Анненков Ю.М., Ивашутенко А.С. Перспективные материалы и технологии в электроизоляционной и кабельной технике
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191
Ɇɟɯɚɧɢɡɦ ɬɟɪɦɢɱɟɫɤɨɝɨ ɫɬɚɪɟɧɢɹ
1. ɋɚɦɨɟ ɫɥɚɛɨɟ ɡɜɟɧɨ ɜ ɩɨɥɢɚɦɢɞɧɨɣ ɦɚɤɪɨɦɨɥɟɤɭɥɟɢɦɢɞɧɵɣ
ɰɢɤɥ:
(2.15)
Ɋɟɡɭɥɶɬɚɬ ɬɟɪɦɨɞɟɫɬɪɭɤɰɢɢ– ɜɵɞɟɥɟɧɢɟ ɦɨɥɟɤɭɥ ɋɈ
2
, ɋɈ, ɇ
2
Ɉ ɢ
ɨɛɪɚɡɨɜɚɧɢɟ ɤɨɧɞɟɧɫɚɬɚ ɢɡ ɛɟɧɡɨɥɶɧɵɯ ɤɨɥɟɰ.
(2.16)
2. ɉɪɢ ɫɬɚɪɟɧɢɢ ɬɚɤ ɠɟ ɪɚɡɪɵɜɚɸɬɫɹ ɦɨɫɬɢɤɨɜɵɟ ɫɜɹɡɢ ɜ Q ɢ R
ɮɪɚɝɦɟɧɬɚɯ. Ɇɚɬɟɪɢɚɥ ɬɟɪɹɟɬ ɦɟɯɚɧɢɱɟɫɤɭɸ ɩɪɨɱɧɨɫɬɶ, ɷɥɚɫɬɢɱɧɨɫɬɶ,
ɫɬɚɧɨɜɢɬɫɹ ɯɪɭɩɤɢɦ.
Ɍɚɛɥɢɰɚ 2.16
Ɍɟɪɦɨɫɬɨɣɤɨɫɬɶ ɩɨɥɢɢɦɢɞɨɜ
Ɇɚɪɤɚ ɏɢɦɢɱɟɫɤɨɟ ɫɬɪɨɟɧɢɟ
ı
Ɋ
(
Ɇɉɚ)
İ %
ȼɪɟɦɹ
ɪɚɛɨɬɵ
ɩɪɢ 723 Ʉ
(ɱɚɫ)
ȾɎ–
ȾɎɗ
ȾɎɈ
ȾɎɈ–Ȼ
ɉɆ
ȾɎ–ɉɎ
173
175
298
176
340
87
85
59
81
13
0,29
0,27
0,7
0,4
4,0
192
Ɇɟɯɚɧɢɡɦ ɬɟɬɦɨɨɤɢɫɥɢɬɟɥɶɧɨɣ ɞɟɫɬɪɭɤɰɢɢ
– Ʉɢɫɥɨɪɨɞ ɚɤɬɢɜɢɪɭɟɬ ɨɬɪɵɜ ɇ ɨɬ ɛɟɧɡɨɥɶɧɨɝɨ ɤɨɥɶɰɚ;
– Ɉɛɪɚɡɨɜɚɜɲɢɣɫɹ ɪɚɞɢɤɚɥ ɜɡɚɢɦɨɞɟɣɫɬɜɭɟɬ ɫ Ɉ
2
ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ
ɩɟɪɨɤɫɢɞɧɨɝɨ ɪɚɞɢɤɚɥɚ.
(2.17)
ɋɯɟɦɚ ɞɟɫɬɪɭɤɰɢɢ ɩɨɥɢɢɦɢɞɚ ɡɚ ɫɱɟɬ ɪɚɡɪɭɲɟɧɢɹ ɢɦɢɞɧɨɝɨ ɰɢɤɥɚ:
1.
(2.18)
2.
(2.19)
Ɋɚɞɢɚɰɢɨɧɧɚɹ ɫɬɨɣɤɨɫɬɶ ɩɨɥɢɢɦɢɞɨɜ
ɉɨɥɢɢɦɢɞɵ ɧɚɢɛɨɥɟɟ ɭɫɬɨɣɱɢɜɵ ɤ ɜɨɡɞɟɣɫɬɜɢɸ ɪɚɞɢɚɰɢɢ. ɂɡɦɟɧɟ-
ɧɢɟ ɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɧɟɤɨɬɨɪɵɯ ɩɨɥɢɢɦɢɞɨɜ ɩɪɢ Ȗ-ɨɛɥɭɱɟɧɢɢ.
