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Файл:Методология расчётов гидродинамических параметров шахтных автоматизированных стационарных установок с центробежными нагнетателями. Монография
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3.6.1. ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱ ɢɫɫɥɟɞɨɜɚɧɢɹ
Ⱦɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɟɫɬɚɰɢɨɧɚɪɧɵɯ ɩɪɨɰɟɫɫɨɜ ɜ ɫɢɫɬɟɦɟ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɜɨɞɨɨɬɥɢɜɧɨɣ ɭɫɬɚɧɨɜɤɨɣ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɢɡɜɟɫɬɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɨɬɞɟɥɶɧɵɯ ɟɟ ɡɜɟɧɶɟɜ ɞɥɹ ɱɟɝɨ ɪɟɲɢɬɶ ɫɥɟɞɭɸɳɢɟ
ɡɚɞɚɱɢ:
1. ɧɚ ɝɢɞɪɚɜɥɢɱɟɫɤɨɣ ɫɯɟɦɟ ɜɨɞɨɨɬɥɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ ɜɵɞɟɥɢɬɶ
ɮɭɧɤɰɢɨɧɚɥɶɧɨ ɡɚɤɨɧɱɟɧɧɵɟ ɡɜɟɧɶɹ ɢ ɞɥɹ ɤɚɠɞɨɝɨ ɢɯ ɧɢɯ ɨɩɪɟɞɟɥɢɬɶ ɨɫɧɨɜɧɵɟ ɪɟɝɭɥɢɪɭɸɳɢɟ ɢ ɜɨɡɦɭɳɚɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ;
ɩɪɨɢɡɜɟɫɬɢ ɚɧɚɥɢɡ ɫɬɚɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜɵɞɟɥɟɧɧɵɯ ɡɜɟɧɶɟɜ
2.
ɢ ɭɫɬɚɧɨɜɤɢ ɜ ɰɟɥɨɦ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɝɪɚɧɢɰ ɢɡɦɟɧɟɧɢɹ ɨɫɧɨɜɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ;
3. ɫɨɫɬɚɜɢɬɶ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ, ɨɩɢɫɵɜɚɸɳɢɟ ɞɢɧɚɦɢ-
ɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɡɜɟɧɶɟɜ, ɢ ɩɨɥɭɱɢɬɶ ɧɚ ɨɫɧɨɜɟ ɷɬɢɯ
ɭɪɚɜɧɟɧɢɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɩɟɪɟɞɚɬɨɱɧɵɟ ɮɭɧɤɰɢɢ ɞɥɹ ɩɨɫɥɟɞɭɸɳɟɝɨ
ɫɢɧɬɟɡɚ ɫɢɫɬɟɦɵ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɜɨɞɨɨɬɥɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ.
3.6.2. Ɋɟɲɟɧɢɟ ɡɚɞɚɱ ɢ
ɪɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɣ
Ɉɛɴɟɤɬɨɦ ɢɫɫɥɟɞɨɜɚɧɢɣ ɹɜɥɹɟɬɫɹ ɲɚɯɬɧɚɹ
ɜɨɞɨɨɬɥɢɜɧɚɹ ɭɫɬɚɧɨɜɤɚ
(ɪɢɫ. 3.4), ɤɨɬɨɪɚɹ ɫɨɫɬɨɢɬ ɢɡ ɩɪɢɺɦɧɨɝɨ ɤɨɥɨɞɰɚ
1, ɜɫɚɫɵɜɚɸɳɟɣ ɬɪɭɛɤɢ 2,
ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɧɚɫɨɫɚ 3,
ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɧɚɩɨɪɧɨɝɨ
ɬɪɭɛɨɩɪɨɜɨɞɚ 4 ɢ ɤɚɧɚɥɢɡɚɰɢɨɧɧɨɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ 5 ɩɨɜɟɪɯɧɨɫɬɢ ɲɚɯɬɵ. ɍɫɬɚɧɨɜɤɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɥɨɠɧɵɣ ɞɢɧɚɦɢɱɟɫɤɢɣ ɨɛɴɟɤɬ ɫ ɧɟɫɤɨɥɶɤɢɦɢ ɜɯɨɞɧɵɦɢ ɢ
ɜɵɯɨɞɧɵɦɢ
ɤɨɨɪɞɢɧɚɬɚɦɢ, ɫɜɹɡɚɧɧɵɦɢ ɦɟɠɞɭ
ɫɨɛɨɣ ɪɚɡɥɢɱɧɵɦɢ ɤɚɧɚɥɚɦɢ, ɞɢɧɚɦɢɤɭ ɤɨɬɨɪɵɯ
ɫɥɟɞɭɟɬ ɨɩɢɫɚɬɶ ɫɨɨɬɜɟɬ-
Ɋɢɫɭɧɨɤ 3.4. ɍɩɪɨɳɟɧɧɚɹ ɫɯɟɦɚ ɜɨɞɨɨɬɥɢɜɧɨɣ
ɭɫɬɚɧɨɜɤɢ
ɫɬɜɭɸɳɢɦɢ ɞɢɮɮɟɪɟɧ-
81
ɰɢɚɥɶɧɵɦɢ ɭɪɚɜɧɟɧɢɹɦɢ. Ɋɚɫɫɦɚɬɪɢɜɚɟɦɵɣ ɪɟɚɥɶɧɵɣ ɨɛɴɟɤɬ ɨɛɥɚɞɚɟɬ
t
ɫɜɨɣɫɬɜɨɦ ɫɚɦɨɜɵɪɚɜɧɢɜɚɧɢɹ, ɩɨɫɤɨɥɶɤɭ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɜɯɨɞɧɨɣ ɜɟɥɢɱɢɧɵ ɩɨ ɥɸɛɨɦɭ ɤɚɧɚɥɭ, ɜɯɨɞɧɵɟ ɜɟɥɢɱɢɧɵ ɫɨ ɜɪɟɦɟɧɟɦ ɫɬɪɟɦɹɬɫɹ ɤ ɫɜɨɟɦɭ
ɭɫɬɚɧɨɜɢɜɲɟɦɭɫɹ ɡɧɚɱɟɧɢɸ. Ⱦɢɧɚɦɢɤɚ ɷɥɟɦɟɧɬɚɪɧɵɯ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ
ɷɥɟɦɟɧɬɨɜ, ɢɡ ɤɨɬɨɪɵɯ ɫɨɫɬɨɢɬ ɨɛɴɟɤɬ ɪɟɝɭɥɢɪɨɜɚɧɢɹ (ɪɢɫ. 3.4), ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ, ɦɨɠɟɬ ɛɵɬɶ ɨɩɢɫɚɧɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦɢ ɭɪɚɜɧɟɧɢɹɦɢ,
ɩɨɥɭɱɟɧɧɵɦɢ ɧɚ ɨɫɧɨɜɚɧɢɢ ɢɡɜɟɫɬɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɦɟɯɚɧɢɤɢ
dv
m
, (3.51)
F
:
d
ɚ ɨɛɴɟɤɬ ɪɟɝɭɥɢɪɨɜɚɧɢɹ, ɫɨɫɬɨɹɳɢɣ ɢɡ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫɨɟɞɢɧɟɧɧɵɯ
ɞɢɧɚɦɢɱɟɫɤɢɯ ɡɜɟɧɶɟɜ – ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɟɣ ɜɢɞɚ:
n
k
s
W
esW
ɝɞɟ m – ɦɚɫɫɚ ɞɜɢɠɭɳɟɝɨɫɹ ɩɨɬɨɤɚ: m = ȡlȦ, ɤɝ;
ȡ – ɩɥɨɬɧɨɫɬɶ ɬɪɚɧɫɩɨɪɬɢɪɭɟɦɨɣ ɠɢɞɤɨɫɬɢ, ɤɝ/ɦ
l – ɥɢɧɟɣɧɵɣ ɪɚɡɦɟɪ ɩɨɬɨɤɚ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ – ɞɥɢɧɚ ɨɬɪɟɡɤɚ
ɬɪɭɛɨɩɪɨɜɨɞɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦɭ ɡɜɟɧɭ), ɦ;
Ȧ – ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɩɨɬɨɤɚ (ɩɪɨɯɨɞɧɨɟ ɫɟɱɟɧɢɟ ɬɪɭɛɨɩɪɨɜɨɞɚ), ɦ
v – ɫɪɟɞɧɹɹ ɫɤɨɪɨɫɬɶ ɩɨɬɨɤɚ, ɦ/ɫ;
F – ɞɜɢɠɭɳɚɹ ɫɢɥɚ, ɩɨɪɨɠɞɚɸɳɚɹ ɞɜɢɠɟɧɢɟ ɩɨɬɨɤɚ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ
ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ ɞɚɜɥɟɧɢɟ ɢɥɢ ɪɚɡɧɨɫɬɶ ɞɚɜɥɟɧɢɣ ɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ
ɭɱɚɫɬɤɟ ɬɪɭɛɨɩɪɨɜɨɞɚ), ɇ;
IJ – ɱɢɫɬɨɟ ɬɪɚɧɫɩɨɪɬɧɨɟ ɡɚɩɚɡɞɵɜɚɧɢɟ, ɡɚɜɢɫɹɳɟɟ ɨɬ ɞɥɢɧɵ ɬɪɚɧɫɩɨɪɬɢɪɨɜɚɧɢɹ ɢ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɭɞɚɪɧɨɣ ɜɨɥɧɵ ɞɚɜɥɟɧɢɹ ɩɪɢ ɜɧɟɡɚɩɧɨɦ ɩɭɫɤɟ ɢɥɢ ɨɫɬɚɧɨɜɤɟ ɩɨɬɨɤɚ, ɫ;
s – ɨɩɟɪɚɬɨɪ Ʌɚɩɥɚɫɚ, ɫ-1;
n – ɱɢɫɥɨ ɡɜɟɧɶɟɜ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɣ ɰɟɩɢ ɨɛɴɟɤɬɨɜ;
i – ɧɨɦɟɪ ɡɜɟɧɚ;
k
– ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ, ɪɚɡɦɟɪɧɨɫɬɶ ɤɨɬɨɪɨɝɨ ɡɚɜɢɫɢɬ ɨɬ ɮɢɡɢɱɟɫɤɢɯ
ni
ɫɜɨɣɫɬɜ ɜɯɨɞɧɵɯ ɢ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ i-ɝɨ ɡɜɟɧɚ;
Ti – ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ i-ɝɨ ɡɜɟɧɚ, ɫ.
ȼɢɞ ɚɩɩɪɨɤɫɢɦɢɪɭɸɳɟɣ ɮɭɧɤɰɢɢ, ɚ ɬɚɤɠɟ ɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ, ɜɯɨɞɹɳɢɯ ɜ ɟɟ ɫɨɫɬɚɜ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɫɥɭɱɚɹ ɫ ɭɱɺɬɨɦ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɢ ɭɫɥɨɜɢɣ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ
ɨɛɴɟɤɬɚ. ɋ ɷɬɨɣ ɰɟɥɶɸ ɛɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɧɚɫɨɫɧɭɸ ɭɫɬɚɧɨɜɤɭ ɤɚɤ ɨɛɴɟɤɬ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫ ɭɱɟɬɨɦ ɪɚɧɟɟ ɫɮɨɪɦɭɥɢɪɨɜɚɧɧɵɯ ɡɚɞɚɱ ɢɫɫɥɟɞɨɜɚɧɢɣ.
ɉɪɢɺɦɧɵɣ ɤɨɥɨɞɟɰ ɫ ɜɨɞɨɫɛɨɪɧɢɤɨɦ ɫɥɭɠɢɬ ɞɥɹ ɚɤɤɭɦɭɥɢɪɨɜɚɧɢɹ
ɲɚɯɬɧɨɝɨ ɩɪɢɬɨɤɚ, ɩɨɫɬɭɩɚɸɳɟɝɨ ɢɡ ɝɨɪɧɵɯ ɜɵɪɚɛɨɬɨɤ, ɢ ɨɪɝɚɧɢɡɚɰɢɢ
i
ni
, (3.52)
sT
1
1
i
3
;
2
;
82
ɰɢɤɥɢɱɟɫɤɨɣ ɪɚɛɨɬɵ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɪɨɜɧɹ
sQths
ɧɚɩɨɥɧɟɧɢɹ ɤɨɥɨɞɰɚ, ɤɨɧɬɪɨɥɢɪɭɟɦɨɝɨ ɷɥɟɤɬɪɨɤɨɧɬɚɤɬɧɵɦɢ ɞɚɬɱɢɤɚɦɢ
(ɧɚ ɪɚɡɧɵɯ ɨɬɦɟɬɤɚɯ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɧɚ ɩɪɢɺɦɧɨɝɨ ɤɨɥɨɞɰɚ). ɐɢɤɥ ɪɚɛɨɬɵ
ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɩɟɪɢɨɞɨɜ: ɪɚɛɨɱɟɝɨ, ɩɪɢ ɤɨɬɨɪɨɦ
ɧɚɫɨɫ ɪɚɛɨɬɚɟɬ ɧɚ ɧɨɦɢɧɚɥɶɧɨɣ ɩɨɞɚɱɟ, ɢ ɩɚɭɡɵ, ɤɨɝɞɚ ɧɚɫɨɫ ɨɬɤɥɸɱɟɧ ɨɬ
ɷɥɟɤɬɪɨɫɟɬɢ. ȼ ɬɟɱɟɧɢɟ ɪɚɛɨɱɟɝɨ ɩɟɪɢɨɞɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɨɬɤɚɱɤɚ ɜɨɞɵ
ɢɡ
ɜɨɞɨɫɛɨɪɧɢɤɚ ɢ ɫɧɢɠɟɧɢɟ ɭɪɨɜɧɹ ɞɨ ɨɬɤɥɸɱɚɸɳɟɣ ɨɬɦɟɬɤɢ Ɉɍ (ɪɢɫ. 3.4),
ɚ ɜ ɬɟɱɟɧɢɟ ɩɚɭɡɵ ɩɪɨɢɫɯɨɞɢɬ ɧɚɩɨɥɧɟɧɢɟ ɜɨɞɨɫɛɨɪɧɢɤɚ ɢ ɩɨɜɵɲɟɧɢɟ
ɭɪɨɜɧɹ ɞɨ ɜɟɪɯɧɟɣ ɨɬɦɟɬɤɢ ȼɍ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɨɦɟɧɬɵ ɧɚɱɚɥɚ ɢ ɤɨɧɰɚ
