Теория электропривода

Ɇɢɧɢɫɬɟɪɫɬɜɨ ɨɛɪɚɡɨɜɚɧɢɹ ɢ ɧɚɭɤɢ Ɋɨɫɫɢɣɫɤɨɣ Ɏɟɞɟɪɚɰɢɢ Ɏɟɞɟɪɚɥɶɧɨɟ ɚɝɟɧɬɫɬɜɨ ɩɨ ɨɛɪɚɡɨɜɚɧɢɸ ɘɠɧɨ-ɍɪɚɥɶɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵ...

Author: Драчев Г.И.

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Ɇɢɧɢɫɬɟɪɫɬɜɨ ɨɛɪɚɡɨɜɚɧɢɹ ɢ ɧɚɭɤɢ Ɋɨɫɫɢɣɫɤɨɣ Ɏɟɞɟɪɚɰɢɢ Ɏɟɞɟɪɚɥɶɧɨɟ ɚɝɟɧɬɫɬɜɨ ɩɨ ɨɛɪɚɡɨɜɚɧɢɸ ɘɠɧɨ-ɍɪɚɥɶɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ Ʉɚɮɟɞɪɚ «ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɢ ɚɜɬɨɦɚɬɢɡɚɰɢɹ ɩɪɨɦɵɲɥɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ»

62-83(07) Ⱦ729

1.

Ƚ.ɂ. ȾɊȺɑȿȼ

ɌȿɈɊɂə ɗɅȿɄɌɊɈɉɊɂȼɈȾȺ ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɑɚɫɬɶ 1

ɑɟɥɹɛɢɧɫɤ ɂɡɞɚɬɟɥɶɫɬɜɨ ɘɍɪȽɍ 2005

ɍȾɄ 62-83.01(075.8) Ⱦɪɚɱɟɜ Ƚ.ɂ. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ. – ɑɟɥɹɛɢɧɫɤ: ɂɡɞ-ɜɨ ɘɍɪȽɍ, 2005. ɑɚɫɬɶ 1. – 209 ɫ. Ɋɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɫɜɨɣɫɬɜɚ ɢ ɫɬɪɭɤɬɭɪɧɵɟ ɫɯɟɦɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɣ, ɜɨɩɪɨɫɵ ɜɵɛɨɪɚ ɞɜɢɝɚɬɟɥɟɣ ɩɨ ɦɨɳɧɨɫɬɢ. Ⱦɥɹ ɤɨɧɬɪɨɥɹ ɭɫɜɨɟɧɢɹ ɦɚɬɟɪɢɚɥɚ ɩɨɫɨɛɢɟ ɫɨɞɟɪɠɢɬ ɩɪɢɦɟɪɵ ɪɚɫɱɟɬɨɜ ɩɨ ɨɬɞɟɥɶɧɵɦ ɪɚɡɞɟɥɚɦ, ɫɧɚɛɠɟɧɨ ɭɩɪɚɠɧɟɧɢɹɦɢ ɩɨ ɤɚɠɞɨɦɭ ɪɚɡɞɟɥɭ, ɫɩɢɫɤɨɦ ɨɫɧɨɜɧɨɣ, ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ, ɫɩɪɚɜɨɱɧɨɣ ɢ ɦɟɬɨɞɢɱɟɫɤɨɣ ɥɢɬɟɪɚɬɭɪɵ. ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɨ ɩɪɢ ɤɭɪɫɨɜɨɦ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɩɨ ɞɢɫɰɢɩɥɢɧɟ “Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ” ɢ ɩɪɢ ɞɢɩɥɨɦɧɨɦ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɫɬɭɞɟɧɬɚɦɢ ɫɩɟɰɢɚɥɶɧɨɫɬɢ 14060400 – “ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɢ ɚɜɬɨɦɚɬɢɤɚ ɩɪɨɦɵɲɥɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɤɨɦɩɥɟɤɫɨɜ”. ɂɥ. 137, ɬɚɛɥ. 7, ɫɩɢɫɨɤ ɥɢɬ.– 31 ɧɚɡɜ. Ɉɞɨɛɪɟɧɨ ɭɱɟɛɧɨ-ɦɟɬɨɞɢɱɟɫɤɨɣ ɤɨɦɢɫɫɢɟɣ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ. Ɋɟɰɟɧɡɟɧɬɵ: ȼ.Ɏ. Ȼɭɯɬɨɹɪɨɜ, ɂ.Ⱦ. Ʉɚɛɚɧɨɜ.

¤ ɂɡɞɚɬɟɥɶɫɬɜɨ ɘɍɪȽɍ, 2004

2

ɉɊȿȾɂɋɅɈȼɂȿ ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɹɜɥɹɟɬɫɹ ɧɟɨɬɴɟɦɥɟɦɨɣ ɱɚɫɬɶɸ ɦɧɨɝɢɯ ɚɝɪɟɝɚɬɨɜ ɢ ɤɨɦɩɥɟɤɫɨɜ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɹɯ ɧɚɪɨɞɧɨɝɨ ɯɨɡɹɣɫɬɜɚ, ɧɚɭɤɢ ɢ ɬɟɯɧɢɤɢ. ɇɚɪɹɞɭ ɫ ɬɟɧɞɟɧɰɢɟɣ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɢ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɵɯ ɩɪɨɰɟɫɫɨɜ ɧɚ ɛɚɡɟ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɬɟɯɧɢɤɢ, ɫɨɜɪɟɦɟɧɧɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɫɬɚɥ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɨɣ ɪɚɡɧɨɜɢɞɧɨɫɬɶɸ ɫɢɫɬɟɦ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɬɟɯɧɢɱɟɫɤɢɦɢ ɨɛɴɟɤɬɚɦɢ. ɗɬɢ ɮɚɤɬɨɪɵ ɨɰɟɧɢɜɚɸɬɫɹ ɤɚɤ ɨɫɧɨɜɧɵɟ, ɩɨɡɜɨɥɢɜɲɢɟ ɭɬɪɨɢɬɶ ɨɛɴɟɦ ɦɢɪɨɜɨɝɨ ɩɪɨɢɡɜɨɞɫɬɜɚ ɡɚ ɩɨɫɥɟɞɧɢɟ ɞɟɫɹɬɢɥɟɬɢɹ. ɉɨɹɜɥɟɧɢɟ ɧɨɜɵɯ ɧɚɭɱɧɵɯ ɢ ɬɟɯɧɢɱɟɫɤɢɯ ɪɟɲɟɧɢɣ ɢ ɢɡɦɟɧɟɧɢɟ ɫɚɦɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɫɨɜɪɟɦɟɧɧɵɯ ɭɫɥɨɜɢɹɯ ɬɪɟɛɭɟɬ ɞɨɩɨɥɧɟɧɢɣ ɜɨ ɦɧɨɝɢɟ ɪɚɡɞɟɥɵ ɞɢɫɰɢɩɥɢɧɵ. Ɏɢɡɢɱɟɫɤɢɟ ɨɛɨɫɧɨɜɚɧɢɹ ɹɜɥɟɧɢɣ, ɩɪɢɫɭɳɢɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ ɤɚɤ ɬɟɯɧɢɱɟɫɤɨɦɭ ɭɫɬɪɨɣɫɬɜɭ ɷɥɟɤɬɪɨɦɟɯɚɧɢɤɢ, ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɫɨɜɦɟɫɬɧɨ ɫ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦɢ ɦɨɞɟɥɹɦɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ ɜ ɩɨɧɹɬɢɹɯ ɢ ɬɟɪɦɢɧɚɯ ɬɟɨɪɢɢ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ. Ɋɚɫɫɦɨɬɪɟɧɢɟ ɫɨɜɪɟɦɟɧɧɵɯ ɫɢɫɬɟɦ ɭɩɪɚɜɥɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɬɪɟɛɭɟɬ ɝɥɭɛɨɤɨɝɨ ɭɫɜɨɟɧɢɹ ɫɨɜɦɟɫɬɧɨɣ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɫ ɭɫɬɪɨɣɫɬɜɚɦɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶɧɨɣ ɬɟɯɧɢɤɢ. ɉɪɟɞɥɚɝɚɟɦɨɟ ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɤɨɧɫɩɟɤɬ ɥɟɤɰɢɣ, ɱɢɬɚɟɦɵɯ ɚɜɬɨɪɨɦ ɛɨɥɟɟ ɞɟɫɹɬɢ ɥɟɬ ɫɬɭɞɟɧɬɚɦ ɫɩɟɰɢɚɥɶɧɨɫɬɢ «ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɢ ɚɜɬɨɦɚɬɢɤɚ ɩɪɨɦɵɲɥɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɤɨɦɩɥɟɤɫɨɜ» ɞɧɟɜɧɨɣ, ɜɟɱɟɪɧɟɣ ɢ ɡɚɨɱɧɨɣ ɮɨɪɦ ɨɛɭɱɟɧɢɹ. ɉɨɫɨɛɢɟ ɪɚɡɪɚɛɨɬɚɧɨ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɪɟɛɨɜɚɧɢɹɦɢ ȽɈɋ ɩɨ ɞɢɫɰɢɩɥɢɧɚɦ «ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɩɪɢɜɨɞ» ɢ «Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ». ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɢɡɥɨɠɟɧɢɹ ɦɚɬɟɪɢɚɥɚ ɫɜɹɡɚɧɚ ɫ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ ɫɜɨɟɜɪɟɦɟɧɧɨɣ ɩɨɞɝɨɬɨɜɤɢ ɫɬɭɞɟɧɬɨɜ ɤ ɜɵɩɨɥɧɟɧɢɸ ɥɚɛɨɪɚɬɨɪɧɵɯ ɪɚɛɨɬ ɢ ɤɭɪɫɨɜɨɝɨ ɩɪɨɟɤɬɚ ɩɨ ɞɢɫɰɢɩɥɢɧɟ. ɇɟɨɛɯɨɞɢɦɨɫɬɶ ɢɡɞɚɧɢɹ ɤɨɧɫɩɟɤɬɚ ɥɟɤɰɢɣ ɨɛɭɫɥɨɜɥɟɧɚ ɧɟɞɨɫɬɚɬɨɱɧɵɦ ɤɨɥɢɱɟɫɬɜɨɦ ɭɱɟɛɧɨɣ ɥɢɬɟɪɚɬɭɪɵ ɩɨ ɞɚɧɧɨɦɭ ɧɚɩɪɚɜɥɟɧɢɸ, ɱɬɨ ɜɵɡɵɜɚɟɬ ɡɚɬɪɭɞɧɟɧɢɟ ɜ ɢɡɭɱɟɧɢɢ ɞɢɫɰɢɩɥɢɧɵ, ɨɫɨɛɟɧɧɨ ɫɬɭɞɟɧɬɚɦɢ ɡɚɨɱɧɨɣ ɮɨɪɦɵ ɨɛɭɱɟɧɢɹ. Ⱥɜɬɨɪ ɩɪɢɡɧɚɬɟɥɟɧ ɞɨɰɟɧɬɭ Ɇ.Ⱥ.Ƚɪɢɝɨɪɶɟɜɭ, ɨɤɚɡɚɜɲɟɦɭ ɛɨɥɶɲɭɸ ɩɨɦɨɳɶ ɩɪɢ ɪɟɞɚɤɬɢɪɨɜɚɧɢɢ ɢ ɩɨɞɝɨɬɨɜɤɟ ɪɭɤɨɩɢɫɢ ɤ ɢɡɞɚɧɢɸ, ɜɵɪɚɠɚɟɬ ɛɥɚɝɨɞɚɪɧɨɫɬɶ ɞɨɰɟɧɬɭ ȼ.ɂ.ɋɦɢɪɧɨɜɭ ɡɚ ɰɟɧɧɵɟ ɩɨɥɟɡɧɵɟ ɡɚɦɟɱɚɧɢɹ, ɚ ɬɚɤɠɟ ɫɬɭɞɟɧɬɚɦ Ⱥ. ɒɟɢɧɭ, Ɇ. ɉɚɭɬɤɢɧɭ, Ⱥ. ȼɚɥɨɜɭ, Ⱥ. ȿɜɫɟɟɜɨɣ, ȼ. Ⱦɟɤɤɟɪɭ ɡɚ ɚɤɬɢɜɧɭɸ ɩɨɦɨɳɶ ɜ ɩɨɞɝɨɬɨɜɤɟ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ.

3

Ƚɥɚɜɚ ɩɟɪɜɚɹ

ȼȼȿȾȿɇɂȿ. ɈɋɇɈȼɇɕȿ ɉɈɇəɌɂə ɂ ɈɉɊȿȾȿɅȿɇɂə 1.1. ɂɫɬɨɪɢɹ ɪɚɡɜɢɬɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ȼ ɥɸɛɨɦ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɦ ɦɟɯɚɧɢɡɦɟ ɦɨɠɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ɬɪɢ ɫɭɳɟɫɬɜɟɧɧɵɟ ɱɚɫɬɢ: – Ⱦ – ɦɚɲɢɧɭ - ɞɜɢɝɚɬɟɥɶ; – ɉɆ – ɩɟɪɟɞɚɬɨɱɧɵɣ ɦɟɯɚɧɢɡɦ; – ɊɆ (ɊɈ) – ɪɚɛɨɱɭɸ ɦɚɲɢɧɭ (ɪɚɛɨɱɢɣ ɨɪɝɚɧ), ɦɚɲɢɧɭ-ɨɪɭɞɢɟ. ɋɨɜɨɤɭɩɧɨɫɬɶ Ⱦ + ɉɆ = ɉ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɢɜɨɞ ɫ ɟɝɨ ɧɚɡɧɚɱɟɧɢɟɦ – ɩɪɢɜɨɞɢɬɶ ɜ ɞɜɢɠɟɧɢɟ ɪɚɛɨɱɭɸ ɦɚɲɢɧɭ. ɇɚ ɩɪɨɬɹɠɟɧɢɢ ɧɟɫɤɨɥɶɤɢɯ ɬɵɫɹɱɟɥɟɬɢɣ ɱɟɥɨɜɟɤ ɫɨɡɞɚɟɬ ɦɚɲɢɧɵ ɢ ɦɟɯɚɧɢɡɦɵ, ɫɩɨɫɨɛɧɵɟ ɢɡɛɚɜɢɬɶ ɟɝɨ ɨɬ ɬɹɠɺɥɨɝɨ ɢ ɢɡɧɭɪɢɬɟɥɶɧɨɝɨ ɬɪɭɞɚ. ɋɩɨɫɨɛ ɩɨɥɭɱɟɧɢɹ ɷɧɟɪɝɢɢ, ɧɟɨɛɯɨɞɢɦɵɣ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɪɚɛɨɬɵ ɜ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɵɯ ɩɪɨɰɟɫɫɚɯ, ɧɚ ɜɫɟɯ ɷɬɚɩɚɯ ɢɫɬɨɪɢɢ ɪɚɡɜɢɬɢɹ ɱɟɥɨɜɟɱɟɫɤɨɝɨ ɨɛɳɟɫɬɜɚ ɨɤɚɡɵɜɚɥ ɪɟɲɚɸɳɟɟ ɜɥɢɹɧɢɟ ɧɚ ɪɚɡɜɢɬɢɟ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɵɯ ɫɢɥ. ɋɨɡɞɚɧɢɟ ɧɨɜɵɯ, ɛɨɥɟɟ ɫɨɜɟɪɲɟɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ, ɩɟɪɟɯɨɞɵ ɤ ɧɨɜɵɦ ɜɢɞɚɦ ɩɪɢɜɨɞɚ ɪɚɛɨɱɢɯ ɦɚɲɢɧ ɹɜɥɹɥɢɫɶ ɤɪɭɩɧɵɦɢ ɢɫɬɨɪɢɱɟɫɤɢɦɢ ɜɟɯɚɦɢ ɧɚ ɩɭɬɢ ɪɚɡɜɢɬɢɹ ɦɚɲɢɧɧɨɝɨ ɩɪɨɢɡɜɨɞɫɬɜɚ. ȼ ɞɪɟɜɧɨɫɬɢ ɨɫɧɨɜɧɵɦ ɜɢɞɨɦ ɩɪɢɜɨɞɚ ɛɵɥ ɪɭɱɧɨɣ ɩɪɢɜɨɞ, ɩɪɢ ɤɨɬɨɪɨɦ ɜ ɤɚɱɟɫɬɜɟ ɦɚɲɢɧɵ-ɞɜɢɝɚɬɟɥɹ ɢɫɩɨɥɶɡɨɜɚɥɚɫɶ ɦɭɫɤɭɥɶɧɚɹ ɫɢɥɚ ɱɟɥɨɜɟɤɚ. ɗɬɨɬ ɜɢɞ ɩɪɢɜɨɞɚ ɫɨɯɪɚɧɢɥɫɹ ɞɨ ɫɢɯ ɩɨɪ – ɦɹɫɨɪɭɛɤɚ, ɲɜɟɣɧɚɹ ɦɚɲɢɧɚ. ɇɚ ɫɦɟɧɭ ɪɭɱɧɨɦɭ ɩɪɢɜɨɞɭ ɩɪɢɲɟɥ ɤɨɧɧɵɣ ɩɪɢɜɨɞ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɭɫɤɭɥɶɧɨɣ ɫɢɥɵ ɠɢɜɨɬɧɵɯ. Ʉ ɩɪɢɦɟɪɭ – ɲɚɯɬɧɵɣ ɩɨɞɴɟɦ, «ɰɵɝɚɧɫɤɚɹ ɥɨɲɚɞɶ». ɉɪɢɦɟɧɟɧɢɟ ɞɥɹ ɩɪɢɜɨɞɚ ɫɢɥɵ ɜɟɬɪɚ ɢ ɩɚɞɚɸɳɟɣ ɫɢɥɵ ɜɨɞɵ ɩɪɢɜɟɥɢ ɤ ɫɨɡɞɚɧɢɸ ɜɨɞɹɧɨɝɨ ɢ ɜɟɬɪɹɧɨɝɨ ɩɪɢɜɨɞɚ. ȼɨɞɹɧɚɹ ɬɭɪɛɢɧɚ, ɭɫɬɚɧɨɜɥɟɧɧɚɹ ɜ ɩɥɨɬɢɧɟ ɜɨɞɨɯɪɚɧɢɥɢɳɚ, ɜɪɚɳɚɟɬ ɨɛɳɢɣ ɬɪɚɧɫɦɢɫɫɢɨɧɧɵɣ ɜɚɥ, ɨɬ ɤɨɬɨɪɨɝɨ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɤ ɤɚɠɞɨɣ ɢɡ ɦɧɨɝɨɱɢɫɥɟɧɧɵɯ ɪɚɛɨɱɢɯ ɦɚɲɢɧ ɩɟɪɟɞɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɲɤɢɜɚ ɢ ɪɟɦɟɧɧɨɣ ɩɟɪɟɞɚɱɢ. ɉɨɫɥɟ ɡɚɦɟɧɵ ɜɨɞɹɧɨɝɨ ɩɪɢɜɨɞɚ ɧɚ ɩɪɢɜɨɞ ɨɬ ɩɚɪɨɜɵɯ ɦɚɲɢɧ ɏIɏ ɜɟɤ ɧɚɡɜɚɧ ɜɟɤɨɦ ɩɚɪɚ. ȼ ɩɚɪɨɜɨɦ ɩɪɢɜɨɞɟ (ɪɢɫ.1.1) ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɩɟɪɟɞɚɺɬɫɹ ɨɬ ɩɚɪɨɜɨɝɨ ɞɜɢɝɚɬɟɥɹ ɤ ɦɧɨɝɨɱɢɫɥɟɧɧɵɦ ɪɚɛɨɱɢɦ ɨɪɝɚɧɚɦ ɱɟɪɟɡ ɬɪɚɧɫȾ ɦɢɫɫɢɨɧɧɵɣ ɜɚɥ ɢ ɪɟɦɟɧɧɭɸ ɩɟɪɟɞɚɱɭ – ɷɬɨ ɝɪɭɩɩɨɜɨɣ ɬɪɚɧɫɦɢɫɫɢɨɧɧɵɣ (ɦɟɯɚɧɢɱɟɫɤɢɣ) ɩɪɢɜɨɞ. ȼ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɪɢɜɨɞɟ ɨɫɧɨɜɧɵɦ ɢɫɬɨɱɧɢɤɨɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɫɬɚɧɨɜɢɬɫɹ ɊɆ ɊɆ ɊɆ ɊɆ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɶ, ɏɏ ɜɟɤ ɦɨɠɧɨ ɧɚɡɜɚɬɶ ɜɟɤɨɦ ɷɥɟɤɬɪɢɱɟɫɬɜɚ, ɨɫɧɨɜɧɨɣ ɬɢɩ ɩɪɢɜɨɞɚ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ – ɷɥɟɤɊɢɫ. 1.1. ɋɯɟɦɚ ɩɚɪɨɜɨɝɨ ɩɪɢɜɨɞɚ: ɬɪɨɩɪɢɜɨɞ. Ⱦ – ɩɚɪɨɜɨɣ ɞɜɢɝɚɬɟɥɶ; ɂɫɬɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɧɚɱɢɧɚɊɆ – ɪɚɛɨɱɚɹ ɦɚɲɢɧɚ ɟɬɫɹ ɫ ɩɟɪɜɨɣ ɩɨɥɨɜɢɧɵ ɏIɏ ɜɟɤɚ. Ɉɬɤɪɵɬɢɟ Ƚ.ɏ. ɗɪɫɬɟɞɨɦ ɡɚɤɨɧɚ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɩɪɨɜɨɞɧɢɤɚ ɫ ɬɨɤɨɦ (1819 ɝ.) ɢ Ɇ. Ɏɚɪɚɞɟɟɦ ɡɚɤɨɧɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ (1831 ɝ.) ɩɨɫɥɭɠɢɥɢ ɦɨɳɧɵɦ ɬɨɥɱɤɨɦ ɤ ɪɚɡɜɢɬɢɸ ɩɪɢɤɥɚɞɧɨɣ ɷɥɟɤɬɪɨɬɟɯɧɢɤɢ. 4

ɍɠɟ ɜ 1834 ɝ. ɪɭɫɫɤɢɣ ɚɤɚɞɟɦɢɤ Ȼ.ɋ. əɤɨɛɢ ɩɪɢ ɭɱɚɫɬɢɢ ɚɤɚɞɟɦɢɤɚ ɗ.ɏ. Ʌɟɧɰɚ ɫɤɨɧɫɬɪɭɢɪɨɜɚɥ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɶ, ɨɫɧɨɜɚɧɧɵɣ ɧɚ ɷɬɢɯ ɡɚɤɨɧɚɯ, ɢ ɜ 1838 ɝ. ɫɨɡɞɚɥ ɩɟɪɜɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɉɪɢɦɟɧɟɧɢɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ ɫɞɟɪɠɢɜɚɥɨɫɶ ɨɬɫɭɬɫɬɜɢɟɦ ɧɚɞɟɠɧɵɯ ɢɫɬɨɱɧɢɤɨɜ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ. ȼɟɥɢɱɚɣɲɟɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɜɫɟɝɨ ɞɚɥɶɧɟɣɲɟɝɨ ɪɚɡɜɢɬɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɢɦɟɥɨ ɨɬɤɪɵɬɢɟ ɜ 1886 ɝ. Ƚ. Ɏɟɪɪɚɪɢɫɨɦ ɢ ɇ. Ɍɟɫɥɚ ɹɜɥɟɧɢɹ ɜɪɚɳɚɸɳɟɝɨɫɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ, ɛɥɚɝɨɞɚɪɹ ɤɨɦɩɥɟɤɫɭ ɜɵɞɚɸɳɢɯɫɹ ɪɚɛɨɬ Ɇ.Ɉ. Ⱦɨɥɢɜɨ-Ⱦɨɛɪɨɜɨɥɶɫɤɨɝɨ, ɤɨɬɨɪɵɣ ɜ 1888 ɝ. ɩɪɟɞɥɨɠɢɥ ɢ ɪɟɚɥɢɡɨɜɚɥ ɬɪɟɯɮɚɡɧɭɸ ɫɢɫɬɟɦɭ ɩɟɪɟɞɚɱɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɢ ɪɚɡɪɚɛɨɬɚɥ ɜ 1889 ɝ. ɬɪɟɯɮɚɡɧɵɣ ɚɫɢɧɯɪɨɧɧɵɣ ɞɜɢɝɚɬɟɥɶ ɫ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɨɛɦɨɬɤɨɣ ɫɬɚɬɨɪɚ ɢ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ ɜ ɜɢɞɟ ɛɟɥɢɱɶɟɝɨ ɤɨɥɟɫɚ. ɗɬɨɬ ɜɢɞ ɩɪɢɜɨɞɚ ɫɬɚɥ ɢɧɬɟɧɫɢɜɧɨ ɜɧɟɞɪɹɬɶɫɹ ɜ ɩɪɨɦɵɲɥɟɧɧɨɫɬɶ. ɗɥɟɤɬɪɨɞɜɢɝɚɬɟɥɶ ɭɫɬɚɧɚɜɥɢɜɚɥɫɹ ɜɦɟɫɬɨ ɩɚɪɨɜɨɝɨ ɞɜɢɝɚɬɟɥɹ – ɩɨɹɜɢɥɫɹ ɝɪɭɩɩɨɜɨɣ ɬɪɚɧɫɦɢɫɫɢɨɧɧɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ, ɫɨɯɪɚɧɹɥɚɫɶ ɪɚɡɜɟɬɜɥɟɧɧɚɹ ɫɟɬɶ ɩɟɪɟɞɚɬɨɱɧɵɯ ɭɫɬɪɨɣɫɬɜ, ɱɟɪɟɡ ɤɨɬɨɪɭɸ ɞɜɢɠɟɧɢɟ ɩɟɪɟɞɚɜɚɥɨɫɶ ɧɟɫɤɨɥɶɤɢɦ ɊɆ, ɫ ɫɨɯɪɚɧɟɧɢɟɦ ɜɫɟɯ ɧɟɞɨɫɬɚɬɤɨɜ ɬɪɚɧɫɦɢɫɫɢɨɧɧɨɝɨ ɩɪɢɜɨɞɚ. ȼ ɫɨɜɪɟɦɟɧɧɨɣ ɩɪɚɤɬɢɤɟ ɩɪɢɦɟɧɹɟɬɫɹ ɝɪɭɩɩɨɜɨɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ (ɪɢɫ.1.2.), ɧɨ ɬɨɥɶɤɨ ɞɥɹ ɨɞɧɨɣ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ, ɜɫɟ ɪɚɛɨɱɢɟ ɨɪɝɚɧɵ ɤɨɬɨɪɨɣ ɩɪɢɜɨɞɹɬɫɹ ɨɞɧɢɦ ɞɜɢɝɚɬɟɥɟɦ ɗȾ (ɩɪɢɦɟɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɲɜɟɣɧɨɣ ɦɚɲɢɧɵ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɩɪɨɫɬɟɣɲɟɝɨ ɬɨɤɚɪɧɨɝɨ ɫɬɚɧɤɚ). ɇɚɫɬɨɹɳɟɣ ɪɟɜɨɥɸɰɢɟɣ ɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ ɢ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ ɫɬɚɥ ɩɟɪɟɯɨɞ ɤ ɢɧɞɢɜɢɞɭɚɥɶɧɨɦɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ, ɜ ɤɨɬɨɪɨɦ ɞɜɢɝɚɬɟɥɶ Ⱦ ɨɛɟɫɩɟ-ɱɢɜɚɟɬ ɞɜɢɠɟɧɢɟ ɬɨɥɶɤɨ ɨɞɧɨɝɨ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ (ɪɢɫ. 1.3).

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Ɋɢɫ.1.2. ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɝɪɭɩɩɨɜɨɣ

Ɋɢɫ.1.3. ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɢɧɞɢɜɢɞɭɚɥɶɧɵɣ

Ⱦɨɫɬɨɢɧɫɬɜɚɦɢ ɢɧɞɢɜɢɞɭɚɥɶɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɹɜɥɹɸɬɫɹ: – ɩɪɢɛɥɢɠɟɧɢɟ ɪɚɛɨɱɢɯ ɫɜɨɣɫɬɜ ɞɜɢɝɚɬɟɥɹ ɤ ɬɪɟɛɨɜɚɧɢɹɦ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. ɇɚ ɪɢɫ. 1.4 ɩɪɟɞɫɬɚɜɥɟɧɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ȺȾ ɢ ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ Ⱦɉȼ ɩɪɢɜɨɞɚ ɫɬɨɥɚ ɩɪɨɞɨɥɶɧɨ-ɫɬɪɨɝɚɥɶɧɨɝɨ ɫɬɚɧɤɚ. ɉɪɢ ɨɞɢɧɚɤɨɜɨɣ ɪɚɛɨɱɟɣ ɫɤɨɪɨɫɬɢ Ⱦɉȼ ɢ ȺȾ ɜ ɪɟɠɢɦɟ ɪɟɡɚɧɢɹ ɜɨɡɜɪɚɳɟɧɢɟ ɫɬɨɥɚ ɜ ɢɫɯɨɞɧɨɟ ɩɨɥɨɠɟɧɢɟ ɜɵɩɨɥɧɹɟɬɫɹ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ, ɩɪɢ ɷɬɨɦ ɫɤɨɪɨɫɬɶ Ⱦɉȼ ɡɧɚɱɢɬɟɥɶɧɨ ɜɵɲɟ ɫɤɨɪɨɫɬɢ ȺȾ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɫɨɤɪɚɬɢɬɶ ɜɪɟɦɹ ɜɨɡɜɪɚɬɚ ɢ ɭɜɟɥɢɱɢɬɶ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɫɬɚɧɤɚ; 5

– ɩɟɪɟɧɨɫ ɨɩɟɪɚɰɢɢ ɭɩɪɚɜɥɟɧɢɹ ɫ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɧɚ ɞɜɢɝɚɬɟɥɶ, ɩɨɹɜɢɥɚɫɶ ɜɨɡɦɨɠɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɩɪɟɨɛɪɚɡɨɜɚɧɧɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ 12 ɫɤɨɪɨɫɬɟɣ ɜɪɚɳɟɧɢɹ ɲɩɢɧɞɟɥɹ ɬɨɤɚɪɧɨɝɨ ɫɬɚɧɤɚ ɩɪɢ ɧɟɪɟɝɭɥɢɪɭɟɦɨɦ ȺȾ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ ɬɪɟɛɭɟɬɫɹ ɞɟɜɹɬɶ ɩɚɪ ɲɟɫɬɟɪɺɧ, ɩɪɢ ɞɜɭɯɫɤɨɪɨɫɬɧɨɦ ȺȾ, ɤɨɝɞɚ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɹɟɬɫɹ ɜ ɞɜɚ ɪɚɡɚ – ɫɟɦɶ ɩɚɪ ɲɟɫɬɟɪɺɧ, ɩɪɢ ɩɪɢɦɟɧɟɧɢɢ ɞɜɢɝɚɬɟɥɹ ɫ ɩɥɚɜɧɵɦ ɪɟɝɭɥɢɪɨɜɚɧɢɟɦ ɫɤɨɪɨɫɬɢ ɨɬ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ – ɬɨɥɶɤɨ ɱɟɬɵɪɟ ɩɚɪɵ ɲɟɫɬɟɪɺɧ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɭɩɪɚɜɥɟɧɢɟ ɪɚȦ ɛɨɱɢɦ ɩɪɨɰɟɫɫɨɦ, ɩɪɢ ɷɬɨɦ ɫɧɢɠɚɸɬɫɹ ɝɚɛɚɪɢɬɵ ɤɨɪɨɛɤɢ ɩɟɪɟɞɚɱ; – ɜɨɡɦɨɠɧɨɫɬɶ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɪɚȦɏɏ ɛɨɱɟɝɨ ɩɪɨɰɟɫɫɚ, ɤɨɝɞɚ ɤɚɠɞɵɦ ɪɚɛɨȾɉȼ ɱɢɦ ɨɪɝɚɧɨɦ ɦɨɠɧɨ ɭɩɪɚɜɥɹɬɶ ɩɨ ɡɚȦɏɏ ɞɚɧɧɨɣ ɩɪɨɝɪɚɦɦɟ ɪɚɛɨɬɵ. ȦɊ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɧɞɢɜɢɞɭɚɥɶɧɵɣ ȺȾ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɩɨɡɜɨɥɹɟɬ ɧɚɥɨɠɢɬɶ ɧɚ ɧɟɝɨ ɮɭɧɤɰɢɢ ɩɪɢɜɟɞɟɧɢɹ ɜ ɞɜɢɠɟɧɢɟ ɢ ɭɩɪɚɜɥɟɧɢɹ ɷɬɢɦ ɞɜɢɠɟɧɢɟɦ. Ʉ ɧɟɞɨɫɬɚɬɤɚɦ ɢɧɞɢɜɢɞɭɚɥɶɧɨɝɨ Ɇ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɦɨɠɧɨ ɨɬɧɟɫɬɢ ɛɨɥɟɟ ɜɵɫɨɤɭɸ ɩɟɪɜɨɧɚɱɚɥɶɧɭɸ ɫɬɨɢɆɏɏ ɆɊ ɦɨɫɬɶ ɨɛɨɪɭɞɨɜɚɧɢɹ, ɚ ɬɚɤɠɟ ɫɧɢɠɟɧɢɟ ɄɉȾ ɢ cosĳ ɩɪɢ ɭɦɟɧɶɲɟɧɢɢ Ɋɢɫ. 1.4. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɟɣ (ɜ ɝɪɭɩɩɨɜɨɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɟɣ ɫɬɨɥɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ – ɜɵɲɟ ɩɨɬɟɪɢ ɦɨɳɩɪɨɞɨɥɶɧɨ-ɫɬɪɨɝɚɥɶɧɨɝɨ ɫɬɚɧɤɚ ɧɨɫɬɢ ɜ ɩɟɪɟɞɚɱɚɯ). Ɋɚɡɧɨɜɢɞɧɨɫɬɶɸ ɢɧɞɢɜɢɞɭɚɥɶɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɹɜɥɹɟɬɫɹ ɦɧɨɝɨɞɜɢɝɚɬɟɥɶɧɵɣ ɜɡɚɢɦɨɫɜɹɡɚɧɧɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ (ɪɢɫ. 1.5), ɜ ɤɨɬɨɪɨɦ ɤɚɠɞɵɣ ɪɚɛɨɱɢɣ ɨɪɝɚɧ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɩɪɢɜɨɞɢɬɫɹ ɜ ɞɜɢɠɟɧɢɟ ɧɟɫɤɨɥɶɤɢɦɢ ɞɜɢɝɚɬɟɥɹɦɢ (ɷɤɫɤɚɜɚɬɨɪ – ɢɡ-ɡɚ ɫɥɨɠɧɨɫɬɢ ɪɚɡɦɟɳɟɧɢɹ ɷɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɹ ɧɚ ɩɨɜɨɪɨɬɧɨɣ ɩɥɚɬɮɨɪɦɟ, ɤɨɧɜɟɣɟɪ – ɢɡ-ɡɚ ɨɝɪɚɧɢɱɟɧɧɨɣ ɩɪɨɱɧɨɫɬɢ ɬɹɝɨɜɨɝɨ ɨɪɝɚɧɚ). ɂɫɤɥɸɱɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɢɯ ɩɟɪɟɞɚɱ ɢ ɩɪɢɛɥɢɠɟɧɢɟ ɞɜɢɝɚɬɟɥɹ ɤ ɪɚɛɨɱɟɦɭ Ⱦ Ⱦ Ⱦ ɨɪɝɚɧɭ ɊɈ ɩɪɢɜɨɞɢɬ ɤ ɫɨɡɞɚɧɢɸ ɛɟɡɪɟɞɭɤɬɨɪɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɮɥɚɧɰɟɜɵɦ ɢɥɢ ɜɫɬɪɨɟɧɧɵɦ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɊɈ ɥɟɦ. ɋɨɡɞɚɧɵ ɷɥɟɤɬɪɨɨɪɭɞɢɹ, ɝɞɟ ɩɢɬɚɧɢɟ ɩɨɞɜɨɞɢɬɫɹ ɤ ɧɟɩɨɞɜɢɠɧɨɦɭ ɪɨɬɨɪɭ, ɚ ɫɬɚɬɨɪ ɹɜɥɹɟɬɫɹ ɱɚɫɬɶɸ ɪɚɛɨɱɟɊɢɫ. 1.5. Ɇɧɨɝɨɞɜɢɝɚɬɟɥɶɧɵɣ ɝɨ ɨɪɝɚɧɚ. ȼ ɷɥɟɤɬɪɨɲɥɢɮɨɜɚɥɤɟ ɧɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɩɨɞɜɢɠɧɨɦ ɫɬɚɬɨɪɟ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɧɚɠɞɚɱɧɵɣ ɤɪɭɝ, ɜ ɷɥɟɤɬɪɨɪɨɥɢɤɟ – ɧɟɫɭɳɚɹ ɱɚɫɬɶ ɪɨɥɢɤɚ, ɬɪɚɧɫɩɨɪɬɢɪɭɸɳɟɝɨ ɡɚɝɨɬɨɜɤɢ ɢɥɢ ɞɪɭɝɢɟ ɲɬɭɱɧɵɟ ɦɚɬɟɪɢɚɥɵ.

6

1.2. Ɏɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɫɨɜɪɟɦɟɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɋɨɜɪɟɦɟɧɧɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɹɜɥɹɟɬɫɹ ɢɧɞɢɜɢɞɭɚɥɶɧɵɦ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɦ. Ɏɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɫɨɜɪɟɦɟɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 1.6. ɋɢɥɨɜɨɣ ɤɚɧɚɥ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ, ɩɨɫɬɭɩɚɸɳɟɣ ɢɡ ɫɢɫɬɟɦɵ ɷɥɟɤɬɪɨɫɧɚɛɠɟɧɢɹ, ɜ ɦɟɯɚɧɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɫ ɩɚɪɚɦɟɬɪɚɦɢ, ɧɟɨɛɯɨɞɢɦɵɦɢ ɞɥɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɭɫɬɚɧɨɜɤɢ. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɷɧɟɪɝɢɢ ɗɉ ɩɪɟɨɛɪɚɡɭɟɬ ɷɧɟɪɝɢɸ ɫɟɬɢ ɜ ɷɧɟɪɝɢɸ, ɩɨɞɚɜɚɟɦɭɸ ɧɚ ɞɜɢɝɚɬɟɥɶ. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɗɆɉ (ɞɜɢɝɚɬɟɥɶ) ɩɪɟɨɛɪɚɡɭɟɬ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɜ ɦɟɯɚɧɢɱɟɫɤɭɸ. Ɇɟɯɚɧɢɱɟɫɤɢɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ Ɇɉ – ɩɪɟɨɛɪɚɡɭɟɬ ɷɧɟɪɝɢɸ ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɜ ɷɧɟɪɝɢɸ ɞɥɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. ɂɧɮɨɪɦɚɰɢɨɧɧɵɣ ɤɚɧɚɥ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɭɸ ɫɢɫɬɟɦɭ ɭɩɪɚɜɥɟɧɢɹ Ⱥɋɍ, ɞɚɬɱɢɤɢ ɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɢ ɢɧɮɨɪɦɚɰɢɢ Ⱦɉɂ, ɡɚɞɚɸɳɢɟ ɭɫɬɪɨɣɫɬɜɚ Ɂɍ, ɭɩɪɚɜɥɹɸɳɢɟ ɭɫɬɪɨɣɫɬɜɚ ɍɍ ɢ ɭɩɪɚɜɥɹɟɬ ɩɨɬɨɤɨɦ ɷɧɟɪɝɢɢ, ɨɫɭɳɟɫɬɜɥɹɟɬ ɫɛɨɪ ɢ ɨɛɪɚɛɨɬɤɭ ɢɧɮɨɪɦɚɰɢɢ ɨ ɫɨɫɬɨɹɧɢɢ ɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɢ ɫɢɫɬɟɦɵ, ɞɢɚɝɧɨɫɬɢɤɭ ɟɟ ɧɟɢɫɩɪɚɜɧɨɫɬɟɣ. ɗɥɟɤɬɪɨɩɪɢɜɨɞɨɦ ɧɚɡɵɜɚɟɬɫɹ ɫɨɜɪɟɦɟɧɧɚɹ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɚɹ ɞɥɹ ɩɪɢɜɟɞɟɧɢɹ ɜ ɞɜɢɠɟɧɢɟ ɪɚɛɨɱɢɯ ɨɪɝɚɧɨɜ ɦɚɲɢɧ ɢ ɭɩɪɚɜɥɟɧɢɹ ɢɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦɢ ɩɪɨɰɟɫɫɚɦɢ ɢ ɫɨɫɬɨɹɳɚɹ ɢɡ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɗɉ, ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɗɆɉ, ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ Ɇɉ ɢ ɭɫɬɪɨɣɫɬɜ ɭɩɪɚɜɥɟɧɢɹ.

1.3. Ɇɟɫɬɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɫɨɜɪɟɦɟɧɧɨɣ ɬɟɯɧɨɥɨɝɢɢ ȼɫɟ ɩɪɨɰɟɫɫɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜ ɦɟɯɚɧɢɱɟɫɤɭɸ ɢ ɨɛɪɚɬɧɨ, ɜɵɩɨɥɧɹɸɬɫɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɦ (§ 90% ɞɜɢɝɚɬɟɥɟɣ ɜ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ - ɷɥɟɤɬɪɢɱɟɫɤɢɟ). Ƚɢɞɪɨɩɪɢɜɨɞ ɢ ɩɧɟɜɦɨɩɪɢɜɨɞ ɧɚɯɨɞɹɬ ɩɪɢɦɟɧɟɧɢɟ ɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɛɨɥɶɲɨɦ ɱɢɫɥɟ ɭɫɬɚɧɨɜɨɤ. ɉɪɟɢɦɭɳɟɫɬɜɚ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ: – ɜɨɡɦɨɠɧɨɫɬɶ ɩɟɪɟɞɚɱɢ ɷɧɟɪɝɢɢ ɧɚ ɛɨɥɶɲɢɟ ɪɚɫɫɬɨɹɧɢɹ; – ɩɨɫɬɨɹɧɧɚɹ ɝɨɬɨɜɧɨɫɬɶ ɤ ɪɚɛɨɬɟ; – ɥɟɝɤɨɫɬɶ ɩɪɟɜɪɚɳɟɧɢɹ ɜ ɞɪɭɝɢɟ ɜɢɞɵ ɷɧɟɪɝɢɢ. ȿɫɥɢ ɜɵɱɢɫɥɢɬɟɥɶɧɭɸ ɬɟɯɧɢɤɭ ɧɚɡɵɜɚɸɬ ɦɨɡɝɨɦ ɫɨɜɪɟɦɟɧɧɵɯ ɬɟɯɧɨɥɨɝɢɣ, ɬɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞ, ɨɛɟɫɩɟɱɢɜɚɹ ɡɚɞɚɧɧɨɟ ɢ ɬɨɱɧɨɟ ɜɵɩɨɥɧɟɧɢɟ ɩɪɨɝɪɚɦɦɢɪɭɟɦɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɪɚɛɨɬɵ, ɹɜɥɹɟɬɫɹ ɦɭɫɤɭɥɚɦɢ ɫɨɜɪɟɦɟɧɧɨɣ ɬɟɯɧɨɥɨɝɢɢ. Ⱦɢɚɩɚɡɨɧ ɦɨɳɧɨɫɬɟɣ ɞɜɢɝɚɬɟɥɟɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɫɨɫɬɚɜɥɹɟɬ 1012 (ɨɬ ɦɤȼɬ – ɜ ɩɪɢɛɨɪɧɵɯ ɫɢɫɬɟɦɚɯ ɞɨ ɞɟɫɹɬɤɨɜ Ɇȼɬ – ɞɥɹ ɩɪɢɜɨɞɚ ɤɨɦɩɪɟɫɫɨɪɚ ɧɚ ɝɚɡɨɜɨɣ ɩɟɪɟɤɚɱɢɜɚɸɳɟɣ ɫɬɚɧɰɢɢ). Ⱦɢɚɩɚɡɨɧ ɩɪɢɦɟɧɹɟɦɵɯ ɫɤɨɪɨɫɬɟɣ ɛɥɢɡɨɤ ɤ 1012 – ɨɬ ɨɞɧɨɝɨ ɨɛɨɪɨɬɚ ɡɚ ɧɟɫɤɨɥɶɤɨ ɱɚɫɨɜ (ɭɫɬɚɧɨɜɤɢ ɞɥɹ ɜɵɬɹɝɢɜɚɧɢɹ ɤɪɢɫɬɚɥɥɨɜ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜ) ɞɨ 150 ɬɵɫɹɱ ɨɛɨɪɨɬɨɜ ɜ ɦɢɧɭɬɭ (ɜ ɜɵɫɨɤɨɬɨɱɧɵɯ ɲɥɢɮɨɜɚɥɶɧɵɯ ɫɬɚɧɤɚɯ). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɨɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɛɟɡɝɪɚɧɢɱɧɨ ɲɢɪɨɤɚ – ɨɬ ɢɫɤɭɫɫɬɜɟɧɧɨɝɨ ɫɟɪɞɰɚ ɞɨ ɲɚɝɚɸɳɟɝɨ ɷɤɫɤɚɜɚɬɨɪɚ.

7

Ⱥɋɍ

ɂɧɮɨɪɦɚɰɢɨɧɧɵɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ

Ⱦɉɂ

ɋɗɋ 8

ɫɟɬɶ

Wɋ Uc Ic fc

ɗɉ

ɍɍ

Ɂɍ

WȾ U I f

WɗɆ ɗɆɉ

ɊȾ M Ȧ

WɊ

WɆ Ɇɉ Mȼ Ȧȼ

Mɪɨ

Ȧɪɨ

Ɍɟɯɧɨɥɨɝɢɱɟɫɤɚɹ ɭɫɬɚɧɨɜɤɚ

Fɪɨ vɪɨ

Ⱦɜɢɝɚɬɟɥɶ ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɱɚɫɬɶ

ɊɈ

Ɇɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ

Ɋɢɫ. 1.6. Ɏɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɗɉ – ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ; ɗɆɉ – ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ; ɊȾ – ɪɨɬɨɪ ɞɜɢɝɚɬɟɥɹ; Ɇɉ – ɦɟɯɚɧɢɱɟɫɤɢɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ; Ⱥɋɍ – ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɚɹ ɫɢɫɬɟɦɚ ɭɩɪɚɜɥɟɧɢɹ; Ⱦɉɂ – ɞɚɬɱɢɤɢ ɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɢ ɢɧɮɨɪɦɚɰɢɢ

1.4. ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɢ ɫɨɜɪɟɦɟɧɧɚɹ ɷɧɟɪɝɟɬɢɤɚ ȼ ɬɟɱɟɧɢɟ ɨɞɧɨɝɨ ɪɚɛɨɱɟɝɨ ɞɧɹ ɨɞɢɧ ɱɟɥɨɜɟɤ ɫ ɩɨɦɨɳɶɸ ɦɭɫɤɭɥɶɧɨɣ ɷɧɟɪɝɢɢ ɦɨɠɟɬ ɜɵɪɚɛɨɬɚɬɶ ɨɤɨɥɨ ɨɞɧɨɝɨ ɤȼɬɱ ɷɧɟɪɝɢɢ. ȼ ɜɵɫɨɤɨɷɥɟɤɬɪɨɮɢɰɢɪɨɜɚɧɧɵɯ ɨɬɪɚɫɥɹɯ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ ɭɫɬɚɧɨɜɥɟɧɧɚɹ ɦɨɳɧɨɫɬɶ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɣ ɜ ɫɪɟɞɧɟɦ ɧɚ ɨɞɧɨɝɨ ɪɚɛɨɬɚɸɳɟɝɨ ɫɨɫɬɚɜɥɹɟɬ ɱɟɬɵɪɟ – ɩɹɬɶ ɤȼɬ, ɱɬɨ ɩɪɢ ɫɟɦɢɱɚɫɨɜɨɦ ɪɚɛɨɱɟɦ ɞɧɟ ɞɚɟɬ ɩɨɬɪɟɛɥɟɧɢɟ 28 – 35 ɤȼɬɱ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɪɚɛɨɱɢɣ ɭɩɪɚɜɥɹɟɬ ɦɟɯɚɧɢɡɦɚɦɢ, ɪɚɛɨɬɚ ɤɨɬɨɪɵɯ ɡɚ ɫɦɟɧɭ ɷɤɜɢɜɚɥɟɧɬɧɚ ɪɚɛɨɬɟ 28-35 ɱɟɥɨɜɟɤ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɟɦ ɜɵɲɟ ɷɥɟɤɬɪɨɜɨɨɪɭɠɟɧɧɨɫɬɶ ɬɪɭɞɚ, ɬɟɦ ɜɵɲɟ ɟɝɨ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ. ɋɨɜɪɟɦɟɧɧɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɨɩɪɟɞɟɥɹɟɬ ɫɨɛɨɣ ɭɪɨɜɟɧɶ ɫɢɥɨɜɨɣ ɷɥɟɤɬɪɨɜɨɨɪɭɠɺɧɧɨɫɬɢ ɬɪɭɞɚ ɢ ɹɜɥɹɟɬɫɹ, ɛɥɚɝɨɞɚɪɹ ɫɜɨɢɦ ɩɪɟɢɦɭɳɟɫɬɜɚɦ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɪɭɝɢɦɢ ɜɢɞɚɦɢ ɩɪɢɜɨɞɨɜ, ɨɫɧɨɜɧɵɦ ɢ ɝɥɚɜɧɵɦ ɫɪɟɞɫɬɜɨɦ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɪɚɛɨɱɢɯ ɦɚɲɢɧ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ. ɗɥɟɤɬɪɨɩɪɢɜɨɞ – ɝɥɚɜɧɵɣ ɩɨɬɪɟɛɢɬɟɥɶ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ (ɛɨɥɟɟ 60% ɜɫɟɣ ɩɪɨɢɡɜɨɞɢɦɨɣ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ), ɨɫɬɚɥɶɧɨɟ ɩɨɬɪɟɛɥɹɸɬ ɷɥɟɤɬɪɨɬɟɯɧɨɥɨɝɢɢ, ɬɪɚɧɫɩɨɪɬ, ɨɫɜɟɳɟɧɢɟ ɢ ɬ.ɩ. ȼ ɭɫɥɨɜɢɹɯ ɞɟɮɢɰɢɬɚ ɷɧɟɪɝɨɪɟɫɭɪɫɨɜ ɷɬɨ ɞɟɥɚɟɬ ɨɫɨɛɨ ɨɫɬɪɨɣ ɩɪɨɛɥɟɦɭ ɷɧɟɪɝɨɫɛɟɪɟɠɟɧɢɹ ɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ. ɋɱɢɬɚɟɬɫɹ, ɱɬɨ ɫɟɝɨɞɧɹ ɫɷɤɨɧɨɦɢɬɶ ɨɞɧɭ ɟɞɢɧɢɰɭ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɪɟɫɭɪɫɨɜ (ɨɞɧɚ ɬɨɧɧɚ ɭɫɥɨɜɧɨɝɨ ɬɨɩɥɢɜɚ) ɜɞɜɨɟ ɞɟɲɟɜɥɟ, ɱɟɦ ɟɺ ɞɨɛɵɬɶ. ɇɟɬɪɭɞɧɨ ɩɪɟɞɜɢɞɟɬɶ, ɱɬɨ ɜ ɩɟɪɫɩɟɤɬɢɜɟ ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɛɭɞɟɬ ɦɟɧɹɬɶɫɹ: ɞɨɛɵɜɚɬɶ ɬɨɩɥɢɜɨ ɜɫɟ ɬɪɭɞɧɟɟ, ɬ.ɤ. ɡɚɩɚɫɵ ɟɝɨ ɜɫɟ ɭɛɵɜɚɸɬ. ɂɬɚɤ, ɧɚɥɢɰɨ ɞɜɟ ɩɪɨɛɥɟɦɵ ɪɚɡɜɢɬɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: 1) ɚɫɲɢɪɟɧɢɟ ɮɭɧɤɰɢɨɧɚɥɶɧɵɯ ɜɨɡɦɨɠɧɨɫɬɟɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɪɚɡɧɨɨɛɪɚɡɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɢɡɜɨɞɫɬɜɚɯ; 2) ɨɫɬɪɨɟ ɬɪɟɛɨɜɚɧɢɟ ɷɤɨɧɨɦɧɨ ɪɚɫɯɨɞɨɜɚɬɶ ɷɧɟɪɝɢɸ ɢ ɞɪɭɝɢɟ ɪɟɫɭɪɫɵ.

1.5. Ɉɛɳɢɟ ɬɪɟɛɨɜɚɧɢɹ ɤ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ Ƚɥɚɜɧɵɟ ɩɨɤɚɡɚɬɟɥɢ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɤɚɤ ɫɢɫɬɟɦɭ, ɨɬɜɟɬɫɬɜɟɧɧɭɸ ɡɚ ɭɩɪɚɜɥɹɟɦɨɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɷɧɟɪɝɢɢ: 1. ɇɚɞɺɠɧɨɫɬɶ – ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɨɛɹɡɚɧ ɜɵɩɨɥɧɢɬɶ ɡɚɞɚɧɧɵɟ ɮɭɧɤɰɢɢ ɜ ɨɝɨɜɨɪɟɧɧɵɯ ɭɫɥɨɜɢɹɯ ɜ ɬɟɱɟɧɢɟ ɨɩɪɟɞɟɥɺɧɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɜɪɟɦɟɧɢ. ȿɫɥɢ ɷɬɨ ɧɟ ɨɛɟɫɩɟɱɟɧɨ, ɜɫɟ ɨɫɬɚɥɶɧɵɟ ɤɚɱɟɫɬɜɚ ɨɤɚɠɭɬɫɹ ɛɟɫɩɨɥɟɡɧɵɦɢ. ɇɟɭɱɺɬ ɧɚɞɺɠɧɨɫɬɢ ɩɪɢɜɨɞɢɬ ɤ ɬɹɠɺɥɵɦ ɩɨɫɥɟɞɫɬɜɢɹɦ; 2. Ɍɨɱɧɨɫɬɶ – ɝɥɚɜɧɚɹ ɮɭɧɤɰɢɹ ɩɪɢɜɨɞɚ – ɨɫɭɳɟɫɬɜɥɹɬɶ ɭɩɪɚɜɥɹɟɦɨɟ ɞɜɢɠɟɧɢɟ ɫ ɡɚɞɚɧɧɨɣ ɬɨɱɧɨɫɬɶɸ; 3. Ȼɵɫɬɪɨɞɟɣɫɬɜɢɟ – ɫɩɨɫɨɛɧɨɫɬɶ ɫɢɫɬɟɦɵ ɞɨɫɬɚɬɨɱɧɨ ɛɵɫɬɪɨ ɪɟɚɝɢɪɨɜɚɬɶ ɧɚ ɪɚɡɥɢɱɧɵɟ ɜɨɡɞɟɣɫɬɜɢɹ; 4. Ʉɚɱɟɫɬɜɨ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ – ɨɛɟɫɩɟɱɟɧɢɟ ɨɩɪɟɞɟɥɺɧɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɢɯ ɩɪɨɬɟɤɚɧɢɹ ɜɨ ɜɪɟɦɟɧɢ; 5. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɷɮɮɟɤɬɢɜɧɨɫɬɶ – ɥɸɛɨɣ ɩɪɨɰɟɫɫ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɟɪɟɞɚɱɢ ɷɧɟɪɝɢɢ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɩɨɬɟɪɹɦɢ. ɇɟɨɩɪɚɜɞɚɧɧɨ ɛɨɥɶɲɢɟ ɩɨɬɟɪɢ – ɷɬɨ ɡɪɹ ɡɚɬɪɚɱɟɧɧɵɟ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɪɟɫɭɪɫɵ ɢ ɬɪɭɞ ɥɸɞɟɣ ɩɨ ɩɪɟɜɪɚɳɟɧɢɸ ɢɯ ɜ ɷɧɟɪɝɢɸ; 6. ɋɨɜɦɟɫɬɢɦɨɫɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɫɢɫɬɟɦɨɣ ɷɥɟɤɬɪɨɫɧɚɛɠɟɧɢɹ, ɨɫɨɛɟɧɧɨ ɩɪɢ ɜɧɟɞɪɟɧɢɢ ɬɢɪɢɫɬɨɪɧɵɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ; 9

7. Ɋɟɫɭɪɫɨɺɦɤɨɫɬɶ – ɦɚɬɟɪɢɚɥɨɺɦɤɨɫɬɶ ɢ ɷɧɟɪɝɨɺɦɤɨɫɬɶ, ɡɚɥɨɠɟɧɧɚɹ ɜ ɤɨɧɫɬɪɭɤɰɢɸ ɢ ɬɟɯɧɨɥɨɝɢɸ ɩɪɨɢɡɜɨɞɫɬɜɚ, ɬɪɭɞɨɺɦɤɨɫɬɶ ɢɡɝɨɬɨɜɥɟɧɢɹ, ɧɚɥɚɞɤɢ, ɪɟɦɨɧɬɚ, ɷɤɫɩɥɭɚɬɚɰɢɢ. ɗɬɨɬ ɩɨɤɚɡɚɬɟɥɶ – ɫɚɦɵɣ ɫɥɨɠɧɵɣ, ɤɨɦɩɥɟɤɫɧɨ ɫɜɹɡɚɧ ɤɚɤ ɫ ɩɪɟɞɵɞɭɳɢɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ, ɬɚɤ ɢ ɫ ɭɪɨɜɧɟɦ ɬɟɯɧɨɥɨɝɢɢ, ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɫɢɬɭɚɰɢɟɣ ɢ ɞɪɭɝɢɦɢ ɮɚɤɬɨɪɚɦɢ. ȼɫɟ ɩɨɤɚɡɚɬɟɥɢ – ɬɟɯɧɢɱɟɫɤɢɟ, ɬ.ɤ. ɨɛɟɫɩɟɱɢɜɚɸɬɫɹ ɬɟɯɧɢɱɟɫɤɢɦɢ ɫɪɟɞɫɬɜɚɦɢ. ɇɨ ɜɦɟɫɬɟ ɫ ɬɟɦ ɜɫɟ ɨɧɢ ɢɦɟɸɬ ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɺɧɧɵɣ ɷɤɨɧɨɦɢɱɟɫɤɢɣ ɫɦɵɫɥ: ɱɟɦ ɜɵɲɟ ɤɚɤɨɣ-ɥɢɛɨ ɩɨɤɚɡɚɬɟɥɶ – ɬɟɦ ɛɨɥɶɲɟ ɡɚɬɪɚɬɵ. Ʉɪɨɦɟ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ ɩɨɤɚɡɚɬɟɥɟɣ ɢɦɟɸɬ ɛɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ ɢ ɬɚɤɢɟ ɩɨɤɚɡɚɬɟɥɢ, ɤɚɤ ɤɨɦɩɥɟɤɬɧɨɫɬɶ, ɡɚɜɨɞɫɤɚɹ ɝɨɬɨɜɧɨɫɬɶ, ɞɢɡɚɣɧɟɪɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɭɞɨɛɫɬɜɨ ɷɤɫɩɥɭɚɬɚɰɢɢ ɢ ɞɪɭɝɢɟ.

1.6. ɋɜɹɡɶ Ɍɗɉ ɫ ɞɪɭɝɢɦɢ ɞɢɫɰɢɩɥɢɧɚɦɢ Ʉɭɪɫ Ɍɗɉ ɨɩɢɪɚɟɬɫɹ ɧɚ ɤɭɪɫɵ ɦɟɯɚɧɢɤɢ, ɌɈɗ, ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɲɢɧ, ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶɧɨɣ ɬɟɯɧɢɤɢ, ɌȺɍ. ɋɜɹɡɶ Ɍɗɉ ɫ ɞɪɭɝɢɦɢ ɞɢɫɰɢɩɥɢɧɚɦɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 1.7. Ɉɛɳɟɬɟɨɪɟɬɢɱɟɫɤɢɟ ɞɢɫɰɢɩɥɢɧɵ

ɌȺɍ

ɗɥɟɤɬɪɢɱɟɫɤɢɟ ɦɚɲɢɧɵ

ɌɈɗ

ɗɥɟɦɟɧɬɵ ɫɢɫɬɟɦ ɚɜɬɨɦɚɬɢɡɚɰɢɢ

Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

ɋɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ

Ɇɢɤɪɨɩɪɨɰɟɫɫɨɪɧɵɟ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ

ɉɪɟɨɛɪɚɡɨɜɚɬɟɥɶɧɚɹ ɬɟɯɧɢɤɚ

Ɇɟɯɚɧɢɤɚ

ɗɥɟɤɬɪɨɫɧɚɛɠɟɧɢɟ ɩɪɨɦɩɪɟɞɩɪɢɹɬɢɣ

Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɬɢɩɨɜɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ

Ⱥɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɬɢɩɨɜɵɯ ɦɟɯɚɧɢɡɦɨɜ

Ɋɢɫ. 1.7. ɋɜɹɡɶ Ɍɗɉ ɫ ɞɪɭɝɢɦɢ ɞɢɫɰɢɩɥɢɧɚɦɢ ȿɫɥɢ ɜ ɤɭɪɫɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɲɢɧ ɢɡɭɱɚɸɬɫɹ ɩɪɢɧɰɢɩɵ ɪɚɛɨɬɵ, ɤɨɧɫɬɪɭɤɰɢɹ, ɪɚɫɱɺɬɵ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɲɢɧ, ɢɯ ɢɫɩɵɬɚɧɢɟ, ɬɨ ɜ ɤɭɪɫɟ Ɍɗɉ – ɜɨɩɪɨɫɵ ɩɪɢɦɟɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɞɜɢɝɚɬɟɥɟɣ, ɦɟɬɨɞɵ ɩɪɢɫɩɨɫɨɛɥɹɟɦɨɫɬɢ ɫɜɨɣɫɬɜ ɞɜɢɝɚɬɟɥɟɣ ɤ ɬɪɟɛɨɜɚɧɢɹɦ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ. Ɉɫɧɨɜɧɨɟ ɜɧɢɦɚɧɢɟ ɫɨɫɪɟɞɨɬɨɱɟɧɨ ɧɚ ɫɬɚɬɢɱɟɫɤɢɯ ɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜɚɯ, ɧɚɝɪɟɜɟ ɜ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɪɚɛɨɬɵ, ɜɵɛɨɪɟ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɟɣ ɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɣ.

10

ɐɟɥɶɸ ɨɛɭɱɟɧɢɹ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɢ «ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɢ ɚɜɬɨɦɚɬɢɤɚ ɩɪɨɦɵɲɥɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɤɨɦɩɥɟɤɫɨɜ» ɹɜɥɹɟɬɫɹ ɩɨɞɝɨɬɨɜɤɚ ɢɧɠɟɧɟɪɨɜ ɲɢɪɨɤɨɝɨ ɩɪɨɮɢɥɹ, ɫɩɨɫɨɛɧɵɯ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɢ ɬɜɨɪɱɟɫɤɢ ɪɟɲɚɬɶ ɡɚɞɚɱɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ, ɢɫɫɥɟɞɨɜɚɧɢɹ, ɧɚɥɚɞɤɢ ɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɫɢɫɬɟɦ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɪɨɦɵɲɥɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ ɜ ɥɸɛɵɯ ɨɬɪɚɫɥɹɯ ɧɚɪɨɞɧɨɝɨ ɯɨɡɹɣɫɬɜɚ. Ƚɥɚɜɚ ɜɬɨɪɚɹ 1.

ɆȿɏȺɇɂɑȿɋɄȺə ɑȺɋɌɖ ɗɅȿɄɌɊɈɉɊɂȼɈȾȺ 2.1. Ʉɢɧɟɦɚɬɢɱɟɫɤɢɟ ɫɯɟɦɵ ɪɚɛɨɱɢɯ ɨɪɝɚɧɨɜ

Ɉɫɧɨɜɧɚɹ ɡɚɞɚɱɚ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ – ɩɪɢɜɟɞɟɧɢɟ ɜ ɞɜɢɠɟɧɢɟ ɢɫɩɨɥɧɢɬɟɥɶɧɵɯ ɦɟɯɚɧɢɡɦɨɜ ɢ ɭɩɪɚɜɥɟɧɢɟ ɢɯ ɞɜɢɠɟɧɢɟɦ. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɜɫɟ ɦɟɯɚɧɢɱɟɫɤɢ ɫɜɹɡɚɧɧɵɟ ɦɟɠɞɭ ɫɨɛɨɣ ɞɜɢɠɭɳɢɟɫɹ ɢɧɟɪɰɢɨɧɧɵɟ ɦɚɫɫɵ ɞɜɢɝɚɬɟɥɹ, ɩɟɪɟɞɚɱɢ ɢ ɪɚɛɨɱɟɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ. ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨ ɞɜɢɠɭɳɢɯɫɹ ɦɚɫɫɚɯ ɭɫɬɚɧɨɜɤɢ ɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɹɡɹɯ ɦɟɠɞɭ ɧɢɦɢ ɞɚɟɬ ɤɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. Ʉɢɧɟɦɚɬɢɱɟɫɤɢɟ ɫɯɟɦɵ ɤɨɧɤɪɟɬɧɵɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɛɟɫɤɨɧɟɱɧɨ ɦɧɨɝɨɨɛɪɚɡɧɵ, ɨɞɧɚɤɨ ɨɛɥɚɞɚɸɬ ɨɛɳɢɦɢ ɨɫɨɛɟɧɧɨɫɬɹɦɢ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ, ɪɚɫɫɦɨɬɪɟɜ ɪɹɞ ɤɨɧɤɪɟɬɧɵɯ ɩɪɢɦɟɪɨɜ. 1. ɉɪɨɫɬɟɣɲɢɦ ɩɪɢɦɟɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɤɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɜɟɧɬɢɥɹɬɨɪɚ, ɢɡɨɛɪɚɠɟɧɧɚɹ ɧɚ ɪɢɫ. 2.1. Ɋɨɬɨɪ ɞɜɢɝɚɬɟɥɹ Ⱦ ɱɟɪɟɡ ɫɨɟɞɢɧɢɬɟɥɶɧɭɸ ɦɭɮɬɭ ɋɆ ɜɪɚɳɚɟɬ ɜɚɥ ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ ɜɟɧɬɢɥɹɬɨɪɚ ȼ. ȼɫɟ ɷɥɟɦɟɧɬɵ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɞɜɢɠɭɬɫɹ ɫ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɫɤɨɪɨɫɬɶɸ. Ȧ ɋɆ

ȦɊɈ ȼ

Ⱦ

Ɇ ǻɆɊɈ

ɆɊɈ

Ɋɢɫ. 2.1. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜɟɧɬɢɥɹɬɨɪɚ Ɇɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɆɊɈ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɫɤɨɪɨɫɬɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ȦɊɈ , ɫɨɡɞɚɟɬɫɹ ɧɚ ɪɚɛɨɱɟɦ ɤɨɥɟɫɟ ɜɟɧɬɢɥɹɬɨɪɚ n

ɆɊɈ

ǻɆɊɈ

§Ȧ · Ɇȼɇ ¨¨ ɊɈ ¸¸ , © Ȧȼɇ ¹

(2.1)

ɝɞɟ ǻɆɊɈ – ɦɨɦɟɧɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɩɨɬɟɪɶ ɧɚ ɬɪɟɧɢɟ ɜ ɩɨɞɲɢɩɧɢɤɚɯ ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ ɜɟɧɬɢɥɹɬɨɪɚ; Ȧȼɇ – ɧɨɦɢɧɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɜɟɧɬɢɥɹɬɨɪɚ; Ɇȼɇ– ɧɨɦɢɧɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɟɧɬɢɥɹɬɨɪɚ ɩɪɢ ɟɝɨ ɧɨɦɢɧɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ; 11

n – ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɦɚɝɢɫɬɪɚɥɢ, ɧɚ ɤɨɬɨɪɭɸ ɪɚɛɨɬɚɟɬ ɜɟɧɬɢɥɹɬɨɪ (n = 2 – ɦɚɝɢɫɬɪɚɥɶ ɛɟɡ ɩɪɨɬɢɜɨɞɚɜɥɟɧɢɹ). Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜɟɧɬɢɥɹɬɨɪɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɤɜɚɞɪɚɬɢɱɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɦɟɧɬɚ ɨɬ ɫɤɨɪɨɫɬɢ (ɫɦ. ɪɢɫ. 2.1). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɜɟɧɬɢɥɹɬɨɪɚ ɹɜɥɹɟɬɫɹ ɛɟɡɪɟɞɭɤɬɨɪɧɵɦ, ɧɟɪɟɜɟɪɫɢɜɧɵɦ, ɫ ɧɟɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɫɤɨɪɨɫɬɢ ɨɬ ɦɨɦɟɧɬɚ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɩɪɚɤɬɢɱɟɫɤɢɯ ɫɥɭɱɚɟɜ ɩɨ ɪɚɡɥɢɱɧɵɦ ɫɨɨɛɪɚɠɟɧɢɹɦ ɰɟɥɟɫɨɨɛɪɚɡɧɚɹ ɧɨɦɢɧɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɧɟ ɫɨɜɩɚɞɚɟɬ ɫ ɧɨɦɢɧɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. ɉɪɢ ɷɬɨɦ ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɫɨɝɥɚɫɨɜɚɧɢɹ ɫɤɨɪɨɫɬɟɣ ɩɭɬɟɦ ɜɜɟɞɟɧɢɹ ɜ ɤɢɧɟɦɚɬɢɱɟɫɤɭɸ ɰɟɩɶ ɪɚɡɥɢɱɧɵɯ ɩɟɪɟɞɚɱ: ɡɭɛɱɚɬɵɯ, ɮɪɢɤɰɢɨɧɧɵɯ, ɰɟɩɧɵɯ, ɤɥɢɧɨɪɟɦɟɧɧɵɯ ɢ ɬ.ɩ. Ⱦɥɹ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɫɬɭɩɟɧɱɚɬɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɢɫɩɨɥɶɡɭɸɬ ɤɨɪɨɛɤɢ ɩɟɪɟɞɚɱ, ɞɥɹ ɩɥɚɜɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ – ɮɪɢɤɰɢɨɧɧɵɟ ɜɚɪɢɚɬɨɪɵ. 2. ȼ ɤɢɧɟɦɚɬɢɱɟɫɤɭɸ ɫɯɟɦɭ ɩɪɢɜɨɞɚ ɲɩɢɧɞɟɥɹ ɬɨɤɚɪɧɨɝɨ ɫɬɚɧɤɚ (ɪɢɫ. 2.2) ɜɜɟɞɟɧɚ ɤɥɢɧɨɪɟɦɟɧɧɚɹ ɩɟɪɟɞɚɱɚ ɄɊɉ ɢ ɤɨɪɨɛɤɚ ɩɟɪɟɞɚɱ Ʉɉ ɞɥɹ ɫɬɭɩɟɧɱɚɬɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ. ȼɵɯɨɞɧɨɣ ɜɚɥ ɤɨɪɨɛɤɢ ɩɟɪɟɞɚɱ ɫɜɹɡɚɧ ɫɨ ɲɩɢɧɞɟɥɟɦ ɫɬɚɧɤɚ ɒ, ɜ ɤɨɬɨɪɨɦ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɡɚɝɨɬɨɜɤɚ Ɂ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɜɪɚɳɚɸɳɟɣɫɹ ɞɟɬɚɥɢ ɫ ɧɟɩɨɞɜɢɠɧɵɦ ɪɟɡɰɨɦ Ɋ ɜɨɡɧɢɤɚɸɬ ɭɫɢɥɢɟ ɪɟɡɚɧɢɹ ɢ ɦɨɦɟɧɬ ɪɟɡɚɧɢɹ ɆZ

FZ rɁ ,

(2.2)

ɝɞɟ ɆZ – ɦɨɦɟɧɬ ɪɟɡɚɧɢɹ; FZ – ɭɫɢɥɢɟ ɪɟɡɚɧɢɹ; rɁ – ɪɚɞɢɭɫ ɡɚɝɨɬɨɜɤɢ. ɉɨ ɬɪɟɛɨɜɚɧɢɹɦ ɬɟɯɧɨɥɨɝɢɢ ɨɛɪɚɛɨɬɤɚ ɞɟɬɚɥɟɣ ɜɟɞɟɬɫɹ ɜ ɪɟɠɢɦɟ ɩɨɫɬɨɹɧɫɬɜɚ ɦɨɳɧɨɫɬɢ

PZ

MZ ȦPO

const ,

(2.3)

ɩɨɷɬɨɦɭ ɦɨɦɟɧɬ ɪɟɡɚɧɢɹ ɛɭɞɟɬ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɫɤɨɪɨɫɬɢ ȦɊɈ ɩɪɢ ɟɟ ɢɡɦɟɧɟɧɢɢ, ɚ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɪɢɧɢɦɚɟɬ ɜɢɞ ɝɢɩɟɪɛɨɥɵ (ɫɦ. ɪɢɫ. 2.2). Ʉɪɨɦɟ ɩɨɥɟɡɧɨɝɨ ɦɨɦɟɧɬɚ MɊɈ MZ , ɜɨ ɜɫɟɯ ɷɥɟɦɟɧɬɚɯ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ ɞɟɣɫɬɜɭɸɬ ɫɢɥɵ ɬɪɟɧɢɹ ɜ ɩɨɞɲɢɩɧɢɤɚɯ, ɜ ɡɭɛɱɚɬɵɯ ɡɚɰɟɩɥɟɧɢɹɯ, ɜ ɬɪɭɳɢɯɫɹ ɩɨɜɟɪɯɧɨɫɬɹɯ ɤɥɢɧɨɪɟɦɟɧɧɨɣ ɩɟɪɟɞɚɱɢ.

ɋɆ

Ʉɉ

ɒ Ȧ

Ⱦ

ȦɊɈ

ȦɊɈ ɄɊɉ

Ɋ

Ɇ ɆɊɈ

Ɋɢɫ. 2.2. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɲɩɢɧɞɟɥɹ ɬɨɤɚɪɧɨɝɨ ɫɬɚɧɤɚ

12

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɒ ɹɜɥɹɟɬɫɹ ɧɟɪɟɜɟɪɫɢɜɧɵɦ, ɫ ɧɟɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɫɤɨɪɨɫɬɢ ɨɬ ɦɨɦɟɧɬɚ, ɞɥɹ ɫɨɝɥɚɫɨɜɚɧɢɹ ɫɤɨɪɨɫɬɟɣ ɞɜɢɝɚɬɟɥɹ ɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɩɪɢɦɟɧɟɧɵ ɪɟɞɭɤɬɨɪ Ʉɉ ɢ ɤɥɢɧɨɪɟɦɟɧɧɚɹ ɩɟɪɟɞɚɱɚ ɄɊɉ. ȼ ɦɟɯɚɧɢɡɦɟ ɩɟɪɟɞɜɢɠɟɧɢɹ ɬɟɥɟɠɤɢ ɦɨɫɬɨɜɨɝɨ ɤɪɚɧɚ (ɪɢɫ. 2.3) ɦɨɦɟɧɬ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɩɪɟɨɞɨɥɟɜɚɟɬ ɬɨɥɶɤɨ ɫɢɥɵ ɬɪɟɧɢɹ. Ⱦɜɢɝɚɬɟɥɶ Ⱦ ɱɟɪɟɡ ɪɟɞɭɤɬɨɪ Ɋ ɜɪɚɳɚɟɬ ɜɟɞɭɳɭɸ ɩɚɪɭ ɤɨɥɟɫ ɬɟɥɟɠɤɢ, ɩɪɟɨɞɨɥɟɜɚɹ ɫɢɥɭ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɬɟɥɟɠɤɢ FPO

kɁ m g f μ r ɲ , RK

(2.4)

ɨɛɭɫɥɨɜɥɟɧɧɭɸ ɬɪɟɧɢɟɦ ɫɤɨɥɶɠɟɧɢɹ ɜ ɩɨɞɲɢɩɧɢɤɚɯ ɢ ɬɪɟɧɢɟɦ ɤɚɱɟɧɢɹ ɤɨɥɟɫ ɩɨ ɪɟɥɶɫɚɦ, ɝɞɟ k Ɂ – ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ; m – ɦɚɫɫɚ ɬɟɥɟɠɤɢ ɫ ɝɪɭɡɨɦ; g – MTPK ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ; f – ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɤɚɱɟɧɢɹ; N FTPC – ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ; MTPK – ɦɨɦɟɧɬ ɬɪɟɧɢɹ ɤɚɱɟɧɢɹ; μ N FTPC – ɫɢɥɚ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ; RK , r – ɪɚɞɢɭɫɵ ɤɨɥɟɫɚ ɢ ɲɟɣɤɢ ɨɫɢ ɤɨɥɟɫɚ.

ɲ

ɋɢɥɚ ɬɪɟɧɢɹ FPO ɜɫɟɝɞɚ ɧɚɩɪɚɜɥɟɧɚ ɧɚɜɫɬɪɟɱɭ ɞɜɢɠɟɧɢɹ ɬɟɥɟɠɤɢ. ɉɨɞ ɪɟɚɤɬɢɜɧɵɦɢ ɫɢɥɚɦɢ ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɬɚɤɢɟ ɫɢɥɵ, ɤɨɬɨɪɵɟ ɩɪɢ ɫɦɟɧɟ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɦɟɧɹɸɬ ɫɜɨɣ ɡɧɚɤ. Ɂɧɚɱɢɬ, FPO – ɪɟɚɤɬɢɜɧɚɹ ɫɢɥɚ. ɂɡ ɮɨɪɦɭɥɵ (2.4) ɫɥɟɞɭɟɬ, ɱɬɨ ɦɨɞɭɥɶ ɫɢɥɵ ɬɪɟɧɢɹ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. ɉɪɢɜɟɞɟɧɧɚɹ ɮɨɪɦɭɥɚ (2.4) ɢ ɜɢɞ ɦɟɯɚɧɢɱɟɊ

Ⱦ

ȦɊɈ

dɄ DɄ

ɆɊɈ

Ɋɢɫ. 2.3. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɟɯɚɧɢɡɦɚ ɩɟɪɟɞɜɢɠɟɧɢɹ ɬɟɥɟɠɤɢ (ɫ ɪɟɚɤɬɢɜɧɵɦ ɯɚɪɚɤɬɟɪɨɦ ɧɚɝɪɭɡɤɢ) ɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɟ ɭɱɢɬɵɜɚɸɬ ɫɭɯɨɟ ɬɪɟɧɢɟ (ɩɨɤɨɹ), ɧɟɫɤɨɥɶɤɨ ɭɜɟɥɢɱɢɜɚɸɳɢɟ ɫɢɥɵ ɬɪɟɧɢɹ ɩɪɢ ɩɭɫɤɟ ɦɟɯɚɧɢɡɦɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɬɟɥɟɠɤɢ ɹɜɥɹɟɬɫɹ ɪɟɜɟɪɫɢɜɧɵɦ, ɫ ɩɨɫɬɨɹɧɧɵɦ, ɧɟɡɚɜɢɫɹɳɢɦ ɨɬ ɫɤɨɪɨɫɬɢ, ɦɨɦɟɧɬɨɦ, ɡɧɚɤ ɤɨɬɨɪɨɝɨ ɢɡɦɟɧɹɟɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ, ɬ.ɟ. ɧɨɫɹɳɢɦ ɪɟɚɤɬɢɜɧɵɣ ɯɚɪɚɤɬɟɪ. ȼ ɨɬɥɢɱɢɟ ɨɬ ɦɟɯɚɧɢɡɦɚ ɩɟɪɟɞɜɢɠɟɧɢɹ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɺɦɚ ɫɨɡɞɚɟɬɫɹ ɫɢɥɨɣ ɬɹɠɟɫɬɢ ɩɨɞɜɟɲɟɧɧɨɝɨ ɝɪɭɡɚ, ɩɪɢɱɟɦ ɟɺ ɧɚɩɪɚɜɥɟɧɢɟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɝɪɭɡɚ. ɉɨɞ ɚɤɬɢɜɧɵɦɢ ɫɢɥɚɦɢ ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɬɚɤɢɟ ɫɢɥɵ, ɤɨɬɨɪɵɟ ɩɪɢ ɫɦɟɧɟ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɧɟ ɦɟɧɹɸɬ ɫɜɨɣ ɡɧɚɤ. Ɂɧɚɱɢɬ, ɫɢɥɚ ɬɹɠɟɫɬɢ – ɚɤɬɢɜɧɚɹ ɫɢɥɚ: (2.5) FPO m g.

13

4. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɟɦɚ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 2.4. Ⱦɜɢɝɚɬɟɥɶ Ⱦ ɱɟɪɟɡ ɪɟɞɭɤɬɨɪ Ɋ ɜɪɚɳɚɟɬ ɛɚɪɚɛɚɧ Ȼ, ɧɚ ɤɨɬɨɪɨɦ ɧɚɦɨɬɚɧ ɬɪɨɫ ɫ ɝɪɭɡɨɦ. ɇɚ ɝɪɭɡ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ ɬɹɠɟɫɬɢ, ɧɟ ɡɚɜɢɫɹɳɚɹ ɨɬ ɫɤɨɪɨɫɬɢ. ɋɆ Ⱦ

Ɋ

Ɍɒ 1

4

ȦɊɈ

Ȼ

ɋɆ

DȻ Mȼ Ȧ

2

ɆɊɈ

3 m

Ƚɪɭɡ

ɆɊɈ

v

ȦɊɈ Ɋɢɫ. 2.4. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɺɦɚ (ɫ ɚɤɬɢɜɧɵɦ ɯɚɪɚɤɬɟɪɨɦ ɧɚɝɪɭɡɤɢ) Ʉɪɨɦɟ ɫɢɥɵ ɬɹɠɟɫɬɢ ɞɜɢɝɚɬɟɥɶ ɩɪɟɨɞɨɥɟɜɚɟɬ ɫɢɥɵ ɬɪɟɧɢɹ ɜ ɩɨɞɲɢɩɧɢɤɚɯ ɢ ɡɭɛɱɚɬɵɯ ɡɚɰɟɩɥɟɧɢɹɯ ɪɟɞɭɤɬɨɪɚ (ɩɭɧɤɬɢɪɧɵɟ ɥɢɧɢɢ ɧɚ ɪɢɫ. 2.4 – ɫ ɭɱɟɬɨɦ FPO ). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɺɦɚ ɜ ɰɟɥɨɦ ɹɜɥɹɟɬɫɹ ɪɟɜɟɪɫɢɜɧɵɦ, ɫ ɩɨɫɬɨɹɧɧɵɦ, ɧɟɡɚɜɢɫɹɳɢɦ ɨɬ ɫɤɨɪɨɫɬɢ, ɦɨɦɟɧɬɨɦ, ɡɧɚɤ ɤɨɬɨɪɨɝɨ ɧɟ ɢɡɦɟɧɹɟɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ, ɬ.ɟ. ɧɨɫɹɳɢɦ ɚɤɬɢɜɧɵɣ ɯɚɪɚɤɬɟɪ. Ɇɨɦɟɧɬ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɧɨɫɢɬ ɚɤɬɢɜɧɵɣ ɯɚɪɚɤɬɟɪ, ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɥɢɮɬɚ – ɪɟɜɟɪɫɢɜɧɵɣ, ɜ ɩɪɢɜɟɞɟɧɧɨɣ ɫɯɟɦɟ – ɪɟɞɭɤɬɨɪɧɵɣ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɦɧɨɝɨɨɛɪɚɡɢɢ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɫɯɟɦ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ ɨɧɢ ɨɛɥɚɞɚɸɬ ɫɥɟɞɭɸɳɢɦɢ ɨɫɨɛɟɧɧɨɫɬɹɦɢ: – ɪɟɜɟɪɫɢɜɧɵɟ ɢɥɢ ɧɟɪɟɜɟɪɫɢɜɧɵɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɵ; – ɪɟɞɭɤɬɨɪɧɵɟ ɢɥɢ ɛɟɡɪɟɞɭɤɬɨɪɧɵɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɵ; – ɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ ɞɟɣɫɬɜɭɸɬ ɞɜɢɠɭɳɢɟ ɦɨɦɟɧɬɵ ɢ ɫɢɥɵ, ɦɨɦɟɧɬɵ ɢ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ, ɚ ɬɚɤɠɟ ɦɨɦɟɧɬɵ ɢ ɫɢɥɵ ɬɪɟɧɢɹ; – ɦɨɦɟɧɬɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɩɨɫɬɨɹɧɧɵ ɢɥɢ ɦɨɝɭɬ ɡɚɜɢɫɟɬɶ ɨɬ ɫɤɨɪɨɫɬɢ, ɭɝɥɚ ɩɨɜɨɪɨɬɚ, ɜɪɟɦɟɧɢ; – ɦɨɦɟɧɬɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɨɝɭɬ ɢɦɟɬɶ ɯɚɪɚɤɬɟɪ ɚɤɬɢɜɧɵɣ (ɷɧɟɪɝɢɹ ɩɨɫɬɭɩɚɟɬ ɨɬ ɞɪɭɝɨɝɨ ɢɫɬɨɱɧɢɤɚ ɢɥɢ ɢɦɟɟɬɫɹ ɡɚɩɚɫ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ) ɢɥɢ ɪɟɚɤɬɢɜɧɵɣ (ɨɛɭɫɥɨɜɥɟɧ ɫɢɥɚɦɢ ɬɪɟɧɢɹ); – ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɪɟɚɤɬɢɜɧɵɟ ɦɨɦɟɧɬɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɫɤɚɱɤɨɦ ɢɡɦɟɧɹɸɬ ɡɧɚɤ, ɚ ɚɤɬɢɜɧɵɟ ɦɨɦɟɧɬɵ – ɡɧɚɤ ɧɟ ɢɡɦɟɧɹɸɬ.

2.2. Ɋɚɫɱɟɬɧɵɟ ɫɯɟɦɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɞɚɟɬ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨɛ ɢɞɟɚɥɶɧɵɯ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɫɜɹɡɹɯ ɦɟɠɞɭ ɞɜɢɠɭɳɢɦɢɫɹ ɦɚɫɫɚɦɢ ɤɨɧɤɪɟɬɧɨɣ ɭɫɬɚɧɨɜɤɢ, ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ ɞɟɮɨɪɦɚɰɢɢ ɷɥɟɦɟɧɬɨɜ ɩɪɢ ɢɯ ɧɚɝɪɭɠɟɧɢɢ. Ʉɪɨɦɟ ɬɨɝɨ, ɢɧɟɪɰɢɨɧɧɵɟ ɦɚɫɫɵ ɫɢɫɬɟɦɵ ɞɜɢɠɭɬɫɹ ɫ ɪɚɡɥɢɱɧɵɦɢ ɫɤɨɪɨɫɬɹɦɢ, ɩɨɷɬɨɦɭ ɧɟɥɶɡɹ ɫɪɚɜɧɢɜɚɬɶ ɫɢ14

ɥɵ ɢɥɢ ɦɨɦɟɧɬɵ, ɞɟɣɫɬɜɭɸɳɢɟ ɜ ɞɜɢɠɭɳɢɯɫɹ ɫ ɪɚɡɧɵɦɢ ɫɤɨɪɨɫɬɹɦɢ ɷɥɟɦɟɧɬɚɯ. ɋ ɩɨɦɨɳɶɸ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɧɟɨɛɯɨɞɢɦɨ ɫɨɫɬɚɜɢɬɶ ɪɚɫɱɟɬɧɭɸ ɫɯɟɦɭ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɜ ɤɨɬɨɪɨɣ ɜɫɟ ɦɨɦɟɧɬɵ ɢɧɟɪɰɢɢ, ɦɨɦɟɧɬɵ ɧɚɝɪɭɡɤɢ ɜɪɚɳɚɸɳɢɯɫɹ ɷɥɟɦɟɧɬɨɜ, ɩɨɫɬɭɩɚɬɟɥɶɧɨ ɞɜɢɠɭɳɢɯɫɹ ɷɥɟɦɟɧɬɨɜ, ɚ ɬɚɤɠɟ ɪɟɚɥɶɧɵɟ ɠɟɫɬɤɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɹɡɟɣ ɡɚɦɟɧɹɸɬɫɹ ɷɤɜɢɜɚɥɟɧɬɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ, ɩɪɢɜɟɞɟɧɧɵɦɢ ɤ ɨɞɧɨɣ ɫɤɨɪɨɫɬɢ, ɱɚɳɟ ɜɫɟɝɨ – ɤ ɫɤɨɪɨɫɬɢ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ. ɉɪɢɜɟɞɟɧɢɟ ɦɨɦɟɧɬɨɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ. Ʉɪɢɬɟɪɢɟɦ ɩɪɢɜɟɞɟɧɢɹ ɦɨɦɟɧɬɨɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɹɜɥɹɟɬɫɹ ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɛɚɥɚɧɫ ɪɟɚɥɶɧɨɣ ɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦ, ɡɚɤɥɸɱɚɸɳɢɣɫɹ ɜ ɪɚɜɟɧɫɬɜɟ ɷɧɟɪɝɢɣ, ɡɚɬɪɚɱɟɧɧɵɯ ɧɚ ɜɵɩɨɥɧɟɧɢɟ ɨɩɪɟɞɟɥɟɧɧɨɣ ɪɚɛɨɬɵ ɜ ɪɟɚɥɶɧɨɣ ɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɚɯ. ȼ ɢɞɟɚɥɶɧɨɦ ɫɥɭɱɚɟ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɩɨɬɟɪɶ ɦɨɳɧɨɫɬɢ ɜ ɩɟɪɟɞɚɱɟ ɦɨɳɧɨɫɬɶ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ PPO ɪɚɜɧɚ ɦɨɳɧɨɫɬɢ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ PB : PPO

PB .

(2.6)

Ɋɚɫɫɦɨɬɪɢɦ ɞɥɹ ɩɪɢɦɟɪɚ ɦɟɯɚɧɢɡɦ ɩɨɞɴɟɦɚ (ɫɦ. ɪɢɫ. 2.4). Ⱦɥɹ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɛɚɪɚɛɚɧɚ: – ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ PPO

MPO ȦPO ,

(2.7)

MB Ȧ ,

(2.8)

– ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ PB

ɉɨɞɫɬɚɜɢɜ ɭɪɚɜɧɟɧɢɹ (2.7) ɢ (2.8) ɜ (2.6), ɩɨɥɭɱɢɦ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ: MPO ȦPO Ȧ

MB

MPO , iP

(2.9)

Ȧ – ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɪɟɞɭɤɬɨɪɚ. ȦPO Ⱦɥɹ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ

ɝɞɟ ip

PPO

MPO ȦPO

mg

Dɛ ȦɊɈ 2

mg v

Gv ,

(2.10)

ɬɨɝɞɚ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ, MB

G

v Ȧ

G , ȡ

(2.11)

v – ɪɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ, ɦ. Ȧ ɉɪɢɜɟɞɟɧɢɟ ɦɨɦɟɧɬɨɜ ɢɧɟɪɰɢɢ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ. Ʉɪɢɬɟɪɢɟɦ ɩɪɢɜɟɞɟɧɢɹ ɹɜɥɹɟɬɫɹ ɪɚɜɟɧɫɬɜɨ ɡɚɩɚɫɚ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɪɟɚɥɶɧɨɣ ɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɪɟɚɥɶɧɨɣ ɫɯɟɦɵ ɪɚɜɧɚ ɫɭɦɦɟ ɤɢɧɟɬɢɱɟɫɤɢɯ ɷɧɟɪɝɢɣ ɤɚɠɞɨɝɨ ɷɥɟɦɟɧɬɚ ɞɜɢɠɟɧɢɹ.

ɝɞɟ ȡ

15

Ⱦɥɹ ɫɯɟɦɵ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɟɦɚ (ɫɦ. ɪɢɫ. 2.4) ɜɵɪɚɠɟɧɢɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ WɄɂɇ ɞɥɹ ɪɚɫɱɟɬɧɨɣ ɢ ɪɟɚɥɶɧɨɣ ɫɯɟɦ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ WɄɂɇ

J

Ȧ2 2

JȾȼ 2

Ȧ2 Ȧ2 Ȧ2 Ȧ2 Ȧ2 JɌɒ J1 J2 J3 2 2 2 2 2 2

ȦɊɈ ȦɊɈ v2 J4 JȻ m , 2 2 2

(2.12)

ɝɞɟ J – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ; JȾȼ, JɌɒ, J1, J2, J3, J4, JȻ – ɦɨɦɟɧɬɵ ɢɧɟɪɰɢɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɞɜɢɝɚɬɟɥɹ, ɬɨɪɦɨɡɧɨɝɨ ɲɤɢɜɚ, ɲɟɫɬɟɪɟɧ ɪɟɞɭɤɬɨɪɚ, ɛɚɪɚɛɚɧɚ; m – ɦɚɫɫɚ ɝɪɭɡɚ; Ȧ1 – ɫɤɨɪɨɫɬɶ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɜɚɥɚ ɪɟɞɭɤɬɨɪɚ. ɉɨɞɟɥɢɜ ɩɪɚɜɭɸ ɢ ɥɟɜɭɸ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (2.12) ɧɚ Ȧ2/2, ɩɨɥɭɱɢɦ ɡɧɚɱɟɧɢɟ ɦɨɦɟɧɬɚ ɢɧɟɪɰɢɢ J ɪɚɫɱɺɬɧɨɣ ɫɯɟɦɵ, ɩɪɢɜɟɞɟɧɧɨɝɨ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ, J

JȾȼ JɌɒ J1 J2

1 1 1 1 J3 2 J4 2 JȻ 2 m ȡ2 . 2 i1 i1 iP iP

(2.13)

ȼ ɩɨɥɭɱɟɧɧɨɦ ɜɵɪɚɠɟɧɢɢ: i1 – ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɞɨ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɜɚɥɚ ɪɟɞɭɤɬɨɪɚ; iɊ – ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɪɟɞɭɤɬɨɪɚ; v – ɪɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ ɨɬ ɥɢɧɟɣɧɨɣ ɫɤɨɪɨɫɬɢ ɝɪɭɡɚ ɞɨ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ. ȡ Ȧ ȼ ɫɜɹɡɢ ɫɨ ɫɥɨɠɧɨɫɬɶɸ ɨɩɪɟɞɟɥɟɧɢɹ ɦɨɦɟɧɬɨɜ ɢɧɟɪɰɢɢ ɷɥɟɦɟɧɬɨɜ ɩɟɪɟɞɚɱɢ, ɪɚɫɱɟɬ ɦɨɦɟɧɬɚ ɢɧɟɪɰɢɢ, ɩɪɢɜɟɞɟɧɧɨɝɨ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ, ɜɵɩɨɥɧɹɸɬ ɩɨ ɮɨɪɦɭɥɟ

į

ɝɞɟ JɉȿɊ

JɌɒ J1

JɉɊ.ɊɈ

JȻ 2

J į J Ⱦȼ JɉɊɊɈ ,

(2.14)

JȾȼ JɉȿɊ JȾȼ

(2.15)

1,1...1,3 ,

J2 J 3 – ɩɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɟɪɟɞɚɱɢ; i1 2 i12

m ȡ2 – ɩɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɜɪɚɳɚɸɳɟɝɨɫɹ ɷɥɟ-

iP ɦɟɧɬɚ (ɛɚɪɚɛɚɧɚ) ɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨ ɞɜɢɠɭɳɟɝɨɫɹ ɷɥɟɦɟɧɬɚ (ɦɚɫɫɵ ɝɪɭɡɚ) ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. Ɋɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ ȡ ɢ ɩɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ Jɩɪ ɦɨɝɭɬ ɛɵɬɶ ɩɟɪɟɦɟɧɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ. ȼ ɤɭɥɚɱɤɨɜɨɦ ɦɟɯɚɧɢɡɦɟ (ɪɢɫ.2.5) ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɡɚɤɪɟɩɥɟɧ ɪɵɱɚɝ ɪɚɞɢɭɫɚ R, ɧɚ ɤɨɧɰɟ ɤɨɬɨɪɨɝɨ ɭɫɬɚɧɨɜɥɟɧ ɪɨɥɢɤ. Ɋɨɥɢɤ ɜɨɡɞɟɣɫɬɜɭɟɬ ɧɚ ɬɚɪɟɥɤɭ ɬɨɥɤɚɬɟɥɹ, ɤɨɬɨɪɵɣ ɩɟɪɟɦɟɳɚɟɬ ɞɟɬɚɥɶ ɦɚɫɫɨɣ m. ɋɢɥɨɜɨɟ ɡɚɦɵɤɚɧɢɟ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɩɪɭɠɢɧɨɣ, ɧɚɞɟɬɨɣ ɧɚ ɬɨɥɤɚɬɟɥɶ. ɉɪɢ ɪɚɜɧɨɦɟɪɧɨɦ ɜɪɚɳɟɧɢɢ ɜɚɥɚ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Ȧ ɦɚɫɫɚ m ɩɟɪɟɦɟɳɚɟɬɫɹ ɩɨ ɡɚɤɨɧɭ Į= R·sin ĳ=R·sin(Ȧt) ɫɨ ɫɤɨɪɨɫɬɶɸ v=dD/dt=Ȧ·R·cos ĳ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɪɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ ɫɬɚɧɨɜɢɬɫɹ ɩɟɪɟɦɟɧɧɨɣ ɜɟɥɢɱɢɧɨɣ ȡ= v/Ȧ=R·cosĳ.

16

v

m

ĳ=Ȧt

R

ɉɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɚ ɩɨɜɨɪɨɬɚ Ɇɫ = F·ȡ= (mg – Fɩɪ) R·cosĳ. ɉɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɚɤɠɟ ɦɟɧɹɟɬ ɫɜɨɸ ɜɟɥɢɱɢɧɭ ɜ ɮɭɧɤɰɢɢ ɭɝɥɚ ɩɨɜɨɪɨɬɚ Jɩɪ= mR2·cos2ĳ. ɉɪɢɜɟɞɟɧɧɵɦ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ ɪɚɫɱɺɬɧɨɣ ɫɯɟɦɵ ɧɚɡɵɜɚɸɬ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɪɨɫɬɟɣɲɟɣ ɫɢɫɬɟɦɵ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɷɥɟɦɟɧɬɨɜ, ɜɪɚɳɚɸɳɢɯɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ ɜɚɥɚ, ɤ ɤɨɬɨɪɨɦɭ ɨɫɭɳɟɫɬɜɥɟɧɨ ɩɪɢɜɟɞɟɧɢɟ, ɢ ɤɨɬɨɪɚɹ ɨɛɥɚɞɚɟɬ ɩɪɢ ɷɬɨɦ ɡɚɩɚɫɨɦ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ, ɪɚɜɧɵɦ ɡɚɩɚɫɭ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ.

2.3. ɍɱɟɬ ɩɨɬɟɪɶ ɜ ɩɟɪɟɞɚɱɚɯ ȼ ɩɪɨɰɟɫɫɟ ɩɟɪɟɞɚɱɢ ɷɧɟɪɝɢɢ ɜɨɡɧɢɤɚɸɬ ɩɨɬɟɪɢ ɜ ɷɥɟɦɟɧɬɚɯ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ (ɜ ɪɟɞɭɤɬɨɪɚɯ, ɤɥɢɧɨɪɟɦɟɧɧɵɯ ɩɟɪɟɞɚɱɢ, ɲɤɢɜɚɯ, ɩɨɬɟɪɢ ɧɚ ɬɪɟɧɢɟ ɜ ɩɨɞɲɢɩɧɢɤɚɯ, ɨɩɨɪɚɯ ɢ ɬ.ɩ.). Ɇɟɬɨɞ ɄɉȾ. ȼɟɥɢɱɢɧɚ ɩɨɬɟɪɶ ɬɪɚɞɢɰɢɨɧɧɨ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ (ɄɉȾ). ɉɪɢ ɷɬɨɦ ɭɱɢɬɵɜɚɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɩɨɬɨɤɚ ɷɧɟɪɝɢɢ: ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɤ ɦɟɯɚɧɢɡɦɭ ɩɪɢ ɪɚɛɨɬɟ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɢɥɢ ɨɬ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ – ɜ ɬɨɪɦɨɡɧɨɦ ɪɟɠɢɦɟ. ȿɫɥɢ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨɞɴɺɦ ɝɪɭɡɚ, ɬɨ ɞɜɢɝɚɬɟɥɶ ɫɨɜɟɪɲɚɟɬ ɩɨɥɟɡɧɭɸ ɪɚɛɨɬɭ ɩɨ ɩɨɞɴɺɦɭ ɝɪɭɡɚ PPO ɢ ɩɨɤɪɵɜɚɟɬ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɧɚ ɬɪɟɧɢɟ ɜ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ ǻɊ (ɪɢɫ. 2.6). ɄɉȾ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ Ɋɢɫ. 2.5. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɤɭɥɚɱɤɨɜɨɝɨ ɦɟɯɚɧɢɡɦɚ

ɊɊɈ

Ɋȼ ǻɊ

Ɋɢɫ. 2.6. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɦɟɯɚɧɢɡɦɚ ɩɪɢ ɩɨɞɴɺɦɟ ɝɪɭɡɚ ɊɊɈ

Ɋȼ ǻɊ

Ɋɢɫ. 2.7. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɦɟɯɚɧɢɡɦɚ ɩɪɢ ɫɩɭɫɤɟ ɝɪɭɡɚ

.Ș

PPO PB

MPO ȦPO MB Ȧ

MPO MB iP

(2.16)

ɉɪɢ ɨɩɭɫɤɚɧɢɢ ɝɪɭɡɚ ɬɟɪɹɟɦɚɹ ɢɦ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɩɟɪɟɞɚɺɬɫɹ ɞɜɢɝɚɬɟɥɸ (ɪɢɫ. 2.7). ɉɨɷɬɨɦɭ ɩɨɬɟɪɢ ɧɚ ɬɪɟɧɢɟ ǻɊ ɜ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ ɩɨɤɪɵɜɚɸɬɫɹ ɭɠɟ ɡɚ ɫɱɺɬ ɷɬɨɣ ɷɧɟɪɝɢɢ, ɢ ɄɉȾ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ Ș

PB PPO

MB Ȧ MPO ȦPO

MB iP . MPO

(2.17)

Ɉɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɪɶ ɱɟɪɟɡ ɄɉȾ ɧɨɫɢɬ ɩɪɢɛɥɢɠɟɧɧɵɣ ɯɚɪɚɤɬɟɪ. ɉɪɢ ɧɨɦɢɧɚɥɶɧɨɣ ɧɚɝɪɭɡɤɟ ɢ ɧɨɦɢɧɚɥɶɧɨɦ ɄɉȾ ɩɟɪɟɞɚɱɢ ɩɨɬɟɪɢ ɜ ɩɟɪɟɞɚɱɟ ɪɚɜɧɵ ɧɨɦɢɧɚɥɶɧɵɦ. ɋɧɢɠɟɧɢɟ ɧɚɝɪɭɡɤɢ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɄɉȾ, ɚ ɩɪɢ ɦɚɥɵɯ ɧɚɝɪɭɡɤɚɯ ɄɉȾ ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɪɶ ǻɊ ɜ 17

ɩɟɪɟɞɚɱɟ ɱɟɪɟɡ ɄɉȾ ɫɬɚɧɨɜɢɬɫɹ ɧɟɞɨɫɬɨɜɟɪɧɵɦ. Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɚɯ ɄɉȾ ɩɟɪɟɞɚɱɢ ɢɡɦɟɧɹɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɨ, ɬɚɤ ɤɚɤ ɢɡɦɟɧɹɟɬɫɹ ɫɤɨɪɨɫɬɶ, ɢ ɱɟɪɟɡ ɩɟɪɟɞɚɱɭ ɩɪɨɯɨɞɹɬ ɫɬɚɬɢɱɟɫɤɢɟ ɢ ɞɢɧɚɦɢɱɟɫɤɢɟ ɦɨɦɟɧɬɵ. ɉɪɢɧɹɬɨ ɩɪɢɦɟɧɹɬɶ ɞɥɹ ɪɚɫɱɟɬɚ ɩɨɬɟɪɶ ɜ ɷɥɟɦɟɧɬɚɯ ɢɯ ɧɨɦɢɧɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ KH (ɧɨɦɢɧɚɥɶɧɵɣ ɄɉȾ ɪɟɞɭɤɬɨɪɚ, ɧɨɦɢɧɚɥɶɧɵɣ ɄɉȾ ɤɥɢɧɨɪɟɦɟɧɧɨɣ ɩɟɪɟɞɚɱɢ ɢ ɬ.ɩ.), ɱɬɨ ɞɚɟɬ ɞɨɫɬɚɬɨɱɧɭɸ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɬɨɱɧɨɫɬɶ. Ɇɟɬɨɞ ɪɚɡɞɟɥɟɧɢɹ ɩɨɬɟɪɶ. ɂɧɨɝɞɚ ɞɥɹ ɬɨɱɧɵɯ ɦɟɯɚɧɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɬɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɹɬɶ ɄɉȾ ɩɪɢ ɱɚɫɬɢɱɧɨɣ ɡɚɝɪɭɡɤɟ. Ɂɚɜɢɫɢɦɨɫɬɢ K f PPO , Z ɜ ɫɩɪɚɜɨɱɧɢɤɚɯ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɩɪɢɜɨɞɹɬɫɹ. Ɍɨɝɞɚ ɩɪɢɦɟɧɹɸɬ ɦɟɬɨɞ ɪɚɡɞɟɥɟɧɢɹ ɩɨɬɟɪɶ. ȼɫɟ ɩɨɬɟɪɢ ɜ ɩɟɪɟɞɚɱɟ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɩɨɫɬɨɹɧɧɵɟ ǻPɉɈɋɌ ɢ ɩɟɪɟɦɟɧɧɵɟ ǻPɉȿɊ . Ɍɨɝɞɚ ɨɛɳɢɟ ɩɨɬɟɪɢ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɤɚɤ ɫɭɦɦɭ ɩɨɫɬɨɹɧɧɵɯ ɢ ɩɟɪɟɦɟɧɧɵɯ ɩɨɬɟɪɶ: ǻɊ

ǻPɉɈɋɌ ǻɊɉȿɊ ,

(2.18)

ɉɨɫɬɨɹɧɧɵɟ ɩɨɬɟɪɢ ǻPɉɈɋɌ ɡɚɜɢɫɹɬ: – ɨɬ ɤɨɧɫɬɪɭɤɰɢɢ ɨɩɨɪ ɡɚɰɟɩɥɟɧɢɣ; – ɨɬ ɜɹɡɤɨɫɬɢ ɫɦɚɡɤɢ; – ɨɬ ɤɚɱɟɫɬɜɚ ɨɛɪɚɛɨɬɤɢ ɡɭɛɰɨɜ; – ɨɬ ɬɨɱɧɨɫɬɢ ɫɛɨɪɤɢ ɩɟɪɟɞɚɱɢ; – ɨɬ ɫɬɟɩɟɧɢ ɢɡɧɨɲɟɧɧɨɫɬɢ ɡɚɰɟɩɥɟɧɢɹ ɢ ɬ.ɩ. ɉɟɪɟɦɟɧɧɵɟ ɩɨɬɟɪɢ ǻPɉȿɊ ɡɚɜɢɫɹɬ ɨɬ ɡɚɝɪɭɡɤɢ ɦɟɯɚɧɢɡɦɚ. Ɇɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɫ ɭɱɟɬɨɦ ɩɨɬɟɪɶ ɜ ɩɟɪɟɞɚɱɟ ɪɚɜɧɚ Ɋȼ

ɊɊɈ ǻɊ ,

(2.19)

ɬɨɝɞɚ ɄɉȾ ɩɟɪɟɞɚɱɢ ɩɪɢ ɱɚɫɬɢɱɧɨ ɡɚɝɪɭɡɤɟ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ Ș

ɊɊɈ ɊɊɈ ǻɊ

ɝɞɟ ǻɆɉɈɋɌ

ɊɊɈ

ɊɊɈ ǻɊɉɈɋɌ ǻɊɉȿɊ

Ɇ

1

Ɇ ǻɆɉɈɋɌ ǻɆɉȿɊ

a 1 b kɁ

,

(2.20)

ɚ Ɇɇ.ɊȿȾ – ɦɨɦɟɧɬ ɩɨɫɬɨɹɧɧɵɯ ɩɨɬɟɪɶ;

ǻɆɉȿɊ b MC – ɦɨɦɟɧɬ ɩɟɪɟɦɟɧɧɵɯ ɩɨɬɟɪɶ; Ɇɋ kɁ – ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɝɪɭɡɤɢ ɦɟɯɚɧɢɡɦɚ. Ɇɇ Ɂɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ a ɢ b ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɡɭɛɱɚɬɵɯ ɡɚɰɟɩɥɟɧɢɣ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɄɉȾ Șɇ ɩɪɢɜɨɞɹɬɫɹ ɜ ɫɩɪɚɜɨɱɧɢɤɚɯ ɩɨ ɦɚɲɢɧɨɫɬɪɨɟɧɢɸ. ɉɪɢɦɟɪ 2.1. Ɋɚɫɫɱɢɬɚɬɶ ɡɧɚɱɟɧɢɹ ɫɤɨɪɨɫɬɟɣ, ɫɬɚɬɢɱɟɫɤɢɯ ɦɨɦɟɧɬɨɜ ɢ ɦɨɦɟɧɬɨɜ ɢɧɟɪɰɢɢ, ɦɨɳɧɨɫɬɟɣ ɧɚ ɜɚɥɭ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɢ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɩɨ ɡɚɞɚɧɧɵɦ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦ ɩɚɪɚɦɟɬɪɚɦ ɦɟɯɚɧɢɡɦɚ ɩɨɞɚɱɢ. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɚɱɢ ɫɬɚɧɤɚ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ.2.8. ȼɪɚɳɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɨɬ ɞɜɢɝɚɬɟɥɹ 1 ɱɟɪɟɡ ɪɟɞɭɤɬɨɪ 2 ɩɟɪɟɞɚɟɬɫɹ ɯɨɞɨɜɨɦɭ ɜɢɧɬɭ 3 ɢ ɱɟɪɟɡ ɝɚɣɤɭ 4, ɡɚɤɪɟɩɥɟɧɧɭɸ ɧɚ ɫɭɩɩɨɪɬɟ, ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɩɨɫɬɭɩɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɩɨɞɚɱɢ ɫɭɩɩɨɪɬɚ 5 ɩɨ ɧɚɩɪɚɜɥɹɸɳɢɦ 6. Ⱦɜɢɝɚɬɟɥɶ ɩɨɞɚɱɢ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɟɪɟɞɜɢɠɟɧɢɟ ɫɭɩɩɨɪɬɚ ɫɨ ɫɤɨɪɨɫɬɶɸ v ɢ ɩɪɟɨɞɨɥɟɧɢɟ

18

ɫɭɦɦɚɪɧɨɝɨ ɭɫɢɥɢɹ ɩɨɞɚɱɢ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɥɢɧɟɣɧɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ ɫɭɩɩɨɪɬɚ 1,2 FX FZ FY 9,81 m μC ,

Fɉ

(2.21)

ɤɨɬɨɪɨɟ ɡɚɜɢɫɢɬ ɨɬ ɫɨɫɬɚɜɥɹɸɳɢɯ ɩɪɨɰɟɫɫɚ ɪɟɡɚɧɢɹ: ɭɫɢɥɢɹ ɩɨɞɚɱɢ FX , ɪɚɞɢɚɥɶɧɨɝɨ ɭɫɢɥɢɹ FY # 0,8 FX , ɭɫɢɥɢɹ ɪɟɡɚɧɢɹ FZ # 2,5 FX , ɨɬ ɦɚɫɫɵ ɫɭɩɩɨɪɬɚ m ɢ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ ɫɭɩɩɨɪɬɚ ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɨ ɧɚɩɪɚɜɥɹɸɳɢɦ μC . Ʉɨɷɮɮɢɰɢɟɧɬ 1,2 ɭɱɢɬɵɜɚɟɬ ɩɟɪɟɤɨɫɵ ɩɪɢ ɞɜɢɠɟɧɢɢ ɫɭɩɩɨɪɬɚ. ɇɚ ɨɛɪɚɬɧɨɦ ɯɨɞɟ ɫɭɩɩɨɪɬɚ ɪɟɡɚɧɢɟ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ. 5 6 4 1 2

3

Ɋɢɫ. 2.8. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɚɱɢ ɫɬɚɧɤɚ: 1– ɞɜɢɝɚɬɟɥɶ; 2– ɪɟɞɭɤɬɨɪ; 3 – ɯɨɞɨɜɨɣ ɜɢɧɬ; 4 – ɝɚɣɤɚ; 5 – ɫɭɩɩɨɪɬ; 6 – ɧɚɩɪɚɜɥɹɸɳɢɟ Ɍɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɞɚɧɧɵɟ ɦɟɯɚɧɢɡɦɚ ɩɨɞɚɱɢ ɫɬɚɧɤɚ: m

2,4 ɬ – ɦɚɫɫɚ ɩɟɪɟɦɟɳɚɟɦɨɝɨ ɝɪɭɡɚ;

v = 42 ɦɦ/ɫ– ɫɤɨɪɨɫɬɶ ɩɟɪɟɦɟɳɟɧɢɹ ɝɪɭɡɚ; FX 6 ɤɇ – ɭɫɢɥɢɟ ɩɨɞɚɱɢ; D XB 44 ɦɦ – ɞɢɚɦɟɬɪ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ; m ɏȼ 100 ɤɝ – ɦɚɫɫɚ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ; μɋ 0,08 – ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ ɫɭɩɩɨɪɬɚ ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɨ ɧɚɩɪɚɜɥɹɸɳɢɦ; i12 5 – ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɲɟɫɬɟɪɟɧɧɨɣ ɩɚɪɵ; Ș12 0,9 – ɄɉȾ ɩɟɪɟɞɚɱɢ; J 0,03 ɤɝ ɦ 2 , J2 1

JȾȼ

0,6 ɤɝ ɦ2 – ɦɨɦɟɧɬɵ ɢɧɟɪɰɢɢ ɲɟɫɬɟɪɟɧ;

0,2 ɤɝ ɦ2 – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɨɬɨɪɚ ɞɜɢɝɚɬɟɥɹ;

Į= 5,5q – ɭɝɨɥ ɧɚɪɟɡɤɢ ɪɟɡɶɛɵ; ĳ = 4q – ɭɝɨɥ ɬɪɟɧɢɹ ɜ ɪɟɡɶɛɟ. ɉɨɫɥɟ ɢɡɭɱɟɧɢɹ ɩɪɢɧɰɢɩɚ ɪɚɛɨɬɵ ɦɟɯɚɧɢɡɦɚ ɢ ɟɝɨ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɨɩɪɟɞɟɥɹɟɦ ɭɱɚɫɬɤɢ ɜɵɞɟɥɟɧɢɹ ɩɨɬɟɪɶ: – ɜ ɪɟɞɭɤɬɨɪɟ (ɩɨɬɟɪɢ ɭɱɢɬɵɜɚɸɬɫɹ ɤɩɞ Ș12 ); – ɜ ɩɟɪɟɞɚɱɟ «ɜɢɧɬ – ɝɚɣɤɚ» (ɩɨɬɟɪɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ɱɟɪɟɡ ɭɝɨɥ ɬɪɟɧɢɹ ĳ); – ɜ ɩɨɞɲɢɩɧɢɤɚɯ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ (ɩɨɬɟɪɢ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɱɟɪɟɡ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɜ ɩɨɞɲɢɩɧɢɤɚɯ, ɨɞɧɚɤɨ ɷɬɢ ɩɨɬɟɪɢ ɦɚɥɵ ɢ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɭɱɢɬɵɜɚɸɬɫɹ). 19

ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ (ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ) ȦɊɈ

v ȡ

42 2,12

19,8 ɪɚɞ ɫ ,

ɝɞɟ ȡ – ɪɚɞɢɭɫ ɩɪɢɜɟɞɟɧɢɹ ɩɟɪɟɞɚɱɢ «ɜɢɧɬ – ɝɚɣɤɚ» ɫ ɲɚɝɨɦ h ɞɢɚɦɟɬɪɨɦ d XB ɢ ɭɝɥɨɦ ɧɚɪɟɡɤɢ ɪɟɡɶɛɵ Į ȡ

v ȦPO

ʌ dXB tgĮ 2ʌ

h 2ʌ

dXB tgĮ 2

44 tg 5,5q 2

ʌ dXB tgĮ ,

2,12 ɦɦ ,

Ɇɨɦɟɧɬ ɧɚ ɜɚɥɭ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ (ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ) ɫ ɭɱɟɬɨɦ ɩɨɬɟɪɶ ɜ ɩɟɪɟɞɚɱɟ «ɜɢɧɬ – ɝɚɣɤɚ» ɭɝɥɨɦ ɬɪɟɧɢɹ ĳ: ɆɊɈ

Fɉ

dCP 0,044 tgĮ ĳ 10,67 tg5,5q 4q 39,27 H ɦ , 2 2

ɝɞɟ Fɉ – ɫɭɦɦɚɪɧɨɟ ɭɫɢɥɢɟ ɩɨɞɚɱɢ Fɉ

1,2 FX FZ FY 9,81 m μC

1,2 FX 2,5 FX 0,8 FX 9,81 m μC

1,2 6 2,5 6 0,8 6 9,81 2,4 0,08 10,67 ɤɇ.

Ɇɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɩɨɥɟɡɧɚɹ: – ɛɟɡ ɭɱɟɬɚ ɩɨɬɟɪɶ ɜ ɩɟɪɟɞɚɱɟ «ɜɢɧɬ – ɝɚɣɤɚ» Fɉ v 10,67 103 42 103

ɊɊɈ

448,14 Bɬ ;

– ɫ ɭɱɟɬɨɦ ɩɨɬɟɪɶ ɊɊɈ

ɆɊɈ ȦɊɈ

39,27 19,8

777,5 ȼɬ .

ɋɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ Ɇȼ

ɆɊɈ i12 Ș12

39,27 5 0,9

8,73 ɇ ɦ .

ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ Ȧ Ⱦȼ

ȦɊɈ i12

19,8 5

99,1 ɪɚɞ ɫ .

Ɇɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ Ɋ Ⱦȼ

Ɇȼ Ȧ Ⱦȼ

8,73 99,1 864,3 ȼɬ .

ɇɚɯɨɞɢɦ ɷɥɟɦɟɧɬɵ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ, ɡɚɩɚɫɚɸɳɢɟ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ: ɫɭɩɩɨɪɬ ɦɚɫɫɨɣ m, ɯɨɞɨɜɨɣ ɜɢɧɬ ɦɚɫɫɨɣ m XB , ɲɟɫɬɟɪɧɢ ɪɟɞɭɤɬɨɪɚ J1 ɢ J2 , ɪɨɬɨɪ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɶ – J Ⱦȼ . Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɚɫɫɨɣ m ɫɭɩɩɨɪɬɚ, ɩɟɪɟɦɟɳɚɸɳɟɣɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v, ɢ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ Jɏȼ . Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨ ɞɜɢɠɭɳɟɝɨɫɹ ɫɭɩɩɨɪɬɚ JC

m v2 ȦPO

2

m ȡ2

2400 0,00212 2

20

0,0106 ɤɝ ɦ2 .

Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɯɨɞɨɜɨɝɨ ɜɢɧɬɚ §d · m ¨ CP ¸ © 2 ¹

J XB

2

§ 0,044 · 100 ¨ ¸ © 2 ¹

2

0,0484 ɤɝ ɦ 2 .

Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ 0,0106 0,0484 0,059 ɤɝ ɦ2 .

JC JXB

JPO

Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ, JɉɊ

JPO 2 i12

0,059 52

0,00236 ɤɝ ɦ2 .

Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɟɪɟɞɚɱɢ, ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ, JɉȿɊ

J1

J2 i12

2

0,03

0,6 52

0,054 ɤɝ ɦ2 .

Ʉɨɷɮɮɢɰɢɟɧɬ, ɭɱɢɬɵɜɚɸɳɢɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɟɪɟɞɚɱɢ ɜ ɦɨɦɟɧɬɟ ɢɧɟɪɰɢɢ ɪɨɬɨɪɚ ɞɜɢɝɚɬɟɥɹ, į

JȾȼ JɉȿɊ 0,2 0,054 JȾȼ

0,2

1,27 .

ɋɭɦɦɚɪɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ

J

į JȾȼ JɉɊ

1,27 0,2 0,00236

0,256 ɤɝ ɦ2 .

2.4. ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ Ɇɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ WȾȼ ɪɚɫɯɨɞɭɟɬɫɹ: – ɧɚ ɫɨɜɟɪɲɟɧɢɟ ɩɨɥɟɡɧɨɣ ɪɚɛɨɬɵ ɢ ɩɪɟɨɞɨɥɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ WC ; – ɧɚ ɫɨɡɞɚɧɢɟ ɡɚɩɚɫɚ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ WɄɂɇ WȾȼ

Wɋ WɄɂɇ .

(2.22)

Ɇɨɳɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɪɚɜɧɚ ɩɪɨɢɡɜɨɞɧɨɣ ɷɧɟɪɝɢɢ ɩɨ ɜɪɟɦɟɧɢ Ɋ Ⱦȼ

dWȾȼ dt

dWC dWɄɂɇ dt dt

Ɋ ɋ Ɋ Ⱦɂɇ

Ɇɋ Ȧ ɆȾɂɇ Ȧ .

(2.23)

Ɍɨɝɞɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ Ɇɋ ɆȾɂɇ .

(2.24)

Ɉɩɪɟɞɟɥɢɦ ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ, ɩɪɨɞɢɮɮɟɪɟɧɰɢɪɨɜɚɜ ɩɨ ɜɪɟɦɟɧɢ ɜɵɪɚɠɟɧɢɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ: dWɄɂɇ dt

§ J Ȧ2 · ¸ d ¨¨ ¸ 2 ¹ © dt

Ȧ2 dJ dȦ JȦ 2 dt dt

21

PȾɂɇ

ɆȾɂɇ Ȧ .

(2.25)

ɂɡ ɮɨɪɦɭɥɵ (2.25) ɫɥɟɞɭɟɬ, ɱɬɨ ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɆȾɂɇ

Ȧ dJ dȦ J . 2 dt dt

(2.26)

Ɇɨɦɟɧɬ Ɇ, ɪɚɡɜɢɜɚɟɦɵɣ ɞɜɢɝɚɬɟɥɟɦ, ɭɪɚɜɧɨɜɟɲɢɜɚɟɬɫɹ ɦɨɦɟɧɬɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ MC ɢ ɞɢɧɚɦɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ ɆȾɂɇ: Ȧ dJ dȦ . J (2.27) 2 dt dt ȼɵɪɚɠɟɧɢɟ (2.27) ɧɚɡɵɜɚɸɬ ɩɨɥɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɞɜɢɠɟɧɢɹ. Ⱦɥɹ ɛɨɥɶɲɢɧɫɬɜɚ ɦɟɯɚɧɢɡɦɨɜ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ J = const. Ɍɨɝɞɚ ɩɨɥɭɱɚɟɦ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: Ɇ

Ɇɋ ɆȾɂɇ

Ɇɋ

Ɇ Ɇɋ J

dȦ . dt

(2.28)

ȼ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɜɯɨɞɹɬ: – Ɇ – ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ; – Ɇɋ – ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɣ ɩɪɟɨɞɨɥɟɧɢɟ ɦɨɦɟɧɬɨɜ ɢ ɫɢɥ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ. ȼ ɞɚɥɶɧɟɣɲɟɦ Ɇɋ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɫɬɚɬɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ, ɞɟɣɫɬɜɭɸɳɢɦ ɜ ɫɬɚɬɢɤɟ ɢ ɞɢɧɚɦɢɤɟ; – ɆȾɂɇ – ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ, ɞɟɣɫɬɜɭɸɳɢɣ ɬɨɥɶɤɨ ɜ ɞɢɧɚɦɢɤɟ. Ɉɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɬɶ ɫɨɫɬɨɹɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɧɚɯɨɞɢɬɫɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞ: dȦ dȦ ! 0 ĺ ɩɪɢ J = const ĺ ! 0 ĺ ȦĹ – ɷɥɟɤɬɪɨɩɪɢɜɨɞ – ɩɪɢ Ɇ > Ɇ ɋ ĺ J dt dt ɪɚɡɝɨɧɹɟɬɫɹ; dȦ dȦ 0 ĺ ɩɪɢ J = const ĺ 0 ĺ ȦĻ – ɷɥɟɤɬɪɨɩɪɢɜɨɞ – ɩɪɢ Ɇ < Ɇɋ ĺ J dt dt ɬɨɪɦɨɡɢɬɫɹ; dȦ dȦ – ɩɪɢ Ɇ = Ɇɋ ĺ J 0 ĺ ɩɪɢ J = const ĺ 0 ĺ Ȧ=const – ɫɤɨɪɨɫɬɶ dt dt ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɨɫɬɨɹɧɧɚ, ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ ɪɟɠɢɦ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ; dȦ <0 ĺ ȦĻ – ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɬɨɪɦɨɡɢɬɫɹ – ɩɪɢ Ɇ = 0 ĺ Ɇ Ⱦɂɇ Ɇɋ ĺ dt ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɩɪɢ ɨɬɤɥɸɱɟɧɧɨɦ ɞɜɢɝɚɬɟɥɟ (ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɜɵɛɟɝɟ). Ɂɧɚɤɢ ɦɨɦɟɧɬɨɜ: – ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɩɨɥɨɠɢɬɟɥɶɧɵɣ – Ɇ (+), ɟɫɥɢ ɧɚɩɪɚɜɥɟɧɢɟ ɞɟɣɫɬɜɢɹ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ; – ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɩɨɥɨɠɢɬɟɥɶɧɵɣ – Ɇɋ (+), ɟɫɥɢ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɧɚɩɪɚɜɥɟɧ ɧɚɜɫɬɪɟɱɭ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ. Ɉɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɜɵɜɨɞɢɬɫɹ ɚɧɚɥɨɝɢɱɧɨ ɢ ɢɦɟɟɬ ɜɢɞ FȾȼ

FC m

dv , dt

ɝɞɟ FȾȼ – ɫɢɥɚ ɞɜɢɝɚɬɟɥɹ (ɥɢɧɟɣɧɨɝɨ); 22

(2.29)

FC – ɫɢɥɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ; m – ɩɟɪɟɞɜɢɝɚɟɦɚɹ ɦɚɫɫɚ; v – ɥɢɧɟɣɧɚɹ ɫɤɨɪɨɫɬɶ ɩɟɪɟɞɜɢɠɟɧɢɹ.

2.5. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɤɚɤ ɨɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ Ɋɚɫɫɦɨɬɪɢɦ ɪɚɫɱɟɬɧɭɸ ɫɯɟɦɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɛɟɫɤɨɧɟɱɧɨɣ ɠɟɫɬɤɨɫɬɶɸ ɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɹɡɟɣ ɦɟɠɞɭ ɷɥɟɦɟɧɬɚɦɢ. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜɪɚɳɚɸɳɢɦɫɹ ɷɥɟɦɟɧɬɨɦ ɫ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ, ɩɪɢɜɟɞɟɧɧɵɦ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ, J į JȾȼ JPO iɉȿɊ , ɩɪɢɜɟɞɟɧɧɵɦ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɫɬɚɬɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ Ɇɋ ɢ ɦɨɦɟɧɬɨɦ ɞɜɢɝɚɬɟɥɹ Ɇ. Ɉɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɩɪɢ ɥɢɧɟɣɧɨɣ (J = const) ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɢ Ɇ Ɇɋ

J

dȦ dt

(2.30)

ɡɚɩɢɲɟɦ ɜ ɨɩɟɪɚɬɨɪɧɨɣ ɮɨɪɦɟ: Mp MC p J Ȧp p .

(2.31)

ɉɟɪɟɞɚɬɨɱɧɭɸ ɮɭɧɤɰɢɸ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɧɚ ɜɵɯɨɞɟ ɤɨɬɨɪɨɣ ɪɚɫɫɦɚɬɪɢɜɚɟɦ Ȧ(p), ɧɚ ɜɯɨɞɟ – ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ MȾɂɇ ɪ Ɇɪ Ɇɋ ɪ , (2.32) ɩɨɥɭɱɚɟɦ ɜ ɜɢɞɟ Ȧɪ Ɇɪ Ɇɋ ɪ

xȼɕɏ ɯȼɏ

W p

1/ J . p

(2.33)

ɀɟɫɬɤɨɟ ɩɪɢɜɟɞɟɧɧɨɟ ɡɜɟɧɨ ɤɚɤ ɨɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɨ ɢɧɬɟɝɪɢɪɭɸɳɢɦ ɡɜɟɧɨɦ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɫɢɥɟɧɢɹ 1/J. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ (ɨɫɨɛɚɹ ɮɨɪɦɚ ɡɚɩɢɫɢ ɭɪɚɜɧɟɧɢɣ) ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɥɨɝɚɪɢɮɦɢɱɟɫɤɚɹ ɚɦɩɥɢɬɭɞɧɚɹ (ɅȺɏ) ɢ ɩɟɪɟɯɨɞɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɡɨɛɪɚɠɟɧɵ ɧɚ ɪɢɫ. 2.9. ɤ Ɇ

ɆȾɂɇ – Ɇɋ

1 J p

1 J

Zof

M Ȧ

Mɞɢɧ=const

Ȧ Ȧ

t

Ɋɢɫ. 2.9. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ, ɅȺɏ ɢ ɩɟɪɟɯɨɞɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɉɪɢ ɫɤɚɱɤɟ ɧɚ ɜɯɨɞɟ MȾɂɇ ɪ Ɇɪ Ɇɋ ɪ const ɢ J = const ɜɵɯɨɞɧɚɹ ɜɟɥɢɱɢɧɚ Ȧ(t) ɛɭɞɟɬ ɧɚɪɚɫɬɚɬɶ ɩɨ ɥɢɧɟɣɧɨɦɭ (ɬɚɤ ɤɚɤ dȦ dt ɮɭɧɤɰɢɢ ɜɪɟɦɟɧɢ ɨɬ Ȧ = 0 ɞɨ Ȧ f . 23

İ

const ) ɡɚɤɨɧɭ ɜ

ɉɟɪɟɣɞɟɦ ɜ ɭɪɚɜɧɟɧɢɢ (2.28) ɤ ɨɬɧɨɫɢɬɟɥɶɧɵɦ ɟɞɢɧɢɰɚɦ (ɨ.ɟ.). ɉɪɢɧɢɦɚɟɦ ɡɚ ɛɚɡɨɜɵɟ ɜɟɥɢɱɢɧɵ: – ɆȻ Ɇɇ – ɧɨɦɢɧɚɥɶɧɵɣ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ; – ȦȻ Ȧ0ɇ – ɫɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɧɚɩɪɹɠɟɧɢɢ ɧɚ ɹɤɨɪɟ ɢ ɧɨɦɢɧɚɥɶɧɨɦ ɬɨɤɟ ɜɨɡɛɭɠɞɟɧɢɹ. Ɉɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɜ ɨ.ɟ. ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ Ɇ Ɇɋ

dȦ , dt

ɌȾ

(2.34)

J Ȧ 0H – ɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɭɱɢɬɵMH ɜɚɸɳɚɹ ɢ ɩɪɢɜɟɞɟɧɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. ɇɚɥɢɱɢɟ ɜ ɭɪɚɜɧɟɧɢɢ Ɍ Ⱦ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɡɚɩɢɫɢ ɭɪɚɜɧɟɧɢɹ ɜ ɨ.ɟ.

ɝɞɟ Ɍ Ⱦ

2.6. ɉɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ Ɋɚɫɫɦɨɬɪɢɦ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ, ɜ ɤɨɬɨɪɵɯ ɭɱɢɬɵɜɚɟɬɫɹ ɢɡɦɟɧɟɧɢɟ ɬɨɥɶɤɨ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɚɫɱɟɬɚ ɧɟɨɛɯɨɞɢɦɨ ɩɨɥɭɱɢɬɶ ɡɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɫɤɨɪɨɫɬɢ Ȧ(t) ɩɪɢ ɡɚɞɚɧɧɨɦ ɡɚɤɨɧɟ ɢɡɦɟɧɟɧɢɹ ɦɨɦɟɧɬɚ Ɇ(t). Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɧɚɝɪɭɡɨɱɧɨɣ ɞɢɚɝɪɚɦɦɵ Ȧ(t) ɪɟɲɚɟɦ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɤɨɪɨɫɬɢ: M MC

J

dȦ . dt

(2.35)

Ɍɚɤ ɤɚɤ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɱɚɳɟ ɜɫɟɝɨ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ Ɇ(Ȧ), ɦɨɦɟɧɬ ɫɬɚɬɢɱɟɫɤɢɣ – ɨɬ ɫɤɨɪɨɫɬɢ, ɜɪɟɦɟɧɢ, ɭɝɥɚ ɩɨɜɨɪɨɬɚ ɜɚɥɚ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ MC Ȧ, t, D , ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ – ɨɬ ɫɤɨɪɨɫɬɢ, ɜɪɟɦɟɧɢ, ɭɝɥɚ ɩɨɜɨɪɨɬɚ ɜɚɥɚ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ J Ȧ, t, D , ɬɨ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɜ ɨɛɳɟɦ ɜɢɞɟ ɧɟɜɨɡɦɨɠɧɨ ɜ ɫɜɹɡɢ ɫ ɨɬɫɭɬɫɬɜɢɟɦ ɭɤɚɡɚɧɧɵɯ ɚɧɚɥɢɬɢɱɟɫɤɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ. ȿɫɥɢ ɩɪɢɧɹɬɶ, ɱɬɨ Ɇ = const, MC const , J const , ɬɨ ɭɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ M MC J

İ

const

ɢ ɜ ɩɪɢɧɹɬɵɯ ɭɫɥɨɜɢɹɯ ɫɤɨɪɨɫɬɶ ɜɨ ɜɪɟɦɟɧɢ ɛɭɞɟɬ ɢɡɦɟɧɹɬɶɫɹ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ Ȧt

ȦɇȺɑ İ t .

Ɋɟɲɟɧɢɟ ɨɫɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɨ.ɟ. M

MC

ɌȾ

dȦ dt

24

(2.36)

ɞɥɹ M

const , MC

const ɩɪɢɧɢɦɚɟɬ ɜɢɞ

const , J t

Ȧ

M MC

³ Ɍ 0 Ⱦ

M MC ǻt ȦɇȺɑ , ɌȾ

dt

(2.37)

Ɇ Ɇɋ . ɌȾ ȼɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɢɡ ɨɫɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ

ɝɞɟ İ

t

t

J

³ M M dȦ .

0

Ⱦɥɹ Ɇ = const, MC

const , J

ǻt

(2.38)

C

const

J (ȦɄɈɇ ȦɇȺɑ ) . M MC

(2.39)

ȼɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɜ ɨ.ɟ. ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ ǻt

Ɍ Ⱦ ǻȦ M MC

.

(2.40)

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɌȾ ɢ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɜɟɥɢɱɢɧɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɆȾɂɇ Ɇ Ɇɋ . ȿɫɥɢ ɪɚɫɫɦɨɬɪɟɬɶ ɩɭɫɤ ɞɜɢɝɚɬɟɥɹ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ ɩɪɢ Ɇ Ɇɇ , Ɇɋ 0 , ȦɇȺɑ 0 , ȦɄɈɇ Ȧ0ɇ , ɬɨɝɞɚ ǻȦ Ȧ0ɇ ɢ ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɩɨ ɮɨɪɦɭɥɟ (2.39) ɛɭɞɟɬ ɪɚɜɧɨ ɦɟɯɚɧɢɱɟɫɤɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

ǻt

J ǻȦ M MC

J Ȧ0ɇ MH

ɌȾ .

Ɉɬɫɸɞɚ ɜɢɞɟɧ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɌȾ: Ɇɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɌȾ ɟɫɬɶ ɜɪɟɦɹ, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɞɜɢɝɚɬɟɥɶ ɫ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ J ɪɚɡɝɨɧɢɬɫɹ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ ɢɡ ɧɟɩɨɞɜɢɠɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɞɨ ɫɤɨɪɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɦɨɦɟɧɬɚ, ɪɚɜɧɨɝɨ ɧɨɦɢɧɚɥɶɧɨɦɭ. ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɡɚ ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ, ɫɜɹɡɚɧɧɨɝɨ ɫ ɜɚɥɨɦ ɞɜɢɝɚɬɟɥɹ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɰɟɩɶɸ. ɉɪɢɪɚɳɟɧɢɟ ɭɝɥɚ ɩɨɜɨɪɨɬɚ ǻĮ ɡɚ ɜɪɟɦɹ ǻt ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Ȧ

dĮ dt

ǻĮ , ǻt

(2.41)

ɨɬɤɭɞɚ ǻĮ Ȧt ǻt . ȿɫɥɢ Ȧ(t) = const, ɬɨ ǻĮ = Ȧ·ǻt. ȿɫɥɢ ɮɭɧɤɰɢɹ Ȧ(t) – ɥɢɧɟɣɧɚɹ, ɬɨ Į

25

³ Ȧ dt

İ

t2 . 2

ɉɪɢ ɧɟɥɢɧɟɣɧɨɣ ɮɭɧɤɰɢɢ Ȧ(t) ɱɚɳɟ ɜɫɟɝɨ ɷɬɭ ɡɚɜɢɫɢɦɨɫɬɶ ɪɚɡɛɢɜɚɸɬ ɧɚ ɥɢɧɟɣɧɵɟ ɭɱɚɫɬɤɢ ɢ ǻĮ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɭɱɚɫɬɤɚɦ ɤɚɤ ɥɢɧɟɣɧɭɸ ɮɭɧɤɰɢɸ ǻĮ

ȦɇȺɑ ȦɄɈɇ ǻt . 2

ȦCP ǻt

(2.42)

Ɉɩɬɢɦɚɥɶɧɨɟ ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɪɟɞɭɤɬɨɪɚ [14] ɩɨɥɭɱɚɸɬ ɢɡ ɭɫɥɨɜɢɹ ɨɛɟɫɩɟɱɟɧɢɹ ɦɢɧɢɦɚɥɶɧɨɝɨ ɜɪɟɦɟɧɢ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɩɟɪɟɞɚɬɨɱɧɨɝɨ ɱɢɫɥɚ ɪɟɞɭɤɬɨɪɚ iP ɩɪɢ ɨɞɧɢɯ ɢ ɬɟɯ ɠɟ ɞɜɢɝɚɬɟɥɟ ɢ ɪɚɛɨɱɟɦ ɨɪɝɚɧɟ ɢɡɦɟɧɹɟɬɫɹ ɢ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɫɤɨɪɨɫɬɹɦɢ ɢ ɭɫɤɨɪɟɧɢɹɦɢ ɞɜɢɝɚɬɟɥɹ ɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ.

M iP MPO

J

dȦdt

2

Ⱦȼ

PO

iP JPO

.

(2.43)

Ɂɚɩɢɲɟɦ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɞɥɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ, ɩɪɢɧɢɦɚɹ ɄɉȾ ɪɟɞɭɤɬɨɪɚ ȘP 1. Ɋɟɲɚɹ (2.43) ɨɬɧɨɫɢɬɟɥɶɧɨ ɭɫɤɨɪɟɧɢɹ ɧɚ ɊɈ, ɩɨɥɭɱɚɟɦ: dȦPO dt

M iP MPO 2

JȾȼ iP JPO

.

(2.44)

Ɉɬɫɸɞɚ ɦɨɠɧɨ ɧɚɣɬɢ ɨɩɬɢɦɚɥɶɧɨɟ ɩɟɪɟɞɚɬɨɱɧɨɟ ɨɬɧɨɲɟɧɢɟ ɪɟɞɭɤɬɨɪɚ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɭɫɤɨɪɟɧɢɹ dȦPO dt , 2

iP.ɈɉɌ

ɆɊɈ J §Ɇ · ¨ ɊɈ ¸ PO . Ɇ J Ⱦȼ © Ɇ ¹

(2.45)

Ɍɚɤ ɤɚɤ ɩɪɢ ɪɚɡɝɨɧɟ ɢ ɬɨɪɦɨɠɟɧɢɢ ɆɊɈ ɪɚɡɥɢɱɧɵ, ɬɨ ɡɧɚɱɟɧɢɟ iɊ.ɈɉɌ ɩɨ ɮɨɪɦɭɥɟ (2.45) ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɥɢɲɶ ɞɥɹ ɆɊɈ 0 , ɤɨɝɞɚ iP.ɈɉɌ

JPO . JȾȼ

(2.46)

ɇɟɨɛɯɨɞɢɦɨ ɩɨɞɱɟɪɤɧɭɬɶ ɭɫɥɨɜɧɨɫɬɶ ɬɟɪɦɢɧɚ «ɨɩɬɢɦɚɥɶɧɨɟ ɩɟɪɟɞɚɬɨɱɧɨɟ ɨɬɧɨɲɟɧɢɟ». ȼɟɥɢɱɢɧɚ iP.ɈɉɌ ɩɨɥɭɱɟɧɚ ɬɨɥɶɤɨ ɢɡ ɨɞɧɨɝɨ ɭɫɥɨɜɢɹ ɨɛɟɫɩɟɱɟɧɢɹ ɧɚɢɛɨɥɶɲɟɝɨ ɭɫɤɨɪɟɧɢɹ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɩɪɢ ɡɚɞɚɧɧɨɦ ɞɜɢɝɚɬɟɥɟ. ȼ ɫɬɨɪɨɧɟ ɨɫɬɚɜɥɟɧɵ ɜɨɩɪɨɫɵ ɫɨɝɥɚɫɨɜɚɧɢɹ ɫɤɨɪɨɫɬɟɣ ɢ ɦɨɳɧɨɫɬɟɣ ɞɜɢɝɚɬɟɥɹ ɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ, ɛɟɡ ɪɟɲɟɧɢɹ ɤɨɬɨɪɵɯ ɡɚɬɪɭɞɧɢɬɟɥɶɧɨ ɩɪɚɜɢɥɶɧɨ ɜɵɛɪɚɬɶ ɧɟɨɛɯɨɞɢɦɨɟ ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɪɟɞɭɤɬɨɪɚ. ɉɪɢɦɟɪ 2.2. Ⱦɥɹ ɦɟɯɚɧɢɡɦɚ ɫ ɞɜɢɝɚɬɟɥɟɦ ( Ɋɇ 9 ɤȼɬ , Kɇ 910 ɦɢɧ 1 , UH 100 B , IH 100 A ) ɢ ɫɭɦɦɚɪɧɵɦ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ J 1 ɤɝ ɦ2 ɪɚɫɫɱɢɬɚɬɶ: ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɆȾɂɇ , ɭɫɤɨɪɟɧɢɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ İ, ɤɨɧɟɱɧɨɟ ɡɧɚ-

ɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ȦɄɈɇ , ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ Į ɡɚ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ ǻt i t i Ɍ Ⱦ 0,5 , ɟɫɥɢ, Ɇɋ 0,5 , ȦɇȺɑ 0,2 . Ɉɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɜ ɨ.ɟ. Ɇ Ɇɋ

ɌȾ

dȦ . dt

26

Ɇɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɞɜɢɝɚɬɟɥɹ: J ZOH . MH Ɂɧɚɱɟɧɢɹ ZOH ɢ MH ɪɚɫɫɱɢɬɚɟɦ ɩɪɢ kɎ ɇ 1 ȼ ɫ (ɪɚɫɱɟɬ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ ɞɜɢɝɚɬɟɥɹ – ɫɦ. ɩɪɢɦɟɪ 3.1). ɋɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɌȾ

UH kɎ ɇ

ZɈɇ

100 1

100 ɪɚɞ ɫ .

ɇɨɦɢɧɚɥɶɧɵɣ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ kɎ ɇ UH

Ɇɇ

1 100

100 ɇ ɦ .

Ɇɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ J ZOH MH

ɌȾ

1 100 100

1ɫ.

Ⱦɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɆȾɂɇ

1,5 0,5 1.

Ɇ Ɇɋ

ɍɫɤɨɪɟɧɢɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ (ɩɪɢ t Ȼ

ɌȾ )

d Z dt ɌȾ

dZ dt

H

M MC

ɉɪɢɪɚɳɟɧɢɟ ɫɤɨɪɨɫɬɢ ɡɚ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ 't i

MȾɂɇ

1.

ti Ɍ Ⱦ

0,5 :

Ɇ Ɇɋ 't i 1,5 0,5 0,5

'Z

0,5 .

Ʉɨɧɟɱɧɨɟ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɧɚ ɭɱɚɫɬɤɟ ZɄɈɇ

ZɇȺɑ 'Z

0,2 0,5

0,7 .

ɉɪɢɪɚɳɟɧɢɟ ɭɝɥɚ ɩɨɜɨɪɨɬɚ

Z

'D

ɄɈɇ

'2t

ZɇȺɑ

0,7 0,2 0,5 2

0,225 .

Ɉɩɪɟɞɟɥɢɦ ɩɨɥɭɱɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɜ ɚɛɫɨɥɸɬɧɵɯ ɟɞɢɧɢɰɚɯ: ɆȾɂɇ

H 'Z ZɄɈɇ 'D

ɆȾɂɇ Ɇɇ

1 100

100 ɇ ɦ ;

H ZɈɇ 1 100 100 ɪɚɞ ɫ 2 ; tȻ 1 ' Z ZɈɇ 0,5 100 50 ɪɚɞ ɫ ; ZɇȺɑ ZɈɇ

'D ZɈɇ t Ȼ

0,7 100

70 ɪɚɞ ɫ ;

0,225 100 1 22,5 ɪɚɞ .

27

ɉɪɢɦɟɪ 2.3. Ⱦɥɹ ɞɜɢɝɚɬɟɥɹ ( Ȧ0ɇ

100 ɪɚɞ ɫ , Ɇɇ

100 ɇ ɦ , J 1 ɤɝ ɦ2 )

ɪɚɫɫɱɢɬɚɬɶ ɭɫɤɨɪɟɧɢɟ ɢ ɩɨɫɬɪɨɢɬɶ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ Ȧ t , ɟɫɥɢ M ȦɇȺɑ

0, Ɇɋ

2,

0.

Ⱦɥɹ ɪɚɫɱɟɬɚ ɢ ɩɨɫɬɪɨɟɧɢɹ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ Ɇ(t) ɢ Ȧ(t) ɢɫɩɨɥɶɡɭɟɬɫɹ ɪɟɲɟɧɢɟ ɨɫɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ dȦ , dt ɢɡ ɤɨɬɨɪɨɝɨ ɞɥɹ ɤɨɧɟɱɧɵɯ ɩɪɢɪɚɳɟɧɢɣ ɩɪɢ Ɇ = const ɢ Ɇɋ = const ɞɥɹ ɡɚɞɚɧɧɨɝɨ ti ɩɨɥɭɱɢɦ ɩɪɢɪɚɳɟɧɢɟ ɫɤɨɪɨɫɬɢ Ɇ Ɇɋ

ɌȾ

M M t C

ǻȦ

Ɍ

i

.

ɞ

ɢ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɜ ɤɨɧɰɟ ɭɱɚɫɬɤɚ Ȧ

ȦɇȺɑ ǻ Ȧ .

Ɇɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɌȾ

J Ȧ 0H MH

1 100 100

1 c.

ɉɪɢɪɚɳɟɧɢɟ ɫɤɨɪɨɫɬɢ ǻȦ

M MC t i 2 0 t i , ɌȾ

ɌȾ

ɢ ɩɪɢ ti = ɌȾ ɩɨɥɭɱɚɟɦ ǻ Ȧ 2 . ɋɤɨɪɨɫɬɶ ɡɚ ɷɬɨ ɜɪɟɦɹ ɞɨɫɬɢɝɧɟɬ ɡɧɚɱɟɧɢɹ Ȧ 2

M

Ȧ ȦɇȺɑ ǻ Ȧ 0 2 2 . Ɂɧɚɱɟɧɢɹ Ȧ 1 ɫɤɨɪɨɫɬɶ ɞɨɫɬɢɝɧɟɬ ɡɚ ¨t = 0,5·ɌȾ, ɜ ɷɬɨɬ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɪɚɡɝɨɧ ɩɪɟɤɪɚɳɚɸɬ, ɫɧɢɠɚɹ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɞɨ ɜɟɥɢɱɢɧɵ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇ = Ɇɋ (ɫɦ. ɪɢɫ. 2.10). ɉɪɢɦɟɪ 2.4. Ⱦɥɹ ɞɜɢɝɚɬɟɥɹ ( Ȧ0ɇ 100 ɪɚɞ ɫ , Ɇɇ 100 ɇ ɦ ,

M( t )

Ȧ( t )

1

t

1 Ɋɢɫ. 2.10. Ɇɟɯɚɧɢɱɟɫɤɢɣ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɪɢ Ɇ=const

J

1 ɤɝ ɦ 2 ɌȾ=1 ɫ) ɪɚɫɫɱɢɬɚɬɶ ɭɫɤɨɪɟ-

ɧɢɟ ɢ ɩɨɫɬɪɨɢɬɶ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɪɟɜɟɪɫɚ Ȧ t , ɟɫɥɢ ȦɇȺɑ 1, Ɇɋ 1, M – 2.

ɉɪɢɪɚɳɟɧɢɟ ɫɤɨɪɨɫɬɢ ǻȦ

M MC ti 2 1 ti . ɌȾ

ɌȾ

28

Ɂɚ ɛɚɡɨɜɨɟ ɜɪɟɦɹ tȻ = ɌȾ ɩɪɢɪɚɳɟɧɢɟ ɫɤɨɪɨɫɬɢ ɪɚɜɧɨ ǻ Ȧ – 3, ɤɨɧɟɱɧɚɹ ɫɤɨɪɨɫɬɶ Ȧ

ȦɇȺɑ ǻ Ȧ

– 2.

1 3

Ⱦɜɢɝɚɬɟɥɶ ɨɫɬɚɧɨɜɢɬɫɹ ( ȦɄɈɇ 0 ) ɩɪɢ ǻ Ȧ – 1 ɡɚ ɜɪɟɦɹ ti = ɌȾ / 3. Ɋɟɜɟɪɫ ɡɚɤɨɧɱɢɬɫɹ ɩɪɢ ȦɄɈɇ – 1, ɩɪɢ ɷɬɨɦ ǻ Ȧ – 2, ti = 2·ɌȾ / 3. ȼ ɷɬɨɬ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɫɥɟɞɭɟɬ ɫɧɢɡɢɬɶ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɞɨ M Ɇɋ . Ɋɚɫɫɦɨɬɪɟɧɧɵɣ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɫɩɪɚɜɟɞɥɢɜ ɞɥɹ ɚɤɬɢɜɧɨɝɨ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ (ɫɦ. ɪɢɫ. 2.11,ɚ). Ȧ

Ȧ

M MC(t)

M

MC(t)

1

1

Ȧ(t)

M(t) Ȧ(t)

TȾ

0

Ȧ(t)

-1

t

TȾ/3

0

TȾ

MC(t)

-1

t Ȧ(t)

Ȧ(t) Ɇ(t)

M(t)

M(t)

-2

-2 ɚ

ɛ

Ɋɢɫ. 2.11. Ʉ ɩɪɢɦɟɪɭ 2.4: ɚ – ɩɪɢ ɚɤɬɢɜɧɨɦ ɆC; ɛ – ɩɪɢ ɪɟɚɤɬɢɜɧɨɦ ɆC ɉɪɢ ɪɟɚɤɬɢɜɧɨɦ ɫɬɚɬɢɱɟɫɤɨɦ ɦɨɦɟɧɬɟ, ɤɨɬɨɪɵɣ ɢɡɦɟɧɹɟɬ ɫɜɨɣ ɡɧɚɤ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ, ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɪɚɫɩɚɞɚɟɬɫɹ ɧɚ ɞɜɚ ɷɬɚɩɚ. Ⱦɨ ɨɫɬɚɧɨɜɤɢ ɞɜɢɝɚɬɟɥɹ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɪɨɬɟɤɚɟɬ ɬɚɤɠɟ, ɤɚɤ ɢ ɩɪɢ ɚɤɬɢɜɧɨɦ Ɇɋ. Ⱦɜɢɝɚɬɟɥɶ ɨɫɬɚɧɨɜɢɬɫɹ, ȦɄɈɇ 0 , ɬɨɝɞɚ ǻ Ȧ – 1, ɜɪɟɦɹ ɬɨɪɦɨɠɟɧɢɹ ti = ɌȾ / 3. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɦɟɧɹɸɬɫɹ ɧɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ: ȦɇȺɑ 0, Ɇɋ –1, M – 2, ɧɚɱɚɥɶɧɨɟ ɜɪɟɦɹ ¨tɇȺɑ = ɌȾ / 3. Ɍɨɝɞɚ ɩɪɢɪɚɳɟɧɢɟ ɫɤɨɪɨɫɬɢ ɫɨɫɬɚɜɢɬ ǻȦ

M MC ti 2 1 ti ɌȾ

ɌȾ

- ti . ɌȾ

ɉɪɢ ti = ɌȾ ɩɪɢɪɚɳɟɧɢɟ ɫɤɨɪɨɫɬɢ ǻ Ȧ – 1, ȦɄɈɇ – 1, ɪɚɡɝɨɧ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ ɩɪɨɢɡɨɣɞɟɬ ɡɚ ¨t = ɌȾ, ɪɟɜɟɪɫ ɡɚɤɨɧɱɢɬɫɹ ɡɚ ¨t = 4·ɌȾ / 3. 29

ȼ ɷɬɨɬ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɫɥɟɞɭɟɬ ɫɧɢɡɢɬɶ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɞɨ M Ɇɋ (ɫɦ. ɪɢɫ. 2.11, ɛ). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɪɟɚɤɬɢɜɧɨɦ Ɇɋ ɜɪɟɦɹ ɪɟɜɟɪɫɚ ɭɜɟɥɢɱɢɥɨɫɶ ɜɞɜɨɟ. ɉɪɢɦɟɪ 2.5. Ⱦɥɹ ɞɜɢɝɚɬɟɥɹ ( Ȧ 0ɇ 100 ɪɚɞ ɫ , Ɇɇ 100 ɇ ɦ , J 1 ɤɝ ɦ2 ) ɩɨɫɬɪɨɢɬɶ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ Ȧ(t), ɟɫɥɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɢɡɦɟɧɹɟɬɫɹ ɩɨ ɡɚɤɨɧɭ M(t) = 0,5 + sin(t), ɚɤɬɢɜɧɵɣ ȦɇȺɑ 0, Ɇɋ 1. Ɋɚɫɫɦɨɬɪɢɦ ɩɨɜɟɞɟɧɢɟ ɞɜɢɝɚɬɟɥɹ ɧɚ ɧɚɱɚɥɶɧɨɦ ɭɱɚɫɬɤɟ. Ʉɨɝɞɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɦɟɧɶɲɟ ɫɬɚɬɢɱɟɫɤɨɝɨ ɚɤɬɢɜɧɨɝɨ ɦɨɦɟɧɬɚ Ɇ < MC, ɬɨ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɚɤɬɢɜɧɨɝɨ MC ɞɜɢɝɚɬɟɥɶ ɧɚɱɢɧɚɟɬ ɪɚɡɝɨɧɹɬɶɫɹ ɜ ɫɬɨɪɨɧɭ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɡɧɚɤɭ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ, Ȧ < 0. ɉɪɢ Ɇ = MC ɫɧɢɠɟɧɢɟ ɫɤɨɪɨɫɬɢ ɩɪɟɤɪɚɬɢɬɫɹ, ɚ ɩɪɢ Ɇ > MC ɫɤɨɪɨɫɬɶ ɧɚɱɧɟɬ ɧɚɪɚɫɬɚɬɶ ɞɨ ɧɭɥɹ, ɢ ɬɨɥɶɤɨ ɩɨɫɥɟ ɩɟɪɟɯɨɞɚ ɱɟɪɟɡ ɧɭɥɶ ɧɚɱɧɟɬɫɹ ɪɚɡɝɨɧ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ȿɫɥɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɜɪɟɦɟɧɢ, ɬɨ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɜɵɪɚɠɟɧɢɹ ɧɚɝɪɭɡɨɱɧɨɣ ɞɢɚɝɪɚɦɦɵ ɫɤɨɪɨɫɬɢ ɩɪɢɯɨɞɢɬɫɹ ɢɧɬɟɝɪɢɪɨɜɚɬɶ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ. Ɍɚɤ ɤɚɤ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɜɵɩɨɥɧɹɟɬɫɹ ɜ ɨ.ɟ., ɬɨ ɜɪɟɦɹ ɬɚɤɠɟ ɩɪɢɯɨɞɢɬɫɹ ɜɜɨɞɢɬɶ ɜ ɨ.ɟ., ɩɪɢ ɷɬɨɦ ɡɚ ɛɚɡɨɜɨɟ ɡɧɚɱɟɧɢɟ ɜɪɟɦɟɧɢ ɭɞɨɛɧɨ ɩɪɢɧɹɬɶ tȻ = ɌȾ. Ɍɨɝɞɚ ɜ ɮɭɧɤɰɢɹɯ sin(t) ɢ cos(t) ɩɨɥɚɝɚɟɦ, ɱɬɨ Ȧ = 1 ɪɚɞ/ɫ, ɢ t ɩɪɢɧɢɦɚɟɬ ɪɚɡɦɟɪɧɨɫɬɶ ɪɚɞɢɚɧɚ. t

t

0

0

Ȧ t ³ M MC dt ³ 0,5 sint MC dt 0,5 MC t 1 cost .

ɇɚ ɪɢɫ. 2.12 ɩɪɢɜɟɞɟɧ ɦɟɯɚɧɢɱɟɫɤɢɣ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɞɥɹ ɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɢɡɦɟɧɟɧɢɹ ɦɨɦɟɧɬɚ Ɇ(t). Ɂɧɚɱɟɧɢɟ t, ɩɪɢ ɤɨɬɨɪɨɦ M MC ɢ ɆȾɂɇ=0, ɚ ɫɤɨɪɨɫɬɶ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɧɚɣɞɟɦ ɢɡ ɮɨɪɦɭɥɵ Ɇ

Ɇɋ

0,5 sint 1 .

Ɍɨɝɞɚ t

ȦɆɂɇ

arcsin1 0,5 0,524 ;

0,5 Ɇɋ t 1 cost 0,5 1 0,524 1 cos0,524

-0,128 .

Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɜɪɟɦɟɧɢ ɩɟɪɟɯɨɞɚ ɫɤɨɪɨɫɬɢ ɱɟɪɟɡ ɧɭɥɶ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɦɟɬɨɞɨɦ ɩɨɞɛɨɪɚ, ɬɚɤ ɤɚɤ ɭɪɚɜɧɟɧɢɟ Ȧ(t) – ɬɪɚɧɫɰɟɧɞɟɧɬɧɨɟ. Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɫɜɟɞɟɧɵ ɜ ɬɚɛɥ. 2.1. Ɍɚɛɥɢɰɚ 2.1 Ɋɚɫɱɟɬ Ȧ(t) ɞɥɹ ɩɪɢɦɟɪɚ 2.5 t,c M(t) cos(t) Ȧ( t )

0 0,5 1 0

0,524 1 0,866 –0,128

1 1,34 0,54 –0,04

1,11 1,4 0,444 0,000

1,5 1,5 0,07 0,16

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɤɨɪɨɫɬɶ ɩɟɪɟɯɨɞɢɬ ɱɟɪɟɡ ɧɭɥɶ ɩɪɢ t ɜɪɟɦɹ t t 1,11 c . 30

2 1,4 –0,416 0,416

3 0,64 –0,99 0,49

1,11. ɉɪɢ tȻ = 1 ɫ

ȼ ɞɚɥɶɧɟɣɲɟɦ ɢɡɦɟɧɟɧɢɟ ɫɤɨɪɨɫɬɢ ɛɭɞɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ, ɹɜɥɹɸɳɟɝɨɫɹ ɨɫɧɨɜɧɵɦ ɭɩɪɚɜɥɹɸɳɢɦ ɜɨɡɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ.

Ɋɢɫ. 2.12. Ɇɟɯɚɧɢɱɟɫɤɢɣ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɪɢ ɫɢɧɭɫɨɢɞɚɥɶɧɨɦ ɢɡɦɟɧɟɧɢɢ ɦɨɦɟɧɬɚ Ɇ(t) ɉɪɢ ɪɟɚɤɬɢɜɧɨɦ ɫɬɚɬɢɱɟɫɤɨɦ ɦɨɦɟɧɬɟ ɞɨ M MC ɞɜɢɝɚɬɟɥɶ ɛɭɞɟɬ ɫɬɨɹɬɶ, ɬɚɤ ɤɚɤ ɧɟ ɫɩɨɫɨɛɟɧ ɪɚɡɨɝɧɚɬɶ ɞɜɢɝɚɬɟɥɶ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ. ɉɪɨɰɟɫɫ ɩɭɫɤɚ ɧɚɱɧɟɬɫɹ ɫ ɬɨɝɨ ɦɨɦɟɧɬɚ ɜɪɟɦɟɧɢ, ɤɨɝɞɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɩɪɟɜɵɫɢɬ ɪɟɚɤɬɢɜɧɵɣ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇ > MC . Ɂɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɫɤɨɪɨɫɬɢ ɞɥɹ ɪɟɚɤɬɢɜɧɨɝɨ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɧɭɠɧɨ ɜɵɜɟɫɬɢ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ.

2.7. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɭɩɪɭɝɨɣ ɫɜɹɡɶɸ Ⱦɨ ɫɢɯ ɩɨɪ ɪɚɫɫɦɚɬɪɢɜɚɥɢɫɶ ɦɟɯɚɧɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ ɫ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɢɦɢ ɫɜɹɡɹɦɢ. ɉɪɚɤɬɢɱɟɫɤɢ ɠɟɫɬɤɨɫɬɢ ɜɚɥɨɜ, ɫɨɟɞɢɧɢɬɟɥɶɧɵɯ ɦɭɮɬ, ɩɟɪɟɞɚɱ (ɤɚɧɚɬɵ, ɪɟɦɧɢ, ɜɚɥɵ ɜ ɩɟɪɟɞɚɱɚɯ ɢ ɬ.ɩ.) ɤɨɧɟɱɧɵ, ɦɟɯɚɧɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ ɩɨɥɭɱɚɟɬ ɧɟɫɤɨɥɶɤɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ, ɢ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɫɨɞɟɪɠɢɬ ɬɟɥɚ, ɩɨɞɜɟɪɝɚɸɳɢɟɫɹ ɤɪɭɱɟɧɢɸ, ɢɡɝɢɛɭ, ɪɚɫɬɹɠɟɧɢɸ ɢ ɫɠɚɬɢɸ. ɀɟɫɬɤɨɫɬɶɸ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɫɜɹɡɢ ɋɄ (ɋɅ) ɦɟɠɞɭ ɭɝɥɨɜɨɣ ɞɟɮɨɪɦɚɰɢɟɣ ɜɚɥɚ ǻĳ (ɢɥɢ ɥɢɧɟɣɧɨɣ ɞɟɮɨɪɦɚɰɢɟɣ ǻL) ɢ ɜɨɡɧɢɤɚɸɳɢɦ ɜ ɭɩɪɭɝɨɦ ɷɥɟɦɟɧɬɟ ɭɩɪɭɝɢɦ ɦɨɦɟɧɬɨɦ Ɇɍ (ɢɥɢ ɭɩɪɭɝɨɣ ɫɢɥɨɣ Fɍ). Ȼɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɥɢɧɟɣɧɵɣ ɡɚɤɨɧ ɞɟɮɨɪɦɚɰɢɢ (ɡɚɤɨɧ Ƚɭɤɚ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɪɢɥɨɠɟɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɧɟ ɩɪɢɜɨɞɢɬ ɤ ɨɫɬɚɬɨɱɧɵɦ ɞɟɮɨɪɦɚɰɢɹɦ, ɚ ɩɪɢ ɫɧɹɬɢɢ ɦɨɦɟɧɬɚ ɧɚ ɜɯɨɞɟ ɫɢɫɬɟɦɚ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɢɫɯɨɞɧɨɟ ɩɨɥɨɠɟɧɢɟ. Ɇɍ

ɋɄ ǻĳ ,

(2.47)

Fɍ

ɋɅ 'L .

(2.48)

31

Ʉɨɷɮɮɢɰɢɟɧɬɵ ɠɺɫɬɤɨɫɬɢ ɋɄ ɢ ɋɅ ɨɩɪɟɞɟɥɹɸɬɫɹ ɝɟɨɦɟɬɪɢɱɟɫɤɢɦɢ ɪɚɡɦɟɪɚɦɢ ɭɩɪɭɝɨɝɨ ɷɥɟɦɟɧɬɚ ɢ ɡɚɜɢɫɹɬ ɨɬ ɦɚɬɟɪɢɚɥɚ, ɢɡ ɤɨɬɨɪɨɝɨ ɨɧ ɢɡɝɨɬɨɜɥɟɧ. Ⱦɥɹ ɜɚɥɚ ɪɚɞɢɭɫɨɦ R ɩɪɢ ɟɝɨ ɤɪɭɱɟɧɢɢ ɤɨɷɮɮɢɰɢɟɧɬ ɠɺɫɬɤɨɫɬɢ CK

JS

G ª MH ɦ º , L «¬ ɪɚɞ »¼

ʌ R4 ɝɞɟ JS – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɜɚɥɚ; 2 G – ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ɫɞɜɢɝɚ; L – ɞɥɢɧɚ ɜɚɥɚ. Ⱦɥɹ ɭɩɪɭɝɨɝɨ ɫɬɟɪɠɧɹ ɩɪɢ ɟɝɨ ɪɚɫɬɹɠɟɧɢɢ ɢɥɢ ɫɠɚɬɢɢ ɤɨɷɮɮɢɰɢɟɧɬ ɠɺɫɬɤɨɫɬɢ

ɋɅ

GS E ª ɇɆ º , L «¬ ɦ »¼

ɝɞɟ L – ɞɥɢɧɚ ɫɬɟɪɠɧɹ; GS – ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ; E – ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ. ȼɟɥɢɱɢɧɭ 1/ɋ, ɨɛɪɚɬɧɭɸ ɠɟɫɬɤɨɫɬɢ, ɧɚɡɵɜɚɸɬ ɩɨɞɚɬɥɢɜɨɫɬɶɸ. Ɏɢɡɢɱɟɫɤɢ ɩɨɞɚɬɥɢɜɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬ ɞɟɮɨɪɦɚɰɢɸ ɷɥɟɦɟɧɬɚ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ, ɚ ɤɨɷɮɮɢɰɢɟɧɬ ɠɟɫɬɤɨɫɬɢ – ɜɟɥɢɱɢɧɭ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɣ ɞɟɮɨɪɦɚɰɢɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɟɦ ɛɨɥɶɲɟ ɤɨɷɮɮɢɰɢɟɧɬ ɠɺɫɬɤɨɫɬɢ ɭɩɪɭɝɨɝɨ ɷɥɟɦɟɧɬɚ, ɬɟɦ ɦɟɧɶɲɚɹ ɞɟɮɨɪɦɚɰɢɹ ɜ ɧɺɦ ɜɨɡɧɢɤɚɟɬ. 2.7.1.

ɉɪɢɜɟɞɟɧɢɟ ɭɩɪɭɝɨɫɬɢ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ

ɉɪɢ ɫɨɫɬɚɜɥɟɧɢɢ ɪɚɫɱɺɬɧɵɯ ɫɯɟɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɪɢɜɟɞɟɧɢɟ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɠɟɫɬɤɨɫɬɢ ɭɩɪɭɝɨɝɨ ɷɥɟɦɟɧɬɚ. Ʉɪɢɬɟɪɢɟɦ ɩɪɢɜɟɞɟɧɢɹ ɹɜɥɹɟɬɫɹ ɪɚɜɟɧɫɬɜɨ ɡɚɩɚɫɚ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɜ ɪɟɚɥɶɧɨɣ ɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɚɯ. Ⱦɥɹ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɞɥɹ ɩɪɢɜɟɞɟɧɧɨɝɨ ɢ ɪɟɚɥɶɧɨɝɨ ɡɜɟɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ Wɉ

ɋɉɊ

2 ǻĳɉɊ 2

ɋɄ

ǻĳi2 , 2

ɬɨɝɞɚ ɩɪɢɜɟɞɟɧɧɚɹ ɠɟɫɬɤɨɫɬɶ CɉɊ

§ ǻĳ i2 · ¸ ɋɄ ¨¨ 2 ¸ ǻĳ ɉɊ ¹ ©

ɋɄ

1 . i2

(2.49)

Ⱦɥɹ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɞɥɹ ɩɪɢɜɟɞɟɧɧɨɝɨ ɢ ɪɟɚɥɶɧɨɝɨ ɡɜɟɧɚ Wɉ

ɋɉɊ

2 ǻĳɉɊ 2

ɋɄ

32

ǻL2i , 2

ɬɨɝɞɚ ɩɪɢɜɟɞɟɧɧɚɹ ɠɟɫɬɤɨɫɬɶ ɨɩɪɟɞɟɥɢɬɫɹ ɤɚɤ CɉɊ

§ ǻL2i · ¸ ɋ Ʌ ¨¨ 2 ¸ © ǻĳ ɉɊ ¹

ɋ Ʌ ȡ2 .

(2.50)

2.7.2. ɉɪɢɜɟɞɟɧɢɟ ɦɧɨɝɨɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɤ ɞɜɭɯɦɚɫɫɨɜɨɣ

Ɋɚɫɫɦɨɬɪɢɦ ɭɩɪɭɝɭɸ ɫɢɫɬɟɦɭ ɫ ɨɞɧɢɦ ɭɩɪɭɝɢɦ ɷɥɟɦɟɧɬɨɦ – ɫɯɟɦɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜɟɧɬɢɥɹɬɨɪɚ (ɪɢɫ. 2.13). ɉɪɢ ɧɚɥɢɱɢɢ ɭɩɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ ɧɟ ȼ ɜɫɟɝɞɚ ɭɞɚɺɬɫɹ ɩɨɥɭɱɢɬɶ ɨɞɧɨɦɚɫɫɨɜɭɸ ɪɚɫɱɺɬɧɭɸ ɫɯɟɦɭ, ɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ Ⱦ ɨɬ ɱɢɫɥɚ ɭɩɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ ɩɨɥɭɱɚɸɬɋɄ ɫɹ ɦɧɨɝɨɦɚɫɫɨɜɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ – ɞɜɭɯɦɚɫɫɨɜɚɹ, ɬɪɟɯɦɚɫɫɨɜɚɹ ɢ ɬ. ɞ. ȼ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɟ ɜɟɧɬɢɥɹɊɢɫ. 2.13. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɬɨɪɚ ɦɨɠɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ɱɟɬɵɪɟ ɦɚɫɜɟɧɬɢɥɹɬɨɪɚ ɫɵ ɫ ɦɨɦɟɧɬɚɦɢ ɢɧɟɪɰɢɢ: ɪɨɬɨɪɚ ɞɜɢɝɚɬɟɥɹ į·JȾȼ, ɩɨɥɭɦɭɮɬ J1 ɢ J2, ɪɚɛɨɱɟJ1 J2 ɝɨ ɤɨɥɟɫɚ JɉɊ, ɫɨɟɞɢɧɟɧɧɵɟ ɬɪɟɦɹ ɭɩį JȾȼ ɪɭɝɢɦɢ ɷɥɟɦɟɧɬɚɦɢ: ɜɚɥɨɦ ɞɜɢɝɚɬɟɥɹ JɉɊ C1 C2 C3 ɞɨ ɩɨɥɭɦɭɮɬɵ ɠɟɫɬɤɨɫɬɶɸ ɋ1, ɭɩɪɭɝɨɣ ɦɭɮɬɨɣ – ɋ2, ɜɚɥɨɦ ɜɟɧɬɢɥɹɬɨɪɚ ɞɨ Ɋɢɫ. 2.14. ɑɟɬɵɪɟɯɦɚɫɫɨɜɚɹ ɭɩɪɭɝɚɹ ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ – ɋ3. ɉɨɥɭɱɢɥɢ ɱɟɬɵɫɢɫɬɟɦɚ ɪɟɯɦɚɫɫɨɜɭɸ ɫɢɫɬɟɦɭ (ɪɢɫ. 2.14), ɜ ɤɨɬɨɪɨɣ ɜɪɚɳɚɸɳɢɟɫɹ ɦɚɫɫɵ ɫɨɟɞɢɧɟɧɵ ɨɬɪɟɡɤɚɦɢ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɦɢ ɩɨɞɚɬɋ12 įǜJȾȼ JɉɊ ɥɢɜɨɫɬɹɦ ɜɚɥɨɜ. Ɉɛɵɱɧɨ ɦɧɨɝɨɦɚɫɫɨɜɭɸ ɫɢɫɬɟɦɭ ɩɪɢɜɨɞɹɬ ɤ ɧɚɢɛɨɥɟɟ ɩɨɞɚɬɥɢɜɨɦɭ ɡɜɟM12 ɧɭ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ – ɋ2), ɩɪɢ ɷɬɨɦ JɉɊ ɜɪɚɳɚɸɳɢɟɫɹ ɦɚɫɫɵ ɫ ɦɚɥɵɦɢ ɦɨɦɟɧįǜJȾȼ ɬɚɦɢ ɢɧɟɪɰɢɢ ɩɪɢɫɨɟɞɢɧɹɸɬ ɤ ɝɥɚɜɧɵɦ ɋ12 Ȧ1 Ȧ2 ɦɚɫɫɚɦ ɫ ɝɨɪɚɡɞɨ ɛɨɥɶɲɢɦɢ ɦɨɦɟɧɬɚM ɋ ɦɢ ɢɧɟɪɰɢɢ. ȼ ɫɯɟɦɟ ɜɟɧɬɢɥɹɬɨɪɚ ɨɬM ǻMC ɧɟɫɟɦ J1 ɤ į·JȾȼ, ɚ J2 – ɤ JɉɊ ɢ ɩɨɥɭɱɢɦ ɞɜɭɯɦɚɫɫɨɜɭɸ ɭɩɪɭɝɭɸ ɫɢɫɬɟɦɭ (ɪɢɫ. Ɋɢɫ. 2.15. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ 2.15). ȼ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɪɚɫɫɦɚɬɪɢɜɚɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɟɦ ɝɥɚɜɧɵɟ ɦɚɫɫɵ į·JȾȼ ɢ JɉɊ. ɗɤɜɢɜɚɥɟɧɬɧɭɸ ɠɟɫɬɤɨɫɬɶ ɋ12 ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɨɩɪɟɞɟɥɹɸɬ ɱɟɪɟɡ ɫɭɦɦɭ ɩɨɞɚɬɥɢɜɨɫɬɟɣ ɭɩɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ ɪɟɚɥɶɧɨɣ ɫɯɟɦɵ 1 ɋɗɄȼ

1 1 1 . ɋ1 ɋ2 ɋ3

(2.51)

Ƚɥɚɜɧɚɹ ɦɚɫɫɚ į·JȾȼ ɜɪɚɳɚɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ Ȧ1, ɤ ɧɟɣ ɩɪɢɥɨɠɟɧ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ ɢ ɦɨɦɟɧɬ ɫɬɚɬɢɱɟɫɤɢɣ ǻɆɋ. Ƚɥɚɜɧɚɹ ɦɚɫɫɚ JɉɊ ɜɪɚɳɚɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ 33

Ȧ2, ɤ ɧɟɣ ɩɪɢɥɨɠɟɧ ɦɨɦɟɧɬ Ɇɋ. Ɋɚɡɪɟɠɟɦ ɫɢɫɬɟɦɭ ɩɨ ɭɩɪɭɝɨɦɭ ɷɥɟɦɟɧɬɭ, ɜ ɦɟɫɬɟ ɪɚɡɪɟɡɚ ɩɪɢɥɨɠɢɦ ɩɚɪɭ ɦɨɦɟɧɬɨɜ Ɇ12. Ɇɨɦɟɧɬ Ɇ12 ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɨɦɟɧɬ ɭɩɪɭɝɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɝɥɚɜɧɵɦɢ ɦɚɫɫɚɦɢ į·JȾȼ ɢ JɉɊ. 2.7.3.ɍɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɢ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ

Ⱦɜɢɠɟɧɢɟ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ (Ⱦɍɋ) ɨɩɢɫɵɜɚɟɬɫɹ ɫɢɫɬɟɦɨɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (ɪɢɫ.2.15): dȦ1 M12 , Ɇ 'Ɇɋ į JȾȼ dt dȦ 2 (2.52) , M12 MC JɉɊ dt Ɇ12 ɋ12 ǻĳ12 ɋ12 ĳ1 ĳ 2 ɋ12 ³ Ȧ1dt ³ Ȧ2dt . ɉɟɪɟɩɢɲɟɦ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (2.52) ɜ ɨɩɟɪɚɬɨɪɧɨɣ ɮɨɪɦɟ: Ɇ ǻɆɋ į JȾȼ p M12 , M12

MC JɉɊ p,

Ɇ12

Ȧ Ȧ2 ɋ12 1 . p

(2.53)

ɉɨ ɫɢɫɬɟɦɟ ɭɪɚɜɧɟɧɢɣ (2.53) ɫɬɪɨɢɬɫɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ (ɪɢɫ. 2.16). Ɉɬɥɢɱɢɟ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ Ⱦɍɋ ɨɬ ɫɯɟɦɵ ɫɢɫɬɟɦɵ ɫ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɢɦɢ ɫɜɹɡɹɦɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɝɥɚɜɧɵɟ ɦɚɫɫɵ ɪɚɡɞɟɥɟɧɵ, ɦɟɠɞɭ ɧɢɦɢ – ɢɧɬɟɝɪɢɪɭɸɳɟɟ ɡɜɟɧɨ ɋ12/ɪ, ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɠɟɫɬɤɨɫɬɶ. ɉɨɥɭɱɢɦ ɩɟɪɟɞɚɬɨɱɧɭɸ ɮɭɧɤɰɢɸ Ⱦɍɋ, ɞɥɹ ɱɟɝɨ ɩɪɟɨɛɪɚɡɭɟɦ ɫɬɪɭɤɬɭɪɧɭɸ ɫɯɟɦɭ ɪɢɫ. 2.16. ɇɚ ɪɢɫ. 2.17 ɩɪɢɜɟɞɟɧɚ ɩɪɟɨɛɪɚɡɨɜɚɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ, ɜ ɤɨɬɨɪɨɣ ɨɛɪɚɬɧɵɟ ɫɜɹɡɢ ɩɟɪɟɧɟɫɟɧɵ ɧɚ ɜɵɯɨɞ ɫɢɫɬɟɦɵ.

Ɇ

Ɇ12 1

Ɇɋ

Ȧ1

JȾȼ p

ǻɆɋ

C12 p

1 JɊɈ p

Ɇ12

Ȧ2

Ȧ2

Ɋɢɫ. 2.16. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ Ɇ

1 į JȾȼ ɪ

Ȧ1

ɋ12 ɪ

M12

1

Ȧ2

JɉɊ ɪ

M12 JɉɊ ɪ įJȾȼp Ɋɢɫ. 2.17. ɉɪɟɨɛɪɚɡɨɜɚɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɩɪɢ ǻɆɋ = 0, Ɇɋ = 0 34

ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɷɬɨɣ ɫɯɟɦɵ ɢɦɟɟɬ ɜɢɞ C12 W p

p 2 į J Ⱦȼ JɉɊ C12 1 2 JɉɊ į J Ⱦȼ ɪ p į J Ⱦȼ JɉɊ

ǻȦ 2 p 'Mp

JɉɊ

1 į J Ⱦȼ ɪ

1

1 į J Ⱦȼ JɉɊ

(2.54)

.

JɉɊ G J Ⱦȼ C12

ɪ

2

Ʉɚɤ ɜɢɞɧɨ ɢɡ (2.54), ɩɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɫɨɞɟɪɠɢɬ ɞɜɚ ɡɜɟɧɚ: – ɢɧɬɟɝɪɢɪɭɸɳɟɟ ɡɜɟɧɨ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɫɢɥɟɧɢɹ 1/J = 1/(į·JȾȼ + JɉɊ) – ɷɬɨ ɡɜɟɧɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɭɸ ɫɢɫɬɟɦɭ; – ɤɨɧɫɟɪɜɚɬɢɜɧɨɟ ɡɜɟɧɨ (ɤɨɥɟɛɚɬɟɥɶɧɨɟ ɡɜɟɧɨ ɛɟɡ ɞɟɦɩɮɢɪɨɜɚɧɢɹ ɤɨɥɟɛɚɧɢɣ) ɫ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ ɌɄ ɢ ɱɚɫɬɨɬɨɣ ɫɪɟɡɚ ȍɄ = ȍ12: ɌɄ

JɉɊ į JȾȼ C12 .

JɉɊ į JȾȼ ; : JɉɊ į JȾȼ C12 K

JɉɊ į JȾȼ

ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɤɨɧɫɟɪɜɚɬɢɜɧɨɝɨ ɡɜɟɧɚ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ W p

Ɍ

1 2 Ʉ

.

ɪ2 1

ɉɪɢ ɋ12 = f ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɌɄ = 0, ɱɚɫɬɨɬɚ ɫɪɟɡɚ ȍ12 = f, ɩɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɩɟɪɟɞɚɬɨɱɧɭɸ ɮɭɧɤɰɢɸ ɡɜɟɧɚ ɫ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɢɦɢ ɫɜɹɡɹɦɢ. 1 ɉɪɢ p = j·ȍ ɩɨɥɭɱɢɦ W j : . 2 2 TK j : 1 Ⱥɦɩɥɢɬɭɞɭ ɤɨɧɫɟɪɜɚɬɢɜɧɨɝɨ ɡɜɟɧɚ ɞɚɟɬ ɦɨɞɭɥɶ ɷɬɨɝɨ ɤɨɦɩɥɟɤɫɧɨɝɨ ɱɢɫɥɚ

A

T

1 2

K

Ɋɢɫ. 2.18. ɑɚɫɬɨɬɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ Ⱦɍɋ

1 T

j ȍ 1 2

ɤ

1/Ɍ

ȍ

1

K

2

ȍ2

.

ɇɟɬɪɭɞɧɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ ɚɦɩɥɢɬɭɞɚ ɤɨɧɫɟɪɜɚɬɢɜɧɨɝɨ ɡɜɟɧɚ ɛɭɞɟɬ ɪɚɜɧɚ ɛɟɫɤɨɧɟɱɧɨɫɬɢ Ⱥ =f ɩɪɢ ȍ =1/ɌɄ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɱɚɫɬɨɬɟ ɫɪɟɡɚ ɤɨɧɫɟɪɜɚɬɢɜɧɨɝɨ ɡɜɟɧɚ ȍ12 ɧɚɫɬɭɩɚɟɬ ɹɜɥɟɧɢɟ ɪɟɡɨɧɚɧɫɚ (ɷɬɭ ɱɚɫɬɨɬɭ ȍ12 = ȍɊȿɁ ɧɚɡɵɜɚɸɬ ɪɟɡɨɧɚɧɫɧɨɣ), ɅȺɑɏ ɷɬɨɝɨ ɡɜɟɧɚ ɬɟɪɩɢɬ ɪɚɡɪɵɜ. ɅȺɑɏ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 2.18. ȿɫɥɢ ɜɨɡɦɭɳɟɧɢɹ ɩɪɨɯɨɞɹɬ ɫ ɱɚɫɬɨɬɨɣ ȍ12, ɜ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ ɜɨɡɧɢɤɚɸɬ ɪɟɡɨɧɚɧɫɧɵɟ ɤɨɥɟɛɚɧɢɹ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɫ ɚɦɩɥɢɬɭɞɨɣ Ⱥ = f.

35

2.7.4. ɉɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ

Ɋɚɫɫɦɨɬɪɢɦ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɪɢɥɨɠɟɧɢɹ ɫɤɚɱɤɨɦ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ Ɇ (ɪɢɫ. 2.19) ɩɪɢ ǻɆɋ = 0 ɢ Ɇɋ = 0 ɩɨ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɟ Ⱦɍɋ (ɫɦ. ɪɢɫ. 2.16). ɉɨɫɥɟ ɩɪɢɥɨɠɟɧɢɹ ɫɤɚɱɤɚ Ɇ ɞɜɢɝɚɬɟɥɹ, ɟɫɥɢ ɋ12 = f, ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ Ȧ2(t) ɩɨɣɞɟɬ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ ɫ ɭɫɤɨɪɟɧɢɟɦ İɋɊ. ɉɪɢ ɋ12 < f, ɩɨɫɥɟ ɩɪɢɥɨɠɟɧɢɹ ɫɤɚɱɤɚ Ɇ ɞɜɢɝɚɬɟɥɹ ɭɩɪɭɝɢɣ ɦɨɦɟɧɬ Ɇ12 = 0, ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ (M – M12)>0 ɢ ɩɨɫɥɟ ɩɟɪɜɨɝɨ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɡɜɟɧɚ ɧɚ ɭɱɚɫɬɤɟ t0…t1 ɫɤɨɪɨɫɬɶ Ȧ1 ɧɚɱɧɟɬ ɧɚɪɚɫɬɚɬɶ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ. ɉɨɫɥɟ ɜɬɨɪɨɝɨ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɡɜɟɧɚ ɧɚɱɧɟɬ ɧɚɪɚɫɬɚɬɶ Ɇ12. Ⱦɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ (M – M12) ɧɚɱɧɟɬ ɫɧɢɠɚɬɶɫɹ, ɬɟɦɩ ɧɚɪɚɫɬɚɧɢɹ Ȧ1 ɫɧɢɠɚɟɬɫɹ. ɋ ɪɨɫɬɨɦ Ɇ12 ɩɨɫɥɟ ɬɪɟɬɶɟɝɨ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɡɜɟɧɚ ɩɨɹɜɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶ Ȧ2, ɧɚ ɜɯɨɞɟ ɜɬɨɪɨɝɨ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɡɜɟɧɚ ɩɨɹɜɥɹɟɬɫɹ ɪɚɡɧɨɫɬɶ (Ȧ1 – Ȧ2) > 0. Ɇ12 ɩɪɨɞɨɥɠɚɟɬ ɧɚɪɚɫɬɚɬɶ ɜ ɫɜɹɡɢ ɫ ɩɪɨɞɨɥɠɚɸɳɢɦɫɹ ɪɨɫɬɨɦ Ȧ1. ȼ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t1 ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ (M – M12) = 0, Ȧ1 ɩɪɟɤɪɚɳɚɟɬ ɧɚɪɚɫɬɚɧɢɟ, ɞɨɫɬɢɝɚɹ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɧɚ ɷɬɨɦ ɭɱɚɫɬɤɟ. Ɋɚɫɫɦɚɬɪɢɜɚɹ ɩɨɞɨɛɧɵɦ ɫɩɨɫɨɛɨɦ ɩɨɫɥɟɞɭɸɳɢɟ ɭɱɚɫɬɤɢ, ɦɨɠɧɨ ɩɪɨɚɧɚɥɢM Ɇ12(t)

Ɇ

t0

t1

t2

t3

t4

t5

t

Ȧ İɋɊ

Ȧ1(t) Ȧ2(t) t0

t1

t2

t3

t4

t5

t

Ɋɢɫ.2.19. ȼɪɟɦɟɧɧɵɟ ɞɢɚɝɪɚɦɦɵ ɦɨɦɟɧɬɚ Ɇ12, ɫɤɨɪɨɫɬɟɣ Ȧ1 ɢ Ȧ2 ɞɥɹ Ⱦɍɋ ɩɪɢ ɫɤɚɱɤɟ ɦɨɦɟɧɬɚ Ɇ

ɡɢɪɨɜɚɬɶ ɞɚɥɶɧɟɣɲɟɟ ɩɨɜɟɞɟɧɢɟ ɫɤɨɪɨɫɬɟɣ Ȧ1, Ȧ2 ɢ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ Ɇ12 ɩɪɢ ɫɤɚɱɤɟ ɦɨɦɟɧɬɚ Ɇ. ȼ ɩɨɦɨɳɶ ɢɡɭɱɟɧɢɸ ɞɚɥɶɧɟɣɲɟɝɨ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɩɪɟɞɥɚɝɚɟɬɫɹ ɬɚɛɥ. 2.2. ɉɪɢɜɟɞɟɧɧɵɣ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɜ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ ɩɨɞɬɜɟɪɠɞɚɟɬ, ɱɬɨ ɨɧ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɧɟɡɚɬɭɯɚɸɳɢɦɢ ɤɨɥɟɛɚɧɢɹɦɢ ɫ ɱɚɫɬɨɬɨɣ ȍɊȿɁ. ɉɪɢ ɧɭɥɟɜɵɯ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɭɩɪɭɝɢɣ ɦɨɦɟɧɬ ɢɡɦɟɧɹɟɬɫɹ ɩɨ ɡɚɤɨɧɭ Ɇ12 t JɉɊ İ 1 cos :t MC ,

36

(2.55)

ɬɨɝɞɚ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɨɩɪɟɞɟɥɢɬɫɹ ɩɨ ɮɨɪɦɭɥɟ JɉɊ İ ɋɊ Ɇɋ ,

M12CP

(2.56)

ɝɞɟ İ ɋɊ

M MC

dȦ dt

į JȾȼ JɉɊ

.

(2.57)

Ɍɚɛɥɢɰɚ 2.2 ɉɨɜɟɞɟɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ Ɇ12 ɢ ɫɤɨɪɨɫɬɟɣ Ȧ1 ɢ Ȧ2 ɩɪɢ ɫɤɚɱɤɟ ɦɨɦɟɧɬɚ Ɇ ɩɨ ɭɱɚɫɬɤɚɦ Ɋɚɡɧɨɫɬɶ M – M12

Ȧ1

Ɋɚɡɧɨɫɬɶ Ȧ1 – Ȧ2

M12

Ȧ2

t0

0

0

0

0

0

t0 – t1

ɛɨɥɶɲɟ ɧɭɥɹ

Ĺ

ɛɨɥɶɲɟ ɧɭɥɹ

Ĺ

Ĺ

t1

0

max1

ɛɨɥɶɲɟ ɧɭɥɹ

ĹĹ

Ĺ

t1 – t2

ɦɟɧɶɲɟ ɧɭɥɹ

Ļ

ɛɨɥɶɲɟ ɧɭɥɹ

Ĺ

Ĺ

t2

ɦɟɧɶɲɟ ɧɭɥɹ

ĻĻ

0

max1

ĹĹ

t2 – t3

ɦɟɧɶɲɟ ɧɭɥɹ

Ļ

ɦɟɧɶɲɟ ɧɭɥɹ

Ļ

Ĺ

t3

0

min1

ɦɟɧɶɲɟ ɧɭɥɹ

ĻĻ

Ĺ

t3 – t4

ɛɨɥɶɲɟ ɧɭɥɹ

Ĺ

ɦɟɧɶɲɟ ɧɭɥɹ

Ļ

Ĺ

t4

ɛɨɥɶɲɟ ɧɭɥɹ

ĹĹ

0

min1

max1

t4 – t5

ɛɨɥɶɲɟ ɧɭɥɹ

Ĺ

ɛɨɥɶɲɟ ɧɭɥɹ

Ĺ

Ĺ

t5

0

max2

ɛɨɥɶɲɟ ɧɭɥɹ

ĹĹ

Ĺ

Ɇɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ Ɇ12ɆȺɄɋ ɜ ɩɟɪɟɞɚɱɟ ɩɪɟɜɵɲɚɟɬ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ ɢ ɦɨɠɟɬ ɜɵɡɜɚɬɶ ɨɫɬɚɬɨɱɧɵɟ ɞɟɮɨɪɦɚɰɢɢ, ɟɫɥɢ ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɧɟ ɩɪɟɞɭɫɦɨɬɪɟɬɶ ɦɟɪɵ ɩɨ ɟɝɨ ɫɧɢɠɟɧɢɸ. Ɉɰɟɧɢɜɚɸɬ ɜɥɢɹɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɫ ɩɨɦɨɳɶɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɧɚɦɢɱɧɨɫɬɢ ɄȾɂɇ, ɩɨɞ ɤɨɬɨɪɵɦ ɩɨɧɢɦɚɸɬ ɨɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɤ ɟɝɨ ɫɪɟɞɧɟɦɭ ɡɧɚɱɟɧɢɸ Ʉ Ⱦɂɇ

Ɇ12ɆȺɄɋ Ɇ12ɋɊ

2 JɉɊ İ ɋɊ Ɇɋ . JɉɊ İ ɋɊ Ɇɋ

(2.58)

ȼ ɪɟɚɥɶɧɵɯ ɷɥɟɦɟɧɬɚɯ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɫɯɟɦ ɜɫɟɝɞɚ ɫɭɳɟɫɬɜɭɸɬ ɫɢɥɵ ɜɧɭɬɪɟɧɧɟɝɨ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ, ɨɤɚɡɵɜɚɸɳɢɟ ɫɭɳɟɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɜ ɦɟɯɚɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦɚɯ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ ɫɤɨɪɨɫɬɢ ɞɟɮɨɪɦɚɰɢɢ ɜɚɥɨɜ, ɤɚɧɚɬɨɜ, ɦɭɮɬ ɢ ɞɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ. Ɇɨɦɟɧɬ ɜɧɭɬɪɟɧɧɟɝɨ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɨɰɟɧɢɜɚɸɬ ɩɨ ɮɨɪɦɭɥɟ 37

ɆȼɌ

E12 Ȧ1 Ȧ2 ,

ɝɞɟ Ȧ1, Ȧ2 – ɫɤɨɪɨɫɬɢ ɧɚ ɜɯɨɞɟ ɢ ɜɵɯɨɞɟ ɞɟɮɨɪɦɢɪɭɟɦɨɝɨ ɷɥɟɦɟɧɬɚ; ȕ12 – ɤɨɷɮɮɢɰɢɟɧɬ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ. ɉɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɭɩɪɭɝɢɯ ɤɨɥɟɛɚɧɢɣ ɜ ɞɟɮɨɪɦɢɪɭɟɦɨɦ ɷɥɟɦɟɧɬɟ ɩɪɨɢɫɯɨɞɢɬ ɩɨɝɥɨɳɟɧɢɟ ɷɧɟɪɝɢɢ ɤɨɥɟɛɚɧɢɣ, ɬɚɤ ɤɚɤ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɫɤɨɪɨɫɬɢ ɢɡɦɟɧɹɟɬɫɹ ɢ ɡɧɚɤ ɦɨɦɟɧɬɚ, ɦɨɳɧɨɫɬɶ ɩɨɬɟɪɶ ɜ ɷɥɟɦɟɧɬɟ ɨɫɬɚɟɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨɣ. Ⱦɥɹ ɭɱɟɬɚ ɦɨɦɟɧɬɚ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɜ ɪɚɫɱɟɬɧɭɸ ɢ ɫɬɪɭɤɬɭɪɧɭɸ ɫɯɟɦɵ Ⱦɍɋ ɜɧɨɫɹɬ ȕ12 (ɪɢɫ. 2.20). ȕ12

ȕ12 į·Jɞɜ

Ȧ1

JɉɊ

C12

Ȧ2

M12

ɋ12 ɪ

Ɋɢɫ. 2.20. Ⱦɍɋ ɫ ɭɱɟɬɨɦ ɷɥɟɦɟɧɬɚ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɍɱɟɬ ɜɧɭɬɪɟɧɧɟɝɨ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɩɨɡɜɨɥɹɟɬ ɩɪɢ ɧɚɢɛɨɥɶɲɢɯ ȕ12 ɫɧɢɡɢɬɶ ɦɚɤɫɢɦɭɦ ɞɢɧɚɦɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɢ ɡɚ ɫɱɟɬ ɟɫɬɟɫɬɜɟɧɧɨɝɨ ɡɚɬɭɯɚɧɢɹ ɩɪɢɦɟɪɧɨ ɧɚ 15%, ɱɬɨ ɫɨɢɡɦɟɪɢɦɨ ɫ ɬɨɱɧɨɫɬɶɸ ɨɩɪɟɞɟɥɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɫɢɫɬɟɦɵ. ɉɨɷɬɨɦɭ ɩɪɢ ɚɧɚɥɢɡɟ ɦɚɤɫɢɦɚɥɶɧɵɯ ɞɢɧɚɦɢɱɟɫɤɢɯ ɧɚɝɪɭɡɨɤ ɜ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɟɫɬɟɫɬɜɟɧɧɵɦ ɞɟɦɩɮɢɪɨɜɚɧɢɟɦ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɝɚɬɶ. 2.7.5. ɉɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ ɫ ɡɚɡɨɪɨɦ

ȼ ɞɟɣɫɬɜɭɸɳɟɦ ɦɟɯɚɧɢɱɟɫɤɨɦ ɨɛɨɪɭɞɨɜɚɧɢɢ ɜɦɟɫɬɟ ɫ ɭɩɪɭɝɨɫɬɶɸ ɞɨɜɨɥɶɧɨ ɱɚɫɬɨ ɜɫɬɪɟɱɚɸɬɫɹ ɡɚɡɨɪɵ ɜ ɦɟɯɚɧɢɱɟɫɤɢɯ ɩɟɪɟɞɚɱɚɯ ɢ ɫɨɱɥɟɧɟɧɢɹɯ. ȼ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ (ɪɢɫ. 2.21) ɡɚɡɨɪ ɪɚɡɪɵɜɚɟɬ ɦɟɯɚɧɢɱɟɫɤɭɸ ɰɟɩɶ. Ɂɚɜɢɫɢɦɨɫɬɶ Ɇ12 = f(ĳ1–ĳ2) ɫɬɚɧɨɜɢɬɫɹ ɧɟɥɢɧɟɣɧɨɣ. Ʉɨɝɞɚ ɜ ɩɪɨɰɟɫɫɟ ɜɨɡɞɟɣɫɬɜɢɹ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɞɟɮɨɪɦɚɰɢɹ ɷɥɟɦɟɧɬɚ ǻĳ ɫɬɚɧɨɜɢɬɫɹ ɦɟɧɶɲɟ ɡɚɡɨɪɚ ǻĳɡ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɩɟɪɟɞɚɱɟ, ɭɩɪɭɝɢɣ ɦɨɦɟɧɬ Ɇ12 ɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɵɦ ɧɭɥɸ, ɤɢɧɟɦɚɬɢɱɟɫɤɚɹ ɰɟɩɶ ɪɚɡɪɵɜɚɟɬɫɹ. ɋɢɫɬɟɦɚ ɩɪɨɞɨɥɠɚɟɬ ɞɜɢɠɟɧɢɟ, ɧɚɪɚɫɬɚɟɬ ɪɚɡɧɨɫɬɶ ɫɤɨɪɨɫɬɟɣ ɢ ɩɨɫɥɟ ɩɪɨɯɨɠɞɟɧɢɹ ɡɚɡɨɪɚ ɦɟɯɚɧɢɱɟɫɤɚɹ ɰɟɩɶ ɡɚɦɵɤɚɟɬɫɹ. ɇɚɪɚɫɬɚɸɳɢɣ ɭɩɪɭɝɢɣ ɦɨɦɟɧɬ ɫɨɡɞɚɟɬ ɭɞɚɪ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɰɟɩɢ. Ɇ12

ǻĳɡ į·JȾȼ

JɉɊ

C12

Ȧ2

Ȧ1 ǻMC

Ɇ

MC

ǻĳɡ/2

ǻĳɡ/2

ǻĳ

Ɋɢɫ. 2.21. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ Ⱦɍɋ ɫ ɡɚɡɨɪɨɦ ɢ ɡɚɜɢɫɢɦɨɫɬɶ Ɇ12 =f(ǻĳ) 38

ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ ɫ ɡɚɡɨɪɨɦ ɢ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɪɢɥɨɠɟɧɢɹ ɦɨɦɟɧɬɚ Ɇ ɞɜɢɝɚɬɟɥɹ ɫɤɚɱɤɨɦ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 2.22, 2.23. ɉɪɟɞɥɚɝɚɟɬɫɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɬɶ ɜɪɟɦɟɧɧɵɟ ɞɢɚɝɪɚɦɦɵ ɤɨɨɪɞɢɧɚɬ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɫ ɡɚɡɨɪɨɦ.

Ɇ

Ȧ1

1 G JȾȼ p

ǻɆɋ

1 p

Ɇ12

ǻĳ

Ɇɋ

C12

Ȧ2

1 JɉɊ p

Ȧ2 Ɋɢɫ. 2.22. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ ɫ ɡɚɡɨɪɨɦ M

Ɇ12(t) Ɇ(t)

t0

t1

t2

t3

t4

t

t5

Ȧ Ȧ1(t)

Ȧ2(t) t0

t1

t2

t3

t4

t5

t

Ɋɢɫ. 2.23. ȼɪɟɦɟɧɧɵɟ ɞɢɚɝɪɚɦɦɵ ɦɨɦɟɧɬɚ Ɇ12, ɫɤɨɪɨɫɬɟɣ Ȧ1 ɢ Ȧ2 ɞɥɹ Ⱦɍɋ ɫ ɡɚɡɨɪɨɦ Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɤɨɥɟɛɚɬɟɥɶɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɫɪɟɞɧɟɦ ɧɟ ɜɥɢɹɸɬ ɧɚ ɞɥɢɬɟɥɶɧɨɫɬɶ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ, ɧɨ ɨɬɪɢɰɚɬɟɥɶɧɨ ɫɤɚɡɵɜɚɸɬɫɹ ɧɚ ɭɫɥɨɜɢɹ ɜɵɩɨɥɧɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɨɩɟɪɚɰɢɣ, ɜ ɱɚɫɬɧɨɫɬɢ, ɜ ɬɨɱɧɨɫɬɢ ɪɚɛɨɬɵ ɭɫɬɚɧɨɜɤɢ. ɉɪɚɤɬɢɱɟɫɤɢ ɜɫɟɝɞɚ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɭɩɪɭɝɢɯ ɤɨɥɟɛɚɧɢɣ ɭɜɟɥɢɱɢɜɚɸɬ ɞɢɧɚɦɢɱɟɫɤɢɟ ɧɚɝɪɭɡɤɢ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ ɢ ɟɝɨ ɢɡɧɨɫ. ɇɚɲɚ ɡɚɞɚɱɚ: ɬɚɤ ɩɪɨɟɤɬɢɪɨɜɚɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞ, ɱɬɨɛɵ ɫɧɢɠɚɬɶ ɜɵɛɪɨɫɵ ɭɩɪɭɝɢɯ ɦɨɦɟɧɬɨɜ (ɭɦɟɧɶɲɚɬɶ ɞɢɧɚɦɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ), ɧɭɠɧɨ ɨɩɪɟɞɟɥɟɧɧɵɦ ɨɛɪɚɡɨɦ ɜɵɛɢɪɚɬɶ ɫɬɪɭɤɬɭɪɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɟɝɨ ɩɚɪɚɦɟɬɪɵ (ɨɝɪɚɧɢɱɢɜɚɬɶ ɭɫɤɨɪɟɧɢɟ, ɩɪɢɦɟɧɹɬɶ ɫɢɫɬɟɦɭ ɜɵɛɨɪɤɢ ɡɚɡɨɪɨɜ ɢ ɬ.ɩ.). 2.8. Ɉɛɨɛɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ȼ ɰɟɥɨɦ ɦɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ – ɫɥɨɠɧɟɣɲɢɣ ɨɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ (ɪɢɫ. 2.24) ɫ ɫɭɳɟɫɬɜɟɧɧɵɦɢ ɧɟɥɢɧɟɣɧɨɫɬɹɦɢ (ɡɚɡɨɪ ǻĳɁ, ɫɭɯɨɟ 39

ɆɋɌ ɢ ɜɹɡɤɨɟ ɬɪɟɧɢɟ ɆȼɌ), ɨɝɪɚɧɢɱɟɧɧɵɣ ɜɟɥɢɱɢɧɚɦɢ ɠɟɫɬɤɨɫɬɢ ɜɚɥɨɜ ɢ ɬ.ɩ. ɇɟɨɛɯɨɞɢɦɨɫɬɶ ɭɱɟɬɚ ɬɟɯ ɢɥɢ ɢɧɵɯ ɩɚɪɚɦɟɬɪɨɜ (ɡɚɡɨɪɵ, ɭɩɪɭɝɨɫɬɢ ɢ ɬ.ɩ.) ɪɟɲɚɸɬɫɹ ɜ ɤɚɠɞɨɦ ɤɨɧɤɪɟɬɧɨɦ ɦɟɯɚɧɢɡɦɟ ɢɧɞɢɜɢɞɭɚɥɶɧɨ. Ɉɛɵɱɧɨ ɫɧɚɱɚɥɚ ɪɟɲɚɸɬɫɹ ɡɚɞɚɱɢ ɫ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɢɦɢ ɫɜɹɡɹɦɢ, ɢ ɥɢɲɶ ɡɚɬɟɦ ɤɨɪɪɟɤɬɢɪɭɸɬɫɹ ɫ ɭɱɟɬɨɦ ɭɩɪɭɝɨɫɬɢ ɢ ɡɚɡɨɪɨɜ. ɆɋɌ

ɆɋɌ

ǻɆɋ

ǻĳɁ 1 G JȾȼ ɪ

Ɇ

Ȧ1

1 ɪ

ȕ12p+ɋ1

Ɇ1

2

1

Ȧ2

JɉɊ p

Ȧ2

ɆȼɌ 1+b·sign(M12) Ɋɢɫ. 2.24. Ɉɛɨɛɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɉɪɢɜɟɞɟɧɢɟ ɜ ɞɜɢɠɟɧɢɟ ɢɫɩɨɥɧɢɬɟɥɶɧɵɯ ɦɟɯɚɧɢɡɦɨɜ ɢ ɭɩɪɚɜɥɟɧɢɟ ɢɯ ɞɜɢɠɟɧɢɟɦ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɨɩɟɪɚɰɢɣ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɨɣ ɡɚɞɚɱɟɣ Ⱥɗɉ. ɉɨɷɬɨɦɭ ɫɩɟɰɢɚɥɢɫɬ ɩɨ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɦɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ ɞɨɥɠɟɧ ɡɧɚɬɶ ɨɛɳɢɟ ɨɫɨɛɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦ, ɜɚɠɧɟɣɲɢɟ ɢɯ ɷɥɟɦɟɧɬɵ, ɫɜɹɡɢ ɢ ɩɚɪɚɦɟɬɪɵ, ɚ ɬɚɤɠɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɢɯ ɨɩɢɫɚɧɢɹ ɢ ɚɧɚɥɢɡɚ. Ɉɧ ɞɨɥɠɟɧ ɭɦɟɬɶ ɧɚ ɨɫɧɨɜɟ ɢɡɜɟɫɬɧɨɣ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɦɟɯɚɧɢɡɦɚ, ɟɝɨ ɬɟɯɧɢɱɟɫɤɢɯ ɞɚɧɧɵɯ ɢ ɫɜɟɞɟɧɢɣ ɨ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ ɫɨɫɬɚɜɥɹɬɶ ɪɚɫɱɟɬɧɵɟ ɫɯɟɦɵ ɢ ɪɚɫɫɱɢɬɵɜɚɬɶ ɩɚɪɚɦɟɬɪɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɨɩɢɫɵɜɚɬɶ ɞɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦɢ ɭɪɚɜɧɟɧɢɹɦɢ, ɪɚɫɫɱɢɬɵɜɚɬɶ ɱɚɫɬɨɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ. Ⱦɨɥɠɟɧ ɩɨ ɢɡɜɟɫɬɧɨɦɭ ɯɚɪɚɤɬɟɪɭ ɢɡɦɟɧɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ ɨɰɟɧɢɜɚɬɶ ɯɚɪɚɤɬɟɪ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. 2.9. ɍɩɪɚɠɧɟɧɢɹ ɞɥɹ ɫɚɦɨɩɪɨɜɟɪɤɢ

2.9.1. Ɉɩɪɟɞɟɥɢɬɟ ɩɪɢɜɟɞɟɧɧɵɟ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ ɢ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ JɉɊ ɝɪɭɡɚ, ɟɫɥɢ ɝɪɭɡ ɦɚɫɫɨɣ m=10 ɬ ɩɨɞɧɢɦɚɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v=1 ɦ/ɫ, ɚ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɩɨɞɴɟɦɟ Ȧ =100 ɪɚɞ/ɫ. 2.9.2. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɩɪɢɜɟɞɟɧɧɵɟ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ ɢ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ JɉɊ ɝɪɭɡɚ, ɟɫɥɢ: – ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɫɧɢɡɢɬɶ ɜɞɜɨɟ? – ɫɤɨɪɨɫɬɶ ɩɨɞɴɟɦɚ ɫɧɢɡɢɬɶ ɜɞɜɨɟ ɩɪɢ ɬɨɣ ɠɟ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ Ȧ = 100 ɪɚɞ/ɫ? 40

2.9.3. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɹɬɫɹ ɩɪɢɜɟɞɟɧɧɵɟ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɫɬɚɬɢɱɟɫɤɢɟ ɦɨɦɟɧɬɵ Ɇɋ ɩɪɢ ɩɨɞɴɟɦɟ ɢ ɫɩɭɫɤɟ ɝɪɭɡɚ, ɟɫɥɢ: – ɄɉȾ ɩɟɪɟɞɚɱɢ Ș = 0,8? – ɄɉȾ ɩɟɪɟɞɚɱɢ Ș = 0,9? 2.9.4. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ, ɟɫɥɢ ɩɪɢɦɟɧɢɬɶ ɪɟɞɭɤɬɨɪ ɫ ɄɉȾ, ɩɨɜɵɲɟɧɧɵɦ ɧɚ 10 %? 2.9.5. Ⱦɥɹ ɞɜɢɝɚɬɟɥɹ Ȧ0ɇ =100 ɪɚɞ/ɫ, Mɇ =100 ɇɦ, J=1 ɤɝɦ2 ɨɩɪɟɞɟɥɢɬɶ: – ɦɟɯɚɧɢɱɟɫɤɭɸ ɩɨɫɬɨɹɧɧɭɸ ɜɪɟɦɟɧɢ ɞɜɢɝɚɬɟɥɹ ɌȾ; – ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ tɉɉ ɨɬ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ȦɇȺɑ 0 ɞɨ ȦɄɈɇ 1, ɟɫɥɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ 2 , ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ 1 ; – ɭɫɤɨɪɟɧɢɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ İ; – ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ Į; ɉɨɫɬɪɨɢɬɶ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ Ȧ(t) ɢ ɨɛɟɫɩɟɱɢɬɶ ɩɨɫɥɟ ɟɝɨ ɨɤɨɧɱɚɧɢɹ ȦɄɈɇ=const. 2.9.6. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɜɪɟɦɹ ɩɭɫɤɚ ɞɜɢɝɚɬɟɥɹ ɩɪɢ Ɇɋ 0,5 , ɟɫɥɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɭɜɟɥɢɱɢɬɶ ɨɬ Ɇ 1 ɞɨ Ɇ 2 ? 2.9.7. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ, ɟɫɥɢ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ JɊɈ ɭɜɟɥɢɱɢɥɫɹ ɜɞɜɨɟ? 2.9.8. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɜɪɟɦɹ ɬɨɪɦɨɠɟɧɢɹ ɩɪɢ Ɇɋ 0,5 , ɟɫɥɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɢɡɦɟɧɢɬɶ ɨɬ Ɇ – 2 ɞɨ Ɇ – 1? 2.9.9. ȼ ɤɚɤɨɦ ɪɟɠɢɦɟ (ɪɚɡɝɨɧɚ, ɬɨɪɦɨɠɟɧɢɹ) ɪɚɛɨɬɚɟɬ ɞɜɢɝɚɬɟɥɶ, ɟɫɥɢ ɩɪɢ ȦɇȺɑ 0 , Ɇ – 1, Ɇɋ 0,5 ? Ɂɚ ɤɚɤɨɟ ɜɪɟɦɹ ɫɤɨɪɨɫɬɶ ɞɨɫɬɢɝɧɟɬ ɡɧɚɱɟɧɢɹ Ȧ 1?

Ʉɚɤɢɦ ɞɨɥɠɟɧ ɛɵɬɶ Ɇ , ɱɬɨɛɵ ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɭɦɟɧɶɲɢɥɨɫɶ ɜ 1,5 ɪɚɡɚ? 2.9.10. ȼ ɤɚɤɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɛɭɞɟɬ ɢɡɦɟɧɹɬɶɫɹ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ȦɇȺɑ 0 , Ɇ 0,5 , Ɇɋ 1 , ɟɫɥɢ: – ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ – ɚɤɬɢɜɧɵɣ? – ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ – ɪɟɚɤɬɢɜɧɵɣ? 2.9.11. Ⱦɥɹ ɞɜɢɝɚɬɟɥɹ (Ȧ0ɇ = 100 ɪɚɞ/ɫ, Mɇ = 100 ɇɦ, J = 1 ɤɝɦ2) ɩɨɫɬɪɨɢɬɶ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɭɫɤɚ Ȧ(t), ɟɫɥɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɢɡɦɟɧɹɟɬɫɹ ɩɨ ɡɚɤɨɧɭ M(t) = t, ɚ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ 0,5 , ɟɫɥɢ: – ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ – ɚɤɬɢɜɧɵɣ? – ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ – ɪɟɚɤɬɢɜɧɵɣ? Ɉɩɪɟɞɟɥɢɬɟ ɭɝɥɨɜɭɸ ɞɟɮɨɪɦɚɰɢɸ ɭɩɪɭɝɨɝɨ ɜɚɥɚ (ɪɚɞ, ɝɪɚɞ), ɨɛɥɚɞɚɸɳɟɝɨ ɠɟɫɬɤɨɫɬɶɸ ɋɄ=10 Ɇɇ·ɦ/ɪɚɞ, ɟɫɥɢ ɤ ɜɚɥɭ ɩɪɢɥɨɠɟɧ ɦɨɦɟɧɬ Ɇ = 10000 ɇɦ. ȿɫɥɢ ɩɟɪɟɞɚɬɨɱɧɨɟ ɱɢɫɥɨ ɪɟɞɭɤɬɨɪɚ ɞɨ ɭɩɪɭɝɨɝɨ ɷɥɟɦɟɧɬɚ IɊȿȾ = 100: – ɱɟɦɭ ɪɚɜɧɚ ɠɟɫɬɤɨɫɬɶ ɭɩɪɭɝɨɝɨ ɜɚɥɚ, ɩɪɢɜɟɞɟɧɧɚɹ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ? – ɱɟɦɭ ɪɚɜɧɚ ɪɟɡɨɧɚɧɫɧɚɹ ɱɚɫɬɨɬɚ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ, ɟɫɥɢ JɉɊ = 1 ɤɝɦ2, įJȾȼ = 4 ɤɝɦ2? – ɧɚ ɤɚɤɨɣ ɭɝɨɥ ɩɨɜɟɪɧɟɬɫɹ ɜɚɥ ɞɜɢɝɚɬɟɥɹ, ɩɪɟɨɞɨɥɟɜɚɹ ɭɝɥɨɜɭɸ ɞɟɮɨɪɦɚɰɢɸ ɭɩɪɭɝɨɝɨ ɜɚɥɚ? – ɱɟɦɭ ɪɚɜɟɧ ɦɚɤɫɢɦɚɥɶɧɵɣ ɭɩɪɭɝɢɣ ɦɨɦɟɧɬ ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɧɚɦɢɱɧɨɫɬɢ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɩɪɢ Ɇɋ = 0?

41

Ƚɥɚɜɚ ɬɪɟɬɶɹ 1. 2.

ɗɅȿɄɌɊɈɆȿɏȺɇɂɑȿɋɄɂȿ ɋȼɈɃɋɌȼȺ

ɂ ɏȺɊȺɄɌȿɊɂɋɌɂɄɂ ɗɅȿɄɌɊɈȾȼɂȽȺɌȿɅȿɃ

3.1. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɚɪɚɥɥɟɥɶɧɨɝɨ (ɧɟɡɚɜɢɫɢɦɨɝɨ) ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɇȼ) 3.1.1 ɍɪɚɜɧɟɧɢɹ ɢ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɇȼ ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɞɜɢɝɚɬɟɥɶ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ – ɨɫɧɨɜɧɨɣ ɬɢɩ ɞɜɢɝɚɬɟɥɹ, ɢɫɩɨɥɶɡɭɟɦɵɣ ɜ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ ɩɪɢ ɧɚɢɛɨɥɟɟ ɜɵɫɨɤɢɯ ɬɪɟɛɨɜɚɧɢɹɯ ɤ ɫɬɚɬɢɱɟɫɤɢɦ ɢ ɞɢɧɚɦɢɱɟɫɤɢɦ ɩɨɤɚɡɚɬɟɥɹɦ ɢ ɹɜɥɹɸɳɢɣɫɹ ɨɫɧɨɜɨɣ ɡɚɦɤɧɭɬɵɯ ɫɢɫɬɟɦ ɪɟɝɭɥɢɪɭɟɦɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. Ɉɛɦɨɬɤɢ Ⱦɇȼ ɩɨɥɭɱɚɸɬ ɩɢɬɚɧɢɟ ɨɬ ɢɫɬɨɱɧɢɤɨɜ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɇɟɨɛɯɨɞɢɦɵɦ ɭɫɥɨɜɢɟɦ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɧɟɪɝɢɢ ɹɜɥɹɟɬɫɹ ɩɪɨɬɟɤɚɧɢɟ ɯɨɬɹ ɛɵ ɩɨ ɱɚɫɬɢ ɨɛɦɨɬɨɤ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ. ȼ ɦɚɲɢɧɟ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɟɪɟɦɟɧɧɵɣ ɬɨɤ ɩɪɨɬɟɤɚɟɬ ɩɨ ɨɛɦɨɬɤɟ ɹɤɨɪɹ. ɉɪɟɨɛɪɚɡɨɜɚɧɢɟ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ I ɰɟɩɢ ɩɢɬɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɜ ɩɟɪɟɦɟɧɧɵɣ ɬɨɤ ɨɛɦɨɬɤɢ ɹɤɨɪɹ ɜɵɩɨɥɧɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɜɪɚɳɚɸɳɟɝɨɫɹ ɤɨɥɥɟɤɬɨɪɚ ɢ ɧɟɩɨɞɜɢɠɧɨɝɨ ɳɟɬɨɱɧɨɝɨ ɚɩɩɚɪɚɬɚ (ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɢɧɜɟɪɬɨɪɚ). ɑɚɫɬɨɬɚ ɷɬɨɝɨ ɬɨɤɚ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɹɤɨɪɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɞ ɤɚɠɞɵɦ ɩɨɥɸɫɨɦ ɩɪɢ ɜɪɚɳɟɧɢɢ ɹɤɨɪɹ ɩɨɹɜɥɹɸɬɫɹ ɩɪɨɜɨɞɧɢɤɢ ɫ ɨɞɧɢɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɬɨɤɚ. ɉɨ ɞɪɭɝɢɦ ɨɛɦɨɬɤɚɦ ɩɪɨɬɟɤɚɟɬ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ I. Ɉɛɦɨɬɤɚ ɞɨɛɚɜɨɱɧɵɯ ɩɨɥɸɫɨɜ Ⱦɉ ɭɥɭɱɲɚɟɬ ɭɫɥɨɜɢɹ ɤɨɦɦɭɬɚɰɢɢ ɬɨɤɚ ɹɤɨɪɹ, ɤɨɦɩɟɧɫɚɰɢɨɧɧɚɹ ɨɛɦɨɬɤɚ ɄɈ ɩɪɢɡɜɚɧɚ ɫɧɢɡɢɬɶ ɞɟɣɫɬɜɢɟ ɪɟɚɤɰɢɢ ɹɤɨɪɹ ɎɊə (ɪɢɫ. 3.1). Ɉɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɩɨɥɭɱɚɟɬ ɩɢɬɚɧɢɟ ɨɬ ɧɟɡɚɜɢɫɢɦɨɝɨ ɢɫɬɨɱɧɢɤɚ, ɨɬɫɸɞɚ ɢ ɞɜɢɝɚɬɟɥɶ ɧɚɡɵɜɚɸɬ ɞɜɢɝɚɬɟɥɟɦ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ Ⱦɇȼ. ɑɚɫɬɧɵɣ ɫɥɭɱɚɣ Ⱦɇȼ, ɤɨɝɞɚ ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɩɨɞɤɥɸɱɚɟɬɫɹ ɤ ɬɨɣ ɠɟ ɫɟɬɢ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ, ɤ ɤɨɬɨɪɨɣ ɩɨɞɤɥɸɱɟɧɚ ɹɤɨɪɧɚɹ ɰɟɩɶ ɞɜɢɝɚɬɟɥɹ. Ɉɛɦɨɬɤɚ ɜɤɥɸɱɚɟɬɫɹ ɩɚɪɚɥɥɟɥɶɧɨ ɹɤɨɪɧɨɣ ɰɟɩɢ, ɨɬɫɸɞɚ ɢ ɧɚɡɜɚɧɢɟ – ɞɜɢɝɚɬɟɥɶ ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ. Ɇɚɝɧɢɬɧɵɣ ɩɨɬɨɤ Ɏȼ, ɫɨɡɞɚɜɚɟɦɵɣ ɬɨɤɨɦ ɨɛɦɨɬɎȼ ɤɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɚ ɬɚɤɠɟ ɩɨɬɨɤɢ ɨɫɬɚɥɶɧɵɯ ɨɛɦɨɬɨɤ ɫɨɡɞɚɸɬ ɪɟɡɭɥɶɬɢɪɭɸɳɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɤɨɬɨɪɨɟ M ɜɡɚɢɦɨɞɟɣɫɬɜɭɟɬ ɫ ɩɪɨɜɨɞɧɢɤɚɦɢ, ɧɚɯɨɞɹɳɢɦɢɫɹ ɜ ɩɚɡɚɯ ɹɤɨɪɹ. ɉɪɢ ɩɪɨɬɟɤɚɧɢɢ ɬɨɤɚ ɜ ɩɪɨɜɨɞɧɢɤɚɯ I I ɎɊə ɹɤɨɪɹ ɬɚɤɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɩɪɢɜɨɞɢɬ ɤ ɩɨɹɜɥɟɧɢɸ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ Ɇ = kɎI. Ⱦɜɢɝɚɬɟɥɶ ɧɚɱɢɧɚɟɬ ɜɪɚɳɚɬɶɫɹ, ɩɪɟɨɞɨɥɟɜɚɹ ɫɬɚM ɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ. ɉɟɪɟɫɟɱɟɧɢɟ ɩɪɨɜɨɞɧɢɤɚɦɢ ɹɤɨɪɹ ɧɟɩɨɞɜɢɠɧɨɝɨ ɩɨɬɨɤɚ ɩɨɥɸɫɨɜ ɧɚɜɨɞɢɬ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɗȾɋ ɜɪɚɳɟɧɢɹ ȿ = kɎZ. ȼɨɡɧɢɤɚɸɳɚɹ ɗȾɋ ɧɚɩɪɚɜɥɟɧɚ ɜɫɬɪɟɱɧɨ ɩɪɢɥɨɠɟɧɧɨɦɭ ɧɚɩɪɹɊɢɫ. 3.1. Ʉ ɩɪɢɧɰɢɩɭ ɠɟɧɢɸ ɫɟɬɢ. ɞɟɣɫɬɜɢɹ Ⱦɇȼ Ʉɨɧɫɬɪɭɤɬɢɜɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɜɯɨɞɹɳɢɣ ɜ ɜɵɪɚɠɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ Ɇ ɢ ɗȾɋ ȿ, 42

Na 2 ʌ pɉ

.k

N pɉ 2ʌ ɚ

ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɢɫɥɨɦ ɚɤɬɢɜɧɵɯ (ɫ ɭɱɟɬɨɦ ɩɚɪɚɥɥɟɥɶɧɨ ɜɤɥɸɱɟɧɧɵɯ) ɩɪɨɜɨɞɧɢɤɨɜ N/a, ɩɪɢɯɨɞɹɳɢɯɫɹ ɧɚ ɨɞɧɨ ɩɨɥɸɫɧɨɟ ɞɟɥɟɧɢɟ 2ʌ / pɉ: ɋɯɟɦɚ ɩɨɞɤɥɸɱɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɢ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3.2. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɪɚɛɨɬɵ Ⱦɇȼ ɫɢɫɬɟɦɨɣ ɭɪɚɜɧɟɧɢɣ ɩɪɢɧɢɦɚɸɬ ɪɹɞ ɞɨɩɭɳɟɧɢɣ: – ɧɚɩɪɹɠɟɧɢɟ, ɩɪɢɤɥɚɞɵɜɚɟɦɨɟ ɤ ɰɟɩɢ ɹɤɨɪɹ, ɩɨɫɬɨɹɧɧɨ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɨɤɚ ɹɤɨɪɹ (ɦɨɳɧɨɫɬɶ ɫɟɬɢ ɛɟɫɤɨɧɟɱɧɚ); – ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R ɢ ɢɧɞɭɤɬɢɜɧɨɫɬɢ ɨɛɦɨɬɨɤ L ɩɨɫɬɨɹɧɧɵ ɢ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɬɨɤɚ ɹɤɨɪɹ; – ɦɚɲɢɧɚ ɤɨɦɩɟɧɫɢɪɨɜɚɧɚ, ɬɨɤ ɹɤɨɪɹ ɧɟ ɜɥɢɹɟɬ ɧɚ ɩɨɬɨɤ, ɫɨɡɞɚɜɚɟɦɵɣ ɨɛɦɨɬɤɨɣ ɜɨɡɛɭɠɞɟɧɢɹ, ɩɪɨɞɨɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɪɟɚɤɰɢɢ ɹɤɨɪɹ ɎɊə = 0; – Ɇ – ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ; – ɦɨɦɟɧɬ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Ɇɏɏ ɞɜɢɝɚɬɟɥɹ ɨɬɧɟɫɟɧ ɤ Ɇɋ.

Ⱦɉ

rɫ

ɄɈ

R

i

Uə I

Ɇ

I

ɟɫ

Uȼ

Lɋ

Uə

L

E=kɎZ

LM

Ɋɢɫ. 3.2. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɢ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ Ⱦɇȼ ɇɚ ɨɫɧɨɜɚɧɢɢ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ɹɤɨɪɧɨɣ ɰɟɩɢ ɦɚɲɢɧɵ (ɫɦ. ɪɢɫ. 3.2) ɭɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɧɚɩɪɹɠɟɧɢɣ ɩɨ ɡɚɤɨɧɭ Ʉɢɪɯɝɨɮɚ ɢɦɟɟɬ ɜɢɞ:

Uɹ

E IR L

dI . dt

(3.1)

ɍɪɚɜɧɟɧɢɹ ɗȾɋ, ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ ɢ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɨɥɭɱɟɧɵ ɜɵɲɟ. E

kɎ Ȧ ,

(3.2)

Ɇ

kɎ I ,

(3.3)

dȦ . (3.4) dt ɍɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɧɚɩɪɹɠɟɧɢɣ ɞɥɹ ɤɨɧɬɭɪɚ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɢɧɢɦɚɟɬ ɜɢɞ M

Uȼ

iȼ rȼ

dȥ dt

MC J

iȼ rȼ

d( w ȼ Ɏ) dt

iȼ rȼ w ȼ

dɎ , dt

(3.5)

ɝɞɟ ȥ, wȼ – ɩɨɬɨɤɨɫɰɟɩɥɟɧɢɟ ɢ ɱɢɫɥɨ ɜɢɬɤɨɜ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ. ɋɜɹɡɶ ɦɟɠɞɭ ɩɨɬɨɤɨɦ Ɏ ɢ ɬɨɤɨɦ ɜɨɡɛɭɠɞɟɧɢɹ iȼ – ɧɟɥɢɧɟɣɧɚɹ ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Ɏ = f(iȼ). 43

ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ – ɷɬɨ ɨɫɨɛɚɹ ɮɨɪɦɚ ɡɚɩɢɫɢ ɭɪɚɜɧɟɧɢɣ. Ɉɧɚ ɩɨɡɜɨɥɹɟɬ ɧɚɝɥɹɞɧɨ ɚɧɚɥɢɡɢɪɨɜɚɬɶ ɪɚɛɨɬɭ ɫɢɫɬɟɦɵ ɦɟɬɨɞɚɦɢ ɌȺɍ. ɉɪɟɞɫɬɚɜɢɦ ɭɪɚɜɧɟɧɢɹ 3.1– 3.6 ɜ ɨɩɟɪɚɬɨɪɧɨɣ ɮɨɪɦɟ: Uə p Ep Ip R L Ip p; Ep kɎɪ Ȧɪ ; Ɇɪ kɎɪ Iɪ ; Ɇɪ Ɇɋ ɪ J Ȧp p;

(3.6)

UB p iB p rB w ȼ Ɏp p; Ɏ

f iB .

ɉɨɥɭɱɢɦ ɩɟɪɟɞɚɬɨɱɧɵɟ ɮɭɧɤɰɢɢ, ɨɩɭɫɬɢɜ ɜ ɜɵɪɚɠɟɧɢɹɯ (ɪ): – ɹɤɨɪɧɨɣ ɰɟɩɢ Wə ɪ

I Uə E

1 R L p

1 1 R 1 L p R

1R , 1 Ɍə ɪ

ɝɞɟ Tə – ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɰɟɩɢ ɹɤɨɪɹ, Ɍ ə – ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ WM p

Ȧ M MC

(3.7)

0,02...0,1 ɫ ;

1 ; Jp

(3.8)

1/ wȼ . p

(3.9)

– ɰɟɩɢ ɜɨɡɛɭɠɞɟɧɢɹ WB p

Ɏ Uȼ iȼ rȼ

Ʉɪɢɜɭɸ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Ɏ = f(iɜ) ɩɪɟɞɫɬɚɜɢɦ ɜ ɜɢɞɟ ɛɥɨɤɚ ɧɟɥɢɧɟɣɧɨɫɬɢ, ɡɧɚɱɟɧɢɹ Ɇ ɢ ȿ ɩɨɥɭɱɢɦ ɫ ɩɨɦɨɳɶɸ ɛɥɨɤɨɜ ɩɪɨɢɡɜɟɞɟɧɢɣ. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ (ɪɢɫ. 3.3) ɢɦɟɟɬ ɞɜɚ ɤɨɧɬɭɪɚ – ɹɤɨɪɧɨɝɨ ɢ ɩɨɥɸɫɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ. Ʉɨɧɬɭɪ ɹɤɨɪɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɜ ɩɪɹɦɨɦ ɤɚɧɚɥɟ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɩɟɪɢɨɞɢɱɟɫɤɨɟ ɡɜɟɧɨ ɹɤɨɪɧɨɣ ɰɟɩɢ ɢ ɢɧɬɟɝɪɢɪɭɸɳɟɟ ɡɜɟɧɨ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ. ɗȾɋ ɜɵɩɨɥɧɹɟɬ ɮɭɧɤɰɢɸ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ ɩɨ ɫɤɨɪɨɫɬɢ, ɩɨɞɞɟɪɠɢɜɚɟɬ ɫɤɨɪɨɫɬɶ ɩɪɢ ɭɩɪɚɜɥɹɸɳɢɯ (ɢɡɦɟɧɟɧɢɟ R, U, Ɏ) ɢ ɜɨɡɦɭɳɚɸɳɢɯ (ɢɡɦɟɧɟɧɢɟ Ɇɋ) ɜɨɡɞɟɣɫɬɜɢɹɯ ɧɚ ɞɜɢɝɚɬɟɥɶ. Ʉɨɧɬɭɪ ɩɨɥɸɫɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɢɧɬɟɝɪɢɪɭɸɳɟɟ ɡɜɟɧɨ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɫɢɥɟɧɢɹ 1/wȼ, ɨɯɜɚɱɟɧɧɨɟ ɧɟɥɢɧɟɣɧɨɣ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɨɛɪɚɬɧɨɣ ɫɜɹɡɶɸ (ɈɈɋ). ɉɪɢ ɡɚɦɵɤɚɧɢɢ ɢɧɬɟɝɪɢɪɭɸɳɟɝɨ ɡɜɟɧɚ ɈɈɋ ɩɨɥɭɱɢɦ ɚɩɟɪɢɨɞɢɱɟɫɤɨɟ ɡɜɟɧɨ ɰɟɩɢ ɜɨɡɛɭɠɞɟɧɢɹ ɫ ɩɟɪɟɦɟɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɫɢɥɟɧɢɹ ɢ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ. Ɋɚɫɫɦɨɬɪɢɦ ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ ɪɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ: Ɇ = Ɇɋ, Ȧ = ȦɍɋɌ =Ȧɋ. ɉɭɫɬɶ ɜɨɡɪɨɫɥɨ Uə, ɪɚɡɧɨɫɬɶ (Uə – ȿ) ɪɚɫɬɟɬ, ɭɜɟɥɢɱɢɜɚɸɬɫɹ ɬɨɤ I ɢ ɦɨɦɟɧɬ Ɇ, ɜɵɡɵɜɚɹ ɪɨɫɬ ɫɤɨɪɨɫɬɢ Ȧ. ɋ ɪɨɫɬɨɦ ɫɤɨɪɨɫɬɢ ɪɚɫɬɟɬ ȿ, ɫɧɢɠɚɟɬɫɹ ɪɚɡɧɨɫɬɶ ɧɚɩɪɹɠɟɧɢɣ ɧɚ ɜɯɨɞɟ (Uə – ȿ), ɩɚɞɚɟɬ ɬɨɤ, ɫɧɢɠɚɟɬɫɹ ɦɨɦɟɧɬ Ɇ, ɫɬɪɟɦɹɫɶ ɤ Ɇɋ, ɧɨ ɭɠɟ ɩɪɢ ɧɨɜɨɦ ɡɧɚɱɟɧɢɢ ɫɤɨɪɨɫɬɢ Ȧ.

44

Uȼ

Ɏ

1/ w ɜ ɪ

iȼ·Rȼ Rȼ

U

Ʉɨɧɬɭɪ ɩɨɥɸɫɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ

ɤ iȼ

iȼ

ɤɎ

Ɏ

1/ rə 1 Tə p

I

M

Ʉɨɧɬɭɪ ɹɤɨɪɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ

MC

1

Ȧ

JȾȼ ɪ

E

Ɋɢɫ. 3.3. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɇȼ ɉɪɢ ɩɨɥɸɫɧɨɦ ɭɩɪɚɜɥɟɧɢɢ ɭɦɟɧɶɲɚɟɦ ɧɚɩɪɹɠɟɧɢɟ ɜɨɡɛɭɠɞɟɧɢɹ Uȼ ɢɥɢ ɜɜɨɞɢɦ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɶ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ RB ȾɈȻ . Ɍɨɤ ɜɨɡɛɭɠɞɟɧɢɹ ɛɭɞɟɬ ɭɦɟɧɶɲɚɬɶɫɹ ɩɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɦɭ ɡɚɤɨɧɭ ɢ ɧɚ ɜɵɯɨɞɟ ɤɨɧɬɭɪɚ ɩɨ ɧɟɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ Ɏ = f (iȼ) ɧɚɱɧɟɬ ɭɦɟɧɶɲɚɬɶɫɹ ɩɨɬɨɤ ɦɚɲɢɧɵ. ɍɦɟɧɶɲɟɧɢɟ ɩɨɬɨɤɚ 'Ɏ ɜɨɡɞɟɣɫɬɜɭɟɬ ɧɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɩɨ ɞɜɭɦ ɧɚɩɪɚɜɥɟɧɢɹɦ: – ɧɟɡɧɚɱɢɬɟɥɶɧɨɟ ɭɦɟɧɶɲɟɧɢɟ 'Ɇ1 ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɢɡɦɟɧɟɧɢɸ ɩɨɬɨɤɚ 'Ɏ; – ɫɭɳɟɫɬɜɟɧɧɨɟ ɭɜɟɥɢɱɟɧɢɟ 'Ɇ2 ɡɚ ɫɱɟɬ ɭɦɟɧɶɲɟɧɢɹ 'ȿ ɢ ɜɵɡɜɚɧɧɨɝɨ ɟɸ ɧɚɪɚɫɬɚɧɢɹ ɬɨɤɚ ɹɤɨɪɹ, ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɩɨ ɷɬɨɦɭ ɧɚɩɪɚɜɥɟɧɢɸ ɧɚ ɩɨɪɹɞɨɤ ɜɵɲɟ. Ɇɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɪɚɫɬɟɬ, ɫɤɨɪɨɫɬɶ ɩɪɢ ɫɧɢɠɟɧɢɢ ɩɨɬɨɤɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɧɟ ɫɪɚɜɧɹɟɬɫɹ ɫɨ ɫɬɚɬɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ. ɇɨ ɷɬɨ ɩɪɨɢɡɨɣɞɟɬ ɩɪɢ ɧɨɜɨɦ ɡɧɚɱɟɧɢɢ ɫɤɨɪɨɫɬɢ. ɉɪɨɚɧɚɥɢɡɢɪɭɣɬɟ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɩɨ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɟ (ɫɦ. ɪɢɫ. 3.3), ɤɚɤ ɛɭɞɟɬ ɜɟɫɬɢ ɫɟɛɹ ɞɜɢɝɚɬɟɥɶ, ɟɫɥɢ ɜ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɪɟɠɢɦɟ: – ɭɜɟɥɢɱɢɬɶ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɧɨɣ ɰɟɩɢ R? – ɭɜɟɥɢɱɢɬɶ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ? – ɭɦɟɧɶɲɢɬɶ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ J? Ȼɨɥɟɟ ɩɪɢɜɵɱɧɨɟ ɢ ɩɨɧɹɬɧɨɟ (ɢɡ ɌȺɍ) ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ ɜ ɨ.ɟ. Ɂɚ ɛɚɡɨɜɵɟ ɜɟɥɢɱɢɧɵ ɩɪɢɧɢɦɚɟɦ ɡɧɚɱɟɧɢɹ, ɩɪɢɜɟɞɟɧɧɵɟ ɜ ɬɚɛɥ. 3.1. Ɍɚɛɥɢɰɚ 3.1 Ȼɚɡɨɜɵɟ ɜɟɥɢɱɢɧɵ Ⱦɇȼ UȻ

IȻ

ɎȻ

Uɇ

Iɇ

Ɏɇ

ȦȻ Ȧ0ɇ= =Uɇ/kɎɇ

ȿȻ

ɆȻ

Uɇ

MɇɗɆ = = kɎɇ Iɇ

45

RȻ Rɇ = = Uɇ/Iɇ

iȼȻ

rȼȻ

Iȼɇ

rȼ

ȼɜɟɞɟɦ ɛɚɡɨɜɵɟ ɜɟɥɢɱɢɧɵ ɜ ɭɪɚɜɧɟɧɢɹ (3.7…3.9) ɢ ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɹ ɩɟɪɟɞɚɬɨɱɧɵɯ ɮɭɧɤɰɢɣ ɜ ɨ.ɟ., ɨɩɭɫɬɢɜ (ɪ):

Wə ɪ

I Uə E

Ȧ Ɇ Ɇɋ

kə ; WɆ (ɪ) 1 Ɍə ɪ

1 ; WB p ɌȾ p

Ɏ Uȼ iȼ rȼ

1 ɌȼȻ p

,

ɝɞɟ kə – ɤɪɚɬɧɨɫɬɶ ɬɨɤɚ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɰɟɩɢ ɹɤɨɪɹ; w ȼ Ɏɇ – MC iȼɇ rȼ I M Ȧ 1 kɹ Uə ɛɚɡɨɜɚɹ ɷɥɟɤɬɪɨɦɚɝTȾ p 1 Ɍɹ p ɧɢɬɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɨɛɦɨɬɤɢ ɜɨɡE ɛɭɠɞɟɧɢɹ ɜ ɧɨɦɢɧɚɥɶɧɨɣ ɬɨɱɤɟ. 1 Uȼ ȼ ɫɬɪɭɤɬɭɪɧɨɣ Ɏ ɫɯɟɦɟ ɜ ɨ.ɟ. (ɪɢɫ.3.3 TȼȻ p ɚ) ɜɫɟ ɤɨɷɮɮɢɰɢɟɧɬɵ Ɋɢɫ.3.3 ɚ. ɋɬɪɭɤɬɭɪɧɚɹ iȼ·Rȼ ɩɪɢ ɩɪɨɢɡɜɨɞɧɵɯ ɫɯɟɦɚ Ⱦɇȼ ɫ ɤɨɧɬɭɪɨɦ ɩɪɢɨɛɪɟɬɚɸɬ ɪɚɡɦɟɪiȼ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɨ.ɟ. Rȼ ɧɨɫɬɶ ɜɪɟɦɟɧɢ ɢ Ɏ ɢɦɟɸɬ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɩɨɫɬɨɹɧɧɵɯ ɜɪɟɦɟɧɢ. ȿɫɥɢ ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɟɧ ɢ ɧɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜ ɟɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɢ, ɩɨɬɨɤ ɩɪɢɧɢɦɚɸɬ ɪɚɜɧɵɦ ɧɨɦɢɧɚɥɶɧɨɦɭ: Ɏ = Ɏɇ. Ɍɨɝɞɚ ɦɨɠɧɨ ɩɟɪɟɣɬɢ ɤ ɨɞɧɨɤɨɧɬɭɪɧɨɣ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɟ. Ʌɢɧɟɚɪɢɡɚɰɢɹ ɛɥɨɤɚ ɩɪɨɢɡɜɟɞɟɧɢɹ ɜ ɧɨɦɢɧɚɥɶɧɨɣ ɬɨɱɤɟ ɞɚɟɬ ɩɨɫɬɨɹɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɤɎɇ (ɪɢɫ. 3.4). ɌȼȻ

Uə E

kɹ 1 Tɹ p

I

kɎɧ

M

MC

1 Jp

Ȧ

kɎɧ Uə E

kɹ 1 Tɹ p

I, Ɇ

MC

1 Ɍɞ p

Ȧ

Ɋɢɫ. 3.4. Ɉɞɧɨɤɨɧɬɭɪɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɇȼ ɋ ɩɨɦɨɳɶɸ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɢ ɭɫɬɚɧɨɜɢɜɲɢɟɫɹ ɪɟɠɢɦɵ, ɞɥɹ ɱɟɝɨ ɜ ɞɢɧɚɦɢɱɟɫɤɢɯ ɡɜɟɧɶɹɯ ɫɥɟɞɭɟɬ ɩɨɥɨɠɢɬɶ ɪ = 0. ɉɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɡɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɨɬ ɦɨɦɟɧɬɚ ɜ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɪɟɠɢɦɟ Ȧ = f (Ɇ), ɤɨɬɨɪɭɸ ɧɚɡɵɜɚɸɬ ɫɬɚɬɢɱɟɫɤɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ, ɱɚɳɟ ɩɪɨɫɬɨ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ. ɉɪɟɨɛɪɚɡɨɜɚɧɢɟ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ ɞɥɹ ɫɬɚɬɢɤɢ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 3.5, ɚ ɩɪɢ Ɍə = 0 ɢ (1/Jp) = k0. 46

Uə

1 R

E

I

MC

M

kɎɧ

Ȧ

K0

kɎɧ ɚ

MC R kɎ ɇ I

1 R

Uə

M

kɎɧ

k0

Ȧ

E kɎɧ

W1(P)

ɛ

MC R kɎ ɧ Uə ɜ

Ɋɢɫ. 3.5. Ɉɞɧɨɤɨɧɬɭɪɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɇȼ ɜ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɪɟɠɢɦɟ

Ȧ

1 kɎɧ

ɇɚ ɪɢɫ. 3.5, ɛ ɩɨɤɚɡɚɧ ɩɟɪɟɧɨɫ Ɇɋ ɧɚ ɜɯɨɞ ɫɢɫɬɟɦɵ, ɬɨɝɞɚ ɩɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ W1(p) ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɤ ɜɢɞɭ: W1 p Uɹ

Z R M k0

kɎ ɇ k 0 R k 0 kɎ ɇ 1 kɎ ɇ R

1 1 kɎ ɇ kɎ ɇ k 0 R

1 . kɎ ɇ

ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɞɥɹ ɫɬɚɬɢɤɢ ɢɦɟɟɬ ɜɢɞ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɧɚ ɪɢɫ. 3.5, ɜ. ɉɨɥɭɱɚɟɦ ɜɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɇȼ Ȧ

U kɎɇ

R

kɎɇ 2

M.

3.1.2. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ Ⱦɇȼ – ɡɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɨɬ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ Ȧ(M) – ɜ ɨɛɳɟɦ ɜɢɞɟ ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɚ ɢɡ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɧɚɩɪɹɠɟɧɢɣ ɞɥɹ ɫɬɚɬɢɤɢ U E IR

47

kɎ Ȧ I R .

Ɋɟɲɢɜ ɭɪɚɜɧɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ Ȧ, ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ȧ = (U – IR) / kɎ, ɚ ɬɚɤ ɤɚɤ I = M / kɎ, ɬɨ ɭɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ U R M (3.10) kɎ kɎ 2 Ɇɟɯɚɧɢɱɟɫɤɚɹ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɥɢɧɟɣɧɵ, ɢɯ ɩɨɥɨɠɟɧɢɟ ɧɚ ɨɫɹɯ Ȧ, Ɇ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɞɜɭɦɹ ɬɨɱɤɚɦɢ (ɪɢɫ. 3.6): 1. Ɇ = 0, I = 0, Ȧ = Ȧ0 = U/kɎ – ɫɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ, ɗȾɋ ȿ=kɎȦ0=U ɩɨɥɧɨɫɬɶɸ ɭɪɚɜɧɨɜɟɲɢɜɚɟɬ ɩɪɢɥɨɠɟɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ; 2. Ȧ = 0, Ɇ = ɆɄɁ, I = IɄɁ – ɬɨɱɤɚ ɦɨɦɟɧɬɧɨɝɨ ɬɨɪɦɨɡɚ, ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ Ɋȼ =0. Ɋɟɲɢɜ ɭɪɚɜɧɟɧɢɟ (3.10) ɨɬɧɨȦ

Ȧ Ȧ0 Ƚɟɧɟɪɚɬɨɪɧɵɣ ɪɟɠɢɦ P<0

Ⱦɜɢɝɚɬɟɥɶɧɵɣ ɪɟɠɢɦ Ɋ = M Ȧ >0

Ɇ

MɄɁ Ⱦɜɢɝɚɬɟɥɶɧɵɣ ɪɟɠɢɦ P>0

Ƚɟɧɟɪɚɬɨɪɧɵɣ ɪɟɠɢɦ P<0

Ɋɢɫ. 3.6. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ Ⱦɇȼ ɫɢɬɟɥɶɧɨ Ɇ:

U kɎ Ȧ kɎ , R R 2

Ɇ

(3.11)

ɩɨɥɭɱɢɦ ɩɪɢ Ȧ = 0 ɬɨɤ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ IɄɁ

U R

(3.12)

ɢ ɦɨɦɟɧɬ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ MɄɁ

U kɎ . R

(3.13)

ȼɚɠɧɵɦ ɩɨɤɚɡɚɬɟɥɟɦ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɹɜɥɹɟɬɫɹ ɦɨɞɭɥɶ ɫɬɚɬɢɱɟɫɤɨɣ ɠɟɫɬɤɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. ɉɪɨɞɢɮɮɟɪɟɧɰɢɪɨɜɚɜ (3.11) ɩɨ ɫɤɨɪɨɫɬɢ, ɩɨɥɭɱɢɦ ɡɧɚɱɟɧɢɟ ɫɬɚɬɢɱɟɫɤɨɣ ɠɟɫɬɤɨɫɬɢ 2 kɎ

dM dȦ

ȕCT

R

ɢ ɦɨɞɭɥɶ ɫɬɚɬɢɱɟɫɤɨɣ ɠɟɫɬɤɨɫɬɢ ȕ

kɎ 2 .

R ȿɫɥɢ ȕ ɫɬɪɟɦɢɬɫɹ ɤ ɛɟɫɤɨɧɟɱɧɨɫɬɢ, ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɠɟɫɬɤɚɹ, ɩɪɢ ɦɚɥɨɣ ǻȦ ɦɨɦɟɧɬ ɞɨɫɬɢɝɚɟɬ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ. ɉɪɢ ɦɚɥɵɯ ȕ – ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɹɝɤɚɹ. Ⱦɥɹ Ⱦɇȼ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɹɤɨɪɧɨɣ ɰɟɩɢ R ɢ ɫɧɢɠɟɧɢɢ ɩɨɬɨɤɚ Ɏ ɠɟɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȕ ɫɧɢɠɚɟɬɫɹ. 48

ɂɫɩɨɥɶɡɭɹ ɜɵɪɚɠɟɧɢɟ ɦɨɞɭɥɹ ɫɬɚɬɢɱɟɫɤɨɣ ɠɟɫɬɤɨɫɬɢ, ɩɨɹɜɥɹɸɬɫɹ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɡɚɩɢɫɢ ɫɬɚɬɢɱɟɫɤɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ: M Ȧ Ȧ0 ; ȕ M ȕ Ȧ0 Ȧ ; M MɄɁ ȕ Ȧ .

Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɨɡɜɨɥɹɟɬ ɫɭɞɢɬɶ ɨ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ. ȿɫɥɢ ɡɧɚɤɢ ɦɨɦɟɧɬɚ ɢ ɫɤɨɪɨɫɬɢ ɫɨɜɩɚɞɚɸɬ, ɦɨɳɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɨɥɨɠɢɬɟɥɶɧɚ (Ɋ > 0), ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ, ɜɵɞɚɟɬ ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. Ɋɚɡɧɵɟ ɡɧɚɤɢ Ɇ ɢ Ȧ ɫɜɢɞɟɬɟɥɶɫɬɜɭɸɬ ɨ ɝɟɧɟɪɚɬɨɪɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ, ɞɜɢɝɚɬɟɥɶ ɢɡɛɵɬɨɱɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɩɨɬɪɟɛɥɹɟɬ ɫ ɜɚɥɚ ɢ ɩɪɟɨɛɪɚɡɭɟɬ ɟɟ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ. 3.1.3. Ɂɨɧɵ ɞɨɩɭɫɬɢɦɵɯ ɧɚɝɪɭɡɨɤ

Ƚɥɚɜɧɵɦ ɬɪɟɛɨɜɚɧɢɟɦ ɤ ɥɸɛɨɣ ɬɟɯɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɹɜɥɹɟɬɫɹ ɬɪɟɛɨɜɚɧɢɟ ɧɚɞɟɠɧɨɫɬɢ, ɡɚɤɥɸɱɚɸɳɟɟɫɹ ɜ ɬɨɦ, ɱɬɨɛɵ ɜ ɩɪɨɰɟɫɫɟ ɪɚɛɨɬɵ ɧɢ ɨɞɧɚ ɢɡ ɩɟɪɟɦɟɧɧɵɯ ɧɟ ɩɪɟɜɵɫɢɥɚ ɞɨɩɭɫɬɢɦɨɝɨ ɡɧɚɱɟɧɢɹ [6].ȼ ɤɚɬɚɥɨɠɧɵɯ ɞɚɧɧɵɯ ɧɚ ɥɸɛɭɸ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɦɚɲɢɧɭ ɢɥɢ ɞɚɠɟ ɧɚ ɟɟ ɡɚɜɨɞɫɤɨɦ ɳɢɬɤɟ ɜɫɟɝɞɚ ɭɤɚɡɵɜɚɸɬɫɹ ɪɟɠɢɦ ɪɚɛɨɬɵ (S1, S2, S3), ɢ ɞɥɹ ɷɬɨɝɨ ɪɟɠɢɦɚ ɩɪɢɜɨɞɹɬɫɹ ɡɧɚɱɟɧɢɹ ɧɨɦɢɧɚɥɶɧɵɯ ɞɚɧɧɵɯ: UH, Iɇ, Iȼɇ, Pɇ, nɇ, nɆȺɄɋ , Șɇ. Ɂɧɚɱɟɧɢɟ ɧɨɦɢɧɚɥɶɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ UH ɨɛɭɫɥɨɜɥɟɧɨ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɱɧɨɫɬɶɸ ɢɡɨɥɹɰɢɢ ɦɚɲɢɧɵ; ɡɧɚɱɟɧɢɹ ɧɨɦɢɧɚɥɶɧɵɯ ɬɨɤɨɜ Iɇ, Iȼɇ, ɢ ɦɨɳɧɨɫɬɢ Ɋɇ ɨɩɪɟɞɟɥɟɧɵ ɭɫɥɨɜɢɹɦɢ ɧɚɝɪɟɜɚ ɨɬɜɟɬɫɬɜɟɧɧɵɯ ɷɥɟɦɟɧɬɨɜ ɦɚɲɢɧɵ; ɡɧɚɱɟɧɢɟ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ nɇ ɫɜɹɡɚɧɨ ɫ ɦɟɯɚɧɢɱɟɫɤɨɣ ɩɪɨɱɧɨɫɬɶɸ ɷɥɟɦɟɧɬɨɜ ɤɨɧɫɬɪɭɤɰɢɢ, ɩɨɞɲɢɩɧɢɤɚɦɢ ɢ ɬ.ɩ.; ɧɨɦɢɧɚɥɶɧɵɣ ɄɉȾ Șɇ ɨɰɟɧɢɜɚɟɬ ɷɮɮɟɤɬɢɜȦ ɧɨɫɬɶ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɧɟɪɝɢɢ ɜ ȦɄɈɇ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ. ȼ ɪɟɠɢɦɚɯ, ɨɬɥɢɱɧɵɯ ɨɬ ɧɨɦɢȾɥɢɬɟɥɶɧɵɣ ɧɚɥɶɧɵɯ, ɨɝɪɚɧɢɱɟɧɢɹ ɩɟɪɟɦɟɧɧɵɯ ɪɟɠɢɦ ɛɭɞɭɬ ɞɪɭɝɢɦɢ. ȿɫɥɢ ɞɜɢɝɚɬɟɥɶ ɪɚɄɪɚɬɤɨɜɪɟɦɟɧɧɵɣ ɛɨɬɚɟɬ ɩɪɢ ɫɤɨɪɨɫɬɹɯ ɜɵɲɟ ɧɨɦɢɪɟɠɢɦ ɧɚɥɶɧɨɣ, ɩɪɟɞɟɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɹɜɥɹɟɬɫɹ ȦɆȺɄɋ. ɉɪɢ ɷɬɨɣ ɫɤɨɪɨɫɬɢ I ɫɤɚɡɵɜɚɟɬɫɹ ɜɥɢɹɧɢɟ ɰɟɧɬɪɨɛɟɠɧɵɯ -2 1 -1 2 ɫɢɥ ɧɚ ɤɪɟɩɨɫɬɶ ɛɚɧɞɚɠɟɣ, ɩɨɞɲɢɩɧɢɤɨɜ ɢ ɬ.ɞ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɢ ɜɵɫɨɤɨɣ ɫɤɨɪɨɫɬɢ ɭɯɭɞɲɚɸɬɫɹ ɭɫɥɨɜɢɹ ɤɨɦɦɭɬɚɰɢɢ ɬɨɤɚ ɧɚ ɤɨɥɥɟɤɬɨɪɟ, ɩɪɢɯɨɞɢɬɫɹ ɨɝɪɚɧɢɱɢɜɚɬɶ ɜɟɥɢɱɢɧɭ ɬɨɤɚ ɹɤɨɪɹ. ɉɪɢ ɪɚɛɨɬɟ ɧɚ ɩɨɧɢɠɟɧɧɵɯ ɫɤɨɪɨɫɬɹɯ ɭɯɭɞɲɚɸɬɫɹ ɭɫɥɨɜɢɹ ɨɯɊɢɫ. 3.7. Ɂɨɧɵ ɞɨɩɭɫɬɢɦɵɯ ɧɚɝɪɭɡɨɤ ɥɚɠɞɟɧɢɹ, ɱɬɨ ɬɚɤɠɟ ɬɪɟɛɭɟɬ ɫɧɢɠɟɧɢɹ ɬɨɤɚ ɹɤɨɪɹ (ɩɭɧɤɬɢɪɧɵɟ ɥɢɧɢɢ ɪɢɫ. 3.7). Ʉɪɚɬɤɨɜɪɟɦɟɧɧɨ (ɫɟɤɭɧɞɵ) ɞɜɢɝɚɬɟɥɢ ɞɨɩɭɫɤɚɸɬ ɡɧɚɱɢɬɟɥɶɧɵɟ (ɞɜɭɯ…ɬɪɟɯɤɪɚɬɧɵɟ) ɩɟɪɟɝɪɭɡɤɢ ɩɨ ɬɨɤɭ, ɤɨɬɨɪɵɟ ɫɜɹɡɚɧɵ ɫ ɭɫɥɨɜɢɹɦɢ ɧɨɪɦɚɥɶɧɨɣ ɤɨɦɦɭɬɚɰɢɢ (ɫɦ. ɫɩɥɨɲɧɵɟ ɥɢɧɢɢ ɪɢɫ. 3.7). 49

3.1.4. ȿɫɬɟɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɇȼ ɢ ɢɯ ɪɚɫɱɟɬ

ȿɫɬɟɫɬɜɟɧɧɵɦɢ ɧɚɡɵɜɚɸɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɤɨɬɨɪɵɦɢ ɨɛɥɚɞɚɟɬ ɞɜɢɝɚɬɟɥɶ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɧɚɩɪɹɠɟɧɢɢ ɩɢɬɚɧɢɹ ɢ ɨɬɫɭɬɫɬɜɢɢ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɹɯ ɨɛɦɨɬɨɤ ɦɚɲɢɧɵ. ȿɫɥɢ ɜ ɜɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (3.10), ɡɚɩɢɫɚɧɧɨɟ ɜ ɨɛɳɟɦ ɜɢɞɟ, ɩɨɞɫɬɚɜɢɬɶ ɧɨɦɢɧɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ U = Uɇ ɢ ɧɟɜɵɤɥɸɱɚɟɦɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɹ R=rə, ɩɨɥɭɱɢɦ ɟɫɬɟɫɬɜɟɧɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ. Ȧ

Uɇ r M ə 2. kɎɇ kɎɇ

(3.14)

kɎɇ ǻɆ ɑɟɪɟɡ ɠɟɫɬɤɨɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȕ ɩɪɢ ȕȿ ǻȦ rə ɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɡɚɩɢɲɟɬɫɹ ɜ ɜɢɞɟ

2

Ɇ ȕȿ Ȧ0ɇ Ȧ , Ȧ

Ȧ 0ɇ

ɢ Ȧ 0ɇ

Ɇ . ȕȿ

Uɇ ɟɫɬɟkɎɇ

(3.15)

ȼɵɪɚɠɟɧɢɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɦɟɟɬ ɜɢɞ Ȧ

Uɇ r I ə ,Ȧ kɎH kɎH

Ȧ 0ɇ

rə I . kɎH

(3.16)

ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɨɯɨɞɹɬ ɱɟɪɟɡ ɬɨɱɤɭ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Ȧ0ɇ ɩɪɢ Ɇ = 0 ɢ I = 0 ɢ ɧɨɦɢɧɚɥɶɧɭɸ ɬɨɱɤɭ Ȧɇ ɩɪɢ Ɇ = Ɇɇ ɢ I = Iɇ. ȿɫɬɟɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɚɸɬ ɨɫɧɨɜɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨɛ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜɚɯ ɞɜɢɝɚɬɟɥɹ: ɨ ɧɨɦɢɧɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ, ɨɛ ɢɡɦɟɧɟɧɢɹɯ ɫɤɨɪɨɫɬɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɦɨɦɟɧɬɚ ɜ ɫɬɚɬɢɱɟɫɤɢɯ ɪɟɠɢɦɚɯ. ɑɟɦ ɜɵɲɟ ɠɟɫɬɤɨɫɬɶ ȕȿ, ɬɟɦ ɜɵɲɟ ɫɬɚɛɢɥɶɧɨɫɬɶ ɪɚɛɨɬɵ ɧɚ ɡɚɞɚɧɧɨɣ ɫɤɨɪɨɫɬɢ. Ɉɰɟɧɤɨɣ ɫɬɚɛɢɥɶɧɨɫɬɢ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɧɚ ɞɚɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɹɜɥɹɟɬɫɹ ɫɬɚɬɢɡɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. Ʉɨɥɢɱɟɫɬɜɟɧɧɚɹ ɨɰɟɧɤɚ ɫɬɚɬɢɡɦɚ – ɫɧɢɠɟɧɢɟ ɫɤɨɪɨɫɬɢ ɩɪɢ ɩɪɢɥɨɠɟɧɢɢ ɧɨɦɢɧɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ǻɆ = Ɇɇ: ǻȦH

Ȧ0H ȦH .

(3.17)

ɋɜɹɡɶ ɫɬɚɬɢɡɦɚ ɫ ɠɟɫɬɤɨɫɬɶɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ǻȦH

MH . ȕE

(3.18)

Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɪɟɚɥɶɧɵɯ ɠɟɫɬɤɨɫɬɹɯ ȕȿ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɭɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ. ɍɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨ.ɟ. ɜ ɨɛɳɟɦ ɜɢɞɟ Ȧ

U R Ɇ. Ɏ Ɏ2

50

(3.19)

ȼɵɪɚɠɟɧɢɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨ.ɟ. U IR . Ɏ

Ȧ

(3.20)

Ⱦɥɹ ɟɫɬɟɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜ ɨ.ɟ. ɢɦɟɟɦ: U 1; Ɏ 1; R rə . ȼɵɪɚɠɟɧɢɟ ɟɫɬɟɫɬɜɟɧɧɵɯ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨ.ɟ. Ȧ

1 Ɇ rə

(3.21)

ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨ.ɟ.: Ȧ

1 I rə.

(3.22)

ȼ ɨ.ɟ. ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɨɜɩɚɞɚɸɬ, M I . Ɉɫɨɛɵɣ ɢɧɬɟɪɟɫ ɩɪɟɞɫɬɚɜɥɹɟɬ ɡɧɚɱɟɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ Ɇ = 1. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ǻȦɇ = rə ɢ ɥɟɝɤɨ ɫɬɪɨɢɬɫɹ ɟɫɬɟɫɬɜɟɧɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɞɜɢɝɚɬɟɥɹ. Ʉɪɚɬɧɨɫɬɶ ɬɨɤɚ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ kə (ɬɨɤ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ IɄɁ ɹɤɨɪɧɨɣ ɰɟɩɢ ɜ ɨ.ɟ.) ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ rə. I

ɄɁ

1 rə

RH rə

Uɇ IH rə

IɄɁ IH

kə .

Ⱦɥɹ ɛɨɥɶɲɢɧɫɬɜɚ ɞɜɢɝɚɬɟɥɟɣ kə = 10…30, ɱɬɨ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɟɬ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɹɤɨɪɹ, ɞɨɩɭɫɬɢɦɨɟ ɩɨ ɭɫɥɨɜɢɹɦ ɤɨɦɦɭɬɚɰɢɢ IȾɈɉ = (2…2,5) Iɇ. ɂɦɟɧɧɨ ɬɨɤ, ɞɨɩɭɫɬɢɦɵɣ ɩɨ ɭɫɥɨɜɢɹɦ ɤɨɦɦɭɬɚɰɢɢ IȾɈɉ, ɨɩɪɟɞɟɥɹɟɬ ɩɟɪɟɝɪɭɡɨɱɧɭɸ ɫɩɨɫɨɛɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɨ ɬɨɤɭ, ɚ ɞɥɹ ɤɨɦɩɟɧɫɢɪɨɜɚɧɧɵɯ ɦɚɲɢɧ ɫɨɜɩɚɞɚɟɬ ɫ ɩɟɪɟɝɪɭɡɨɱɧɨɣ ɫɩɨɫɨɛɧɨɫɬɶɸ ɩɨ ɦɨɦɟɧɬɭ. Ɇɚɲɢɧɵ ɦɚɥɨɣ ɦɨɳɧɨɫɬɢ ɢ ɛɨɥɶɲɢɧɫɬɜɨ ɫɪɟɞɧɟɣ ɦɨɳɧɨɫɬɢ ɧɟ ɢɦɟɸɬ ɤɨɦɩɟɧɫɚɰɢɨɧɧɨɣ ɨɛɦɨɬɤɢ ɄɈ. ȼɢɞ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɬɚɤɢɯ ɦɚɲɢɧ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɥɢɧɟɣɧɨɣ, ɤɨɬɨɪɵɣ ɫɩɪɚɜɟɞɥɢɜ ɞɥɹ ɤɨɦɩɟɧɫɢɪɨɜɚɧɧɵɯ ɦɚɲɢɧ, ɡɚ ɫɱɟɬ ɜɥɢɹɧɢɹ ɩɪɨɞɨɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɪɟɚɤɰɢɢ ɹɤɨɪɹ. Ɋɚɫɱɟɬ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ:

1. ɋɚɦɵɟ ɬɨɱɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɷɬɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɡɚɜɨɞɚ – ɢɡɝɨɬɨɜɢɬɟɥɹ, ɫɧɢɦɚɟɦɵɟ ɜ ɭɫɥɨɜɢɹɯ ɢɫɩɵɬɚɧɢɣ ɞɜɢɝɚɬɟɥɹ ɢ ɨɬɪɚɠɟɧɧɵɟ ɜ ɞɨɤɭɦɟɧɬɚɰɢɢ ɧɚ ɞɜɢɝɚɬɟɥɶ ɢ ɜ ɤɚɬɚɥɨɝɚɯ ɷɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɨɣ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ. ɗɬɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɞɚɥɶɧɟɣɲɟɦ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɤɚɬɚɥɨɠɧɵɦɢ. Ʉɪɨɦɟ ɤɚɬɚɥɨɠɧɵɯ ɤɪɢɜɵɯ ɦɨɳɧɨɫɬɢ Ɋ(I), ɫɤɨɪɨɫɬɢ n(I), ɄɉȾ Ș(I), ɦɨɦɟɧɬɚ Ɇ(I) ɜ ɤɚɬɚɥɨɝɚɯ ɩɪɢɜɨɞɹɬɫɹ ɧɨɦɢɧɚɥɶɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɨɫɧɨɜɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ PH, nH, IH, UH. Șɇ ɢ ɞɪɭɝɢɟ. 2. Ⱦɥɹ ɧɟɤɨɬɨɪɵɯ ɬɢɩɨɜ ɞɜɢɝɚɬɟɥɟɣ (ɧɚɩɪɢɦɟɪ, ɬɢɩɚ Ⱦ) ɜ ɫɩɪɚɜɨɱɧɢɤɚɯ ɩɪɢɜɨɞɹɬɫɹ, ɤɪɨɦɟ ɧɨɦɢɧɚɥɶɧɵɯ ɞɚɧɧɵɯ PH, nH, IH, ɡɧɚɱɟɧɢɹ ɞɨɩɭɫɤɚɟɦɵɯ ɩɨ ɧɚɝɪɟɜɭ ɧɚɝɪɭɡɨɤ ɩɪɢ ɪɚɡɥɢɱɧɨɣ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɜɤɥɸɱɟɧɢɹ ɉȼ (P, n, I), ɱɬɨ ɩɨɡɜɨɥɢɬ ɩɨɫɬɪɨɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨ ɱɟɬɵɪɟɦ – ɩɹɬɢ ɬɨɱɤɚɦ. Ɉɞɧɚɤɨ ɱɚɳɟ ɜɫɟɝɨ ɷɬɢɯ ɞɚɧɧɵɯ ɞɥɹ ɜɫɟɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɛɵɜɚɟɬ ɧɟɞɨɫɬɚɬɨɱɧɨ. 3. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɞɚɧɧɵɯ ɩɨ ɩ.1 ɢ ɩ.2 ɩɪɢɯɨɞɢɬɫɹ ɧɚ ɫɬɚɞɢɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɪɚɫɫɱɢɬɵɜɚɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɟɣ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ. ɂɡ ɤɚɬɚɥɨɠɧɵɯ ɞɚɧɧɵɯ ɞɜɢɝɚɬɟɥɹ ɛɟɪɺɦ ɧɨɦɢɧɚɥɶɧɵɟ ɞɚɧɧɵɟ PH, nH, IH, UH., ɚ ɬɚɤɠɟ ɞɚɧɧɵɟ ɨ ɞɨɩɭɫɤɚɟɦɵɯ ɧɚɝɪɭɡɤɚɯ (ɆɆȺɄɋ, ȦɆȺɄɋ), ɩɨ ɜɨɡɦɨɠɧɨɫɬɢ – ɨɛɦɨɬɨɱɧɵɟ ɞɚɧɧɵɟ (rə).

51

ɉɨɪɹɞɨɤ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤ Ⱦɇȼ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ ɪɚɫɫɦɨɬɪɢɦ ɧɚ ɩɪɢɦɟɪɟ ɤɨɧɤɪɟɬɧɨɝɨ ɞɜɢɝɚɬɟɥɹ. ɉɪɢɦɟɪ 3.1. Ɋɚɫɫɱɢɬɚɬɶ ɟɫɬɟɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɭɸ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɬɢɩɚ Ⱦ32: Ɋɇ = 9,5 ɤȼɬ, Iɇ = 51 Ⱥ, Uɇ = 220 ȼ, nɇ = 800 ɨɛ/ɦɢɧ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɫɩɨɥɶɡɭɸɬɫɹ ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ PH, nH, IH, UH ɢ ɜɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (3.16) Ȧ

Uɇ r I ə . kɎH kɎH

Ɉɬɫɭɬɫɬɜɭɸɳɢɟ ɜ ɤɚɬɚɥɨɠɧɵɯ ɞɚɧɧɵɯ kɎɇ ɢ rə ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɩɨ ɩɪɢɛɥɢɠɟɧɧɵɦ ɮɨɪɦɭɥɚɦ. ȼɟɥɢɱɢɧɭ ɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɹɤɨɪɧɨɣ ɰɟɩɢ rə ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɩɪɢɛɥɢɠɟɧɧɨ ɢɡ ɭɫɥɨɜɢɹ ɪɚɜɟɧɫɬɜɚ ɩɨɫɬɨɹɧɧɵɯ ɢ ɩɟɪɟɦɟɧɧɵɯ ɩɨɬɟɪɶ ɦɨɳɧɨɫɬɢ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ ɩɨ ɮɨɪɦɭɥɟ rə

UH IH PH 103

ǻɊɇ 2 IH

2

2 IH

220 51 9500 2 512

2

0,33 Ɉɦ ,

ɝɞɟ ǻɊɇ – ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ; rə rɈə rȾɉ rɄɈ – ɧɟɜɵɤɥɸɱɚɟɦɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɹ, rɈə – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɦɨɬɤɢ ɹɤɨɪɹ, rȾɉ – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɦɨɬɨɤ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɩɨɥɸɫɨɜ, rɄɈ – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɦɩɟɧɫɚɰɢɨɧɧɨɣ ɨɛɦɨɬɤɢ. ȼɟɥɢɱɢɧɭ kɎɇ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ (3.16), ɩɨɞɫɬɚɜɥɹɹ ɜ ɧɟɟ ɧɨɦɢɧɚɥɶɧɵɟ ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ, ɚ ɬɚɤɠɟ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɹ ɦɚɲɢɧɵ; kɎH

UH IH rə ȦH

220 51 0,33 83,8

2,424 ȼ ɫ .

ɋɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɜ ɫɢɫɬɟɦɟ ɋɂ ɢɡɦɟɪɹɟɬɫɹ ɜ ɪɚɞ/ɫ. ɉɨɫɤɨɥɶɤɭ ɜ ɤɚɬɚɥɨɝɚɯ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɪɢɜɨɞɢɬɫɹ ɜ ɨɛ/ɦɢɧ, ɬɨ ɧɟɨɛɯɨɞɢɦɨ ɟɺ ɩɟɪɟɫɱɢɬɚɬɶ ɜ ɪɚɞ/ɫ ɩɨ ɮɨɪɦɭɥɟ Ȧɇ

2 ʌ nH 60

nH 9,55

800 9,55

83,8

1 . c

ɋɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Ȧ 0H

UH kɎɇ

220 2,424

90,76

1 . ɫ

ɇɨɦɢɧɚɥɶɧɵɣ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ Ɇɇ

kɎɇ IH

2,424 51 123,6 ɇ ɦ .

ɇɨɦɢɧɚɥɶɧɵɣ ɦɨɦɟɧɬ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ Ɋɇ 9500 Ɇȼɇ 113,4 ɇ ɦ Ȧɇ 83,8 Ɇɨɦɟɧɬ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ ǻ Ɇ ɏɇ Ɇ ɇ Ɇ ȼɇ 123 ,6 113 ,4 10 ,2 ɇ ɦ 52

ɉɪɨɜɟɞɟɧɧɵɟ ɪɚɫɱɟɬɵ ɩɨɡɜɨɥɹɸɬ ɩɨɥɭɱɢɬɶ ɜɵɪɚɠɟɧɢɟ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ Ȧ

Ȧ 0ɇ

rə Ɇ

90,76

kɎH

2

Ɇ 0,33

2,424 2

90,76 Ɇ 0,056 ,

ɨɩɪɟɞɟɥɢɬɶ ɞɜɟ ɬɨɱɤɢ, ɱɟɪɟɡ ɤɨɬɨɪɵɟ ɩɪɨɯɨɞɹɬ ɟɫɬɟɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ: (Ɇ = 0, Ȧ0ɇ = 90,76 1/ɫ) ɢ (Ɇɇ = 123,6 ɇɦ; Ȧɇ = 83,8 1/ɫ) ɢ ɩɨɫɬɪɨɢɬɶ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ (ɪɢɫ. 3.8,ɚ). Ȧ

Ȧ Ȧ0ɇ

ɟɫɬ

1

rə

Ȧɧ

Ȧɇ

ɟɫɬ

Ɇ

Ɇ

Ɇɇ

1

ɚ) ɛ) Ɋɢɫ. 3.8 – ȿɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜ ɚɛɫɨɥɸɬɧɵɯ ɚ) ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɛ) ɟɞɢɧɢɰɚɯ Ƚɨɪɚɡɞɨ ɩɪɨɳɟ ɫɬɪɨɢɬɫɹ ɟɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜ ɨ.ɟ. ɍɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨ.ɟ. ɜ ɨɛɳɟɦ ɜɢɞɟ U R 2 Ɇ. Ɏ Ɏ Ɉɩɪɟɞɟɥɢɦ ɛɚɡɨɜɵɟ ɜɟɥɢɱɢɧɵ ɞɜɢɝɚɬɟɥɹ Ⱦ32 ɢɡ ɩɪɟɞɵɞɭɳɟɝɨ ɪɚɫɱɟɬɚ: UȻ = Uɇ = 220 ȼ, IȻ = Iɇ = 51 Ⱥ, kɎȻ = kɎɇ = 2,424 ȼ·ɫ, ȿȻ = Uɇ = 220 ȼ, ȦȻ = Ȧ0ɇ = Uɇ/kɎɇ = 90,76 ɪɚɞ/ɫ, ɆȻ = MɇɗɆ = kɎɇ Iɇ = 123,6 ɇɦ, UH 220 Ȼɚɡɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ RH 4,31 Ɉɦ . IH 51 ɇɟɜɵɤɥɸɱɚɟɦɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɨ.ɟ. Ȧ

rə

rə RH

0,33 4,31

0,076 .

ȼɵɪɚɠɟɧɢɟ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨ.ɟ. Ȧ

Ȧ0H M rə

1 Ɇ 0,076 .

ȼɵɪɚɠɟɧɢɟ ɟɫɬɟɫɬɜɟɧɧɨɣ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨ.ɟ ɫɨɜɩɚɞɚɟɬ ɫ ɜɵɪɚɠɟɧɢɟɦ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨ.ɟ. Ȧ 1 Ɇ 0,076 . Ⱦɚɥɟɟ ɩɪɢ Ȧ 1 ɩɪɨɜɨɞɢɬɫɹ ɝɨɪɢɡɨɧɬɚɥɶ ɢ ɩɪɢ Ɇ 1 ɨɬɦɟɱɚɟɬɫɹ rə . ɑɟɪɟɡ ɩɨɥɭɱɟɧɧɭɸ ɬɨɱɤɭ ɢ Ȧ0H 1 ɫɬɪɨɢɬɫɹ ɟɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜ ɨ.ɟ.(ɪɢɫ. 3.8,ɛ). 53

3.1.5. ɂɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɇȼ ɢ ɢɯ ɪɚɫɱɟɬ

ɂɫɤɭɫɫɬɜɟɧɧɵɦɢ ɧɚɡɵɜɚɸɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɟɣ ɩɪɢ ɧɟɧɨɦɢɧɚɥɶɧɵɯ ɩɚɪɚɦɟɬɪɚɯ ɩɢɬɚɸɳɟɣ ɫɟɬɢ ɢɥɢ ɩɪɢ ɧɚɥɢɱɢɢ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɹɯ ɨɛɦɨɬɨɤ ɦɚɲɢɧ. ɂɡ ɜɵɪɚɠɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨɛɳɟɦ ɜɢɞɟ Ȧ

Uɇ r M ə 2, kɎɇ kɎɇ

(3.23)

ɫɥɟɞɭɟɬ, ɱɬɨ ɩɚɪɚɦɟɬɪɚɦɢ, ɢɡɦɟɧɹɸɳɢɦɢ ɟɟ ɜɢɞ, ɹɜɥɹɸɬɫɹ U, R, Ɏ. ɂɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɇȼ ɩɨɥɭɱɚɸɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ U ɧɚ ɡɚɠɢɦɚɯ ɰɟɩɢ ɹɤɨɪɹ, ɩɪɢ ɜɜɨɞɟ ɜ ɰɟɩɶ ɹɤɨɪɹ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R ɢɥɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɬɨɤɚ Ɏ. ȼɥɢɹɧɢɟ ɧɚ ɜɢɞ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜɜɟɞɟɧɢɹ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RȾɈȻ ɜ ɰɟɩɶ ɹɤɨɪɹ. ɉɪɢ ɜɜɟɞɟɧɢɢ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RȾɈȻ ɜ ɰɟɩɶ ɹɤɨɪɹ ɫɧɢɠɚɟɬɫɹ ɬɨɤ I, ɭɦɟɧɶɲɚɟɬɫɹ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ, ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ MȾɂɇ = (Ɇ – Ɇɋ) < 0 – ɫɬɚɧɨɜɢɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɵɦ, ɧɚɱɢɧɚɟɬ ɫɧɢɠɚɬɶɫɹ ɫɤɨɪɨɫɬɶ Ȧ, ɭɦɟɧɶɲɚɟɬɫɹ ɗȾɋ ɞɜɢɝɚɬɟɥɹ E, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɪɨɫɬɭ ɬɨɤɚ ɢ ɦɨɦɟɧɬɚ. Ɇɨɦɟɧɬ Ɇ ɫɬɪɟɦɢɬɫɹ ɤ Ɇɋ, ɧɨ ɭɫɬɚɧɨɜɢɜɲɟɟɫɹ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ Ȧ ɛɭɞɟɬ ɦɟɧɶɲɟ ɫɤɨɪɨɫɬɢ ɩɪɟɞɵɞɭɳɟɝɨ ɪɟɠɢɦɚ. ȼɜɟɞɟɧɢɟ RȾɈȻ – ɩɪɨɫɬɟɣɲɢɣ ɫɩɨɫɨɛ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɢ ɨɝɪɚɧɢɱɟɧɢɹ ɬɨɤɚ ɜ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ. ɉɨɫɤɨɥɶɤɭ ɧɚɩɪɹɠɟɧɢɟ U = Uɇ ɢ ɩɨɬɨɤ kɎ = kɎɇ ɨɫɬɚɥɢɫɶ ɪɚɜɧɵɦɢ ɧɨɦɢɧɚɥɶɧɵɦ ɡɧɚɱɟɧɢɹɦ, ɬɨ ɫɤɨɪɨɫɬɶ Ȧ0ɇ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ Ȧ 0ɇ

UH kɎɇ

const .

ɀɟɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȕɂ

Ȧ 1

rɹ

ɟɫɬ

RȾɈȻ

ɢɫɤ

M

1 Ɋɢɫ. 3.9. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɜɜɟɞɟɧɢɢ RȾɈȻ

kɎɇ 2 rə R ȾɈȻ

ȕE .

Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ (3.23) ɜ ɨ.ɟ. ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ Ȧ 1 Ɇ RȾɈȻ rə (3.24) ɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ, ɢɡɨɛɪɚɠɟɧɧɵɣ ɧɚ ɪɢɫ. 3.9. Ɋɚɫɱɟɬ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɜɜɟɞɟɧɢɢ RȾɈȻ ɩɪɨɫɬ. ɇɟɨɛɯɨɞɢɦɨ ɪɚɫɫɱɢɬɚɬɶ RȾɈȻ ɜ ɨ.ɟ. ɢ ɩɨɥɭɱɟɧɧɭɸ ɜɟɥɢɱɢɧɭ R ȾɈȻ RȾɈȻ RH ɨɬɥɨɠɢɬɶ ɜ ɦɚɫɲɬɚɛɟ ɜɧɢɡ ɨɬ ɧɨɦɢɧɚɥɶɧɨɣ ɬɨɱɤɢ (ɪɢɫ. 3.9).

ȼɥɢɹɧɢɟ ɧɚ ɜɢɞ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢɡɦɟɧɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɡɚɠɢɦɚɯ ɹɤɨɪɹ. ɍɦɟɧɶɲɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ U ɧɚ ɹɤɨɪɟ ɞɜɢɝɚɬɟɥɹ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɬɨɤɚ I, ɭɦɟɧɶɲɟɧɢɸ ɦɨɦɟɧɬɚ M, ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɫɬɚɧɨɜɢɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɵɦ MȾɂɇ < 0, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɫɤɨɪɨɫɬɢ Ȧ, ɭɦɟɧɶɲɚɟɬɫɹ E, ɫɧɢ

54

ɠɟɧɢɟ ɤɨɬɨɪɨɣ ɜɟɞɟɬ ɤ ɪɨɫɬɭ ɬɨɤɚ I, ɧɚɪɚɫɬɚɧɢɸ ɦɨɦɟɧɬɚ M, ɤɨɬɨɪɵɣ ɫɬɪɟɦɢɬɫɹ ɤ MC, ɧɨ ɭɫɬɚɧɨɜɢɜɲɟɟɫɹ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ Ȧ ɦɟɧɶɲɟ ɫɤɨɪɨɫɬɢ ɩɪɟɞɵɞɭɳɟɝɨ ɪɟɠɢɦɚ. ɉɨɫɤɨɥɶɤɭ ɩɨɬɨɤ kɎ = kɎɇ ɪɚɜɟɧ ɧɨɦɢɧɚɥɶɧɨɦɭ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɧɨɣ ɰɟɩɢ R = rə ɪɚɜɧɨ ɧɟɜɵɤɥɸɱɚɟɦɨɦɭ, ɬɨ ɢɡɦɟɧɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ U ɩɪɢɜɨɞɢɬ ɤ ɢɡɦɟɧɟɧɢɸ ɫɤɨɪɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Ȧ0

U kɎɇ

var .

ɀɟɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȕɂ

kɎɇ 2 rə

1 Ȧ ɟɫɬ

1

ɢɫɤ

M

Ɋɢɫ. 3.10. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ

Ȧ0

Ȧ0 Ȧ 0ɇ

ȕE

ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɥɭɱɚɸɬɫɹ ɩɚɪɚɥɥɟɥɶɧɵɦ ɩɟɪɟɧɨɫɨɦ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ (3.23) ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ U rə Ȧ 3.25) kɎɇ kɎɇ 2 ɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ, ɩɨɤɚɡɚɧɧɵɣ ɧɚ ɪɢɫ. 3.10. Ɋɚɫɱɟɬ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜ ɨ.ɟ. ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ U ɩɪɨɫɬ. ɇɟɨɛɯɨɞɢɦɨ ɪɚɫɫɱɢɬɚɬɶ Ȧ0 ɜ ɨ.ɟ. ɢ ɩɨɥɭɱɟɧɧɭɸ ɜɟɥɢɱɢɧɭ U UH

ɨɬɥɨɠɢɬɶ ɜ ɦɚɫɲɬɚɛɟ ɩɪɢ Ɇ = 0 (ɫɦ. ɪɢɫ. 3.10). ɂɡɦɟɧɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ U ɧɚ ɡɚɠɢɦɚɯ ɹɤɨɪɹ ɩɨɡɜɨɥɹɟɬ ɧɟ ɬɨɥɶɤɨ ɪɟɝɭɥɢɪɨɜɚɬɶ ɫɤɨɪɨɫɬɶ Ȧ, ɧɨ ɢ ɨɝɪɚɧɢɱɢɜɚɬɶ IɄɁ. ɉɥɚɜɧɨɟ ɢɡɦɟɧɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ U ɫɨɡɞɚɟɬ ɛɥɚɝɨɩɪɢɹɬɧɵɟ ɭɫɥɨɜɢɹ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ. ȼɥɢɹɧɢɟ ɧɚ ɜɢɞ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢɡɦɟɧɟɧɢɹ ɩɨɬɨɤɚ Ɏ ɞɜɢɝɚɬɟɥɹ. ɍɜɟɥɢɱɟɧɢɟ ɩɨɬɨɤɚ ɞɜɢɝɚɬɟɥɹ Ɏ > Ɏɇ ɜɵɲɟ ɧɨɦɢɧɚɥɶɧɨɝɨ ɜɨɡɦɨɠɧɨ ɥɢɲɶ ɧɚ (10…20)% ɢɡ-ɡɚ ɧɚɫɵɳɟɧɢɹ ɦɚɝɧɢɬɧɨɣ ɫɢɫɬɟɦɵ ɞɜɢɝɚɬɟɥɹ, ɧɨ ɢ ɷɬɨ ɦɨɠɧɨ ɜɵɩɨɥɧɢɬɶ ɥɢɲɶ ɡɚ ɫɱɟɬ ɫɭɳɟɫɬɜɟɧɧɨɝɨ (ɜ ɧɟɫɤɨɥɶɤɨ ɪɚɡ) ɭɜɟɥɢɱɟɧɢɹ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ. ɗɬɨ ɭɜɟɥɢɱɢɜɚɟɬ ɧɚɝɪɟɜ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɪɚɫɫɱɢɬɚɧɧɨɣ ɬɨɥɶɤɨ ɧɚ ɧɨɦɢɧɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɬɨɤɚ. ɉɨɷɬɨɦɭ ɢɡɦɟɧɟɧɢɟ ɩɨɬɨɤɚ Ɏ ɩɪɨɢɡɜɨɞɹɬ ɬɨɥɶɤɨ ɜɧɢɡ ɨɬ ɧɨɦɢɧɚɥɶɧɨɝɨ. ɋɧɢɠɟɧɢɟ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ iȼ ɩɭɬɟɦ ɭɦɟɧɶɲɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ Uȼ ɧɚ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɢɥɢ ɜɜɟɞɟɧɢɟɦ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ Rȼ ɜ ɰɟɩɶ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɜɵɡɵɜɚɟɬ ɭɦɟɧɶɲɟɧɢɟ ɩɨɬɨɤɚ Ɏ, ɫɧɢɠɟɧɢɟ ȿ, ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɪɚɫɬɟɬ ɬɨɤ ɹɤɨɪɹ I, ɪɚɫɬɟɬ ɦɨɦɟɧɬ M, ɩɨɹɜɥɹɟɬɫɹ ɢ ɫɬɚɧɨɜɢɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɵɦ ɞɢ-

55

ɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ MȾɂɇ > 0, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɪɨɫɬɭ ɫɤɨɪɨɫɬɢ Ȧ. ɋ ɪɨɫɬɨɦ ɫɤɨɪɨɫɬɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ E, ɫɧɢɠɚɟɬɫɹ ɬɨɤ I, ɦɨɦɟɧɬ M, ɤɨɬɨɪɵɣ ɫɬɪɟɦɢɬɫɹ ɤ MC, ɧɨ ɭɫɬɚɧɨɜɢɜɲɟɟɫɹ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ Ȧ ɛɭɞɟɬ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɩɪɟɞɵɞɭɳɟɝɨ ɪɟɠɢɦɚ. ɉɨɫɤɨɥɶɤɭ ɧɚɩɪɹɠɟɧɢɟ U = Uɇ ɪɚɜɧɨ ɧɨɦɢɧɚɥɶɧɨɦɭ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɧɨɣ ɰɟɩɢ R = rə ɪɚɜɧɨ ɧɟɜɵɤɥɸɱɚɟɦɨɦɭ, ɬɨ ɭɦɟɧɶɲɟɧɢɟ ɩɨɬɨɤɚ kɎ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɫɤɨɪɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Uɇ kɎ

Ȧ0

var .

ɀɟɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɭɦɟɧɶɲɚɟɬɫɹ

kɎ 2

ȕɂ

rə

ȕE

ɢ ɢɫɤɭɫɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ (3.23) ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ Ȧ

Uɇ r ə2, kɎ kɎ

(3.26)

Ȧ

1 Ɏ

(3.27)

ɜ ɨ.ɟ. rə Ɇ, Ɏ2

ɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ, ɩɨɤɚɡɚɧɧɵɣ ɧɚ ɪɢɫ. 3.11.

Ȧ

2

2

Ȧ

ɢɫɤ

ɢɫɤ 1 1 ɟɫɬ

ɟɫɬ M

I 1 2

1

IɄɁ

MɄɁ1

MɄ

ɛ)

ɚ)

Ɋɢɫ. 3.11. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɚ) ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɛ) ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɬɨɤɚ Ɏ

56

Ʉɚɤ ɜɢɞɧɨ, ɢɡɦɟɧɟɧɢɟ ɩɨɬɨɤɚ Ɏ ɧɟ ɜɥɢɹɟɬ ɧɚ ɬɨɤ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ IɄɁ ɞɜɢɝɚɬɟɥɹ, ɢ ɩɪɢ ɥɸɛɨɦ ɩɨɬɨɤɟ IɄɁ = const (ɫɦ.ɪɢɫ. 3.11). Ɇɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ = kɎI ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɩɨɬɨɤɭ, ɢ ɡɧɚɱɟɧɢɟ ɆɄɁ ɫɧɢɠɚɟɬɫɹ ɩɪɢ ɭɦɟɧɶɲɟɧɢɢ ɩɨɬɨɤɚ ɞɨ ɆɄɁ1. Ɉɛɵɱɧɨ ɢɡɦɟɧɟɧɢɟ ɩɨɬɨɤɚ ɜɵɩɨɥɧɹɸɬ ɞɥɹ ɫɤɨɪɨɫɬɟɣ ɜɵɲɟ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɤɨɝɞɚ U = Uɇ ɢ R = rə. ȼ ɷɬɨɦ ɫɥɭɱɚɟ IɄɁ = (10…20)Iɇ ɢ ɡɨɧɚ ɞɨɩɭɫɬɢɦɨɣ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɩɨ ɭɫɥɨɜɢɹɦ ɤɨɦɦɭɬɚɰɢɢ IȾɈɉ = (2…2,5) Iɇ ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɜɵɲɟ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. Ɋɚɫɱɟɬ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɢɡɜɟɫɬɧɨɣ ɜɟɥɢɱɢɧɟ ɩɨɬɨɤɚ Ɏ ɧɟɫɥɨɠɟɧ. ɉɨ ɮɨɪɦɭɥɚɦ (3.26), (3.27) ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ȦɈ, ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɦɨɦɟɧɬɟ – ɩɚɞɟɧɢɟ ɫɤɨɪɨɫɬɢ ǻȦ. ɋɥɨɠɧɨɫɬɶ ɩɪɟɞɫɬɚɜɥɹɟɬ ɪɚɫɱɟɬ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ iȼ ɩɨ ɢɡɜɟɫɬɧɨɦɭ ɩɨɬɨɤɭ Ɏ, ɤɨɝɞɚ ɧɟ ɩɪɢɜɨɞɢɬɫɹ ɤɪɢɜɚɹ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɫɨɛɫɬɜɟɧɧɨɣ ɤɪɢɜɨɣ ɩɪɢɯɨɞɢɬɫɹ ɩɪɢɦɟɧɹɬɶ ɞɥɹ ɪɚɫɱɟɬɨɜ ɭɧɢɜɟɪɫɚɥɶɧɭɸ ɤɪɢɜɭɸ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ, ɩɪɢɜɨɞɢɦɭɸ ɜ ɫɩɪɚɜɨɱɧɢɤɚɯ. Ɋɟɠɢɦ ɢɡɦɟɧɟɧɢɹ ɩɨɬɨɤɚ (ɨɫɥɚɛɥɟɧɢɹ ɩɨɥɹ) ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɟɬɫɹ ɜ ɭɫɬɚɧɨɜɤɚɯ, ɬɪɟɛɭɸɳɢɯ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɦɨɳɧɨɫɬɢ (ɧɚɩɪɢɦɟɪ, ɜ ɦɟɬɚɥɥɨɪɟɠɭɳɢɯ ɫɬɟɧɤɚɯ), ɜ ɫɜɹɡɢ ɫ ɟɝɨ ɜɵɫɨɤɨɣ ɷɤɨɧɨɦɢɱɧɨɫɬɶɸ (ɦɨɳɧɨɫɬɶ ɰɟɩɟɣ ɜɨɡɛɭɠɞɟɧɢɹ ɫɨɫɬɚɜɥɹɟɬ 2…5% ɨɬ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ). 3.1.6. Ɋɟɨɫɬɚɬɧɵɣ ɩɭɫɤ Ⱦɇȼ

ɉɪɢ ɩɭɫɤɟ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɨɛɟɫɩɟɱɢɜɚɬɶ ɧɚɞɟɠɧɨɫɬɶ ɢ ɛɟɡɨɩɚɫɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ. ȼ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɞɨɥɠɧɚ ɛɵɬɶ ɩɨɞɤɥɸɱɟɧɚ ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɢ ɩɪɟɞɭɫɦɨɬɪɟɧɚ ɡɚɳɢɬɚ ɨɬ ɨɛɪɵɜɚ ɩɨɥɹ. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɩɨɬɨɤɚ ɧɟ ɫɨɡɞɚɟɬɫɹ ɗȾɋ, ɢ ɩɨɬɨɦɭ ɜ ɰɟɩɢ ɹɤɨɪɹ ɦɨɠɟɬ ɨɫɬɚɬɶɫɹ ɬɨɥɶɤɨ ɧɟɜɵɤɥɸɱɚɟɦɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ. ȼɨɡɧɢɤɚɸɳɢɣ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɬɨɤ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɦɨɠɟɬ ɜɵɜɟɫɬɢ ɞɜɢɝɚɬɟɥɶ ɢɡ ɫɬɪɨɹ. Ɍɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɬɪɟɛɨɜɚɧɢɹ, ɩɪɟɞɴɹɜɥɹɟɦɵɟ ɤ ɩɭɫɤɭ: – ɮɨɪɫɢɪɨɜɚɧɧɵɣ ɩɭɫɤ (ɦɢɧɢɦɚɥɶɧɨɟ ɜɪɟɦɹ ɩɭɫɤɚ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɞɪɭɝɢɯ ɨɝɪɚɧɢɱɟɧɢɣ), ɤɨɬɨɪɵɣ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɦɚɤɫɢɦɚɥɶɧɵɦ ɩɭɫɤɨɜɵɦ ɦɨɦɟɧɬɨɦ, ɨɝɪɚɧɢɱɢɜɚɟɦɵɦ ɞɨɩɭɫɬɢɦɵɦ ɬɨɤɨɦ ɩɨ ɭɫɥɨɜɢɹɦ ɤɨɦɦɭɬɚɰɢɢ IȾɈɉ = (2…2,5)Iɇ; – ɩɭɫɤ ɫ ɨɝɪɚɧɢɱɟɧɢɟɦ ɩɨ ɭɫɤɨɪɟɧɢɸ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ aȾɈɉ. Ɉɝɪɚɧɢɱɟɧɢɟ ɩɨ ɭɫɤɨɪɟɧɢɸ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɩɪɢɜɟɞɟɧɧɵɦ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɞɢɧɚɦɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ, ɜɟɥɢɱɢɧɚ ɤɨɬɨɪɨɝɨ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ dZPO R dt

ɚ ȾɈɉ

dv dt

ɆȾɈɉ

§ dȦ · J¨ ¸ © dt ¹ ȾɈɉ

ɆɆȺɄɋ

R iɊȿȾ

§ dȦ · ¨ ¸ ; © dt ¹ ȾɈɉ

J ɚ ȾɈɉ iɊȿȾ R

;

(3.28)

ɆȾɂɇ.ȾɈɉ Ɇɋ .

– ɧɨɪɦɚɥɶɧɵɣ ɩɭɫɤ (ɜɪɟɦɹ ɩɭɫɤɚ ɧɟ ɪɟɝɥɚɦɟɧɬɢɪɭɟɬɫɹ, ɪɟɞɤɢɟ ɩɭɫɤɢ), ɤɨɬɨɪɵɣ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɭɫɥɨɜɢɟɦ: Ɇ t 1,2 Ɇɋ , ɱɬɨɛɵ ɞɜɢɝɚɬɟɥɶ ɬɨɥɶɤɨ ɪɚɡɨɝɧɚɥɫɹ.

57

ɋɩɨɫɨɛɵ ɩɭɫɤɚ Ⱦɇȼ: – ɩɨɫɬɟɩɟɧɧɵɦ ɭɜɟɥɢɱɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ, ɞɥɹ ɱɟɝɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɪɚɡɥɢɱɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɢ ɧɚɩɪɹɠɟɧɢɹ (ɷɬɢ ɫɩɨɫɨɛɵ ɛɭɞɭɬ ɢɡɭɱɚɬɶɫɹ ɩɨɡɞɧɟɟ); – ɩɪɢ ɩɢɬɚɧɢɢ ɞɜɢɝɚɬɟɥɹ ɨɬ ɫɟɬɢ ɧɟɢɡɦɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɧɚɩɪɹɠɟɧɢɟ ɩɨɞɚɟɬɫɹ ɧɚ ɹɤɨɪɶ ɫɤɚɱɤɨɦ, ɩɨɷɬɨɦɭ ɧɟɨɛɯɨɞɢɦɨ ɨɝɪɚɧɢɱɢɬɶ ɫɤɚɱɨɤ ɬɨɤɚ ɹɤɨɪɹ ɞɨɩɭɫɬɢɦɵɦ ɡɧɚɱɟɧɢɟɦ ɩɨ ɭɫɥɨɜɢɹɦ ɤɨɦɦɭɬɚɰɢɢ IȾɈɉ = (2…2,5)Iɇ ɜɜɟɞɟɧɢɟɦ ɧɚ ɜɪɟɦɹ ɩɭɫɤɚ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RȾɈȻ. Ɋɟɨɫɬɚɬɧɵɣ ɩɭɫɤ Ⱦɇȼ. ɇɚ ɪɢɫ. 3.12 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɫɢɥɨɜɵɯ ɰɟɩɟɣ ɪɟɨɫɬɚɬɧɨɝɨ ɩɭɫɤɚ ɞɜɢɝɚɬɟɥɹ. Ɋɟɨɫɬɚɬɧɵɣ ɩɭɫɤ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬ ɩɪɢ ɩɨɞɚɱɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɧɭɸ ɰɟɩɶ ɜɜɟɞɟɧɢɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, 4. ɨɝɪɚɧɢɱɢɜɚɸɳɟɝɨ ɜɟɥɢɱɢɧɭ ɬɨɤɚ LM ɹɤɨɪɹ ɞɨɩɭɫɬɢɦɵɦ ɡɧɚɱɟɧɢɟɦ ɩɨ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦ ɭɫɥɨɜɢɹɦ ɩɭɫɤɚ. ɇɚ ɪɢɫ. 3.13 ɩɪɢɜɟɞɟɧɵ ɦɟɯɚɧɢɄɍ1 Ʉɍ2 ɄɅ ɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɩɭɫɤ ɞɜɢɝɚɬɟɥɹ. ɉɪɢ ɡɚɆ ɦɵɤɚɧɢɢ ɤɨɧɬɚɤɬɨɪɚ ɄɅ ɩɪɨɬɟɤɚɟɬ R2ȾɈȻ R1ȾɈȻ ɬɨɤ I1 ɱɟɪɟɡ ɨɛɦɨɬɤɭ ɹɤɨɪɹ ɢ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R1ȾɈȻ ɢ Ɋɢɫ. 3.12. ɋɯɟɦɚ ɩɭɫɤɚ Ⱦɇȼ R2ȾɈȻ, ɫɨɡɞɚɟɬɫɹ ɦɨɦɟɧɬ Ɇ1. Ⱦɜɢɝɚɬɟɥɶ ɪɚɡɝɨɧɹɟɬɫɹ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 1, ɬɨɤ ɹɤɨɪɹ ɫɧɢɠɚɟɬɫɹ, ɢ ɩɪɢ ɫɤɨɪɨɫɬɢ Ȧ1 ɢ ɦɨɦɟɧɬɟ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 ɜɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ Ʉɍ1, ɲɭɧɬɢɪɭɹ R1ȾɈȻ. Ⱦɜɢɝɚɬɟɥɶ ɩɟɪɟɜɨɞɢɬɫɹ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ 2. Ɍɨɤ ɹɤɨɪɹ ɜɧɨɜɶ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɞɨ ɡɧɚɱɟɧɢɹ I1, ɦɨɦɟɧɬ – ɞɨ Ɇ1. ɉɪɨɢɫɯɨɞɢɬ ɪɚɡɝɨɧ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 2 ɞɨ ɫɤɨɪɨɫɬɢ Ȧ2, ɝɞɟ ɩɪɢ ɦɨɦɟɧɬɟ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 ɜɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ Ʉɍ2, ɩɟɪɟɜɨɞɹ ɞɜɢɝɚɬɟɥɶ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ. ɇɚ ɷɬɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɩɪɨɞɨɥɠɚɟɬɫɹ ɪɚɡɝɨɧ ɞɨ ɫɤɨɪɨɫɬɢ Ȧɋ, ɝɞɟ ɩɪɢ Ɇ = Ɇɋ ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɯɨɞɢɬ ɜ ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ ɪɟɠɢɦ ɪɚɛɨɬɵ. ȼ ɩɪɨɰɟɫɫɟ ɪɚɡɝɨɧɚ ɞɜɢɝɚɬɟɥɹ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɭɦɟɧɶɲɚɸɬ ɩɨ ɜɟɥɢɱɢɧɟ, ɨɛɟɫɩɟɱɢɜɚɹ ɩɟɪɟɤɥɸɱɟɧɢɟ ɫɬɭɩɟɧɟɣ ɩɭɫɤɨɜɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɩɨ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɟ. ɉɟɪɟɤɥɸɱɟɧɢɟ ɫɬɭɩɟɧɟɣ ɜɵɩɨɥɧɹɟɬɫɹ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɜ ɮɭɧɤɰɢɢ ɜɪɟɦɟɧɢ, ɬɨɤɚ, ɫɤɨɪɨɫɬɢ. ɉɪɚɜɢɥɶɧɚɹ ɩɭɫɤɨɜɚɹ ɞɢɚɝɪɚɦɦɚ ɫɬɪɨɢɬɫɹ ɢɡ ɭɫɥɨɜɢɹ ɩɨɞɞɟɪɠɚɧɢɹ ɩɨɫɬɨɹɧɫɬɜɚ ɫɪɟɞɧɟɝɨ ɩɭɫɤɨɜɨɝɨ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ, ɨɛɟɫɩɟɱɢɜɚɹ ɪɚɜɟɧɫɬɜɨ ɦɚɤɫɢɦɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ Ɇ1 ɧɚ ɤɚɠɞɨɣ ɢɡ ɩɭɫɤɨɜɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɚ ɬɚɤɠɟ ɪɚɜɟɧɫɬɜɨ ɦɨɦɟɧɬɨɜ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 (ɫɦ. ɪɢɫ. 3.13). ɉɨɪɹɞɨɤ ɪɚɫɱɟɬɚ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ ɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ: – ɩɨ ɡɚɞɚɧɧɨɦɭ ɫɩɨɫɨɛɭ ɩɭɫɤɚ (ɮɨɪɫɢɪɨɜɚɧɧɵɣ, ɫ ɞɨɩɭɫɬɢɦɵɦ ɭɫɤɨɪɟɧɢɟɦ, ɧɨɪɦɚɥɶɧɵɣ) ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɨɦɟɧɬ Ɇ1 (ɢɥɢ Ɇ2); – ɩɪɢ Ȧ = 0 ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ R = Uɇ / I1, ɝɞɟ I1 = Ɇ1 / kɎɇ; – ɪɚɡɛɢɜɚɟɬɫɹ RȾɈȻ ɧɚ ɫɬɭɩɟɧɢ, ɨɛɟɫɩɟɱɢɜɚɹ ɩɪɚɜɢɥɶɧɭɸ ɩɭɫɤɨɜɭɸ ɞɢɚɝɪɚɦɦɭ. ɋɨɜɪɟɦɟɧɧɵɟ ɫɬɚɧɰɢɢ ɭɩɪɚɜɥɟɧɢɹ ɜɵɩɭɫɤɚɸɬ ɫ ɞɜɭɦɹ – ɬɪɟɦɹ ɫɬɭɩɟɧɹɦɢ. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɱɢɫɥɚ ɫɬɭɩɟɧɟɣ ɪɚɫɬɭɬ ɝɚɛɚɪɢɬɵ ɢ ɫɬɨɢɦɨɫɬɶ ɭɫɬɚɧɨɜɤɢ, ɧɨ ɫɧɢ-

58

ɡɢɬɶ ɜɪɟɦɹ ɩɭɫɤɚ ɧɟ ɭɞɚɟɬɫɹ, ɬɚɤ ɤɚɤ ɤɚɠɞɵɣ ɚɩɩɚɪɚɬ ɨɛɥɚɞɚɟɬ ɤɨɧɟɱɧɵɦ ɛɵɫɬɪɨɞɟɣɫɬɜɢɟɦ. Ȧ

Ȧ ɨɧ Ȧɫ

ɟɫɬ

Ȧ2

2

Ȧ1

1 Ɇɋ

Ɇ2

Ɇ

Ɇ1

Ɋɢɫ. 3.13. ɉɪɚɜɢɥɶɧɚɹ ɩɭɫɤɨɜɚɹ ɞɢɚɝɪɚɦɦɚ ɉɪɢ Ȧ = Ȧ1 ɬɨɤɢ ɹɤɨɪɹ I2

UH E1 , I

1

UH E1 ,

ɬɨɝɞɚ

I1 I2

R1 . R2

UH E2 , I

UH E ,

ɬɨɝɞɚ

I1 I2

R1 . rə

R1

R2

ɉɪɢ Ȧ = Ȧ2 ɬɨɤɢ ɹɤɨɪɹ I2

1

R2

rə

ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɢ ɩɪɢ ɛɨɥɶɲɟɦ ɱɢɫɥɟ ɫɬɭɩɟɧɟɣ ɨɬɧɨɲɟɧɢɟ ɬɨɤɨɜ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɨɫɬɚɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɩɨɫɬɨɹɧɧɨɣ I1 I2

R1 R2

R2 R3

...

Rm rə

O,

ɨɬɤɭɞɚ R1 = Ȝ ǜ R2 = Ȝ2 R3 =…= Ȝm rə. Ɉɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ Ɇ1 ɤ ɦɨɦɟɧɬɭ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2: Ȝ

I1 I2

M1 M2

m

R1 rə

m

1 . I1 rə

(3.29)

ɇɟɨɛɯɨɞɢɦɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ Ɇ2 t 1,2 Ɇɋ . ȿɫɥɢ ɷɬɨ ɧɟɪɚɜɟɧɫɬɜɨ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɩɪɢɞɟɬɫɹ ɭɜɟɥɢɱɢɬɶ ɱɢɫɥɨ ɫɬɭɩɟɧɟɣ m, ɟɫɥɢ Ɇ1 = ɆɆȺɄɋ ȾɈɉ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɪɚɡɛɢɟɧɢɹ RȾɈȻ = R1 ɧɚ ɫɬɭɩɟɧɢ ɡɚɞɚɟɦɫɹ ɬɨɤɨɦ I1, ɱɢɫɥɨɦ ɫɬɭɩɟɧɟɣ m ɢ ɨɩɪɟɞɟɥɹɟɦ Ȝ = I1 / I2. ɉɨ ɜɟɥɢɱɢɧɟ Ȝ ɪɚɫɫɱɢɬɵɜɚɟɦ ɩɨɥɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɧɚ ɩɭɫɤɨɜɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ: – R1 – ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 1; – R2 = R1 / Ȝ – ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 2; – R3 = R2 / Ȝ = R1 / Ȝ2 – ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 3 ɢ ɬ.ɞ. 59

ɋɨɩɪɨɬɢɜɥɟɧɢɹ ɫɬɭɩɟɧɟɣ: R1ȾɈȻ

R1 R 2 ; R 2 ȾɈȻ

R 2 rə .

Ɋɚɫɱɟɬ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ ɦɨɠɧɨ ɜɵɩɨɥɧɢɬɶ ɝɪɚɮɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ ɩɪɢɛɥɢɠɟɧɧɨɫɬɶ ɬɚɤɨɝɨ ɦɟɬɨɞɚ ɪɚɫɱɟɬɚ ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɫ ɩɪɹɦɨɥɢɧɟɣɧɵɦɢ ɦɟɯɚɧɢɱɟɫɤɢɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ, ɪɚɫɫɦɨɬɪɟɧɧɵɦ ɜɵɲɟ. ɇɢɠɟ ɭɛɟɞɢɦɫɹ, ɱɬɨ ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɫ ɧɟɥɢɧɟɣɧɵɦɢ ɦɟɯɚɧɢɱɟɫɤɢɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɛɟɡ ɝɪɚɮɢɱɟɫɤɨɝɨ ɦɟɬɨɞɚ ɧɟ ɨɛɨɣɬɢɫɶ. Ɋɚɫɱɟɬ ɝɪɚɮɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ ɩɪɨɳɟ ɜɟɫɬɢ ɜ ɨ.ɟ. 1. ɋɬɪɨɢɬɫɹ ɟɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ (ɪɢɫ 3.14). 2. Ɂɚɞɚɟɦɫɹ ɬɨɤɚɦɢ I1 ɢ I2 (ɢɥɢ ɦɨɦɟɧɬɚɦɢ Ɇ1 ɢ Ɇ2 , ɜ ɨ.ɟ. ɨɧɢ ɪɚɜɧɵ). 3. Ɇɟɬɨɞɨɦ ɩɨɞɛɨɪɚ ɫɬɪɨɢɬɫɹ ɩɪɚɜɢɥɶɧɚɹ ɩɭɫɤɨɜɚɹ ɞɢɚɝɪɚɦɦɚ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɩɟɪɟɯɨɞ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɫɨɜɩɚɥ ɫ ɦɨɦɟɧɬɨɦ Ɇ1 . ȿɫɥɢ ɦɨɦɟɧɬɵ ɧɟ ɫɨɜɩɚɥɢ, ɜɧɨɜɶ ɡɚɞɚɸɬɫɹ ɦɨɦɟɧɬɨɦ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 ɢ ɩɨɜɬɨɪɹɸɬ ɩɨɫɬɪɨɟɧɢɟ, ɢ ɬɚɤ ɞɨ ɫɨɜɩɚɞɟɧɢɹ ɦɨɦɟɧɬɨɜ.

Ȧ

a

1

b

ɟɫɬ

c d

Ȧɋ

3

e

2

1 Ɇɋ

1

Ɇ2

Ɇ

Ɇ1

Ɋɢɫ. 3.14. Ɋɚɫɱɟɬ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ ɝɪɚɮɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ 4. ɉɨɫɥɟ ɩɨɫɬɪɨɟɧɢɹ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ ɩɪɢ Ɇ = 1 ɢɡɦɟɪɹɸɬ ɨɬɪɟɡɤɢ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ ɞɨɛɚɜɨɱɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦ ɜ ɞɨɥɹɯ ɨɬ ɢɡɜɟɫɬɧɨɣ ɜɟɥɢɱɢɧɵ ɧɟɜɵɤɥɸɱɚɟɦɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɹɤɨɪɹ ab Ł rə, bc Ł R3ȾɈȻ, cd Ł R2ȾɈȻ, de Ł R1ȾɈȻ, ɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɬɭɩɟɧɟɣ de cd bc . R1ȾɈȻ rə , R 2 ȾɈȻ rə ,R3 ȾɈȻ rə ab ab ab 60

ɉɪɢ ɧɨɪɦɚɥɶɧɨɦ ɩɭɫɤɟ ɡɚɞɚɸɬɫɹ ɦɨɦɟɧɬɨɦ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 ~ 1,2Ɇɋ ɢ ɪɚɫɱɟɬ ɜɵɩɨɥɧɹɸɬ ɩɨ ɮɨɪɦɭɥɟ Ȝ

M1 M2

m 1

1 , I2 rə

(3.30)

ɚ ɞɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ ɚɧɚɥɨɝɢɱɟɧ ɩɪɟɞɵɞɭɳɟɦɭ ɚɧɚɥɢɬɢɱɟɫɤɨɦɭ. ɇɟɨɛɯɨɞɢɦɨ ɥɢɲɶ ɩɪɨɜɟɪɢɬɶ ɜɟɥɢɱɢɧɭ Ɇ1 d ɆɆȺɄɋ ȾɈɉ, ɱɬɨɛɵ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɧɟ ɩɪɟɜɨɫɯɨɞɢɥɨ ɞɨɩɭɫɬɢɦɨɟ ɡɧɚɱɟɧɢɟ ɩɨ ɭɫɥɨɜɢɹɦ ɤɨɦɦɭɬɚɰɢɢ. 3.1.7. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ Ⱦɇȼ

ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɩɪɢɡɜɚɧɚ ɧɚɝɥɹɞɧɨ ɩɨɤɚɡɚɬɶ ɩɨɬɪɟɛɥɹɟɦɭɸ ɢɡ ɫɟɬɢ ɢ ɩɨɥɟɡɧɭɸ ɧɚ ɜɚɥɭ ɦɨɳɧɨɫɬɢ ɢ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɩɪɨɰɟɫɫɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɧɟɪɝɢɢ ɢ ɩɨɤɚɡɚɬɶ ɢɯ ɫɨɨɬɧɨɲɟɧɢɟ. Ɋɚɫɫɦɨɬɪɢɦ ɞɜɢɝɚɬɟɥɶɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ (Ɇ > 0, Ȧ > 0). ɇɚɩɪɹɠɟɧɢɟ, ɩɪɢɥɨɠɟɧɧɨɟ ɤ ɹɤɨɪɸ ɞɜɢɝɚɬɟɥɹ, ɭɪɚɜɧɨɜɟɲɢɜɚɟɬɫɹ ɗȾɋ ɢ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɤɬɢɜɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ. U E I rə R ȾɈȻ .

ɍɦɧɨɠɢɦ ɨɛɟ ɱɚɫɬɢ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɧɚ ɬɨɤ ɹɤɨɪɹ I U I E I I2 rə I2 R ȾɈȻ ,

(3.31)

ɝɞɟ UI = Ɋɋ – ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɢɡ ɫɟɬɢ; I2rə = 'Ɋ ə – ɩɨɬɟɪɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɦɨɳɧɨɫɬɢ ɜ ɧɟɜɵɤɥɸɱɚɟɦɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɹɤɨɪɹ; I2RȾɈȻ = ǻɊȾɈȻ – ɩɨɬɟɪɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɦɨɳɧɨɫɬɢ ɜ ɞɨɛɚɜɨɱɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɹɤɨɪɹ; EI = (kɎɇ Ȧ) (M / kɎɇ) = Ɇ Ȧ = ɊɆ – ɦɟɯɚɧɢɱɟɫɤɚɹ (ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ) ɦɨɳɧɨɫɬɶ; Ɋȼ – ɩɨɥɟɡɧɚɹ ɦɨɳɧɨɫɬɶ (ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ); ǻɊɆȿɏ – ɩɨɬɟɪɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɦɨɳɧɨɫɬɢ (ɜɧɭɬɪɢ ɞɜɢɝɚɬɟɥɹ – ɧɚ ɬɪɟɧɢɟ ɜ ɩɨɞɲɢɩɧɢɤɚɯ, ɧɚ ɜɟɧɬɢɥɹɰɢɸ, ɧɚ ɩɟɪɟɦɚɝɧɢɱɢɜɚɧɢɟ ɜ ɫɬɚɥɢ ɹɤɨɪɹ). Ɉɛɵɱɧɨ ɫɱɢɬɚɸɬ ǻɊɆȿɏ § const, ɧɟ ɡɚɜɢɫɹɳɢɦɢ ɨɬ ɧɚɝɪɭɡɤɢ. Ɉɰɟɧɤɭ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɧɟɪɝɢɢ ɜɵɩɨɥɧɹɸɬ ɫ ɩɨɦɨɳɶɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ ɄɉȾ Ș = Ș ɊɉɈɅ / ɊɁȺɌɊ, ɱɢɫɥɟɧɧɨ ɪɚɜɧɨɝɨ ɨɬɧɨɲɟɧɢɸ ɦɨɳɧɨȘɇ Ɋ ȼ ɫɬɢ ɩɨɥɟɡɧɨɣ ɊɉɈɅ ɤ ɦɨɳɊɆ Ɋɋ ɧɨɫɬɢ ɡɚɬɪɚɱɟɧɧɨɣ ɊɁȺɌɊ. ɇɚ ɪɢɫ. 3.15 ɩɪɢɜɟɞɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ Ș = f(PɉɈɅ), ǻPɆȿɏ ɩɨɫɬɪɨɟɧɧɚɹ ɩɪɢ ɪɚɛɨɬɟ ǻPȾɈȻ Ɋ ɞɜɢɝɚɬɟɥɹ ɧɚ ɟɫɬɟɫɬɜɟɧǻPə ɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ. Ɋɇ ɉɪɢ ɧɨɦɢɧɚɥɶɧɨɣ ɦɨɳɧɨɫɬɢ Ș ɇ = 0.75…0.95, Ɋɢɫ. 3.15. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɧɨɦɢɢ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ Ⱦɇȼ ɧɚɥɶɧɨɣ ɦɨɳɧɨɫɬɢ Ɋɇ 61

ɞɜɢɝɚɬɟɥɹ ɄɉȾ ɪɚɫɬɟɬ. ɉɪɢ ɧɚɪɚɫɬɚɧɢɢ ɧɚɝɪɭɡɤɢ ɊɉɈɅ ɧɚ ɜɚɥɭ ɄɉȾ ɪɚɫɬɟɬ ɜ ɫɜɹɡɢ ɫ ɪɨɫɬɨɦ ɩɨɥɟɡɧɨɣ ɦɨɳɧɨɫɬɢ, ɩɪɢ ɊɉɈɅ § Ɋɇ ɄɉȾ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɭɦɚ, ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɪɨɫɬɟ ɊɉɈɅ ɄɉȾ ɫɧɢɠɚɟɬɫɹ ɜ ɫɜɹɡɢ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɩɨɬɟɪɶ ɦɨɳɧɨɫɬɢ ɜɧɭɬɪɢ ɦɚɲɢɧɵ. 3.1.8. Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ Ⱦɇȼ

Ɍɨɪɦɨɡɧɵɦ ɧɚɡɵɜɚɸɬ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɢɡɛɵɬɨɱɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɩɪɟɜɪɚɳɚɟɬ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɜɨɞɢɬɫɹ ɜ ɝɟɧɟɪɚɬɨɪɧɵɣ ɪɟɠɢɦ. ɂɫɬɨɱɧɢɤɚɦɢ ɢɡɛɵɬɨɱɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɹɜɥɹɸɬɫɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ, ɡɚɩɚɫɟɧɧɚɹ ɩɨɞɧɹɬɵɦ ɝɪɭɡɨɦ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɟɦɚ ɢɥɢ ɞɜɢɠɭɳɢɦɫɹ ɩɨɞ ɭɤɥɨɧ ɬɪɚɧɫɩɨɪɬɧɵɦ ɦɟɯɚɧɢɡɦɨɦ, ɢ ɢɡɛɵɬɨɱɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ, ɫɨɡɞɚɜɚɟɦɚɹ ɩɪɢ ɫɧɢɠɟɧɢɢ ɫɤɨɪɨɫɬɢ ɞɜɢɠɭɳɢɦɢɫɹ ɢɧɟɪɰɢɨɧɧɵɦɢ ɦɚɫɫɚɦɢ. ɋ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɬɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ: – ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɫɩɭɫɤɟ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɩɨɞɞɟɪɠɚɧɢɟ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɢ ɦɟɯɚɧɢɡɦɚ ɩɪɢ ɞɜɢɠɟɧɢɢ ɧɚ ɫɩɭɫɤɟ (ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɞɥɹ ɚɤɬɢɜɧɨɝɨ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ); – ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɜɵɛɟɝɟ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɰɟɥɶɸ ɨɫɬɚɧɨɜɤɢ ɩɪɢɜɨɞɚ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɡɚɞɚɧɧɨɟ ɜɪɟɦɹ ɨɫɬɚɧɨɜɤɢ ɞɜɢɝɚɬɟɥɹ (Ɍȼ). ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɩɨɬɪɟɛɥɟɧɢɹ ɢɡɛɵɬɨɱɧɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɬɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ: – ɪɟɤɭɩɟɪɚɬɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ (ɊɌ), ɩɪɢ ɤɨɬɨɪɨɦ ɢɡɛɵɬɨɱɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɫɟɬɶ; – ɬɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ (ɉȼ), ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɢɡɛɵɬɨɱɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɩɨɥɭɱɚɟɬ ɫ ɜɚɥɚ, ɩɪɟɨɛɪɚɡɭɟɬ ɟɟ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɟɠɢɦɚ ɉȼ ɩɨɬɪɟɛɥɹɟɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɢɡ ɫɟɬɢ. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫ ɜɚɥɚ ɢ ɢɡ ɫɟɬɢ ɪɚɫɫɟɢɜɚɟɬɫɹ ɧɚ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ; – ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ (ȾɌ), ɩɪɢ ɤɨɬɨɪɨɦ ɞɜɢɝɚɬɟɥɶ ɢɡɛɵɬɨɱɧɭɸ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɪɚɫɫɟɢɜɚɟɬ ɧɚ ɨɬɞɟɥɶɧɨ ɜɤɥɸɱɺɧɧɵɣ ɪɟɡɢɫɬɨɪ. Ɋɟɤɭɩɟɪɚɬɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ (ɊɌ). Ɋɟɤɭɩɟɪɚɬɢɜɧɵɦ ɬɨɪɦɨɠɟɧɢɟɦ, ɢɥɢ ɩɪɨɫɬɨ ɪɟɤɭɩɟɪɚɰɢɟɣ, ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɝɟɧɟɪɚɬɨɪɧɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɨɬɞɚɱɟɣ ɷɧɟɪɝɢɢ ɜ ɫɟɬɶ. ɉɪɢ ɪɚɛɨɬɟ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɞɜɢɝɚɬɟɥɶ ɩɨɬɪɟɛɥɹɟɬ ɬɨɤ I ɢɡ ɫɟɬɢ (ɫɩɥɨɲɧɵɟ ɫɬɪɟɥɤɢ ɧɚ ɪɢɫ. 3.16). Ⱦɥɹ ɨɬɞɚɱɢ ɷɧɟɪɝɢɢ ɜ ɫɟɬɶ ɬɨɤ ɹɤɨɪɹ ɞɨɥɠɟɧ ɢɡɦɟɧɢɬɶ ɧɚɩɪɚɜɥɟɧɢɟ (ɩɭɧɤɬɢɪɧɵɟ ɫɬɪɟɥɤɢ I < 0). I UE . I R rə ȿ=kɎȦ Ʉɪɨɦɟ ɬɨɝɨ, ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɜ ɫɟɬɢ ɩɨɬɪɟɛɢɬɟɥɹ ɷɬɨɣ ɷɧɟɪɝɢɢ, ɩɪɢ ɷɬɨɦ ɧɚɩɪɹɠɟɧɢɟ ɩɨɬɪɟɛɢɬɟɥɹ U E>U ɞɨɥɠɧɨ ɛɵɬɶ ɧɚɩɪɚɜɥɟɧɨ ɜɫɬɪɟɱɧɨ ɗȾɋ ȿ ɞɜɢɝɚɬɟɥɹ, ɪɚɛɨɬɚɸɳɟɝɨ ɝɟɧɟɪɚɬɨɪɨɦ, ɢ ɞɨɥɠɧɨ ɛɵɬɶ ɦɟɧɶɲɟ ɩɨ ɜɟɥɢɱɢɧɟ U < ȿ.. Ɋɢɫ. 3.16. ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ Ⱦɇȼ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɟɠɢɦ ɪɟɤɭɩɟɪɚ–––– ɞɜɢɝɚɬɟɥɶ; – – – ɝɟɧɟɪɚɬɨɪ ɰɢɢ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬ ɩɚɪɚɥɥɟɥɶɧɨɟ ɜɤɥɸɱɟɧɢɟ ɫɟɬɢ ɢ ɝɟɧɟɪɚɬɨɪɚ. 62

ȼɚɪɢɚɧɬɵ ɨɛɟɫɩɟɱɟɧɢɹ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (ɪɢɫ. 3.17): 1. Ⱦɜɢɠɟɧɢɟ ɬɪɚɧɫɩɨɪɬɧɨɝɨ Ȧ ɫɪɟɞɫɬɜɚ ɩɨɞ ɭɤɥɨɧ – ɜ ɷɬɨɦ ɫɥɭȦ0ɇ 2 ɱɚɟ ɩɪɢ ɨɞɧɨɦ ɡɧɚɤɟ ɫɤɨɪɨɫɬɢ ɢɡ1 ɦɟɧɹɟɬ ɡɧɚɤ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɨɬ 4 Ɇ Ɇɋ1 < 0. ɞɜɢɝɚɬɟɥɶ ɧɚ ɟɫɬɟɋ ɧɚ Ȧ0 ɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɩɟɪɟɯɨ5 ɞɢɬ ɢɡ ɬɨɱɤɢ 1 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɩɪɢ ɩɨɞɴɟɦɟ ɜ ɬɨɱɤɭ 2 ɪɟɠɢɆ ɦɚ ɪɟɤɭɩɟɪɚɰɢɢ (ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɧɚ ɫɩɭɫɤɟ). Ɇɋ1 Ɇɋ 2. ɋɩɭɫɤ ɝɪɭɡɚ – ɩɪɢ ɧɟɢɡɦɟɧɧɨɦ ɡɧɚɤɟ Ɇɋ ɞɜɢɝɚɬɟɥɶ ɪɟɜɟɪɫɢɪɭɟɬɫɹ ɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɝɪɭɡɚ ɜɪɚɳɚɟɬɫɹ ɫ ɭɫɬɚɧɨɜɢɜɲɟɣɫɹ ɫɤɨɪɨɫɬɶɸ (ɜ ɬɨɱɤɟ 3) ɜɵɲɟ ɫɤɨɪɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ (Ȧ > 3 Ȧ0ɇ). Ɍɚɤɨɣ ɪɟɠɢɦ ɜɨɡɦɨɠɟɧ ɜ ɫɯɟ-Ȧ0ɇ ɦɟ ɪɢɫ. 3.21. 3. ɉɪɢ ɫɧɢɠɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ (ɜɚɪɢɚɧɬ ɩɢɬɚɧɢɹ ɞɜɢɝɚɬɟɥɹ Ɋɢɫ. 3.17. ȼɚɪɢɚɧɬɵ ɩɪɢɦɟɧɟɧɢɹ ɨɬ ɢɧɞɢɜɢɞɭɚɥɶɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɬɟɥɹ) ɫɧɢɠɚɟɬɫɹ ɫɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Ȧ0 < Ȧ0ɇ. Ⱦɜɢɝɚɬɟɥɶ ɢɡ-ɡɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɢɧɟɪɰɢɢ ɧɟ ɦɨɠɟɬ ɦɝɧɨɜɟɧɧɨ ɢɡɦɟɧɢɬɶ ɫɤɨɪɨɫɬɶ ɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɟɪɟɯɨɞ ɢɡ ɬɨɱɤɢ 1 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɜ ɬɨɱɤɭ 4 ɪɟɠɢɦɚ ɪɟɤɭɩɟɪɚɰɢɢ. ɉɪɢ ɬɚɤɨɦ ɩɟɪɟɯɨɞɟ ɫɨɡɞɚɟɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ, ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇ Ɇɋ

Ɋɋ

J

dȦ dt ɬɚɤ ɠɟ ɨɬɪɢɰɚɬɟɥɶɧɵɣ, ɩɨɷɬɨɦɭ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɧɚɱɢɧɚɟɬ ɫɧɢɠɚɬɶɫɹ, ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɭɦɟɧɶɲɚɟɬɫɹ ɢ ɫɬɪɟɦɢɬɫɹ ɤ Ɇɋ ɜ ɬɨɱɤɭ 5. ɇɚ ɭɱɚɫɬɤɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɨɬ ɬɨɱɤɢ 4 ɞɨ Ȧ0 – ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɪɟɠɢɦɟ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɹ ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɜɵɛɟɝɟ – ɬɨɪɦɨɠɟɧɢɟ ɫ ɰɟɥɶɸ ɨɫɬɚɧɨɜɤɢ. ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɪɟɤɭɩɟɪɚɬɢɜɧɨɦ ɬɨɪɦɨɠɟɧɢɢ ɧɟ ɢɡɦɟɧɹɟɬɫɹ (3.10), ɥɢɲɶ ɢɡɦɟɧɹɟɬɫɹ ɡɧɚɤ ɬɨɤɚ ɹɤɨɪɹ I. ɇɚ ɪɢɫ. 3.18 ɩɪɢɜɟɞɟɧɚ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɪɟɠɢɦɚ ɪɟɤɭ-

Ɋȼ

ǻɊɆȿɏ ǻɊə Ɋɢɫ. 3.18. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ

63

ɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. ɇɚɩɪɚɜɥɟɧɢɟ ɩɨɬɨɤɚ ɦɨɳɧɨɫɬɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɜɢɝɚɬɟɥɶɧɵɦ ɪɟɠɢɦɨɦ – ɨɛɪɚɬɧɨɟ, ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɜ ɫɟɬɶ. Ⱦɨɫɬɨɢɧɫɬɜɚ ɪɟɠɢɦɚ ɊɌ: – ɠɺɫɬɤɢɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɛɟɫɩɟɱɢɜɚɸɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɥɭɱɟɧɢɹ ɭɫɬɨɣɱɢɜɨɣ ɫɤɨɪɨɫɬɢ ɫɩɭɫɤɚ ɩɪɢ ɡɧɚɱɢɬɟɥɶɧɵɯ ɢɡɦɟɧɟɧɢɹɯ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ; – ɜɵɫɨɤɚɹ ɷɤɨɧɨɦɢɱɧɨɫɬɶ, ɢɡɛɵɬɨɱɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɫɟɬɶ ɢ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɚ ɞɪɭɝɢɦ ɦɟɯɚɧɢɡɦɨɦ, ɱɟɦ ɫɧɢɠɚɟɬɫɹ ɩɨɬɪɟɛɥɟɧɢɟ ɷɧɟɪɝɢɢ ɢɡ ɫɟɬɢ. ɇɟɞɨɫɬɚɬɤɢ ɪɟɠɢɦɚ ɊɌ: – ɫɥɨɠɧɨɫɬɶ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɞɚɧɧɨɝɨ ɪɟɠɢɦɚ ɩɪɢ ɩɢɬɚɧɢɹ Ⱦɇȼ ɨɬ ɫɟɬɢ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ; – ɧɟɨɛɯɨɞɢɦ ɩɨɬɪɟɛɢɬɟɥɶ ɷɧɟɪɝɢɢ ɪɟɤɭɩɟɪɚɰɢɢ. ɉɪɢ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɧɚ ɩɟɪɟɦɟɧɧɨɦ ɬɨɤɟ ɢɫɬɨɱɧɢɤɢ ɷɧɟɪɝɢɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɱɚɫɬɨ ɫɨɡɞɚɸɬɫɹ ɧɚ ɛɚɡɟ ɧɟɭɩɪɚɜɥɹɟɦɵɯ ɜɵɩɪɹɦɢɬɟɥɟɣ, ɤɨɬɨɪɵɟ ɧɟ ɦɨɝɭɬ ɩɪɢɧɢɦɚɬɶ ɷɧɟɪɝɢɸ ɪɟɤɭɩɟɪɚɰɢɢ. ȿɫɥɢ ɩɨɬɪɟɛɢɬɟɥɶ ɷɧɟɪɝɢɢ ɪɟɤɭɩɟɪɚɰɢɢ ɨɬɫɭɬɫɬɜɭɟɬ, ɩɨ ɰɟɩɢ ɹɤɨɪɹ ɬɨɤ ɧɟ ɩɪɨɬɟɤɚɟɬ, ɧɟ ɫɨɡɞɚɟɬɫɹ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ, ɝɪɭɡ ɩɚɞɚɟɬ (!?). Ɉɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɊɌ: – ɝɪɭɡɨɩɨɞɴɟɦɧɵɟ ɦɟɯɚɧɢɡɦɵ (ɤɪɚɧɵ, ɥɢɮɬɵ ɢ ɬ.ɩ.); – ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɪɚɧɫɩɨɪɬ; – ɫɢɫɬɟɦɵ ɫ ɢɧɞɢɜɢɞɭɚɥɶɧɵɦ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɦ (Ɍɉ – Ⱦ, Ƚ – Ⱦ). Ɍɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ (ɉȼ). Ɋɟɠɢɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ – ɬɨɪɦɨɡɧɨɣ ɪɟɠɢɦ, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɜɤɥɸɱɺɧ ɞɥɹ ɨɞɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɜɪɚɳɟɧɢɹ, ɧɨ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɢɯ ɫɢɥ ɜɪɚɳɚɟɬɫɹ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɫɬɨɪɨɧɭ. ɋɦɵɫɥ ɪɟɠɢɦɚ ɉȼ ɦɨɠɧɨ ɩɨɹɫɧɢɬɶ ɧɚ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ (ɪɢɫ. 3.19). ɉɭɫɬɶ ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ 1 ɫ ɚɤɬɢɜɧɵɦ ɫɬɚɬɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ Ɇɋ. ɉɪɢ ɜɜɟɞɟɧɢɢ ɜ ɰɟɩɶ ɹɤɨɪɹ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R1 ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɫɧɢɡɢɬɫɹ, ɧɨ ɟɫɥɢ ɭɜɟɥɢɱɢɬɶ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɞɨ (R1 + R2), ɬɨ Ɇɋ > ɆɄɁ, ɢ ɚɤɬɢɜɧɵɣ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ ɡɚɫɬɚɜɢɬ ɞɜɢɝɚɬɟɥɶ ɜɪɚɳɚɬɶɫɹ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɜ ɬɨɱɤɟ 2. ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɬɚɤɨɝɨ ɪɟɠɢɦɚ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. Ȧ 3.20. ȿɫɥɢ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ȿ ɧɚ1 ɩɪɚɜɥɟɧɚ ɧɚɜɫɬɪɟɱɭ ɧɚɩɪɹɠɟɧɢɸ ɫɟɬɢ U ɟɫɬ 3 (ɫɩɥɨɲɧɵɟ ɫɬɪɟɥɤɢ), ɬɨ ɜ ɬɨɱɤɟ 2 ɩɪɢ ɧɟɢɡɦɟɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɬɨɤɚ ɢɡɦɟɧɢɥɨɫɶ ɧɚR1 ɉȼ Ɇ ɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɟ ɞɜɢɝɚɬɟɥɹ, ɡɧɚɤ ȿ ɩɨɦɟɧɹɥɫɹ ɧɚ ɨɛɪɚɬɧɵɣ (ɩɭɧɤɬɢɪɧɚɹ ɫɬɪɟɥɤɚ) ɢ ɫɬɚɥ ɫɨɜɩɚɞɚɸɳɢɦ ɫ ɧɚɩɪɹɠɟɧɢɟɦ ɫɟɬɢ. 4 ɆC Ɍɟɩɟɪɶ ɝɟɧɟɪɚɬɨɪ ɪɚɛɨɬɚɟɬ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫ ɫɟɬɶɸ, ɫɭɦɦɚ ɧɚɩɪɹɠɟɧɢɣ U + ȿ R1+R2 ɩɪɢɥɨɠɟɧɚ ɤ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦ ɰɟɩɢ ɹɤɨɪɹ, ɢ ɉȼ ɞɥɹ ɨɝɪɚɧɢɱɟɧɢɹ ɬɨɤɚ ɹɤɨɪɹ ɜɟɥɢɱɢɧɚ ɷɬɢɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɞɨɥɠɧɚ ɛɵɬɶ ɭɜɟɥɢɱɟɧɚ. 2 ɗɬɨ ɢ ɟɫɬɶ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɉȼ. -Ȧ0ɇ ɇɚ ɪɢɫ. 3.21 ɢɡɨɛɪɚɠɺɧɚ ɫɯɟɦɚ ɷɥɟɤɊɢɫ. 3.19. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɬɪɨɩɪɢɜɨɞɚ ɩɨɞɴɺɦɧɨɝɨ ɦɟɯɚɧɢɡɦɚ. Ʉɨɧɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɪɟɠɢɦɟ ɬɚɤɬɨɪɵ Ʉȼ ɜɤɥɸɱɚɸɬɫɹ ɞɥɹ ɞɜɢɠɟɧɢɹ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɜɜɟɪɯ, ɨɫɭɳɟɫɬɜɥɹɹ ɩɨɞɴɟɦ ɝɪɭɡɚ. Ɋɟɡɢ-

64

ɫɬɨɪ R1 ɨɝɪɚɧɢɱɢɜɚɟɬ ɩɭɫɤɨɜɵɟ ɬɨɤɢ. ɨɛɟɫɩɟɱɢɜɚɹ ɩɪɚɜɢɥɶɧɭɸ ɩɭɫɤɨɜɭɸ ɞɢɚ+ ɝɪɚɦɦɭ. Ʉɨɧɬɚɤɬɨɪ Ʉɉȼ ɨɬɤɥɸɱɚɟɬɫɹ ɬɨɥɶɤɨ ɜ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ, ɜ I UC E=kɎȦ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ Ʉɉ ɜɫɟɝɞɚ ɜɤɥɸɱɟɧ. – Ⱦɜɢɝɚɬɟɥɶ ɪɚɡɝɨɧɹɟɬɫɹ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɫ R1, ɩɨɫɥɟ ɜɤɥɸɱɟɧɢɹ Ʉɍ1 ɩɟɊɢɫ. 3.20. ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɪɟɯɨɞɢɬ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢȾɇȼ ɜ ɪɟɠɢɦɟ ɬɨɪɦɨɠɟɧɢɹ ɤɭ ɢ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ 1 (ɫɦ. ɪɢɫ. 3.19). ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ Ⱦɥɹ ɨɫɬɚɧɨɜɤɢ ɞɜɢɝɚɬɟɥɹ ɩɨ ɨɤɨɧɱɚɧɢɢ ɩɨɞɴɟɦɚ ɨɬɤɥɸɱɚɸɬ ɤɨɧɬɚɤɬɨɪɵ Ʉȼ, Ʉɍ1 ɢ Ʉɉ, ɜ ɰɟɩɶ ɹɤɨɪɹ ɜɜɨɞɹɬɫɹ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R1 + R2, ɡɚɬɟɦ ɜɤɥɸɱɚɸɬɫɹ ɤɨɧɬɚɤɬɨɪɵ Ʉɇ. Ʉɨɧɬɚɤɬɨɪɵ Ʉɇ ɨɛɟɫɩɟɱɢɜɚɸɬ ɢɡɦɟɧɟɧɢɟ ɩɨɥɹɪɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ ɞɜɢɝɚɬɟɥɹ (ɪɟɜɟɪɫ ɞɜɢɝɚɬɟɥɹ) ɢ ɜɤɥɸɱɚɸɬɫɹ ɞɥɹ ɉȼ ɧɚ ɜɵɛɟɝɟ ɫ ɰɟɥɶɸ ɨɫɬɚɧɨɜɤɢ ɢ ɞɥɹ ɞɜɢɠɟɧɢɹ ɜɧɢɡ ɞɥɹ ɫɩɭɫɤɚ ɝɪɭɡɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɷɬɢɯ ɩɟɪɟɤɥɸɱɟɧɢɣ ɞɜɢɝɚɬɟɥɶ ɢɡ ɬɨɱɤɢ 1 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɩɟɪɟɯɨɞɢɬ ɜ ɬɨɱɤɭ 3 ɪɟɠɢɦɚ ɉȼ ɢ ɫɧɢɠɚɟɬ ɫɤɨɪɨɫɬɶ ɞɨ ɨɫɬɚɧɨɜɤɢ ɜ ɬɨɱɤɟ 4. ȿɫɥɢ ɜ ɬɨɱɤɟ 4 ɧɟ ɨɬɤɥɸɱɢɬɶ ɤɨɧɬɚɤɬɨɪɵ Ʉɇ ɢ ɨɫɬɚɜɢɬɶ ɹɤɨɪɶ ɩɨɞɤɥɸɱɟɧɧɵɦ ɤ ɫɟɬɢ, ɞɜɢɝɚɬɟɥɶ ɧɚɱɧɟɬ ɪɚɡɝɨɧ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ, ɱɬɨ ɱɚɫɬɨ ɩɪɨɫɬɨ ɨɩɚɫɧɨ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɫɩɭɫɤɚ ɝɪɭɡɚ ɜ ɪɟɠɢɦɟ ɉȼ ɞɨɫɬɚɬɨɱɧɨ ɩɪɢ ɜɤɥɸɱɟɧɧɨɦ Ʉȼ ɜɜɟɫɬɢ ɜ ɰɟɩɶ ɹɤɨɪɹ ɪɟɡɢɫɬɨɪɵ R1 + R2, ɢ ɞɜɢɝɚɬɟɥɶ ɡɚ ɫɱɟɬ ɦɚɫɫɵ ɝɪɭɡɚ ɢɡɦɟɧɢɬ ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɹ ɢ ɨɛɟɫɩɟɱɢɬ ɫɩɭɫɤ ɝɪɭɡɚ ɜ ɪɟɠɢɦɟ ɉȼ. ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɉȼ ɧɟ ɢɡɦɟɧɹɟɬɫɹ (3.10), ɥɢɲɶ ɢɡɦɟɧɹɟɬɫɹ ɡɧɚɤ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢ ɪɟɜɟɪɫɟ. ȼ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɗȾɋ ɞɜɢɝɚɬɟɥɹ ɞɟɣɫɬɜɭɟɬ ɫɨɝɥɚɫɧɨ ɫ ɧɚɩɪɹɠɟɧɢɟɦ ɫɟɬɢ (ɫɦ. ɪɢɫ. 3.19), ɢ ɬɨɤ ɹɤɨɪɹ ɛɭɞɟɬ ɪɚɜɟɧ Rɉȼ

rə

I

UE R

(3.32)

ɢ ɧɟɨɛɯɨɞɢɦɨ ɫɭɳɟɫɬɜɟɧɧɨ ɭɜɟɥɢɱɢɬɶ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɹ, ɱɬɨɛɵ ɬɨɤ ɧɟ ɜɵɲɟɥ ɡɚ ɩɪɟɞɟɥɵ ɞɨɩɭɫɬɢɦɨɝɨ. LM Ʉȼ

Ʉɇ

Ʉɍ1

Ʉɉȼ

RȾɌ ɄȾ Ʉɇ

R1

Ɇ

Ʉȼ

Ɋɢɫ. 3.21. ɋɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɟɦɚ 65

R2

ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɪɟɠɢɦɚ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 3.22, ɢɡ ɤɨɬɨɪɨɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ ɦɨɳɧɨɫɬɶ ɩɨɬɪɟɛɥɹɟɬɫɹ ɢɡ ɫɟɬɢ ɢ ɫ ɜɚɥɚ ɢ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɹɤɨɪɧɨɣ ɰɟɩɢ. UC E I R ȾɈȻ I rə, PC PM

u I

'PȾɈȻ 'Ɋə.

Ⱦɨɫɬɨɢɧɫɬɜɚ ɬɨɪɦɨɠɟɧɢɹ ɉȼ: – ɢɧɬɟɧɫɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ ɞɨ ɩɨɥɧɨɣ ɨɫɬɚɧɨɜɤɢ; PC PB PɆ – ɩɪɨɫɬɨɬɚ ɨɫɭɳɟɫɬɜɥɟɧɢɹ – ɜɤɥɸɱɟɧɢɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜǻPə ǻPȾɈȻ ɥɟɧɢɹ. ǻPɆȿɏ ɇɟɞɨɫɬɚɬɤɢ ɪɟɠɢɦɚ: – ɨɱɟɧɶ ɦɹɝɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – Ɋɢɫ. 3.22. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɫɭɳɟɫɬɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ ɫɤɨɪɨɫɬɢ ɞɢɚɝɪɚɦɦɚ ɉȼ ɫɩɭɫɤɚ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɦɚɫɫɵ ɝɪɭɡɚ; – ɷɧɟɪɝɢɹ ɢɡ ɫɟɬɢ ɢ ɷɧɟɪɝɢɹ ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɢɞɟɬ ɧɚ ɩɨɬɟɪɢ – ɧɟɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɚɹ ɷɧɟɪɝɟɬɢɤɚ; – ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɨɬɤɥɸɱɟɧɢɹ ɩɪɢɜɨɞɚ ɩɪɢ ɫɤɨɪɨɫɬɢ, ɛɥɢɡɤɨɣ ɤ ɧɭɥɸ ɢɡ-ɡɚ ɨɩɚɫɧɨɫɬɢ ɪɚɡɜɨɪɨɬɚ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ. Ɉɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɪɟɠɢɦɚ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɧɚ ɞɜɢɝɚɬɟɥɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ (ɞɨ 100 ɤȼɬ), ɝɞɟ ɩɨɬɟɪɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟ ɜɟɥɢɤɢ, ɚ ɩɪɨɫɬɨɬɚ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɪɟɠɢɦɚ ɢɦɟɟɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ (ɤɪɚɧɨɜɨɟ ɯɨɡɹɣɫɬɜɨ ɢ ɩɪɨɫɬɟɣɲɢɟ ɦɟɯɚɧɢɡɦɵ ɫ ɧɢɡɤɢɦɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦɢ ɬɪɟɛɨɜɚɧɢɹɦɢ). Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ (ȾɌ). Ɋɟɠɢɦɨɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɧɚɡɵɜɚɸɬ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ, ɩɪɢ ɤɨɬɨɪɨɦ ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɨɫɬɚɺɬɫɹ ɩɨɞɤɥɸɱɟɧɧɨɣ ɤ ɫɟɬɢ, ɚ ɹɤɨɪɶ ɞɜɢɝɚɬɟɥɹ ɨɬɤɥɸɱɚɟɬɫɹ ɨɬ ɫɟɬɢ ɢ ɡɚɦɵɤɚɟɬɫɹ ɧɚ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ (RȾɌ), ɚ ɜ ɧɟɤɨɬɨɪɵɯ ɫɥɭɱɚɹɯ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɧɢɡɤɢɯ ɫɤɨɪɨɫɬɟɣ ɫɩɭɫɤɚ – ɩɪɨɫɬɨ ɡɚɤɨɪɚɱɢɜɚɟɬɫɹ (RȾɌ = 0). Ⱦɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ 1 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ. Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɪɟɠɢɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (ɫɦ. ɪɢɫ. 3.21) ɧɟɨɛɯɨɞɢɦɨ ɨɬɤɥɸɱɢɬɶ ɤɨɧɬɚɤɬɨɪɵ ɧɚɩɪɚɜɥɟɧɢɹ Ʉȼ, Ʉɇ ɢ ɜɤɥɸɱɢɬɶ ɤɨɧɬɚɤɬɨɪ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɄȾ. ɉɪɢ ɷɬɨɦ ɫɯɟɦɚ ɛɭɞɟɬ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɪɢɫ. 3.23.

UC Ȧ

LM

1

ɟɫɬ

2 Ɇ

Ɇ RȾɌ

3

MC RȾɌ

ǻɊȾɌ

ɊɆȿɏ

ǻPə ǻPɆȿɏ

Ɋɢɫ. 3.23. ɋɯɟɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ, ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ 66

Ɋȼ

ɉɨɬɨɤ ɞɜɢɝɚɬɟɥɹ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɵɦ, ɗȾɋ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ, ɩɪɢ ɡɚɦɵɤɚɧɢɢ ɹɤɨɪɹ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɗȾɋ ɫɨɡɞɚɟɬ ɬɨɤ ɬɨɪɦɨɡɧɨɝɨ ɪɟɠɢɦɚ, ɜɨɡɧɢɤɚɟɬ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ ɜ ɬɨɱɤɟ 2. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɝɨ ɦɨɦɟɧɬɚ ɢ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɫɤɨɪɨɫɬɶ ɫɧɢɠɚɟɬɫɹ, ɭɦɟɧɶɲɚɟɬɫɹ ɗȾɋ, ɚ ɜɦɟɫɬɟ ɫ ɧɟɣ – ɬɨɤ ɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ. Ɍɚɤ ɜɵɩɨɥɧɹɟɬɫɹ ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɜɵɛɟɝɟ. ɉɪɢ Ȧ = 0 ɗȾɋ, ɬɨɤ ɢ ɦɨɦɟɧɬ ɨɬɫɭɬɫɬɜɭɸɬ. ȿɫɥɢ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ – ɚɤɬɢɜɧɵɣ, ɬɨ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɝɨ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɶ ɛɭɞɟɬ ɪɚɡɝɨɧɹɬɶɫɹ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ, ɢ ɜɧɨɜɶ ɜɨɡɧɢɤɚɟɬ ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. ȼ ɬɨɱɤɟ 3 ɫɨɡɞɚɟɬɫɹ ɭɫɬɨɣɱɢɜɵɣ ɪɟɠɢɦ ɩɨɞɞɟɪɠɚɧɢɹ ɫɤɨɪɨɫɬɢ – ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɫɩɭɫɤɟ (ɫɦ. ɪɢɫ. 3.23). ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɞɢɧɚɦɢɱɟɫɤɨɦ ɬɨɪɦɨɠɟɧɢɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ (3.10), ɧɨ ɧɚɩɪɹɠɟɧɢɟ, ɩɪɢɤɥɚɞɵɜɚɟɦɨɟ ɤ ɹɤɨɪɸ, ɪɚɜɧɨ ɧɭɥɸ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ Ȧ

U R R R . M M -I 2 2 kɎɇ kɎɇ kɎɇ kɎɇ

(3.33)

ɂɡ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɫɥɟɞɭɟɬ, ɱɬɨ ɜɫɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɨɯɨɞɹɬ ɱɟɪɟɡ ɧɭɥɶ. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 3.23. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (ɫɦ. ɪɢɫ.3.23) ɨɬɪɚɠɚɟɬ ɷɧɟɪɝɟɬɢɱɟɫɤɨɟ ɩɨɥɨɠɟɧɢɟ ɪɟɠɢɦɚ. ɗɧɟɪɝɢɹ ɫ ɜɚɥɚ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɩɨɬɟɪɢ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɹɤɨɪɧɨɣ ɰɟɩɢ. ɂɡ ɫɟɬɢ ɩɨɬɪɟɛɥɹɟɬɫɹ ɬɨɥɶɤɨ ɷɧɟɪɝɢɹ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ɞɜɢɝɚɬɟɥɹ, ɧɨ ɨɧɚ ɫɨɫɬɚɜɥɹɟɬ ɥɢɲɶ 2…5% ɨɬ ɧɨɦɢɧɚɥɶɧɨɣ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ. Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ȾɌ ɡɚɧɢɦɚɟɬ ɩɪɨɦɟɠɭɬɨɱɧɨɟ ɩɨɥɨɠɟɧɢɟ ɦɟɠɞɭ ɪɟɤɭɩɟɪɚɬɢɜɧɵɦ ɬɨɪɦɨɠɟɧɢɟɦ ɊɌ ɢ ɬɨɪɦɨɠɟɧɢɟɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɉȼ ɩɨɱɬɢ ɩɨ ɜɫɟɦ ɩɨɤɚɡɚɬɟɥɹɦ: – ɜ ɷɧɟɪɝɟɬɢɤɟ – ɢɡɛɵɬɨɱɧɚɹ ɷɧɟɪɝɢɹ ɜ ɫɟɬɶ ɧɟ ɨɬɞɚɺɬɫɹ (ɤɚɤ ɩɪɢ ɪɟɤɭɩɟɪɚɬɢɜɧɨɦ ɬɨɪɦɨɠɟɧɢɢ), ɧɨ ɢ ɧɟ ɩɨɬɪɟɛɥɹɟɬɫɹ ɢɡ ɫɟɬɢ (ɤɚɤ ɩɪɢ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɢ); – ɬɨɱɧɨɫɬɶ ɩɨɞɞɟɪɠɚɧɢɹ ɫɤɨɪɨɫɬɢ ɧɚ ɫɩɭɫɤɟ – ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɠɺɫɬɱɟ, ɱɟɦ ɜ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ, ɧɨ ɦɹɝɱɟ, ɱɟɦ ɩɪɢ ɪɟɤɭɩɟɪɚɬɢɜɧɨɦ ɬɨɪɦɨɠɟɧɢɢ; – ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɬɨɪɦɨɠɟɧɢɹ ɧɢɠɟ, ɱɟɦ ɩɪɢ ɩɪɨɬɢɜɨɜɥɸɱɟɧɢɢ, ɩɨ ɦɟɪɟ ɫɧɢɠɟɧɢɹ ɫɤɨɪɨɫɬɢ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ ɩɚɞɚɟɬ; ȼɚɠɧɨɟ ɞɨɫɬɨɢɧɫɬɜɨ – ɜɨɡɦɨɠɧɨɫɬɶ ɬɨɱɧɨɣ ɨɫɬɚɧɨɜɤɢ ɩɪɢ ɪɟɚɤɬɢɜɧɨɦ ɫɬɚɬɢɱɟɫɤɨɦ ɦɨɦɟɧɬɟ. Ɉɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ – ɧɟɪɟɜɟɪɫɢɜɧɵɣ ɩɪɢɜɨɞ, ɜ ɪɟɜɟɪɫɢɜɧɨɦ – ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɬɨɱɧɨɣ ɨɫɬɚɧɨɜɤɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɫɫɦɨɬɪɟɜ ɩɪɟɞɥɨɠɟɧɧɵɟ ɜɚɪɢɚɧɬɵ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɡɛɵɬɨɱɧɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɤɚɤ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɭɞɨɜɥɟɬɜɨɪɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɣ, ɬɚɤ ɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɟɟ ɢɫɩɨɥɶɡɨɜɚɧɢɹ, ɜɚɠɧɨ ɧɚɭɱɢɬɶɫɹ ɪɚɡɛɢɪɚɬɶɫɹ ɜ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɚɯ ɢ ɩɪɢɦɟɧɹɬɶ ɢɯ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɫɥɨɜɢɹɦɢ ɪɚɛɨɬɵ ɦɟɯɚɧɢɡɦɚ. ɇɚ ɩɥɨɫɤɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɨɩɪɟɞɟɥɟɧɢɸ ɬɨɪɦɨɡɧɨɝɨ ɪɟɠɢɦɚ ɩɨɦɨɝɭɬ ɬɚɤɢɟ ɢɯ ɨɫɨɛɟɧɧɨɫɬɢ (ɪɢɫ. 3.24): – ɡɧɚɤ Ȧ0ɇ ɨɩɪɟɞɟɥɹɟɬ ɩɨɥɹɪɧɨɫɬɶ ɧɚɩɪɹɠɟɧɢɹ U ɧɚ ɹɤɨɪɟ; – ɡɧɚɤ Ȧ ɨɩɪɟɞɟɥɹɟɬ ɩɨɥɹɪɧɨɫɬɶ ɗȾɋ ɞɜɢɝɚɬɟɥɹ ȿ; – ɟɫɥɢ ɡɧɚɤɢ ɫɤɨɪɨɫɬɟɣ ɫɨɜɩɚɞɚɸɬ ɢ |Ȧ0ɇ| > |Ȧ| – ɪɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɶɧɵɣ; – ɟɫɥɢ ɡɧɚɤɢ ɫɤɨɪɨɫɬɟɣ ɫɨɜɩɚɞɚɸɬ ɢ Ȧ > Ȧ0ɇ > 0 ɢɥɢ – Ȧ < – Ȧ0ɇ < 0 – ɪɟɠɢɦ ɪɟɤɭɩɟɪɚɰɢɢ; 67

– ɟɫɥɢ ɡɧɚɤɢ ɫɤɨɪɨɫɬɟɣ Ȧ ɢ Ȧ0ɇ ɧɟ ɫɨɜɩɚɞɚɸɬ – ɪɟɠɢɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ; – ɩɪɢ Ȧ0ɇ = 0 – ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ.

ɊɌ ȾɌ

Ȧ Ȧ0ɇ ȾɊ

ɉȼ

Ɇ ɉȼ

3.1.9. Ɋɚɫɱɟɬ ɫɯɟɦ ɜɤɥɸɱɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɪɚɛɨɬɭ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ

ȾɊ

Ɉɫɧɨɜɧɨɣ ɡɚɞɚɱɟɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɹɜɥɹɟɬɫɹ ɜɵɩɨɥɧɟɧɢɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɬɪɟɛɨ- Ȧ0ɇ ɊɌ ɜɚɧɢɣ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ – ɨɛɟɫɩɟɱɟɧɢɟ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɫ ɡɚɞɚɧɧɨɣ ɬɟɯɧɨɥɨɝɚɦɢ ɫɤɨɪɨɊɢɫ. 3.24. Ʉ ɨɩɪɟɞɟɥɟɧɢɸ ɪɟɠɢɦɨɜ ɫɬɶɸ ȦɁȺȾ ɩɪɢ ɡɚɞɚɧɧɨɣ ɜɟɥɢɪɚɛɨɬɵ ɧɚ ɩɥɨɫɤɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɱɢɧɟ ɦɨɦɟɧɬɚ ɆɁȺȾ. ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɉɨ ɡɚɞɚɧɧɨɦɭ ɦɨɦɟɧɬɭ ɆɁȺȾ ɢ ɡɚɞɚɧɧɨɣ ɫɤɨɪɨɫɬɢ ȦɁȺȾ ɬɪɟɛɭɟɬɫɹ ɜɵɛɪɚɬɶ ɫɯɟɦɭ ɜɤɥɸɱɟɧɢɹ, ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɭɸ ɞɥɹ ɡɚɞɚɧɧɨɝɨ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɢ ɪɚɫɫɱɢɬɚɬɶ ɢɥɢ ɧɚɩɪɹɠɟɧɢɟ U, ɢɥɢ ɩɨɬɨɤ Ɏ, ɢɥɢ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɪɚɛɨɬɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɟɨɛɯɨɞɢɦɨ ɩɟɪɟɣɬɢ ɨɬ ɦɨɦɟɧɬɚ, ɨɛɵɱɧɨ ɡɚɞɚɧɧɨɝɨ ɧɚ ɜɚɥɭ, ɤ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɦɭ ɦɨɦɟɧɬɭ ɞɜɢɝɚɬɟɥɹ, ɞɥɹ ɱɟɝɨ ɧɭɠɧɨ ɭɱɟɫɬɶ ɩɨɬɟɪɢ ɦɨɦɟɧɬɚ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ ɞɜɢɝɚɬɟɥɹ ǻɆɏɏ ɢ ɪɚɫɫɱɢɬɚɬɶ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ: Ɇɋ ɆɁȺȾ r 'Ɇ ɏɏ ɆɗɆɁȺȾ , (3.34) ȾɌ

ɩɪɢ ɷɬɨɦ ɡɧɚɤ «+» – ɞɥɹ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ, ɤɨɝɞɚ ɩɨɬɟɪɢ ɩɨɤɪɵɜɚɸɬɫɹ ɞɜɢɝɚɬɟɥɟɦ, ɢ «-» – ɞɥɹ ɬɨɪɦɨɡɧɨɝɨ ɪɟɠɢɦɚ, ɜ ɤɨɬɨɪɨɦ ɩɨɬɟɪɢ ɩɨɤɪɵɜɚɸɬɫɹ ɡɚ ɫɱɟɬ ɦɨɳɧɨɫɬɢ, ɢɞɭɳɟɣ ɫ ɜɚɥɚ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. Ɋɚɫɱɟɬ ɜɵɩɨɥɧɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɡɚɩɢɫɚɧɧɨɣ ɜ ɨɛɳɟɦ ɜɢɞɟ (3.10): ȦɁȺȾ

U R MC , kɎ kɎ 2

(3.35)

ɤɨɬɨɪɚɹ ɪɟɲɚɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɫɤɨɦɨɝɨ ɩɚɪɚɦɟɬɪɚ. Ⱦɪɭɝɢɟ ɩɚɪɚɦɟɬɪɵ ɩɪɢɧɢɦɚɸɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɟɫɬɟɫɬɜɟɧɧɨɣ ɫɯɟɦɟ ɜɤɥɸɱɟɧɢɹ: – ɩɪɢ ɪɚɫɱɟɬɟ ɧɚɩɪɹɠɟɧɢɹ UɁȺȾ ɩɪɢɧɢɦɚɸɬ kɎ = kɎɇ ɢ R = rə; – ɩɪɢ ɪɚɫɱɟɬɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RɁȺȾ – kɎ = kɎɇ ɢ U = Uɇ; – ɩɪɢ ɪɚɫɱɟɬɟ ɩɨɬɨɤɚ kɎɁȺȾ – U = Uɇ ɢ R = rə. ɉɪɢ ɪɚɫɱɟɬɟ ɜ ɨ.ɟ. ɪɟɲɟɧɢɟ ɩɨɫɬɚɜɥɟɧɧɨɣ ɡɚɞɚɱɢ ɭɩɪɨɳɚɟɬɫɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɭɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɡɚɩɢɫɵɜɚɟɬɫɹ ɫ ɭɱɟɬɨɦ ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɩɚɪɚɦɟɬɪɚ, ɤɨɝɞɚ ɞɪɭɝɢɟ ɩɚɪɚɦɟɬɪɵ ɩɪɢɧɢɦɚɸɬ ɛɚɡɨɜɵɟ ɡɧɚɱɟɧɢɹ.

68

ȦɁȺȾ

U R MC . Ɏ Ɏ2

(3.36)

ɉɪɢ ɪɚɫɱɟɬɟ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢ kɎ = kɎɇ ɢ R = rə ɭɪɚɜɧɟɧɢɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ ȦɁȺȾ

U rə MC ,

ȦɁȺȾ

1 R MC ,

(3.37)

ɩɪɢ ɪɚɫɱɟɬɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɪɢ ɪɚɫɱɟɬɟ ɩɨɬɨɤɚ 1 r ə2 MC . Ɏ Ɏ ɉɪɢ ɝɪɚɮɢɱɟɫɤɨɦ ɦɟɬɨɞɟ ɪɚɫɱɟɬɚ (ɪɢɫ. 3.25): – ɫɬɪɨɢɬɫɹ ɟɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜ ɨ.ɟ.; – ɧɚɧɨɫɢɬɫɹ ɡɚɞɚɧɧɚɹ ɬɨɱɤɚ ȦɁȺȾ, Ɇɋ; – ɩɚɪɚɥɥɟɥɶɧɵɦ ɩɟɪɟɧɨɫɨɦ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ ɫɬɪɨɢɦ ɢɫɤɭɫɫɬɜɟɧɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɩɪɢ ɫɧɢɠɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ U, ɨɩɪɟɞɟɥɹɟɦ Ȧ0ɁȺȾ, ɤɨɬɨɪɚɹ ɜ ɨ.ɟ. ɪɚɜɧɚ UɁȺȾ; – ɫɨɟɞɢɧɹɹ ɬɨɱɤɭ ɫɤɨɪɨɫɬɢ Ȧ0ɇ ɫ ɡɚɞɚɧɧɨɣ ɬɨɱɤɨɣ, ɫɬɪɨɢɦ ɢɫɤɭɫɫɬɜɟɧɧɭɸ ɪɟɨɫɬɚɬɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ, ɩɪɢ Ɇ=1 (ɫɦ. ɪɢɫ.3.25) ɨɩɪɟɞɟɥɹɟɦ RȾɈȻ. ȦɁȺȾ

Ȧ

1

rə

Ȧɇ

ɟɫɬ

Ȧ 0ɁȺȾ

R ȾɈȻ

Ȧ ɁȺȾ

Uə Ļ RĹ

Ɇɋ

1

Ɇ

Ɋɢɫ. 3.25. Ɉɛɟɫɩɟɱɟɧɢɟ ɪɚɛɨɬɵ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɫɧɢɠɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ U, ɜɜɟɞɟɧɢɟɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɩɪɟɞɟɥɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɚɪɚɦɟɬɪɵ ɢ ɩɨɫɬɪɨɟɧɵ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. ɇɚ ɪɢɫ.3.26 ɩɪɢɜɟɞɟɧ ɩɪɢɦɟɪ ɝɪɚɮɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɩɚɪɚɦɟɬɪɨɜ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɪɚɡɥɢɱɧɵɯ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɚɯ. ɗɬɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɫɬɪɨɟɧɵ ɩɨ ɜɵɲɟ ɩɪɢɜɟɞɟɧɧɨɣ ɦɟɬɨɞɢɤɟ. 69

ɉɪɢɦɟɪ 3.2. Ɋɚɫɫɱɢɬɚɬɶ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɹɤɨɪɹ RȾɈȻ (ɢ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ Uə) ɞɜɢɝɚɬɟɥɹ Ⱦ32 (ɫɦ. ɩɪɢɦɟɪ 3.1), ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: ɆɁȺȾ 0,5, ȦɁȺȾ 0,5 . Ɋɚɫɱɟɬ ɜɵɩɨɥɧɢɦ ɜ ɨ.ɟ. ɍɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨɛɳɟɦ ɜɢɞɟ (3.36) ɜ ɨ.ɟ. U R MC . Ɏ Ɏ2 Ɋɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ – ɞɜɢɝɚɬɟɥɶɧɵɣ. ɉɪɢ ɪɚɫɱɟɬɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RȾɈȻ ɩɪɢɧɢɦɚɟɦ kɎ = kɎɇ ɢ U = Uɇ. ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ Ɏ 1, U 1 ɩɪɢɧɢɦɚɟɬ ɜɢɞ: ɍɱɢɬɵɜɚɟɦ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɨɬɟɪɢ ɜ ɞɜɢɝɚɬɟɥɟ ǻɆXX = 17,7 ɇɦ ȦɁȺȾ

ȦɁȺȾ

ǻɆɏɏ Ɇɇ

ǻ Ɇɏɏ

1 R MC .

10,2 123,6

0,0825 .

Ɍɨɝɞɚ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ

ɆɁȺȾ ǻ Ɇɏɏ

0,5 0,0825 0,5825 .

ɉɨɥɧɨɟ ɢ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɢ ɹɤɨɪɹ R

1 ȦɁȺȾ Ɇɋ

1 0,5 0,5825

RȾɈȻ

R rə

R ȾɈȻ

RȾɈȻ RH

0,858,

0,858 0,12

0,738,

0,738 4,31 3,18 Ɉɦ.

ɇɚ ɪɢɫ.3.25 ɩɪɢɜɟɞɟɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ R Ĺ, ɩɪɨɯɨɞɹɳɚɹ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ ɩɪɢ ɜɜɟɞɟɧɢɢ RȾɈȻ = 3,18 Ɉɦ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ RȾɈȻ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɝɪɚɮɢɱɟɫɤɢ ɩɪɢ M 1 (ɫɦ. ɪɢɫ.3.25). ɉɪɢ ɪɚɫɱɟɬɟ ɧɚɩɪɹɠɟɧɢɹ UɁȺȾ ɩɪɢɧɢɦɚɸɬ kɎ = kɎɇ ɢ R = rə. ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ Ɏ 1, R rə ɩɪɢɧɢɦɚɟɬ ɜɢɞ ȦɁȺȾ

U rə MC .

ɋɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɨɫɬɚɥɫɹ ɩɪɟɠɧɢɦ Ɇɋ

ɆɁȺȾ ' Ɇɏɏ

0,5 0,0825 0,5825 .

ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ ɜ ɨ.ɟ. ɪɚɜɧɨ ɫɤɨɪɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɜ ɨ.ɟ. UɁȺȾ

Ȧ0ɁȺȾ

UɁȺȾ

UɁȺȾ UH

Ȧ0ɁȺȾ

ȦɁȺȾ rə Ɇɋ

0,5 0,12 0,5825

0,57.

0,57 220 125,4 B.

Ȧ0ɁȺȾ Ȧ0H

0,57 90,76

51,73 1 c .

ɇɚ ɪɢɫ.3.25 ɩɪɢɜɟɞɟɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ UI, ɩɪɨɯɨɞɹɳɚɹ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ ɩɪɢ ɧɚɩɪɹɠɟɧɢɢ Uə = 125,4 ȼ. ȼɟɥɢɱɢɧɭ ɧɚɩɪɹɠɟɧɢɹ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɝɪɚɮɢ70

ɱɟɫɤɢ ɩɨ Ȧ0ɁȺȾ, ɟɫɥɢ ɜɵɩɨɥɧɢɬɶ ɩɚɪɚɥɥɟɥɶɧɵɣ ɩɟɪɟɧɨɫ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ. ɉɪɢɦɟɪ 3.3. Ɋɚɫɫɱɢɬɚɬɶ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɹɤɨɪɹ RȾɈȻ, ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ Uə ɞɜɢɝɚɬɟɥɹ Ⱦ32 (ɫɦ. ɩɪɢɦɟɪ 3.1), ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: ɆɁȺȾ 0,88, ȦɁȺȾ – 0,7. Ɋɚɫɱɟɬ ɜɵɩɨɥɧɢɦ ɜ ɨ.ɟ. ɍɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨɛɳɟɦ ɜɢɞɟ ɜ ɨ.ɟ.: U R MC . Ɏ Ɏ2 Ɋɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ – ɬɨɪɦɨɡɧɨɣ, ɜɨɡɦɨɠɧɨ ɩɪɢɦɟɧɟɧɢɟ ɬɨɪɦɨɠɟɧɢɹ ɉȼ, ȾɌ, ɊɌ. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɨɬɟɪɢ ɜ ɞɜɢɝɚɬɟɥɟ ɜ ɬɨɪɦɨɡɧɨɦ ɪɟɠɢɦɟ ǻɆɏɏ = 0,135 ɩɨɤɪɵɜɚɸɬɫɹ ɫɨ ɫɬɨɪɨɧɵ ɊɈ, ɬɨɝɞɚ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ȦɁȺȾ

Ɇɋ

ɆɁȺȾ ' Ɇɏɏ

0,88 0,0825

0,8 .

ɉɪɢ ɪɚɫɱɟɬɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RȾɈȻ ɞɥɹ ɬɨɪɦɨɠɟɧɢɹ ɉȼ ɜ ɱɟɬɜɟɪɬɨɦ ɤɜɚɞɪɚɧɬɟ (ɫɦ. ɪɢɫ. 3.26) ɩɪɢɧɢɦɚɟɦ Ɏ 1, U 1. ȦɁȺȾ

1 R MC .

Ⱦɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɢ ɹɤɨɪɹ ɩɪɢ ɉȼ: 1 ȦɁȺȾ Ɇɋ

1 0,7 0,5825

RȾɈȻ

R rə

2,125 0,076

R ȾɈȻ

RȾɈȻ RH

R

2,125, 2,05,

2,05 4,31 8,83 Ɉɦ.

ɇɚ ɪɢɫ. 3.26 ɩɪɢɜɟɞɟɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ, ɩɪɨɯɨɞɹɳɚɹ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ 2 ɩɪɢ ɜɜɟɞɟɧɢɢ RȾɈȻ = 8,83 Ɉɦ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ RȾɈȻ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɝɪɚɮɢɱɟɫɤɢ ɩɪɢ Ɇ 1, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 3.26. ɉɪɢ ɪɚɫɱɟɬɟ ɪɟɠɢɦɚ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɜɨ ɜɬɨɪɨɦ ɤɜɚɞɪɚɧɬɟ ( Ɇɋ 0 ) ɢɡɦɟɧɹɟɬɫɹ ɧɚ ɨɛɪɚɬɧɵɣ ɡɧɚɤ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɞɜɢɝɚɬɟɥɟ U 1 . ɉɪɢ ɪɚɫɱɟɬɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RȾɈȻ ɞɥɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (ɫɦ. ɪɢɫ. 3.26) ɩɪɢɧɢɦɚɟɦ Ɏ

1, U

ȦɁȺȾ

0.

-R MC .

Ⱦɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɢ ɹɤɨɪɹ ɩɪɢ ɞɢɧɚɦɢɱɟɫɤɨɦ ɬɨɪɦɨɠɟɧɢɢ R

ȦɁȺȾ Ɇɋ

- 0,7 0,8

R ȾɈȻ

R rə

R ȾɈȻ

R ȾɈȻ R H

0,875,

0,875 0,076

0,8,

0,8 4,31 3,45 Ɉɦ.

ɇɚ ɪɢɫ. 3.26 ɩɪɢɜɟɞɟɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ, ɩɪɨɯɨɞɹɳɚɹ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ 2 ɩɪɢ ɜɜɟɞɟɧɢɢ RȾɈȻ=3,45 Ɉɦ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ RȾɈȻ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɝɪɚɮɢɱɟɫɤɢ ɩɪɢ Ɇ

1 , ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 3.26.

71

ɉɪɢ ɪɚɫɱɟɬɟ ɧɚɩɪɹɠɟɧɢɹ

UɁȺȾ ɩɪɢ ɊɌ Ɏ

1, R

rə . ɋɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɨɫ-

ɬɚɥɫɹ ɩɪɟɠɧɢɦ Ɇɋ 0,8 . ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ ɜ ɨ.ɟ. ɪɚɜɧɨ ɫɤɨɪɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɜ ɨ.ɟ. UɁȺȾ

Ȧ0ɁȺȾ

UɁȺȾ

UɁȺȾ UH

Ȧ0ɁȺȾ

ȦɁȺȾ rə Ɇɋ

0,7 0,076 0,8

0,64.

0,64 220 140,8 B.

Ȧ0ɁȺȾ Ȧ0H

0,64 90,76

58,08 1 c .

ɇɚ ɪɢɫ. 3.26 ɩɪɢɜɟɞɟɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ rə ɬɨɪɦɨɠɟɧɢɹ, ɩɪɨɯɨɟɫɬ ɞɹɳɚɹ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ 2 ɩɪɢ ɧɚɩɪɹɠɟɧɢɢ Uə = -140,8 ȼ. ȼɟɥɢɱɢɧɭ ɧɚɩɪɹɠɟɆɋ 1 ɧɢɹ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɝɪɚɮɢɱɟɫɤɢ ɩɨ Ɇ Ȧ0ɁȺȾ, ɟɫɥɢ ɜɵɩɨɥɧɢɬɶ R ȾɈȻ ɩɚɪɚɥɥɟɥɶɧɵɣ ɩɟɪɟȦ0 ɧɨɫ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟȦɁȺȾ ɪɢɫɬɢɤɢ ɱɟɪɟɡ ɡɚɞɚɧ2 UĻ ɊɌ ɧɭɸ ɬɨɱɤɭ 2. ɉɪɢɦɟɪ 3.4. Ɉɛɟɫɩɟɱɢɬɶ ɪɚɛɨɬɭ ɞɜɢɝɚɉȼ ȾɌ ɬɟɥɹ Ⱦ32 (ɫɦ. ɩɪɢɦɟɪ 3.1), ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: ɆɁȺȾ 0,5, ȦɁȺȾ 1,2 . Ɋɢɫ.3.26. Ɉɛɟɫɩɟɱɟɧɢɟ ɪɚɛɨɬɵ ɜ ɡɚɞɚɧɧɨɣ Ɋɟɠɢɦ ɪɚɛɨɬɵ ɬɨɱɤɟ 2 ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɨɜ ɞɜɢɝɚɬɟɥɹ – ɞɜɢɝɚɬɟɥɶɧɵɣ. ɋɤɨɪɨɫɬɶ ȦɁȺȾ ! ȦȿɋɌ , ɩɨɷɬɨɦɭ ɨɛɟɫɩɟɱɢɬɶ ɪɚɛɨɬɭ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɦɨɠɧɨ ɨɫɥɚɛɥɟɧɢɟɦ ɩɨɥɹ – ɎĻ (ɫɧɢɠɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ Uȼ ɧɚ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɢɥɢ ɜɜɟɞɟɧɢɟɦ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ Rȼ ȾɈȻ ɜ ɟɟ ɰɟɩɶ). Ɋɚɫɱɟɬ ɜɵɩɨɥɧɢɦ ɜ ɨ.ɟ. ɍɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨɛɳɟɦ ɜɢɞɟ ɜ ɨ.ɟ. Ȧ

U R MC . Ɏ Ɏ2 ɋɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ȦɁȺȾ

Ɇɋ

ɆɁȺȾ ' Ɇɏɏ

ɉɪɢ ɨɫɥɚɛɥɟɧɢɢ ɩɨɥɹ U = 1 , R

0,5 0,135 0,635 .

r ə ɭɪɚɜɧɟɧɢɟ ɩɪɟɨɛɪɚɡɭɟɬɫɹ

ȦɁȺȾ

1 rə MC Ɏ Ɏ2 72

Ɋɟɲɚɟɦ ɤɜɚɞɪɚɬɧɨɟ ɭɪɚɜɧɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɬɨɤɚ Ɏ1,2

1 1 r 1 4 Ɇɋ ȦɁȺȾ rə 2 ȦɁȺȾ

ɉɨɥɭɱɢɥɢ Ɏ1

1 1 r 1 4 0,5825 1,2 0,076 . 2 1,2

0,047 . ɉɪɢɧɢɦɚɟɦ ɢɡ ɮɢɡɢɱɟɫɤɢɯ ɫɨɨɛɪɚɠɟɧɢɣ

0,786, Ɏ2

Ɏ1

0,786 . Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɛɚɡɨɜɨɝɨ ɡɧɚɱɟɧɢɹ ɩɨɬɨɤɚ Ɏɇ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɤɚɬɚɥɨɝɚ [16] N pɉ 558 2 177,6 , 2ʌ ɚ 2ʌ 2 ɝɞɟ N = 558 – ɱɢɫɥɨ ɚɤɬɢɜɧɵɯ ɩɪɨɜɨɞɧɢɤɨɜ; ɪɉ = 2 – ɱɢɫɥɨ ɩɚɪ ɩɨɥɸɫɨɜ; 2ɚ = 2 – ɱɢɫɥɨ ɩɚɪɚɥɥɟɥɶɧɵɯ ɜɟɬɜɟɣ ɨɛɦɨɬɤɢ ɹɤɨɪɹ. ɉɪɢ kɎɇ = 2,3 ȼɫ ɜɟɥɢɱɢɧɚ ɧɨɦɢɧɚɥɶɧɨɝɨ ɩɨɬɨɤɚ k

kɎɇ k

Ɏɇ

2,242 177,6

0,01365 ȼɛ ,

ɉɨ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ Ⱦ32 [16] ɩɨ ɜɟɥɢɱɢɧɟ ɩɨɬɨɤɚ Ɏ1

Ɏ1 Ɏ ɇ

0,786 0,01356

0,0107 ȼɛ ,

ɨɩɪɟɞɟɥɢɦ ɧɚɦɚɝɧɢɱɢɜɚɸɳɭɸ ɫɢɥɭ FB

iB ȦB

1500 A .

Ɂɧɚɱɟɧɢɟ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɢ ɪɚɛɨɬɟ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: iB

FB ȦB

1500 1470

1A.

ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɩɚɪɚɥɥɟɥɶɧɨɣ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɢ Iȼɇ=1,85 Ⱥ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɫɟɬɢ ɧɨɦɢɧɚɥɶɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ Uȼɇ: rOB

UBH IBH

220 1,85

119 Ɉɦ .

Ⱦɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ Rȼ ȾɈȻ UBH rOB IBH

RȼȾɈȻ

220 119 1

101 Ɉɦ .

ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɧɞɢɜɢɞɭɚɥɶɧɨɝɨ ɜɨɡɛɭɞɢɬɟɥɹ: UB

IB rOB

1 119

73

119 B .

Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɫɬɚɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ: Ȧ0

1 Ɏ1

1 0,786

Ȧ0

Ȧ 0 Ȧ 0ɇ

1,27;

1,27 90,76 115,5 1 ɫ .

Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: IɁȺȾ

Ɇɋ Ɏ1

IɁȺȾ

IɁȺȾ IH

0,5825 0,786

0,741;

0,741 51 37,8 A.

3.1.10. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɰɟɯɨɜɨɣ ɫɟɬɢ

Ɋɚɧɟɟ, ɜ ɝɥɚɜɟ «Ɇɟɯɚɧɢɤɚ», ɪɚɫɫɦɚɬɪɢɜɚɥɢ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ Ȧ(t) ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨɦ ɡɚɞɚɧɢɢ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ, ɧɟ ɡɚɜɢɫɹɳɟɝɨ ɨɬ ɫɤɨɪɨɫɬɢ. Ɉɞɧɚɤɨ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɱɚɳɟ ɜɫɟɝɨ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɫɤɨɪɨɫɬɢ. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɢɯ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ (ɛɟɡ ɭɱɟɬɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɢɧɟɪɰɢɢ ɞɜɢɝɚɬɟɥɹ) ɢ ɪɚɫɱɟɬɚ ɜɪɟɦɟɧɢ ɢɯ ɩɪɨɬɟɤɚɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɫɨɜɦɟɫɬɧɨ ɪɟɲɚɬɶ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ dȦ dt ɢ ɭɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ɇɋ J

(3.38)

M ȕ Ȧ0 Ȧ .

(3.39)

Ɇ

Ɋɟɲɢɦ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɨ Ȧ, ɩɨɞɫɬɚɜɢɜ (3.38) ɜ (3.39): ȕ Ȧ0 Ȧ Ɇɋ J

dȦ . dt

Ɋɚɡɞɟɥɢɦ ɧɚ ȕ:

Ȧ0 Ȧ

Ɇɋ J dȦ . ȕ ȕ dt

ɍɱɢɬɵɜɚɹ, ɱɬɨ: – Ɇɋ / ȕ = ¨Ȧɋ – ɨɬɤɥɨɧɟɧɢɟ ɫɤɨɪɨɫɬɢ, ɡɚɜɢɫɹɳɟɟ ɨɬ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇɋ; – J / ȕ = ɌM – ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɞɜɢɝɚɬɟɥɹ; – Ȧ0 – ¨Ȧɋ = Ȧɋ – ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɩɪɢ Ɇ = Ɇɋ. ɉɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ, ɨɩɢɫɵɜɚɸɳɟɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ TM

dȦ Ȧ dt

ȦC ,

74

(3.40)

ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɫɨɛɨɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɫ ɩɨɫɬɨɹɧɧɨɣ ɩɪɚɜɨɣ ɱɚɫɬɶɸ. Ɋɚɡɞɟɥɢɦ (3.40) ɧɚ ɌɆ: ȦC . TM

dȦ Ȧ dt TM

(3.41)

ȼ ɨɛɳɟɦ ɜɢɞɟ ɪɟɲɟɧɢɟ ɷɬɨɝɨ ɥɢɧɟɣɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ: Ȧt ȦC C e

t TM

(3.42)

.

ɉɨɫɬɨɹɧɧɭɸ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɋ ɨɩɪɟɞɟɥɢɦ ɩɪɢ t = 0, ɤɨɝɞɚ ɫɤɨɪɨɫɬɶ ɪɚɜɧɚ ɧɚ

ɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ = ȦɇȺɑ, ɚ e

t TM

ȦɇȺɑ

1.

ȦC C ,

ɬɨɝɞɚ ɋ = ȦɇȺɑ – Ȧɋ. Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ Ȧt ȦC ȦɇȺɑ Ȧɋ e

t TM

(3.43)

.

ɇɚɝɪɭɡɨɱɧɭɸ ɞɢɚɝɪɚɦɦɭ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ Ɇ(t) ɩɨɥɭɱɢɦ, ɩɨɞɫɬɚɜɢɜ (3.43) ɜ ɭɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ: Ɇt ȕ Ȧ0 Ȧt ȕ Ȧ0 ȕ ȦC ȕ ȦɇȺɑ ȕ Ȧɋ ɟ

t TM

.

ɍɱɢɬɵɜɚɹ, ɱɬɨ ȕ·(Ȧ0 – Ȧɋ) =Ɇɋ ɢ ȕ·(Ȧ0 – ȦɇȺɑ) =ɆɇȺɑ, ɩɨɥɭɱɢɦ ɧɚɝɪɭɡɨɱɧɭɸ ɞɢɚɝɪɚɦɦɭ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ: Ɇt MC MɇȺɑ Mɋ ɟ

t TM

.

(3.44)

Ⱥɧɚɥɢɡɢɪɭɹ ɩɨɥɭɱɟɧɧɵɟ ɜɵɪɚɠɟɧɢɹ, ɦɨɠɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ t = 0 e ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɪɚɜɧɚ Ȧ = ȦɇȺɑ, ɦɨɦɟɧɬ ɪɚɜɟɧ Ɇ = ɆɇȺɑ.

t TM

1

t TM

ɉɪɢ t = f – e 0 , ɬɨɝɞɚ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɪɚɜɧɚ Ȧ = Ȧɋ, ɦɨɦɟɧɬ ɪɚɜɟɧ Ɇ = Ɇɋ. Ɂɚ ɷɬɨ ɜɪɟɦɹ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɹɟɬɫɹ ɨɬ ȦɇȺɑ ɩɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɦɭ ɡɚɤɨɧɭ exp(–TM) ɞɨ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ Ȧɋ, ɚ ɦɨɦɟɧɬ – ɨɬ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɆɇȺɑ ɞɨ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ – ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇɋ. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɌȾ ɌȾ Ȧ Ɇ Ȧ0 J J ǻȦ , J 0 ɇ J (3.45) 'M 'M MɄɁ Ɇɇ MɄɁ Ɇɇ ɆɄɁ k ə ǻȦ ɝɞɟ kə = ɆɄɁ / Ɇɇ – ɤɪɚɬɧɨɫɬɶ ɦɨɦɟɧɬɚ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ (ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɩɨɬɨɤɟ Ɏ = Ɏɇ – ɤɪɚɬɧɨɫɬɶ ɬɨɤɚ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ), ɠɺɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȕ ɜ ɨ.ɟ; Ɍɦ – ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɩɪɢɜɨɞɚ ɟɫɬɶ ɜɪɟɦɹ, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɫ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ J ɪɚɡɝɨɧɢɬɫɹ ɢɡ ɧɟ TM

J ȕ

75

ɩɨɞɜɢɠɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɞɨ ɫɤɨɪɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɨɫɬɨɹɧɧɨɝɨ ɦɨɦɟɧɬɚ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɆɄɁ. ȼ ɨɬɥɢɱɢɟ ɨɬ ɦɟɯɚɧɢɱɟɫɤɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ ɌȾ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɌɆ ɜ kə ɪɚɡ ɦɟɧɶɲɟ ɢ ɨɬɪɚɠɚɟɬ ɧɟ ɬɨɥɶɤɨ ɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɤɚɤ ɌȾ, ɧɨ ɢ ɫɯɟɦɭ ɜɤɥɸɱɟɧɢɹ ɞɜɢɝɚɬɟɥɹ. Ɋɚɫɫɦɨɬɪɢɦ ɩɨɥɭɱɟɧɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɧɚ ɩɪɢɦɟɪɟ ɩɭɫɤɚ Ⱦɇȼ. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɩɪɢ ɩɭɫɤɟ ɞɜɢɝɚɬɟɥɹ ɫ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɩɭɫɤɟ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ.3.12. ȼɵɲɟ ɪɚɫɫɦɨɬɪɟɧɚ ɦɟɬɨɞɢɤɚ ɪɚɫɱɟɬɚ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ. Ɋɚɫɱɟɬ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ ɩɪɨɢɡɜɨɞɢɦ ɩɨ ɮɨɪɦɭɥɚɦ (3.43) ɢ (3.44): Ȧt ȦC ȦɇȺɑ Ȧɋ ɟ Ɇt MC MɇȺɑ Mɋ ɟ

t TM t TM

, .

ɉɭɫɤ ɧɚɱɢɧɚɟɬɫɹ ɜɤɥɸɱɟɧɢɟɦ ɥɢɧɟɣɧɨɝɨ ɤɨɧɬɚɤɬɨɪɚ ɄɅ ɩɪɢ ɨɬɤɥɸɱɟɧɧɵɯ ɤɨɧɬɚɤɬɨɪɚɯ ɭɫɤɨɪɟɧɢɹ Ʉɍ1 ɢ Ʉɍ2. Ⱦɜɢɝɚɬɟɥɶ ɧɚɱɢɧɚɟɬ ɪɚɛɨɬɚɬɶ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 1 (ɪɢɫ.3.27). ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɹɤɨɪɹ R1 = R1ȾɈȻ+ R2ȾɈȻ+ rə. ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 1: ɆɇȺɑ =Ɇ1; ȦɇȺɑ = 0; Ȧɋ = Ȧɋ1=Ȧ2. ɇɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ ɫ ɭɱɟɬɨɦ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ: Ɇt MC M1 Mɋ ɟ

t TM

;

Ȧt

t § · TM ¸ ¨ . Ȧ2 1 ɟ ¨ ¸ © ¹

ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 1: Ɍ Ɇ1

J

Ȧ 0H ɆɄɁ

J

Ȧ 0H . Ɇ1

ɂɡ ɜɵɪɚɠɟɧɢɹ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ ɫɥɟɞɭɟɬ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɧɚɪɚɫɬɚɟɬ ɨɬ ɧɭɥɹ ɞɨ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɪɟɠɢɦɚ Ȧ = Ȧ2 ɚ ɦɨɦɟɧɬ ɫɧɢɠɚɟɬɫɹ ɨɬ Ɇ1 ɞɨ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ Ɇɋ. ɂɡɦɟɧɟɧɢɟ Ȧ(t) ɢ Ɇ(t) ɩɪɨɢɫɯɨɞɢɬ ɩɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɫ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ ɌɆ1 Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɩɭɫɤɚ ɩɨ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɟ ɩɪɢ ɞɨɫɬɢɠɟɧɢɢ ɦɨɦɟɧɬɨɦ ɡɧɚɱɟɧɢɹ ɦɨɦɟɧɬɚ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ = Ɇ2 ɜɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ ɭɫɤɨɪɟɧɢɹ Ʉɍ1, ɡɚɤɨɪɚɱɢɜɚɟɬɫɹ R1ȾɈȻ ɢ ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɜɨɞɢɬɫɹ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ 2 ɩɪɢ ɫɤɨɪɨɫɬɢ Ȧ1. ɉɪɢ ɩɟɪɟɤɥɸɱɟɧɢɢ ɦɨɦɟɧɬɚ ɨɬ Ɇ2 ɤ Ɇ1 ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ Ȧ1 ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɹɤɨɪɹ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 2 R2 = R2ȾɈȻ+ rə. ȼɪɟɦɹ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ t1 ɧɚ ɩɟɪɜɨɣ ɫɬɭɩɟɧɢ (ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 1) ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɜɵɪɚɠɟɧɢɹ ɧɚɝɪɭɡɨɱɧɨɣ ɞɢɚɝɪɚɦɦɵ ɦɨɦɟɧɬɚ (3.49) ɩɪɢ Ɇ = Ɇ2 ɢɥɢ ɫɤɨɪɨɫɬɢ ɩɪɢ Ȧ = Ȧ1: Ɇ2

MC M1 Mɋ ɟ

76

t TM1

Ȧ

Ȧ0ɧ

Ȧ

Ȧɋ2 Ȧ2=Ȧɋ1 Ȧ1

Ȧ Ȧ1 2

1 Ɇɋ

Ɇ2

t

Ɇ TɆ t1

Ɇ1

t2

tɉɉ

Ɇ Ɇ1 Ɇ2 Ɇɋ t TɆ t1 t2

tɉɉ

Ɋɢɫ.3.27. ɉɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɭɫɤɚ Ⱦɇȼ Ɍɨɝɞɚ t1

TM1 ln

M1 MC . M2 MC

(3.46)

ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 2: ɆɇȺɑ = Ɇ1, ȦɇȺɑ = Ȧ1, Ȧɋ = Ȧɋ2. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 2: Ɍ Ɇ2

J

ǻȦ ǻɆ

J

Ȧ0H Ȧ1 . Ɇ1

ȼɢɞɧɨ, ɱɬɨ Ɍɦ2 < Ɍɦ1, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɚ ɜɬɨɪɨɣ ɫɬɭɩɟɧɢ ɞɜɢɝɚɬɟɥɶ ɛɭɞɟɬ ɪɚɡɝɨɧɹɬɶɫɹ ɛɵɫɬɪɟɟ. ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɪɚɡɝɨɧɟ ɩɨ ɟɯɪ(ɌɆ2) ɞɜɢɝɚɬɟɥɶ ɫɬɪɟɦɢɬɫɹ ɤ Ȧ = Ȧɋ2 ɢ Ɇ = Ɇɋ, ɧɨ ɩɪɢ ɞɨɫɬɢɠɟɧɢɢ Ɇ = Ɇ2 ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪɨɦ Ʉɍ2 ɧɚ ɫɥɟɞɭɸɳɭɸ ɫɬɭɩɟɧɶ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ – ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ). ȼɪɟɦɹ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ t2 ɧɚ ɜɬɨɪɨɣ ɫɬɭɩɟɧɢ t2

TM2 ln

M1 MC . M2 MC

77

ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ: ɆɇȺɑ = Ɇ1, ȦɇȺɑ = Ȧ2. Ⱦɜɢɝɚɬɟɥɶ ɧɚ ɷɬɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɫɬɪɟɦɢɬɫɹ ɤ ɭɫɬɚɧɨɜɢɜɲɟɦɭɫɹ ɪɟɠɢɦɭ ɜ ɬɨɱɤɟ Ȧɋ, Ɇɋ. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ Ɍ ɦɟ

J

ǻȦ ǻɆ

J

Ȧ 0H Ȧ 2 TM2 , Ɇ1

ɧɨ ɜɪɟɦɹ ɪɚɛɨɬɵ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨ ɮɨɪɦɭɥɟ (3.46) ɪɚɫɫɱɢɬɚɬɶ ɧɟɥɶɡɹ (tɟ=f), ɩɪɢɛɥɢɠɟɧɧɨ ɫɱɢɬɚɸɬ tɟ § 3·Ɍɦɟ. ȼɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɩɭɫɤɚ ɞɜɢɝɚɬɟɥɹ t1 t 2 t e .

t ɉɉ

Ⱦɥɹ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɪɚɫɱɟɬɚ ɜɪɟɦɟɧɢ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɨɫɧɨɜɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɞɜɢɠɟɧɢɹ: ǻt

J

ǻȦ , Ɇɉ.ɋɊ Ɇɋ

ɝɞɟ Ɇɉ.ɋɊ = (Ɇ1 + Ɇ2) / 2 – ɫɪɟɞɧɢɣ ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ; ǻȦ = Ȧ0ɇ. ȼ ɨ.ɟ ǻt

ɌȾ

ǻȦ . Ɇɉ.ɋɊ Ɇɋ

Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɞɜɢɝɚɬɟɥɹ ɫ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ. ɇɚ ɪɢɫ.3.21 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɜɤɥɸɱɟɧɢɹ Ⱦɇȼ, ɨɛɟɫɩɟɱɢɜɚɸɳɚɹ ɬɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ. ȼ ɩ.3.1.5 ɪɚɫɫɦɨɬɪɟɧɚ ɪɚɛɨɬɚ ɷɬɨɣ ɫɯɟɦɵ. Ⱦɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɜ ɬɨɱɤɟ Ȧɋ, Ɇɋ. Ⱦɥɹ ɩɟɪɟɯɨɞɚ ɜ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɪɟɜɟɪɫɢɪɭɟɬɫɹ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ (ɨɬɤɥɸɱɚɟɬɫɹ Ʉȼ, ɜɤɥɸɱɚɟɬɫɹ Ʉɇ), ɚ ɜ ɰɟɩɶ ɹɤɨɪɹ ɜɜɨɞɹɬɫɹ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ (ɨɬɤɥɸɱɚɸɬɫɹ Ʉɍ ɢ Ʉɉ). Ⱦɜɢɝɚɬɟɥɶ ɩɟɪɟɯɨɞɢɬ ɜ ɬɨɱɤɭ 1 ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɫ ɜɜɟɞɟɧɧɵɦɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ - Ȧ0ɇ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɢɫɩɨɥɶɡɭɟɦ ɜɵɪɚɠɟɧɢɹ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ (3.43), (3.44): Ȧt ȦC ȦɇȺɑ Ȧɋ ɟ Ɇt MC MɇȺɑ Mɋ ɟ

t TM t TM

, .

ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ: ɆɇȺɑ = – ɆɌɇȺɑ; ȦɇȺɑ = Ȧɋ; Ȧɋ= – Ȧɋ1. ɋ ɭɱɟɬɨɦ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ: Ȧt ȦC1 ȦɇȺɑ Ȧɋ1 ɟ

78

t TMɉȼ

,

Ɇt MC MɌɇȺɑ Mɋ ɟ

t TMɉȼ

.

ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ Ɍ Ɇɉȼ

J

ǻȦ ǻɆ

J

ȦHȺɑ ɆɌɇȺɑ ɆɄɁ

ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɩɭɫɤɨɜɵɯ ɪɟɠɢɦɚɯ ɢɡ-ɡɚ ɡɧɚɱɢɬɟɥɶɧɨɣ ɜɟɥɢɱɢɧɵ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ. ɉɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɧɚɱɢɧɚɟɬɫɹ ɜ ɬɨɱɤɟ 1 ɜ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɢ ɩɨ Ȧ 1

Ȧ, Ɇ ȦC

Ȧ0ɇ

Ȧɋ

ɟɫɬ

1

Ɇɋ - ɆɌɇȺɑ

- ɆɄɁ

Ɇ

Ɇɋ

tɉȼ

M(t)

t

2 3

2 2 -ɆɄɁ 3 -Ȧ0ɇ

-ɆɌɇȺɑ

1

ɟɫɬ

3 Ȧ(t)

ɌɆɉȼ

-ȦC1

Ɋɢɫ.3.28. ɉɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ Ⱦɇȼ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɟɯɪ(–ɌɆɉȼ) ɫɬɪɟɦɢɬɫɹ ɤ ɭɫɬɚɧɨɜɢɜɲɟɦɭɫɹ ɪɟɠɢɦɭ Ɇɋ, - Ȧɋ1. Ɇɨɦɟɧɬ ɢ ɫɤɨɪɨɫɬɶ ɜ ɦɟɯɚɧɢɱɟɫɤɨɦ ɩɟɪɟɯɨɞɧɨɦ ɩɪɨɰɟɫɫɟ ɫɜɹɡɚɧɵ ɭɪɚɜɧɟɧɢɟɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɩɨɷɬɨɦɭ ɤɪɢɜɵɟ Ɇ(t) ɢ Ȧ(t) ɩɪɨɯɨɞɹɬ ɱɟɪɟɡ ɯɚɪɚɤɬɟɪɧɵɟ ɬɨɱɤɢ. ɉɪɢ Ȧ = 0 ɦɨɦɟɧɬ ɪɚɜɟɧ ɦɨɦɟɧɬɭ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ Ɇ = ɆɄɁ (ɬɨɱɤɚ 2), ɩɪɢ Ȧ = - Ȧ0ɇ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɪɚɜɟɧ ɧɭɥɸ Ɇ = 0 (ɬɨɱɤɚ 3). Ɍɚɤɨɣ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɜɨɡɦɨɠɟɧ ɥɢɲɶ ɩɪɢ ɚɤɬɢɜɧɨɦ ɫɬɚɬɢɱɟɫɤɨɦ ɦɨɦɟɧɬɟ, ɟɫɥɢ ɩɪɢ Ȧ = 0 ɧɟ ɨɬɤɥɸɱɢɬɶ ɞɜɢɝɚɬɟɥɶ. ɉɪɢ ɪɟɚɤɬɢɜɧɨɦ ɫɬɚɬɢɱɟɫɤɨɦ ɦɨɦɟɧɬɟ ɞɜɢɝɚɬɟɥɶ ɨɫɬɚɧɨɜɢɬɫɹ, ɟɫɥɢ ɆɄɁ < Ɇɋ.

79

ȼɪɟɦɹ ɬɨɪɦɨɠɟɧɢɹ ɞɨ ɫɤɨɪɨɫɬɢ Ȧ = 0 ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ (3.46) ɫ ɭɱɟɬɨɦ ɪɟɠɢɦɚ ɬɨɪɦɨɠɟɧɢɹ: t ɉȼ

Ɍ Ɇɉȼ ln

ȦɇȺɑ Ȧɋ Ȧɋ

.

Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɫ ɚɤɬɢɜɧɵɦ ɫɬɚɬɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɪɚɡɥɢɱɧɵɟ ɪɟɠɢɦɵ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ: – ɧɚ ɭɱɚɫɬɤɟ 1 – 2 – ɬɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ; – ɧɚ ɭɱɚɫɬɤɟ 2 – 3 – ɞɜɢɝɚɬɟɥɶɧɵɣ ɪɟɠɢɦ; – ɡɚ ɬɨɱɤɨɣ 3 – ɪɟɠɢɦ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɩɪɢ ɞɢɧɚɦɢɱɟɫɤɨɦ ɬɨɪɦɨɠɟɧɢɢ. ɇɚ ɪɢɫ.3.21 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɜɤɥɸɱɟɧɢɹ Ⱦɇȼ, ɨɛɟɫɩɟɱɢɜɚɸɳɚɹ ɤɪɨɦɟ ɪɟɠɢɦɚ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɟɳɟ ɢ ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. ȼ ɩ.3.1.5 ɪɚɫɫɦɨɬɪɟɧɚ ɪɚɛɨɬɚ ɫɯɟɦɵ ɢ ɜ ɷɬɨɦ ɪɟɠɢɦɟ. Ȧ

Ȧ, Ɇ

Ȧ0ɇ ɟɫɬ

Ȧɋ Ȧ(t)

Ɇɋ Ɇ

t

Ɇɋ

–ɆɌɇȺɑ

t

- Ȧɋ1

ȾɌ

- Ȧɋ1 -ɆɌɇȺɑ

Ɇ(t)

Ɋɢɫ.3.29. ɉɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ Ⱦɇȼ ɉɨɩɪɨɛɭɣɬɟ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɨɩɪɟɞɟɥɢɬɶ ɧɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ, ɩɨɥɭɱɢɬɶ ɜɵɪɚɠɟɧɢɹ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ, ɪɚɫɫɱɢɬɚɬɶ ɜɪɟɦɹ ɬɨɪɦɨɠɟɧɢɹ, ɩɨɹɫɧɢɬɶ ɯɚɪɚɤɬɟɪ ɩɪɨɬɟɤɚɧɢɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ. Ʉɚɤ ɢɡɦɟɧɢɬɫɹ ɜɢɞ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ, ɟɫɥɢ: ɆC = 0? Ɇɋ – ɪɟɚɤɬɢɜɧɵɣ? – ɜ ɞɜɚ ɪɚɡɚ ɭɜɟɥɢɱɢɬɶ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɹɤɨɪɹ? – ɜ ɞɜɚ ɪɚɡɚ ɭɦɟɧɶɲɢɬɶ ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ?

80

3.1.11. ɍɩɪɚɠɧɟɧɢɹ ɞɥɹ ɫɚɦɨɩɪɨɜɟɪɤɢ (ɪɚɫɱɟɬɵ ɜɵɩɨɥɧɹɸɬɫɹ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ)

3.1.11.1. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ Ⱦɇȼ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɩɪɢ Ɇ=1 ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ Ȧɇ / 2. ɉɪɢɧɹɬɶ r = 0,05, Ɏ =1. 3.1.11.2. Ɉɩɪɟɞɟɥɢɬɶ RȾɈȻ ɜ ɰɟɩɢ Ⱦɇȼ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɩɪɢ Ɇ=1 ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ Ȧɇ / 2. ɉɪɢɧɹɬɶ r=0,1, U=1, Ɏ=1. 3.1.11.3. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ ɩɪɢ U=1, Ɇ=1, Ɏ=1 ɜɜɟɫɬɢ ɜ ɰɟɩɶ ɹɤɨɪɹ RȾɈȻ=0,5. ɉɪɢɧɹɬɶ r = 0,05. 3.1.11.4. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ ɩɪɢ Ɏ=1, RȾɈȻ=0,5 ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ=2. ɉɪɢɧɹɬɶ r = 0,05. 3.1.11.5. Ɉɩɪɟɞɟɥɢɬɶ Rɞɨɛ ɜ ɰɟɩɢ ɹɤɨɪɹ Ⱦɇȼ ɜ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ

ɬɨɪɦɨɠɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɩɪɢ Ɇ=1 ɫɤɨɪɨɫɬɶ Ȧ = – 1. ɉɪɢɧɹɬɶ Ɏ=1, r = 0,05. 3.1.11.6. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɢ ɬɨɤ ɞɜɢɝɚɬɟɥɹ ɩɪɢ U = 1, Ɇ = 1, Ɏ = 0,5. ɉɪɢɧɹɬɶ r=0,1. 3.1.11.7. Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɦɨɦɟɧɬ, ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ U = 0,5, Ɇ = 1, Ɏ = 1, r = 0,05, RȾɈȻ = 0,5. 3.1.11.8. Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɦɨɦɟɧɬ, ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ U = 0,5, Ɇ =1, Ɏ = 1, RȾɈȻ = 1. ɉɪɢɧɹɬɶ r = 0,05. 3.1.11.9. Ⱦɇȼ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ Ɇɋ = 0,5, Ȧɋ = 0,5. ȼɨɡɪɨɫ Ɇɋ =1,5. ɇɚ ɫɤɨɥɶɤɨ ɧɭɠɧɨ ɭɜɟɥɢɱɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɞɜɢɝɚɬɟɥɟ, ɱɬɨɛɵ ɜɨɫɫɬɚɧɨɜɢɬɶ ɫɤɨɪɨɫɬɶ, ɟɫɥɢ r = 0,05? 3.1.11.10. Ⱦɇȼ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ Ɇɋ = 0,5, Ȧɋ = 1. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɩɨɞɞɟɪɠɚɧɢɹ ɫɤɨɪɨɫɬɢ, ɟɫɥɢ Ɇɋ ɜɨɡɪɨɫ ɜ 2 ɪɚɡɚ, ɚ r = 0,05? 3.1.11.11. Ⱦɇȼ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ Ɇɋ =1, Ȧɋ = 0,5.Ɉɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɞɜɢɝɚɬɟɥɟ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɩɨɞɞɟɪɠɚɧɢɹ ɫɤɨɪɨɫɬɢ, ɟɫɥɢ ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ ɭɦɟɧɶɲɢɥɫɹ ɞɨ 0,8 ɩɪɢ r=0,1. 3.1.11.12. ɇɚ ɫɤɨɥɶɤɨ ɢɡɦɟɧɢɬɫɹ ɫɤɨɪɨɫɬɶ ɢ ɬɨɤ Ⱦɇȼ, ɟɫɥɢ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ ɜɨɡɪɨɫɥɨ ɧɚ 0,1. ɉɪɢɧɹɬɶ Ɇɋ = 1, r = 0,05. 3.1.11.13. Ɉɩɪɟɞɟɥɢɬɶ ɛɪɨɫɨɤ ɬɨɤɚ ɹɤɨɪɹ, ɟɫɥɢ ɩɪɢ ɪɚɛɨɬɟ Ⱦɇȼ ɫ Ɇɋ = 0,5 ɢ Ȧɋ = 0,5 ɧɚɩɪɹɠɟɧɢɟ ɫɤɚɱɤɨɦ ɫɧɢɡɢɥɨɫɶ ɧɚ 0,1. ɉɪɢɧɹɬɶ Ɏ = 1, r = 0,05. 3.1.11.14. Ɉɩɪɟɞɟɥɢɬɶ ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ ɩɪɢ Ɇɋ = 0,5, Ȧɋ = 0,95, U = 1 ɩɨɬɨɤ ɭɦɟɧɶɲɢɥɫɹ ɞɨ Ɏ = 0,8. 3.1.11.15. ɉɪɢ ɩɟɪɟɜɨɞɟ Ⱦɇȼ, ɪɚɛɨɬɚɜɲɟɝɨ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɜ ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɛɪɨɫɨɤ ɬɨɤɚ ɹɤɨɪɹ ɫɨɫɬɚɜɢɥ 2,5. Ɉɩɪɟɞɟɥɢɬɶ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɧɨɣ ɰɟɩɢ ɞɜɢɝɚɬɟɥɹ. 3.1.11.16. ɉɪɢ ɩɟɪɟɜɨɞɟ Ⱦɇȼ, ɪɚɛɨɬɚɜɲɟɝɨ ɛɟɡ ɧɚɝɪɭɡɤɢ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɜ ɪɟɠɢɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɹɤɨɪɹ R=1,2. Ɉɩɪɟɞɟɥɢɬɶ ɜɟɥɢɱɢɧɭ ɬɨɤɚ ɹɤɨɪɹ ɜ ɦɨɦɟɧɬ ɩɟɪɟɤɥɸɱɟɧɢɹ. 3.1.11.17. Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ U = - 0,5, Ɇ = 1, r = 0,05, Ɏ = 1. 3.1.11.18. Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɦɨɦɟɧɬ, ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ U = 0, Ɇ = 0,5, r = 0,05. 3.1.11.19. Ɉɩɪɟɞɟɥɢɬɶ ɩɪɢɛɥɢɠɟɧɧɨ ɦɢɧɢɦɚɥɶɧɨɟ ɜɪɟɦɹ ɩɭɫɤɚ Ⱦɇȼ, ɟɫɥɢ ɌȾ =1 ɫ, Ɇɋ = 0,5. 81

3.1.11.20. ɇɚ ɫɤɨɥɶɤɨ ɢɡɦɟɧɢɬɫɹ ɜɪɟɦɹ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ, ɟɫɥɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɹɤɨɪɹ ɭɦɟɧɶɲɢɬɶ ɜɞɜɨɟ, ɚ Ⱦɇȼ ɪɚɛɨɬɚɥ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ? 3.1.11.21. ɇɚ ɫɤɨɥɶɤɨ ɢɡɦɟɧɢɬɫɹ ɫɤɨɪɨɫɬɶ ɫɩɭɫɤɚ ɝɪɭɡɚ ɜ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ Ⱦɇȼ, ɟɫɥɢ ɭɜɟɥɢɱɢɬɶ ɜɞɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɹɤɨɪɹ? ɭɦɟɧɶɲɢɬɶ ɜɞɜɨɟ ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ?

3.2. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɉȼ) 3.2.1. ɍɪɚɜɧɟɧɢɹ ɢ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɉȼ ȼ ɨɬɥɢɱɢɟ ɨɬ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ Ⱦɇȼ ɜ ɞɜɢɝɚɬɟɥɹɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɉȼ) ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɜɤɥɸɱɚɟɬɫɹ ɜ ɰɟɩɶ ɹɤɨɪɹ. Ɍɨɤ ɹɤɨɪɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɹɜɥɹɟɬɫɹ ɬɨɤɨɦ ɜɨɡɛɭɠɞɟɧɢɹ. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɫɯɟɦɚ Ⱦɉȼ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 3.30. Ⱦɜɢɝɚɬɟɥɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɦɟɯɚɧɢɡɦɚɯ U ɩɪɨɤɚɬɧɵɯ ɫɬɚɧɨɜ, ɜ ɤɪɚɧɨɜɨɦ ɯɨɡɹɣɫɬɜɟ LM ɩɨɫɬɟɩɟɧɧɨ ɜɵɬɟɫɧɹɸɬɫɹ ɛɨɥɟɟ ɩɪɨɫɬɵɦ RȾɈȻ ɢ ɞɟɲɟɜɵɦ ɚɫɢɧɯɪɨɧɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɡɚ Ɇ ɫɱɟɬ ɢɯ ɛɨɥɶɲɟɣ ɩɪɨɫɬɨɬɵ ɢ ɥɭɱɲɢɯ I ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ. ɋɨɯɪɚɧɹɸɬ Ɋɢɫ. 3.30. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɫɯɟɦɚ Ⱦɉȼ ɫɜɨɢ ɩɨɡɢɰɢɢ ɜ ɦɚɝɢɫɬɪɚɥɶɧɨɦ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɷɥɟɤɬɪɨɬɪɚɧɫɩɨɪɬɟ, ɬɪɚɦɜɚɟ, ɜɧɭɬɪɢɡɚɜɨɡɛɭɠɞɟɧɢɹ ɜɨɞɫɤɨɦ ɬɪɚɧɫɩɨɪɬɟ ɛɥɚɝɨɞɚɪɹ ɫɜɨɢɦ ɞɨɫɬɨɢɧɫɬɜɚɦ: – ɞɥɹ ɩɢɬɚɧɢɹ ɞɨɫɬɚɬɨɱɧɨ ɢɦɟɬɶ ɨɞɢɧ ɩɪɨɜɨɞ (ɬɪɨɥɥɟɣ); – ɧɟ ɛɨɢɬɫɹ ɛɨɥɶɲɢɯ ɫɧɢɠɟɧɢɣ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢ ɡɧɚɱɢɬɟɥɶɧɨɦ ɭɞɚɥɟɧɢɢ ɭɫɬɚɧɨɜɨɤ ɨɬ ɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹ (ɩɨɬɨɤ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɢɹ); – ɥɭɱɲɟ ɜɵɞɟɪɠɢɜɚɸɬ ɩɟɪɟɝɪɭɡɤɢ ɧɚ ɩɨɞɴɟɦɟ, ɨɛɥɚɞɚɹ ɛɨɥɶɲɟɣ ɩɟɪɟɝɪɭɡɨɱɧɨɣ ɫɩɨɫɨɛɧɨɫɬɶɸ ɩɨ ɦɨɦɟɧɬɭ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ Ⱦɇȼ ɩɪɢ ɨɞɢɧɚɤɨɜɨɣ ɫ ɧɢɦ ɩɟɪɟɝɪɭɡɨɱɧɨɣ ɫɩɨɫɨɛɧɨɫɬɶɸ ɩɨ ɬɨɤɭ; – ɪɚɡɜɢɜɚɟɬ ɩɪɢɦɟɪɧɨ ɩɨɫɬɨɹɧɧɭɸ ɦɨɳɧɨɫɬɶ (ɦɚɥɵɣ ɝɪɭɡ – ɜɵɫɨɤɚɹ ɫɤɨɪɨɫɬɶ, ɬɹɠɟɥɵɣ ɝɪɭɡ – ɦɟɞɥɟɧɧɚɹ ɫɤɨɪɨɫɬɶ), ɧɟɨɛɯɨɞɢɦɭɸ ɞɥɹ ɬɪɚɧɫɩɨɪɬɧɵɯ ɦɚɲɢɧ; – ɛɨɥɟɟ ɧɚɞɟɠɧɵ ɡɚ ɫɱɟɬ ɛɨɥɶɲɨɝɨ ɫɟɱɟɧɢɹ ɩɪɨɜɨɞɨɜ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɢ ɦɚɥɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɦɟɠɞɭ ɜɢɬɤɚɦɢ. ȼɤɥɸɱɟɧɢɟ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɰɟɩɶ ɹɤɨɪɹ, ɦɨɳɧɨɫɬɶ ɤɨɬɨɪɨɣ ɧɚ ɞɜɚ ɩɨɪɹɞɤɚ ɜɵɲɟ, ɱɟɦ ɦɨɳɧɨɫɬɶ ɜɨɡɛɭɠɞɟɧɢɹ, ɫɨɡɞɚɟɬ ɭɫɥɨɜɢɹ ɞɥɹ ɮɨɪɫɢɪɨɜɚɧɧɨɝɨ ɢɡɦɟɧɟɧɢɹ ɩɨɬɨɤɚ ɞɜɢɝɚɬɟɥɹ. ȼ ɞɢɧɚɦɢɤɟ ɩɪɢɯɨɞɢɬɫɹ ɭɱɢɬɵɜɚɬɶ ɜɥɢɹɧɢɟ ɜɢɯɪɟɜɵɯ ɬɨɤɨɜ, ɜɨɡɧɢɤɚɸɳɢɯ ɩɪɢ ɛɵɫɬɪɵɯ ɢɡɦɟɧɟɧɢɹɯ ɩɨɬɨɤɚ. ɉɨɜɟɞɟɧɢɟ Ⱦɉȼ ɨɩɢɫɵɜɚɟɬɫɹ ɬɟɦɢ ɠɟ ɭɪɚɜɧɟɧɢɹɦɢ ɞɥɹ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ, ɱɬɨ ɢ Ⱦɇȼ. ɂɯ ɨɬɥɢɱɢɟ – ɜ ɫɩɨɫɨɛɟ ɫɨɡɞɚɧɢɹ ɩɨɬɨɤɚ. Ɉɫɧɨɜɧɵɟ ɭɪɚɜɧɟɧɢɹ Ⱦɉȼ ɛɟɡ ɭɱɟɬɚ ɜɢɯɪɟɜɵɯ ɬɨɤɨɜ [1]: dI dɎ U E I R (L ə L Ɉȼ ) w ȼ ; ȿ = ɤɎ(I)·Ȧ; Ɇ = ɤɎ(I)·I. dt dt Ɉɩɭɫɤɚɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɭɪɚɜɧɟɧɢɣ, ɩɨɫɬɪɨɢɦ ɫɬɪɭɤɬɭɪɧɭɸ ɫɯɟɦɭ (ɪɢɫ. 3.31). 82

ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɹɤɨɪɧɨɣ ɰɟɩɢ ɨɫɬɚɥɚɫɶ ɩɪɟɠɧɟɣ (ɫɦ. ɪɢɫ. 3.31), ɨɬɫɭɬɫɬɜɭɟɬ ɤɨɧɬɭɪ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ, ɬɨɤ ɹɤɨɪɹ ɜɵɩɨɥɧɹɟɬ ɮɭɧɤɰɢɸ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɢ ɫɨɡɞɚɟɬ ɧɚɦɚɝɧɢɱɢɜɚɸɳɭɸ ɫɢɥɭ ɜ ɦɚɝɧɢɬɧɨɣ ɰɟɩɢ ɞɜɢɝɚɬɟɥɹ. ɇɚ ɜɯɨɞɟ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ – ɬɨɤ ɹɤɨɪɹ, ɧɚ ɜɵɯɨɞɟ – ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ R ɹɤɨɪɧɨɣ ɰɟɩɢ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ rɈȼ

R rə rOB R ȾɈȻ ,

(3.47)

ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɹɤɨɪɧɨɣ ɰɟɩɢ ɭɱɢɬɵɜɚɟɬ ɫɭɦɦɚɪɧɭɸ ɢɧɞɭɤɬɢɜɧɨɫɬɶ ɨɛɦɨɬɨɤ ɹɤɨɪɹ ɢ ɜɨɡɛɭɠɞɟɧɢɹ

L ə LOB .

Ɍə

(3.48)

R

ɉɨ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɟ ɦɨɠɧɨ ɢɡɭɱɚɬɶ ɩɨɜɟɞɟɧɢɟ ɞɜɢɝɚɬɟɥɹ ɜ ɫɬɚɬɢɤɟ ɢ ɞɢɧɚɦɢɤɟ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɢɯ ɭɱɟɬɚ ɜɢɯɪɟɜɵɯ ɬɨɤɨɜ ɧɭɠɧɨ ɨɛɪɚɬɢɬɶɫɹ ɤ ɛɨɥɟɟ ɩɨɥɧɵɦ ɭɱɟɛɧɵɦ ɩɨɫɨɛɢɹɦ [1, 14].

U

E

M

I

1/ R 1 Tə p

MC 1 Jp

Ȧ

Ɏ I Ɏ

Ɋɢɫ. 3.31. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɉȼ

wȼ·ɪ

3.2.2. ȿɫɬɟɫɬɜɟɧɧɵɟ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɉȼ

ɍɪɚɜɧɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɢɯ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜ ɨɛɳɟɦ ɜɢɞɟ ɨɞɢɧɚɤɨɜɵ ɞɥɹ ɜɫɟɯ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ (3.11). Ȧ

U R M. kɎ kɎ 2

Ⱦɥɹ Ⱦɉȼ ɩɨɬɨɤ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɬɨɤɚ ɹɤɨɪɹ Ɏ = f(I) ɢ ɜɫɟ ɩɪɨɰɟɫɫɵ, ɩɪɨɬɟɤɚɸɳɢɟ ɜ ɦɚɲɢɧɟ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ (ɪɢɫ. 3.32). Ȧ

U R M . kɎI kɎI 2

ɇɚ ɪɢɫ. 3.32 ɩɪɢɜɟɞɟɧɵ ɬɚɤɠɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ. ɉɪɢ ɬɨɤɚɯ ɹɤɨɪɹ I < Iɇ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɦɟɸɬ ɜɢɞ ɝɢɩɟɪɛɨɥɵ ɢ ɩɪɢ ɫɬɪɟɦɥɟɧɢɢ ɦɨɦɟɧɬɚ ɢ ɬɨɤɚ ɤ ɧɭɥɸ ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɩɪɢɛɥɢɠɚɸɬɫɹ ɤ ɨɫɢ ɨɪɞɢɧɚɬ. ɉɪɢ I = 0 ɩɨɬɨɤ Ɏ = 0 ɢ ɫɤɨɪɨɫɬɶ ɫɬɪɟɦɢɬɫɹ ɤ ɛɟɫɤɨɧɟɱɧɨɫɬɢ, ɱɬɨɛɵ ɗȾɋ 83

ɭɪɚɜɧɨɜɟɫɢɥɚ ɩɪɢɥɨɠɟɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ. Ɋɟɚɥɶɧɨ ɫɭɳɟɫɬɜɭɟɬ ɨɫɬɚɬɨɱɧɵɣ ɩɨɬɨɤ ɎɈɋɌ, ɢ ɫɤɨɪɨɫɬɶ ɧɟ ɪɚɜɧɚ ɛɟɫɤɨɧɟɱɧɨɫɬɢ, ɧɨ ɨɫɬɚɟɬɫɹ ɨɱɟɧɶ ɜɵɫɨɤɨɣ. Ⱦɉȼ ɞɨɥɠɟɧ ɢɦɟɬɶ ɝɚɪɚɧɬɢɪɨɜɚɧɧɵɣ ɦɢɧɢɦɭɦ ɧɚɝɪɭɡɤɢ (~0.4Ɇɇ), ɢɧɚɱɟ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɛɭɞɟɬ ɛɨɥɶɲɟ ɦɚɤɫɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɨɣ ɩɨ ɭɫɥɨɜɢɹɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɩɪɨɱɧɨɫɬɢ. Ɏ

Ȧ

Ȧ

Ɏɇ Ȧɇ I

I

M

Iɇ

Iɇ

Mɇ Ɋɢɫ. 3.32. Ʉɪɢɜɚɹ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ, ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɉɪɢ I > Iɇ ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɡɨɧɟ ɧɚɫɵɳɟɧɢɹ, ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɞɨɛɧɵ Ⱦɇȼ, ɧɨ ɠɟɫɬɤɨɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɟɪɟɦɟɧɧɚ

kɎ 2

ȕ

(3.49)

var .

R

ɂɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɉȼ ɢɡɦɟɧɹɸɬɫɹ ɚɧɚɥɨɝɢɱɧɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ Ⱦɇȼ (ɪɢɫ. 3.33). Ȧ

Ȧ

U kɎI

R

kɎI 2

M.

Ȧ ɟɫɬ UĻ

Ȧ Ɏɇ>Ɏ

ɟɫɬ M

RĹ

ɚ – UĻĻ

ɟɫɬ M

M

ɛ – RĹĹ

ɜ – ɎĻ

Ɋɢɫ. 3.33. ɂɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɉȼ ɩɪɢ: ɚ) ɭɦɟɧɶɲɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ; ɛ) ɭɜɟɥɢɱɟɧɢɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ; ɜ) ɭɦɟɧɶɲɟɧɢɢ ɩɨɬɨɤɚ ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɦɟɳɚɸɬɫɹ ɩɪɢɦɟɪɧɨ ɩɚɪɚɥɥɟɥɶɧɨ ɟɫɬɟɫɬɜɟɧɧɨɣ, ɩɪɢ ɜɜɟɞɟɧɢɢ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢɡɦɟɧɹɸɬ ɧɚɤɥɨɧ, ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɬɨɤɚ ɫɤɨɪɨɫɬɶ ɜɨɡɪɚɫɬɚɟɬ (ɞɥɹ ɷɬɨɝɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɭɸ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ ɲɭɧɬɢɪɭɸɬ ɞɨɛɚɜɨɱɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ). 3.2.3. Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ Ⱦɉȼ

Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ. Ɉɫɭɳɟɫɬɜɥɟɧɢɟ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɨɜ ɞɜɢɝɚɬɟɥɟɣ ɞɪɭɝɨɝɨ 84

ɫɩɨɫɨɛɚ ɜɨɡɛɭɠɞɟɧɢɹ ɫɜɹɡɚɧɨ ɫ ɩɨɞɤɥɸɱɟɧɢɟɦ ɨɛɦɨɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɧɟɨɛɯɨɞɢɦɭɸ ɜɟɥɢɱɢɧɭ ɩɨɬɨɤɚ. ɋɩɨɫɨɛɵ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɡɛɵɬɨɱɧɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɨɫɬɚɸɬɫɹ ɩɪɟɠɧɢɦɢ: – ɜɨɡɜɪɚɬ ɷɧɟɪɝɢɢ ɜ ɫɟɬɶ – ɪɟɤɭɩɟɪɚɰɢɹ; – ɬɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ; – ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ. Ɋɚɫɫɦɨɬɪɢɦ, ɤɚɤ ɨɫɭɳɟɫɬɜɥɹɸɬɫɹ ɷɬɢ ɫɩɨɫɨɛɵ ɭ Ⱦɉȼ. Ɋɟɤɭɩɟɪɚɬɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ (ɊɌ). ɍɫɥɨɜɢɟ ɊɌ – ɗȾɋ ɞɜɢɝɚɬɟɥɹ ɛɨɥɶɲɟ ɩɪɢɥɨɠɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ȿ > U. ȿɫɥɢ ɗȾɋ ɛɭɞɟɬ ɪɚɜɧɨ ɩɪɢɥɨɠɟɧɧɨɦɭ ɧɚɩɪɹɠɟɧɢɸ, ɬɨ ɩɪɢ I = 0, Ɏ = 0, Ȧ = f ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɪɟɠɢɦɚ ɊɌ ɜ ɟɫɬɟɫɬɜɟɧɧɨɣ ɫɯɟɦɟ ɜɤɥɸɱɟɧɢɹ Ⱦɉȼ ɧɟɨɛɯɨɞɢɦɚ Ȧ > f, ɢ ɪɟɠɢɦ ɊɌ ɧɟɜɨɡɦɨɠɟɧ. ȼ ɭɫɬɚɧɨɜɤɚɯ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɞɜɢɠɧɨɝɨ ɫɨɫɬɚɜɚ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɊɌ ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɢɫɤɥɸɱɚɟɬɫɹ ɢɡ ɫɯɟɦɵ ɢ ɩɨɞɤɥɸɱɚɟɬɫɹ ɤ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ. ɇɨ ɷɬɨ ɩɨɥɭɱɚɟɬɫɹ Ⱦɇȼ! Ɋɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ (ɉȼ). Ɋɟɠɢɦ ɉȼ ɚɧɚɥɨɝɢɱɟɧ ɉȼ Ⱦɇȼ. Ɉɫɨɛɟɧɧɨɫɬɶ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɤɚɤ ɩɨɞɤɥɸɱɢɬɶ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɥɹɪɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ ɩɨɬɨɤ ɦɚɲɢɧɵ ɧɟ ɞɨɥɠɟɧ ɦɟɧɹɬɶ ɧɚɩɪɚɜɥɟɧɢɹ, ɨɛɦɨɬɤɚ ɞɨɥɠɧɚ ɛɵɬɶ ɜɤɥɸɱɟɧɚ ɜ ɰɟɩɶ, ɝɞɟ ɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɧɟ ɦɟɧɹɟɬɫɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɟɟ ɦɟɫɬɨ – ɡɚ ɪɟɜɟɪɫɨɪɨɦ (ɪɢɫ. 3.34).ɉɪɢ ɜɤɥɸɱɟɧɢɢ Ʉȼ ɢ ɩɪɢ ɜɤɥɸɱɟɧɢɢ Ʉɇ ɩɨɥɹɪɧɨɫɬɶ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ ɢɡɦɟɧɹɟɬɫɹ, ɚ ɬɨɤ ɜ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɧɟ ɢɡɦɟɧɹɟɬ ɧɚɩɪɚɜɥɟɧɢɹ, ɧɟ ɦɟɧɹɟɬ ɧɚɩɪɚɜɥɟɧɢɹ ɢ ɩɨɬɨɤ. ɉɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɜ ɨɞɧɨɦ ɢɡ ɧɚɩɪɚɜɥɟɧɢɣ ɩɟɪɟɤɥɸɱɟɧɢɟɦ ɤɨɧɬɚɤɬɨɪɨɜ Ʉȼ ɢ Ʉɇ ɢɡɦɟɧɹɟɬɫɹ ɩɨɥɹɪɧɨɫɬɶ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ, ɚ ɨɬɤɥɸɱɟɧɢɟ ɤɨɧɬɚɤɬɨɪɚ Ʉɉȼ ɜɜɨɞɢɬ ɜ ɰɟɩɶ ɹɤɨɪɹ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ RȾɈȻ. Ⱦɜɢɝɚɬɟɥɶ ɩɟɪɟɯɨɞɢɬ ɜ ɪɟɠɢɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɟɪɟɯɨɞɚ ɜ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɞɥɹ ɬɨɪɦɨɠɟɧɢɹ ɧɚ ɜɵɛɟɝɟ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3.34. Ⱦɨɫɬɨɢɧɫɬɜɚ ɢ ɧɟɞɨɫɬɚɬɤɢ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɩɨɞɪɨɛɧɨ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɪɚɡɞɟɥɟ 3.1.6.

Ʉȼ

Ʉɇ

Ȧ

U LɆ

RȾɈȻ

Ɇ Ʉɇ

ɉȼ

Ɇ MC

Ʉȼ

ɉȼ

Ʉɉȼ

Ɋɢɫ. 3.34. ɋɯɟɦɚ Ⱦɉȼ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɟɠɢɦɚ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ (ȾɌ). ɇɚ ɩɪɚɤɬɢɤɟ ɩɪɢɦɟɧɹɸɬɫɹ ɞɜɟ ɫɯɟɦɵ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ: – ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ; – ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ.

85

ɚ) Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ ɜɵɩɨɥɧɹɟɬɫɹ ɩɨɞɤɥɸɱɟɧɢɟɦ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɤ ɨɬɞɟɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɢɬɚɧɢɹ. ȼ ɱɚɫɬɧɨɫɬɢ ɷɬɢɦ ɢɫɬɨɱɧɢɤɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɫɟɬɶ, ɤ ɤɨɬɨɪɨɣ ɨɛɦɨɬɤɚ ɩɨɞɤɥɸɱɚɟɬɫɹ ɱɟɪɟɡ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ. Ɍɚɤɚɹ ɫɯɟɦɚ ɩɨ ɫɜɨɢɦ ɦɟɯɚɧɢɱɟɫɤɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɩɨɜɬɨɪɹɟɬ ɫɯɟɦɭ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ. ɇɚ ɪɢɫ. 3.35 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ ɄɌ RȾɌ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ. ȼ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɜɤɥɸɱɟɧ LM ɄɅ ɤɨɧɬɚɤɬɨɪ ɄɅ ɢ ɹɤɨɪɧɚɹ ɰɟɩɶ ɩɨɞɤɥɸɱɟɧɚ ɤ ɫɟɬɢ. Ⱦɥɹ ɩɟɪɟɯɨɆ ɞɚ ɜ ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɄɌ Rȼ ɦɨɠɟɧɢɹ ɨɬɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ ɄɅ ɢ ɜɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ ɄɌ. Ɉɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɤɨɧɬɚɤɬɨɦ ɄɌ ɱɟɪɟɡ ɞɨɛɚɜɨɱɧɨɟ ɫɨɊɢɫ. 3.35. ɋɯɟɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɬɢɜɥɟɧɢɟ Rȼ ɩɨɞɤɥɸɱɚɟɬɫɹ ɤ ɬɨɪɦɨɠɟɧɢɹ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ ɫɟɬɢ. ɐɟɩɶ ɹɤɨɪɹ ɞɪɭɝɢɦ ɤɨɧɬɚɤɬɨɦ ɄɌ ɡɚɦɵɤɚɟɬɫɹ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ RȾɌ. ɉɨɫɥɟ ɩɟɪɟɤɥɸU ɱɟɧɢɹ ɜɨ ɜɪɚɳɚɸɳɟɦɫɹ ɩɨ ɄɌ RȾɌ ɢɧɟɪɰɢɢ ɹɤɨɪɟ ɧɚɜɨɞɢɬɫɹ ɗȾɋ, ɜɨɡɧɢɤɚɸɳɢɣ ɬɨɤ ɫɨɜɩɚɞɚɟɬ ɩɨ ɄɅ ɄɅ LɆ ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɗȾɋ ɢ ɜɨ ɜɡɚɢɆ ɦɨɞɟɣɫɬɜɢɢ ɫ ɩɨɬɨɤɨɦ ɫɨɡɞɚɟɬɄɌ ɫɹ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ. ȼɟɥɢɱɢɧɚ ɩɨɬɨɤɚ ɡɚɜɢɫɢɬ ɨɬ Ɋɢɫ. 3.36. ɋɯɟɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɤɚ ɜ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ. ɬɨɪɦɨɠɟɧɢɹ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ Ⱦɥɹ ɫɨɡɞɚɧɢɹ ɩɨɬɨɤɚ, ɛɥɢɡɤɨɝɨ ɤ ɧɨɦɢɧɚɥɶɧɨɦɭ Ɏ § Ɏɇ, ɩɨ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɩɭɫɬɢɬɶ ɧɨɦɢɧɚɥɶɧɵɣ ɬɨɤ ɞɜɢɝɚɬɟɥɹ Iɇ. Ɋɚɫɯɨɞ ɦɨɳɧɨɫɬɢ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ɫɨɫɬɚɜɥɹɟɬ ~Ɋɇ (ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ – 0,02…0,05 Ɋɇ). ɂɡ ɷɬɢɯ ɫɨɨɛɪɚɠɟɧɢɣ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ Rȼ = Uɇ / Iȼ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ RȾɌ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɡɚɞɚɧɧɨɦɭ ɧɚɱɚɥɶɧɨɦɭ ɬɨɪɦɨɡɧɨɦɭ ɦɨɦɟɧɬɭ. Ⱦɨɫɬɨɢɧɫɬɜɚ ɢ ɧɟɞɨɫɬɚɬɤɢ ɪɚɫɫɦɨɬɪɟɧɵ ɩɨɞɪɨɛɧɨ ɜ ɩ. 3.1.6. ɛ) Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ (ɪɢɫ.3.36) ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɤɪɚɧɨɜɵɯ ɦɟɯɚɧɢɡɦɚɯ. ȼ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɜɤɥɸɱɟɧ ɤɨɧɬɚɤɬɨɪ ɄɅ ɢ ɹɤɨɪɧɚɹ ɰɟɩɶ ɩɨɞɤɥɸɱɟɧɚ ɤ ɫɟɬɢ. Ⱦɥɹ ɩɟɪɟɯɨɞɚ ɜ ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɶ ɤɨɧɬɚɤɬɨɪɨɦ ɄɅ ɨɬɤɥɸɱɚɟɬɫɹ ɨɬ ɫɟɬɢ. ȼɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ ɄɌ ɢ ɫɨɛɢɪɚɟɬɫɹ ɤɨɧɬɭɪ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. Ɉɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɤɨɧɬɚɤɬɚɦɢ ɄɌ ɱɟɪɟɡ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ RȾɌ ɫɨɟɞɢɧɹɟɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫ ɰɟɩɶɸ ɹɤɨɪɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɜ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɫɨɜɩɚɥɨ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɬɨɤɚ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɟɠɢɦɟ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɫɬɚɬɨɱɧɨɟ ɧɚɦɚɝɧɢɱɢɜɚɧɢɟ ɞɜɢɝɚɬɟɥɹ. Ⱦɜɢɝɚɬɟɥɶ ɩɟɪɟɜɨɞɢɬɫɹ ɜ ɪɟɠɢɦ ɝɟɧɟɪɚɬɨɪɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ. 86

ɍɫɥɨɜɢɹ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɝɟɧɟɪɚɬɨɪɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ: 1. ɇɚɥɢɱɢɟ ɨɫɬɚɬɨɱɧɨɝɨ ɩɨɬɨɤɚ ɎɈɋɌ. 2. Ɍɨɤ, ɜɨɡɧɢɤɚɸɳɢɣ ɜ ɰɟɩɢ, ɞɨɥɠɟɧ ɫɨɡɞɚɜɚɬɶ ɩɨɬɨɤ, ɫɨɜɩɚɞɚɸɳɢɣ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɎɈɋɌ. 3. ɗȾɋ, ɧɚɜɨɞɢɦɚɹ ɜ ɞɜɢɝɚɬɟɥɟ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɜ ɰɟɩɢ ɹɤɨɪɹ ȿ > I (rə + rɈȼ + RȾɌ). ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɷɬɢɯ ɭɫɥɨɜɢɣ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. Ɉɫɬɚɬɨɱɧɨɟ ɧɚɦɚɝɧɢɱɢɜɚɧɢɟ ɞɜɢɝɚɬɟɥɹ ɎɈɋɌ ɩɪɢ ɜɪɚɳɟɧɢɢ ɹɤɨɪɹ ɧɚɜɨɞɢɬ ɗȾɋ ȿɈɋɌ (ɪɢɫ. 3.37), ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɤɨɬɨɪɨɣ ɩɨ ɹɤɨɪɸ ɢ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɨɬɟɤɚɟɬ ɬɨɤ I1. ɗɬɨɬ ɬɨɤ ɫɨɡɞɚɺɬ ɨɫɧɨɜɧɨɣ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ Ɏ, ɤɨɬɨɪɵɣ, ɫɨɜɩɚɞɚɹ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɨɫɬɚɬɨɱɧɵɦ ɩɨɬɨɤɨɦ, ɩɪɢɜɟɞɺɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɗȾɋ ɞɨ ȿ1. ɗɬɨ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɩɨɜɥɟɱɺɬ ɡɚ ɫɨɛɨɣ ɭɜɟɥɢɱɟɧɢɟ ɬɨɤɚ ɞɨ I2. Ɍɚɤɨɣ ɩɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɛɭɞɟɬ ɩɪɨɞɨɥɠɚɬɶɫɹ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɗȾɋ ɧɟ ɫɪɚɜɧɹɟɬɫɹ ɫ ɫɭɦɦɚɪɧɵɦ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɰɟɩɢ ɹɤɨɪɹ ȿ = I (rə + rɈȼ + RȾɌ) ɜ ɬɨɱɤɟ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɪɟɠɢɦɚ ɪɚɛɨɬɵ. ɍɫɬɚɧɨɜɢɜɲɢɣɫɹ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɢ ɨɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɹɤɨɪɧɨɣ ɰɟɩɢ. ɉɪɢ ɫɧɢɠɟɧɢɢ ɫɤɨɪɨɫɬɢ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɢ R1 ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ ɪɟɠɢɦ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɬɨɱɤɚɦ 1,2,3 ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ IR1. ɍɜɟɥɢɱɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R2 > R1 ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɬɨɤɚ ɢ ɦɨɦɟɧɬɚ, ɭɫɬɚɧɨɜɢɜɲɢɟɫɹ ɪɟɠɢɦɵ ɩɟɪɟɯɨɞɹɬ ɜ ɬɨɱɤɢ 4,5 ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ IR2. Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɩɪɢ ɫɨɩɪɨɬɢɜɥɟɧɢɢ R2 ɢ ɫɤɨɪɨɫɬɢ Ȧ3 < Ȧ2 ɧɟ ɩɪɨɢɫɯɨɞɢɬ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ, ɬɨɤ ɧɟ ɩɪɨɬɟɤɚɟɬ, ɦɨɦɟɧɬ ɨɬɫɭɬɫɬɜɭɟɬ, ɬɨɪɦɨɠɟɧɢɟ ɧɟ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɧɚɱɢɧɚɟɬɫɹ ɧɟ ɫ ɧɭɥɟɜɨɣ, ɚ ɫ ɤɪɢɬɢɱɟɫɤɨɣ ɫɤɨɪɨɫɬɢ (ɫɦ. ɪɢɫ. 3.37). Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɥɭɱɚɸɬɫɹ ɧɟɥɢɧɟɣɧɵɦɢ. Ʉɚɠɞɨɦɭ ɫɨɩɪɨɬɢɜɥɟɧɢɸ R ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɜɨɹ ɤɪɢɬɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ ȦɄɊ. ȿ

IR

IR2

IR1

ȿ2

Ȧ Ȧ1

ȦɄɊ1 ȦɄɊ2 ȦɄɊ3

1

ȿ1

Ȧ2

5 4

2

Ȧ3

Ɇ

Ɇɋ

3

ȿɈɋɌ I I1

I2

2 1

Ɋɢɫ. 3.37. ɉɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ ȿɫɥɢ ɫɨɛɪɚɬɶ ɫɯɟɦɭ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ ɩɪɢ ɫɩɭɫɤɟ ɝɪɭɡɚ, ɬɨ ɩɨɫɥɟ ɨɬɩɭɫɤɚ ɬɨɪɦɨɡɚ ɝɪɭɡ ɛɭɞɟɬ ɩɚɞɚɬɶ ɞɨ ɤɪɢɬɢɱɟɫɤɨɣ ɫɤɨɪɨ 87

ɫɬɢ, ɩɪɢ ɤɨɬɨɪɨɣ ɧɚɱɧɟɬɫɹ ɩɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ, ɜɨɡɧɢɤɧɟɬ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ, ɢ ɤɪɚɧ ɢɫɩɵɬɚɟɬ ɞɢɧɚɦɢɱɟɫɤɢɣ ɭɞɚɪ. ɗɬɨɬ ɧɟɞɨɫɬɚɬɨɤ ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶɸ ɫɩɭɫɤɚ ɝɪɭɡɚ ɩɪɢ ɫɧɹɬɢɢ ɧɚɩɪɹɠɟɧɢɹ ɩɢɬɚɧɢɹ ɤɪɚɧɚ. Ɍɚɤɨɣ ɜɢɞ ɬɨɪɦɨɠɟɧɢɹ ɦɨɠɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ ɤɚɤ ɚɜɚɪɢɣɧɵɣ. ɋɯɟɦɭ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɫɯɟɦɨɣ ɛɟɡɨɩɚɫɧɨɝɨ ɫɩɭɫɤɚ. 3.2.4. Ɋɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ Ⱦɉȼ Ɋɚɫɱɟɬ ɟɫɬɟɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. ɇɟɥɢɧɟɣɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ Ɏ = f (I) ɩɪɟɞɨɩɪɟɞɟɥɹɟɬ ɪɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ. Ⱦɥɹ ɪɚɫɱɺɬɚ ɢɫɩɨɥɶɡɭɸɬɫɹ ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ ɞɜɢɝɚɬɟɥɹ: PH, UH, IH, nH, Șɇ, JȾȼ ɢ ɤɚɬɚɥɨɠɧɵɟ ɤɪɢɜɵɟ: n, P, M, Ș = f (I). ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɫɥɟɞɭɟɬ ɩɟɪɟɜɟɫɬɢ ɜ ɫɢɫɬɟɦɭ ɋɂ ɡɧɚɱɟɧɢɹ ɫɤɨɪɨɫɬɢ ɢɡ ɨɛ/ɦɢɧ ɜ ɪɚɞ/ɫ (Ȧ = n / 9,55) ɢ ɦɨɦɟɧɬɚ ɢɡ ɤȽɦ ɜ ɇɦ (Ɇ = ɆɄȺɌ ǜ9,81). ȿɫɬɟɫɬɜɟɧɧɚɹ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɪɟɞɫɬɚɜɥɟɧɚ Ȧ Ɇ ɤɚɬɚɥɨɠɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ n (I). ɋ ɩɨɦɨɳɶɸ ɆɌ ɆɗɆ ɞɪɭɝɨɣ ɤɚɬɚɥɨɠɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɆɄȺɌ = f (I) ȦɄȺɌ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɆɄȺɌ ǻɆ Ȧ = f(Ɇ). Ɂɚɞɚɸɬɫɹ ɬɨɤɨɦ ȦȿɋɌ IɁȺȾ, ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɤɪɢɜɨɣ Ȧ(I) ɝɪɚɮɢɱɟɫɤɢ ɨɩȦ1 (ɪɢɫ. ɪɟɞɟɥɹɸɬ ȦȿɋɌ 3.38), ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɡɚɆȼ – ɜɢɫɢɦɨɫɬɢ ɆɄȺɌ(I) Ɇȼ I ɡɧɚɱɟɧɢɟ Ɇȼ. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤIɁȺȾ IɁȺȾ1 ɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ Ȧ = f(M) ɫɬɪɨɹɬɫɹ ɞɥɹ ɷɥɟɤɬɪɨɊɢɫ. 3.38. Ʉɚɬɚɥɨɠɧɵɟ ɤɪɢɜɵɟ ȦɄȺɌ(I), ɆɄȺɌ(I) ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɆɗɆ. ɢ ɪɚɫɱɟɬ ɆɗɆ(I) ɢ ɆɌ(I) ɇɚ ɤɚɬɚɥɨɠɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ ɩɪɢɜɨɞɢɬɫɹ ɡɧɚɱɟɧɢɟ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ ɆɄȺɌ = Ɇȼ = f (I). ɋɯɟɦɚ ɪɚɫɱɟɬɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ȧ = f (MɗɆ ): – ɡɚɞɚɸɬɫɹ ɬɨɤɨɦ IɁȺȾ1; – ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɤɪɢɜɨɣ Ȧ (I) ɨɩɪɟɞɟɥɹɸɬ Ȧ1; – ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɤɪɢɜɨɣ Ɇȼ (I) – ɡɧɚɱɟɧɢɟ Ɇȼ; – ɨɩɪɟɞɟɥɹɸɬ ɜɟɥɢɱɢɧɭ kɎ ɁȺȾ

UH IɁȺȾ1 rə rOB ; Ȧ1

88

– ɪɚɫɫɱɢɬɵɜɚɸɬ ɡɧɚɱɟɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ

MɗɆ

kɎ ɁȺȾ IɁȺȾ1 ;

– ɩɨɥɭɱɚɸɬ ɤɨɨɪɞɢɧɚɬɵ ɨɞɧɨɣ ɬɨɱɤɢ ɆɗɆ, Ȧ1. Ⱦɚɥɟɟ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɤɨɨɪɞɢɧɚɬɵ ɧɟɫɤɨɥɶɤɢɯ ɬɨɱɟɤ ɢ ɫɬɪɨɢɬɫɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ. Ⱦɥɹ ɞɚɥɶɧɟɣɲɢɯ ɪɚɫɱɟɬɨɜ ɩɨɥɟɡɧɨ ɩɨɫɬɪɨɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɆɗɆ(I). Ɋɚɡɧɨɫɬɶ ǻɆ = ɆɗɆ – Ɇȼ ɩɪɟɞɫɬɚɜɥɹɟɬ ɩɨɬɟɪɢ ɦɨɦɟɧɬɚ ɜ ɞɜɢɝɚɬɟɥɟ. ȼ ɬɨɪɦɨɡɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɨɬɟɪɢ ɜ ɞɜɢɝɚɬɟɥɟ ɩɨɤɪɵɜɚɸɬɫɹ ɫɨ ɫɬɨɪɨɧɵ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. Ɇɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ

ɆɌ I MɗɆ ǻM , ɩɨɡɜɨɥɹɸɳɭɸ ɪɚɫɫɱɢɬɵɜɚɬɶ ɬɨɤɢ ɹɤɨɪɹ ɜ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɚɯ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɵɯ ɬɨɱɤɚɯ. Ɋɚɫɱɟɬ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɬɚɤɠɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɣ ɦɟɬɨɞ ɪɚɫɱɟɬɚ, ɬɚɤ ɤɚɤ ɨɬɫɭɬɫɬɜɭɟɬ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. Ȧ

U MR . kɎI kɎI 2

Ɂɚɞɚɜɚɹɫɶ ɩɨɫɬɨɹɧɧɵɦ ɡɧɚɱɟɧɢɟɦ ɬɨɤɚ IɁȺȾ =const, ɩɨɥɭɱɚɟɦ ɢ ɩɨɫɬɨɹɧɧɨɟ ɡɧɚɱɟɧɢɟ ɩɨɬɨɤɚ kɎɁȺȾ = const. ɉɪɢ ɩɨɫɬɨɹɧɧɨɦ ɩɨɬɨɤɟ ɨɬɧɨɲɟɧɢɟ ɫɤɨɪɨɫɬɟɣ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɸ ɗȾɋ ȦȿɋɌ

ȿȿɋɌ kɎ ɁȺȾ

Uɇ IɁȺȾ rə ; kɎ ɁȺȾ

ȦɂɋɄ

ȿɂɋɄ kɎ ɁȺȾ

U IɁȺȾ R , kɎ ɁȺȾ

ɬɨɝɞɚ ɫɤɨɪɨɫɬɶ ɧɚ ɢɫɤɭɫɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɩɪɢ ɡɚɞɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ U ɢ R ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɩɨ ɮɨɪɦɭɥɟ ȦɂɋɄ

ȦȿɋɌ

U IɁȺȾ R . Uɇ IɁȺȾ rə

(3.50)

ɉɨ ɞɚɧɧɵɦ ɫɨɨɬɧɨɲɟɧɢɹɦ ɦɨɠɧɨ ɪɚɫɫɱɢɬɵɜɚɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɥɸɛɵɯ ɪɟɠɢɦɚɯ ɪɚɛɨɬɵ (ɞɜɢɝɚɬɟɥɶɧɨɦ, ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ, ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ). Ɋɚɫɱɟɬ ɫɯɟɦ ɜɤɥɸɱɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ. Ɋɟɲɟɧɢɟ ɨɫɧɨɜɧɨɣ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɡɚɞɚɱɢ – ɨɛɟɫɩɟɱɢɬɶ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ – ɜɵɩɨɥɧɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɮɨɪɦɭɥɵ (3.50). ɋɨ ɫɬɨɪɨɧɵ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɜɵɫɬɚɜɥɹɸɬɫɹ ɤɨɨɪɞɢɧɚɬɵ ɡɚɞɚɧɧɨɣ ɬɨɱɤɢ: ɆɁȺȾ, ȦɁȺȾ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɩɨ ɪɚɫɫɱɢɬɚɧɧɵɦ ɪɚɧɟɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ Ɇȼ(I) – ɞɥɹ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɢɥɢ ɆɌ(I) – ɞɥɹ ɬɨɪɦɨɡɧɨɝɨ ɪɟɠɢɦɚ ɩɨ ɆɁȺȾ ɨɩɪɟɞɟɥɹɸɬ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɹɤɨɪɹ IɁȺȾ. ɉɨ ɟɫɬɟɫɬɜɟɧɧɨɣ ɤɚɬɚɥɨɠɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ Ȧ(I) ɩɨ ɬɨɤɭ IɁȺȾ ɧɚɯɨɞɹɬ ȦȿɋɌ. ɉɨɞɫɬɚɜɥɹɹ ɜ 3.50 ȦȿɋɌ, IɁȺȾ, ȦɂɋɄ = ȦɁȺȾ, ɨɩɪɟɞɟɥɹɸɬ ɬɪɟɛɭɟɦɨɟ ɡɧɚɱɟɧɢɟ U ɢɥɢ R ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɯɟɦɵ ɜɤɥɸɱɟɧɢɹ. ɉɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱɢ ɫɥɟɞɭɟɬ ɨɛɪɚɬɢɬɶ ɨɫɨɛɨɟ ɜɧɢɦɚɧɢɟ ɧɚ ɡɧɚɤɢ ɦɨɦɟɧɬɚ, ɫɤɨɪɨɫɬɢ,

89

ɧɚɩɪɹɠɟɧɢɹ ɞɥɹ ɪɚɛɨɬɵ ɜ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɢ ɪɚɡɥɢɱɧɵɯ ɤɜɚɞɪɚɧɬɚɯ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. ɉɪɢɦɟɪ 3.6. Ɋɚɫɫɱɢɬɚɬɶ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RȾɈȻ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɬɢɩɚ Ⱦ32 (Ɋɇ = 9,5 ɤȼɬ, Iɇ= 53 Ⱥ, Uɇ = 220 ȼ, nɇ = 760 ɨɛ/ɦɢɧ, ɆɆȺɄɋ = 677 ɇɦ, rɈə = 0,2 Ɉɦ, rȾɉ = 0,08 Ɉɦ, rɈȼ = 0,0972 Ɉɦ) ɜ ɬɨɱɤɚɯ ɆɁȺȾ = 0,8; ȦɁȺȾ= +/- 0,4. ȼɨɫɩɨɥɶɡɭɟɦɫɹ ɤɚɬɚɥɨɠɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ Ɇ(I) ɢ n(I) ɞɜɢɝɚɬɟɥɹ ɢ ɫɜɟɞɟɦ ɢɯ ɜ ɬɚɛɥɢɰɭ 3.2.1. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨɜɵɟ ɡɧɚɱɟɧɢɹ ɜ ɫɢɫɬɟɦɭ ɋɂ: Ɇɇ ɦ 9,81 ɆɤȽɦ ;

Ȧɪɚɞ ɫ

nɨɛ ɦɢɧ . 9,55

Ɋɚɫɫɱɢɬɚɟɦ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɆɗɆ = kɎI. ȼɵɩɨɥɧɢɦ ɪɚɫɱɟɬ ɞɥɹ ɨɞɧɨɣ ɬɨɱɤɢ. Ɂɚɞɚɟɦɫɹ ɬɨɤɨɦ I = Iɇ = 53 Ⱥ, ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ Ȧ(I) ɨɩɪɟɞɟɥɹɟɦ ȦȿɋɌ

Ȧɇ

79,6 ɪɚɞ ɫ ,

ɨɩɪɟɞɟɥɹɟɦ ɤɎ ɩɨ ɮɨɪɦɭɥɟ: kɎ

UH I rə ȦȿɋɌ

220 53 0,377 79,6

2,5 ȼɫ ,

ɝɞɟ rə

rɈȼ rȾɉ rɈə

0,0972 0,08 0,2

0,377 Ɉɦ .

ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɩɪɢ ɡɚɞɚɧɧɨɦ ɬɨɤɟ ɆɗɆ

kɎ I 2,5 53 132,5 ɇ ɦ .

Ɇɨɦɟɧɬ ɩɨɫɬɨɹɧɧɵɯ ɩɨɬɟɪɶ ǻɆ ɆɗɆ Ɇȼ

132,5 120 12,5 ɇ ɦ ,

ɝɞɟ Ɇȼ ɜɡɹɬ ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ Ɇȼ(I) ɩɪɢ IɁȺȾ= 53 Ⱥ. Ɍɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ ɧɚ ɜɚɥɭ ɩɪɢ ɡɚɞɚɧɧɨɦ ɬɨɤɟ ɹɤɨɪɹ ɆɌ

ɆɗɆ ǻɆ 132,5 12,5 145 ɇ ɦ .

ɉɨ ɬɚɤɨɣ ɫɯɟɦɟ ɪɚɫɫɱɢɬɵɜɚɸɬ ɞɪɭɝɢɟ ɬɨɱɤɢ (ɫɦ. ɬɚɛɥ. 3.2) ɢ ɫɬɪɨɢɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶ ɆɌ(I). ɉɨ ɡɚɞɚɧɧɨɣ ɜɟɥɢɱɢɧɟ ɦɨɦɟɧɬɚ ɆɁȺȾ ɝɪɚɮɢɱɟɫɤɢ ɩɨ Ɇȼ (I) ɢɥɢ ɆɌ (I) ɨɩɪɟɞɟɥɹɸɬ ɬɨɤ ɹɤɨɪɹ IɁȺȾ, ɩɪɢ ɷɬɨɦ ɡɧɚɱɟɧɢɢ ɬɨɤɚ ɩɨɬɨɤ ɧɚ ɜɫɟɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ ɩɨɫɬɨɹɧɟɧ, ɚ ɨɬɧɨɲɟɧɢɟ ɫɤɨɪɨɫɬɟɣ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɸ ɗȾɋ. Ɋɟɲɚɹ ɭɪɚɜɧɟɧɢɟ (3.50) ɨɬɧɨɫɢɬɟɥɶɧɨ U ɢɥɢ R, ɩɨɥɭɱɚɟɦ ɧɟɨɛɯɨɞɢɦɵɣ ɩɚɪɚɦɟɬɪ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɚɛɨɬɵ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɆɁȺȾ 0,8 ɢ ȦɁȺȾ 0,4 ɜɜɟɞɟɧɢɟɦ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɶ ɹɤɨɪɹ RȾɈȻ ɨɩɪɟɞɟɥɢɦ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɜ ɚɛɫɨɥɸɬɧɵɯ ɟɞɢɧɢɰɚɯ. Ɇɨɦɟɧɬ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɨɛɵɱɧɨ ɹɜɥɹɟɬɫɹ ɦɨɦɟɧɬɨɦ ɧɚ ɜɚɥɭ. ɆɁȺȾ

ɆɁȺȾ Ɇȼɇ

0,8 Ɋɇ Ȧɇ

0,8 9500 79,6 90

0,8 119,35

95,5 ɇɦ.

Ɍɚɛɥɢɰɚ 3.2 Ʉɚɬɚɥɨɠɧɵɟ ɢ ɪɚɫɱɟɬɧɵɟ ɞɚɧɧɵɟ ɞɜɢɝɚɬɟɥɹ Ⱦ32 I

Ⱥ

20

32

40

48

53

60

80

100

150

n

ɦɢɧ-1

1300

1000

880

810

760

720

630

550

400

M

ɤȽɦ

2,5

6

8

10

12

14

22

30

47

Ȧ

1/ɫ

136

105

92,1

84,8

79,6

75,4

66

57,6

41,9

Ɇȼ

ɇɦ

24,5

58,9

78,5

98,1

119

137

216

294

461

ɤɎ

ȼɫ

1,56

1,98

2,22

2,38

2,5

2,62

2,88

3,16

3,9

ɆɗɆ

ɇɦ

31,2

63,5

88,8

114

132

157

230

316

585

¨Ɇ

ɇɦ

6,7

4,6

10,3

15,9

13

20

14

22

124

ɆɌ

ɇɦ

37,9

68,1

99,1

130

145

177

244

338

-

Ɂɚ ɛɚɡɨɜɨɟ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɩɪɢɧɢɦɚɸɬ ɧɨɦɢɧɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ Ȧɇ, ɬɚɤ ɤɚɤ ɫɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Ⱦɉȼ ɡɚɜɢɫɢɬ ɨɬ ɩɨɬɨɤɚ ɢ ɹɜɥɹɟɬɫɹ ɩɟɪɟɦɟɧɧɨɣ ɜɟɥɢɱɢɧɨɣ Ȧ0ɇ(I), ɬɨɝɞɚ

ȦɁȺȾ

ȦɁȺȾ Ȧɇ

0,4 79,6

31,8 ɪɚɞ ɫ .

ɉɪɢ ɆɁȺȾ = Ɇȼ = 95,5 ɇɦ ɩɨ Ɇȼ(I) ɧɚɯɨɞɢɦ IɁȺȾ = 47 Ⱥ, ɩɪɢ ɷɬɨɦ ɬɨɤɟ ȦȿɋɌ = 85,7 ɪɚɞ/ɫ, ɚ ɩɨ ɮɨɪɦɭɥɟ (3.50) ɨɩɪɟɞɟɥɹɟɦ RȾɈȻ: – ɞɥɹ ȦɁȺȾ 0,4 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ U UH IɁȺȾ rə R ȾɈȻ rə R ȾɈȻ

ȦɂɋɄ ȦȿɋɌ

220 220 47 0,377

IɁȺȾ

3,08 0,377

31,8 85,7

47

3,08 Ɉɦ,

2,71 Ɉɦ.

– ɞɥɹ ȦɁȺȾ 0,4 ɞɥɹ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ IɁȺȾ ɧɭɠɧɨ ɧɚɯɨɞɢɬɶ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɆɌ(I), ɞɥɹ ɷɬɨɝɨ ɪɟɠɢɦɚ IɁȺȾ = 39 Ⱥ, ȦȿɋɌ = 93,7 ɪɚɞ/ɫ, U UH IɁȺȾ rə R ȾɈȻ rə R ȾɈȻ

7,43 0,377

ȦɂɋɄ ȦȿɋɌ

220 220 39 0,377

IɁȺȾ

39

- 31,8 93,7

7,43 Ɉɦ,

7,05 Ɉɦ.

– ɞɥɹ ȦɁȺȾ -0,4 ɞɥɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ IɁȺȾ ɧɭɠɧɨ ɧɚɯɨɞɢɬɶ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɆɌ(I), ɞɥɹ ɷɬɨɝɨ ɪɟɠɢɦɚ IɁȺȾ = 39 Ⱥ, ɩɪɢ ɷɬɨɦ ɬɨɤɟ ȦȿɋɌ = 93,7 ɪɚɞ/ɫ, ɜ ɮɨɪɦɭɥɟ (3.50) ɩɪɢɧɢɦɚɟɦ U= 0,

91

ȦɂɋɄ ȦȿɋɌ

U UH IɁȺȾ rə R ȾɈȻ rə R ȾɈȻ

0 220 39 0,377

IɁȺȾ

- 31,8 93,7

39

1,79 Ɉɦ,

1,79 0,377 1,41 Ɉɦ.

– ɞɥɹ ȦɁȺȾ -0,4 ɞɥɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ IɁȺȾ ɧɭɠɧɨ ɧɚɯɨɞɢɬɶ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɆɌ(I), ɞɥɹ ɷɬɨɝɨ ɪɟɠɢɦɚ IɁȺȾ = 39 Ⱥ, ɜ ɮɨɪɦɭɥɟ (3.50) ɩɪɢɧɢɦɚɟɦ U = 0, ɚ ɬɚɤɠɟ ɭɫɬɚɧɨɜɢɦ ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ, ɩɪɢɦɟɪɧɨ ɪɚɜɧɵɣ ɧɨɦɢɧɚɥɶɧɨɦɭ, IɈȼ = Iɇ = 53 Ⱥ, ɩɪɢ ɷɬɨɦ ɬɨɤɟ ȦȿɋɌ = 79,6 ɪɚɞ/ɫ. U UH IɁȺȾ rə R ȾɈȻ rə R ȾɈȻ

ȦɂɋɄ ȦȿɋɌ

0 220 53 0,377

IɁȺȾ

2,05 0,377

- 31,8 79,6

39

2,05 Ɉɦ,

1,67 Ɉɦ,

ɚ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɰɟɯɨɜɨɣ ɫɟɬɢ R ȾɈȻ.ȼɈɁȻ

UH rOB IOB

220 0,0972 53

4,05 Ɉɦ.

3.2.5. Ɋɟɨɫɬɚɬɧɵɣ ɩɭɫɤ Ⱦɉȼ

Ɍɪɟɛɨɜɚɧɢɹ ɤ ɩɭɫɤɭ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɚɧɚɥɨɝɢɱɧɵ ɪɚɫɫɦɨɬɪɟɧɧɵɦ ɜɵɲɟ (ɫɦ. ɩ. 3.1) ɬɪɟɛɨɜɚɧɢɹɦ ɤ ɩɭɫɤɭ Ⱦɇȼ: – ɩɭɫɤ ɮɨɪɫɢɪɨɜɚɧɧɵɣ, ɫ ɞɨɩɭɫɬɢɦɵɦ ɭɫɤɨɪɟɧɢɟɦ, ɧɨɪɦɚɥɶɧɵɣ; – ɩɟɪɟɤɥɸɱɟɧɢɟ ɩɭɫɤɨɜɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɞɨɥɠɧɨ ɨɛɟɫɩɟɱɢɜɚɬɶ ɩɪɚɜɢɥɶɧɭɸ ɩɭɫɤɨɜɭɸ ɞɢɚɝɪɚɦɦɭ. ɇɚ ɪɢɫ. 3.39 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɩɭɫɤɚ ɞɜɢɝɚɬɟɥɹ. ɉɪɢ ɩɨɞɚɱɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɧɭɸ ɰɟɩɶ ɬɨɤ ɩɪɨɬɟɤɚɟɬ ɱɟɪɟɡ ɹɤɨɪɶ Ɇ, U ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ LM, R2ȾɈȻ LM R1ȾɈȻ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R1ȾɈȻ ɢ R2ȾɈȻ. ɉɨ ɦɟɪɟ ɪɚɡɝɨɆ ɧɚ ɞɜɢɝɚɬɟɥɹ ɜɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ Ʉɍ1 ɢ ɡɚɤɨɪɚɱɢɜɚɟɬɫɹ R1ȾɈȻ. ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ Ʉɍ1 Ʉɍ2 ɪɚɡɝɨɧɟ ɜɤɥɸɱɚɟɬɫɹ Ʉɍ2, ɡɚɤɨɪɚɱɢɜɚɟɬɫɹ R2ȾɈȻ ɢ ɞɜɢɝɚɊɢɫ. 3.39. ɋɯɟɦɚ ɩɭɫɤɚ Ⱦɉȼ ɬɟɥɶ ɜɵɯɨɞɢɬ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ. Ɋɚɫɱɺɬ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ 1. Ɉɩɪɟɞɟɥɹɟɦ ɦɚɤɫɢɦɚɥɶɧɵɣ ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ M1 ɢɡ ɭɫɥɨɜɢɣ, ɩɪɟɞɴɹɜɥɹɟɦɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦɢ ɬɪɟɛɨɜɚɧɢɹɦɢ; 2. Ɂɧɚɹ M1, ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɤɪɢɜɵɦ ɧɚɯɨɞɢɦ ɬɨɤ I1, ɨɛɟɫɩɟɱɢɜɚɸɳɢɣ ɡɚɞɚɧɧɵɣ ɦɨɦɟɧɬ;

92

3. Ɋɚɫɫɱɢɬɵɜɚɟɦ ɩɨɥɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ R1 = Uɇ / I1; 4. Ɋɚɡɛɢɜɚɟɦ ɧɚ ɫɬɭɩɟɧɢ R1 = R1ȾɈȻ + R2ȾɈȻ + ... + (rə + rɈȼ). ɉɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɬɨɤɚ I ɢ ɩɨɬɨɤɚ Ɏ ɭɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɨ ɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɫɤɨɪɨɫɬɢ ɨɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ Ȧ

UH I R k ɎI k ɎI

a b R .

5. ȼ ɨɫɹɯ Ȧ, R ɫɬɪɨɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ Ȧ = f (R) ɩɪɢ I1 =const ɱɟɪɟɡ ɬɨɱɤɢ (Ȧ = 0, R = R1) ɢ (Ȧ = ȦȿɋɌ ɩɪɢ I = I1, R = rə + rɈȼ). ɉɨɫɬɪɨɟɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 3.40. 6. ȼɵɛɢɪɚɟɦ ɬɨɤ ɩɟɪɟɤɥɸɱɟɧɢɹ I2, ɩɪɢ ɤɨɬɨɪɨɦ ɦɨɦɟɧɬ ɩɟɪɟɤɥɸɱɟɧɢɹ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ Ɇ2 >1,2 Mɋ. ɗɬɨɦɭ ɬɨɤɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R2 = Uɇ / I2. ȼ ɨɫɹɯ Ȧ, R ɫɬɪɨɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ Ȧ = f (R) ɩɪɢ I2 =const ɱɟɪɟɡ ɬɨɱɤɢ (Ȧ = 0, R = R2) ɢ (Ȧ = ȦȿɋɌ ɩɪɢ I = I2, R = rə + rɈȼ). ɉɪɢ ɩɭɫɤɟ ɞɜɢɝɚɬɟɥɹ (ɫɦ. ɪɢɫ. 3.40) ɪɚɡɝɨɧ ɢɞɟɬ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R = R1 ɞɨ ɬɨɤɚ I2, ɩɨɫɥɟ ɱɟɝɨ ɢɡ ɰɟɩɢ ɜɵɜɨɞɢɬɫɹ ɩɟɪɜɚɹ ɫɬɭɩɟɧɶ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R1ȾɈȻ. Ⱦɜɢɝɚɬɟɥɶ ɩɟɪɟɯɨɞɢɬ ɧɚ ɫɥɟɞɭɸɳɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɩɪɢ ɬɨɤɟ I1. Ⱦɚɥɟɟ ɪɚɡɝɨɧ ɩɪɨɞɨɥɠɚɟɬɫɹ ɞɨ ɬɨɤɚ I2 ɢ ɜɧɨɜɶ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜɵɜɨɞ ɨɱɟɪɟɞɧɨɣ ɫɬɭɩɟɧɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R2ȾɈȻ. Ȧ

ɟɫɬ

I2=const

R2

I1=const

R1

R R2

Iɋ

R1 R1ȾɈȻ

R2ȾɈȻ

I2

I

I1

rə+rɈȼ

Ɋɢɫ. 3.40. Ʉ ɪɚɫɱɟɬɭ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ Ⱦɉȼ ɉɨɫɬɪɨɟɧɢɟ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ ɜɵɩɨɥɧɟɧɨ ɜɟɪɧɨ, ɟɫɥɢ ɜɵɯɨɞ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɩɪɨɢɡɜɟɞɟɧ ɩɪɢ ɬɨɤɟ I1. ɉɪɢ ɧɟɜɵɩɨɥɧɟɧɢɢ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɩɪɢɞɟɬɫɹ ɜɟɪɧɭɬɶɫɹ ɤ ɜɵɛɨɪɭ ɬɨɤɚ I2 ɢ ɩɨɜɬɨɪɢɬɶ ɪɚɫɱɟɬ ɞɨ ɩɨɥɭɱɟɧɢɹ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ. Ɉɬɪɟɡɤɢ ɧɚ ɨɫɢ R ɩɨɡɜɨɥɹɸɬ ɨɩɪɟɞɟɥɢɬɶ ɫɬɭɩɟɧɢ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ R1ȾɈȻ ɢ R2ȾɈȻ. ɉɨɫɥɟ ɜɵɯɨɞɚ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɢɞɺɬ ɪɚɡɝɨɧ ɞɜɢɝɚɬɟɥɹ ɞɨ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɪɟɠɢɦɚ ɩɪɢ Ɇ = Ɇɋ. 93

ɉɟɪɟɤɥɸɱɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɢ ɹɤɨɪɹ ɨɛɵɱɧɨ ɜɵɩɨɥɧɹɸɬɫɹ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɫ ɩɨɦɨɳɶɸ ɪɟɥɟ ɜɪɟɦɟɧɢ, ɬɨɤɚ ɢɥɢ ɧɚɩɪɹɠɟɧɢɹ. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɩɪɢ ɧɟɥɢɧɟɣɧɵɯ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ. Ⱦɥɹ ɪɚɫɱɺɬɚ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɩɪɢ ɧɟɥɢɧɟɣɧɵɯ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ ɢɫɩɨɥɶɡɭɸɬ ɦɟɬɨɞɵ ɭɫɪɟɞɧɟɧɢɹ ɢɥɢ ɥɢɧɟɚɪɢɡɚɰɢɢ. Ⱦɥɹ ɪɚɫɱɺɬɚ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɢɫɩɨɥɶɡɭɸɬ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɤɨɧɟɱɧɵɯ ɩɪɢɪɚɳɟɧɢɹɯ. ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɦɟɬɨɞɚ ɭɫɪɟɞɧɟɧɢɹ ɧɟɥɢɧɟɣɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɞɜɢɝɚɬɟɥɹ ɪɚɡɛɢɜɚɟɦ ɧɚ i–ɬɵɟ ɭɱɚɫɬɤɢ ɢ ɜ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɩɨɞɫɬɚɜɥɹɟɦ ɞɥɹ ɤɚɠɞɨɝɨ ɭɱɚɫɬɤɚ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ ɆɋɊi, ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇɋ ɋɊi ɢ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɜ ɧɚɱɚ-

ɥɟ ȦɇȺɑ i ɢ ɜ ɤɨɧɰɟ ȦɄɈɇ i ɭɱɚɫɬɤɚ Ɇ ɋɊi

Ɇɋ ɋɊi Ji

ǻȦi ǻt i

Ɇɋ ɋɊi Ji

ȦɄɈɇ ȦɇȺɑi . ǻt i

ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɩɪɟɞɟɥɹɟɦ ɜɪɟɦɹ ɪɚɛɨɬɵ ɧɚ ɭɱɚɫɬɤɟ ǻt i

Ji

ȦɄɈɇ ȦɇȺɑi . Ɇ ɋɊi Ɇɋ ɋɊi

ɉɨɫɥɟ ɪɚɫɱɟɬɚ ǻti ɞɥɹ ɤɚɠɞɨɝɨ ɭɱɚɫɬɤɚ ɫɬɪɨɢɦ ɝɪɚɮɢɤ ɫɤɨɪɨɫɬɢ Ȧ(t). Ɍɨɱɧɨɫɬɶ ɪɚɫɱɟɬɚ ɡɚɜɢɫɢɬ ɨɬ ɱɢɫɥɚ ɭɱɚɫɬɤɨɜ. ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɦɟɬɨɞɚ ɥɢɧɟɚɪɢɡɚɰɢɢ ɧɟɥɢɧɟɣɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɪɚɡɛɢɜɚɸɬɫɹ ɧɚ ɭɱɚɫɬɤɢ, ɧɚ ɤɨɬɨɪɵɯ ɧɟɥɢɧɟɣɧɵɟ ɨɬɪɟɡɤɢ ɛɥɢɡɤɢ ɤ ɥɢɧɟɣɧɵɦ. ɋɱɢɬɚɟɦ, ɱɬɨ ɧɚ ɤɚɠɞɨɦ ɥɢɧɟɣɧɨɦ ɭɱɚɫɬɤɟ ɩɪɢɦɟɧɢɦɚ ɦɟɬɨɞɢɤɚ ɪɚɫɱɺɬɚ ɦɟɯɚɧɢɱɟɫɤɢɯ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɞɥɹ ɩɪɹɦɨɥɢɧɟɣɧɵɯ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. ɉɨɫɥɟ ɪɚɡɛɢɟɧɢɹ ɧɟɥɢɧɟɣɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚ ɥɢɧɟɣɧɵɟ ɭɱɚɫɬɤɢ ɨɩɪɟɞɟɥɹɟɦ ɧɚɱɚɥɶɧɵɟ ɢ ɤɨɧɟɱɧɵɟ ɡɧɚɱɟɧɢɹ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ ɆɇȺɑ i ɢ ɆɄɈɇ i ɢ ɫɤɨɪɨɫɬɢ ȦɇȺɑ i ɢ ȦɄɈɇ i. Ⱦɥɹ ɤɚɠɞɨɝɨ ɢɡ ɭɱɚɫɬɤɨɜ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɭɸ ɩɨɫɬɨɹɧɧɭɸ ɜɪɟɦɟɧɢ TMi

Ji

ǻȦi ǻMi

Ji

ȦɄɈɇ ȦɇȺɑi . Ɇ ɇȺɑi ɆɄɈɇ i

ɢ ɜɪɟɦɹ ɪɚɛɨɬɵ ɧɚ ɭɱɚɫɬɤɟ ǻt i

TMi ln

MɇȺɑi MC . MKOHi MC

ȼ ɪɟɡɭɥɶɬɚɬɟ ɫɬɪɨɹɬɫɹ ɧɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ Ȧ(t) ɢ M(t) ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ.

94

3.3. Ɉɫɨɛɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɞɜɢɝɚɬɟɥɹ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɋȼ)

ɉɪɢɦɟɧɟɧɢɟ ɞɜɢɝɚɬɟɥɟɣ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɨɛɭɫɥɨɜɥɟɧɨ ɫɬɪɟɦɥɟɧɢɟɦ ɫɨɯɪɚɧɢɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɫɜɨɣɫɬɜɚ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɢ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ: ɛɨɥɶɲɢɟ ɩɟɪɟɝɪɭɡɨɱɧɵɟ ɫɩɨɫɨɛɧɨɫɬɢ ɢ ɧɚɞɟɠɧɨɫɬɶ ɩɟɪɜɵɯ ɢ ɥɭɱɲɢɟ ɬɨɪɦɨɡɧɵɟ ɫɜɨɣɫɬɜɚ ɢ ɠɟɫɬɤɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜɬɨɪɵɯ. Ⱦɜɢɝɚɬɟɥɢ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɞɨɫɬɚɬɨɱɧɨ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɸɬɫɹ ɜ ɩɨɞɴɟɦɧɨ-ɬɪɚɧɫɩɨɪɬɧɨɦ, ɦɟɬɚɥɥɭɪɝɢɱɟɫɤɨɦ ɨɛɨɪɭɞɨɜɚɧɢɢ ɢ ɞɪɭɝɢɯ ɭɫɬɚɧɨɜɤɚɯ, ɝɞɟ ɜɨɡɦɨɠɧɵ ɡɧɚɱɢɬɟɥɶɧɵɟ ɤɪɚɬɤɨɜɪɟɦɟɧɧɵɟ ɩɟɪɟɝɪɭɡɤɢ ɩɪɢɜɨɞɚ ɢ ɱɚɫɬɵ ɬɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ. Ɉɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɧɚ ɪɚɛɨɱɢɟ ɦɚɲɢɧɵ, ɭ ɤɨɬɨɪɵɯ ɜɨɡɦɨɠɟɧ ɪɟɠɢɦ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɨɜɟɞɟɧɚ ɧɚ ɪɢɫ. 3.41. Ⱦɜɢɝɚɬɟɥɶ ɢɦɟɟɬ ɞɜɟ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ – ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɭɸ ɉɈȼ, ɜɤɥɸɱɺɧɧɭɸ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫ ɹɤɨɪɟɦ, ɢ ɧɟɡɚɜɢɫɢɦɭɸ ɇɈȼ. Ɇɚɝɧɢɬɧɵɣ ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɭɦɦɭ ɞɜɭɯ ɩɨɬɨɤɨɜ: ɩɨɬɨɤɚ ɎɇɈȼ, ɫɨɡɞɚɜɚɟɦɨɝɨ ɇɈȼ, ɢ ɩɨɬɨɤɚ ɎɉɈȼ, ɫɨɡɞɚɜɚɟɦɨɝɨ ɉɈȼ. Ɏ

U ɇɈȼ

Rȼ.ȾɈȻ ɉɈȼ

Ɏ ɎɇɈȼ

RȾɈȻ

I

Ɇ

-I1

Iɇ

Ɋɢɫ. 3.41. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ Ɂɚɜɢɫɢɦɨɫɬɶ ɫɭɦɦɚɪɧɨɝɨ ɩɨɬɨɤɚ ɞɜɢɝɚɬɟɥɹ Ɏ ɜ ɮɭɧɤɰɢɢ ɬɨɤɚ ɹɤɨɪɹ I ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 3.41. Ⱦɜɢɝɚɬɟɥɶ ɢɦɟɟɬ ɫɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ UH k ɎɇɈȼ

Ȧ 0ɇ

1,3...1,6 Ȧɇ .

ȿɫɬɟɫɬɜɟɧɧɵɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3.40. Ɇɚɬɟɦɚɬɢɱɟɫɤɢ ɨɧɢ ɨɩɢɫɵɜɚɸɬɫɹ ɢɡɜɟɫɬɧɵɦɢ ɜɵɪɚɠɟɧɢɹɦɢ ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ Ȧ Ȧ

UH R ; I kɎI kɎI UH R M . kɎI kɎI 2

ȼɥɢɹɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɢ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɧɚ ɜɢɞ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɚɧɚɥɨɝɢɱɧɨ ɪɚɫɫɦɨɬɪɟɧɧɵɦ ɜɵɲɟ ɞɜɢɝɚɬɟɥɹɦ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɇɚɥɢɱɢɟ ɧɟɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɦɟɠɞɭ ɩɨɬɨɤɨɦ ɢ ɬɨɤɨɦ ɹɤɨɪɹ ɨɛɭɫɥɨɜɥɢɜɚɟɬ ɩɪɢɦɟɧɟɧɢɟ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɦɟɬɨɞɚ ɢɯ ɪɚɫɱɟɬɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɤɚ95

ɬɚɥɨɠɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɤɚɤ ɷɬɨ ɜɵɩɨɥɧɹɥɨɫɶ ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ. Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ (ɪɟɤɭɩɟɪɚɬɢɜɧɨɟ ɢ ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɹ) ɨɛɵɱɧɨ ɨɛɟɫɩɟɱɢɜɚɸɬɫɹ ɬɨɥɶɤɨ ɧɟɡɚɜɢɫɢɦɨɣ ɨɛɦɨɬɤɨɣ ɜɨɡɛɭɠɞɟɧɢɹ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɚɹ ɨɛɦɨɬɤɚ ɜ ɷɬɢɯ ɪɟɠɢɦɚɯ ɢɫɤɥɸɱɚɟɬɫɹ ɢɡ ɫɯɟɦɵ. ȼɚɠɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɬɨɤɟ ɹɤɨɪɹ, ɫɬɪɟɦɹɳɟɝɨɫɹ ɤ ɡɧɚɱɟɧɢɸ -I1, ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ, ɬɨ ɟɫɬɶ ɞɜɢɝɚɬɟɥɶ ɪɚɡɦɚɝɧɢɱɢɜɚɟɬɫɹ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɩɪɢ ɨɬɪɢɰɚɬɟɥɶɧɨɦ ɬɨɤɟ ɹɤɨɪɹ ɫɧɢɠɚɟɬɫɹ ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ ɢ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨɝɨ ɦɨɦɟɧɬɚ ɩɪɢɯɨɞɢɬɫɹ ɡɧɚɱɢɬɟɥɶɧɨ ɭɜɟɥɢɱɢɜɚɬɶ ɬɨɤ ɹɤɨɪɹ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ ɬɨɤɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɞɚɠɟ ɭɦɟɧɶɲɚɟɬɫɹ. Ɉɬɫɭɬɫɬɜɢɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɣ ɨɛɦɨɬɤɢ ɩɪɢɞɚɟɬ ɞɜɢɝɚɬɟɥɸ ɫɜɨɣɫɬɜɚ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ (ɩɭɧɤɬɢɪɧɵɟ ɥɢɧɢɢ ɧɚ ɪɢɫɭɧɤɟ 3.42). Ȧ

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Ɋɢɫ. 3.42. ȿɫɬɟɫɬɜɟɧɧɵɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ Ʉɚɤ ɩɪɚɜɢɥɨ, ɞɜɢɝɚɬɟɥɢ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɝɨ ɧɚɡɧɚɱɟɧɢɹ (ɧɚɩɪɢɦɟɪ, ɫɟɪɢɢ 2ɉ) ɢɦɟɸɬ ɧɟɛɨɥɶɲɭɸ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɭɸ (ɫɬɚɛɢɥɢɡɢɪɭɸɳɭɸ) ɨɛɦɨɬɤɭ, ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ ɤɨɬɨɪɨɣ, ɞɟɣɫɬɜɭɹ ɫɨɝɥɚɫɧɨ ɫ ɩɨɬɨɤɨɦ ɨɫɧɨɜɧɨɣ ɨɛɦɨɬɤɢ, ɤɨɦɩɟɧɫɢɪɭɟɬ ɜɥɢɹɧɢɟ ɪɚɡɦɚɝɧɢɱɢɜɚɸɳɟɣ ɪɟɚɤɰɢɢ ɹɤɨɪɹ. Ɍɟɦ ɫɚɦɵɦ ɩɨɜɵɲɚɟɬɫɹ ɠɟɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɜɢɝɚɬɟɥɹ. ɇɨ ɬɚɤɢɟ ɦɚɲɢɧɵ ɧɟ ɨɬɧɨɫɹɬ ɤ ɪɚɡɪɹɞɭ ɞɜɢɝɚɬɟɥɟɣ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ. ɉɨɬɨɤ ɫɬɚɛɢɥɢɡɢɪɭɸɳɟɣ ɨɛɦɨɬɤɢ ɫɨɫɬɚɜɥɹɟɬ ~ 0,1 Ɏɇ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɬɨɤɟ ɹɤɨɪɹ Iɇ.

3.4. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɩɢɬɚɧɢɢ ɹɤɨɪɹ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ Ⱦɨ ɫɢɯ ɩɨɪ ɦɵ ɪɚɫɫɦɚɬɪɢɜɚɥɢ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɟɣ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɗȾɋ, ɤɨɝɞɚ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ ɞɜɢɝɚɬɟɥɹ ɫɱɢɬɚɥɢ ɧɟɡɚɜɢɫɹɳɢɦ ɨɬ ɬɨɤɚ. ȼ ɫɨɜɪɟɦɟɧɧɵɯ ɫɢɫɬɟɦɚɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɞɨɜɨɥɶɧɨ ɱɚɫɬɨ ɜɧɭɬɪɟɧɧɢɦ ɤɨɧɬɭɪɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɜɵɛɢɪɚɸɬ ɤɨɧɬɭɪ ɬɨɤɚ, ɩɨɡɜɨɥɹɸɳɢɣ ɩɨɞɞɟɪɠɢɜɚɬɶ ɡɚɞɚɧɧɵɣ ɬɨɤ ɹɤɨɪɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ. ɇɚ ɪɢɫ. 3.43 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫ ɝɥɭɛɨɤɨɣ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɨɛɪɚɬɧɨɣ ɫɜɹɡɶɸ ɩɨ ɬɨɤɭ ɹɤɨɪɹ. əɤɨɪɶ ɞɜɢɝɚɬɟɥɹ ɩɨɥɭɱɚɟɬ ɩɢɬɚɧɢɟ ɨɬ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ, ɜɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɤɨɬɨɪɨɝɨ ɩɨɞɞɟɪɠɢɜɚɟɬ ɬɨɤ ɹɤɨɪɹ ɧɚ ɡɚɞɚɧɧɨɦ ɭɪɨɜɧɟ. ɇɚɩɪɹɠɟɧɢɟ ɡɚɞɚɧɢɹ UɁȺȾ ɫɪɚɜɧɢɜɚɟɬɫɹ ɫ ɧɚɩɪɹɠɟɧɢɟɦ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ ɩɨ ɬɨɤɭ UɈɌ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɦ ɩɚɞɟɧɢɸ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɲɭɧɬɟ RS ɢ ɭɫɢɥɟɧɧɵɦ ɞɚɬɱɢɤɨɦ ɬɨɤɚ ȾɌ, ɪɚɡɧɨɫɬɶ ɷɬɢɯ ɧɚɩɪɹɠɟɧɢɣ ɭɫɢɥɢɜɚɟɬɫɹ ɪɟ96

ɝɭɥɹɬɨɪɨɦ ɬɨɤɚ ɊɌ ɢ ɩɨɞɚɟɬɫɹ ɧɚ ɜɯɨɞ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ. ɉɪɢ ɨɬɤɥɨɧɟɧɢɢ ɬɨɤɚ ɨɬ ɡɚɞɚɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɢɡɦɟɧɹɟɬɫɹ UɈɌ, ɪɚɡɧɨɫɬɶ (UɁȺȾ – UɈɌ) ɜɨɡɞɟɣɫɬɜɭɟɬ ɧɚ ɜɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɊɌ ɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ. ȼɟɥɢɱɢɧɚ ɬɨɤɚ ɹɤɨɪɹ ɡɚɞɚɟɬɫɹ ɧɚɩɪɹɠɟɧɢɟɦ UɁȺȾ ɢ ɬɨɤ ɹɤɨɪɹ ɩɨɞɞɟɪɠɢɜɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɹɤɨɪɶ ɞɜɢɝɚɬɟɥɹ ɩɨɥɭɱɚɟɬ ɩɢɬɚɧɢɟ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ. ~380 ȼ

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Ɋɢɫ. 3.43. ɋɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɨɛɪɚɬɧɨɣ ɫɜɹɡɶɸ ɩɨ ɬɨɤɭ ɏɨɬɹ ɨɛɳɢɟ ɭɪɚɜɧɟɧɢɹ ɦɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɫɩɨɫɨɛɚ ɟɟ ɩɢɬɚɧɢɹ, ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɛɭɞɭɬ ɢɦɟɬɶ ɩɪɢɧɰɢɩɢɚɥɶɧɵɟ ɨɬɥɢɱɢɹ ɨɬ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɜɵɲɟ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɗȾɋ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɩɨɫɤɨɥɶɤɭ I = const ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ȿ ɢɥɢ ɨɬ U, ɬɨ ɤɚɤ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ, ɬɚɤ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɜɟɪɬɢɤɚɥɶɧɵɟ ɩɪɹɦɵɟ ɥɢɧɢɢ: ɩɪɢ ɥɸɛɨɣ ɫɤɨɪɨɫɬɢ I = IɁȺȾ = const ɢ Ɇ = k Ɏ IɁȺȾ = = const. ɉɪɢɜɨɞ ɩɪɢɨɛɪɟɥ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɨɜɨɟ ɫɜɨɣɫɬɜɨ: ɟɫɥɢ ɪɚɧɶɲɟ – ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɗȾɋ – ɟɝɨ ɫɤɨɪɨɫɬɶ ɩɪɢ ɦɚɥɵɯ R ɦɚɥɨ ɡɚɜɢɫɟɥɚ ɨɬ ɦɨɦɟɧɬɚ ɧɚɝɪɭɡɤɢ, ɬɨ ɬɟɩɟɪɶ ɦɨɦɟɧɬ ɪɚɜɟɧ ɡɚɞɚɧɧɨɦɭ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ. Ɋɟɝɭɥɢɪɨɜɚɧɢɟ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɩɢɬɚɧɢɢ ɰɟɩɢ ɹɤɨɪɹ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 3.44. ɉɨɞɞɟɪɠɢɜɚɹ ɩɨɫɬɨɹɧɧɵɦ ɩɨɬɨɤ Ɏ, ɦɨɠɧɨ ɢɡɦɟɧɟɧɢɟɦ ɬɨɤɚ ɹɤɨɪɹ ɨɬ - 2ǜIɇ ɞɨ 2ǜIɇ ɪɟɝɭɥɢɪɨɜɚɬɶ ɦɨɦɟɧɬ ɨɬ - 2ǜɆɇ ɞɨ 2ǜɆɇ. ɉɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɬɨɤɚ ɹɤɨɪɹ I = IɁȺȾ = const ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɦɨɦɟɧɬɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɢɡɦɟɧɟɧɢɟɦ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɫ ɩɨɦɨɳɶɸ ɜɨɡɛɭɞɢɬɟɥɹ Ɍȼ. ɂɡɦɟɧɹɹ ɩɨɬɨɤ ɦɚɲɢɧɵ ɨɬ - Ɏɇ ɞɨ Ɏɇ ɩɪɢ I = 2 Iɇ, ɦɨɠɧɨ ɪɟɝɭɥɢɪɨɜɚɬɶ ɦɨɦɟɧɬ ɨɬ - 2Ɇɇ ɞɨ 2Ɇɇ. Ɉɝɪɚɧɢɱɟɧɢɟɦ ɨɛɥɚɫɬɢ ɞɟɣɫɬɜɢɹ Ɇ = const ɹɜɥɹɟɬɫɹ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ U = Uɇ. ɉɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɩɨɬɨɤɚ Ɏ = Ɏɇ ɨɝɪɚɧɢɱɟɧɢɟɦ ɹɜɥɹɟɬɫɹ ɟɫɬɟɫɬɜɟɧɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ. ɉɪɢ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɦɨɦɟɧɬɚ ɢɡɦɟɧɟɧɢɟɦ ɩɨɬɨɤɚ ɩɪɢ IɁȺȾ = const ɢ U = Uɇ ɡɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɨɬ ɩɨɬɨɤɚ Ɏ ɫɬɚɧɨɜɢɬɫɹ ɧɟɥɢɧɟɣɧɨɣ UH IɁȺȾ R Ȧ . k Ɏ ȼ ɩɪɢɜɟɞɟɧɧɨɣ ɮɨɪɦɭɥɟ ɱɢɫɥɢɬɟɥɶ – ɩɨɫɬɨɹɧɧɚɹ ɜɟɥɢɱɢɧɚ, ɩɪɢ ɫɧɢɠɟɧɢɢ ɩɨɬɨɤɚ ɫɤɨɪɨɫɬɶ ɛɭɞɟɬ ɪɚɫɬɢ ɢ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɩɪɢ ɦɚɥɵɯ ɩɨɬɨɤɚɯ ɭɫɥɨɜɢɹɦɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɩɪɨɱɧɨɫɬɢ. 97

Ȧ U=Uɇ

Ȧ

U=Uɇ ɟɫɬ

Ȧ0ɇ

Ɇɇ

-2Ɇɇ -Ɇɇ -2Iɇ

-Iɇ

0

Ȧ0ɇ 2Ɇɇ Iɇ

Ɇ

-2Ɇɇ -Ɇɇ

2Iɇ

-Ɏɇ

-Ɏɇ/2 0

ɟɫɬ Ɇɇ

Ɇ

2Ɇɇ Ɏɇ/2

Ɏɇ

-Ȧ0ɇ ɚ) Ɏ=Ɏɇ

-Ȧ0ɇ U=Uɇ

Ɋɢɫ.3.44. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɩɪɢ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɚ) ɬɨɤɚ ɹɤɨɪɹ I ɩɪɢ Ɏ=Ɏɇ ɢ ɛ) ɩɨɬɨɤɚ Ɏ ɩɪɢ I=2Iɇ

U=Uɇ ɛ) I=2Iɇ

Ⱦɨɫɬɨɢɧɫɬɜɚɦɢ ɩɢɬɚɧɢɹ ɹɤɨɪɹ ɞɜɢɝɚɬɟɥɹ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɹɜɥɹɟɬɫɹ ɩɨɞɞɟɪɠɚɧɢɟ ɩɨɫɬɨɹɧɫɬɜɚ ɦɨɦɟɧɬɚ ɩɪɢ ɥɸɛɨɣ ɫɤɨɪɨɫɬɢ, ɜɨɡɦɨɠɧɨɫɬɶ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɦɨɦɟɧɬɚ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ. Ʉ ɧɟɞɨɫɬɚɬɤɚɦ ɦɨɠɧɨ ɨɬɧɟɫɬɢ ɛɨɥɶɲɭɸ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɭɸ ɢɧɟɪɰɢɨɧɧɨɫɬɶ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɤɨɬɨɪɚɹ ɞɥɹ ɤɪɭɩɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɞɨɫɬɢɝɚɟɬ 3…5 ɫ.

3.5. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɚɫɢɧɯɪɨɧɧɨɝɨ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ 3.5.1. Ɉɫɧɨɜɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ (ȺȾ)

Ɋɚɫɫɦɨɬɪɟɧɧɵɟ ɜ ɩɪɟɞɵɞɭɳɢɯ ɝɥɚɜɚɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɢɦɟɸɬ ɛɨɝɚɬɭɸ ɢɫɬɨɪɢɸ. ȼ ɬɟɱɟɧɢɟ ɞɟɫɹɬɢɥɟɬɢɣ ɨɧɢ ɨɫɬɚɜɚɥɢɫɶ ɩɪɚɤɬɢɱɟɫɤɢ ɟɞɢɧɫɬɜɟɧɧɵɦ ɜɢɞɨɦ ɲɢɪɨɤɨ ɪɟɝɭɥɢɪɭɟɦɨɝɨ ɩɪɢɜɨɞɚ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɦ ɜɫɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɭɫɬɚɧɨɜɤɢ, ɬɪɟɛɭɸɳɢɟ ɬɨɧɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɫɥɨɠɧɵɦ ɞɜɢɠɟɧɢɟɦ. ɗɥɟɤɬɪɨɩɪɢɜɨɞɭ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɨɬɜɨɞɢɥɚɫɶ ɪɨɥɶ ɩɪɨɫɬɨɝɨ, ɧɟɭɩɪɚɜɥɹɟɦɨɝɨ ɢɥɢ ɭɩɪɚɜɥɹɟɦɨɝɨ ɩɪɢɦɢɬɢɜɧɨ ɢɫɬɨɱɧɢɤɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ, ɧɟɫɦɨɬɪɹ ɧɚ ɬɨ, ɱɬɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ, ɫɨɜɟɪɲɟɧɫɬɜɭɹɫɶ, ɭɞɟɪɠɢɜɚɟɬ ɫɜɨɢ ɩɨɡɢɰɢɢ ɜɨ ɦɧɨɝɢɯ ɨɬɜɟɬɫɬɜɟɧɧɵɯ ɭɫɬɚɧɨɜɤɚɯ, ɩɨɥɨɠɟɧɢɟ ɞɟɥ ɜ ɰɟɥɨɦ ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɢɥɨɫɶ. ɇɚ ɪɵɧɤɟ ɜɫɟɯ ɬɟɯɧɢɱɟɫɤɢ ɪɚɡɜɢɬɵɯ ɫɬɪɚɧ ɩɨɹɜɢɥɢɫɶ ɲɢɪɨɤɨ ɢ ɝɢɛɤɨ ɭɩɪɚɜɥɹɟɦɵɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɵ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ. ɂɯ ɜɵɩɭɫɤ ɜ ɪɹɞɟ ɫɥɭɱɚɟɜ ɩɪɟɜɵɫɢɥ ɜɵɩɭɫɤ ɩɪɢɜɨɞɨɜ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɉɪɢɱɢɧɵ ɪɟɡɤɨɝɨ ɩɨɜɨɪɨɬɚ ɜɧɢɦɚɧɢɹ ɤ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ, ɜɨɩɟɪɜɵɯ, ɜ ɩɪɨɫɬɨɬɟ ɢ ɧɟɜɵɫɨɤɨɣ ɫɬɨɢɦɨɫɬɢ ɦɚɲɢɧ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɢ, ɜɨɜɬɨɪɵɯ, ɜ ɧɨɜɵɯ ɜɨɡɦɨɠɧɨɫɬɹɯ ɭɩɪɚɜɥɹɬɶ ɢɦɢ, ɫɨɡɞɚɧɧɵɯ ɪɚɡɜɢɬɢɟɦ ɫɢɥɨɜɨɣ ɢ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɷɥɟɤɬɪɨɧɢɤɢ. 98

ɂɡ ɜɫɟɯ ɜɢɞɨɜ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɣ ɚɫɢɧɯɪɨɧɧɵɟ ɞɜɢɝɚɬɟɥɢ (ȺȾ) ɩɨɥɭɱɢɥɢ ɧɚɢɛɨɥɟɟ ɲɢɪɨɤɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ ɢ ɩɪɨɞɨɥɠɚɸɬ ɜɵɬɟɫɧɹɬɶ ɜɫɺ ɛɨɥɶɲɟ ɢ ɛɨɥɶɲɟ ɞɜɢɝɚɬɟɥɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. Ɉɬɥɢɱɢɟ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɨɬ ɦɚɲɢɧ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɜɵɪɚɠɚɟɬɫɹ ɜ ɨɬɫɭɬɫɬɜɢɢ ɩɨɥɸɫɨɜ, ɨɬɫɭɬɫɬɜɢɢ ɤɨɥɥɟɤɬɨɪɚ, ɪɚɜɧɨɦɟɪɧɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɨɛɦɨɬɨɤ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ. Ɉɛɦɨɬɤɚ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɨɝɨ ɪɨɬɨɪɚ ɧɚ ɦɨɳɧɨɫɬɢ ɞɨ 100 ɤȼɬ ɜɵɩɨɥɧɹɟɬɫɹ ɡɚɥɢɜɤɨɣ. ɍ ɞɜɢɝɚɬɟɥɹ ɫ ɮɚɡɧɵɦ ɪɨɬɨɪɨɦ ɤɨɧɰɵ ɪɨɬɨɪɧɨɣ ɨɛɦɨɬɤɢ ɜɵɜɨɞɹɬɫɹ ɧɚ ɤɨɧɬɚɤɬɧɵɟ ɤɨɥɶɰɚ, ɩɨɡɜɨɥɹɸɳɢɟ ɜɤɥɸɱɚɬɶ ɜ ɰɟɩɶ ɪɨɬɨɪɚ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢɥɢ ɪɚɡɥɢɱɧɨɝɨ ɪɨɞɚ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɢ. ȺȾ ɩɨɥɭɱɢɥ ɲɢɪɨɤɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɛɥɚɝɨɞɚɪɹ ɫɥɟɞɭɸɳɢɦ ɫɜɨɢɦ ɞɨɫɬɨɢɧɫɬɜɚɦ: – ɩɪɨɫɬ ɢ ɭɞɨɛɟɧ ɜ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɧɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ ɤɨɥɥɟɤɬɨɪɚ; – ɭ ɞɜɢɝɚɬɟɥɹ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ ɨɬɫɭɬɫɬɜɭɸɬ ɳɟɬɤɢ, ɬɨɤɨɩɨɞɜɨɞ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɤ ɫɬɚɬɨɪɭ; – ɞɟɲɟɜɥɟ ɢ ɥɟɝɱɟ ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɪɢ ɨɞɢɧɚɤɨɜɨɣ ɦɨɳɧɨɫɬɢ; – ɩɪɢ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɧɚ ɩɟɪɟɦɟɧɧɨɦ ɬɨɤɟ ɧɟ ɧɭɠɧɵ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶɧɵɟ ɭɫɬɚɧɨɜɤɢ (ɬɨɥɶɤɨ ɬɪɚɧɫɮɨɪɦɚɬɨɪ). ɇɟɞɨɫɬɚɬɤɚɦɢ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɹɜɥɹɸɬɫɹ: – ɤɜɚɞɪɚɬɢɱɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ ɨɬ ɧɚɩɪɹɠɟɧɢɹ, ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɩɪɢ ɫɧɢɠɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɜ ɫɟɬɢ ɫɭɳɟɫɬɜɟɧɧɨ ɭɦɟɧɶɲɚɸɬɫɹ ɩɭɫɤɨɜɨɣ ɢ ɦɚɤɫɢɦɚɥɶɧɵɣ ɦɨɦɟɧɬɵ; – ɩɥɨɯɨ ɩɟɪɟɧɨɫɢɬ ɤɨɥɟɛɚɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɫɟɬɢ – ɩɟɪɟɝɪɟɜ ɫɬɚɬɨɪɚ ɩɪɢ ɩɨɜɵɲɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɢ ɪɨɬɨɪɚ – ɩɪɢ ɟɝɨ ɩɨɧɢɠɟɧɢɢ; – ɦɚɥɵɣ ɜɨɡɞɭɲɧɵɣ ɡɚɡɨɪ, ɧɟɫɤɨɥɶɤɨ ɩɨɧɢɠɚɸɳɢɣ ɧɚɞɺɠɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ. ɉɢɬɚɧɢɟ ɨɛɦɨɬɨɤ ɫɬɚɬɨɪɚ ɬɪɟɯɮɚɡɧɵɦ ɬɨɤɨɦ ɢ ɪɚɫɩɨɥɨɠɟɧɢɟ ɮɚɡɧɵɯ ɨɛɦɨɬɨɤ ɩɨɞ ɭɝɥɨɦ 120 ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɝɪɚɞɭɫɨɜ ɫɨɡɞɚɺɬ ɜ ɦɚɝɧɢɬɧɨɣ ɰɟɩɢ ɦɚɲɢɧɵ ɜɪɚɳɚɸɳɟɟɫɹ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. ɋɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɩɨɥɹ (ɫɢɧɯɪɨɧɧɚɹ ɫɤɨɪɨɫɬɶ) Ȧ0

2 ʌ f1 pɉ

ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɚɫɬɨɬɨɣ ɩɪɨɬɟɤɚɸɳɟɝɨ ɬɨɤɚ f1 ɢ ɱɢɫɥɨɦ ɩɚɪ ɩɨɥɸɫɨɜ pɉ: ɋɢɧɯɪɨɧɧɭɸ ɫɤɨɪɨɫɬɶ ɥɟɝɤɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɧɨɦɢɧɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ nɇ ɞɜɢɝɚɬɟɥɹ, ɤɨɬɨɪɚɹ ɭɤɚɡɵɜɚɟɬɫɹ ɜ ɨɛ/ɦɢɧ ɜ ɤɚɬɚɥɨɠɧɵɯ ɞɚɧɧɵɯ ɢ ɧɚ ɬɚɛɥɢɱɤɟ ɞɜɢɝɚɬɟɥɹ. Ɂɧɚɱɟɧɢɟ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ f1ɇ = 50 Ƚɰ ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɱɢɫɥɚ ɩɚɪ ɩɨɥɸɫɨɜ 60 f1H 3000 [ɨɛ/ɦɢɧ] n0H pɉ pɉ ɢ ɫɨɫɬɚɜɥɹɟɬ 3000, 1500, 1000, 750, …ɨɛ/ɦɢɧ. ɇɨɦɢɧɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɫɢɧɯɪɨɧɧɨɣ ɧɚ 50…100 ɨɛ/ɦɢɧ, ɩɨɷɬɨɦɭ ɛɥɢɠɚɣɲɚɹ ɤ ɧɨɦɢɧɚɥɶɧɨɣ ɛɨɥɶɲɚɹ ɫɤɨɪɨɫɬɶ ɢɡ ɪɹɞɚ ɫɢɧɯɪɨɧɧɵɯ ɢ ɛɭɞɟɬ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɶɸ ɞɚɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ. Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɫɢɧɯɪɨɧɧɚɹ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɚɦɩɥɢɬɭɞɵ ɧɚɩɪɹɠɟɧɢɹ ɩɢɬɚɧɢɹ ɞɜɢɝɚɬɟɥɹ, ɚ ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɟɝɨ ɱɚɫɬɨɬɵ. ɇɚ ɪɢɫ. 3.45 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɨɞɧɨɣ ɮɚɡɵ ɞɜɢɝɚɬɟɥɹ. Ʉ ɨɛɦɨɬɤɚɦ ɫɬɚɬɨɪɚ ɩɪɢɥɨɠɟɧɨ ɧɚɩɪɹɠɟɧɢɟ U1. ȼ ɰɟɩɢ ɨɛɦɨɬɤɢ ɫɬɚɬɨɪɚ ɱɟɪɟɡ ɚɤɬɢɜɧɨɟ ɫɨ99

ɩɪɨɬɢɜɥɟɧɢɟ ɨɛɦɨɬɤɢ r1, ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɫɫɟɹɧɢɹ x1 ɢ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ xμ ɩɪɨɬɟɤɚɟɬ ɬɨɤ I1. ɉɪɢ ɜɪɚɳɟɧɢɢ ɪɨɬɨɪɚ ɜ ɨɛɦɨɬɤɟ ɪɨɬɨɪɚ ɧɚɜɨɞɢɬɫɹ ɗȾɋ ȿ2S, ɤɨɬɨɪɚɹ ɜɵɡɵɜɚɟɬ ɬɨɤ I2 ɱɟɪɟɡ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɫɫɟɹɧɢɹ x2S ɢ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɦɨɬɤɢ ɪɨɬɨɪɚ r2.

r1

x1

x2S xμ

I1 U1

I2 Ȧ

E1

r2 E2S Ɋɢɫ. 3.45. ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɨɞɧɨɣ ɮɚɡɵ ȺȾ

ɉɪɢ ɫɤɨɪɨɫɬɢ ɪɨɬɨɪɚ Ȧ Ȧ0 , ɪɚɜɧɨɣ ɫɤɨɪɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɩɪɨɜɨɞɧɢɤɢ ɪɨɬɨɪɚ ɧɟ ɩɟɪɟɫɟɤɚɸɬɫɹ ɜɪɚɳɚɸɳɢɦɫɹ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɫɬɚɬɨɪɚ. ɗȾɋ, ɢɧɞɭɤɬɢɪɭɟɦɚɹ ɜ ɨɛɦɨɬɤɟ ɪɨɬɨɪɚ, ɛɭɞɟɬ ɪɚɜɧɚ ɧɭɥɸ e 2 0 , ɢ ɱɚɫɬɨɬɚ f2 = 0. Ɍɨɤ ɫɬɚɬɨɪɚ ɩɪɢ Ȧ Ȧ0 ɪɚɜɟɧ ɬɨɤɭ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ I1 = Iμ. ɉɪɢɥɨɠɟɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɭɪɚɜɧɨɜɟɲɢɜɚɟɬɫɹ ɗȾɋ ɫɚɦɨɢɧɞɭɤɰɢɢ ȿ1 ɢ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɫɬɚɬɨɪɚ r1 ɢ ɯ1 ɨɬ ɩɪɨɬɟɤɚɸɳɟɝɨ ɬɨɤɚ ǻ U1 Iμ r12 x12 . ɇɚɜɨɞɢɦɚɹ ɜ ɩɟɪɜɢɱɧɨɣ ɨɛɦɨɬɤɟ ɗȾɋ L I = j Ȧ ȿ = j x I = j Ȧ ɨɷɥ μ μ 1 μ μ ɨɷɥ

Ȍɦɚɤɫ 2

.

ɋɜɹɡɶ ɦɟɠɞɭ ɬɨɤɨɦ Iμ ɢ ɩɨɬɨɤɨɦ ɎɆȺɄɋ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ. Ⱦɟɣɫɬɜɭɸɳɟɟ ɡɧɚɱɟɧɢɟ ɗȾɋ Ɏ E1 2ʌ f1 w 1 MȺɄɋ 4,44 f1 w 1 ɎMȺɄɋ . 2 ɉɪɢ ɡɚɬɨɪɦɨɠɟɧɧɨɦ (Ȧ = 0) ɪɚɡɨɦɤɧɭɬɨɦ ɪɨɬɨɪɟ ȺȾ ɛɭɞɟɬ ɩɪɟɞɫɬɚɜɥɹɬɶ ɫɨɛɨɣ ɬɪɚɧɫɮɨɪɦɚɬɨɪ ɢ ɗȾɋ ɪɨɬɨɪɚ ɛɭɞɟɬ ɪɚɜɧɚ ɥɢɧɟɣɧɨɦɭ ɧɚɩɪɹɠɟɧɢɸ ɧɚ ɤɨɥɶɰɚɯ ɪɨɬɨɪɚ ȿ20. ɑɚɫɬɨɬɚ ɷɬɨɣ ɗȾɋ f2 ɪɚɜɧɚ ɱɚɫɬɨɬɟ ɧɚɩɪɹɠɟɧɢɹ ɫɬɚɬɨɪɚ f1. Ɉɬɫɸɞɚ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɞɜɢɝɚɬɟɥɹ ɩɨ ɗȾɋ E1 . kE ȿ 20 / 3 ɇɚ ɢɧɬɟɪɜɚɥɟ ɫɤɨɪɨɫɬɢ ɪɨɬɨɪɚ Ȧ0 ! Ȧ ! 0 ɢɡɦɟɧɹɟɬɫɹ ɱɚɫɬɨɬɚ ɩɟɪɟɫɟɱɟɧɢɹ ɜɪɚɳɚɸɳɢɦɫɹ ɩɨɥɟɦ ɫɬɚɬɨɪɚ ɩɪɨɜɨɞɧɢɤɨɜ ɪɨɬɨɪɚ, ɢɡɦɟɧɹɟɬɫɹ ɱɚɫɬɨɬɚ ɗȾɋ ɪɨɬɨɪɚ 0 < f2 < f1ɇ ȼɟɥɢɱɢɧɨɣ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɣ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɫɤɨɪɨɫɬɶ ɪɨɬɨɪɚ, ɬɨɤɢ ɢ ɗȾɋ ɨɛɦɨɬɨɤ, ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ, ɹɜɥɹɟɬɫɹ ɫɤɨɥɶɠɟɧɢɟ s

100

s

Ȧ0 Ȧ Ȧ0

ǻȦ , Ȧ0

(3.51)

ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɫɨɛɨɣ ɨɬɧɨɲɟɧɢɟ ɪɚɡɧɨɫɬɢ ǻȦ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɩɨɥɹ ɫɬɚɬɨɪɚ Ȧ0 ɢ ɫɤɨɪɨɫɬɢ ɪɨɬɨɪɚ Ȧ ɤ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ0 . ȼ ɰɟɩɢ ɪɨɬɨɪɚ ɜɫɟ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɤɨɥɶɠɟɧɢɟɦ: – ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɪɨɬɨɪɚ Ȧ Ȧ0 s ; – ɱɚɫɬɨɬɚ ɬɨɤɚ ɪɨɬɨɪɚ f2S = f1ǜs; E 20 s – ɗȾɋ ɪɨɬɨɪɚ E 2S ; 3 – ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ x2S = x2ǜs; – ɬɨɤ ɪɨɬɨɪɚ I2

E 20 s 2

3 2

r2 x 2 s

E 20 2

3

r2 s

2

x2

2

.

(3.52)

Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ: ɩɪɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦ ɪɚɜɟɧɫɬɜɟ ɜɵɪɚɠɟɧɢɣ ɞɥɹ ɬɨɤɚ ɪɨɬɨɪɚ I2 ɜ ɧɢɯ ɡɚɤɥɸɱɟɧ ɪɚɡɧɵɣ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ: ɜ ɩɟɪɜɨɦ ɜɵɪɚɠɟɧɢɢ ɱɚɫɬɨɬɚ ɬɨɤɚ ɪɨɬɨɪɚ ɪɚɜɧɚ ɬɟɤɭɳɟɦɭ ɟɟ ɡɧɚɱɟɧɢɸ f2 = f1ǜs, ɜɨ ɜɬɨɪɨɦ (ɩɨɫɥɟ ɫɨɤɪɚɳɟɧɢɹ ɧɚ s) – f2 = f1. 3.5.2. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ

ɇɟɫɦɨɬɪɹ ɧɚ ɩɪɨɫɬɨɬɭ ɮɢɡɢɱɟɫɤɢɯ ɹɜɥɟɧɢɣ ɩɨɥɧɨɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɩɪɨɰɟɫɫɨɜ ɜ ɚɫɢɧɯɪɨɧɧɨɣ ɦɚɲɢɧɟ ɜɟɫɶɦɚ ɫɥɨɠɧɨ. ɗɬɚ ɫɥɨɠɧɨɫɬɶ ɩɨɪɨɠɞɟɧɚ ɧɟɫɤɨɥɶɤɢɦɢ ɩɪɢɱɢɧɚɦɢ: – ɜɫɟ ɧɚɩɪɹɠɟɧɢɹ, ɬɨɤɢ, ɩɨɬɨɤɨɫɰɟɩɥɟɧɢɹ – ɩɟɪɟɦɟɧɧɵɟ, ɬ.ɟ. ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɱɚɫɬɨɬɨɣ, ɚɦɩɥɢɬɭɞɨɣ, ɮɚɡɨɣ ɢɥɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɜɟɤɬɨɪɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ; – ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɞɜɢɠɭɳɢɟɫɹ ɤɨɧɬɭɪɵ, ɜɡɚɢɦɧɨɟ ɩɨɥɨɠɟɧɢɟ ɤɨɬɨɪɵɯ ɢɡɦɟɧɹɟɬɫɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ; – ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ ɧɟɥɢɧɟɣɧɨ ɫɜɹɡɚɧ ɫ ɧɚɦɚɝɧɢɱɢɜɚɸɳɢɦ ɬɨɤɨɦ (ɩɪɨɹɜɥɹɟɬɫɹ ɧɚɫɵɳɟɧɢɟ ɦɚɝɧɢɬɧɨɣ ɰɟɩɢ), ɚɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɨɬɨɪɧɵɯ ɰɟɩɟɣ ɡɚɜɢɫɹɬ ɨɬ ɱɚɫɬɨɬɵ (ɩɪɨɹɜɥɹɟɬɫɹ ɷɮɮɟɤɬ ɜɵɬɟɫɧɟɧɢɹ ɬɨɤɚ), ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɫɟɯ ɰɟɩɟɣ ɫɭɳɟɫɬɜɟɧɧɨ ɡɚɜɢɫɹɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɬ.ɩ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɫɬɚɬɢɱɟɫɤɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢɧɢɦɚɸɬ ɫɥɟɞɭɸɳɢɟ ɞɨɩɭɳɟɧɢɹ: – ɗȾɋ, ɬɨɤɢ, ɩɨɬɨɤɨɫɰɟɩɥɟɧɢɹ – ɫɢɧɭɫɨɢɞɚɥɶɧɵ ɜɨ ɜɪɟɦɟɧɢ ɢ ɩɪɨɫɬɪɚɧɫɬɜɟ; – ɩɪɨɜɨɞɢɦɨɫɬɶ ɧɚɦɚɝɧɢɱɢɜɚɸɳɟɝɨ ɤɨɧɬɭɪɚ ɩɨɫɬɨɹɧɧɚ (ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ ɤɪɢɜɚɹ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ); – ɩɚɪɚɦɟɬɪɵ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɵ (ɚɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢ ɢɧɞɭɤɬɢɜɧɨɫɬɢ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɱɚɫɬɨɬɵ, ɧɚɫɵɳɟɧɢɟ ɧɟ ɜɥɢɹɟɬ ɧɚ ɢɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɚɫɫɟɹɧɢɹ ɯ1 ɢ ɯ2); – ɧɟ ɭɱɢɬɵɜɚɟɦ ɦɨɦɟɧɬɵ, ɫɨɡɞɚɜɚɟɦɵɟ ɜɵɫɲɢɦɢ ɝɚɪɦɨɧɢɤɚɦɢ ɩɨɬɨɤɚ ɢ ɬɨɤɚ, ɪɚɫɱɟɬ ɜɟɞɟɦ ɩɨ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɟ; – ɝɢɫɬɟɪɟɡɢɫ ɢ ɜɢɯɪɟɜɵɟ ɬɨɤɢ ɨɬɫɭɬɫɬɜɭɸɬ; – ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɨɬɟɪɢ ɧɚ ɬɪɟɧɢɟ ɢ ɜɟɧɬɢɥɹɰɢɸ ɨɬɫɭɬɫɬɜɭɸɬ (ɨɬɧɟɫɟɧɵ ɤ ɫɬɚɬɢɱɟɫɤɨɦɭ ɦɨɦɟɧɬɭ). 101

ȼ ɫɜɹɡɢ ɫ ɩɪɢɧɹɬɵɦɢ ɞɨɩɭɳɟɧɢɹɦɢ ɫɱɢɬɚɟɦ, ɱɬɨ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɫɨɡɞɚɟɬɫɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɦɨɳɧɨɫɬɶɸ, ɩɨɫɬɭɩɚɸɳɟɣ ɫɨ ɫɬɨɪɨɧɵ ɫɬɚɬɨɪɚ, ɊɗɆ

Ɇ Ȧ0

3 ȿ2S I2 cos ĳ2 ,

(3.53)

ɬɨɝɞɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɊɗɆ Ȧ0

Ɇ

3 ȿ 2S I2 cos ĳ 2 , Ȧ0

(3.54)

ɬɨɤ ɪɨɬɨɪɚ I2

E2 s 2

E2

2

r2 x 2 s

r2 /s

2

2

x2

2

,

ɝɞɟ ȿ2S = ȿ2·s. ȼ ɩɨɥɭɱɟɧɧɨɦ ɜɵɪɚɠɟɧɢɢ ɞɥɹ ɬɨɤɚ ɪɨɬɨɪɚ ɗȾɋ ɪɨɬɨɪɚ ȿ2 ɢɦɟɟɬ ɱɚɫɬɨɬɭ ɫɬɚɬɨɪɚ f1 (ɡɧɚɱɢɬ, ɞɜɢɝɚɬɟɥɶ ɨɫɬɚɧɨɜɥɟɧ), ɚ ɜ ɰɟɩɢ ɪɨɬɨɪɚ ɜɜɟɞɟɧɨ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ r2 / s = r2 + r2ȾɈȻ. Ɍɚɤɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɯɟɦɟ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ. Ɉɫɬɚɟɬɫɹ ɬɨɥɶɤɨ ɩɪɢɜɟɫɬɢ ɩɚɪɚɦɟɬɪɵ ɰɟɩɢ ɪɨɬɨɪɚ ɤ ɰɟɩɢ ɫɬɚɬɨɪɚ. ɉɪɢɜɟɞɟɧɧɵɟ ɩɚɪɚɦɟɬɪɵ ɨɛɨɡɧɚɱɚɸɬɫɹ ɲɬɪɢɯɚɦɢ “ c ”. ɂɡ ɡɚɤɨɧɚ ɪɚɜɟɧɫɬɜɚ ɆȾɋ w 1 Iμ w 1 I1 w 2 I2 ɧɚɣɞɟɦ ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ I μ

I I w 2 1 2 w1

I Ic , 1 2

I 2 – ɩɪɢɜɟɞɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɪɨɬɨɪɚ. kE ɉɪɢɜɟɞɟɧɧɚɹ ɗȾɋ ɪɨɬɨɪɚ ȿc2 = ȿ2·kȿ.

ɝɞɟ Ic2

ɉɪɢɜɟɞɟɧɧɨɟ ɩɨɥɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ Ec2 E 2 k E 2 z2 kE , Ic2 I2 /k E ɩɪɢɜɟɞɟɧɧɨɟ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ 2 r2c r2 k E , ɩɪɢɜɟɞɟɧɧɨɟ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɫɫɟɹɧɢɹ ɪɨɬɨɪɚ: xc2 = x2 ǜkE2. ɇɚ ɪɢɫ. 3.46 ɩɪɢɜɟɞɟɧɚ Ɍ – ɨɛɪɚɡɧɚɹ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ȺȾ ɤɚɤ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ. ȼ ɷɬɨɣ ɫɯɟɦɟ ɧɟ ɭɱɢɬɵɜɚɸɬɫɹ ɩɨɬɟɪɢ ɚɤɬɢɜɧɨɣ ɦɨɳɧɨɫɬɢ ɧɚ ɩɟɪɟɦɚɝɧɢɱɢɜɚɧɢɟ. ɗȾɋ ɫɬɚɬɨɪɚ ɢ ɩɪɢɜɟɞɟɧɧɚɹ ɗȾɋ ɪɨɬɨɪɚ ɪɚɜɧɵ: ȿ = ȿ1 = ȿc2; I I ( Ic ) ; zc2

1

μ

2

rc2 ȾɈȻ = rc2 / s – rc2= rc2 (1-s) / s. ɉɨɬɟɪɢ ɚɤɬɢɜɧɨɣ ɦɨɳɧɨɫɬɢ ɜ ɞɨɛɚɜɨɱɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ rc2ȾɈȻ ɪɚɜɧɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ. ɉɨɞɫɬɚɜɢɜ ɜ (3.54) ɩɪɢɜɟɞɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɗȾɋ ɪɨɬɨɪɚ ȿc2 ɢ ɬɨɤɚ ɪɨɬɨɪɚ Ic2, ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ: 102

r1

x1

xc2 Ic2

I1

rc2 U1

Iμ

xμ

E

rc2(1-s)/s

Ɋɢɫ. 3.46. Ɍ – ɨɛɪɚɡɧɚɹ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ȺȾ

3 Ec2 Ȧ0

3 ȿc2 Ic2 cos ĳ 2 Ȧ0

ɊɗɆ Ȧ0

Ɇ Ec2

r2c /s 2 xc2 2

2

r2c /s

r2c /s 2 xc2 2

3 Ic2 r2c /s Ȧ0

ǻP2 . Ȧ0 s

(3.55)

Ⱦɥɹ ɪɚɫɱɟɬɚ ɦɨɦɟɧɬɚ Ɇ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɫɤɨɥɶɠɟɧɢɹ s ɧɭɠɧɨ ɡɧɚɬɶ ɬɨɤ Ic2, ɪɚɫɱɟɬ ɤɨɬɨɪɨɝɨ ɜɵɩɨɥɧɹɟɬɫɹ ɨɩɟɪɚɰɢɹɦɢ ɫ ɤɨɦɩɥɟɤɫɧɵɦɢ ɱɢɫɥɚɦɢ ɞɥɹ ɞɜɭɯɤɨɧɬɭɪɧɨɣ ɫɯɟɦɵ ɫ ɧɟɥɢɧɟɣɧɨɫɬɶɸ ɜ ɜɢɞɟ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. ɉɨɥɭɱɚɸɬɫɹ ɝɪɨɦɨɡɞɤɢɟ ɜɵɪɚɠɟɧɢɹ. ɗɬɢɦ ɦɵ ɡɚɣɦɟɦɫɹ ɩɨɡɠɟ. Ⱦɥɹ ɭɩɪɨɳɟɧɢɹ ɪɚɫɱɟɬɨɜ ɩɟɪɟɯɨɞɹɬ ɤ Ƚ – ɨɛɪɚɡɧɨɣ ɫɯɟɦɟ ɡɚɦɟɳɟɧɢɹ, ɜɵɧɨɫɹ ɤɨɧɬɭɪ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɧɚ ɡɚɠɢɦɵ ɫɬɚɬɨɪɚ (ɪɢɫ. 3.47). ȼ ɷɬɨɣ ɫɯɟɦɟ ɥɟɝɤɨ ɪɚɫɫɱɢɬɚɬɶ ɬɨɤ ɪɨɬɨɪɚ Ic2 U1

Ic2

(r1 r2c /s)2 (x1 xc2 )2

.

(3.56)

ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɜɟɧɫɬɜɨɦ 2

MɗɆ

3 Ic2 r2c /s Ȧ0

2 3 U1 r2c /s . 2 Ȧ0 r1 r2c /s (x1 xc2 )2

>

@

(3.57)

ɋɥɟɞɭɟɬ ɫɪɚɡɭ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɧɚɦɚɝɧɢɱɢɜɚɸɳɢɣ ɬɨɤ IP ɜ ɷɬɨɣ ɫɯɟɦɟ ɩɨɫɬɨɹɧɟɧ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɝɪɭɡɤɢ. Iμ

U1 2

r1 (x1 xμ )2

103

const.

(3.58)

Ɉɞɧɚɤɨ ɩɪɢ ɩɪɨɫɬɨɦ ɩɟɪɟɧɨɫɟ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɜɨɡɧɢɤɚɸɬ ɩɨɝɪɟɲɧɨɫɬɢ ɪɚɫɱɟɬɚ. ɍɜɟɥɢɱɟɧɢɟ ɦɨɦɟɧɬɚ ɩɪɢɜɨɞɢɬ ɤ ɪɨɫɬɭ ɬɨɤɚ ɪɨɬɨɪɚ Ic2, ɧɨ ɟɝɨ ɢɡɦɟɧɟɧɢɟ ɧɟ ɨɬɪɚɠɚɟɬɫɹ ɧɚ Iμ,, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɧɚ ɩɨɬɨɤ ɦɚɲɢɧɵ. I1

r1 r1

x1

xc2

x1

Ic2 rc2

Iμ

U1

xμ

E1 rc2(1-s)/s

Ɋɢɫ. 3.47. Ƚ – ɨɛɪɚɡɧɚɹ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ȺȾ Ⱥɧɚɥɢɡɢɪɭɹ ɜɵɪɚɠɟɧɢɟ ɦɨɦɟɧɬɚ (3.57), ɩɪɢɯɨɞɢɦ ɤ ɜɵɜɨɞɭ, ɱɬɨ ɩɪɢ s ĺ 0 ɢ s ĺ f ɦɨɦɟɧɬ ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ Ɇ ĺ 0. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɚɧɧɚɹ ɮɭɧɤɰɢɹ ɢɦɟɟɬ ɷɤɫɬɪɟɦɭɦ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɦɚɤɫɢɦɭɦɚ ɮɭɧɤɰɢɢ M(s): M

3 U 2 rc 1 2 Ȧ 0

1

c

s ª r r c /s 2 x x c 2 º «¬ 1 2 1 2 ¼»

u v

.

ɜɨɡɶɦɟɦ ɩɪɨɢɡɜɨɞɧɭɸ dM / ds ɢ ɩɪɢɪɚɜɧɹɟɦ ɟɟ ɧɭɥɸ § | |· ¨ u v uv ¸ dM u ¸ 0. c ( )| ¨ c 2 ¨ ¸ ds v v ¨ ¸ © ¹ | Ɍɚɤ ɤɚɤ u = 0, ɬɨ ɧɭɥɸ ɞɨɥɠɟɧ ɛɵɬɶ ɪɚɜɟɧ ɱɢɫɥɢɬɟɥɶ. dM 2 u v| {s r1 r2c /s (x1 xc2 )2 }| ds = – [(r1 + rc2 / s)2 + (x1 + xc2)2] – sǜ2 (r1+rc2 / s) ǜrc2 / s2 =

>

@

= – r12 – 2r1ǜ rc2 / s – (rc2 / s)2 – (x1 + xc2)2 +2r1ǜsǜrc2 / s2 + 2ǜ(rc2 / s)2 = = – r12 – (x1+xc2)2 + (rc2/s)2 = 0. Ʉɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ sɄ, ɩɪɢ ɤɨɬɨɪɨɦ ɦɨɦɟɧɬ ɪɚɜɟɧ ɦɚɤɫɢɦɚɥɶɧɨɦɭ (ɤɪɢɬɢɱɟɫɤɨɦɭ) – Ɇ = ɆɄ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɜɵɪɚɠɟɧɢɟɦ: sɄ

r

r2c r12

(x1 xc2 )

2

.

(3.59)

Ɉɩɪɟɞɟɥɢɦ ɤɪɢɬɢɱɟɫɤɢɣ (ɦɚɤɫɢɦɚɥɶɧɵɣ) ɦɨɦɟɧɬ ɆɄ, ɞɥɹ ɱɟɝɨ ɩɨɞɫɬɚɜɢɦ ɡɧɚɱɟɧɢɟ s = sɄ (3.59) ɜ ɮɨɪɦɭɥɭ (3.57). 104

M

3 U 2 r c /s 2 Ʉ 1 ª Ȧ r r c /s 2 x 2 º Ʉ »¼ 0 «¬ 1 2 Ʉ

K

3 U 2 r 2 x 2 k 1 1 r 2 ª º § · Ȧ «¨ r r r 2 x 2 ¸ x 2 » 0 «© 1 1 k ¹ K »

¬

r

¼

3 U 2 r 2 x 2 k 1 1

r

ª§ º · Ȧ «¨ r 2 r 2 r r 2 x 2 r 2 x 2 ¸ x 2 » 0 ¬© 1 1 1 k 1 k ¹ K ¼

3 U 2 1

§ · ¨ r 2 x 2 ¸ 1 k r r )¸ 2 Ȧ ¨( 1 ¸ 0 ¨ ¨ r 2 x 2 ¸ k 1 © ¹

.

2

3 U1

Ʉɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ MK

(3.60) 2 2 · § 2 Ȧ0 ¨ r1 r r1 x K ¸ ¹ © Ɂɧɚɤ «+» ɩɪɢɧɢɦɚɸɬ ɞɥɹ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ sɄ > 0 (ɩɪɢ s < 1 – ɪɚɛɨɬɚ ɜ ɪɟɠɢɦɟ ɞɜɢɝɚɬɟɥɹ), ɡɧɚɤ «–» – ɞɥɹ sɄ < 0 (ɝɟɧɟɪɚɬɨɪɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ). ɉɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɢɫɤɥɸɱɢɜ ɢɡ ɮɨɪɦɭɥ ɚɤɬɢɜɧɵɟ ɢ ɢɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɬɚɤ ɤɚɤ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɢ ɪɚɫɱɟɬɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɨɛɦɨɬɨɱɧɵɟ ɞɚɧɧɵɟ ɞɜɢɝɚɬɟɥɟɣ ɱɚɫɬɨ ɨɬɫɭɬɫɬɜɭɸɬ. Ɉɬɧɨɲɟɧɢɟ ɤɪɢɬɢɱɟɫɤɢɯ ɦɨɦɟɧɬɨɜ ɝɟɧɟɪɚɬɨɪɧɨɝɨ ɆɄȽ ɢ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɆɄȾ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɩɨɡɜɨɥɹɟɬ ɩɟɪɟɣɬɢ ɤ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦɭ ɜɵɪɚɠɟɧɢɸ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ MɄȽ ɆɄȾ

ɝɞɟ a sK

r1 2

r1 x k

2

r2c r2c

2

2

2 r1

2

r1 r1 x k r1

xk

1 a sK

,

1 a sK

r1 r2c ; 2 2 r2c r1 x k

a = r1 / rc2 – ɨɬɧɨɲɟɧɢɟ ɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɬɚɬɨɪɧɨɣ ɨɛɦɨɬɤɢ ɤ ɩɪɢɜɟɞɟɧɧɨɦɭ ɫɨɩɪɨɬɢɜɥɟɧɢɸ ɪɨɬɨɪɧɨɣ ɨɛɦɨɬɤɢ. Ɋɚɡɞɟɥɢɦ (3.57) ɧɚ (3.60):

M M

ɤɞ

3 U 2 r2c /s 1 Ȧ 0 ª r r c /s 2 x 2 º «¬ 1 2 K »¼ 3 U 2 1 . 2 2· § 2 Ȧ 0 ¨ r1 r1 x K ¸ ¹ ©

§ ©

2 r2c /s ¨ r1

2 2· r1 x K ¸ ¹

r1 r2c /s 2 x K 2

· ¸ 1¸ ¸ ¨ r 2 x 2 K ¹ © 1 §

2 2 ¨ 2 r2c /s r1 x K ¨

r1

2 2 r1 2 r1 r2c /s (r2c /s) 2 x K 2 (1 as K )

2 (1 as K )

2 2 (r1 x K ) 2 r1 r2c /s (r2c /s) 2 2 2 2 2 2 2 (r2c /s) r1 x K (r2c /s) r1 x K (r2c /s) r1 x K

105

s sK

sK s

2 as K

.

ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɩɪɢɧɢɦɚɟɬ ɜɢɞ

Ɇ

2 MK (1 asK ) . s sK 2 asK sK s

(3.61)

ȼ ɩɪɢɜɟɞɟɧɧɨɣ ɮɨɪɦɭɥɟ ɨɬɫɭɬɫɬɜɭɸɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɟɣ ɞɜɢɝɚɬɟɥɹ, ɱɬɨ ɭɩɪɨɳɚɟɬ ɪɚɫɱɟɬ. ȼɵɪɚɠɟɧɢɟ (3.61) ɧɚɡɵɜɚɸɬ ɭɬɨɱɧɺɧɧɨɣ ɮɨɪɦɭɥɨɣ Ʉɥɨɫɫɚ ɜ ɱɟɫɬɶ ɧɟɦɟɰɤɨɝɨ ɷɥɟɤɬɪɨɬɟɯɧɢɤɚ, ɩɨɥɭɱɢɜɲɟɝɨ ɷɬɭ ɮɨɪɦɭɥɭ. ȿɫɥɢ ɜ ɜɵɪɚɠɟɧɢɢ (3.61) ɩɪɢɧɹɬɶ r1 = 0 (ɞɥɹ ɞɜɢɝɚɬɟɥɟɣ ɛɨɥɶɲɨɣ ɢ ɫɪɟɞɧɟɣ ɦɨɳɧɨɫɬɢ r1 = 0,1…0,15ǜxK), ɬɨɝɞɚ a = r1 / rc2 = 0, ɬɨ ɦɵ ɩɨɥɭɱɢɦ ɭɩɪɨɳɟɧɧɭɸ ɮɨɪɦɭɥɭ Ʉɥɨɫɫɚ Ɇ

2 MK . s sK sK s

(3.62)

ȼ ɷɬɨɣ ɮɨɪɦɭɥɟ ɩɪɢ ɩɪɢɧɹɬɵɯ ɧɨɜɵɯ ɞɨɩɭɳɟɧɢɹɯ 2

MK

3 U1 ; 2 Ȧ0 x K

sK

r2c . xK

(3.63)

ȼɫɟ ɩɪɢɧɹɬɵɟ ɜɵɲɟ ɞɨɩɭɳɟɧɢɹ ɜɧɨɫɹɬ ɧɟɤɨɬɨɪɭɸ ɩɨɝɪɟɲɧɨɫɬɶ ɜ ɪɚɫɱɟɬɵ. Ɉɞɧɚɤɨ ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɩɪɢɜɟɞɺɧɧɵɦ ɜɵɲɟ ɮɨɪɦɭɥɚɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɛɥɢɡɤɢ ɤ ɨɩɵɬɧɵɦ ɢ ɹɜɥɹɸɬɫɹ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɵɦɢ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɰɟɥɟɣ. ɇɚ ɪɢɫ. 3.48 ɩɪɢɜɟɞɟɧɚ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ, ɩɪɨɯɨɞɹɳɚɹ ɱɟɪɟɡ ɬɨɱɤɭ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ0 . ȦɄȽ

Ȧ Ȧ0ɇ

Ȧɇ ȦɄȾ

Ɇ

0 Ɇɇ

ɆɄȽ

ɆɄȾ

Ɋɢɫ. 3.48. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ȺȾ ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɤɨɥɶɠɟɧɢɹ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɞɨ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɆɄ ɩɪɢ ɤɪɢɬɢɱɟɫɤɨɣ ɫɤɨɪɨɫɬɢ ȦK Ȧ0 1 sK . ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ ɫɤɨɥɶɠɟɧɢɹ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɧɚɱɢɧɚɟɬ ɭɦɟɧɶɲɚɬɶɫɹ. ɉɪɢ ɫɤɨɪɨɫɬɢ Ȧ = 0 ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɫɧɢɠɟɧ ɭɠɟ ɫɭɳɟɫɬɜɟɧɧɨ. ɉɪɢ ɪɚɫɱɺɬɟ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɬɚɤɠɟ ɦɨɠɧɨ ɩɪɢɧɹɬɶ, ɱɬɨ s / sK << sK / s, ɬɨɝɞɚ s / sK = 0, ɚ ɜɵɪɚɠɟɧɢɟ (3.62) ɩɪɢɧɢɦɚɟɬ ɜɢɞ 106

Ɇ

2 ɆɄ sK /s

2 ɆɄ Ȧ0 Ȧ sɄ Ȧ0

ȕ (Ȧ0 Ȧ) .

(3.64)

ȼɵɪɚɠɟɧɢɟ (3.64) ɫɩɪɚɜɟɞɥɢɜɨ ɞɥɹ ɪɚɛɨɱɟɝɨ ɭɱɚɫɬɤɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɤɨɝɞɚ Ɇ d 0,8ǜɆɄ. ɀɟɫɬɤɨɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȕ ɬɚɤɠɟ ɦɨɠɟɬ ɛɵɬɶ ɩɪɢɧɹɬɚ ɩɨɫɬɨɹɧɧɨɣ. Ɋɚɫɱɟɬ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɦɨɠɧɨ ɜɵɩɨɥɧɢɬɶ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɚɫɩɨɥɚɝɚɟɦɵɯ ɤɨɧɫɬɪɭɤɬɢɜɧɵɯ ɢ ɤɚɬɚɥɨɠɧɵɯ ɞɚɧɧɵɯ ɞɜɢɝɚɬɟɥɹ ɪɚɡɥɢɱɧɵɦɢ ɦɟɬɨɞɚɦɢ: – ɫ ɩɨɦɨɳɶɸ Ƚ – ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ɩɪɢ ɧɚɥɢɱɢɢ ɤɚɬɚɥɨɠɧɵɯ ɞɚɧɧɵɯ; – ɫ ɩɨɦɨɳɶɸ Ɍ – ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ, ɟɫɥɢ ɢɡɜɟɫɬɧɵ ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɟɣ ɦɚɲɢɧɵ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢɫɩɨɥɶɡɭɸɬɫɹ ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ ɞɜɢɝɚɬɟɥɹ, ɩɪɟɞɫɬɚɜɥɹɟɦɵɟ ɡɚɜɨɞɨɦ-ɢɡɝɨɬɨɜɢɬɟɥɟɦ. ȼ ɤɚɬɚɥɨɝɚɯ ɩɪɢɜɨɞɹɬɫɹ ɧɨɦɢɧɚɥɶɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɨɫɧɨɜɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ: – PH – ɧɨɦɢɧɚɥɶɧɚɹ ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ, ɤȼɬ; – nH – ɧɨɦɢɧɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ, ɨɛ/ɦɢɧ; – I1ɇ – ɧɨɦɢɧɚɥɶɧɵɣ ɬɨɤ ɫɬɚɬɨɪɚ, Ⱥ; – U1ɇ – ɧɨɦɢɧɚɥɶɧɨɟ ɥɢɧɟɣɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɫɬɚɬɨɪɚ, ȼ; – cos ĳ1ɇ – ɧɨɦɢɧɚɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ; – Șɇ – ɧɨɦɢɧɚɥɶɧɵɣ ɄɉȾ; – ɆɆȺɄɋ – ɦɚɤɫɢɦɚɥɶɧɵɣ (ɤɪɢɬɢɱɟɫɤɢɣ) ɦɨɦɟɧɬ, ɤȽɦ; – JȾȼ – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɨɬɨɪɚ, ɤɝɦ2; – m – ɦɚɫɫɚ ɞɜɢɝɚɬɟɥɹ, ɤɝ. Ʉɪɨɦɟ ɬɨɝɨ, ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɫ ɮɚɡɧɵɦ ɪɨɬɨɪɨɦ (ȺȾɎɊ): – ȿ20 (ɢɧɨɝɞɚ UɄ) – ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɤɨɥɶɰɚɯ ɡɚɬɨɪɦɨɠɟɧɧɨɝɨ ɪɚɡɨɦɤɧɭɬɨɝɨ ɪɨɬɨɪɚ, ȼ; – I2ɇ – ɧɨɦɢɧɚɥɶɧɵɣ ɬɨɤ ɪɨɬɨɪɚ, Ⱥ. Ⱦɥɹ ɞɜɢɝɚɬɟɥɹ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ (ȺȾɄɁ): – Ɇɉ – ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ, ɤȽɦ; – Iɉ – ɩɭɫɤɨɜɨɣ ɬɨɤ, Ⱥ. ȼ ɧɟɤɨɬɨɪɵɯ ɤɚɬɚɥɨɝɚɯ ɩɪɢɜɨɞɹɬɫɹ ɤɚɬɚɥɨɠɧɵɟ ɤɪɢɜɵɟ – ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɤɨɥɶɠɟɧɢɹ s: – ɦɨɦɟɧɬɚ Ɇ(s); – ɬɨɤɚ ɫɬɚɬɨɪɚ I1(s); – ɤɨɷɮɮɢɰɢɟɧɬɚ ɦɨɳɧɨɫɬɢ cos ĳ. Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɆɆȺɄɋ ɢ nɇ ɜ ɤɚɬɚɥɨɝɚɯ ɩɪɢɜɨɞɹɬɫɹ ɜ ɤȽɦ ɢ ɨɛ/ɦɢɧ (ɜ ɩɪɚɤɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ). ȼ ɪɚɫɱɟɬɚɯ ɷɬɢ ɡɧɚɱɟɧɢɹ ɧɭɠɧɨ ɩɟɪɟɫɱɢɬɚɬɶ ɜ ɧɆ ɢ ɪɚɞ/ɫ (ɜ ɫɢɫɬɟɦɟ ɋɂ) Ʉɚɬɚɥɨɠɧɵɟ ɤɪɢɜɵɟ ɹɜɥɹɸɬɫɹ ɫɚɦɵɦɢ ɬɨɱɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ – ɷɬɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɡɚɜɨɞɚ – ɢɡɝɨɬɨɜɢɬɟɥɹ, ɫɧɢɦɚɟɦɵɟ ɜ ɭɫɥɨɜɢɹɯ ɢɫɩɵɬɚɧɢɣ ɞɜɢɝɚɬɟɥɹ ɢ ɨɬɪɚɠɟɧɧɵɟ ɜ ɞɨɤɭɦɟɧɬɚɰɢɢ ɧɚ ɞɜɢɝɚɬɟɥɶ ɢ ɜ ɤɚɬɚɥɨɝɚɯ ɷɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɨɣ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ. ɂɦɢ ɦɨɠɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɪɚɫɱɟɬɨɜ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɦɢ ɦɟɬɨɞɚɦɢ. Ⱦɥɹ ɧɟɤɨɬɨɪɵɯ ɬɢɩɨɜ ɞɜɢɝɚɬɟɥɟɣ (ɧɚɩɪɢɦɟɪ, ɬɢɩɚ ɆɌF(H), 4ɆɌF(H) ɢ ɞɪ.) ɜ ɫɩɪɚɜɨɱɧɢɤɚɯ ɩɪɢɜɨɞɹɬɫɹ, ɤɪɨɦɟ ɧɨɦɢɧɚɥɶɧɵɯ ɞɚɧɧɵɯ, ɡɧɚɱɟɧɢɹ ɞɨɩɭɫɤɚɟɦɵɯ

107

ɩɨ ɧɚɝɪɟɜɭ ɧɚɝɪɭɡɨɤ ɩɪɢ ɪɚɡɥɢɱɧɨɣ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɜɤɥɸɱɟɧɢɹ ɉȼ (P, n, I), ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɩɨɫɬɪɨɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨ 4…5 ɬɨɱɤɚɦ. Ɉɞɧɚɤɨ ɱɚɳɟ ɜɫɟɝɨ ɷɬɢɯ ɞɚɧɧɵɯ ɞɥɹ ɜɫɟɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɛɵɜɚɟɬ ɧɟɞɨɫɬɚɬɨɱɧɨ. Ɋɚɫɱɟɬ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ ɜɵɩɨɥɧɹɸɬ, ɢɫɩɨɥɶɡɭɹ ɭɪɚɜɧɟɧɢɟ (3.61, 3.62), ɩɨɥɭɱɟɧɧɨɟ ɢɡ Ƚ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ (ɭɬɨɱɧɟɧɧɭɸ ɢɥɢ ɭɩɪɨɳɟɧɧɭɸ ɮɨɪɦɭɥɭ Ʉɥɨɫɫɚ). ȼ ɤɚɬɚɥɨɠɧɵɯ ɞɚɧɧɵɯ ɡɧɚɱɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɫɬɚɬɨɪɚ r1 ɢ x1 ɢ ɪɨɬɨɪɚ rc2 ɢ xc2 ɱɚɫɬɨ ɧɟ ɩɪɢɜɨɞɹɬɫɹ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɤɪɢɬɢɱɟɫɤɨɝɨ ɫɤɨɥɶɠɟɧɢɹ sɄ ɢɫɩɨɥɶɡɭɸɬ ɬɨɱɤɭ ɧɨɦɢɧɚɥɶɧɨɝɨ ɪɟɠɢɦɚ, ɩɨɞɫɬɚɜɥɹɸɬ ɜ ɮɨɪɦɭɥɭ Ʉɥɨɫɫɚ ɧɨɦɢɧɚɥɶɧɵɣ ɦɨɦɟɧɬ Ɇɇ, ɧɨɦɢɧɚɥɶɧɨɟ ɫɤɨɥɶɠɟɧɢɟ sɇ, ɤɚɬɚɥɨɠɧɨɟ ɡɧɚɱɟɧɢɟ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɆɄ (ɬɨɝɞɚ μɄ = ɆɄ / Ɇɇ), ɩɪɢɧɢɦɚɸɬ a = 1 ɢ ɪɟɲɚɸɬ ɭɪɚɜɧɟɧɢɟ (3.61) ɨɬɧɨɫɢɬɟɥɶɧɨ sK sɄ = sɇ

μɄ ±

2

μɄ - 1 + 2 ɚ sɇ (μk - 1) . 1 - 2 ɚ sɇ (μɄ - 1)

(3.65)

ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɭɩɪɨɳɟɧɧɨɣ ɮɨɪɦɭɥɵ Ʉɥɨɫɫɚ (3.62, 3.63), ɜ ɤɨɬɨɪɨɣ r1 = 0, a = r1 / rc2 = 0, ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ sɄ ɩɪɢ ɧɟɢɡɜɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɰɟɩɟɣ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɛɨɥɟɟ ɩɪɨɫɬɨɣ ɢ ɩɨɬɨɦɭ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɨɣ ɮɨɪɦɭɥɟ: sK

sɇ (μK r (μK2 1) .

(3.66)

Ⱦɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɨ ɮɨɪɦɭɥɚɦ 3.61, 3.62 ɩɪɢ ɢɡɜɟɫɬɧɵɯ ɆɄ, sɄ ɢ a ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɥɨɠɧɨɫɬɢ. ɉɪɢɦɟɪ 3.6. Ɋɚɫɫɱɢɬɚɬɶ ɟɫɬɟɫɬɜɟɧɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ Ȧ(M) ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 4ȺɄ200Ɇ8ɍ3 ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ. Ⱦɚɧɧɵɟ ɞɜɢɝɚɬɟɥɹ 4AK200M8ɍ3 [14]: U1ɇ = 380 ȼ, PH = 15 ɤȼɬ, Kɇ = 86 %, cos Mɇ = 0,7, I2ɇ = 28 Ⱥ, U2ɇ = 360 ȼ, μɄ = 3, sɇ = 0,035, sɄ = 0,23, JȾȼ = 0,6 ɤɝɦ2. ɋɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɟɣ ɜ ɨ.ɟ.: r1 0,04 ; x1 0,081; x μ 1,8 ; r2c 0,048 ; xc2 0,12 . Ɋɟɲɟɧɢɟ ɉɪɢɜɟɞɟɧɧɵɟ ɞɚɧɧɵɟ ɞɜɢɝɚɬɟɥɹ 4AK200M8ɍ3 (ɫɟɪɢɢ 4, ɚɫɢɧɯɪɨɧɧɵɣ Ⱥ, ɫ ɮɚɡɧɵɦ ɪɨɬɨɪɨɦ Ʉ, ɫ ɜɵɫɨɬɨɣ ɨɫɢ ɜɪɚɳɟɧɢɹ 200 ɦɦ, ɭɫɥɨɜɧɨɣ ɞɥɢɧɨɣ ɫɬɚɧɢɧɵ Ɇ, ɱɢɫɥɨ ɩɨɥɸɫɨɜ – 8, ɤɥɢɦɚɬɢɱɟɫɤɨɟ ɢɫɩɨɥɧɟɧɢɟ ɍ, ɤɚɬɟɝɨɪɢɹ ɪɚɡɦɟɳɟɧɢɹ 3) ɩɨɡɜɨɥɹɸɬ ɪɚɫɫɱɢɬɚɬɶ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɩɨ ɮɨɪɦɭɥɟ (3.61) ɛɟɡ ɨɫɨɛɵɯ ɡɚɬɪɭɞɧɟɧɢɣ, ɬɚɤ ɤɚɤ ɢɡɜɟɫɬɧɵ μɄ, sɄ ɢ a = r1 / rc2 = 0,04 / 0,048 = 0,833. ɉɪɨɜɟɪɢɦ ɫɨɜɩɚɞɟɧɢɟ ɪɚɫɱɟɬɨɜ sɄ ɩɨ ɮɨɪɦɭɥɚɦ (3.65), (3.66) ɫ ɩɚɫɩɨɪɬɧɵɦɢ ɞɚɧɧɵɦɢ ɞɜɢɝɚɬɟɥɹ. Ⱦɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɞɜɢɝɚɬɟɥɹ μK = 3, sɇ = 0,035. ɉɪɢ ɚ = 1 ɩɨ ɮɨɪɦɭɥɟ (3.65) ɩɨɥɭɱɢɦ sɄ

sɇ

μɄ ±

0,035

2

μɄ - 1+ 2 ɚ sɇ (μɄ - 1) 1 - 2 ɚ sɇ (μɄ - 1)

3 r 3 2 1 2 1 0,035 (3 1) 1 2 1 0,035 (3 1)

ɩɪɢ ɚ = 0,826 ɩɨɥɭɱɢɦ sɄ = 0,231.

108

0,238;

ɉɨ ɮɨɪɦɭɥɟ (3.66)

sK sH (μK r μK2 1) 0,035 (3 r 32 1) 0,204 . Ɉɩɪɟɞɟɥɢɦ sɄ ɱɟɪɟɡ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɟɣ ɩɨ ɮɨɪɦɭɥɟ (3.59) r2c 0,048 sK r 0,221 . r12 (x1 xc2 )2 0,04 2 (0,081 0,12) 2 ɉɪɢ r1 = 0 ɡɧɚɱɟɧɢɟ sɄ = rc2 / xɄ = 0,048 / (0,081+0,12) = 0,239. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɩɚɫɩɨɪɬɧɨɦ ɡɧɚɱɟɧɢɢ sɄ = 0,23 ɩɨ ɮɨɪɦɭɥɟ (3.65) ɫ ɭɱɟɬɨɦ ɚ = 0,826 ɩɨɥɭɱɟɧɨ ɩɪɚɤɬɢɱɟɫɤɢ ɨɞɢɧɚɤɨɜɨɟ ɡɧɚɱɟɧɢɟ sɄ = 0,231. ɉɨɝɪɟɲɧɨɫɬɶ ɩɪɢ ɚ = 1 ɩɨ ɮɨɪɦɭɥɟ 3.61 ɫɨɫɬɚɜɢɥɚ ǻ% = 3,48%. Ɋɚɫɱɟɬ ɩɨ ɮɨɪɦɭɥɟ (3.59) ɱɟɪɟɡ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫ ɭɱɟɬɨɦ r1 ɞɚɥ ɩɨɝɪɟɲɧɨɫɬɶ ǻ% = – 3,9%. Ɋɚɫɱɟɬ ɱɟɪɟɡ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɪɢ r1= 0 ɩɨɝɪɟɲɧɨɫɬɶ ɫɨɫɬɚɜɢɥɚ ǻ% = 3,91%, ɩɪɢ ɪɚɫɱɟɬɟ ɩɨ ɭɩɪɨɳɟɧɧɨɣ ɮɨɪɦɭɥɟ Ʉɥɨɫɫɚ – ɩɨ ɮɨɪɦɭɥɟ (3.66) ǻ% = – 11,3%. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɚɢɛɨɥɟɟ ɬɨɱɧɵɣ ɪɟɡɭɥɶɬɚɬ ɩɨɥɭɱɟɧ ɩɪɢ ɭɱɟɬɟ ɪɟɚɥɶɧɨɝɨ ɚ (ɫɨɩɪɨɬɢɜɥɟɧɢɣ r1 ɢ rc2). Ɉɫɬɚɥɶɧɵɟ ɪɚɫɱɟɬɵ ɞɚɥɢ ɩɨɝɪɟɲɧɨɫɬɶ ɛɨɥɟɟ 3,5%. Ⱦɥɹ ɬɨɱɧɵɯ ɪɚɫɱɟɬɨɜ ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɰɟɩɟɣ ɞɜɢɝɚɬɟɥɹ. Ɋɚɫɱɟɬ ɩɨ Ɍ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɟ ɡɚɦɟɳɟɧɢɹ (ɪɢɫ. 3.46) ɜɨɡɦɨɠɟɧ ɩɪɢ ɧɚɥɢɱɢɢ ɞɚɧɧɵɯ ɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɦɚɲɢɧɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɥɹ ɪɚɫɱɟɬɚ ɫɯɟɦɵ ɩɪɢɦɟɧɹɸɬ ɦɟɬɨɞɵ, ɢɡɜɟɫɬɧɵɟ ɢɡ ɤɭɪɫɚ ɌɈɗ. Ʉɚɤ ɨɬɦɟɱɚɥɨɫɶ ɜɵɲɟ, ɞɥɹ ɪɚɫɱɟɬɚ ɦɨɦɟɧɬɚ Ɇ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɫɤɨɥɶɠɟɧɢɹ s ɩɨ ɮɨɪɦɭɥɟ (3.55) ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɧɢɟ ɬɨɤɚ ɪɨɬɨɪɚ Ic2, ɤɨɬɨɪɵɣ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɥɢɲɶ ɩɪɢ ɢɡɜɟɫɬɧɵɯ ɡɧɚɱɟɧɢɹɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɰɟɩɟɣ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ (ɫɦ. ɩ. 3.5.2). Ɉɛɨɡɧɚɱɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɟɬɜɟɣ:

z1 = r1 + jǜx1;

zc2= rc2/ s+ jǜxc2;

zμ = jǜxμ.

Ɉɬɫɸɞɚ ɪɟɡɭɥɶɬɢɪɭɸɳɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ: z2μ = z2ǜzμ / (z2+zμ); zC = z1 + z2μ = rC+ jǜxC. Ɋɚɫɱɟɬ ɬɨɤɨɜ ɜɵɩɨɥɧɹɟɦ ɤɨɦɩɥɟɤɫɧɵɦ ɦɟɬɨɞɨɦ ɩɨ ɧɢɠɟ ɩɪɢɜɟɞɟɧɧɵɦ ɮɨɪɦɭɥɚɦ: E E U 1 I I Z ; I c ; ; I ; E 1 1 2μ μ 2 Z2 Zμ ZC (3.67) 2 3 Ic2 r2c /s M ; Ȧ Ȧ0H (1 s); Ȧ0H MȦ . 3 U1 I1 cos ĳ1 Ɋɚɫɱɟɬ ɩɨ ɩɪɢɜɟɞɟɧɧɵɦ ɮɨɪɦɭɥɚɦ ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɢɧɞɭɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɯμ = const. ȼ ɩɪɨɰɟɫɫɟ ɪɚɫɱɟɬɚ ɩɪɢ ɯμ = var ɩɨ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɦɟɬɨɞɨɦ ɢɧɬɟɪɩɨɥɹɰɢɢ ɭɬɨɱɧɹɟɬɫɹ ɡɧɚɱɟɧɢɟ ɬɨɤɚ Iμ, ɢ ɦɟɬɨɞɨɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɩɪɢɛɥɢɠɟɧɢɣ ɞɨɜɨɞɹɬ ɪɚɫɱɟɬ ɞɨ ɡɚɞɚɜɚɟɦɨɣ ɬɨɱɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɬɨɤɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. Ɋɚɫɱɟɬ ɷɬɨɣ ɧɟɫɥɨɠɧɨɣ ɡɚɞɚɱɢ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧ ɜ ɩɪɨɝɪɚɦɦɚɯ Matlab, Mathcad. Ⱦɥɹ ɩɪɢɦɟɪɚ ɧɚ ɪɢɫ. 3.49 ɩɪɢɜɟɞɟɧɵ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ, ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɞɚɧɧɨɣ ɦɟɬɨɞɢɤɟ ɜ ɩɪɨɝɪɚɦɦɟ «harad», ɞɚɸɳɢɟ ɞɨɫɬɚɬɨɱɧɭɸ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɬɨɱɧɨɫɬɶ (ɫɦ. ɩ. 3.7). cos ĳ1

cos(arctg (x C /rC )); Ș

109

3.5.3. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ

ȿɫɥɢ ɭɞɚɥɨɫɶ ɩɨɥɭɱɢɬɶ ɜɵɪɚɠɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜ ɮɨɪɦɭɥɚɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɰɟɩɟɣ ɦɚɲɢɧɵ, ɬɨ ɞɥɹ ɪɚɫɱɟɬɚ ɬɨɤɨɜ ɬɚɤɨɣ ɩɨɞɯɨɞ ɤɪɚɣɧɟ ɫɥɨɠɟɧ. ȼɵɲɟ ɞɥɹ Ƚɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɩɨɥɭɱɟɧɨ ɜɵɪɚɠɟɧɢɟ (3.52) ɞɥɹ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɡɚɜɢɫɢɦɨɫɬɶ ɬɨɤɚ ɪɨɬɨɪɚ ɨɬ ɫɤɨɥɶɠɟɧɢɹ: U1 Ic2 . (r1 r2c /s)2 (x1 xc2 )2 ɇɚ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ 0 , ɤɨɝɞɚ ɫɤɨɥɶɠɟɧɢɟ s = 0, ɬɨɤ ɪɨɬɨɪɚ Ic2 ɬɚɤɠɟ ɪɚɜɟɧ ɧɭɥɸ. Ɍɨɤ ɫɬɚɬɨɪɚ ɩɪɢ Ȧ Ȧ 0 ɪɚɜɟɧ ɬɨɤɭ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ I1 = Iμ. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɤɨɥɶɠɟɧɢɹ ɬɨɤ ɪɨɬɨɪɚ ɧɚɱɢɧɚɟɬ ɧɚɪɚɫɬɚɬɶ. ɉɪɢ s = 1, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɨɫɬɚɧɨɜɥɟɧ, Ɋɢɫ. 3.49. ȿɫɬɟɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɬɨɤ ɪɨɬɨɪɚ ɪɚɜɟɧ ɩɭɫɤɨɞɜɢɝɚɬɟɥɹ ɜɨɦɭ Ic2 ɉɍɋɄ, ɚ ɩɪɢ s ĺf ɬɨɤ ɪɨɬɨɪɚ ɫɬɪɟɦɢɬɫɹ ɤ ɩɪɟɞɟɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ U1 Ic2ɉɊȿȾ . 2 2 r1 xK Ɉɞɧɚɤɨ ɩɪɢ ɨɬɪɢɰɚɬɟɥɶɧɨɦ ɫɤɨɥɶɠɟɧɢɢ s ĺ - f, ɤɨɝɞɚ r1 = - rc2 / s, ɬɨɤ ɪɨɬɨɪɚ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ U1 Ic2ɆȺɄɋ , xK ɩɨɫɥɟ ɤɨɬɨɪɨɝɨ ɬɨɤ ɪɨɬɨɪɚ ɫɬɪɟɦɢɬɫɹ ɤ Ic2ɉɊȿȾ. ɋɤɨɥɶɠɟɧɢɟ ɩɪɢ Ic2 = Ic2ɆȺɄɋ ɧɚɡɵɜɚɸɬ ɝɪɚɧɢɱɧɵɦ sȽɊ = – rc2 / r1 = – 1 / a,ɩɨ ɚɛɫɨɥɸɬɧɨɣ ɜɟɥɢɱɢɧɟ | sȽɊ | > | sK |. ɇɚ ɪɢɫ. 3.50 ɩɪɢɜɟɞɟɧɵ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ. Ɍɨɤ Iμ ɩɪɢ ɞɨɩɭɳɟɧɢɹɯ, ɭɤɚɡɚɧɧɵɯ ɜɵɲɟ, ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɫɤɨɥɶɠɟɧɢɹ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ. Ɍɨɤ ɫɬɚɬɨɪɚ I 1

I ( Ic ) μ 2

ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɟɤɬɨɪɧɨɣ ɫɭɦɦɨɣ ɩɪɢɜɟɞɟɧɧɨɝɨ ɬɨɤɚ ɪɨɬɨɪɚ Ic2 ɢ ɬɨɤɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Iμ. ɇɚ ɪɢɫ. 3.50 ɬɨɤ ɫɬɚɬɨɪɚ ɩɨɤɚɡɚɧ ɭɫɥɨɜɧɨɣ ɫɭɦɦɨɣ ɷɬɢɯ ɞɜɭɯ ɬɨɤɨɜ. 110

Ɋɚɫɱɟɬ ɟɫɬɟɫɬɜɟɧɧɵɯ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. Ⱦɥɹ Ƚ - ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ɩɨɥɭɱɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ (3.56) ɬɨɤɚ ɪɨɬɨɪɚ ɨɬ ɫɤɨɥɶɠɟɧɢɹ. Ɂɚɜɢɫɢɦɨɫɬɶ ɬɨɤɚ ɫɬɚɬɨȦ ɪɚ ɨɬ ɫɤɨɥɶɠɟɧɢɹ I1(s) ɩɪɢɜɨɞɢɬɫɹ ɜ ȦȽɊ ɤɚɬɚɥɨɝɚɯ. ȿɣ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɩɪɢ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɯ ɫɩɨɫɨɛɚɯ Ȧ0ɇ ɪɚɫɱɟɬɚ, ɱɬɨ ɧɟ ɜɫɟɝɞɚ ɩɪɢɦɟɧɢɦɨ. ɂɡ ɜɨɡɦɨɠɧɵɯ ɦɟɬɨɞɨɜ ɪɚɫɱɟɬɚ I1 ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ: Ic2 Ic2ɆȺɄɋ – ɩɨ ɢɡɜɟɫɬɧɵɦ ɩɚɪɚɦɟɬɪɚɦ Ƚ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ; I – ɩɨ ɮɨɪɦɭɥɚɦ ɒɭɛɟɧɤɨ ȼ.Ⱥ.; – ɩɨ Ɍ – ɨɛɪɚɡɧɨɣ ɫɯɟɦɟ ɡɚɦɟɳɟIμ ɧɢɹ ɬɨɥɶɤɨ ɮɨɪɦɭɥɵ ɩɪɨɮɟɫɫɨɪɚ ȼ.Ⱥ.ɒɭɛɟɧɤɨ ɩɨɡɜɨɥɹɸɬ ɜɵɩɨɥɧɢɬɶ Ic2ɉɊȿȾ ɪɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ. Ɉɞɧɚɤɨ ɫɥɟɞɭɟɬ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɜ ɷɬɢɯ ɮɨɪɦɭɥɚɯ ɩɪɢɧɹɬɨ ɞɨɊɢɫ. 3.50. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɩɭɳɟɧɢɟ r1 ~ 0, ɢ ɬɚɦ, ɝɞɟ ɜɥɢɹɧɢɟ r1 ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɫɭɳɟɫɬɜɟɧɧɨ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɱɚɫɬɨɬɧɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɢ, ɨɧɢ ɞɚɸɬ ɛɨɥɶɲɭɸ ɩɨɝɪɟɲɧɨɫɬɶ. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɟɞɫɬɚɜɥɟɧɵ ɩɪɨɮɟɫɫɨɪɨɦ ɒɭɛɟɧɤɨ ȼ.Ⱥ. ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ (ɩɪɢɜɨɞɹɬɫɹ ɛɟɡ ɜɵɜɨɞɚ): – ɬɨɤ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ (ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ) IμH

I1H (sin ĳH

sH cos ĳH ) ; sK

(3.68)

– ɬɨɤ ɪɨɬɨɪɚ I2

I2ɇ

Ɇ s ; Mɇ sɇ

(3.69)

– ɬɨɤ ɫɬɚɬɨɪɚ

I1

2 Iμ2 ) Iμ2 (I1H

Ms . MH sH

(3.70)

Ɋɚɫɱɟɬ ɬɨɤɨɜ ɩɨ Ɍ – ɨɛɪɚɡɧɨɣ ɫɯɟɦɟ ɡɚɦɟɳɟɧɢɹ ɜɵɩɨɥɧɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ (3.67). Ɉɞɧɚɤɨ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɷɬɢɯ ɮɨɪɦɭɥ ɧɟ ɫɥɟɞɭɟɬ ɡɚɛɵɜɚɬɶ, ɱɬɨ ɜ ɧɢɯ ɩɪɢɧɢɦɚɟɬɫɹ ɯμ = const (ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ ɢɡɦɟɧɟɧɢɟ ɯμ ɩɨ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ). ɉɪɢɦɟɪ 3.7. Ɋɚɫɫɱɢɬɚɬɶ ɟɫɬɟɫɬɜɟɧɧɵɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ȧ (I2), Ȧ (I1), Ȧ (Iμ) ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 4AK200M8 (ɫɦ. ɩɪɢɦɟɪ 3.6) ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ. Ɋɚɫɱɟɬ ɩɨ Ƚ – ɨɛɪɚɡɧɨɣ ɫɯɟɦɟ ɡɚɦɟɳɟɧɢɹ. Ɋɚɫɫɱɢɬɚɟɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ ɩɨ ɞɚɧɧɵɦ ɫɩɪɚɜɨɱɧɢɤɚ [14].

111

ɇɨɦɢɧɚɥɶɧɵɣ ɬɨɤ ɫɬɚɬɨɪɚ I1ɇ = Ɋɇ / (3ǜU1ɇɎǜKɇǜcos Mɇ) =15000 / (3ǜ220ǜ0,86ǜ0,7) = 37,8 Ⱥ. Ȼɚɡɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ zȻ = U1ɇɎ / I1ɇ = 220 / 37,8 = 5,82 Ɉɦ. ɋɨɩɪɨɬɢɜɥɟɧɢɹ ɫɬɚɬɨɪɚ: r1 = r 1 ǜzȻ = 0,04ǜ5,82=0,233 Ɉɦ; x1 = x1 ǜzȻ = 0,081ǜ5,82 = 0,471 Ɉɦ; xP = x μ ǜzȻ = 1,8ǜ5,82 = 10,48 Ɉɦ. ɉɪɢɜɟɞɟɧɧɵɟ ɤ ɰɟɩɢ ɫɬɚɬɨɪɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɨɬɨɪɚ: rc2 = r2c rc2 ǜzȻ = 0,048ǜ5,82 = 0,28 Ɉɦ; xc2 = xc2 ǜzȻ = 0,12ǜ5,82 = 0,7 Ɉɦ. Ɍɨɤ ɪɨɬɨɪɚ (I2ɇ= 28 Ⱥ ɩɪɢ sɇ = 0,035) U1 Ic2 (r1 r2c /s)2 (x1 xc2 )2 220 2

2

26,46 A;

(0,233 0,28/0,035 ) (0,471 0,7) ɉɨɝɪɟɲɧɨɫɬɶ ɪɚɫɱɟɬɚ ɞɚɠɟ ɩɨ ɢɡɜɟɫɬɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦ ɫɨɫɬɚɜɥɹɟɬ ǻ% = 5,5%, ɱɬɨ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɬɨɱɧɨɫɬɢ ɜɫɟɯ ɩɨɫɥɟɞɭɸɳɢɯ ɪɚɫɱɟɬɨɜ ɜ Ƚ – ɨɛɪɚɡɧɨɣ ɫɯɟɦɟ ɡɚɦɟɳɟɧɢɹ. Ɍɨɤ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ U1 220 IμH 20,09 A. 2 2 2 2 r1 (x1 xμ ) 0,233 (0,471 10,48)

Ɋɚɫɱɟɬ ɩɨ ɮɨɪɦɭɥɚɦ ɒɭɛɟɧɤɨ ȼ.Ⱥ. Ɍɨɤ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ (ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ) ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɞɜɢɝɚɬɟɥɹ ɪɚɫɫɱɢɬɵɜɚɟɦ ɩɨ ɮɨɪɦɭɥɟ ɒɭɛɟɧɤɨ ȼ.Ⱥ. (3.68) ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɫɤɨɥɶɠɟɧɢɢ sɇ = 0,035, ɤɚɬɚɥɨɠɧɨɦ ɡɧɚɱɟɧɢɢ cos ĳɇ = 0,7 (ɬɨɝɞɚ sin ĳɇ = 0,714), ɧɨɦɢɧɚɥɶɧɨɦ ɬɨɤɟ ɫɬɚɬɨɪɚ I1ɇ = 37,8 Ⱥ ɢ ɩɨɥɭɱɟɧɧɵɯ ɜɵɲɟ sɄ = 0,204 (ɞɥɹ ɚ = 0) ɢ sɄ = 0,238 (ɞɥɹ ɚ = 1): s 0,035 IμH I1H (sinĳH H cosĳH ) 37,8 (0,714 0,7) 22,45 A. sK 0,204 sH 0,035 cosĳH ) 37,8 (0,714 0,7) 23,1 A. sK 0,239 ɂɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ UPɇ 220 x μH x1 0,471 9,33 Oɦ. IμH 22,45 IμH

I1H (sinĳH

ɉɪɢ ɩɚɫɩɨɪɬɧɨɦ ɡɧɚɱɟɧɢɢ ɯμ = 10,48 Ɉɦ ɩɨɝɪɟɲɧɨɫɬɶ ɪɚɫɱɟɬɚ ɬɨɤɚ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɞɥɹ Ƚ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɫɨɫɬɚɜɥɹɟɬ ɛɨɥɟɟ 10%. ɉɪɢ ɪɚɫɱɟɬɟ ɬɨɤɨɜ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ ɜ ɮɨɪɦɭɥɵ ȼ.Ⱥ. ɒɭɛɟɧɤɨ ɩɨɞɫɬɚɜɥɹɸɬ ɡɧɚɱɟɧɢɹ ɦɨɦɟɧɬɨɜ Ɇ ɢ Ɇɇ ɢ ɫɤɨɥɶɠɟɧɢɣ s ɢ sɇ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɨɞɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɬ.ɟ. ɩɪɢ ɪɚɫɱɟɬɟ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɨɦɢɧɚɥɶɧɨɦɭ ɦɨɦɟɧɬɭ Ɇɇ ɫɨɨɬɜɟɬɫɬɜɭɟɬ sɇ, ɩɪɢ ɪɚɫɱɟɬɟ ɢɫɤɭɫɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ɇɇ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɢɧɚɥɶɧɨɟ ɫɤɨɥɶɠɟɧɢɟ ɧɚ ɢɫɤɭɫɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ sɇɂ. 112

Ɋɇ 10 3 Ɋɇ 10 3 15 10 3 Ɇɇ 198 ɇɦ. Ȧɇ Ȧ 0ɇ (1 sɇ ) 78,5 (1 0,035) Ɋɚɫɱɟɬɧɵɟ ɮɨɪɦɭɥɵ ɟɫɬɟɫɬɜɟɧɧɵɯ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɥɹ ɬɨɤɨɜ ɪɨɬɨɪɚ (3.69) ɢ ɫɬɚɬɨɪɚ (3.70) ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɞɜɢɝɚɬɟɥɹ ɢɦɟɸɬ ɜɢɞ Ms Ms I2 I2H 28 ; MH sH 198 0,035 I1

2 Iμ2 ) Iμ2 (I1H

Ms MH sH

22,45 2 (37,8 2 22,45 2 )

Ms , 198 0,035

ɝɞɟ Ɇɇ – ɧɨɦɢɧɚɥɶɧɵɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ. ɉɨ ɩɨɥɭɱɟɧɧɵɦ ɜɵɪɚɠɟɧɢɹɦ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɟɫɬɟɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɯμ = const. Ɋɚɫɱɟɬ ɩɨ Ɍ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɟ ɡɚɦɟɳɟɧɢɹ. ɇɚ ɪɢɫ. 3.49 ɩɪɢɜɟɞɟɧɵ ɦɟɯɚɧɢɱɟɫɤɚɹ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ, ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ Ɍ – ɨɛɪɚɡɧɨɣ ɫɯɟɦɟ ɩɪɨɝɪɚɦɦɨɣ «harad» ɩɨ ɮɨɪɦɭɥɚɦ (3.67). Ɋɚɫɱɟɬ ɜ ɷɬɨɣ ɩɪɨɝɪɚɦɦɟ ɜɟɞɟɬɫɹ ɫ ɭɱɟɬɨɦ ɢɡɦɟɧɟɧɢɹ ɯP ɩɨ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ. Ʉɨɨɪɞɢɧɚɬɵ ɧɨɦɢɧɚɥɶɧɨɝɨ ɪɟɠɢɦɚ (ɜ ɨ.ɟ.): ɩɪɢ Ȧɇ = 0,96, Ɇ = 1,01, I1 = 1,01, Ic2 = 0,64 ( ɜ ɦɚɫɲɬɚɛɟ ɬɨɤɚ ɫɬɚɬɨɪɚ), IP = 0,64. Ɍɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɩɪɢ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ IP = 0,75. Ɂɧɚɱɟɧɢɟ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ μK = 3,05 ɩɪɢ ɤɚɬɚɥɨɠɧɨɦ ɡɧɚɱɟɧɢɢ μK = 3. ɋɪɚɜɧɟɧɢɟ ɫ ɩɪɟɞɵɞɭɳɢɦ ɪɚɫɱɟɬɨɦ ɩɨɤɚɡɵɜɚɟɬ ɞɨɫɬɚɬɨɱɧɭɸ ɬɨɱɧɨɫɬɶ ɩɪɢɛɥɢɠɟɧɧɵɯ ɪɚɫɱɟɬɨɜ. ɉɪɢɛɥɢɠɟɧɧɵɣ ɪɚɫɱɟɬ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ȺȾ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ. ɉɪɢ ɪɚɫɱɟɬɚɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢ ɩɚɪɚɦɟɬɪɨɜ ɫɯɟɦ ɜɤɥɸɱɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɬɶ ɜɟɥɢɱɢɧɵ ɚɤɬɢɜɧɵɯ ɢ ɢɧɞɭɤɬɢɜɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɮɚɡɧɵɯ ɨɛɦɨɬɨɤ ɞɜɢɝɚɬɟɥɹ, ɩɪɢɯɨɞɢɬɫɹ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɢɛɥɢɠɟɧɧɵɣ ɪɚɫɱɟɬ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ. Ɋɚɫɱɟɬ ɜɵɩɨɥɧɹɸɬ ɞɥɹ ɧɨɦɢɧɚɥɶɧɨɣ ɬɨɱɤɢ, ɨɛɥɚɞɚɸɳɟɣ ɞɨɫɬɚɬɨɱɧɵɦɢ ɤɚɬɚɥɨɠɧɵɦɢ ɞɚɧɧɵɦɢ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɨɬɨɪɧɨɣ ɨɛɦɨɬɤɢ ɨɩɪɟɞɟɥɹɸɬ ɛɚɡɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɪɨɬɨɪɚ R2ɇ (ɩɪɢ I2 = I2ɇ ɢ s = 1). ȿ 20 ȿ 20 sɇ R 2ɇ , r2 R 2ɇ sɇ . 3 I2ɇ 3 I2ɇ

Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɗȾɋ ɞɜɢɝɚɬɟɥɹ ɤȿ = 0,95·U1ɇ / U2ɇ. ɉɪɢɜɟɞɟɧɧɨɟ ɤ ɰɟɩɢ ɫɬɚɬɨɪɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ rc2= r2·kR = r2·kȿ2. Ⱥɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɬɚɬɨɪɚ r1: – ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɱɟɪɟɡ ɆɄ 2 3 U1H rc r1 2 , 2 Ȧ0H MK sK 113

ɝɞɟ sK

sɇ (μK μK2 1 2 a sɇ (μK 1) ) 1 2 a sɇ (μK 1)

,

– ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɚ = 1, ɬɨɝɞɚ r1 = rc2. ɂɡ ɮɨɪɦɭɥ MK r r2c μK , a 1 , sɄ r MH r2c r12 (x1 xc2 )2 ɩɨɥɭɱɢɦ ɢɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɚɫɫɟɹɧɢɹ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ r2c xK x1 xc2 1 a 2 sK2 . 2 2 sK ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ x Pɇ

(

U1Ɏɇ 2 2 ) r1 x 1, Iμɇ

ɝɞɟ Iμɇ – ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɜ ɧɨɦɢɧɚɥɶɧɨɣ ɬɨɱɤɟ, ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ ȼ.Ⱥ. ɒɭɛɟɧɤɨ (3.68). ɉɪɢɦɟɪ 3.8. Ɋɚɫɫɱɢɬɚɬɶ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ ɚɤɬɢɜɧɵɟ ɢ ɢɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɮɚɡɧɵɯ ɨɛɦɨɬɨɤ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 4AK200M8ɍ3 ɢ ɫɪɚɜɧɢɬɶ ɫ ɞɚɧɧɵɦɢ ɫɩɪɚɜɨɱɧɢɤɚ [14]. Ɉɛɦɨɬɨɱɧɵɟ ɞɚɧɧɵɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɞɜɢɝɚɬɟɥɹ ɩɪɢɜɟɞɟɧɵ ɜ ɩɪɢɦɟɪɟ 3.6. ȼ ɫɨɩɨɫɬɚɜɥɟɧɢɢ ɞɚɧɧɵɯ ɫɩɪɚɜɨɱɧɢɤɚ ɫ ɢɬɨɝɚɦɢ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɪɚɫɱɟɬɚ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ ɦɨɠɧɨ ɫɭɞɢɬɶ ɨ ɩɨɝɪɟɲɧɨɫɬɢ ɬɚɤɢɯ ɪɚɫɱɟɬɨɜ. Ȼɚɡɨɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɪɨɬɨɪɚ R2ɇ (ɩɪɢ I2 = I2ɇ ɢ s = 1) E 20 360 R 2H 7,42 Ɉɦ. 3 I2H 3 28 Ⱥɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɮɚɡɵ ɪɨɬɨɪɚ

r2 = R2ɇ·sɇ = 7,42·0,035 = 0,26 Ɉɦ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɗȾɋ ɞɜɢɝɚɬɟɥɹ ɤȿ = 0,95·U1ɇ / U2ɇ = 0,95·380 / 360=1. ɉɪɢɜɟɞɟɧɧɨɟ ɤ ɰɟɩɢ ɫɬɚɬɨɪɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ rc2 = r2·kr = r2·kȿ2 = 0,26·12 = 0,26 Ɉɦ. Ⱥɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɬɚɬɨɪɚ r1 2 3 U1Ɏ r2c 3 220 2 0,26 r1 2 Ȧ0ɇ ɆɄ sɄ 2 78,5 3 198 0,21

0,319 Ɉɦ.

ɉɪɢ ɚ = r1 / rc2 = 1 ɦɨɠɧɨ ɩɪɢɧɹɬɶ r1 = rc2=0,26 Ɉɦ. ɂɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɨɩɪɟɞɟɥɢɦ ɢɡ ɜɵɪɚɠɟɧɢɹ ɤɪɢɬɢɱɟɫɤɨɝɨ ɫɤɨɥɶɠɟɧɢɹ sɄ: rc 2 x Ʉ ɯ1 ɯ c2 ( 2 )2 r1 (0,26/0,21)2 0,26 2 1,21 Ɉɦ, sɄ ɯ1 = ɯc2 = ɯɄ / 2 = 1,21 / 2=0,605 Ɉɦ. 114

ɂɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɜ ɧɨɦɢɧɚɥɶɧɨɣ ɬɨɱɤɟ (ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Iμɇ = 22,45 Ⱥ ɪɚɫɫɱɢɬɚɧ ɜ ɩɪɢɦɟɪɟ 3.7) U1ɮɇ

2

§ 220 · 2 ) x1 x PH ( ¸ 0,26 0,605 9,14 Ɉɦ. ¨ Iμɇ © 22,45 ¹ ɋɪɚɜɧɢɬɟ ɩɨɥɭɱɟɧɧɵɟ ɩɪɢɛɥɢɠɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɣ (ɩɪɢɜɟɞɟɧɵ ɜ ɫɤɨɛɤɚɯ) ɫ ɞɚɧɧɵɦɢ ɫɩɪɚɜɨɱɧɢɤɚ [14]: ɯP = 12,8 (9,14) Ɉɦ, r1 = 0,22 (0,26) Ɉɦ, x1 = 0,518 ( 0,605 ) Ɉɦ, r2 | = 0,268 (0,26) Ɉɦ, xc2 = 0,7 (0,605) Ɉɦ ɢ ɨɰɟɧɢɬɟ ɬɨɱɧɨɫɬɶ ɪɚɫɱɟɬɚ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɩɨ ɩɪɢɛɥɢɠɟɧɧɵɦ ɮɨɪɦɭɥɚɦ. Ɉɬɫɸɞɚ ɜɵɜɨɞ: – ɞɥɹ ɪɚɫɱɟɬɨɜ ɫɥɟɞɭɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɨ ɞɚɧɧɵɦ ɫɩɪɚɜɨɱɧɢɤɨɜ ɢ ɤɚɬɚɥɨɝɨɜ; – ɪɟɡɭɥɶɬɚɬɚɦɢ ɪɚɫɱɟɬɨɜ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ ɧɭɠɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɨɱɟɧɶ ɨɫɬɨɪɨɠɧɨ ɢ ɥɢɲɶ ɞɥɹ ɩɪɢɛɥɢɠɟɧɧɵɯ ɪɚɫɱɟɬɨɜ. 2

r12

3.5.4. Ɏɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɜɢɞɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

ɂɡɭɱɟɧɢɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɪɢɭɱɢɥɨ ɤ ɦɵɫɥɢ, ɱɬɨ ɭɜɟɥɢɱɟɧɢɟ ɬɨɤɚ ɹɤɨɪɹ ɜɫɟɝɞɚ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɦɨɦɟɧɬɚ. ɇɚ ɪɢɫ. 3.51 ɩɪɢɜɟɞɟɧɵ ɫɨɜɦɟɳɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɚɹ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ, ɢɡ ɤɨɬɨɪɵɯ ɫɥɟɞɭɟɬ, ɱɬɨ ɩɪɢ ɦɚɥɵɯ ɫɤɨɥɶɠɟɧɢɹɯ ɭɜɟɥɢɱɟɧɢɟ ɬɨɤɚ ɪɨɬɨɪɚ ɭɜɟɥɢɱɢɜɚɟɬ ɦɨɦɟɧɬ. ɇɨ ɩɪɢ ɛɨɥɶɲɢɯ ɫɤɨɥɶɠɟɧɢɹɯ ɬɨɤ ɪɨɬɨɪɚ ɩɪɨɞɨɥɠɚɟɬ ɪɚɫɬɢ, ɚ ɦɨɦɟɧɬ – ɭɦɟɧɶɲɚɟɬɫɹ. Ȧ cos ĳ2 I22 I22A Ȧ0ɇ ĳ22 I21A Ȧ1 I2 I21 ĳ21 E21 Ȧ2 E22 M I2, M, cos ĳ2 Mɉ

I2ɉ

Ɋɢɫ. 3.51. Ɏɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɜɢɞɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ Ɇɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɩɨ (3.54) 3 ȿ2S I2 cos ĳ 2 Ɇ Ȧ0

115

3 E2S I2 cos ĳ2 Ȧ0

ɡɚɜɢɫɢɬ ɨɬ ɚɤɬɢɜɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɬɨɤɚ ɪɨɬɨɪɚ I2ǜcos ĳ2. E2 s r2 , cos ĳ2 . I2 2 2 2 2 r2 x 2 s2 r2 x 2 s2 ɂ ɟɫɥɢ ɬɨɤ ɪɨɬɨɪɚ I2 ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɤɨɥɶɠɟɧɢɹ ɩɨɫɬɨɹɧɧɨ ɧɚɪɚɫɬɚɟɬ ɢ ɩɪɢ s ĺ f ɫɬɪɟɦɢɬɫɹ ɤ I2ɉɊȿȾ, ɬɨ ɟɝɨ ɚɤɬɢɜɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɨɩɪɟɞɟɥɹɟɬɫɹ cos ĳ2, ɤɨɬɨɪɵɣ ɩɪɢ s = 0 ɪɚɜɟɧ 1, ɚ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ s ɭɦɟɧɶɲɚɟɬɫɹ, ɢ ɩɪɢ s ĺ f ɪɚɜɟɧ ɧɭɥɸ. ɇɚ ɪɢɫ. 3.51 ɩɨɤɚɡɚɧɚ ɡɚɜɢɫɢɦɨɫɬɶ Ȧ (cos ĳ2). ɇɚ ɜɟɤɬɨɪɧɨɣ ɞɢɚɝɪɚɦɦɟ ɫɩɥɨɲɧɵɦɢ ɜɟɤɬɨɪɚɦɢ ɢɡɨɛɪɚɠɟɧɵ ɗȾɋ ɪɨɬɨɪɚ ȿ21 ɢ ɬɨɤ ɪɨɬɨɪɚ I21 ɞɥɹ ɫɤɨɪɨɫɬɢ Ȧ1, ɚ ɩɭɧɤɬɢɪɧɵɦɢ – ȿ22 ɢ I22 ɞɥɹ ɫɤɨɪɨɫɬɢ Ȧ2 < Ȧ1. ɉɪɢ ɫɧɢɠɟɧɢɢ ɫɤɨɪɨɫɬɢ ɪɚɫɬɟɬ ɫɤɨɥɶɠɟɧɢɟ s, ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɗȾɋ ɪɨɬɨɪɚ ɨɬ ȿ21 ɞɨ ȿ22, ɪɚɫɬɟɬ ɬɨɤ ɪɨɬɨɪɚ ɨɬ I21 ɞɨ I22, ɧɨ ɨɞɧɨɜɪɟɦɟɧɧɨ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɭɝɨɥ – ɨɬ ĳ21 ɞɨ ĳ22, ɢ ɫɧɢɠɚɟɬɫɹ ɚɤɬɢɜɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɬɨɤɚ ɪɨɬɨɪɚ – ɨɬ I21A ɞɨ I22Ⱥ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɫɧɢɠɟɧɢɢ ɫɤɨɪɨɫɬɢ ɫɧɢɠɚɟɬɫɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɚ ɪɚɛɨɱɟɦ ɭɱɚɫɬɤɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɬɨɤɚ ɪɨɬɨɪɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɪɚɫɬɟɬ. ɋɧɢɠɟɧɢɟ ɫɤɨɪɨɫɬɢ ɧɢɠɟ ɤɪɢɬɢɱɟɫɤɨɣ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɦɨɦɟɧɬɚ ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɪɨɫɬɟ ɬɨɤɚ ɪɨɬɨɪɚ, ɢ ɩɪɨɢɫɯɨɞɢɬ ɷɬɨ ɧɚ ɧɟɭɫɬɨɣɱɢɜɨɦ ɭɱɚɫɬɤɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. 3.5.5. ɍɩɪɨɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ

Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ ɨɛɵɱɧɨ ɡɚɩɢɫɵɜɚɸɬɫɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɵ. ȼ ɫɜɹɡɢ ɫɨ ɫɥɨɠɧɨɫɬɶɸ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɞɜɢɝɚɬɟɥɹ (ɲɟɫɬɶ ɨɛɦɨɬɨɤ, ɩɟɪɟɦɟɧɧɵɣ ɬɨɤ, ɜɪɚɳɚɸɳɟɟɫɹ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ) ɱɢɫɥɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɜɟɥɢɤɨ. ɉɨɥɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɦɧɨɝɨ ɛɥɨɤɨɜ ɩɪɨɢɡɜɟɞɟɧɢɣ, ɤɪɢɜɭɸ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ, ɩɟɪɟɤɪɟɫɬɧɵɟ ɨɛɪɚɬɧɵɟ ɫɜɹɡɢ [1]. ɇɚɡɧɚɱɟɧɢɟ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ (ɨɛɥɟɝɱɟɧɢɟ ɩɨɧɢɦɚɧɢɹ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɜ ɞɜɢɝɚɬɟɥɟ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɭɩɪɚɜɥɹɸɳɢɯ ɢ ɜɨɡɦɭɳɚɸɳɢɯ ɜɨɡɞɟɣɫɬɜɢɹɯ) ɜ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ. Ɉɝɪɚɧɢɱɢɦɫɹ ɪɚɫɫɦɨɬɪɟɧɢɟɦ ɭɩɪɨɳɟɧɧɨɣ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ, ɞɥɹ ɱɟɝɨ ɢɫɩɨɥɶɡɭɟɦ ɜɵɪɚɠɟɧɢɟ ɦɨɦɟɧɬɚ (3.57) 2 3 U1 r2c /s MɗɆ f(U1, f1, Ȧ) . 2 Ȧ0 r1 r2c /s (x1 xc2 )2 ȼɨɡɶɦɺɦ ɱɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɬɚɬɨɪɟ U1, ɱɚɫɬɨɬɵ ɩɢɬɚɸɳɟɣ ɫɟɬɢ f1 ɢ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ Ȧ:

>

ǻɆ

@

wɆ wɆ wɆ ǻU ǻf ǻȦ . wU wf wȦ

(3.71)

Ɉɛɨɡɧɚɱɢɦ: wɆ wU wɆ wf wɆ wȦ

½ kU ° ° ° k ¾. f ° ° kȦ ° ¿

116

(3.72)

ȼ ɜɵɪɚɠɟɧɢɢ (3.72) – kU, kf, kZ - ɤɨɷɮɮɢɰɢɟɧɬɵ ɭɫɢɥɟɧɢɹ ɩɨ ɧɚɩɪɹɠɟɧɢɸ, ɱɚɫɬɨɬɟ, ɫɤɨɪɨɫɬɢ. ɉɨɥɭɱɢɥɢ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɦɨɦɟɧɬɚ ɜ ɩɪɢɪɚɳɟɧɢɹɯ: ǻɆ k U ǻU k f ǻf k Ȧ ǻȦ .

(3.73)

Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ ȺȾ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ: Ɇ ɆɋɌ J

dȦ . dt

(3.74)

ɉɨ ɜɵɪɚɠɟɧɢɹɦ (3.73) ɢ (3.74) ɧɚ ɪɢɫ. 3.52 ɩɨɫɬɪɨɟɧɚ ɭɩɪɨɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ȺȾ. ¨f1 Kf ¨U1 KU

¨Mf MC -

¨MU

1 Jp

¨Ȧ

MȦ KȦ Ɋɢɫ. 3.52. ɍɩɪɨɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ȺȾ Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ȺȾ ɹɜɥɹɟɬɫɹ ɧɟɥɢɧɟɣɧɨɣ. ɉɨɥɭɱɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɩɨɡɜɨɥɹɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɩɨɜɟɞɟɧɢɟ ɞɜɢɝɚɬɟɥɹ ɜ ɫɬɚɬɢɤɟ ɢ ɞɢɧɚɦɢɤɟ ɜ ɩɪɢɪɚɳɟɧɢɹɯ, ɧɨ ɬɨɥɶɤɨ ɧɚ ɥɢɧɟɚɪɢɡɨɜɚɧɧɵɯ ɨɬɪɟɡɤɚɯ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. Ʉɨɷɮɮɢɰɢɟɧɬɵ ɭɫɢɥɟɧɢɹ ɩɨ ɪɚɡɥɢɱɧɵɦ ɭɩɪɚɜɥɹɸɳɢɦ ɢ ɜɨɡɦɭɳɚɸɳɢɦ ɜɨɡɞɟɣɫɬɜɢɹɦ ɹɜɥɹɸɬɫɹ ɬɚɤɠɟ ɧɟɥɢɧɟɣɧɵɦɢ. Ⱦɥɹ ɢɯ ɨɩɪɟɞɟɥɟɧɢɹ ɩɪɢɞɟɬɫɹ ɢɡɭɱɢɬɶ ɜɥɢɹɧɢɟ ɭɩɪɚɜɥɹɸɳɢɯ ɢ ɜɨɡɦɭɳɚɸɳɢɯ ɜɨɡɞɟɣɫɬɜɢɣ ɧɚ ɜɢɞ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɢɡɭɱɢɬɶ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. 3.5.6. ɂɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɢ ɢɯ ɪɚɫɱɟɬ

ɂɫɩɨɥɶɡɭɹ ɭɩɪɨɳɟɧɧɭɸ ɫɬɪɭɤɬɭɪɧɭɸ ɫɯɟɦɭ (ɪɢɫ. 3.52) ɢ ɜɵɪɚɠɟɧɢɟ ɦɨɦɟɧɬɚ (3.57) 2 3 U1 r2c /s M f(U1, f1, r1, x1, r2, x 2 ) , 2 Ȧ0 r1 r2c /s (x1 xc2 )2 ɨɬɦɟɬɢɦ, ɱɬɨ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ: – ɢɡɦɟɧɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɫɟɬɢ U1; – ɜɜɟɞɟɧɢɟɦ ɜ ɰɟɩɶ ɫɬɚɬɨɪɚ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ R1ȾɈȻ, X1ȾɈȻ; – ɜɜɟɞɟɧɢɟɦ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɶ ɪɨɬɨɪɚ ȺȾ ɫ ɮɚɡɧɵɦ ɪɨɬɨɪɨɦ R2ȾɈȻ, X2ȾɈȻ; – ɢɡɦɟɧɟɧɢɟɦ ɱɚɫɬɨɬɵ ɩɢɬɚɸɳɟɣ ɫɟɬɢ f1.

>

@

117

Ⱦɥɹ ɢɡɭɱɟɧɢɹ ɜɥɢɹɧɢɹ ɧɚ ɜɢɞ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜɵɲɟ ɩɚɪɚɦɟɬɪɨɜ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɮɨɪɦɭɥɨɣ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ0 = 2 ʌ ǜf1 / pɉ ɢ ɮɨɪɦɭɥɨɣ Ʉɥɨɫɫɚ, ɩɨɡɜɨɥɹɸɳɟɣ ɨɩɪɟɞɟɥɢɬɶ ɜɢɞ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨ ɤɪɢɬɢɱɟɫɤɢɦ ɡɧɚɱɟɧɢɹɦ ɆɄ, sɄ: Ɇ

2 MK ; MK s sK sK s

2

3 U1

2 2 2 Ȧ0 §¨ r1 r r1 xK ·¸ © ¹

;

sɄ

r2c r12 xɄ2

.

(3.75)

Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɫɟɬɢ. Ⱦɥɹ ɢɡɦɟɧɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɜ ɰɟɩɶ ɫɬɚɬɨɪɚ ɭɫɬɚɧɚɜɥɢɜɚɸɬ ɪɟɝɭɥɹɬɨɪ ɧɚɩɪɹɠɟɧɢɹ Ɋɇ (ɬɢɪɢɫɬɨɪɧɵɣ, ɬɪɚɧɡɢɫɬɨɪɧɵɣ, ɷɥɟɤɬɪɨɦɚɲɢɧɧɵɣ). ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ Ɋɇ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 3.53. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚ ɜɯɨɞɟ Ɋɇ ɧɚɩɪɹɠɟɧɢɹ ɭɩɪɚɜɥɟɧɢɹ Uɍ ɢɡɦɟɧɹɟɬɫɹ ɚɦɩɥɢɬɭɞɚ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɬɚɬɨɪɟ ɞɜɢɝɚɬɟɥɹ, ɱɚɫɬɨɬɚ ɷɬɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ f1 = const.

Ȧ

~ PH Uɭ

0,8·Uɇ

Ȧ0ɇ 2

Ȧɇ

U1ɇɈɆ U1=var

3

ȦɄ

1

0,9·Uɇ ɟɫɬ Uɇ

Ɇ

Ɇ ɆɄ ɂ2 ɆɄ ɂ1 ɆɄ ȿɋɌ

Ɋɢɫ. 3.53. ɋɯɟɦɚ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ U1 = var

Ʉɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ 2

MK

3 U1

2 2 2Ȧ0 §¨ r1 r r1 xK ·¸ © ¹

{ U12

ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɤɜɚɞɪɚɬɭ ɧɚɩɪɹɠɟɧɢɹ, ɚ ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɢ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ r2c const. sɄ r12 xɄ2 118

ɉɪɢ ɭɦɟɧɶɲɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɤɪɢɬɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ ȦɄ = Ȧ0·(1 – sK) = const ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ, ɚ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɆɄ ɫɧɢɠɚɟɬɫɹ. Ɋɚɫɱɟɬ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɜɨɞɢɬɫɹ ɤ ɨɩɪɟɞɟɥɟɧɢɸ ɤɪɢɬɢɱɟɫɤɨɝɨ ɫɤɨɥɶɠɟɧɢɹ sɄ (ɫɤɨɪɨɫɬɢ ȦɄ) ɢ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɆɄ. Ɍɚɤ, ɩɪɢ U1 = 0,5·U1ɇ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɪɚɜɟɧ ɆɄ ɂɋɄ = 0,25·ɆɄ ȿɋɌ, ɩɪɢ U1 = 0,7·U1ɇ – ɆɄ ɂɋɄ = 0,49·ɆɄ ȿɋɌ. Ⱦɨɩɭɫɤɚɟɦɵɟ ɩɨɫɚɞɤɢ ɧɚɩɪɹɠɟɧɢɹ ɜ ɩɪɨɦɵɲɥɟɧɧɵɯ ɷɥɟɤɬɪɨɫɟɬɹɯ ɫɨɫɬɚɜɥɹɸɬ 10% ɨɬ ɧɨɦɢɧɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ (ǻU1ȾɈɉ = – 10%, + 15%), ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɦɨɠɟɬ ɫɨɫɬɚɜɢɬɶ MK ȾɈɉ 0,81 MK ȿɋɌ . Ʉɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɩɨ ɧɚɩɪɹɠɟɧɢɸ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɦɟɯɚɧɢɱɟɫɤɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ, ɩɨɫɬɪɨɟɧɧɵɦ (ɢɥɢ ɫɧɹɬɵɦ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ) ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɧɚ ɫɬɚɬɨɪɟ ǻM M1 M2 ɩɪɢ f1 = const, Ȧ = const. kU ǻU U1 U2 Ɍɚɤ ɤɚɤ ɧɚɤɥɨɧ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɬɚɬɨɪɟ ɢɡɦɟɧɹɟɬɫɹ ɧɟɡɧɚɱɢɬɟɥɶɧɨ, ɬɨ ɞɢɚɩɚɡɨɧ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɛɨɥɶɲɢɦ. ɗɬɨɬ ɫɩɨɫɨɛ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɧɚ ɩɪɚɤɬɢɤɟ ɩɪɢɦɟɧɹɟɬɫɹ ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɭɫɤɨ-ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɨɜ (ɦɹɝɤɢɣ ɩɭɫɤ) ɢ ɞɥɹ ɷɤɨɧɨɦɢɱɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɜ ɧɟɛɨɥɶɲɢɯ ɩɪɟɞɟɥɚɯ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɢ ɧɟɤɨɬɨɪɨɦ ɡɧɚɱɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɆɄ < Ɇɋ ɜɨɡɦɨɠɧɨ ɨɩɪɨɤɢɞɵɜɚɧɢɟ ɞɜɢɝɚɬɟɥɹ. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɜɜɟɞɟɧɢɢ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɶ ɫɬɚɬɨɪɚ. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 3.54. Ⱦɨɛɚɜɨɱɧɵɟ ɚɤɬɢɜɧɵɟ ɢɥɢ ɪɟɚɤɬɢɜɧɵɟ (ɞɪɨɫɫɟɥɢ) ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɤɥɸɱɚɸɬɫɹ ɜ ɰɟɩɶ ɫɬɚɬɨɪɚ ɫ ɰɟɥɶɸ ɫɧɢɠɟɧɢɹ ɩɭɫɤɨɜɵɯ ɬɨɤɨɜ, ɤɨɝɞɚ ɩɪɨɫɚɞɤɚ ɧɚɩɪɹɠɟɧɢɹ ɫɟɬɢ ɩɪɢ ɩɭɫɤɟ ɞɜɢɝɚɬɟɥɹ ɩɪɟɜɵɲɚɟɬ ɞɨɩɭɫɬɢɦɨɟ ɡɧɚɱɟɧɢɟ.

Ȧ

~ Ȧɇ RȾɈȻ

ȦɄ ȿɋɌ ȦɄ ɂ

Ɇ Ɇ

0 ɆɄ ɂ

ɆɄ ȿɋɌ

Ɋɢɫ. 3.54. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ R1ȾɈȻ= var ɢ ɏ1ȾɈȻ= var

119

ɉɪɢ ɜɜɟɞɟɧɢɢ ɜ ɰɟɩɶ ɫɬɚɬɨɪɚ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ R1ȾɈȻ ɢ ɏ1ȾɈȻ ɭɦɟɧɶɲɚɟɬɫɹ ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ r2c 1 1 sɄ { { , 2 2 r1 xɄ r1 x1 ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɜɨɡɪɚɫɬɚɟɬ ɤɪɢɬɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ ȦɄ ɢ ɩɚɞɚɟɬ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ 2 3 U1 1 1 MK { { . 2 2 2 Ȧ0 §¨ r1 r r1 xK ·¸ r1 x1 © ¹ ɉɪɢ R1ȾɈȻ ɜɨɡɪɚɫɬɚɸɬ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɰɟɩɢ ɫɬɚɬɨɪɚ ǻɊ1 I12 r1 R1ȾɈȻ , ɩɪɢ ɏ1ȾɈȻ – ɫɧɢɠɚɟɬɫɹ cos M1. ɉɪɢ ɢɡɜɟɫɬɧɵɯ ɜɟɥɢɱɢɧɚɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ R1ȾɈȻ ɢ ɏ1ȾɈȻ ɪɚɫɱɟɬ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɩɪɟɞɟɥɟɧɢɢ sɄɂ (ɫɤɨɪɨɫɬɢ ȦɄ) ɢ ɆɄ ɂɋɄ ɢ ɩɨɞɫɬɚɧɨɜɤɢ ɢɯ ɜ ɮɨɪɦɭɥɭ Ʉɥɨɫɫɚ (3.57, 3.58). Ʉɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɩɨ ɫɤɨɪɨɫɬɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɠɟɫɬɤɨɫɬɶɸ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ǻM M1 M2 kȦ ȕ ɩɪɢ f1 = const, U1 = const. ǻȦ Ȧ1 Ȧ2 Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɜɜɟɞɟɧɢɢ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɶ ɪɨɬɨɪɚ. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɜɜɟɞɟɧɢɢ ɜ ɰɟɩɶ ɪɨɬɨɪɚ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ R2ȾɈȻ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 3.55. Ⱦɨɛɚɜɨɱɧɵɟ ɚɤɬɢɜɧɵɟ ɢɥɢ ɪɟɚɤɬɢɜɧɵɟ (ɞɪɨɫɫɟɥɢ) ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɤɥɸɱɚɸɬɫɹ ɜ ɰɟɩɶ ɪɨɬɨɪɚ ɫ ɰɟɥɶɸ ɨɛɟɫɩɟɱɟɧɢɹ ɧɟɨɛɯɨɞɢɦɵɯ ɩɭɫɤɨɜɵɯ ɦɨɦɟɧɬɨɜ ɢ ɬɨɤɨɜ, ɚ ɬɚɤɠɟ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɡɚɞɚɧɧɵɯ ɫɤɨɪɨɫɬɟɣ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɩɨɥɧɨɦɭ ɪɨɬɨɪɧɨɦɭ ɫɨɩɪɨɬɢɜɥɟɧɢɸ r2c sɄ { Rc2 , 2 2 r1 xɄ ɚ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɧɚ ɢɫɤɭɫɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɆɄ ɂɋɄ ɧɟ ɡɚɜɢɫɢɬ ɨɬ R2 ɢ ɪɚɜɟɧ ɤɪɢɬɢɱɟɫɤɨɦɭ ɦɨɦɟɧɬɭ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɆɄ ȿɋɌ 2 3 U1 MK MK ɂɋɄ ɆɄ ȿɋɌ const. 2 2 2 Ȧ0 §¨ r1 r r1 xK ·¸ © ¹ ɉɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɫ Ɇ = Ɇɋ ɫɨ ɫɤɨɪɨɫɬɶɸ Ȧɋ ɜɜɟɞɟɧɢɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R2ȾɈȻ ɭɜɟɥɢɱɢɜɚɟɬ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ R2, ɬɨɤ ɪɨɬɨɪɚ I2 ɭɦɟɧɶɲɚɟɬɫɹ, ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɦɨɦɟɧɬ Ɇ ɧɚ ɜɚɥɭ ȺȾ ɫɧɢɠɚɟɬɫɹ, ɚ ɩɨɹɜɢɜɲɢɣɫɹ ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɆȾɂɇ ɛɭɞɟɬ ɨɬɪɢɰɚɬɟɥɶɧɵɦ (ɆȾɂɇ < 0). ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɫɤɨɪɨɫɬɶ Ȧ ȺȾ ɭɦɟɧɶɲɚɟɬɫɹ, ɚ ɫɤɨɥɶɠɟɧɢɟ s ɭɜɟɥɢɱɢɜɚɟɬɫɹ. ɍɜɟɥɢɱɟɧɢɟ ɫɤɨɥɶɠɟɧɢɹ ɜɵɡɵɜɚɟɬ ɪɨɫɬ ɗȾɋ ɪɨɬɨɪɚ, ɪɚɫɬɟɬ ɬɨɤ ɪɨɬɨɪɚ ɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɦɨɦɟɧɬ. ɋɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɛɭɞɟɬ ɫɧɢɠɚɬɶɫɹ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɧɟ ɫɪɚɜɧɹɟɬɫɹ ɫɨ ɫɬɚɬɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ Ɇ = Ɇɋ, ɧɨ ɷɬɨ ɩɪɨɢɡɨɣɞɟɬ ɩɪɢ ɫɤɨɪɨɫɬɢ ȦC1 < ȦC. ɉɪɢ ɢɡɜɟɫɬɧɵɯ ɜɟɥɢɱɢɧɚɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ R2ȾɈȻ ɪɚɫɱɟɬ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɆɄ, sɄɂ (ɫɤɨɪɨɫɬɢ ȦɄɂ) ɢ ɩɨɞɫɬɚɧɨɜɤɢ ɢɯ ɜ ɮɨɪɦɭɥɭ Ʉɥɨɫɫɚ (3.61, 3.62).

120

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Ȧ U1ɇɈɆ

Ȧ0ɇ

ɟɫɬ R2

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ȦɄ ɂ1 Rƍƍ2

Ɇ ȦɄ ɂ2 R2ȾɈȻ

ȦɄ ɂ3 0

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Ɋɢɫ. 3.55. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ R2ȾɈȻ = var Ɋɚɫɱɟɬ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɭɳɟɫɬɜɟɧɧɨ ɭɩɪɨɳɚɟɬɫɹ ɩɪɢ ɩɨɫɬɪɨɟɧɧɨɣ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ. ȿɫɥɢ ɜ ɭɪɚɜɧɟɧɢɢ (3.57) 2 3 U1 r2c /s r2c { M 2 s Ȧ0 r1 r2c /s (x1 xc2 )2 ɩɪɢɧɹɬɶ Ɇ = const, ɬɨ ɨɬɧɨɲɟɧɢɟ ɫɤɨɥɶɠɟɧɢɣ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɸ ɫɨɩɪɨɬɢɜɥɟɧɢɣ: sȿɋɌ r2c r2 . (3.76) sɂɋɄ Rc2 R 2

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Ɂɚɞɚɜɚɹɫɶ ɩɪɢ Ɇ = const ɫɤɨɥɶɠɟɧɢɟɦ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ sȿɋɌ, ɩɪɢ ɢɡɜɟɫɬɧɨɦ ɧɟɜɵɤɥɸɱɚɟɦɨɦ ɚɤɬɢɜɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɮɚɡɧɨɣ ɨɛɦɨɬɤɢ ɪɨɬɨɪɚ r2 ɢ ɩɨɥɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɪɨɬɨɪɧɨɣ ɰɟɩɢ R2 ɩɨ ɮɨɪɦɭɥɟ (3.76) ɪɚɫɫɱɢɬɵɜɚɸɬ sɂɋɄ. ɗɬɨɣ ɠɟ ɮɨɪɦɭɥɨɣ ɦɨɠɧɨ ɪɚɫɫɱɢɬɵɜɚɬɶ R2 ɩɨ ɡɚɞɚɧɧɨɦɭ ɡɧɚɱɟɧɢɸ ɫɤɨɪɨɫɬɢ (ɫɤɨɥɶɠɟɧɢɹ sɂɋɄ). Ʉɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɩɨ ɫɤɨɪɨɫɬɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɠɟɫɬɤɨɫɬɶɸ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ǻM M1 M2 kZ 0 ɩɪɢ f1 = const, U1 = const. ǻȦ Ȧ1 - Ȧ 2 ɇɚ ɪɚɛɨɱɟɦ ɭɱɚɫɬɤɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤȦ < 0, ɨɛɪɚɬɧɚɹ ɫɜɹɡɶ ɩɨ ɫɤɨɪɨɫɬɢ ɧɚ ɭɩɪɨɳɟɧɧɨɣ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɟ – ɨɬɪɢɰɚɬɟɥɶɧɚɹ, ɫɢɫɬɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ – ɭɫɬɨɣɱɢɜɚɹ. ɉɪɢ ɤȦ > 0 ɨɛɪɚɬɧɚɹ ɫɜɹɡɶ ɩɨ ɫɤɨɪɨɫɬɢ – ɩɨɥɨɠɢɬɟɥɶɧɚɹ, ɫɢɫɬɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫɬɚɧɨɜɢɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɣ, ɢ ɷɬɨɬ ɭɱɚɫɬɨɤ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɹɜɥɹɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɵɦ. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɜɜɟɞɟɧɢɢ ɜ ɰɟɩɶ ɪɨɬɨɪɚ ɪɟɚɤɬɨɪɨɜ ɢ ɚɤɬɢɜɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ. 3.56.

121

ȼɜɟɞɟɧɢɟ ɜ ɰɟɩɶ ɪɨɬɨɪɚ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɢɧɞɭɤɬɢɜɧɵɯ ɏ2 ɫɨɩɪɨɬɢɜɥɟɧɢɣ (ɪɟɚɤɬɨɪɨɜ), ɨɛɟɫɩɟɱɢɜɚɹ ɫɧɢɠɟɧɢɟ ɬɨɤɚ ɪɨɬɨɪɚ ɢ ɫɧɢɠɚɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɫɬɟɩɟɧɶ ɧɚɝɪɟɜɚ ɞɜɢɝɚɬɟɥɹ, ɨɫɨɛɟɧɧɨ ɩɪɢ ɱɚɫɬɵɯ ɩɭɫɤɚɯ ɢ ɬɨɪɦɨɠɟɧɢɹɯ, ɫɧɢɠɚɟɬ ɩɪɢ ɷɬɨɦ ɤɚɤ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ (ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ 1) 2 3 U1 1 , MK { 2 2· x § 2 2 Ȧ0 ¨ r1 r r1 xK ¸ © ¹ ɬɚɤ ɢ ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ r2c 1 sɄ { . r12 xɄ2 x 2 ȿɫɥɢ ɨɫɬɚɜɢɬɶ ɜ ɰɟɩɢ ɪɨɬɨɪɚ ɬɨɥɶɤɨ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R2, ɬɨ ɞɜɢɝɚɬɟɥɶ ɛɭɞɟɬ ɪɚɛɨɬɚɬɶ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 2. Ȧ

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R2ʜʜX2

Ȧ0ɇ

ɟɫɬ

U1ɇɈɆ ȦɄ ɂ ȦɄȿɋɌ 2 Ɇ

3

R2ʜʜX2

1

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0 ɆɄ ɂɋɄ

ɆɄ ȿɋɌ

Ɋɢɫ. 3.56. ɋɯɟɦɚ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ R2 || X2 ɉɚɪɚɥɥɟɥɶɧɨɟ ɜɤɥɸɱɟɧɢɟ R2 || X2 ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɫ ɩɪɢɦɟɪɧɨ ɩɨɫɬɨɹɧɧɵɦ ɦɨɦɟɧɬɨɦ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɫɤɨɪɨɫɬɢ ɨɬ ɧɭɥɹ ɞɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ 1. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɩɪɢ ɫɤɨɪɨɫɬɢ, ɛɥɢɡɤɨɣ ɤ ɧɭɥɸ, ɱɚɫɬɨɬɚ ɬɨɤɚ ɪɨɬɨɪɚ ɛɥɢɡɤɚ ɤ ɱɚɫɬɨɬɟ ɬɨɤɚ ɫɬɚɬɨɪɚ, ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɟɥɢɤɨ, ɢ ɬɨɤ ɪɨɬɨɪɚ ɩɪɨɬɟɤɚɟɬ ɜ ɨɫɧɨɜɧɨɦ ɱɟɪɟɡ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R2. ɉɪɢ ɫɤɨɪɨɫɬɹɯ, ɛɥɢɡɤɢɯ ɤ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɱɚɫɬɨɬɚ ɬɨɤɚ ɪɨɬɨɪɚ ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ, ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɏ2 ɬɚɤɠɟ ɫɭɳɟɫɬɜɟɧɧɨ ɫɧɢɠɚɟɬɫɹ ɢ ɲɭɧɬɢɪɭɟɬ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R2. Ɋɟɡɭɥɶɬɢɪɭɸɳɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɢɦɟɟɬ ɜɢɞ 3. Ɍɚɤɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɨɫɬɨɹɧɫɬɜɨ ɦɨɦɟɧɬɚ ɩɪɢ ɩɭɫɤɟ, ɧɟɨɛɯɨɞɢɦɨɟ ɭɫɤɨɪɟɧɢɟ ɩɪɢɜɨɞɚ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɩɭɫɤɨɪɟɝɭɥɢɪɭɸɳɟɣ ɚɩɩɚɪɚɬɭɪɵ ɜ ɰɟɩɢ ɪɨɬɨɪɚ. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ ɧɚɩɪɹɠɟɧɢɹ, ɩɨɞɜɨɞɢɦɨɝɨ ɤ ɫɬɚɬɨɪɭ. Ⱦɥɹ ɢɡɦɟɧɟɧɢɹ ɱɚɫɬɨɬɵ ɧɚɩɪɹɠɟɧɢɹ ɜ ɰɟɩɶ ɫɬɚɬɨɪɚ 122

ɞɜɢɝɚɬɟɥɹ ɜɤɥɸɱɚɸɬ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɱɚɫɬɨɬɵ ɉɑ (ɬɢɪɢɫɬɨɪɧɵɣ, ɬɪɚɧɡɢɫɬɨɪɧɵɣ, ɷɥɟɤɬɪɨɦɚɲɢɧɧɵɣ), ɩɨɡɜɨɥɹɸɳɢɣ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚ ɜɯɨɞɟ ɧɚɩɪɹɠɟɧɢɹ ɭɩɪɚɜɥɟɧɢɹ ɩɨ ɧɚɩɪɹɠɟɧɢɸ Uɍɇ ɢɡɦɟɧɹɬɶ ɚɦɩɥɢɬɭɞɭ ɧɚɩɪɹɠɟɧɢɹ U1 = var ɧɚ ɜɵɯɨɞɟ ɉɑ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɱɚɫɬɨɬɵ. ɂɡɦɟɧɟɧɢɟ ɧɚ ɜɯɨɞɟ ɧɚɩɪɹɠɟɧɢɹ ɭɩɪɚɜɥɟɧɢɹ ɱɚɫɬɨɬɨɣ Uɍf ɨɛɟɫɩɟɱɢɜɚɟɬ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɱɚɫɬɨɬɵ f1 = var ɧɚ ɜɵɯɨɞɟ ɉɑ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɚɦɩɥɢɬɭɞɵ U1. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɉɑ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 3.57. ɋɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɦɚɲɢɧɵ (ɫɢɧɯɪɨɧɧɚɹ ɫɤɨɪɨɫɬɶ) ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ f1 ɢɡɦɟɧɹɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɱɚɫɬɨɬɟ 2ʌ f1 Ȧ0 { f1 , pɉ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɢɡɦɟɧɹɟɬɫɹ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɤɜɚɞɪɚɬɭ ɱɚɫɬɨɬɵ 2 3 U1 1 1 MK { { 2, 2 2 2 Ȧ0 §¨ r1 r r1 xK ·¸ Ȧ0 xK f1 © ¹ ɚ ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ – ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɱɚɫɬɨɬɟ r2c 1 sɄ { . r12 xɄ2 f1 ɉɪɢ ɷɬɨɦ ɩɪɨɢɡɜɟɞɟɧɢɟ 'ȦK = Ȧ0·sK ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ Ȧ0·sK = Ȧ0·(Ȧ0 – ȦK) / Ȧ0 ='ȦK = const. Ɍɚɤɨɟ ɜɥɢɹɧɢɟ ɱɚɫɬɨɬɵ ɧɚ ǻȦɄ ɩɨɡɜɨɥɹɟɬ ɞɨɜɨɥɶɧɨ ɩɪɨɫɬɨ ɩɨɫɬɪɨɢɬɶ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɱɚɫɬɨɬ. ɉɪɢ ɡɚɞɚɧɧɨɣ ɱɚɫɬɨɬɟ f1ɁȺȾ ɫɬɪɨɢɬɫɹ Ȧ0ɁȺȾ. Ɉɬɥɨɠɢɜ ɜɧɢɡ ɨɬ Ȧ0ɁȺȾ ɜɟɥɢɱɢɧɭ 'ȦK, ɩɨɫɬɨɹɧɧɭɸ ɞɥɹ ɜɫɟɯ ɱɚɫ ɬɨɬ, ɨɩɪɟɞɟɥɹɸɬ ɤɪɢɬɢɱɟɫɤɭɸ ɫɤɨɪɨɫɬɶ ȦɄɁȺȾ ɞɥɹ ɡɚɞɚɧɧɨɣ ɱɚɫɬɨɬɵ. ɉɪɢ ɷɬɨɣ ɫɤɨɪɨɫɬɢ ȦɄɁȺȾ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɪɚɜɟɧ ɤɪɢɬɢɱɟɫɤɨɦɭ ɆɄ ɞɥɹ ɡɚɞɚɧɧɨɣ ɱɚɫɬɨɬɵ. Ɍɚɤɨɟ ɩɨɫɬɪɨɟɧɢɟ ɜɵɩɨɥɧɟɧɨ ɧɚ ɪɢɫ. 3.57, ɝɞɟ ɩɨɫɬɪɨɟɧɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ: ɟɫɬɟɫɬɜɟɧɧɚɹ – ɩɪɢ f1 = f1ɇ, ɞɥɹ ɱɚɫɬɨɬɵ f1 > f1ɇ – ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɪɨ Ȧ

~

Ȧ0ɂ1 ɉɑ

Uɭf

U1ɇɈɆ f1 ɇɈɆ

U1=var f1=var

¨ȦɄ

ȦɄ ɂ1 Ȧ0H ȿɋɌ ɟɫɬ.

¨ȦɄ ȦɄ ȿɋɌ Ȧ0ɂ2 ¨ȦɄ

Ɇ

ȦɄ ɂ2 Ɇ

0 ɆɄ ɂ1

ɆɄ ȿɋɌ

ɆɄ ɂ2

Ɋɢɫ. 3.57. ɋɯɟɦɚ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ f1 = var ɢ U1 = const 123

ɯɨɞɢɬ ɜɵɲɟ ɟɫɬɟɫɬɜɟɧɧɨɣ, ɢ ɞɥɹ f1 < f1ɇ – ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɢɠɟ ɟɫɬɟɫɬɜɟɧɧɨɣ. Ɂɧɚɱɟɧɢɟ ɆɄ ɩɪɢ ɫɧɢɠɟɧɢɢ ɱɚɫɬɨɬɵ ɧɚɱɢɧɚɟɬ ɭɜɟɥɢɱɢɜɚɬɶɫɹ. ȿɫɥɢ ɫɧɢɡɢɬɶ ɱɚɫɬɨɬɭ ɜɞɜɨɟ, ɬɨ ɆɄɂɋɄ ɜɨɡɪɚɫɬɟɬ ɜ ɱɟɬɵɪɟ ɪɚɡɚ. ȼɨɬ ɤ ɱɟɦɭ ɩɪɢɜɨɞɹɬ ɩɪɢɧɹɬɵɟ ɞɨɩɭɳɟɧɢɹ. ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɧɟɨɛɯɨɞɢɦ ɭɱɺɬ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. ɉɪɢ ɫɧɢɠɟɧɢɢ ɱɚɫɬɨɬɵ ɜɞɜɨɟ ɗȾɋ ɫɬɚɬɨɪɚ ȿ1 = 4,44·w1·f1·ɎɆȺɄɋ ɬɚɤɠɟ ɞɨɥɠɧɚ ɫɧɢɡɢɬɶɫɹ ɜɞɜɨɟ, ɧɨ ɨɧɚ ɞɨɥɠɧɚ ɭɪɚɜɧɨɜɟɫɢɬɶ ɩɪɢɥɨɠɟɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ, ɤɨɬɨɪɨɟ ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɨɫɬɚɥɨɫɶ ɩɨɫɬɨɹɧɧɵɦ. Ⱦɥɹ ɫɨɡɞɚɧɢɹ ȿ1 § U1 ɧɟɨɛɯɨɞɢɦɨ ɩɨɬɨɤ ɦɚɲɢɧɵ ɭɜɟɥɢɱɢɬɶ ɜɞɜɨɟ, ɱɬɨ ɧɟɜɨɡɦɨɠɧɨ ɢɡ-ɡɚ ɧɚɫɵɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɬɨɤ ɫɬɚɬɨɪɚ ɫɭɳɟɫɬɜɟɧɧɨ ɜɨɡɪɚɫɬɚɟɬ, ɢ ɦɚɲɢɧɚ ɩɟɪɟɝɪɟɜɚɟɬɫɹ, ɟɫɥɢ ɟɟ ɧɟ ɨɬɤɥɸɱɢɬ ɡɚɳɢɬɚ. Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ ɜɵɲɟɢɡɥɨɠɟɧɧɨɝɨ, ɩɪɢ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɱɚɫɬɨɬɵ f1 = var ɧɟɨɛɯɨɞɢɦɨ ɨɞɧɨɜɪɟɦɟɧɧɨ ɪɟɝɭɥɢɪɨɜɚɬɶ ɢ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪɟ ɞɜɢɝɚɬɟɥɹ U1 = var. ɉɪɢ f1 > f1ɇ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪɟ ɭɜɟɥɢɱɢɜɚɬɶ (U1 > U1ɇ) ɧɟɜɨɡɦɨɠɧɨ ɩɨ ɭɫɥɨɜɢɹɦ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɱɧɨɫɬɢ ɢɡɨɥɹɰɢɢ. ɉɪɢ f1 < f1ɇ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪɟ ɫɧɢɠɚɸɬ, ɩɪɢ ɷɬɨɦ ɡɚɤɨɧ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɟɫɤɨɥɶɤɢɦɢ ɨɛɫɬɨɹɬɟɥɶɫɬɜɚɦɢ, ɨ ɤɨɬɨɪɵɯ ɪɟɱɶ ɩɨɣɞɟɬ ɧɢɠɟ. Ɋɚɫɫɦɚɬɪɢɜɚɹ ɜɥɢɹɧɢɟ ɢɡɦɟɧɟɧɢɹ ɱɚɫɬɨɬɵ ɧɚ ɜɢɞ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɡɚɫɥɭɠɢɜɚɟɬ ɜɧɢɦɚɧɢɹ ɬɚɤɨɣ ɡɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ, ɩɪɢ ɤɨɬɨɪɨɦ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ ɩɟɪɟɝɪɭɡɨɱɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ, ɟɝɨ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɆɄ. Ɍɚɤɨɦɭ ɡɚɤɨɧɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɦɟɧɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɱɚɫɬɨɬɟ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɟɫɥɢ ɩɪɢɦɟɧɢɬɶ ɡɚɤɨɧ ɪɟɝɭɥɢɪɨɜɚɧɢɹ U1/f1 = const, ɬɨ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ. 2 2 3 U1 U1 MK { 2 const . 2 2· § 2 Ȧ0 ¨ r1 r r1 xK ¸ f1 © ¹ ɇɟ ɫɥɟɞɭɟɬ ɡɚɛɵɜɚɬɶ, ɱɬɨ ɜɵɪɚɠɟɧɢɟ Ȧ ɞɥɹ ɆɄ ɩɨɥɭɱɟɧɨ ɞɥɹ Ƚ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ Ȧ0ɇ ɡɚɦɟɳɟɧɢɹ ɫɨ ɜɫɟɦɢ ɟɟ ɞɨɩɭɳɟɧɢɹɦɢ. ɇɚ ɪɢɫ. 3.58 ɩɪɢɜɟɞɟɧɵ ɦɟɯɚɧɢɱɟɫɤɢɟ Ȧ01 ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɥɹ ɡɚɤɨɧɚ U1 /f1 = const. ɟɫɬ ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ȧ02 ɩɟɪɟɦɟɳɚɸɬɫɹ ɩɚɪɚɥɥɟɥɶɧɨ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɱɬɨ Ȧ03 ɧɚɩɨɦɢɧɚɟɬ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɢɡɦɟɧɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ. Ʉɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɩɨ ɱɚɫɬɨɬɟ kf M ɞɥɹ ɭɩɪɨɳɟɧɧɨɣ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɦɟɯɚɧɢɱɟɫɤɢɦ ɯɚMK Mɇ ɪɚɤɬɟɪɢɫɬɢɤɚɦ ɧɚ ɪɢɫ. 3.58 ɩɪɢU1 = const Ɋɢɫ. 3.58. ɋɯɟɦɚ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɢ Ȧ = const ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ f1 = var ɢ U1/f1 = const ǻM Mɇ Mɇ Mɇ 1 , kf ǻf1 f1 sɇ Į f1ɇ sɇ f1ɇ Įsɇ

124

ɝɞɟ Į = f1 / f1ɇ – ɱɚɫɬɨɬɚ ɜ ɨ.ɟ.; Ȧ -Ȧ Ȧ Ȧ -Ȧ Ȧ -Ȧ f Įs = 1 ɨ = ɨ ɨ = ɨ – ɚɛɫɨɥɸɬɧɨɟ ɫɤɨɥɶɠɟɧɢɟ, ɨɬɥɢf Ȧ Ȧ Ȧ Ȧ 1ɧ ɨ ɨɧ ɨ ɨɧ ɱɚɸɳɟɟɫɹ ɨɬ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɫɤɨɥɶɠɟɧɢɹ s ɬɟɦ, ɱɬɨ ɜ ɡɧɚɦɟɧɚɬɟɥɟ ɜɦɟɫɬɨ Ȧ0, ɢɡɦɟɧɹɸɳɟɣɫɹ ɩɪɢ f1 = var, ɩɨɹɜɢɥɚɫɶ Ȧ0ɇ, ɨɬ ɱɚɫɬɨɬɵ ɧɟ ɡɚɜɢɫɹɳɚɹ. Ⱥɛɫɨɥɸɬɧɨɟ ɫɤɨɥɶɠɟɧɢɟ Ds ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɜɚɬɶ ɠɟɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɬɨɤɢ ɪɨɬɨɪɧɨɣ ɰɟɩɢ ɢ ɜ ɡɚɦɤɧɭɬɵɯ ɫɢɫɬɟɦɚɯ ɩɨɡɜɨɥɢɬ ɪɟɲɚɬɶ ɧɟɤɨɬɨɪɵɟ ɡɚɞɚɱɢ. Ɋɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ. ɂɡɦɟɧɟɧɢɟ ɱɚɫɬɨɬɵ ɩɢɬɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢɜɨɞɢɬ ɧɟ ɬɨɥɶɤɨ ɤ ɢɡɦɟɧɟɧɢɸ Ȧ0, ɯ1 ɢ ɯ2, ɧɨ ɢ ɤ ɢɡɦɟɧɟɧɢɸ ɬɨɤɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Iμ. ȼɵɲɟ ɪɚɫɫɦɨɬɪɟɧɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɯμ = const. ɉɨɷɬɨɦɭ ɩɪɢ ɪɚɫɱɟɬɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ f1 ɧɟɨɛɯɨɞɢɦɨ: – ɭɱɢɬɵɜɚɬɶ ɢɡɦɟɧɟɧɢɟ ɢɧɞɭɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɯ μ; – ɢɡɦɟɧɹɬɶ ɚɦɩɥɢɬɭɞɭ ɩɢɬɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ U1, ɩɪɢɱɟɦ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ U1 ɢ f1 ɡɚɜɢɫɹɬ ɨɬ ɬɪɟɛɨɜɚɧɢɣ ɤ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ ɢ ɡɚɤɨɧɨɜ ɢɡɦɟɧɟɧɢɹ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇɋ; – ɩɪɢɦɟɧɹɬɶ Ɍ-ɨɛɪɚɡɧɭɸ ɫɯɟɦɭ ɡɚɦɟɳɟɧɢɹ ȺȾ, ɬɚɤ ɤɚɤ ɫɭɳɟɫɬɜɟɧɧɨ ɫɤɚɡɵɜɚɟɬɫɹ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɬɚɬɨɪɚ r1, ɨɫɨɛɟɧɧɨ ɩɪɢ ɦɚɥɵɯ ɱɚɫɬɨɬɚɯ. ɂɡɦɟɧɟɧɢɟ ɱɚɫɬɨɬɵ ɭɱɢɬɵɜɚɟɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ

Į =f1 / f1ɇ. ɋɢɧɯɪɨɧɧɚɹ ɫɤɨɪɨɫɬɶ Ȧ0 = ĮǜȦ0ɇ. ɂɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɡɧɚɱɟɧɢɹɦ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ ɢɡɦɟɧɹɸɬɫɹ ɜ Į ɪɚɡ – Įɯ1, Įɯc2, Įɯμ. ɗȾɋ ɪɨɬɨɪɚ ɩɪɢɧɢɦɚɟɬ ɡɧɚɱɟɧɢɟ Įȿ. r1 Įx1 Įxc2 Ɍ-ɨɛɪɚɡɧɚɹ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɫ ɭɱɟɬɨɦ ɷɬɢɯ Ic2 ɢɡɦɟɧɟɧɢɣ ɩɪɢɜɟɞɟɧɚ ɧɚ I1 ɪɢɫ. 3.59. rc2 Ɉɛɨɡɧɚɱɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɟɬɜɟɣ U1 Iμ Įxμ ĮE z1 = r1+jǜĮx1; rc2(1-s)/s

zc2 = rc2 / s+jǜĮxc2; zμ = jǜĮxμ. Ɉɬɫɸɞɚ ɪɟɡɭɥɶɬɢɪɭɸɳɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ z2μ = z2ǜzμ / (z2+zμ); zC = z1+z2μ = rC+ jǜxC.

Ɋɢɫ. 3.59. Ɍ-ɨɛɪɚɡɧɚɹ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ȺȾ ɩɪɢ f1 =var

125

Ɋɚɫɱɟɬ ɜɵɩɨɥɧɹɟɦ ɤɨɦɩɥɟɤɫɧɵɦ ɦɟɬɨɞɨɦ ɩɨ ɮɨɪɦɭɥɚɦ (3.77) I1 Ȧ

U1 ; zC

ĮE

I1 z 2μ ; Iμ

§ · Į Ȧ0ɇ ¨1 s ¸; © ¹

ĮE c ; I2 zμ

ĮE ; M z2

arctg x C /rC ;

ĳ1

Ș

3 Ic2 2 r2c /s ; Į Ȧ0ɇ

(3.77)

MȦ . 3 U1 I1 cos ĳ1

Ɋɚɫɱɟɬ ɩɨ ɩɪɢɜɟɞɟɧɧɵɦ ɮɨɪɦɭɥɚɦ ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɢɧɞɭɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɯμ = const. ȼ ɩɪɨɰɟɫɫɟ ɪɚɫɱɟɬɚ ɩɪɢ ɯμ=var ɩɨ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɦɟɬɨɞɨɦ ɢɧɬɟɪɩɨɥɹɰɢɢ ɭɬɨɱɧɹɟɬɫɹ ɡɧɚɱɟɧɢɟ ɬɨɤɚ Iμ ɢ ɦɟɬɨɞɨɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɩɪɢɛɥɢɠɟɧɢɣ ɞɨɜɨɞɹɬ ɪɚɫɱɟɬ ɞɨ ɡɚɞɚɜɚɟɦɨɣ ɬɨɱɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɬɨɤɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. Ɋɚɫɱɟɬ ɷɬɨɣ ɧɟɫɥɨɠɧɨɣ ɡɚɞɚɱɢ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧ ɜ ɩɪɨɝɪɚɦɦɚɯ Matlab, Mathcad. Ⱦɥɹ ɩɪɢɦɟɪɚ ɧɚ ɪɢɫ. 3.49 ɩɪɢɜɟɞɟɧɵ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ, ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɞɚɧɧɨɣ ɦɟɬɨɞɢɤɟ ɜ ɩɪɨɝɪɚɦɦɟ «harad», ɞɚɸɳɢɟ ɞɨɫɬɚɬɨɱɧɭɸ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɬɨɱɧɨɫɬɶ (ɫɦ. ɩ. 3.7). ɉɪɢɛɥɢɠɟɧɧɨ ɦɨɠɧɨ ɜɵɩɨɥɧɢɬɶ ɪɚɫɱɟɬ ɩɨ ɮɨɪɦɭɥɚɦ Ʉɥɨɫɫɚ, ɤɨɬɨɪɵɟ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɢɡ Ƚ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ȺȾ, ɟɫɥɢ ɭɱɟɫɬɶ ɢɡɦɟɧɟɧɢɟ ɱɚɫɬɨɬɵ Į = f1 / f1ɇ. Ɉɞɧɚɤɨ ɫɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ ɨɧɢ ɧɟ ɭɱɢɬɵɜɚɸɬ ɜɥɢɹɧɢɟ ɧɚɝɪɭɡɤɢ ɧɚ ɩɨɬɨɤ ɦɚɲɢɧɵ, ɩɪɢɧɢɦɚɸɬ ɩɨɫɬɨɹɧɧɵɦ ɯμ = const. Ⱦɥɹ ɩɪɢɛɥɢɠɟɧɧɵɯ ɪɚɫɱɟɬɨɜ ɢɫɩɨɥɶɡɭɸɬ ɭɩɪɨɳɟɧɧɭɸ ɮɨɪɦɭɥɭ Ʉɥɨɫɫɚ, ɜ ɤɨɬɨɪɨɣ r1 = 0. Ɇ

2 MK ;. MK Įs ĮsK ĮsK Įs sK Įs

3 U12 2 Ȧ0 (r1 r r12 xK2 ) r

r2c r12 xK2

#

r2c ; Į xK

3 U12 ; 2 Į2 Ȧ0H xK

ĮsK

(3.78)

r2c ; xK

Į Ȧ0ɇ Ȧ

, Ȧ Ȧ0 Įs Ȧ0ɇ Į Ȧ0ɇ (1 s) Ȧ0ɇ (Į Įs). Ȧ0ɇ Ʉɚɤ ɜɢɞɧɨ ɢɡ ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɮɨɪɦɭɥ 3.78, ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɷɬɨɝɨ ɦɟɬɨɞɚ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɨɫɬɨɹɧɫɬɜɨ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɆɄ = const ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɩɪɢ ɡɚɤɨɧɟ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɧɚɩɪɹɠɟɧɢɹ U1 / f1 = const. ɂɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɯμ ɜ ɮɨɪɦɭɥɚɯ ɨɬɫɭɬɫɬɜɭɟɬ, ɢɡ ɱɟɝɨ ɫɥɟɞɭɟɬ ɩɪɢɛɥɢɠɟɧɧɵɣ ɯɚɪɚɤɬɟɪ ɪɚɫɱɟɬɚ. Ⱦɥɹ ɭɩɪɨɳɟɧɧɵɯ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɯ ɪɚɫɱɟɬɨɜ ɩɪɢ ɡɚɤɨɧɟ ɭɩɪɚɜɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɟɦ U1 / f1 = const ɜɨɡɦɨɠɧɨ ɩɨɫɬɪɨɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ f1 = var ɦɟɬɨɞɨɦ ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɩɟɪɟɧɨɫɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. ɗɬɢɦ ɦɟɬɨɞɨɦ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɨ ɨɩɪɟɞɟɥɢɬɶ ɧɟɨɛɯɨɞɢɦɭɸ ɱɚɫɬɨɬɭ ɩɢɬɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ f1ɁȺȾ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɆɁȺȾ, ȦɁȺȾ. Ɉɩɪɟɞɟɥɢɜ ɩɪɢ ɆɁȺȾ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɨɬɤɥɨɧɟɧɢɟ ɫɤɨɪɨɫɬɢ ɨɬ ɫɢɧɯɪɨɧɧɨɣ ǻȦȿɋɌ ɢ ɫɱɢɬɚɹ, ɱɬɨ ɧɚɤɥɨɧ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ ɩɪɢ f1=var, ɪɚɫɫɱɢɬɵɜɚɸɬ

Ȧ0 = ȦɁȺȾ + ǻȦȿɋɌ , Į = Ȧ0 / Ȧ0ɇ = f1ɁȺȾ / f1ɇ. ɉɪɢɛɥɢɠɟɧɧɵɟ ɦɟɬɨɞɵ ɬɪɟɛɭɸɬ ɭɬɨɱɧɟɧɢɹ ɩɪɢ ɪɚɫɱɟɬɟ ɬɨɤɨɜ ɢ ɦɨɦɟɧɬɚ, ɨɫɨɛɟɧɧɨ ɞɥɹ ɦɚɥɵɯ ɱɚɫɬɨɬ. 126

3.5.7. ȿɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ

Ⱦɥɹ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɫ ɮɚɡɧɵɦ ɪɨɬɨɪɨɦ (ȺȾɎɊ) ɨɩɪɟɞɟɥɹɸɳɢɦ ɞɥɹ ɬɟɯɧɨɥɨɝɢɢ ɹɜɥɹɟɬɫɹ ɪɚɛɨɱɢɣ ɭɱɚɫɬɨɤ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ s < sK. Ɏɨɪɦɢɪɨɜɚɧɢɟ ɠɟɥɚɟɦɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɡɚ ɫɱɟɬ ɢɡɦɟɧɟɧɢɹ ɪɚɛɨɱɟɝɨ ɭɱɚɫɬɤɚ ɩɭɬɟɦ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɬɚɬɨɪɟ U1 = var, ɜɜɟɞɟɧɢɹ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɢ ɫɬɚɬɨɪɚ R1 = var ɢɥɢ ɪɨɬɨɪɚ R2 = var. Ⱦɥɹ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ (ȺȾɄɁ) ɞɥɹ ɬɟɯɧɨɥɨɝɢɢ ɜɚɠɧɵ ɩɪɨɛɥɟɦɵ ɩɪɹɦɨɝɨ ɩɭɫɤɚ, ɪɚɛɨɬɚ ɧɚ ɭɫɬɚɧɨɜɢɜɲɟɣɫɹ ɫɤɨɪɨɫɬɢ ɢ ɬɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ, ɩɨɡɜɨɥɹɸɳɢɟ ɢɫɩɨɥɶɡɨɜɚɬɶ ɟɝɨ ɨɫɧɨɜɧɵɟ ɩɪɟɢɦɭɳɟɫɬɜɚ. ɍɱɚɫɬɨɤ s > sK ɢɦɟɟɬ ɞɥɹ ȺȾɄɁ ɜɚɠɧɨɟ ɡɧɚɱɟɧɢɟ, ɨɩɪɟɞɟɥɹɹ ɩɭɫɤɨɜɵɟ ɢ ɬɨɪɦɨɡɧɵɟ ɜɨɡɦɨɠɧɨɫɬɢ. ