ɋɨɫɬɚɜɥɹɸɳɢɟ ɤɨɦɩɥɟɤɫɧɨɣ ɦɚɝɧɢɬɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɢ ɬɚɧɝɟɧɫ ɭɝɥɚ ɦɚɝɧɢɬɧɵɯ ɩɨɬɟɪɶ ɧɚɢɛɨɥɟɟ ɩɨɥɧɨ ɨɩɢɫɵɜɚɸɬ ɩɪɨɰɟɫɫɵ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɜ ɩɟɪɟɦɟɧɧɵɯ ɩɨɥɹɯ.
ȼɥɢɹɧɢɟ ɜɢɯɪɟɜɵɯ ɬɨɤɨɜ ɜ ɨɛɥɚɫɬɢ ɫɥɚɛɵɯ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɫ ɩɨɦɨɳɶɸ ɫɥɟɞɭɸɳɢɯ ɜɵɪɚɠɟɧɢɣ, ɩɨɥɭɱɟɧɧɵɯ ɢɡ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ ɞɥɹ ɩɪɨɜɨɞɹɳɢɯ ɮɟɪɪɨɦɚɝɧɟɬɢɤɨɜ:
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P |
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sh p sin p |
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Pc = |
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ɪɧ |
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; |
(4.20) |
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ch p cos p |
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tg į |
ɦ |
= |
sh p sin p |
, |
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(4.21) |
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sh p sin p |
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ɝɞɟ ȝɧ – ɧɚɱɚɥɶɧɚɹ ɦɚɝɧɢɬɧɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ (ɧɢɡɤɨɱɚɫɬɨɬɧɨɟ ɡɧɚɱɟɧɢɟ); ɪ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
ɪ = 2ʌd |
Pɧ f |
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, |
(4.22) |
U10 |
9 |
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ɜ ɤɨɬɨɪɨɦ d – ɧɚɢɦɟɧɶɲɢɣ ɪɚɡɦɟɪ ɫɟɱɟɧɢɹ ɫɟɪɞɟɱɧɢɤɚ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ [ɫɦ]; ȡ – ɭɞɟɥɶɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɟɪɞɟɱɧɢɤɚ [Ɉɦ · ɫɦ].
4.2. ɉɪɨɰɟɫɫɵ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ
ɋɦɟɳɟɧɢɟ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ
ȼ ɬɨɣ ɨɛɥɚɫɬɢ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ, ɤɨɬɨɪɚɹ ɨɛɭɫɥɨɜɥɟɧɚ ɨɛɪɚɬɢɦɵɦɢ ɢ ɧɟɨɛɪɚɬɢɦɵɦɢ ɫɦɟɳɟɧɢɹɦɢ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ, ɧɚɦɚɝɧɢɱɢɜɚɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɡɚ ɫɱɟɬ ɭɜɟɥɢɱɟɧɢɹ ɨɛɴɟɦɨɜ ɞɨɦɟɧɨɜ, ɜɟɤɬɨɪ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɤɨɬɨɪɵɯ ɫɨɫɬɚɜɥɹɟɬ ɧɚɢɦɟɧɶɲɢɣ ɭɝɨɥ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɪɢɫ. 4.7).
Ɍɚɤɨɣ ɩɨɞɯɨɞ ɹɜɥɹɟɬɫɹ ɭɩɪɨɳɟɧɧɵɦ, ɬɚɤ ɤɚɤ ɜ ɨɛɪɚɡɰɟ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚ ɢɦɟɟɬɫɹ ɦɧɨɝɨ ɜɡɚɢɦɨɫɜɹɡɚɧɧɵɯ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ, ɬ. ɟ. ɫɦɟɳɟɧɢɟ ɹɜɥɹɟɬɫɹ ɤɨɨɩɟɪɚɬɢɜɧɵɦ ɩɪɨɰɟɫɫɨɦ. Ɍɟɦ ɧɟ ɦɟɧɟɟ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɦɨɠɧɨ ɡɚɦɟɧɢɬɶ ɜɫɸ ɫɨɜɨɤɭɩɧɨɫɬɶ ɝɪɚɧɢɰ ɨɞɧɨɣ ɭɫɪɟɞɧɟɧɧɨɣ ɢɡɨɥɢɪɨɜɚɧɧɨɣ ɝɪɚɧɢɰɟɣ, ɜɤɥɸɱɚɸɳɟɣ ɜ ɫɟɛɹ ɫɜɨɣɫɬɜɚ ɞɪɭɝɢɯ ɝɪɚɧɢɰ (ɷɬɨ ɜ ɩɪɢɧɰɢɩɟ ɩɨɡɜɨɥɹɟɬ ɜɵɹɜɢɬɶ ɜɫɟ ɹɜɥɟɧɢɹ, ɫɜɹɡɚɧɧɵɟɫɞɜɢɠɟɧɢɟɦɝɪɚɧɢɰ).
Ɉɛɨɡɧɚɱɢɦ ɫɢɦɜɨɥɨɦ S ɩɥɨɳɚɞɶ ɝɪɚɧɢɰɵ, ɪɚɡɞɟɥɹɸɳɟɣ ɞɜɚ ɞɨɦɟɧɚ ɫ ɨɛɴɟɦɚɦɢ V1 ɢ V2 ɢ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɹɦɢ Ɇ1 ɢ Ɇ2 (ɪɢɫ. 4.7).
