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4) ɜɵɱɢɫɥɹɸɬ ɩɨɬɪɟɛɧɵɣ ɲɚɝ
, ɦɦ, ɡɚɤɥɟɩɨɤ ɩɨ ɮɨɪɦɭɥɟ
t
, (2.57)
tLn
ɝɞɟ L – ɨɛɳɚɹ ɞɥɢɧɚ ɲɜɚ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.23;
5) ɩɨ ɮɨɪɦɭɥɟ (2.52) ɜɵɱɢɫɥɹɸɬ ɩɨɬɪɟɛɧɭɸ ɬɨɥɳɢɧɭ ɥɢɫɬɚ ɩɨɞ ɜɵɛɪɚɧ-
ɧɭɸ ɡɚɤɥɟɩɤɭ. ȿɫɥɢ ɷɬɚ ɬɨɥɳɢɧɚ ɦɟɧɶɲɟ, ɱɟɦ ɞɟɣɫɬɜɢɬɟɥɶɧɚɹ ɬɨɥɳɢɧɚ ɫɨɟɞɢɧɹɟɦɵɯ ɞɟɬɚɥɟɣ, ɬɨ ɷɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫɨɟɞɢɧɟɧɢɟ ɛɭɞɟɬ ɢɦɟɬɶ ɡɚɩɚɫ ɩɪɨɱɧɨɫɬɢ
ɩɨ ɫɦɹɬɢɸ, ɚ ɟɫɥɢ ɛɨɥɶɲɟ, ɬɨ ɬɪɟɛɭɸɬɫɹ
ɤɨɧɫɬɪɭɤɬɢɜɧɵɟ ɦɟɪɨɩɪɢɹɬɢɹ ɩɨ
ɭɬɨɥɳɟɧɢɸ ɥɢɫɬɚ ɜ ɡɨɧɟ ɫɨɟɞɢɧɟɧɢɹ ɜ ɜɢɞɟ ɧɚɜɚɪɢɜɚɟɦɨɣ ɧɚ ɥɢɫɬ ɩɨɥɨɫɵ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.23, ɚ, ɢɥɢ ɜ ɜɢɞɟ ɫɩɥɨɲɧɨɝɨ ɦɟɫɬɧɨɝɨ ɭɬɨɥɳɟɧɢɹ, ɜ
ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.23, ɛ;
ɚ – ɫ ɩɨɞɜɚɪɤɨɣ ɥɢɫɬɚ
ɛ – ɫ ɦɟɫɬɧɵɦ ɭɬɨɥɳɟɧɢɟɦ ɥɢɫɬɚ
Ɋɢɫɭɧɨɤ 2.23 – ȼɨɡɦɨɠɧɵɟ ɤɨɧɫɬɪɭɤɬɢɜɧɵɟ ɪɟɲɟɧɢɹ
ɡɚɤɥɟɩɨɱɧɨɝɨ ɫɨɟɞɢɧɟɧɢɹ
6) ɩɨ ɮɨɪɦɭɥɟ (2.54) ɜɵɱɢɫɥɹɸɬ ɩɨɬɪɟɛɧɵɣ ɲɚɝ ɡɚɤɥɟɩɨɤ. ȿɫɥɢ ɨɧ ɨɤɚɡɵɜɚɟɬɫɹ ɛɨɥɶɲɢɦ (ɢɥɢ ɪɚɜɧɵɦ) ɱɟɦ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɵɣ ɧɚ ɲɢɪɢɧɟ L, ɬɨ
ɷɬɨɬ ɩɨɫɥɟɞɧɢɣ
ɢ ɩɪɢɧɢɦɚɟɬɫɹ ɨɤɨɧɱɚɬɟɥɶɧɨ. ɉɪɢ ɷɬɨɦ ɨɱɟɜɢɞɧɨ, ɩɨɹɜ-
tLn
ɥɹɟɬɫɹ ɧɟɤɨɬɨɪɵɣ ɡɚɩɚɫ ɩɪɨɱɧɨɫɬɢ ɩɨ ɪɚɡɪɵɜɭ ɥɢɫɬɚ;
7) ɩɨ ɮɨɪɦɭɥɟ (2.53) ɜɵɱɢɫɥɹɸɬ ɩɨɬɪɟɛɧɵɣ ɪɚɡɦɟɪ ɚ, ɦɦ.