ɉɨɬɟɪɹ ɦɚɫɫɵ ɩɪɢ ɬɟɪɦɢɱɟɫɤɨɦ ɫɬɚɪɟɧɢɢ ɩɨɥɢɢɦɢɞɚ ɩɪɢ 900 Ʉ
ɦɟɧɶɲɟ ɞɥɹ ɨɛɥɭɱɟɧɧɵɯ ɨɛɪɚɡɰɨɜ. Ɍɟɪɦɨɥɢɡ ɬɨɪɦɨɡɢɬɫɹ ɨɛɥɭɱɟɧɢɟɦ ɡɚ
ɫɱɟɬ ɫɲɢɜɚɧɢɹ ɦɚɤɪɨɦɨɥɟɤɭɥ.
ɗɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɨɛɥɭɱɟɧɧɨɝɨ ɩɨɥɢɢɦɢɞɚ:
– ȡ
V
ɩɪɢ D = 410
8
Ƚɪ ɧɟ ɦɟɧɹɟɬɫɹ;
– ȿ
ɉɊ
ɩɪɢ D = 410
8
Ƚɪ ɭɦɟɧɶɲɚɟɬɫɹ ɫ 240 ɞɨ 180 Ɇȼ/ɦ;
– Ⱦɥɹ ɩɨɥɢɢɦɢɞɚ ɢɦɟɟɬɫɹ ɞɜɟ ɨɛɥɚɫɬɢ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɪɟɥɚɤɫɚɰɢɢ
ɩɪɢ 200 ɢ 400 Ʉ. ɉɪɢɱɢɧɚ–ɩɨɥɹɪɧɨɫɬɶ ɢɦɢɞɧɵɯ ɰɢɤɥɨɜ. ɉɨ ɷɬɨɣ ɩɪɢ-
ɱɢɧɟ tgį ɜɵɫɨɤ. Ɉɛɥɭɱɟɧɢɟ ɧɟɫɤɨɥɶɤɨ ɫɦɟɳɚɟɬ ɦɚɤɫɢɦɭɦɵ tgį;
– İ § (3,5–3,8).
ɉɪɢɱɢɧɵ ɜɵɫɨɤɨɣ ɪɚɞɢɚɰɢɨɧɧɨɣ ɫɬɨɣɤɨɫɬɢ ɩɨɥɢɢɦɢɞɨɜ:
– ɉɨɥɢɢɦɢɞ – ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɫɲɢɜɚɸɳɢɣɫɹ ɩɨɥɢɦɟɪ. ɋɲɢɜɤɢ
ɩɪɟɨɛɥɚɞɚɸɬ ɧɚɞ ɞɟɫɬɪɭɤɰɢɟɣ.
– Ɋɨɥɶ ɛɟɧɡɨɥɶɧɵɯ ɤɨɥɟɰ
. Ȼɟɧɡɨɥɶɧɵɟ ɤɨɥɶɰɚ ɹɜɥɹɸɬɫɹ ɭɫɬɨɣɱɢ-
ɜɵɦɢ ɨɛɪɚɡɨɜɚɧɢɹɦɢ. ɗɧɟɪɝɢɹ ɜɨɡɛɭɠɞɟɧɢɹ ɡɚ ɫɱɟɬ ɨɛɴɟɞɢɧɟɧɧɵɯ
ʌ-ɷɥɟɤɬɪɨɧɨɜ, ɪɚɡɦɚɡɵɜɚɟɬɫɹ ɩɨ ɨɛɴɟɦɭ ɛɟɧɡɨɥɶɧɨɝɨ ɤɨɥɶɰɚ, ɱɬɨ
ɭɦɟɧɶɲɚɟɬ ɜɟɪɨɹɬɧɨɫɬɶ ɪɚɡɪɵɜɚ ɨɞɧɨɣ ɫɜɹɡɢ. Ⱦɵɪɤɢ ɜɧɭɬɪɢ ɛɟɧɡɨɥɶɧɵɯ
ɤɨɥɟɰ ɨɱɟɧɶ ɩɨɞɜɢɠɧɵ, ɫɜɹɡɶ ɞɥɢɬɟɥɶɧɨɟ ɜɪɟɦɹ ɧɟ ɪɚɡɪɵɜɚɟɬɫɹ, ɱɬɨ
193
ɫɩɨɫɨɛɫɬɜɭɟɬ ɩɪɨɬɟɤɚɧɢɸ ɨɛɪɚɬɧɵɯ ɪɟɤɨɦɛɢɧɚɰɢɨɧɧɵɯ ɩɪɨɰɟɫɫɨɜ. ȼɵ-
ɫɨɤɚɹ ɜɟɪɨɹɬɧɨɫɬɶ ɪɟɤɨɦɛɢɧɚɰɢɢ ɪɚɞɢɤɚɥɨɜ ɜ ɢɦɢɞɧɵɯ ɰɢɤɥɚɯ. Ɉɛɪɚ-
ɡɭɸɬɫɹ ɦɚɥɨɩɨɞɜɢɠɧɵɟ ɪɚɞɢɤɚɥɵ, ɤɨɬɨɪɵɟ ɛɵɫɬɪɨ ɪɟɤɨɦɛɢɧɢɪɭɸɬ.