121
Ɉɪɢɟɧɬɚɰɢɹ ɝɪɚɧɢɰɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɟɤɬɨɪɨɜ Ɇ1 ɢ Ɇ2 ɨɩɪɟɞɟɥɹɟɬɫɹ ɨɛ-
ɳɢɦ ɬɪɟɛɨɜɚɧɢɟɦ ɧɟɩɪɟɪɵɜɧɨɫɬɢ ɧɨɪɦɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɧɚ ɝɪɚɧɢɰɟ, ɩɨɷɬɨɦɭ ɝɪɚɧɢɰɚ ɩɚɪɚɥɥɟɥɶɧɚ ɪɚɡɧɨɫɬɢ ɜɟɤɬɨɪɨɜ (Ɇ1 – Ɇ2). ɗɧɟɪɝɢɹ ɨɛɨɢɯ ɞɨɦɟ-
ɧɨɜ ɜɨ ɜɧɟɲɧɟɦ ɩɨɥɟ ɇ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ (V1Ɇ1 + V2Ɇ2) ɇ. ɉɨɥɟ ɞɨɥɠɧɨ ɛɵɬɶ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɵɦ, ɱɬɨɛɵ ɨɫɧɨɜ-
ɧɚɹ ɤɨɧɮɢɝɭɪɚɰɢɹ ɞɨɦɟɧɨɜ ɧɟ ɢɡɦɟɧɢɥɚɫɶ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɩɨɥɹ ɝɪɚɧɢɰɚ ɫɦɟɳɚɟɬɫɹ ɧɚ įɯ, ɩɪɢ ɷɬɨɦ ɷɧɟɪɝɢɹ ɢɡɦɟɧɹɟɬɫɹ ɧɚ ɜɟɥɢɱɢɧɭ
įȿɇ = –ȝ0 (Ɇ1 – Ɇ2)ɇSįɯ = –ȝ0ɆSH(cos Į1 – cos Į2)Sįɯ. (4.23)
ȼ ɱɚɫɬɧɨɦ ɫɥɭɱɚɟ 180º-ɣ ɝɪɚɧɢɰɵ ɢ ɩɨɥɹ, ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɸ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ, Į1 = 0 ɢ Į2 = 180º, ɨɬɤɭɞɚ ɫɥɟɞɭɟɬ
įȿɇ = –2ȝ0ɆSHSįɯ = –2ȝ0ɆSHįV. |
(4.24) |
ȿɫɥɢ ɞɨ ɜɨɡɞɟɣɫɬɜɢɹ ɩɨɥɹ ɇ ɝɪɚɧɢɰɚ ɧɚɯɨɞɢɥɚɫɶ ɜ ɫɨɫɬɨɹɧɢɢ ɪɚɜɧɨɜɟɫɢɹ, ɬɨ ɩɪɢ ɜɤɥɸɱɟɧɢɢ ɩɨɥɹ ɢɡ ɨɛɳɟɝɨ ɭɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ ɫɥɟɞɭɟɬ
įȿɩɨɥɧ = į(ȿ + ȿɇ) = 0, |
(4.25) |
ɝɞɟ ȿ ɜɤɥɸɱɚɟɬ ɜɫɟ ɜɨɡɦɨɠɧɵɟ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɜɤɥɚɞɵ, ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɜɨ ɜɧɟɲɧɟɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ȿɇ.
ȼɵɪɚɠɟɧɢɟ (4.25) ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
–įȿɇ = ȝ0ɆSH(cos Į1 – cos Į2)Sįɯ = įȿ. |
(4.26) |
ɂɡ (4.26) ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɜɧɟɲɧɟɟ ɩɨɥɟ ɇ = ɇ(x), ɭɞɟɪɠɢɜɚɸɳɟɟ ɝɪɚɧɢɰɭ ɜ ɫɨɫɬɨɹɧɢɢ ɪɚɜɧɨɜɟɫɢɹ ɜ ɩɨɥɨɠɟɧɢɢ ɯ:
ɇ(ɯ) = |
1 |
§ wE · |
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¨ ¸ . |
(4.27) |
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>SMS (cos D1 |
cos D2 )@P0 |
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© wx ¹x |
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ɂɡɦɟɧɟɧɢɟ ɷɧɟɪɝɢɢ įȿɇ (4.23) ɷɤɜɢɜɚɥɟɧɬɧɨ ɪɚɛɨɬɟ, ɫɨɜɟɪɲɚɟɦɨɣ ɩɪɢ ɩɟɪɟɦɟɳɟɧɢɢ ɝɪɚɧɢɰɵ ɧɚ ɪɚɫɫɬɨɹɧɢɟ įɯ ɫɢɥɨɣ, ɩɪɢɥɨɠɟɧɧɨɣ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɟɟ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɪɚɜɧɨɣ ɆSH(cos Į1 – cos Į2)S. ɂɧɵ-
ɦɢ ɫɥɨɜɚɦɢ: ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɤɚɡɵɜɚɟɬ ɧɚ ɟɞɢɧɢɰɭ ɩɨɜɟɪɯɧɨɫɬɢ ɝɪɚɧɢɰɵ ɷɮɮɟɤɬɢɜɧɨɟ ɞɚɜɥɟɧɢɟ ɪ:
122
ɪ = ȝ0ɆSH(cos Į1 – cos Į2) = ȝ0(Ɇ1 – Ɇ2)ɇ. |
(4.28) |
ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɞɚɜɥɟɧɢɹ ɪ ɝɪɚɧɢɰɚ ɩɪɢɯɨɞɢɬ ɜ ɞɜɢɠɟɧɢɟ, ɤɨɬɨɪɨɟ ɩɪɨɞɨɥɠɚɟɬɫɹ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɫɨɡɞɚɧɧɨɟ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɞɚɜɥɟɧɢɟ ɧɟ ɭɪɚɜɧɨɜɟɫɢɬɫɹ ɜɨɡɜɪɚɳɚɸɳɟɣ ɫɢɥɨɣ R, ɩɪɟɩɹɬɫɬɜɭɸɳɟɣ ɢɡɦɟɧɟɧɢɸ ɩɨɥɨɠɟɧɢɹ ɝɪɚɧɢɰɵ ɢ ɨɛɭɫɥɨɜɥɟɧɧɨɦɭ ɢɦ ɭɜɟɥɢɱɟɧɢɸ ɷɧɟɪɝɢɢ ȿ. ȼɨɡɜɪɚɳɚɸɳɚɹ ɫɢɥɚ, ɪɚɫɫɱɢɬɚɧɧɚɹ, ɤɚɤ ɢ ɞɚɜɥɟɧɢɟ, ɧɚ ɟɞɢɧɢɰɭ ɩɨɜɟɪɯɧɨɫɬɢ ɝɪɚɧɢɰɵ, ɪɚɜɧɚ:
R = – |
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wE |
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(4.29) |
S |
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wx |
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ȼ ɫɨɫɬɨɹɧɢɢ ɪɚɜɧɨɜɟɫɢɹ |
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ɪ(ɇ) + R(x) = 0, |
(4.30) |
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ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɫɥɨɜɢɸ (4.27), ɢɡ ɤɨɬɨɪɨɝɨ ɜɵɬɟɤɚɟɬ, ɱɬɨ ɩɨɞɜɢɠɧɨɫɬɶ ɝɪɚɧɢɰɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɨɢɡɜɨɞɧɨɣ wȿ
wɯ , ɚ ɷɧɟɪɝɢɹ ɤɪɢɫɬɚɥɥɚ ɡɚɜɢɫɢɬ ɨɬ ɩɨɥɨɠɟɧɢɹ ɝɪɚɧɢɰɵ.
