɝɨɭɬɚ
Ɋɢɫɭɧɨɤ 2.54 – ɋɯɟɦɚ ɧɚɝɪɭɠɟɧɢɹ ɫɟɤɰɢɢ ɫɨɫɬɚɜɧɨɝɨ ɲɩɚɧɝɨɭɬɚ
ɪɭɥɟɜɨɝɨ ɨɬɫɟɤɚ
90
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