ɭɩɨɦɹɧɭɬɵɯ ɩɟɪɢɨɞɨɜ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɡɧɚɱɟɧɢɹɦɢ
ɭɪɨɜɧɹ ɜɨɞɵ ɜ ɩɪɢɺɦɧɨɦ ɤɨɥɨɞɰɟ. Ɉɛɴɺɦ ɜɨɞɵ, ɡɚɤɥɸɱɺɧɧɵɣ ɦɟɠɞɭ
ɨɬɦɟɬɤɚɦɢ Ɉɍ ɢ ȼɍ, ɹɜɥɹɟɬɫɹ ɪɟɝɭɥɢɪɨɜɨɱɧɨɣ ɺɦɤɨɫɬɶɸ
, ɜ ɩɪɟɞɟɥɚɯ
ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɢɬ ɢɡɦɟɧɟɧɢɟ ɭɪɨɜɧɹ ɜɨ ɜɪɟɦɟɧɢ ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ
ɜɢɞɚ:
tQtQ
)()(
tdh
)(
dt
ɧɩ
, (3.53)
F
ɝɞɟ h(t) – ɬɟɤɭɳɢɣ ɭɪɨɜɟɧɶ ɜ ɩɪɢɺɦɧɨɦ ɤɨɥɨɞɰɟ, ɦ;
2
F – ɩɥɨɳɚɞɶ ɡɟɪɤɚɥɚ ɜɨɞɵ, ɦ
Q
(t), Qɧ(t) – ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɬɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ ɲɚɯɬɧɨɝɨ ɩɪɢɬɨɤɚ ɢ ɩɨɞɚɱɢ
ɩ
ɧɚɫɨɫɚ, ɦ
3
/ɫ.
Ɉɛɨɡɧɚɱɢɜ ɪɚɡɧɨɫɬɶ ɜɟɥɢɱɢɧ Q
;
(t) ɢ Qɧ(t) ɱɟɪɟɡ ǻQ(t), ɭɪɚɜɧɟɧɢɟ
ɩ
(3.53) ɡɚɩɢɲɟɦ ɜ ɜɢɞɟ:
tdh
)(
)(
F ' . (3.54)
tQ
dt
ɋ ɭɱɺɬɨɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ Ʌɚɩɥɚɫɚ ɢɫɯɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ ɩɪɟɞɫɬɚɜɢɦ ɜ
ɜɢɞɟ:
Ɉɬɤɭɞɚ ɩɨɥɭɱɢɦ ɩɟɪɟɞɚɬɨɱɧɭɸ ɮɭɧɤɰɢɸ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɡɜɟɧɚ:
F '
sW
, (3.56)
)(
1
'
ɝɞɟ k1 = 1/F – ɩɟɪɟɞɚɬɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɦ-2.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɞɢɧɚɦɢɱɟɫɤɨɦ ɨɬɧɨɲɟɧɢɢ ɩɪɢɺɦɧɵɣ ɤɨɥɨɞɟɰ
ɜɨɞɨɨɬɥɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɢɧɬɟɝɪɢɪɭɸɳɟɟ ɡɜɟɧɨ.
ȼɫɚɫɵɜɚɸɳɢɣ ɬɪɭɛɨɩɪɨɜɨɞ ɹɜɥɹɟɬɫɹ ɧɟɨɬɴɟɦɥɟɦɨɣ ɱɚɫɬɶɸ ɧɚɫɨɫɧɨɣ
ɭɫɬɚɧɨɜɤɢ ɢ ɜɨ ɦɧɨɝɨɦ ɨɩɪɟɞɟɥɹɟɬ ɟɺ ɷɤɨɧɨɦɢɱɧɨɫɬɶ ɢ ɛɟɡɚɜɚɪɢɣɧɨɫɬɶ
ɷɤɫɩɥɭɚɬɚɰɢɢ. Ⱦɥɹ ɨɰɟɧɤɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɜɫɚɫɵɜɚɸɳɟɝɨ ɬɪɭɛɨ-
)()(
. (3.55)
)(
k
th
1
s
sQ
)(
83
ɩɪɨɜɨɞɚ ɤɚɤ ɡɜɟɧɚ ɫɢɫɬɟɦɵ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɨɫɬɚɜɢɦ
Z
ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɭ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɪɢɥɨɠɟɧɧɵɯ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɢɥ, ɩɨɥɭɱɟɧɧɵɯ ɧɚ ɨɫɧɨɜɚɧɢɢ ɚɧɚɥɢɡɚ ɫɬɚɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ. Ⱦɥɹ ɷɬɨɝɨ
ɪɚɫɫɦɨɬɪɢɦ ɪɚɫɱɺɬɧɭɸ ɫɯɟɦɭ (ɪɢɫ. 3.4), ɢ ɞɥɹ ɜɵɛɪɚɧɧɵɯ ɫɟɱɟɧɢɣ I – I,
II – II, ɫɨɫɬɚɜɢɦ ɭɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɥɨɫɤɨɫɬɢ ɫɪɚɜɧɟɧɢɹ
0 – 0:
2
D
P
U
g
v
11
g
P
z
ȱȱȱ
1
U
g
2
D
v
22
22
g
ɇz
'
2
, (3.57)
ȱȱȱɩɨɬ
ɝɞɟ PI ɢ PII – ɩɨɥɧɵɟ ɞɚɜɥɟɧɢɹ ɜ ɫɟɱɟɧɢɹɯ I – I ɢ II – II, IIɚ;
v
ɢ v2 – ɫɪɟɞɧɢɟ ɫɤɨɪɨɫɬɢ ɠɢɞɤɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨɧɢɠɟɧɢɹ (ɩɨɜɵɲɟ-
1
ɧɢɹ) ɭɪɨɜɧɹ ɜ ɩɪɢɟɦɧɨɦ ɤɨɥɨɞɰɟ ɢ ɞɜɢɠɟɧɢɟ ɜɨɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ (ɫɟɱɟɧɢɟ II – II), ɦ/ɫ;
ɢ z2 – ɪɚɫɫɬɨɹɧɢɟ ɰɟɧɬɪɨɜ ɬɹɠɟɫɬɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫɟɱɟɧɢɣ I – I ɢ II – II
z
1
ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɥɨɫɤɨɫɬɢ ɫɪɚɜɧɟɧɢɹ 0 – 0, ɦ;
ǻɇ
ɩɨɬ I – II
– ɩɨɬɟɪɹ ɧɚɩɨɪɚ ɧɚ ɜɫɚɫɵɜɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ ɧɚ ɭɱɚɫɬɤɟ,
ɡɚɤɥɸɱɟɧɧɨɦ ɦɟɠɞɭ ɫɟɱɟɧɢɹɦɢ I – I ɢ II – II, ɦ;
Į1 ɢ Į2 – ɤɨɷɮɮɢɰɢɟɧɬɵ Ʉɨɪɢɨɥɢɫɚ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɟ ɷɩɸɪɵ ɫɤɨɪɨɫɬɟɣ
ɩɨ ɫɟɱɟɧɢɸ ɩɨɬɨɤɚ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɟɱɟɧɢɹɯ.
ȼ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɫɥɭɱɚɟ ɜɟɥɢɱɢɧɵ, ɭɤɚɡɚɧɧɵɟ ɜ (3.57), ɩɪɢɧɢɦɚɸɬ
ɡɧɚɱɟɧɢɹ: v
ɇ
= 0; z1 = –ɇɜɝ; z2 = 0; PI = Ɋɚ; PII = Ɋɚ + Ɋɜ;
1
2
D
v
2Qɚg
22
'
2
, ɝɞɟ Ɋɚ – ɚɬɦɨɫɮɟɪɧɨɟ ɞɚɜɥɟɧɢɟ, ɉɚ; Ɋɜ – ɜɚ-
ɜȱȱȱɩɨɬ
ɤɭɭɦɦɟɬɪɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ, ɪɚɡɜɢɜɚɟɦɨɟ ɧɚɫɨɫɨɦ, ɉɚ; Q – ɩɨɞɚɱɚ ɧɚɫɨɫɚ,
ɦ3/c; aɜ – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɫɚɫɵɜɚɸɳɟɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ, ɫ2/ɦ5; aɜQ2 – ɨɛɳɢɟ
ɩɨɬɟɪɢ ɧɚɩɨɪɚ ɜɨ ɜɫɚɫɵɜɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ, ɦ.
ɉɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɜɟɥɢɱɢɧ ɜ ɭɪɚɜɧɟɧɢɟ (3.57) ɢ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ
ɩɨɥɭɱɢɦ:
U
2
. (3.58)
QɚɇgɊ
ɜɜɝɜ
ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɜɚɤɭɭɦɦɟɬɪɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɩɨ
ɮɨɪɦɭɥɟ (3.58), ɩɪɨɢɫɯɨɞɢɬ ɞɜɢɠɟɧɢɟ ɠɢɞɤɨɫɬɢ ɩɨ ɜɫɚɫɵɜɚɸɳɟɦɭ ɬɪɭɛɨɩɪɨɜɨɞɭ. Ⱦɢɧɚɦɢɤɚ ɞɜɢɠɟɧɢɹ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ (3.51). Ⱦɜɢɠɭɳɚɹ
ɫɢɥɚ F ɫɜɹɡɚɧɚ ɫ ɩɨɪɨɠɞɚɸɳɢɦ ɟɺ ɞɚɜɥɟɧɢɟɦ Ɋ
ɜɊF . (3.59)
ɭɪɚɜɧɟɧɢɟɦ ɜɢɞɚ:
ɜ
ɍɪɚɜɧɟɧɢɟ (3.51) ɫ ɭɱɺɬɨɦ (3.58), (3.59) ɢ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ
ɫɨɨɬɧɨɲɟɧɢɣ ɡɚɩɢɲɟɦ ɜ ɜɢɞɟ:
84
l
dQ
ɜ
Z
g
dt
2
Qɚɇ
. (3.60)
ɜɜɝ
ɍɪɚɜɧɟɧɢɟ (3.60) ɧɟɥɢɧɟɣɧɨ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɚɪɚɦɟɬɪɚ Q. ɋ ɰɟɥɶɸ
ɥɢɧɟɚɪɢɡɚɰɢɢ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɩɪɨɢɡɜɟɞɟɦ ɪɚɡɥɨɠɟɧɢɟ ɧɟɥɢɧɟɣɧɨɝɨ ɱɥɟɧɚ
Q2 ɜ ɪɹɞ Ɍɟɣɥɨɪɚ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɬɨɱɤɢ Q0 = Qɧ = const:
a
ɜ
22
ɚ Q ɚ Q ɚ QQQ
|
ɜɜ ɜ
2,
ɚ QQ ɚ QnQn
ɜɜ
2
000
0012
2
ɝɞɟ n1 = 2aɜQɧ; n2 = aɜQɧ;
Q
– ɩɨɞɚɱɚ ɧɚɫɨɫɚ ɜ ɬɨɱɤɟ ɪɚɡɥɨɠɟɧɢɹ;
ɧ
Q = f(t) – ɡɧɚɱɟɧɢɟ ɩɨɞɚɱɢ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɞɫɬɚɧɨɜɤɢ ɡɧɚɱɟɧɢɹ a
Q2 ɜ (3.60) ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɜ
ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɩɨɥɭɱɢɦ ɥɢɧɟɚɪɢɡɨɜɚɧɧɨɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ
ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ ɜɨ ɜɫɚɫɵɜɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ:
l
dQ
ɜ
Z
g
dt
ɜɚɤ
ɜɚɤ
Qnɇ
, (3.61)
1
= ɇɜɝ – n2, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣ
ɝɞɟ H
– ɜɚɤɭɭɦɦɟɬɪɢɱɟɫɤɢɣ ɧɚɩɨɪ: H
ɜɚɤ
ɨɛɳɢɟ ɩɨɬɟɪɢ ɜɨ ɜɫɚɫɵɜɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ, ɦ.
Ɋɚɡɞɟɥɢɜ ɨɛɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (3.61) ɧɚ n1, ɩɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɩɨ
Ʌɚɩɥɚɫɭ ɨɤɨɧɱɚɬɟɥɶɧɨ ɢɦɟɟɦ:
)()(
ɜɚɤ
sɇksQsɌ
,
22
ɝɞɟ s – ɨɩɟɪɚɬɨɪ Ʌɚɩɥɚɫɚ;
– ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ: k2 = l/n1;
k
2
l
Ɍ
– ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ:
2
Ɍ
2
ɜ
, c.
ng
Z
1
ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɢɦɟɟɬ ɜɢɞ:
sQ
sW
2
ɜɚɤ
sɇ
k
2
2
. (3.62)
1
sɌ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɞɢɧɚɦɢɱɟɫɤɨɦ ɫɨɨɬɧɨɲɟɧɢɢ ɜɫɚɫɵɜɚɸɳɢɣ
ɬɪɭɛɨɩɪɨɜɨɞ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɚɩɟɪɢɨɞɢɱɟɫɤɨɟ ɡɜɟɧɨ. Ɂɧɚɤ ɦɢɧɭɫ ɜ
ɜɵɪɚɠɟɧɢɢ (3.62) ɭɤɚɡɵɜɚɟɬ ɧɚ ɬɨ, ɱɬɨ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɩɨɞɚɱɢ ɧɚɫɨɫɚ ɟɝɨ
ɜɚɤɭɭɦɦɟɬɪɢɱɟɫɤɢɣ ɧɚɩɨɪ ɭɦɟɧɶɲɚɟɬɫɹ ɡɚ ɫɱɺɬ ɜɨɡɪɚɫɬɚɸɳɢɯ ɩɨɬɟɪɶ ɜɨ
ɜɫɚɫɵɜɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ. ȼ ɞɚɥɶɧɟɣɲɟɦ ɷɬɨɬ ɡɧɚɤ ɦɨɠɟɬ ɛɵɬɶ ɨɩɭɳɟɧ.
ɐɟɧɬɪɨɛɟɠɧɵɣ ɧɚɫɨɫ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɵɦ ɧɚɝɧɟɬɚɬɟɥɟɦ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɦ ɨɬɤɚɱɤɭ ɜɨɞɵ ɢɡ ɜɨɞɨɫɛɨɪɧɢɤɚ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɲɚɯɬɵ ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɧɨɣ ɫɟɬɢ ɡɚ ɫɱɺɬ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɞɜɢɝɚɬɟɥɹ ɜ
85
ɷɧɟɪɝɢɸ ɩɟɪɟɤɚɱɢɜɚɟɦɨɣ ɠɢɞɤɨɫɬɢ. Ɉɫɧɨɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɭɞɟɥɶɧɨɣ
Z
U
ɇ
ɷɧɟɪɝɢɢ ɹɜɥɹɟɬɫɹ ɧɚɩɨɪ ɧɚɫɨɫɚ. ɗɬɨ ɜɟɥɢɱɢɧɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɪɢɪɚɳɟɧɢɟ
ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ, ɩɨɥɭɱɚɟɦɨɣ ɠɢɞɤɨɫɬɶɸ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɧɚɫɨɫ,
ɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɪɚɡɧɨɫɬɶ ɧɚɩɨɪɨɜ ɩɪɢ ɜɵɯɨɞɟ ɢɡ ɧɚɫɨɫɚ ɢ ɩɪɢ ɜɯɨɞɟ
ɜ ɧɟɝɨ. ɗɬɨ ɩɪɢɪɚɳɟɧɢɟ ɷɧɟɪɝɢɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɹ Ȼɟɪɧɭɥɥɢ, ɫɨɫɬɚɜɥɟɧɧɨɝɨ ɞɥɹ ɜɵɛɪɚɧɧɵɯ ɫɟɱɟɧɢɣ II – II, III – III (ɪɢɫ. 3.4) ɨɬɧɨɫɢɬɟɥɶɧɨ
ɩɥɨɫɤɨɫɬɢ ɫɪɚɜɧɟɧɢɹ 0 – 0, ɩɪɨɜɟɞɟɧɧɨɣ ɱɟɪɟɡ ɰɟɧɬɪ ɧɚɫɨɫɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ
ɭɪɚɜɧɟɧɢɟ ɢɦɟɟɬ ɜɢɞ:
Ɋ
ȱȱ
ɇ
g
Ɋ
ȱȱȱ
'
ȱȱȱȱȱ
, (3.63)
g
UU
ɝɞɟ PII = Pa + Pɜ – ɩɨɥɧɨɟ ɞɚɜɥɟɧɢɟ ɜ ɫɟɱɟɧɢɢ II – II;
= Pa + Pɧ – ɩɨɥɧɨɟ ɞɚɜɥɟɧɢɟ ɜ ɫɟɱɟɧɢɢ III – III;
P
III
P
– ɚɬɦɨɫɮɟɪɧɨɟ ɞɚɜɥɟɧɢɟ;
a
– ɜɚɤɭɭɦɦɟɬɪɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ;
P
ɜ
P
– ɞɚɜɥɟɧɢɟ, ɪɚɡɜɢɜɚɟɦɨɟ ɧɚɫɨɫɨɦ;
ɧ
ɊɊ
ɇ
'
ȱȱȱȱȱ
ɜɧ
U
g
ɇɇ
– ɪɚɡɧɨɫɬɶ ɧɚɩɨɪɨɜ, ɨɛɭɫɥɨɜɥɢɜɚɸɳɚɹ ɞɜɢ-
ɜɧ
ɠɭɳɭɸ ɫɢɥɭ F ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɢɬ ɞɜɢɠɟɧɢɟ ɠɢɞɤɨɫɬɢ ɨɬ
ɜɫɚɫɵɜɚɸɳɟɝɨ ɩɚɬɪɭɛɤɚ ɧɚɫɨɫɚ ɞɨ ɧɚɝɧɟɬɚɬɟɥɶɧɨɝɨ:
, (3.64)
ɇɇgF
ɜɧ
ɝɞɟ Ȧ – ɩɥɨɳɚɞɶ ɩɪɨɯɨɞɧɨɝɨ ɫɟɱɟɧɢɹ ɩɚɬɪɭɛɤɨɜ, ɦ2 (Ȧɜ = Ȧɧ);
ȡ – ɩɥɨɬɧɨɫɬɶ ɩɟɪɟɤɚɱɢɜɚɟɦɨɣ ɠɢɞɤɨɫɬɢ, ɤɝ/ɦ
, Ȧɧ – ɩɥɨɳɚɞɢ ɩɪɨɯɨɞɧɵɯ ɫɟɱɟɧɢɣ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɜɫɚɫɵɜɚɸɳɟɝɨ ɢ
Ȧ
ɜ
ɧɚɩɨɪɧɨɝɨ ɩɚɬɪɭɛɤɨɜ, ɦ
2
.
3
;
Ⱦɢɧɚɦɢɤɚ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɢɫɵɜɚɟɬɫɹ ɬɟɦ ɠɟ
ɭɪɚɜɧɟɧɢɟɦ ɦɟɯɚɧɢɤɢ, ɱɬɨ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ (3.51). ɉɨɞɫɬɚɜɢɜ ɜ
ɭɪɚɜɧɟɧɢɟ (3.51) ɜɟɥɢɱɢɧɭ F ɢɡ (3.64) ɢ ɩɪɢɜɟɞɟɧɧɵɟ ɜɵɲɟ ɫɨɨɬɧɨɲɟɧɢɹ,
ɩɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɧɚɯɨɞɢɦ:
l
dQ
ɝɞɟ ɇ
– ɧɚɩɨɪ, ɪɚɡɜɢɜɚɟɦɵɣ ɧɚɫɨɫɨɦ;
ɧ
– ɩɨɬɟɪɹ ɧɚɩɨɪɚ ɜɨ ɜɫɚɫɵɜɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ.