Ɍɚɛɥɢɰɚ 2.17
Ɋɚɞɢɚɰɢɨɧɧɚɹ ɫɬɨɣɤɨɫɬɶ ɩɨɥɢɢɦɢɞɨɜ
ɉɨɥɢɦɟɪ ɆɊɚɞ ɂɡɦɟɧɟɧɢɟ ı
Ɋ
ɜ %
ɇɟɣɥɨɧ
ɉɨɥɢɷɮɢɪ
ɉɨɥɢɢɦɢɞ ȾɎɈ
ɉɨɥɢɢɦɢɞ ɉɆ
(ɩɨɥɢɩɢɪɨɦɟɥɥɢɬ ɢɦɢɞ)
Ʉɪɟɦɧɟɨɪɝɚɧɢɱɟɫɤɢɣ ɩɨɥɢɦɟɪ
17,6
10
4
30
10
3
10
4
2.10
4
10
3
–3
–100
–11
0
–3
0
–13
Ɋɢɫ. 2.27. Ʉɢɧɟɬɢɤɚ ɪɚɞɢɚɰɢɨɧɧɨɝɨ ɢɡɦɟɧɟɧɢɹ ɩɪɨɱɧɨɫɬɢ ɩɨɥɢɢɦɢɞɚ Ɋ–Ɋ
ɉɨɬɟɪɹ ɦɚɫɫɵ ɩɪɢ ɬɟɪɦɢɱɟɫɤɨɦ ɫɬɚɪɟɧɢɢ ɩɨɥɢɢɦɢɞɚ ɩɪɢ 900Ʉ
ɦɟɧɶɲɟ ɞɥɹ ɨɛɥɭɱɟɧɧɵɯ ɨɛɪɚɡɰɨɜ. Ɍɟɪɦɨɥɢɡ ɬɨɪɦɨɡɢɬɫɹ ɨɛɥɭɱɟɧɢɟɦ ɡɚ
ɫɱɟɬ ɫɲɢɜɚɧɢɹ ɦɚɤɪɨɦɨɥɟɤɭɥ.
194
2.9.4. Ɉɩɬɢɱɟɫɤɢɟ ɢ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɨɥɢɢɦɢɞɨɜ
Ɍɚɛɥɢɰɚ 2.18
Ɉɫɧɨɜɧɵɟ ɮɢɡɢɱɟɫɤɢɟ ɢ ɨɩɬɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɨɥɢɢɦɢɞɨɜ
Ɇɚɪɤɚ Ɏɨɪɦɭɥɚ ɩɨɥɢɢɦɢɞɚ
ȡ,
(ɝ/ɫɦ
3
)
n ɐɜɟɬ
1.ɉɆȻ
2. ȾɎȻ
3. ɉɆ
4.ȾɎɈ
640
620
580
560
1,43
1,4
1,4
1,37
Ʉɨɪɢɱ-
ɧɟɜɵɣ
Ɍɟɦɧ.
Ʉɪɚɫɧ.
Ɍɟɦɧ.
ɀɟɥɬ.
ɀɟɥɬɵɣ
Ɍɚɛɥɢɰɚ 2.19
ɋɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɰɜɟɬɧɨɫɬɶɸ ɢ ɦɚɯ. ɩɨɝɥɨɳɟɧɢɹ
Ɋɢɫ. 2.28. Ɂɨɧɧɚɹ ɫɯɟɦɚ ɩɨɥɢɢɦɢɞɨɜ
ɐɜɟɬ ɂɧ.ɤɪɚɫ. Ʉɪɚɫ. Ɉɪɚɧɠ ɀ Ɂ Ƚ ɋ Ɏ ɍɎ
ȁ(ɧɦ) 760 620 590 560 500 480 50 400 < 400
ȿ(ɷȼ) 1,8 2,05 2,15 2,3 2,5 2,65 2,8 3,2 > 3,2
195
ɏɢɦɢɱɟɫɤɚɹ ɫɜɹɡɶ ɦɟɠɞɭ Q- ɢ R-ɮɪɚɝɦɟɧɬɚɦɢ ɞɨɧɨɪɧɨ-
ɚɤɰɟɩɬɨɪɧɚɹ. Ɂɨɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ ɮɨɪɦɢɪɭɸɬ ɭɪɨɜɧɢ ɞɢɚɧɝɢɞɪɢɞɧɨɝɨ
ɮɪɚɝɦɟɧɬɚ (ɚɤɰɟɩɬɨɪɵ) ɜɚɥɟɧɬɧɭɸ ɡɨɧɭ ɫɨɫɬɚɜɥɹɸɬ ɭɪɨɜɧɢ ɞɢɚɦɢɧɧɨɝɨ
ɮɪɚɝɦɟɧɬɚ (ɞɨɧɨɪɵ). Ƚɪɚɧɢɰɵ ɦɟɠɞɭ ɡɨɧɚɦɢ ɜ ɩɨɥɢɢɦɢɞɚɯ, ɤɚɤ ɞɥɹ
ɜɫɟɯ ɚɦɨɪɮɧɵɯ ɫɬɪɭɤɬɭɪ ɪɚɫɩɥɵɜɱɚɬɵ, ɨɧɢ ɮɨɪɦɢɪɭɸɬɫɹ ɪɚɡɥɢɱɧɵɦɢ
ɰɟɧɬɚɦɢ ɡɚɯɜɚɬɚ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 2.28.
ɉɪɢ ɜɨɡɛɭɠɞɟɧɢɢ ɫɜɟɬɨɦ ɫ ɷɧɟɪɝɢɟɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɲɢɪɢɧɟ ɡɚ-
ɩɪɟɳɟɧɧɨɣ ɡɨɧɵ
, (ȿ
Ʉȼ
= ȿ
g
)
ɧɚɱɢɧɚɸɬɫɹ ɩɟɪɟɯɨɞɵ «ɡɨɧɚ-ɡɨɧɚ», ɫɨɩɪɨ-
ɜɨɠɞɚɸɳɢɟɫɹ ɜɵɫɨɤɢɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɨɝɥɨɳɟɧɢɹ ɢ ɮɨɬɨɩɪɨɜɨɞɢɦɨ-
ɫɬɶɸ. ɂɡ ɫɩɟɤɬɪɚ ɨɩɬɢɱɟɫɤɨɝɨ ɩɨɝɥɨɳɟɧɢɹ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ȿ
g
.
Ɋɢɫ. 2.29. Ɉɩɬɢɱɟɫɤɢɟ ɫɩɟɤɬɪɵ ɩɨɝɥɨɳɟɧɢɹ ɩɨɥɢɢɦɢɞɨɜ
O
O
1270
ȿ
, (2.4)
ɝɞɟ E
Ȝ
– ɫɨɛɫɬɜɟɧɧɨɟ ɩɨɝɥɨɳɟɧɢɟ.
ɍ ɩɨɥɢɢɦɢɞɨɜ:
ɷȼȿȿ
g
)32(
O
. (2.5)
ȼ ɪɹɞɭ ɩɨɥɢɢɦɢɞɨɜ ɫ ɪɨɫɬɨɦ ɲɢɪɢɧɵ ɡɚɩɪɟɳɟɧɧɨɣ ɡɨɧɵ
ɫɨɛɫɬɜɟɧɧɨɟ ɩɨɝɥɨɳɟɧɢɟ ɫɦɟɳɚɟɬɫɹ ɜ ɤɨɪɨɬɤɨɜɨɥɧɨɜɭɸ ɨɛɥɚɫɬɶ
ɭɮ ɮ ɫ ɝ ɡ ɠ ɨ ɤ ɢɤ
ɗɬɨ ɨɛɴɹɫɧɹɟɬ ɰɜɟɬ ɩɨɥɢɢɦɢɞɚ
Ɋɢɫ. 2.30. ɗɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ ɩɨɥɢɢɦɢɞɨɜ ɉɆ
196
Ɇɟɬɨɞɵ ɨɩɪɟɞɟɥɟɧɢɹ ɬɢɩɚ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ
1. Ɇɟɬɨɞ Ɍɭɛɚɧɞɬɚ
ɗɬɨ ɩɟɪɜɵɣ ɦɟɬɨɞ ɢɡɦɟɪɟɧɢɹ ɱɢɫɟɥ ɩɟɪɟɧɨɫɚ ɜ ɢɨɧɧɵɯ ɤɪɢɫɬɚɥɥɚɯ.
Ɉɧ ɩɪɟɞɥɨɠɟɧ Ɍɭɛɚɧɞɬɨɦ ɜ 1920 ɝ. Ɇɟɬɨɞ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɨɞɢɮɢ-
ɤɚɰɢɸ ɢɡɜɟɫɬɧɨɝɨ ɦɟɬɨɞɚ ɨɩɪɟɞɟɥɟɧɢɹ ɱɢɫɟɥ ɩɟɪɟɧɨɫɚ ɢɨɧɨɜ ɜ ɪɚɫɬɜɨ-
ɪɚɯ ɩɨ Ƚɢɬɬɨɪɮɭ.
ɋɯɟɦɚ ɹɱɟɣɤɢ ɞɥɹ ɢɡɦɟɪɟɧɢɹ ɱɢɫɟɥ ɩɟɪɟɧɨɫɚ ɩɨ Ɍɭɛɚɧɞɬɭ ɩɪɢɜɟɞɟ-
ɧɚ ɧɚ ɪɢɫ. 2.31.