ȿɫɥɢ ɠɟ ɧɚ ɲɢɪɢɧɟ ɫɨɟɞɢɧɟɧɢɹ L ɧɟ ɭɦɟɳɚɟɬɫɹ ɜ ɨɞɢɧ ɪɹɞ ɩɨɬɪɟɛɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɡɚɤɥɟɩɨɤ ɫ ɩɨɬɪɟɛɧɵɦ ɲɚɝɨɦ, ɬɨ ɫɥɟɞɭɟɬ ɪɚɡɦɟɳɚɬɶ ɷɬɢ ɡɚɤɥɟɩɤɢ ɜ
ɞɜɚ ɪɹɞɚ (
ɜ ɲɚɯɦɚɬɧɨɦ ɩɨɪɹɞɤɟ), ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.24, ɚ.
ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɞɜɭɯɪɹɞɧɨɝɨ ɲɜɚ ɫɜɨɞɢɬɫɹ ɤ ɨɩɪɟɞɟɥɟɧɢɸ ɪɚɫɫɬɨɹɧɢɹ
ɦɟɠɞɭ ɪɹɞɚɦɢ h. ɉɨɬɪɟɛɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɡɚɤɥɟɩɨɤ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ (ɟɫɥɢ ɧɟ ɭɱɢɬɵɜɚɬɶ ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɢɥɵ Ɋ ɩɨ ɡɚɤɥɟɩɤɚɦ) ɨɩɪɟɞɟɥɹɟɬɫɹ
ɚɧɚɥɨɝɢɱɧɨ, ɤɚɤ ɢ ɞɥɹ ɨɞɧɨɪɹɞɧɨɝɨ ɲɜɚ. ɇɨ ɜɨɡɦɨɠɧɵɟ ɮɨɪɦɵ ɪɚɡɪɭɲɟɧɢɹ ɥɢ-
51
ɫɬɨɜ ɢɧɵɟ. Ɋɚɡɪɵɜ ɫɨ ɫɞɜɢɝɨɦ ɥɢɫɬɨɜ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɩɨ
ɩɢɥɨɨɛɪɚɡɧɨɣ ɥɢɧɢɢ abc, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.24, ɛ, ɚ ɬɚɤɠɟ ɩɨ ɥɢɧɢɢ
ɚɫ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.24, ɜ. ɋɯɟɦɚ ɧɚɝɪɭɠɟɧɢɹ ɨɞɧɨɣ ɫɟɤɰɢɢ «ɩɢɥɨ-
ɨɛɪɚɡɧɨɝɨ» ɷɥɟɦɟɧɬɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.24, ɛ.
ɚ – ɲɨɜ ɞɨ ɪɚɡɪɭɲɟɧɢɹ
Ɋɢɫɭɧɨɤ 2.24, ɥɢɫɬ 1 – ȼɨɡɦɨɠɧɵɟ ɮɨɪɦɵ ɪɚɡɪɭɲɟɧɢɹ
ɞɜɭɯɪɹɞɧɨɝɨ ɡɚɤɥɟɩɨɱɧɨɝɨ ɲɜɚ
ɛ – ɪɚɡɪɵɜ ɫɨ ɫɞɜɢɝɨɦ
ɜ – ɪɚɡɪɵɜ
Ɋɢɫɭɧɨɤ 2.24, ɥɢɫɬ 2
52
ɋɭɦɦɚɪɧɚɹ ɫɢɥɚ ɧɚ ɷɥɟɦɟɧɬ
N, ɇ, ɢ ɤɚɫɚɬɟɥɶɧɵɟ Ɍ, ɇ, ɢ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɝɞɟ
ɭɱɟɬɨɦ ɨɫɥɚɛɥɟɧɢɹ ɨɬɜɟɪɫɬɢɹɦɢ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɜɟɪɫɬɢɹɦɢ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɦɭɥɵ (2.60) ɢ (2.61). ɋ ɭɱɟɬɨɦ (2.59) ɩɨɫɥɟ ɧɟɤɨɬɨɪɵɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɩɨɥɭɱɚɸɬ
ɥɨɫɶ, ɫɨɫɬɨɢɬ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɩɨɬɪɟɛɧɨɝɨ ɪɚɫɫɬɨɹɧɢɹ h, ɧɚ ɤɨɬɨɪɨɟ ɧɭɠɧɨ ɫɞɜɢɧɭɬɶ ɩɨɥɨɜɢɧɭ ɡɚɤɥɟɩɨɤ ɜɧɭɬɪɶ ɥɢɫɬɚ. Ⱦɥɹ ɷɬɨɝɨ ɩɨ ɢɦɟɸɳɢɦɫɹ ɭɠɟ ɞɚɧɧɵɦ
ɞɥɹ ɨɞɧɨɪɹɞɧɨɝɨ ɲɜɚ ɜɵɱɢɫɥɹɸɬ ɜɟɥɢɱɢɧɭ d/t ɢ ɢɡ ɭɪɚɜɧɟɧɢɹ (2.62) ɜɵɱɢɫɥɹɸɬ
ɩɨɬɪɟɛɧɭɸ ɜɟɥɢɱɢɧɭ h/t. ɉɨɫɥɟ ɷɬɨɝɨ ɩɨ
ɱɢɫɥɹɸɬ ɪɚɡɦɟɪ h.