ɇ
ɜ
ȼɟɥɢɱɢɧɵ ɇ
ɫɬɢɤ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɧɚɫɨɫɚ ɢ ɜɫɚɫɵɜɚɸɳɟɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ:
ɢ ɇɜ ɨɩɪɟɞɟɥɹɸɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɣ ɧɚɩɨɪɧɵɯ ɯɚɪɚɤɬɟɪɢ-
ɧ
ɜ
Z
dt
g
0
ɧ
ɇɚQ ,
ɜɜɝɜ
86
ɇɇ
, (3.65)
ɜɧ
2
;
QBQȺɇɇ
ɝɞɟ H0 – ɧɚɩɨɪ, ɪɚɡɜɢɜɚɟɦɵɣ ɧɚɫɨɫɨɦ ɩɪɢ ɧɭɥɟɜɨɣ ɩɨɞɚɱɟ (ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɧɚɫɨɫɚ ɜɟɥɢɱɢɧɚ ɩɚɫɩɨɪɬɧɚɹ);
Ⱥ ɢ ȼ – ɷɦɩɢɪɢɱɟɫɤɢɟ ɤɨɷɮɮɢɰɢɟɧɬɵ, ɬɚɤɠɟ ɡɚɜɢɫɹɳɢɟ ɨɬ ɬɢɩɚ ɧɚɫɨɫɚ
(ɜɟɥɢɱɢɧɵ ɫɩɪɚɜɨɱɧɵɟ);
Q – ɩɨɞɚɱɚ ɧɚɫɨɫɚ;
– ɜɚɤɭɭɦɦɟɬɪɢɱɟɫɤɚɹ ɜɵɫɨɬɚ ɜɫɚɫɵɜɚɧɢɹ;
ɇ
ɜɝ
– ɨɛɨɛɳɟɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜɫɚɫɵɜɚ-
ɚ
ɜ
ɸɳɟɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ.
ɉɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɧɚɣɞɟɧɧɵɯ ɜɟɥɢɱɢɧ ɜ (3.65) ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɩɨɥɭɱɢɦ ɩɟɪɟɞɚɬɨɱɧɭɸ ɮɭɧɤɰɢɸ ɢɫɫɥɟɞɭɟɦɨɝɨ ɡɜɟɧɚ,
ɚɧɚɥɨɝɢɱɧɭɸ (3.62):
sQ
Ɍ
ɝɞɟ
3
= 1/A1 – ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɡɜɟɧɚ, ɦ2/ɫ;
k
3
Ⱥ
= n3 – Ⱥ;
1
c
– ɩɨɬɟɪɢ ɧɚɩɨɪɚ, ɩɪɢɜɟɞɟɧɧɵɟ ɤ ɜɵɯɨɞɧɨɦɭ ɩɚɬɪɭɛɤɭ ɧɚɫɨɫɚ, ɦɨɠɟɬ
ɇ
1
l
– ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ, ɫ;
Ⱥg
Z
1
c
400 ɧɜɧɜɝ
sW
c
sɇ
1
ɧɜɧ
k
3
, (3.66)
1
sɌ
3
c
;;22
nɇɇQɚȼQȼn
4013
22
;;
QɚȼQȼnɇɇɇ
ɛɵɬɶ ɜɵɪɚɠɟɧ ɱɟɪɟɡ ɢɡɜɟɫɬɧɵɟ ɜɟɥɢɱɢɧɵ ɫɥɟɞɭɸɳɟɣ ɡɚɜɢɫɢɦɨɫɬɶɸ:
2
c
01
c
. (3.67)
QBQȺɇɇ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɰɟɧɬɪɨɛɟɠɧɵɣ ɧɚɫɨɫ ɜ ɞɢɧɚɦɢɱɟɫɤɨɦ ɨɬɧɨɲɟɧɢɢ,
ɤɚɤ ɢ ɜɫɚɫɵɜɚɸɳɢɣ ɬɪɭɛɨɩɪɨɜɨɞ, ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɩɪɟɞɫɬɚɜɥɹɟɬ
ɫɨɛɨɣ ɚɩɟɪɢɨɞɢɱɟɫɤɨɟ ɡɜɟɧɨ.
ɇɚɩɨɪɧɵɣ ɬɪɭɛɨɩɪɨɜɨɞ ɫɨɫɬɨɢɬ ɢɡ ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɢ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ
ɭɱɚɫɬɤɨɜ, ɨɛɪɚɡɭɹ ɧɚɩɨɪɧɭɸ ɬɪɭɛɨɩɪɨɜɨɞɧɭɸ ɫɟɬɶ, ɜ ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɹɬ
ɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɞɜɢɠɟɧɢɟɦ ɩɨɬɨɤɚ ɜɨɞɵ ɨɬ ɧɚɫɨɫɚ ɞɨ
ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɨɬɫɬɨɣɧɢɤɨɜ. ɋɬɪɨɢɬɟɥɶɧɚɹ ɞɥɢɧɚ ɬɚɤɨɣ ɫɟɬɢ ɫɨɫɬɚɜɥɹɟɬ
ɧɟɫɤɨɥɶɤɢɯ ɫɨɬɟɧ ɦɟɬɪɨɜ ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɤɢɥɨɦɟɬɪɨɜ. ɉɨɷɬɨɦɭ ɩɪɢ ɫɨ-
ɨɬ
ɫɬɚɜɥɟɧɢɢ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ ɬɚɤɨɝɨ ɡɜɟɧɚ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ
ɬɪɚɧɫɩɨɪɬɧɨɟ ɡɚɩɚɡɞɵɜɚɧɢɟ ɜ ɜɢɞɟ ɬɪɚɧɫɰɟɧɞɟɧɬɧɨɣ ɮɭɧɤɰɢɢ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɤɥɸɱɟɧɧɨɣ ɫ ɥɢɧɟɣɧɨɣ ɱɚɫɬɶɸ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ. Ⱦɥɹ ɫɨɫɬɚɜɥɟɧɢɹ ɥɢɧɟɣɧɨɣ ɱɚɫɬɢ ɮɭɧɤɰɢɢ ɫɨɫɬɚɜɢɦ ɭɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ ɞɥɹ
ɫɟɱɟɧɢɣ III – III ɢ IV – IV ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɥɨɫɤɨɫɬɢ ɫɪɚɜɧɟɧɢɹ 0 – 0 (ɫɦ.