Ɋɢɫ. 2.31. ɋɯɟɦɚ ɦɟɬɨɞɚ Ɍɭɛɚɧɞɬɚ
ȼ ɷɬɨɦ ɦɟɬɨɞɟ ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ ɨɞɢɧ ɢɡ ɷɥɟɤɬɪɨɞɨɜ ɹɜɥɹɟɬɫɹ ɨɛɪɚ-
ɬɢɦɵɦ ɤ ɨɞɧɨɦɭ ɢɡ ɤɨɦɩɨɧɟɧɬɨɜ ɢɫɫɥɟɞɭɟɦɨɝɨ ɜɟɳɟɫɬɜɚ. ȼɬɨɪɨɣ ɷɥɟɤ-
ɬɪɨɞ ɹɜɥɹɟɬɫɹ ɢɧɟɪɬɧɵɦ (P
t
). Ʉɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɢɱɟɫɬɜɚ, ɩɪɨɲɟɞɲɟɟ ɱɟ-
ɪɟɡ ɫɢɫɬɟɦɭ, ɢɡɦɟɪɹɟɬɫɹ ɤɭɥɨɧɨɦɟɬɪɨɦ (Ʉ). ɉɪɨɩɭɫɤɚɸɬ ɱɟɪɟɡ ɹɱɟɣɤɭ Q
0
ɤɭɥɨɧɨɜ ɷɥɟɤɬɪɢɱɟɫɬɜɚ, ɩɨ ɢɡɦɟɧɟɧɢɸ ɜɟɫɚ ɫɟɤɰɢɣ I ɢ II ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ
ɫ ɡɚɤɨɧɨɦ Ɏɚɪɚɞɟɹ ɨɩɪɟɞɟɥɹɸɬ ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɢɱɟɫɬɜɚ Q
i
, ɩɟɪɟɧɟ-
ɫɺɧɧɨɟ, ɧɚɩɪɢɦɟɪ, ɢɨɧɚɦɢ ɦɟɬɚɥɥɚ Ɇ, ɬɨɝɞɚ ɱɢɫɥɨ ɩɟɪɟɧɨɫɚ ɢɨɧɨɜ ɦɟ-
ɬɚɥɥɚ Ɇ. əɫɧɨ, ɱɬɨ ɷɥɟɤɬɪɨɧɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɷɬɢɦ ɦɟɬɨɞɨɜ ɧɟ ɮɢɤɫɢ-
ɪɭɟɬɫɹ. ɉɨɷɬɨɦɭ ɦɟɬɨɞ Ɍɭɛɚɧɞɬɚ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɬɨɥɶɤɨ ɬɢɩ ɢɨɧ-
ɧɵɯ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ
0
ɦ
ɦ
Q
t
Q
. (2.6)
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɨɤɫɢɞɚ, ɜ ɤɨɬɨɪɨɦ ɧɨɫɢɬɟɥɹɦɢ ɡɚɪɹɞɚ ɹɜɥɹ-
ɸɬɫɹ ɷɥɟɤɬɪɨɧɧɵɟ ɞɟɮɟɤɬɵ ɢ ɞɟɮɟɤɬɵ ɤɢɫɥɨɪɨɞɧɨɣ ɩɨɞɪɟɲɺɬɤɢ (ɦɟɠ-
ɞɨɭɡɟɥɶɧɵɣ ɤɢɫɥɨɪɨɞ ɢɥɢ ɤɢɫɥɨɪɨɞɧɵɟ ɜɚɤɚɧɫɢɢ), ɢɡɦɟɧɟɧɢɹ ɜɟɫɚ ɫɟɤ-
ɰɢɣ ɧɟ ɩɪɨɢɡɨɣɞɺɬ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɢɡɦɟɪɹɬɶ ɤɨɥɢɱɟɫɬɜɨ ɤɢɫɥɨɪɨ-
ɞɚ, ɜɵɞɟɥɹɸɳɟɟɫɹ ɩɪɢ ɩɪɨɩɭɫɤɚɧɢɢ ɨɩɪɟɞɟɥɺɧɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɷɥɟɤɬɪɢ-
ɱɟɫɬɜɚ. ɂɡɦɟɪɢɬɟɥɶɧɚɹ ɹɱɟɣɤɚ ɦɨɠɟɬ ɛɵɬɶ ɨɪɝɚɧɢɡɨɜɚɧɚ, ɬɚɤ
ɤɚɤ ɩɨɤɚ-
ɡɚɧɨ ɧɚ ɪɢɫ. 2.32.
ɧ
ɩ
(
ɢ
ɹ
Ⱦ
ɛ
ɬ
ɫ
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ɞ
Ɋ
ɢ
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4
6
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(
2
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1)
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4
–
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6
–
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)
,
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2.