ɝɚɹ ɜ ɭɪɚɜɧɟɧɢɢ (2.62)
arctg h t
D
ɇɨɪɦɚɥɶɧɵɟ
ɉɪɢɜɟɞɟɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ
ɇɨɪɦɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ
ɍɫɥɨɜɢɟ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ ɩɨ ɥɢɧɢɹɦ abc ɢ ɚɫ ɩɨɥɭɱɚɸɬ, ɩɪɢɪɚɜɧɹɜ ɮɨɪ-
ɉɪɨɰɟɞɭɪɚ ɩɟɪɟɯɨɞɚ ɨɬ ɨɞɧɨɪɹɞɧɨɝɨ ɤ ɞɜɭɯɪɹɞɧɨɦɭ ɲɜɭ, ɤɚɤ ɭɠɟ ɝɨɜɨɪɢ-
Ⱦɥɹ ɩɪɢɛɥɢɠɟɧɧɨɣ, ɧɨ ɛɵɫɬɪɨɣ ɨɰɟɧɤɢ ɪɚɡɦɟɪɨɜ ɞɜɭɯɪɹɞɧɨɝɨ ɲɜɚ, ɩɨɥɚ-
.
, ɇ/ɦɦ2, ɢ ɤɚɫɚɬɟɥɶɧɵɟ IJ, ɇ/ɦɦ2, ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɝɪɚɧɹɯ ɫ
V
VDDG
°
®
Pn h d
WDDG
°
¯
VG
21421 1dt ht ht ht dt
/0dto
2 Ɋɩ
N Ɋɩ
°
®
T Ɋɩ
°
¯
cos sin
Ɋɩ hd
sin sin
V
ɩɪ
VVW
ɩɪ
, ɇ/ɦɦ2, ɧɚ ɝɪɚɧɢ ɚɫ ɫ ɭɱɟɬɨɦ ɨɫɥɚɛɥɟɧɢɹ ɨɬ-
V
ɚɫ
212
Ɋɩ td
ɚɫ
222
, ɪɚɡɦɟɪ h, ɦɦ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɪɚɫɤɥɚɞɵɜɚɟɬɫɹ ɧɚ ɧɨɪɦɚɥɶɧɵɟ ɫɢɥɵ
cos
D
, (2.58)
sin
D
. (2.59)
, ɇ/ɦɦ2, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
22
. (2.60)
4
ɢɡɜɟɫɬɧɨɦɭ ɲɚɝɭ t ɢ ɜɟɥɢɱɢɧɟ h/t ɜɵ-
. (2.63)
2ht|
. (2.61)
§·
¨¸
©¹
. (2.62)
53
ɋɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɩɪɢ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɢ ɢɡ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɫɨɨɛɪɚɠɟɧɢɣ ɩɪɢɯɨɞɢɬɶɫɹ ɨɬɫɬɭɩɚɬɶ ɨɬ ɪɚɫɱɟɬɧɵɯ ɪɚɡɦɟɪɨɜ ɲɜɚ. Ʉɪɨɦɟ ɬɨɝɨ,
ɞɢɚɦɟɬɪ d ɢ ɲɚɝ ɡɚɤɥɟɩɨɤ ɤɨɪɪɟɤɬɢɪɭɟɬɫɹ (ɬɚɤɠɟ ɜ ɡɚɩɚɫ ɩɪɨɱɧɨɫɬɢ) ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɧɨɪɦɚɥɹɦɢ ɞɥɹ ɨɛɥɟɝɱɟɧɢɹ ɦɟɯɚɧɢɡɚɰɢɢ ɢ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ
ɤɥɟɩɤɢ. ɗɬɨ ɤ ɬɨɦɭ ɠɟ ɭɩɪɨɳɚɟɬ ɩɨɞɝɨɬɨɜɤɭ
ɩɪɨɢɡɜɨɞɫɬɜɚ (ɪɚɡɦɟɬɤɭ, ɢɡɝɨɬɨɜ-
ɥɟɧɢɟ ɲɚɛɥɨɧɨɜ, ɤɨɧɞɭɤɬɨɪɨɜ ɢ ɬ. ɞ.).