ɪɢɫ. 3.4):
87
P
ɂ
ɝɞɟ Ɋ
P
Ɋ
= Pa + P1 – ɩɨɥɧɨɟ ɞɚɜɥɟɧɢɟ ɜ ɫɟɱɟɧɢɢ III – III;
III
= Pa – ɞɚɜɥɟɧɢɟ ɜ ɫɟɱɟɧɢɢ IV – IV;
IV
– ɞɚɜɥɟɧɢɟ, ɩɪɢɜɟɞɟɧɧɨɟ ɤ ɜɵɯɨɞɧɨɦɭ ɩɚɬɪɭɛɤɭ ɧɚɫɨɫɚ, ɜɵɪɚɠɟɧɧɨɟ
1
g
U
33
g
P
z
ȱȱȱȱȱ
3
U
g
2
v
D
2
v
D
44
g
22
ɇz
'
4
, (3.68)
ȱVȱȱȱɩɨɬ
ɱɟɪɟɡ ɩɨɬɟɪɢ ɧɚɩɨɪɚ, ɢ ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɮɨɪɦɭɥɟ (3.67);
Į3 = Į4 – ɤɨɷɮɮɢɰɢɟɧɬɵ Ʉɨɪɢɨɥɢɫɚ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɟɱɟɧɢɹɯ;
= v4 – ɫɪɟɞɧɢɟ ɫɤɨɪɨɫɬɢ ɩɨɬɨɤɚ ɜ ɬɟɯ ɠɟ ɫɟɱɟɧɢɹɯ;
v
3
z
, z4 – ɪɚɫɫɬɨɹɧɢɹ ɰɟɧɬɪɨɜ ɬɹɠɟɫɬɢ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɫɟɱɟɧɢɣ ɨɬ
3
ɩɥɨɫɤɨɫɬɢ ɫɪɚɜɧɟɧɢɹ 0 – 0: z
z
4
ǻɇ
IV:
a
ɧɬ
= H
;
ɫɬɜ
– ɩɨɬɟɪɢ ɧɚɩɨɪɚ ɧɚ ɭɱɚɫɬɤɟ ɫɟɬɢ ɦɟɠɞɭ ɫɟɱɟɧɢɹɦɢ III – III ɢ IV –
ɩɨɬ III–IV
'
ɧɬȱVȱȱȱɩɨɬ
– ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɧɚɩɨɪɧɨɝɨ ɬɪɭɛɨ-
= 0;
3
2
Qaɇ
;
ɩɪɨɜɨɞɚ;
Q – ɪɚɫɯɨɞ ɜɨɞɵ ɜ ɬɪɭɛɨɩɪɨɜɨɞɧɨɣ ɫɟɬɢ, ɱɢɫɥɟɧɧɨ ɪɚɜɧɵɣ ɩɨɞɚɱɟ ɧɚɫɨɫɚ;
– ɝɥɭɛɢɧɚ ɫɬɜɨɥɚ ɲɚɯɬɵ.
H
ɫɬɜ
ɉɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɜɟɥɢɱɢɧ ɜ (3.68) ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɜ ɜɢɞɟ:
HH ɚ Q . (3.69)
1 ɫɬɜ ɧɬ
2
ɉɪɚɜɚɹ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ (3.69) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɭɪɚɜɧɟɧɢɟ ɧɚɩɨɪɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɬɪɭɛɨɩɪɨɜɨɞɧɨɣ ɫɟɬɢ, ɚ ɥɟɜɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɧɚɫɨɫɚ,
ɩɪɢɜɟɞɟɧɧɭɸ ɤ ɟɝɨ ɜɵɯɨɞɧɨɦɭ ɩɚɬɪɭɛɤɭ ɢ ɨɩɪɟɞɟɥɹɟɦɭɸ ɜɵɪɚɠɟɧɢɟɦ
(3.67). Ɋɚɡɧɨɫɬɶ ɷɬɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɭɪɚɜɧɟɧɢɟ ɢɧɟɪɰɢɨɧɧɨɝɨ ɧɚɩɨɪɚ, ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɤɨɬɨɪɨɝɨ ɩɪɨɢɫɯɨɞɢɬ ɞɜɢɠɟɧɢɟ ɩɨɬɨɤɚ
ɠɢɞɤɨɫɬɢ ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɭ ɨɬ ɧɚɫɨɫɚ ɞɨ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɨɬɫɬɨɣɧɢɤɚ:
ɂ
0
ɡɞɟɫɶ ɋ = ȼ + Ⱥ; ɚ = ɚɜ + ɚɧɬ; ǻɇ0 = ɇ0 – ɇɜ2 – ɇ
ɉɨɫɥɟ ɥɢɧɟɚɪɢɡɚɰɢɢ ɱɥɟɧɚ ɋÂQ
ɝɞɟ ǻɇ0' = ǻɇ0 – ɋÂQ
n = 2ÂCÂQ
– A.
ɧ
2
;
ɧ
2
ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɬɨɱɤɢ Qɧ ɧɚɯɨɞɢɦ:
c
'|
0
2
, (3.70)
QɋQȺHH
'
.
ɫɬɜ
QnHH
, (3.71)
Ⱦɢɧɚɦɢɤɭ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ ɨɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟɦ (3.51), ɩɨɥɨɠɢɜ ɜ
ɧɟɦ: F = ȡÂgÂȦ
ɧɬÂHɂ
; m = ȡÂl
ɫɧɬÂȦɧɬ
.
88
ɉɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ, ɫ ɭɱɺɬɨɦ (3.71) ɩɨɥɭɱɢɦ:
l
ɫɬ
Z
ɫɬ
l
ɝɞɟ
k
4
ɫɬ
Z
ɫɬ
= 1/n – ɩɟɪɟɞɚɬɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ. ɂɥɢ ɜ ɮɨɪɦɟ Ʌɚɩɥɚɫɚ:
– ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ, ɫ;
T
4
ng
tdQ
dt
ng
'
'
c
,
tHktQ
04
c
sHksQsQsT
,
044
ɨɬɤɭɞɚ ɥɢɧɟɣɧɚɹ ɱɚɫɬɶ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ ɢɫɫɥɟɞɭɟɦɨɝɨ ɡɜɟɧɚ ɢɦɟɟɬ
ɜɢɞ:
sQ
sW
4
ɥ.ɱ.
c
'
sH
0
k
4
4
,
sT
1
ɚ ɫ ɭɱɟɬɨɦ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɡɚɩɚɡɞɵɜɚɧɢɹ ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɢɦ:
k
s
W
l
ɫɧɬ
ɝɞɟ
W
C
– ɫɤɨɪɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɭɞɚɪɧɨɣ ɜɨɥɧɵ ɜ ɬɪɚɧɫɩɨɪɬɧɨɦ
ɭɞ
– ɬɪɚɧɫɩɨɪɬɧɨɟ ɡɚɩɚɡɞɵɜɚɧɢɟ, ɫ;
ɋ
ɭɞ
4
esW
4
, (3.72)
1
sT
4
ɬɪɭɛɨɩɪɨɜɨɞɟ, ɦ/ɫ (ɞɥɹ ɜɨɞɵ ɢ ɫɬɚɥɶɧɵɯ ɬɪɭɛ ɩɪɢɧɢɦɚɟɬɫɹ ɫɨɝɥɚɫɧɨ
[2]:Cɭɞ = 1300 ɦ/ɫ).
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɞɢɧɚɦɢɱɟɫɤɨɦ ɨɬɧɨɲɟɧɢɢ ɧɚɩɨɪɧɚɹ ɬɪɭɛɨɩɪɨɜɨɞɧɚɹ ɫɟɬɶ ɜɨɞɨɨɬɥɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɦɨɠɟɬ ɛɵɬɶ
ɩɪɟɞɫɬɚɜɥɟɧɚ ɡɜɟɧɨɦ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɫ ɡɚɩɚɡɞɵɜɚɧɢɟɦ.
ɂɡɥɨɠɟɧɧɨɟ ɩɨɡɜɨɥɹɟɬ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ.
1. Ɉɛɨɛɳɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɣ ɫɬɚɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ
ɬɪɭɛɨɩɪɨɜɨɞɧɨɣ ɫɟɬɢ ɢ ɰɟɧɬɪɨɛɟɠɧɵɯ ɧɚɝɧɟɬɚɬɟɥɟɣ.
2. Ɉɩɪɟɞɟɥɟɧɵ ɞɢɚɩɚɡɨɧɵ ɢɡɦɟɧɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ
ɜɨɞɨɨɬɥɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ ɜ ɡɨɧɟ ɩɪɨɦɵɲɥɟɧɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɧɚɫɨɫɚ,
ɩɨɡɜɨɥɹɸɳɢɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɥɢɧɟɣɧɨɝɨ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɩɩɚɪɚɬɚ ɞɥɹ
ɨɩɢɫɚɧɢɹ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɜ ɨɛɴɟɤɬɟ ɪɟɝɭɥɢɪɨɜɚɧɢɹ.
3. ɉɨɥɭɱɟɧɵ ɩɟɪɟɞɚɬɨɱɧɵɟ ɮɭɧɤɰɢɢ ɨɫɧɨɜɧɵɯ ɡɜɟɧɶɟɜ ɫɢɫɬɟɦɵ
ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɜɨɞɨɨɬɥɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ.
4. Ɋɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɣ ɧɟ ɩɪɨɬɢɜɨɪɟɱɚɬ ɨɫɧɨɜɧɵɦ ɩɨɥɨɠɟɧɢɹɦ
ɬɟɨɪɢɢ ɥɨɩɚɫɬɧɵɯ ɬɭɪɛɨɦɚɲɢɧ ɢ ɬɟɨɪɢɢ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ
ɨɛɴɟɤɬɨɜ ɩɨɞɨɛɧɨɝɨ ɤɥɚɫɫɚ.
89
3.7. ɍɫɥɨɜɢɹ ɭɫɬɨɣɱɢɜɨɣ ɪɚɛɨɬɵ ɨɛɪɚɬɧɨɝɨ ɤɥɚɩɚɧɚ
ɜ ɩɭɫɤɨɜɨɦ ɪɟɠɢɦɟ ɜɨɞɨɨɬɥɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ
ɉɪɢ ɩɭɫɤɟ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɧɚɫɨɫɚ ɜɨɞɨɨɬɥɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ ɩɪɢ ɩɨɥɧɨɫɬɶɸ ɡɚɩɨɥɧɟɧɧɨɦ ɜɨɞɨɣ ɧɚɝɧɟɬɚɬɟɥɶɧɨɦ ɬɪɭɛɨɩɪɨɜɨɞɟ ɚɤɬɭɚɥɶɧɵɦɢ
ɹɜɥɹɸɬɫɹ ɜɨɩɪɨɫɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɧɚɞɟɠɧɨɫɬɶɸ ɪɚɛɨɬɵ ɧɚɩɨɪɧɨɝɨ ɨɛɪɚɬɧɨɝɨ
ɤɥɚɩɚɧɚ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɬɤɪɵɥɫɹ ɨɛɪɚɬɧɵɣ ɤɥɚɩɚɧ, ɧɚɩɨɪ,
ɪɚɡɜɢɜɚɟɦɵɣ ɧɚɫɨɫɨɦ ɩɪɢ ɧɭɥɟɜɨɣ ɩɨɞɚɱɟ H
ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɜɵɫɨɬɵ ɜɨɞɨɩɨɞɴɺɦɚ H
ɤɥɚɩɚɧɟ ǻH
ɄɅ
:
0
, ɞɨɥɠɟɧ ɛɵɬɶ ɪɚɜɟɧ ɫɭɦɦɟ
0
ɢ ɩɨɬɟɪɟ ɧɚɩɨɪɚ ɧɚ ɨɛɪɚɬɧɨɦ
Ƚ
HHH '
. (3.73)
ɄɅȽ
ɉɨɬɟɪɹ ɧɚɩɨɪɚ ɧɚ ɨɛɪɚɬɧɨɦ ɤɥɚɩɚɧɟ, ɪɚɫɱɺɬɧɚɹ ɫɯɟɦɚ ɤɨɬɨɪɨɝɨ
ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 3.5, ɩɪɢ ɟɝɨ ɨɬɤɪɵɬɢɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:
PP
H
ɄɅ
'
21
, (3.74)
g
U
ɝɞɟ Ɋ1 ɢ Ɋ2 – ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɞɚɜɥɟɧɢɟ ɜɨɞɵ
ɩɟɪɟɞ ɤɥɚɩɚɧɨɦ ɢ ɡɚ ɤɥɚɩɚɧɨɦ, ɉɚ;
ȡ – ɩɥɨɬɧɨɫɬɶ ɜɨɞɵ, ɤɝ/ɦ3;
2
g – ɭɫɤɨɪɟɧɢɟ ɫɢɥɵ ɬɹɠɟɫɬɢ, ɦ/ɫ
.
Ⱦɥɹ ɨɬɤɪɵɬɢɹ ɨɛɪɚɬɧɨɝɨ ɤɥɚɩɚɧɚ ɛɟɡ
ɭɱɺɬɚ ɟɝɨ ɜɟɫɚ ɞɨɥɠɧɨ ɢɦɟɬɶ ɦɟɫɬɨ ɭɫɥɨɜɢɟ:
Ɋɢɫɭɧɨɤ 3.5. Ɋɚɫɱɟɬɧɚɹ
ɫɯɟɦɚ ɨɛɪɚɬɧɨɝɨ ɤɥɚɩɚɧɚ
P
1
2
d
P
2
ɉɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫɨɨɬɧɨɲɟɧɢɹ (3.75)
ɢɦɟɟɦ:
PP
21
2
D
·
§
t
. (3.76)
¸
¨
d
¹
©
2
D
SS
t
. (3.75)
44
ɂɫɩɨɥɶɡɭɹ ɜɵɪɚɠɟɧɢɹ (3.74) ɢ (3.76), ɚ ɬɚɤɠɟ ɫɱɢɬɚɹ, ɱɬɨ ɩɪɢɛɥɢ-
P
2
ɠɟɧɧɨ
H
|
H
, ɩɨɥɭɱɢɦ:
U
' 11
Ƚ
g
2
D
§
P
PP
21
g
·
¨
¸
2
d
©
¹
g
ª
P
UUU
D
·
§
2
¸
¨
«
d
g
¹
©
«
¬
22
ª
º
D
§
¨
«
»
d
©
«
»
¬
¼
º
·
¸
¹
H
. (3.77)
»
ȽɄɅ
»
¼
90
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