ȼɨɬɫɭɬɫɬɜɢɟ ɜɧɟɲɧɟɝɨ ɩɨɥɹ ɷɧɟɪɝɢɹ ɤɪɢɫɬɚɥɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɟ ɬɨɥɶɤɨ ɷɧɟɪɝɟɬɢɱɟɫɤɢɦɢ ɜɤɥɚɞɚɦɢ (ɫɦ. ɝɥ. 3), ɤɨɬɨɪɵɟ ɜ ɡɧɚɱɢɬɟɥɶɧɨɣ ɫɬɟɩɟɧɢ ɨɩɪɟɞɟɥɹɸɬ ɞɨɦɟɧɧɭɸ ɫɬɪɭɤɬɭɪɭ ɢ ɩɨɥɨɠɟɧɢɟ ɝɪɚɧɢɰ, ɧɨ ɢ ɷɧɟɪɝɢɟɣ, ɫɜɹɡɚɧɧɨɣ ɫ ɪɚɡɥɢɱɧɵɦɢ ɞɟɮɟɤɬɚɦɢ ɢ ɧɟɫɨɜɟɪɲɟɧɫɬɜɚɦɢ ɤɪɢɫɬɚɥɥɚ (ɞɢɫɥɨɤɚɰɢɹɦɢ, ɩɨɪɚɦɢ, ɧɟɦɚɝɧɢɬɧɵɦɢ ɜɤɥɸɱɟɧɢɹɦɢ, ɦɟɯɚɧɢɱɟɫɤɢɦɢ ɧɚɩɪɹɠɟɧɢɹɦɢ ɢ ɬ. ɞ.). ȼɥɢɹɧɢɟ ɩɨɫɥɟɞɧɢɯ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɷɧɟɪɝɢɢ ɤɪɢɫɬɚɥɥɚ ɨɬ ɩɨɥɨɠɟɧɢɹ ɝɪɚɧɢɰ ɧɨɫɢɬ ɧɟɪɟɝɭɥɹɪɧɵɣ, ɮɥɭɤɬɭɢɪɭɸɳɢɣ ɯɚɪɚɤɬɟɪ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.8, ɚ.
ȼɨɬɫɭɬɫɬɜɢɟ ɩɨɥɹ ɝɪɚɧɢɰɚ ɡɚɧɢɦɚɟɬ ɤɚɤɨɟ-ɥɢɛɨ ɫɬɚɛɢɥɶɧɨɟ ɩɨɥɨɠɟɧɢɟ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɥɨɤɚɥɶɧɵɦ ɦɢɧɢɦɭɦɨɦ ɧɚ ɤɪɢɜɨɣ ȿ(ɯ) ɢɥɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɧɭɥɹɦɢ ɮɭɧɤɰɢɢ R(x) (ɪɢɫ. 4.8, ɛ), ɧɚɩɪɢɦɟɪ ɩɨɥɨɠɟɧɢɟɦ ɯ0. ȿɫɥɢ ɜɤɥɸɱɢɬɶ ɢ ɧɚɱɚɬɶ ɭɜɟɥɢɱɢɜɚɬɶ ɦɚɝɧɢɬɧɨɟ ɩɨ-
ɥɟ, ɬɨ ɝɪɚɧɢɰɚ ɫɧɚɱɚɥɚ ɛɭɞɟɬ ɨɛɪɚɬɢɦɨ ɞɜɢɝɚɬɶɫɹ ɜ ɩɪɟɞɟɥɚɯ ɫɜɨɟɣ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɹɦɵ ɞɨ ɤɨɨɪɞɢɧɚɬɵ ɯ1, ɩɪɢ ɷɬɨɦ ȿ(ɯ) ɛɭɞɟɬ ɭɜɟɥɢɱɢɜɚɬɶɫɹ (ɪɢɫ. 4.8, ɚ). Ɉɛɪɚɬɢɦɨɫɬɶ ɫɦɟɳɟɧɢɹ ɝɪɚɧɢɰɵ ɜɵɪɚɠɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɟɫɥɢ ɨɬɤɥɸɱɢɬɶ ɩɨɥɟ ɞɨ ɦɨɦɟɧɬɚ ɞɨɫɬɢɠɟɧɢɹ ɝɪɚɧɢɰɟɣ ɤɨɨɪɞɢɧɚɬɵ ɯ1, ɬɨ ɝɪɚɧɢɰɚ ɜɨɡɜɪɚɬɢɬɫɹ ɜ ɬɨɱɤɭ ɯ0.
123
Ɋɢɫ. 4.8. ȼɥɢɹɧɢɟ ɩɨɥɨɠɟɧɢɹ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɧɚ ɷɧɟɪɝɢɸ ɤɪɢɫɬɚɥɥɚ (ɚ) ɢ ɜɨɡɜɪɚɳɚɸɳɭɸ ɫɢɥɭ (ɛ)
ɉɪɢ ɞɨɫɬɢɠɟɧɢɢ ɩɨɥɟɦ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɤɪɢɬɢɱɟɫɤɨɝɨ ɡɧɚɱɟɧɢɹ ɯ1, ɤɨɬɨɪɨɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɨɥɨɠɟɧɢɸ ɦɚɤɫɢɦɭɦɚ ɧɚ ɤɪɢɜɨɣ R(x), ɝɪɚɧɢɰɚ ɨɫɜɨɛɨɠɞɚɟɬɫɹ ɢɡ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɹɦɵ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɬɨɱɤɢ ɯ0 ɢ ɧɟɨɛɪɚɬɢɦɨ ɩɟɪɟɦɟɳɚɟɬɫɹ ɫɤɚɱɤɨɦ ɜ ɬɨɱɤɭ ɯ2 (ɫɤɚɱɨɤ
Ȼɚɪɤɝɚɭɡɟɧɚ). ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ ɩɨɥɹ ɫɧɨɜɚ ɩɪɨɢɫɯɨɞɢɬ ɨɛɪɚɬɢɦɨɟ ɫɦɟɳɟɧɢɟ ɝɪɚɧɢɰɵ ɜɩɥɨɬɶ ɞɨ ɬɨɱɤɢ ɯ3, ɡɚ ɤɨɬɨɪɵɦ ɫɥɟ-
ɞɭɟɬ ɫɤɚɱɨɤ ɜ ɩɨɥɨɠɟɧɢɟ ɯ4 ɢ ɬ. ɞ. ȼɨɡɧɢɤɧɨɜɟɧɢɟ ɝɢɫɬɟɪɟɡɢɫɚ ɨɛɴ-
ɹɫɧɹɟɬɫɹ ɬɟɦ, ɱɬɨ ɩɪɢ ɭɦɟɧɶɲɟɧɢɢ ɩɨɥɹ ɞɨ ɧɭɥɹ ɝɪɚɧɢɰɚ ɧɟ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɢɫɯɨɞɧɨɟ ɩɨɥɨɠɟɧɢɟ, ɚ ɨɫɬɚɟɬɫɹ ɜ ɛɥɢɠɚɣɲɟɣ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɹɦɟ ɧɚ ɤɪɢɜɨɣ ȿ(ɯ).