Ⱦɥɹ ɨɞɧɨɪɹɞɧɨɝɨ ɡɚɤɥɟɩɨɱɧɨɝɨ ɲɜɚ, ɩɟɪɟɞɚɸɳɟɝɨ ɫɞɜɢɝɚɸɳɭɸ ɫɢɥɭ Ɋ
(ɱɬɨ ɷɤɜɢɜɚɥɟɧɬɧɨ ɩɟɪɟɞɚɱɟ ɫɞɜɢɝɚɸɳɟɝɨ ɩɨɬɨɤɚ ɫɢɥ
/qPL
), ɧɚɩɪɹɠɟɧɢɹ
ɫɪɟɡɚ ɢ ɫɦɹɬɢɹ ɜ ɡɚɤɥɟɩɤɚɯ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɬɟɦ ɠɟ ɮɨɪɦɭɥɚɦ (2.60) ɢ (2.61),
ɱɬɨ ɢ ɞɥɹ ɨɞɧɨɪɹɞɧɨɝɨ ɩɨɩɟɪɟɱɧɨɝɨ ɲɜɚ. ɉɨɷɬɨɦɭ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɞɢɚɦɟɬɪɨɦ ɡɚɤɥɟɩɤɢ d, ɦɦ, ɢ ɬɨɥɳɢɧɨɣ ɥɢɫɬɚ į, ɦɦ, (ɩɪɢ ɬɟɯ ɠɟ ɩɪɟɞɩɨɥɨɠɟɧɢɹɯ) ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
2,5dG
0, 4 d
G
, (2.64)
. (2.65)
ɋɪɟɡ ɩɟɪɟɦɵɱɟɤ ɦɟɠɞɭ ɨɬɜɟɪɫɬɢɹɦɢ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɩɪɨɢɫɯɨɞɢɬ ɧɟ ɩɨɩɟɪɟɤ ɲɜɚ, ɚ ɜɞɨɥɶ ɢ ɩɪɢɱɟɦ ɨɞɧɨɫɬɨɪɨɧɧɟ. ɉɨɷɬɨɦɭ ɭɫɥɨɜɢɟ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ
ɡɚɤɥɟɩɨɤ ɩɪɢ ɫɦɹɬɢɢ ɢ ɫɪɟɡɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ-ɞɪɭɝɨɦɭ. ɍɫɥɨɜɢɟ ɩɪɨɱɧɨɫɬɢ ɡɚɤɥɟɩɤɢ ɩɪɢ ɫɦɹɬɢɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ Ɋ
, ɇ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɷ
1, 5
Ɋ d
VG
ȼɷ
. (2.66)
ɍɫɥɨɜɢɟ ɩɪɨɱɧɨɫɬɢ ɥɢɫɬɚ ɩɪɢ ɫɪɟɡɟ,
, ɇ/ɦɦ2, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧ-
V
ȼ
ɤɨɦ 2.26 ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
0,75
Ptd
VG
ȼɁ
. (2.67)
ɂɡ ɭɫɥɨɜɢɹ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ ɫ ɭɱɟɬɨɦ (2.66) ɢ (2.69) ɲɚɝ
, ɦɦ, ɜɵɱɢɫɥɹɸɬ
t
ɩɨ ɮɨɪɦɭɥɟ
3,14td
. (2.68)
ɉɟɪɟɦɵɱɤɢ ɦɟɠɞɭ ɨɬɜɟɪɫɬɢɟɦ ɢ ɤɪɚɟɦ ɥɢɫɬɚ (
) ɡɞɟɫɶ ɬɚɤɠɟ ɪɚ-
2ɚ d
ɛɨɬɚɸɬ ɩɨ-ɞɪɭɝɨɦɭ, ɬ. ɟ. ɧɟ ɧɚ ɫɪɟɡ, ɤɚɤ ɜ ɩɨɩɟɪɟɱɧɨɦ ɲɜɟ, ɚ ɧɚ ɪɚɡɪɵɜ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ Ɋ
/2, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.25.
3
ɂɡ ɭɫɥɨɜɢɹ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ ɡɚɤɥɟɩɤɢ ɧɚ ɫɦɹɬɢɟ ɢ ɪɚɡɪɵɜ ɩɟɪɟɦɵɱɤɢ
d
(
) ɜɟɥɢɱɢɧɭ ɚ, ɦɦ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɚ
2
1, 7 5ɚ d
. (2.69)
54
Ɋɢɫɭɧɨɤ 2.25 – ɋɯɟɦɚ ɪɚɛɨɬɵ ɨɞɧɨɪɹɞɧɨɝɨ ɡɚɤɥɟɩɨɱɧɨɝɨ ɲɜɚ ɧɚ ɫɞɜɢɝ:
1 – ɥɢɧɢɹ ɫɪɟɡɚ ɩɟɪɟɦɵɱɤɢ ɦɟɠɞɭ ɨɬɜɟɪɫɬɢɹɦɢ; 2 – ɥɢɧɢɹ ɪɚɡɪɵɜɚ ɩɟɪɟɦɵɱɤɢ
ɦɟɠɞɭ ɨɬɜɟɪɫɬɢɹɦɢ ɢ ɤɪɚɟɦ ɥɢɫɬɚ
ɉɪɨɰɟɞɭɪɚ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɬɪɟɛɧɵɯ ɪɚɡɦɟɪɨɜ ɡɚɤɥɟɩɨɱɧɨɝɨ ɲɜɚ, ɪɚɛɨɬɚɸɳɟɝɨ ɧɚ ɫɞɜɢɝ, ɦɨɠɟɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧɚ ɩɪɢɦɟɪɧɨ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɩɪɨɰɟɞɭɪɚ ɪɚɫɱɟɬɚ ɩɨɩɟɪɟɱɧɨɝɨ ɲɜɚ,
Ɂɞɟɫɶ ɬɚɤɠɟ ɦɨɠɟɬ ɜɨɡɧɢɤɧɭɬɶ ɫɢɬɭɚɰɢɹ, ɤɨɝɞɚ ɩɨɬɪɟɛɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɡɚɤɥɟɩɨɤ
ɪɚɡɦɟɫɬɢɬɶ ɜ ɨɞɢɧ ɪɹɞ ɫ ɩɨɬɪɟɛɧɵɦ ɲɚɝɨɦ ɧɟɜɨɡɦɨɠɧɨ. Ɉɝɪɚɧɢɱɟɧɢɟɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɹɜɥɹɟɬɫɹ ɫɪɟɡ ɩɟɪɟɦɵɱɟɤ ɦɟɠɞɭ ɨɬɜɟɪɫɬɢɹɦɢ. ɉɪɢ ɷɬɨɦ ɨɛɟɫɩɟɱɢɬɶ
ɩɪɨɱɧɨɫɬɶ ɲɜɚ ɦɨɠɧɨ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ, ɜɵɞɜɢɠɟɧɢɟɦ
ɜɢɧɵ ɡɚɤɥɟɩɨɤ ɜɨ ɜɬɨɪɨɣ ɪɹɞ ɜ ɲɚɯɦɚɬɧɨɦ ɩɨɪɹɞɤɟ ɧɚ ɪɚɫɫɬɨɹɧɢɟ h ɨɬ ɩɟɪɜɨɝɨ
ɪɹɞɚ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.26, ɚ.
ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɜɨɡɦɨɠɧɵ ɞɜɟ ɮɨɪɦɵ ɪɚɡɪɭɲɟɧɢɹ ɥɢɫɬɚ ɩɨ ɨɬɜɟɪɫɬɢɹɦ:
ɧɨ ɫ ɭɱɟɬɨɦ ɭɤɚɡɚɧɧɵɯ ɜɵɲɟ ɨɫɨɛɟɧɧɨɫɬɟɣ ɪɚɛɨɬɵ.
ɩɨɥɨ-
ɚ – ɲɨɜ ɞɨ ɪɚɡɪɭɲɟɧɢɹ
Ɋɢɫɭɧɨɤ 2.26, ɥɢɫɬ 1 – ȼɨɡɦɨɠɧɵɟ ɮɨɪɦɵ ɪɚɡɪɭɲɟɧɢɹ ɞɜɭɯɪɹɞɧɨɝɨ ɲɜɚ,
ɪɚɛɨɬɚɸɳɟɝɨ ɧɚ ɫɞɜɢɝ
55
ɛ – ɪɚɡɪɵɜ ɫɨ ɫɞɜɢɝɨɦ
ɜ – ɱɢɫɬɵɣ ɫɞɜɢɝ
Ɋɢɫɭɧɨɤ 2.26, ɥɢɫɬ 2 – ȼɨɡɦɨɠɧɵɟ ɮɨɪɦɵ ɪɚɡɪɭɲɟɧɢɹ ɞɜɭɯɪɹɞɧɨɝɨ ɲɜɚ,
ɪɚɛɨɬɚɸɳɟɝɨ ɧɚ ɫɞɜɢɝ
ɚ) ɪɚɡɪɵɜ ɫɨ ɫɞɜɢɝɨɦ ɩɨ ɩɢɥɨɨɛɪɚɡɧɨɣ ɥɢɧɢɢ abc, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.26, ɛ;
ɛ) ɫɪɟɡ ɩɨ ɥɢɧɢɢ ac, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.26, ɜ.
Ⱦɥɹ ɩɟɪɜɨɣ ɮɨɪɦɵ ɪɚɡɪɭɲɟɧɢɹ ɫɭɦɦɚɪɧɚɹ ɫɢɥɚ
ɝɪɚɧɹɯ ɬɪɟɭɝɨɥɶɧɨɝɨ ɷɥɟɦɟɧɬɚ ɧɚ ɧɨɪɦɚɥɶɧɵɟ N, ɇ, ɢ ɤɚɫɚɬɟɥɶɧɵɟ Ɍ, ɇ, ɤɨɬɨɪɵɟ
ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
N Ɋɩ
ɂɫɩɨɥɶɡɭɹ, ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ, ɭɫɥɨɜɢɟ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ ɲɜɚ ɩɨ
ɥɢɧɢɢ abc ɢ ac, ɩɨɥɭɱɚɟɦ ɩɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɬɪɟɛɧɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ h/t ɩɪɢ ɢɡɜɟɫɬɧɨɦ d/t ɫɥɟɞɭɸɳɟɝɨ ɜɢɞɚ
24 2,861 1dt ht ht ht dt
°
®
T Ɋɩ
°
¯
222
56
ɪɚɫɤɥɚɞɵɜɚɟɬɫɹ ɧɚ
2Ɋɩ
sin
D
. (2.70)
cos
D
§·
¨¸
©¹
. (2.71)
ȼɨ ɦɧɨɝɢɯ ɫɥɭɱɚɹɯ ɡɚɤɥɟɩɨɱɧɵɟ ɲɜɵ ɜɨɫɩɪɢɧɢɦɚɸɬ ɤɚɤ ɧɨɪɦɚɥɶɧɭɸ P
ɬɚɤ ɢ ɫɞɜɢɝɚɸɳɭɸ
ɧɚɝɪɭɡɤɭ ɨɞɧɨɜɪɟɦɟɧɧɨ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.27.
Ɋ
W
,
N
Ɋɢɫɭɧɨɤ 2.27 – ɋɯɟɦɚ ɨɞɧɨɪɹɞɧɨɝɨ ɡɚɤɥɟɩɨɱɧɨɝɨ ɲɜɚ, ɜɨɫɩɪɢɧɢɦɚɸɳɟɝɨ
ɧɨɪɦɚɥɶɧɭɸ ɢ ɫɞɜɢɝɚɸɳɭɸ ɧɚɝɪɭɡɤɢ ɨɞɧɨɜɪɟɦɟɧɧɨ
ȼ ɷɬɢɯ ɫɥɭɱɚɹɯ ɧɚɩɪɹɠɟɧɢɹ ɜ ɤɚɠɞɨɣ ɡɚɤɥɟɩɤɟ
ɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
22 2
PP n d
WS
ɉɪɢ ɬɟɯ ɠɟ ɞɨɩɭɳɟɧɢɹɯ, ɱɬɨ ɢ ɞɥɹ ɲɜɨɜ ɫ ɩɪɨɫɬɵɦ ɧɚɝɪɭɠɟɧɢɟɦ, ɩɨɬɪɟɛɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɞɢɚɦɟɬɪɨɦ ɡɚɤɥɟɩɨɤ d, ɦɦ, ɢ ɬɨɥɳɢɧɨɣ ɥɢɫɬɚ
ɚɧɚɥɨɝɢɱɧɵ ɢ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɍɫɥɨɜɢɟ ɠɟ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ ɩɪɢ ɫɦɹɬɢɢ ɡɚɤɥɟɩɤɢ ɢ ɩɪɢ ɫɪɟɡɟ ɥɢɫɬɚ ɩɨ
ɧɨɪɦɚɥɢ ɤ ɲɜɭ ɛɭɞɟɬ ɞɪɭɝɢɦ. ɍɫɥɨɜɢɟ ɩɪɨɱɧɨɫɬɢ ɩɪɢ ɫɦɹɬɢɢ ɡɚɤɥɟɩɤɢ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɍɫɥɨɜɢɟ ɩɪɨɱɧɨɫɬɢ ɩɪɢ ɫɪɟɡɟ ɩɟɪɟɦɵɱɤɢ ɦɟɠɞɭ ɨɬɜɟɪɫɬɢɟɦ ɢ ɤɪɚɟɦ ɥɢɫɬɚ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
Nx
3
22
V
PPndS
ɫɦ Nx
G
1, 5
V
ɫɦ Nx
2,5dG
, (2.74)
0, 4 d
PPndS
. (2.75)
22
, ɇ/ɦɦ2,
W
3
4
, (2.72)
. (2.73)
. (2.76)
, ɇ/ɦɦ2, ɜɵ-
V
ɫɦ
G
, ɦɦ,
57
ɂɡ ɭɫɥɨɜɢɹ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ ɫ ɭɱɟɬɨɦ (2.76) ɢ (2.77) ɜɟɥɢɱɢɧɭ ɚ, ɦɦ, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɉɨɬɪɟɛɧɵɣ ɲɚɝ ɡɚɤɥɟɩɨɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɫɥɨɜɢɹ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ ɩɪɢ
ɫɦɹɬɢɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ
ɫɬɢɹɦɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɪɟɡɚɸɳɟɣ ɫɢɥɵ
ɩɨ ɮɨɪɦɭɥɚɦ
ȿɫɥɢ ɧɚ ɲɢɪɢɧɟ ɫɨɟɞɢɧɟɧɢɹ L ɧɟ ɭɦɟɳɚɟɬɫɹ ɜ ɨɞɢɧ ɪɹɞ ɩɨɬɪɟɛɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɡɚɤɥɟɩɨɤ ɫ ɩɨɬɪɟɛɧɵɦ ɲɚɝɨɦ, ɬɨ ɫɥɟɞɭɟɬ ɩɟɪɟɯɨɞɢɬɶ ɧɚ ɞɜɭɯɪɹɞɧɵɣ ɲɨɜ
ɜ ɲɚɯɦɚɬɧɨɦ ɩɨɪɹɞɤɟ, ɜɵɞɜɢɝɚɹ ɩɨɥɨɜɢɧɭ ɡɚɤɥɟɩɨɤ ɜɨ ɜɬɨɪɨɣ ɪɹɞ ɧɚ ɪɚɫɫɬɨɹɧɢɟ h. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɡɦɟɪɚ h ɬɚɤ ɠɟ, ɤɚɤ ɢ ɞɥɹ ɲɜɨɜ ɫ ɩɪɨɫɬɵɦ
ɟɦ, ɢɫɩɨɥɶɡɭɟɬɫɹ ɭɫɥɨɜɢɟ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ ɩɨ ɥɢɧɢɹɦ abc ɢ ac, ɧɨ ɫ ɨɞɧɨɜɪɟɦɟɧɧɵɦ ɧɚɝɪɭɠɟɧɢɟɦ ɫɢɥɚɦɢ
ɥɭɱɚɟɦ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɧɨɪɦɚɥɶɧɵɯ
ɠɟɧɢɣ ɧɚ ɝɪɚɧɹɯ ɬɪɟɭɝɨɥɶɧɨɝɨ ɷɥɟɦɟɧɬɚ, ɤɨɬɨɪɵɟ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
ɉɪɢɜɟɞɟɧɧɵɟ ɧɚɩɪɹɠɟɧɢɹ
ɦɭɥɟ
ɂɡ ɭɫɥɨɜɢɹ ɪɚɜɧɨɩɪɨɱɧɨɫɬɢ ɩɨ ɥɢɧɢɹɦ abc ɢ ac ɫ ɭɱɟɬɨɦ ɮɨɪɦɭɥ (2.81)–
(2.83) ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɬɪɟɛɧɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ h/t ɩɪɢ
ɢɡɜɟɫɬɧɵɯ ɜɟɥɢɱɢɧɚɯ d/t ɢ
PP nd P Pntd
VDD DG
WDD DG
0,7 2 2
ɚ dPP
22 2 2
Nx N x
t d PP PP
1, 5 4
§·
11,5 14 1
¨¸
©¹
cos sin sin
PPnhd
Nx
sin cos sin
PP nhd
Nx
ɚɫ ntd P P
VG
ɩɪ N
Pnad
VG
ȼ N
§·
¨¸
©¹
0,5 1,07 1
22
PP
N
W
xN
ɢ ɪɚɡɪɭɲɟɧɢɹ ɩɟɪɟɦɵɱɤɢ ɦɟɠɞɭ ɨɬɜɟɪ-
ɢ ɧɨɪɦɚɥɶɧɨɣ ɫɢɥɵ ɊN ɜɵɱɢɫɥɹɸɬ
Ɋ
W
GG
ɢ ɊN. Ɉɛɴɟɞɢɧɹɹ ɨɛɟ ɫɯɟɦɵ ɧɚɝɪɭɠɟɧɢɹ, ɩɨ-
Ɋ
W
ɚɫ
V
ɩɪ
22 4
/ɊN, ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
Ɋ
W
22
xN xN
, ɇ/ɦɦ2, ɢ ɤɚɫɚɬɟɥɶɧɵɯW, ɇ/ɦɦ2, ɧɚɩɪɹ-
V
, ɇ/ɦɦ2, ɧɚ ɝɪɚɧɢ ac ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪ-
. (2.77)
2
. (2.78)
22
W
, (2.79)
. (2.80)
ɧɚɝɪɭɠɟɧɢ-
, (2.81)
. (2.82)
. (2.83)
58
§·§·
dhh
§·
21 4
¨¸
©¹
¨¸¨¸
tPttP
©¹©¹
22
§·
hhd
§· §·
21 1 1 4
¨¸
¨¸ ¨¸
tttP
¨¸
©¹ ©¹
©¹
22
PP
WW
NN
(2.84)
2
§·
P
W
¨¸
N
©¹
Ɂɚɞɚɱɚ ɪɚɛɨɬɵ
Ɋɚɫɫɱɢɬɚɬɶ ɢ ɫɤɨɧɫɬɪɭɢɪɨɜɚɬɶ ɡɚɤɥɟɩɨɱɧɨɟ ɫɨɟɞɢɧɟɧɢɟ ɫɬɵɤɨɜɨɝɨ ɲɩɚɧɝɨɭɬɚ (ɬɨɥɳɢɧɚ ɩɨɹɫɚ
ɜɵɟ ɧɚɝɪɭɡɤɢ, ɤɨɬɨɪɵɟ ɜɨɡɧɢɤɚɸɬ ɨɬ ɢɡɝɢɛɚɸɳɟɝɨ ɦɨɦɟɧɬɚ
ɫɢɥɵ
d, t, ɚ
, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫɭɧɤɨɦ 2.28, ɚ. Ɉɩɪɟɞɟɥɢɬɶ ɩɨɬɪɟɛɧɵɟ ɪɚɡɦɟɪɵ:
Nr
, ɚɲɩ.
ɨɛ
) ɫ ɨɛɲɢɜɤɨɣ ɬɨɥɳɢɧɨɣ
G
ɲɩ
, ɜɨɫɩɪɢɧɢɦɚɸɳɟɣ ɨɫɟ-
G
ɨɛ
ɢ ɩɪɨɞɨɥɶɧɨɣ
Ɇr
ȼ ɫɥɭɱɚɟ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɟɪɟɯɨɞɚ ɧɚ ɞɜɭɯɪɹɞɧɵɣ ɲɨɜ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ
ɪɢɫɭɧɤɨɦ 2.28, ɛ, ɨɩɪɟɞɟɥɢɬɶ ɬɚɤɠɟ ɪɚɡɦɟɪ h ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɡɧɚɱɟɧɢɟ ɚ
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ 2.5.
.
ɲɩ
ɚ – ɫɯɟɦɚ ɧɚɝɪɭɠɟɧɢɹ ɲɩɚɧɝɨɭɬɚ
Ɋɢɫɭɧɨɤ 2.28, ɥɢɫɬ 1 – Ɂɚɤɥɟɩɨɱɧɨɟ ɫɨɟɞɢɧɟɧɢɟ
ɫɬɵɤɨɜɨɝɨ ɲɩɚɧɝɨɭɬɚ ɤɨɪɩɭɫɚ
59
ʋ
ɜɚɪ.
D,
ɦɦ
,
(ɇ
)·10
-2
,
ɇ
·10
-2
,
ɦɦ
,
ɦɦ
Ɇɚɬɟɪɢɚɥ ɢ ɟɝɨ ɩɪɨɱɧɨɫɬɶ
ɩɪɢ ɪɚɫɱɟɬɧɨɣ t
°C
Ɉɛɲɢɜɤɚ
ɒɩɚɧɝɨɭɬ
Ɂɚɤɥɟɩɤɢ
1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
300
300
300
300
300
300
50
75
100
125
150
175
250
375
500
625
750
875
2
2,2
2,5
2,8
3
3,2
1
1,5
2
2,2
2,5
2,8
ɇ/ɦɦ
2
ɇ/ɦɦ
2
ɇ/ɦɦ
2
ɛ – ɨɞɧɨɪɹɞɧɵɣ ɲɨɜ
Ɋɢɫɭɧɨɤ 2.28, ɥɢɫɬ 2 – Ɂɚɤɥɟɩɨɱɧɨɟ ɫɨɟɞɢɧɟɧɢɟ
Ɇ
ɢɡɝ
ɦ
ɜ – ɞɜɭɯɪɹɞɧɵɣ ɲɨɜ
ɫɬɵɤɨɜɨɝɨ ɲɩɚɧɝɨɭɬɚ ɤɨɪɩɭɫɚ
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ
G
ɲɩ
G
ɨɛ
N
Al
ɫɩɥɚɜ
= 350
V
Bt
60
Ɍɚɛɥɢɰɚ 2.5
Al
ɫɩɥɚɜ
= 320
V
Bt
Al
ɫɩɥɚɜ
= 300
V
Bt
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