3
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–
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2.
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:
ɢ
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:
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r
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9
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Y
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;
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).
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;
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;
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(
2
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,
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;
ɤ;
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;
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)
.
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-
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.
ɢ
-
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)
ɹ
:
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-
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-
198
ɳɟɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɫɚɦɚ ɜɟɥɢɱɢɧɚ ɱɢɫɥɚ ɩɟɪɟɧɨɫɚ ɤɢɫɥɨɪɨɞɚ,
ɦɟɬɨɞ ɩɪɢɦɟɧɢɦ ɥɢɲɶ ɞɥɹ ɫɨɟɞɢɧɟɧɢɣ, ɝɞɟ 01 0 Ot. ɉɪɢ t
0
< 0.01 ɞɨɥɹ
ɬɨɤɚ, ɩɟɪɟɧɨɫɢɦɚɹ ɞɟɮɟɤɬɚɦɢ, ɨɬɜɟɬɫɬɜɟɧɧɵɦɢ ɡɚ ɬɪɚɧɫɩɨɪɬ ɤɢɫɥɨɪɨɞɚ,
ɫɥɢɲɤɨɦ ɦɚɥɚ, ɞɚɜɥɟɧɢɟ ɤɢɫɥɨɪɨɞɚ ɜ ɹɱɟɣɤɟ ɦɟɧɹɟɬɫɹ ɨɱɟɧɶ ɫɥɚɛɨ, ɱɬɨ
ɩɪɢɜɨɞɢɬ ɤ ɛɨɥɶɲɢɦ ɩɨɝɪɟɲɧɨɫɬɹɦ ɜ ɨɩɪɟɞɟɥɟɧɢɢ I
out
.
2. Ɇɟɬɨɞ ɏɨɥɥɚ
əɜɥɟɧɢɟ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɩɨɩɟɪɟɱɧɨɣ ɪɚɡɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɨɜ (ɧɚɡɵ-
ɜɚɟɦɨɣ ɬɚɤɠɟ ɯɨɥɥɨɜɫɤɢɦ ɧɚɩɪɹɠɟɧɢɟɦ) ɩɪɢ ɩɨɦɟɳɟɧɢɢ ɩɪɨɜɨɞɧɢɤɚ ɫ
ɩɨɫɬɨɹɧɧɵɦ ɬɨɤɨɦ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. Ɉɬɤɪɵɬ ɗɞɜɢɧɨɦ ɏɨɥɥɨɦ ɜ
1879 ɝɨɞɭ ɜ ɬɨɧɤɢɯ ɩɥɚɫɬɢɧɤɚɯ ɡɨɥɨɬɚ.
ɗɮɮɟɤɬ ɏɨɥɥɚ, ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɬɢɩ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ (ɷɥɟɤ-
ɬɪɨɧɧɵɣ ɢɥɢ ɞɵɪɨɱɧɵɣ) ɜ ɦɟɬɚɥɥɟ ɢɥɢ ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ, ɱɬɨ ɞɟɥɚɟɬ ɟɝɨ
ɧɟɡɚɦɟɧɢɦɵɦ ɦɟɬɨɞɨɦ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɜɨɣɫɬɜ
ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜ. ȼ ɞɚɧ-
ɧɨɦ ɫɥɭɱɚɟ ɧɚ ɨɛɪɚɡɟɰ ɞɟɣɫɬɜɭɸɬ ɫɤɪɟɳɟɧɧɵɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɢ ɦɚɝɧɢɬ-
ɧɨɟ ɩɨɥɹ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɷɬɨɝɨ ɫɢɥɚ Ʌɨɪɟɧɰɚ ɫɨɫɬɨɪɨɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
ɞɟɣɫɬɜɭɟɬ ɧɚ ɧɨɫɢɬɟɥɶ ɬɨɤɚ, ɱɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɩɨɩɟɪɟɱ-
ɧɨɣ ɪɚɡɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɨɜ, ɡɧɚɤ ɤɨɬɨɪɨɣ ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɱɬɨ ɹɜɥɹɟɬɫɹ
ɧɨɫɢɬɟɥɟɦ ɡɚɪɹɞɚ – ɷɥɟɤɬɪɨɧ ɢɥɢ ɞɵɪɤɚ.
ɇɚ ɨɫɧɨɜɟ ɷɮɮɟɤɬɚ ɏɨɥɥɚ ɪɚɛɨɬɚɸɬ ɞɚɬɱɢɤɢ
ɏɨɥɥɚ: ɩɪɢɛɨɪɵ, ɢɡ-
ɦɟɪɹɸɳɢɟ ɧɚɩɪɹɠɺɧɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ⱦɚɬɱɢɤɢ ɏɨɥɥɚ ɩɨɥɭɱɢɥɢ
ɨɱɟɧɶ ɛɨɥɶɲɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜ ɛɟɫɤɨɥɥɟɤɬɨɪɧɵɯ, ɢɥɢ ɜɟɧɬɢɥɶɧɵɯ,
ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹɯ (ɫɟɪɜɨɦɨɬɨɪɚɯ). Ⱦɚɬɱɢɤɢ ɡɚɤɪɟɩɥɹɸɬɫɹ ɧɟɩɨɫɪɟɞɫɬ-
ɜɟɧɧɨ ɧɚ ɫɬɚɬɨɪɟ ɞɜɢɝɚɬɟɥɹ ɢ ɜɵɫɬɭɩɚɸɬ ɜ ɪɨɥɢ ȾɉɊ (ɞɚɬɱɢɤɚ ɩɨɥɨɠɟ-
ɧɢɹ ɪɨɬɨɪɚ). ȾɉɊ ɪɟɚɥɢɡɭɟɬ ɨɛɪɚɬɧɭɸ ɫɜɹɡɶ ɩɨ ɩɨɥɨɠɟɧɢɸ ɪɨɬɨɪɚ, ɜɵ-
ɩɨɥɧɹɟɬ ɬɭ ɠɟ ɮɭɧɤɰɢɸ, ɱɬɨ ɢ ɤɨɥɥɟɤɬɨɪ
ɜ ɤɨɥɥɟɤɬɨɪɧɨɦ ȾɉɌ.
Ɍɚɤɠɟ ɧɚ ɨɫɧɨɜɟ ɷɮɮɟɤɬɚ ɏɨɥɥɚ ɪɚɛɨɬɚɸɬ ɧɟɤɨɬɨɪɵɟ ɜɢɞɵ ɢɨɧɧɵɯ
ɪɟɚɤɬɢɜɧɵɯ ɞɜɢɝɚɬɟɥɟɣ.
Ɋɢɫ. 2.33. ɗɮɮɟɤɬ ɏɨɥɥɚ
199
3. Ɇɟɬɨɞ Ⱦɟɦɛɟɪɚ
Ɇɟɬɨɞ Ⱦɟɦɛɟɪɚ ɜ ɮɢɡɢɤɟ ɬɜɺɪɞɨɝɨ ɬɟɥɚ ɝɚɥɶɜɚɧɨɨɩɬɢɱɟɫɤɢɣ ɷɮ-
ɮɟɤɬ, ɫɨɫɬɨɹɳɢɣ ɜ ɜɨɡɧɢɤɧɨɜɟɧɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɗȾɋ ɜ ɨɞɧɨ-
ɪɨɞɧɨɦ ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ ɩɪɢ ɟɝɨ ɧɟɪɚɜɧɨɦɟɪɧɨɦ ɨɫɜɟɳɟɧɢɢ.
Ɉɬɤɪɵɬ ɧɟɦɟɰɤɢɦ ɮɢɡɢɤɨɦ X. Ⱦɟɦɛɟɪɨɦ (ɇ. Dember; 1931); ɬɟɨɪɢɹ
ɪɚɡɪɚɛɨɬɚɧɚ ə.ɂ. Ɏɪɟɧɤɟɥɟɦ (1933), ɧɟɦɟɰɤɢɦ ɮɢɡɢɤɨɦ X. Ɏɪɺɥɢɯɨɦ
(1935), ȿ.Ɇ. Ʌɢɮɲɢɰɟɦ ɢ Ʌ.Ⱦ. Ʌɚɧɞɚɭ (1936).
ɗɮɮɟɤɬ Ⱦɟɦɛɟɪɚ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɜɨɡɧɢɤɧɨɜɟɧɢɢ ɗȾɋ
ɜ ɨɞɧɨɪɨɞɧɨɦ
ɩɨɥɭɩɪɨɜɨɞɧɢɤɟ ɩɪɢ ɟɝɨ ɧɟɪɚɜɧɨɦɟɪɧɨɦ ɨɫɜɟɳɟɧɢɢ ɢɥɢ ɩɪɢ ɧɚɥɢɱɢɢ
ɝɪɚɞɢɟɧɬɚ ɬɟɦɩɟɪɚɬɭɪ.
ɗȾɋ ɜɨɡɧɢɤɚɟɬ ɡɚ ɫɱɟɬ ɪɚɡɧɢɰɵ ɤɨɧɰɟɧɬɪɚɰɢɣ ɧɨɜɵɯ ɧɨɫɢɬɟɥɟɣ ɡɚ-
ɪɹɞɚ, ɤɨɬɨɪɵɟ ɩɨɹɜɢɥɢɫɶ ɜ ɪɟɡɭɥɶɬɚɬɟ ɨɫɜɟɳɟɧɢɹ. ȼɧɨɜɶ ɜɨɡɧɢɤɲɢɟ
ɷɥɟɤɬɪɨɧɵ ɢ ɞɵɪɤɢ ɞɢɮɮɭɧɞɢɪɭɸɬ ɢɡ ɨɛɥɚɫɬɢ ɛɨɥɟɟ ɨɫɜɟɳɚɟɦɨɣ ɜ ɛɨ-
ɥɟɟ ɡɚɬɟɦɧɟɧɧɭɸ. Ⱦɢɮɮɭɡɢɹ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɞɵɪɨɤ ɢɦɟɟɬ ɪɚɡɥɢɱɧɵɟ
ɡɧɚɱɟɧɢɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ
, ɷɥɟɤɬɪɨɧɵ ɛɵɫɬɪɟɟ ɪɚɫɩɪɨɫɬɪɚɧɹɸɬɫɹ ɨɬ ɨɫ-
ɜɟɳɟɧɧɨɝɨ ɦɟɫɬɚ. ȼɨɡɧɢɤɚɟɬ ɗȾɋ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɨɬ ɨɫɜɟɳɟɧɧɨɝɨ ɭɱɚɫɬ-
ɤɚ ɩɨɥɭɩɪɨɜɨɞɧɢɤɚ ɤ ɡɚɬɟɦɧɟɧɧɨɦɭ.
ȼɟɥɢɱɢɧɚ ɗȾɋ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ:
0
l
np
np
DD
d
U
V
P
PV
³
(2.8)
ɝɞɟ D
n
– ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ ɷɥɟɤɬɪɨɧɨɜ; D
p
– ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭ-
ɡɢɢ ɞɵɪɨɤ; ȝ
n
– ɩɨɞɜɢɠɧɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ; ȝ
p
– ɩɨɞɜɢɠɧɨɫɬɶ ɞɵɪɨɤ.
Ɇɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɨɥɢɢɦɢɞɨɜ
ɍɩɪɭɝɢɟ ɫɜɨɣɫɬɜɚ ɦɚɬɟɪɢɚɥɨɜ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɦɨɞɭɥɹɦɢ ɭɩɪɭɝɨ-
ɫɬɢ. Ɇɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɢɥɨɣ ɯɢɦɢɱɟɫɤɨɣ ɫɜɹɡɢ ɱɚɫɬɢɰ ɜ
ɦɚɬɟɪɢɚɥɟ.
ɋɜɹɡɢ ɛɵɜɚɸɬ ɞɜɭɯ ɬɢɩɨɜ: ɏɢɦɢɱɟɫɤɚɹ ɫɜɹɡɶ (ɏɋ); ɋɜɹɡɶ ȼɚɧ ɞɟɪ
ȼɚɥɶɫɚ (ɋȼ). Ⱦɥɹ ɦɚɬɟɪɢɚɥɨɜ ɫ ɏɋ ȿ = 100–250 Ƚɉɚ. Ⱦɥɹ ɦɚɬɟɪɢɚɥɨɜ ɫ
ɋȼ ȿ = 2–8 Ƚɉɚ. Ⱦɥɹ ɩɨɥɢɢɦɢɞɧɵɯ ɩɥɟɧɨɤ ȿ = 3–10 Ƚɉɚ. ɇɚɢɛɨɥɶɲɟɟ
ɡɧɚɱɟɧɢɟ ȿ
ɘ
ɞɥɹ ɝɪɭɩɩɵ Ⱥ. ɇɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɟ ȿ
ɘ
ɞɥɹ ɝɪɭɩɩɵ Ƚ,
ɭɤɚɡɚɧɧɵɟ ɡɧɚɱɟɧɢɹ ɯɚɪɚɤɬɟɪɧɵ ɞɥɹ ɚɦɨɪɮɧɵɯ ɩɥɟɧɨɤ. Ⱦɥɹ ɤɪɢɫɬɚɥɥɢ-
ɱɟɫɤɢɯ ɩɥɟɧɨɤ ɝɪɭɩɩɵ Ⱥ ɢɦɟɟɦ ȿ
ɘ
§ 200 Ƚɉɚ.
200
Ɍɚɛɥɢɰɚ 2.20
ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɭɩɪɭɝɨɫɬɢ ɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯ ɩɨɥɢɢɦɢɞɨɜ
Ƚɪɭɩɩɚ
ɏɢɦ. ɮɨɪɦɭɥɚ ɩɨɥɢɢɦɢɞɚ
Ɇɚɪɤɚ
ȿ
ɘ
Ƚɉɚ
Ⱥ
1)
2)
–
ɉɆɎ–Ʌ
230
260
Ȼ
3)
4)
ȾȻɎ
––––
180
150
ȼ
5)
6)
ɉɆ
ɉɎȽ
14–22
40–63
7)
–––
34
Ƚ
8)
–––
45