ɇɚ ɨɫɧɨɜɚɧɢɢ ɷɬɢɯ ɪɚɫɫɭɠɞɟɧɢɣ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɨɛɳɟɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ, ɜɵɡɜɚɧɧɨɣ ɫɦɟɳɟɧɢɟɦ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɜ ɩɨɥɟ ɇ ɝɪɚɧɢɰɚ ɧɚɯɨɞɢɬɫɹ ɜ ɧɟɤɨɬɨɪɨɦ ɪɚɜɧɨɜɟɫɧɨɦ ɩɨɥɨɠɟɧɢɢ ɯ. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɩɨɥɹ ɧɚ ǻɇ ɝɪɚɧɢɰɚ ɫɦɟɫɬɢɬɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ ǻɯ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɤɨɦɩɨɧɟɧɬɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɨɥɹ ɜɨɡɪɚɫɬɟɬ ɧɚ ɜɟɥɢɱɢɧɭ, ɪɚɜɧɭɸ MS (cos Į1 – cos Į2)ǻV/V, ɝɞɟ ǻV = S ǻx – ɨɛɴɟɦ ɩɟɪɟɦɚɝɧɢɱɟɧɧɨɣ ɨɛɥɚɫɬɢ. Ɉɬɫɸɞɚ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ:
Ȥ = 'M = |
S'x |
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– cos Į |
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ɉɪɢ ǻɇ 0 ɢɡ (4.27) ɩɨɥɭɱɚɟɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɨɛɪɚɬɢɦɨɣ ɱɚɫɬɢ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ:
Ȥ |
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§ dM · |
= |
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ȝ |
Ɇ |
(cos Į – cos Į ) |
§ dH · 1 |
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ɨɛɪ |
¨ |
¸ |
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dx ¹ |
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S2 |
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ȝ |
MS2(cosD1 cos D2 )2 . |
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Ⱦɥɹ ɦɧɨɝɢɯ ɦɚɝɧɢɬɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɨɫɨɛɟɧɧɨ ɜɚɠɟɧ ɫɥɭɱɚɣ ɧɚ-
ɱɚɥɶɧɨɣ ɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ Ȥɧ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɪɚɡɦɚɝ-
ɧɢɱɟɧɧɨɦɭ ɫɨɫɬɨɹɧɢɸ ɨɛɪɚɡɰɚ ɩɪɢ ɇ = 0 (ɩɨɥɨɠɟɧɢɟ ɝɪɚɧɢɰɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨɨɪɞɢɧɚɬɨɣ ɯ0).
ɉɪɢɜɟɞɟɧɧɵɟ ɪɚɫɫɭɠɞɟɧɢɹ ɫɞɟɥɚɧɵ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ɞɨɦɟɧɧɵɟ ɝɪɚɧɢɰɵ ɹɜɥɹɸɬɫɹ ɩɥɨɫɤɢɦɢ ɢ ɠɟɫɬɤɢɦɢ, ɬ. ɟ. ɧɟ ɞɟɮɨɪɦɢɪɭɸɬɫɹ ɩɪɢ ɞɜɢɠɟɧɢɢ. ȼ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ ɩɪɚɤɬɢɱɟɫɤɢ ɥɸɛɨɣ ɮɟɪɪɨɦɚɝɧɟɬɢɤ ɫɨɞɟɪɠɢɬ ɪɚɡɥɢɱɧɵɟ ɞɟɮɟɤɬɵ (ɩɨɪɵ, ɧɟɦɚɝɧɢɬɧɵɟ ɜɤɥɸɱɟɧɢɹ ɢ ɬ. ɞ.), ɩɪɟɩɹɬɫɬɜɭɸɳɢɟ ɞɜɢɠɟɧɢɸ ɝɪɚɧɢɰɵ. ɉɨɞɨɛɧɵɟ ɞɟɮɟɤɬɵ ɦɨɝɭɬ ɪɚɫɩɨɥɚɝɚɬɶɫɹ ɤɚɤ ɜ ɦɚɫɫɢɜɟ ɤɪɢɫɬɚɥɥɚ, ɬɚɤ ɢ ɧɚ ɝɪɚɧɢɰɚɯ ɡɟɪɟɧ ɩɨɥɢɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯ ɦɚɝɧɢɬɧɵɯ ɦɚɬɟɪɢɚɥɨɜ. ȼ ɬɚɤɨɦ ɫɥɭɱɚɟ ɝɪɚɧɢɰɵ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɜ ɨɛɪɚɡɰɟ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨ ɜɤɥɸɱɚɸɬ ɜ ɫɟɛɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɞɟɮɟɤɬɵ, ɡɚɤɪɟɩɥɹɹɫɶ ɧɚ ɧɢɯ. Ɋɢɫ. 4.9 ɢɥɥɸɫɬɪɢɪɭɟɬ ɞɟɮɟɤɬ ɢ ɩɪɢɱɢɧɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫ ɧɢɦ ɝɪɚɧɢɰɵ.
Ɋɢɫ. 4.9. ȼɨɡɦɨɠɧɵɟ ɪɚɫɩɨɥɨɠɟɧɢɹ ɝɪɚɧɢɰɵ ɢ ɞɟɮɟɤɬɚ:
ɚ– ɝɪɚɧɢɰɚ ɧɟ ɜɡɚɢɦɨɞɟɣɫɬɜɭɟɬ ɫ ɞɟɮɟɤɬɨɦ; ɛ – ɢɡɦɟɧɟɧɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɦɚɝɧɢɬɧɵɯ ɩɨɥɸɫɨɜ ɞɟɮɟɤɬɚ ɩɪɢ ɟɝɨ ɩɟɪɟɫɟɱɟɧɢɢ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɟɣ
ȼɢɞɧɨ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɪɚɫɩɨɥɨɠɟɧɢɹ ɞɟɮɟɤɬɚ ɜɧɭɬɪɢ ɞɨɦɟɧɚ (ɪɢɫ. 4.9, ɚ) ɜɨɤɪɭɝ ɞɟɮɟɤɬɚ ɨɛɪɚɡɭɸɬɫɹ ɦɚɝɧɢɬɧɵɟ ɩɨɥɸɫɚ, ɱɬɨ ɩɪɢ-
125
ɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɷɧɟɪɝɢɢ ɪɚɡɦɚɝɧɢɱɢɜɚɧɢɹ. ȿɫɥɢ ɝɪɚɧɢɰɚ ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ ɞɟɮɟɤɬ (ɪɢɫ. 4.9, ɛ), ɬɨ ɷɧɟɪɝɢɹ ɪɚɡɦɚɝɧɢɱɢɜɚɧɢɹ ɭɦɟɧɶɲɚɟɬɫɹ ɩɨɱɬɢ ɜɞɜɨɟ. ȼ ɬɚɤɨɦ ɫɥɭɱɚɟ ɝɪɚɧɢɰɚ, ɫɦɟɳɚɹɫɶ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɧɟ ɫɨɯɪɚɧɹɟɬ ɫɬɪɨɝɨ ɩɥɨɫɤɭɸ ɮɨɪɦɭ, ɚ ɫɢɥɚ, ɭɞɟɪɠɢɜɚɸɳɚɹ ɝɪɚɧɢɰɭ ɜ ɪɚɜɧɨɜɟɫɢɢ, ɨɛɭɫɥɨɜɥɟɧɚ ɢɡɦɟɧɟɧɢɟɦ ɷɧɟɪɝɢɢ ɫɚɦɨɣ ɝɪɚɧɢɰɵ ɡɚ ɫɱɟɬ ɭɜɟɥɢɱɟɧɢɹ ɟɟ ɩɥɨɳɚɞɢ, ɫ ɨɞɧɨɣ ɫɬɨɪɨɧɵ, ɢ, ɫ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɥɢɛɨ ɢɡɦɟɧɟɧɢɟɦ ɷɧɟɪɝɢɢ ɚɧɢɡɨɬɪɨɩɢɢ ɢɫɤɪɢɜɥɟɧɧɨɣ ɝɪɚɧɢɰɵ, ɥɢɛɨ ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɦɚɝɧɢɬɧɵɯ ɩɨɥɸɫɨɜ, ɜɨɡɧɢɤɚɸɳɢɯ ɧɚ ɬɚɤɨɣ ɝɪɚɧɢɰɟ. Ɉɛɚ ɭɤɚɡɚɧɧɵɯ ɜɚɪɢɚɧɬɚ ɢɥɥɸɫɬɪɢɪɭɟɬ ɪɢɫ. 4.10.
Ɋɢɫ. 4.10. ȼɚɪɢɚɧɬɵ ɢɫɤɪɢɜɥɟɧɢɹ ɡɚɤɪɟɩɥɟɧɧɨɣ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɩɨɥɹ: ɚ – ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɢɡɝɢɛ ɝɪɚɧɢɰɵ; ɛ – ɫɮɟɪɢɱɟɫɤɢɣ ɢɡɝɢɛ ɝɪɚɧɢɰɵ
ȿɫɥɢ ɞɟɮɟɤɬɵ, ɭɞɟɪɠɢɜɚɸɳɢɟ ɝɪɚɧɢɰɭ, ɪɚɫɩɨɥɨɠɟɧɵ ɜɞɨɥɶ ɩɪɹɦɵɯ, ɩɚɪɚɥɥɟɥɶɧɵɯ ɜɟɤɬɨɪɭ (Ɇ1 – Ɇ2), ɬɨ ɩɪɨɢɫɯɨɞɢɬ ɰɢɥɢɧɞ-
ɪɢɱɟɫɤɢɣ ɢɡɝɢɛ ɝɪɚɧɢɰɵ (ɪɢɫ. 4.10, ɚ). ɉɪɢ ɷɬɨɦ ɜ ɦɟɫɬɟ ɪɚɫɩɨɥɨɠɟɧɢɹ ɝɪɚɧɢɰɵ ɦɚɝɧɢɬɧɵɟ ɩɨɥɸɫɚ ɧɟ ɜɨɡɧɢɤɚɸɬ, ɬɚɤ ɤɚɤ ɜɟɤɬɨɪɵ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɩɨ ɨɛɟ ɫɬɨɪɨɧɵ ɝɪɚɧɢɰɵ ɨɫɬɚɸɬɫɹ ɩɚɪɚɥɥɟɥɶɧɵɦɢ ɟɟ ɩɥɨɫɤɨɫɬɢ. ɍɫɥɨɜɢɟ ɪɚɜɧɨɜɟɫɢɹ ɜ ɩɨɥɟ ɇ ɢɦɟɟɬ ɜɢɞ
ȝ0ɇ(Ɇ1 – Ɇ2)įV = į(SȖɝɪ) § JɝɪGS , |
(4.33) |
ɝɞɟ Jɝɪ – ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɭɞɟɥɶɧɨɣ ɷɧɟɪɝɢɢ ɢɫɤɪɢɜɥɟɧɧɨɣ ɞɨɦɟɧ-
ɧɨɣ ɝɪɚɧɢɰɵ.
ȿɫɥɢ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢɡɜɟɫɬɧɵɟ ɮɨɪɦɭɥɵ, ɫɩɪɚɜɟɞɥɢɜɵɟ ɩɪɢ ɦɚɥɵɯ ɢɡɝɢɛɚɯ, ɬɨ ɩɨɥɭɱɢɦ:
126
V = 2 3 DlL, |
S = DL 1 8l2 |
3D2 . |
(4.34) |
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ȼɵɪɚɠɟɧɢɟ ɞɥɹ ɡɚɜɢɫɹɳɟɣ ɨɬ ɩɨɥɹ ɜɟɥɢɱɢɧɵ l, ɯɚɪɚɤɬɟɪɢɡɭɸ- |
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ɳɟɣ ɢɡɝɢɛ ɝɪɚɧɢɰɵ, ɜɵɝɥɹɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: |
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l = |
P |
0 |
M |
S |
(cos D cos D |
2 |
)D2 |
(4.35) |
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1 |
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ɇ. |
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8Jɝɪ |
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ȿɫɥɢ ɩɨɥɨɠɢɬɶ, ɱɬɨ ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɞɨɦɟɧɧɵɦɢ ɝɪɚɧɢɰɚɦɢ ɜ ɨɛɪɚɡɰɟ ɪɚɜɧɨ d, ɬɨ ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɧɚɱɚɥɶɧɨɣ ɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ:
§ |
'Ɇ · |
= |
P |
M 2D2 |
. |
(4.36) |
Ȥɫɦ = ¨ |
¸ |
0 |
S |
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© |
ɇ ¹ɇo0 |
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6Jɝɪd |
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ȿɫɥɢ ɞɟɮɟɤɬɵ ɪɚɫɩɨɥɨɠɟɧɵ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨ ɝɪɚɧɢɰɚ ɭɞɟɪɠɢɜɚɟɬɫɹ ɜɞɨɥɶ ɧɟɤɨɬɨɪɨɝɨ ɡɚɦɤɧɭɬɨɝɨ ɤɨɧɬɭɪɚ (ɧɚɩɪɢɦɟɪ, ɜ ɫɮɟɪɢɱɟɫɤɨɦ ɡɟɪɧɟ, ɤɨɝɞɚ ɨɧɚ, ɩɨɞɨɛɧɨ ɦɟɦɛɪɚɧɟ, ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɜ ɫɪɟɞɧɟɣ ɱɚɫɬɢ ɡɟɪɧɚ), ɬɨ ɩɪɢ ɢɡɝɢɛɟ ɨɧɚ ɩɪɢɨɛɪɟɬɚɟɬ ɮɨɪɦɭ ɷɥɥɢɩɫɨɢɞɚ ɜɪɚɳɟɧɢɹ ɫ ɦɚɥɨɣ ɨɫɶɸ l ɢ ɛɨɥɶɲɨɣ ɨɫɶɸ D (ɪɢɫ. 4.10, ɛ). Ɋɚɫɱɟɬɵ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɧɚɱɚɥɶɧɨɣ ɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɩɪɢɦɟɬ ɜɢɞ
P2M 4D
Ȥɫɦ = 0 2S , (4.37)
K d
ɝɞɟ K – ɤɨɧɫɬɚɧɬɚ ɚɧɢɡɨɬɪɨɩɢɢ.
Ʉɨɷɪɰɢɬɢɜɧɚɹ ɫɢɥɚ. ȿɫɥɢ ɦɨɧɨɬɨɧɧɨ ɭɜɟɥɢɱɢɜɚɬɶ ɡɧɚɱɟɧɢɟ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɬɨ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫ. 4.8, ɚ ɞɨɦɟɧɧɚɹ ɝɪɚɧɢɰɚ ɛɭɞɟɬ ɜɫɟ ɞɚɥɶɲɟ ɞɜɢɝɚɬɶɫɹ ɜɞɨɥɶ ɨɫɢ x, ɩɟɪɟɯɨɞɹ ɢɡ ɨɞɧɨɣ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɹɦɵ ɜ ɞɪɭɝɭɸ. ɇɟ ɢɫɤɥɸɱɟɧɨ, ɱɬɨ ɜ ɤɚɤɨɣ-ɬɨ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɹɦɟ ɷɬɚ ɝɪɚɧɢɰɚ ɜɫɬɪɟɬɢɬ ɞɪɭɝɭɸ ɝɪɚɧɢɰɭ, ɩɪɢɲɟɞɲɭɸ ɫ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɣ ɫɬɨɪɨɧɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɜɟ ɝɪɚɧɢɰɵ ɭɧɢɱɬɨɠɚɬ ɞɪɭɝ ɞɪɭɝɚ ɢ ɞɨɦɟɧ ɢɫɱɟɡɧɟɬ. ȼɟɥɢɱɢɧɚ ɤɪɢɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɚɤɫɢɦɚɥɶɧɵɦ ɡɧɚɱɟɧɢɟɦ wȿ
wx . Ɍɚɤɨɟ ɩɨɥɟ ɧɚɡɵɜɚɟɬɫɹ ɤɨɷɪɰɢɬɢɜɧɵɦ ɩɨɥɟɦ, ɚ ɱɚɳɟ – ɤɨɷɪɰɢɬɢɜɧɨɣ ɫɢɥɨɣ:
ɇ = |
1 |
§ wE · . |
(4.38) |
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ɫ |
2P0ɆS |
¨ ¸ |
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© wx ¹max |
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127
Ʉɨɷɪɰɢɬɢɜɧɚɹ ɫɢɥɚ ɹɜɥɹɟɬɫɹ ɫɬɪɭɤɬɭɪɧɨ-ɱɭɜɫɬɜɢɬɟɥɶɧɵɦ ɩɚɪɚɦɟɬɪɨɦ ɮɟɪɪɨɦɚɝɧɢɬɧɵɯ ɦɚɬɟɪɢɚɥɨɜ, ɟɟ ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɪɚɫɫɦɚɬɪɢɜɚɹ ɤɨɧɤɪɟɬɧɵɟ ɩɪɢɱɢɧɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɭɞɟɪɠɚɧɢɸ (ɮɢɤɫɚɰɢɢ) ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɩɨɥɨɠɟɧɢɢ.
Ʉɚɤ ɭɠɟ ɨɬɦɟɱɚɥɨɫɶ ɪɚɧɟɟ, ɢɡɦɟɧɟɧɢɟ ɷɧɟɪɝɢɢ ɤɪɢɫɬɚɥɥɚ ɩɪɢ ɫɦɟɳɟɧɢɢ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɦɨɠɧɨ ɨɬɧɟɫɬɢ ɤ ɢɡɦɟɧɟɧɢɸ ɫɨɛɫɬɜɟɧɧɨɣ ɷɧɟɪɝɢɢ ɝɪɚɧɢɰɵ. Ʉɨɝɞɚ ɧɚ ɩɭɬɢ ɫɦɟɳɟɧɢɹ ɝɪɚɧɢɰɵ ɩɪɨɢɫɯɨɞɢɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ ɟɟ ɩɥɨɳɚɞɢ (ɱɬɨ ɢɦɟɟɬ ɦɟɫɬɨ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɨɛɬɟɤɚɧɢɢ ɟɸ ɛɨɥɶɲɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɞɟɮɟɤɬɨɜ), ɤɨɷɪɰɢɬɢɜɧɭɸ ɫɢɥɭ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
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1 |
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§ w |
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· |
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ɇɫ = |
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S |
, |
(4.39) |
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©¨ wx ¹¸max |
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2P0ɆS |
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S |
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ɝɞɟ S – ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɩɥɨɳɚɞɢ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ.
Ɇ. Ʉɟɪɫɬɟɧ ɪɚɫɫɦɨɬɪɟɥ ɜɨɩɪɨɫ ɨɩɪɟɞɟɥɟɧɢɹ ɇɫ ɩɪɢ ɛɨɥɶɲɨɦ
ɤɨɥɢɱɟɫɬɜɟ ɞɟɮɟɤɬɨɜ ɤɪɢɫɬɚɥɥɚ (ɬɟɨɪɢɹ ɜɤɥɸɱɟɧɢɣ). ɉɨ Ʉɟɪɫɬɟɧɭ, ɜ ɨɬɫɭɬɫɬɜɢɟ ɜɧɟɲɧɟɝɨ ɩɨɥɹ ɝɪɚɧɢɰɚ ɪɚɫɩɨɥɨɠɢɬɫɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɜɤɥɸɱɢɬɶ ɜ ɫɟɛɹ ɤɚɤ ɦɨɠɧɨ ɛɨɥɶɲɟ ɞɟɮɟɤɬɨɜ, ɬɚɤ ɤɚɤ ɩɪɢ ɷɬɨɦ ɟɟ ɩɥɨɳɚɞɶ ɭɦɟɧɶɲɚɟɬɫɹ (ɞɟɮɟɤɬɵ «ɜɵɪɟɡɚɸɬ» ɱɚɫɬɶ ɩɥɨɳɚɞɢ ɝɪɚɧɢɰɵ). ɉɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɩɨɥɹ ɝɪɚɧɢɰɚ ɦɨɠɟɬ ɨɬɨɪɜɚɬɶɫɹ ɨɬ ɞɟɮɟɤɬɨɜ, ɟɟ ɩɥɨɳɚɞɶ ɭɜɟɥɢɱɢɬɫɹ. Ɂɧɚɱɟɧɢɟ ɇɫ ɨɩɪɟɞɟɥɹ-
ɟɬɫɹ ɦɚɤɫɢɦɚɥɶɧɵɦ ɭɜɟɥɢɱɟɧɢɟɦ ɝɪɚɧɢɱɧɨɣ ɷɧɟɪɝɢɢ ɩɪɢ ɫɦɟɳɟɧɢɢ ɝɪɚɧɢɰ. Ⱦɥɹ ɦɨɞɟɥɢ, ɜ ɤɨɬɨɪɨɣ ɞɟɮɟɤɬɵ ɪɚɫɩɨɥɨɠɟɧɵ ɜ ɜɢɞɟ ɤɜɚɞɪɚɬɧɨɣ ɪɟɝɭɥɹɪɧɨɣ ɫɟɬɤɢ ɢ ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɵɟ ɪɚɡɦɟɪɵ, ɤɨɷɪɰɢɬɢɜɧɭɸ ɫɢɥɭ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
ɇ = ɪ |
K |
ȕn, |
(4.40) |
ɫ P0M S
ɝɞɟ K – ɤɨɧɫɬɚɧɬɚ ɚɧɢɡɨɬɪɨɩɢɢ; ȕ – ɤɨɧɰɟɧɬɪɚɰɢɹ ɞɟɮɟɤɬɨɜ; ɪ – ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɨɬɧɨɲɟɧɢɹ ɬɨɥɳɢɧɵ ɝɪɚɧɢɰɵ ɤ ɪɚɡɦɟɪɭ ɞɟɮɟɤɬɚ; n – ɩɨɤɚɡɚɬɟɥɶ ɫɬɟɩɟɧɢ.
ɂɡ ɞɚɧɧɨɣ ɦɨɞɟɥɢ ɫɥɟɞɭɟɬ, ɱɬɨ ɇɫ ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɤɨɧ-
ɰɟɧɬɪɚɰɢɢ ɞɟɮɟɤɬɨɜ ɢ ɢɦɟɟɬ ɧɚɢɛɨɥɶɲɟɟ ɡɧɚɱɟɧɢɟ ɜ ɫɥɭɱɚɟ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨɝɨ ɪɚɜɟɧɫɬɜɚ ɬɨɥɳɢɧɵ ɝɪɚɧɢɰɵ ɢ ɪɚɡɦɟɪɚ ɞɟɮɟɤɬɚ.
ȼ ɪɚɦɤɚɯ ɦɨɞɟɥɢ ɛɟɡɞɟɮɟɤɬɧɨɝɨ ɤɪɢɫɬɚɥɥɚ, ɫɨɞɟɪɠɚɳɟɝɨ ɜɧɭɬɪɟɧɧɢɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɧɚɩɪɹɠɟɧɢɹ, ȿ. ɂ. Ʉɨɧɞɨɪɫɤɢɣ ɩɨɤɚɡɚɥ, ɱɬɨ
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ɞɥɹ ɫɥɭɱɚɹ, ɨɩɢɫɵɜɚɟɦɨɝɨ (4.38), ɤɨɷɪɰɢɬɢɜɧɚɹ ɫɢɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɨɫɧɨɜɧɨɦ ɝɪɚɞɢɟɧɬɨɦ ɜɧɭɬɪɟɧɧɢɯ ɧɚɩɪɹɠɟɧɢɣ ɢ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɜɢɞɟ
ɇ § |
OSGɝɪ |
§ wV· |
, |
(4.41) |
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¨ ¸ |
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ɫ |
2P0 |
ɆS |
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© wx ¹max |
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ɝɞɟ ȜS – ɤɨɧɫɬɚɧɬɚ ɦɚɝɧɢɬɨɫɬɪɢɤɰɢɢ; ı – ɫɪɟɞɧɹɹ ɚɦɩɥɢɬɭɞɚ ɦɟɯɚɧɢɱɟɫɤɢɯ ɧɚɩɪɹɠɟɧɢɣ; įɝɪ – ɬɨɥɳɢɧɚ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ. Ɍɟɨɪɢɹ Ʉɨɧɞɨɪɫɤɨɝɨ ɩɨɥɭɱɢɥɚ ɧɚɡɜɚɧɢɟ ɬɟɨɪɢɹ ɧɚɩɪɹɠɟɧɢɣ.
ȼ ɪɟɚɥɶɧɵɯ ɮɟɪɪɨɦɚɝɧɢɬɧɵɯ ɦɚɬɟɪɢɚɥɚɯ ɨɛɵɱɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɤɚɤ ɞɟɮɟɤɬɵ, ɬɚɤ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɧɚɩɪɹɠɟɧɢɹ, ɩɨɷɬɨɦɭ ɚɧɚɥɢɬɢɱɟɫɤɢɣ ɪɚɫɱɟɬɤɨɷɪɰɢɬɢɜɧɨɣɫɢɥɵɩɪɟɞɫɬɚɜɥɹɟɬɡɧɚɱɢɬɟɥɶɧɵɟ ɬɪɭɞɧɨɫɬɢ.
ȼɪɚɳɟɧɢɟ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ
ȿɫɥɢ ɩɪɢ ɩɨɞɚɱɟ ɧɚ ɨɛɪɚɡɟɰ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɞɨɦɟɧɧɵɟ ɝɪɚɧɢɰɵ ɩɨ ɤɚɤɨɣ-ɬɨ ɩɪɢɱɢɧɟ ɧɟ ɦɨɝɭɬ ɞɜɢɝɚɬɶɫɹ (ɧɚɩɪɢɦɟɪ, ɩɨɥɟ ɧɚɩɪɚɜɥɟɧɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ ɝɪɚɧɢɰ) ɢɥɢ ɟɫɥɢ ɝɪɚɧɢɰɵ ɨɬɫɭɬɫɬɜɭɸɬ, ɱɬɨ ɯɚɪɚɤɬɟɪɧɨ ɞɥɹ ɤɨɧɟɱɧɨɣ ɫɬɚɞɢɢ ɩɪɨɰɟɫɫɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ (ɨɛɥɚɫɬɶ ɩɪɢɛɥɢɠɟɧɢɹ ɤ ɧɚɫɵɳɟɧɢɸ), ɬɨ ɧɚɦɚɝɧɢɱɢɜɚɧɢɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɡɚ ɫɱɟɬ ɜɪɚɳɟɧɢɹ (ɩɨɜɨɪɨɬɚ) ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ. ɇɚ ɪɢɫ. 4.11 ɩɨɤɚɡɚɧ ɨɞɢɧ ɢɡ ɜɚɪɢɚɧɬɨɜ ɪɚɫɩɨɥɨɠɟɧɢɹ ɩɨɥɹ ɢ ɝɪɚɧɢɰ (ɪɢɫ. 4.11, ɚ) ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɜɟɤɬɨɪɨɜ (ɪɢɫ. 4.11, ɛ).
ɉɪɢ ɜɪɚɳɚɬɟɥɶɧɨɦ ɦɟɯɚɧɢɡɦɟ ɜɟɤɬɨɪ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɨɬɤɥɨɧɹɟɬɫɹ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɥɟɝɤɨɝɨ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ (ɇȺ) ɢ ɩɨɜɨɪɚɱɢɜɚɟɬɫɹ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɨɥɹ (ɪɢɫ. 4.11, ɛ). ɉɪɢ ɷɬɨɦ ɧɚɦɚɝɧɢɱɢɜɚɧɢɟ ɩɨɥɧɨɫɬɶɸ ɨɛɪɚɬɢɦɨ, ɬɚɤ ɤɚɤ ɩɨɫɥɟ ɫɧɹɬɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɟɤɬɨɪ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɜɨɡɜɪɚɳɚɟɬɫɹ ɤ ɫɜɨɟɦɭ ɩɪɟɠɧɟɦɭ ɧɚɩɪɚɜɥɟɧɢɸ ɜɞɨɥɶ «ɥɟɝɤɨɣ» ɨɫɢ.
Ɇɚɝɧɢɬɧɨɟ ɩɨɥɟ ɫɨɡɞɚɟɬ ɜɪɚɳɚɬɟɥɶɧɵɣ ɦɨɦɟɧɬ Ɍ = ȝ0(Ɇ u ɇ), ɞɟɣɫɬɜɭɸɳɢɣ ɧɚ ɜɟɤɬɨɪ Ɇ. ȼ ɫɨɫɬɨɹɧɢɢ ɪɚɜɧɨɜɟɫɢɹ ɷɬɨɬ ɦɨɦɟɧɬ ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɧɵɦ ɦɨɦɟɧɬɨɦ ɫɢɥ ɚɧɢɡɨɬɪɨɩɢɢ, ɫɬɪɟɦɹɳɢɯɫɹ ɜɟɪɧɭɬɶ ɜɟɤɬɨɪ Ɇ ɜ ɧɚɩɪɚɜɥɟɧɢɟ «ɥɟɝɤɨɣ» ɨɫɢ.
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ɚ ɛ Ɋɢɫ. 4.11. ɇɚɦɚɝɧɢɱɢɜɚɧɢɟ ɦɧɨɝɨɞɨɦɟɧɧɨɝɨ ɤɪɢɫɬɚɥɥɚ ɜɪɚɳɟɧɢɟɦ ɜɟɤɬɨɪɚ
ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ (ɚ) ɢ ɢɥɥɸɫɬɪɚɰɢɹ ɪɚɫɩɨɥɨɠɟɧɢɹ ɜɟɤɬɨɪɨɜ ɞɥɹ ɪɚɫɱɟɬɚ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɩɪɢ ɜɪɚɳɚɬɟɥɶɧɨɦ ɦɟɯɚɧɢɡɦɟ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ (ɛ).
ɇȺ – ɜɧɭɬɪɟɧɧɟɟ ɩɨɥɟ ɚɧɢɡɨɬɪɨɩɢɢ (ɫɦ. (3.5))
ȼ ɫɥɭɱɚɟ ɦɚɬɟɪɢɚɥɨɜ ɫ ɨɞɧɨɨɫɧɨɣ ɚɧɢɡɨɬɪɨɩɢɟɣ ɢɦɟɟɦ:
ȿ = K sin2 ș – ȝ M Hcos(Į – ș), |
(4.42) |
0 S |
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ɝɞɟ K – ɤɨɧɫɬɚɧɬɚ ɚɧɢɡɨɬɪɨɩɢɢ.
Ɉɬɫɸɞɚ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɪɚɜɧɨɜɟɫɧɵɣ ɭɝɨɥ ș0, ɭɱɢɬɵɜɚɹ ɭɫ-
ɥɨɜɢɹ wE
wT 0 ɢ w2E
wT2 T T0 > 0.
Ⱦɥɹ ɫɥɭɱɚɹ Į = 90º ɧɚɯɨɞɢɦ ɫɥɟɞɭɸɳɟɟ ɪɟɲɟɧɢɟ:
sin ș0 |
= |
P0M S H |
= |
H |
ɩɪɢ ɇ ɇȺ, |
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2K |
H A |
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ɤɨɬɨɪɨɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɟ ɡɚɜɢɫɹɳɟɣ ɨɬ ɩɨɥɹ ɇ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ:
Ȥ |
ɜɪ |
= P0M S2 |
= |
MS |
ɩɪɢ ɇ < ɇ . |
(4.43) |
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2K |
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Ⱥ |
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H A |
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ȿɫɥɢ ɠɟ ɇ > ɇȺ, ɬɨ ș = 90º ɢ Ȥɜɪ = 0.
Ⱦɥɹ ɫɥɭɱɚɹ Į = 180º ɫɬɚɛɢɥɶɧɵ ɥɢɲɶ ɩɨɥɨɠɟɧɢɹ, ɨɬɜɟɱɚɸɳɢɟ ɭɝɥɚɦ ș = 0 ɢɥɢ ș = 180º, ɩɪɢɱɟɦ ɩɟɪɟɜɨɪɨɬ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɩɪɨɢɫɯɨɞɢɬ ɩɪɢ ɇ = ɇȺ. Ʉɪɢɜɵɟ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɥɹ ɨɛɨɢɯ ɫɥɭɱɚɟɜ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 4.12. ȼɢɞɧɨ, ɱɬɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɤɨɷɪɰɢɬɢɜɧɚɹ ɫɢɥɚ ɇɫ = ɇȺ (ɪɢɫ. 4.12, ɛ).
Ʉɨɝɞɚ 90º < Į < 180º, ɜɟɤɬɨɪ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɩɟɪɟɜɨɪɚɱɢɜɚɟɬɫɹ ɩɪɢ (1/2)ɇȺ < ɇɫ < ɇȺ. Ɂɧɚɱɟɧɢɟ ɇɫ = (1/2)ɇȺ ɩɨɹɜɥɹɟɬɫɹ ɩɪɢ Į= 135º.
ȼ ɫɥɭɱɚɟ Į < 90º ɩɨɫɥɟ ɩɟɪɟɜɨɪɚɱɢɜɚɧɢɹ ɜɟɤɬɨɪ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɩɨɫɬɟɩɟɧɧɨɩɨɜɨɪɚɱɢɜɚɟɬɫɹ, ɩɪɢɛɥɢɠɚɹɫɶɤ ɧɚɩɪɚɜɥɟɧɢɸ ɩɨɥɹ.
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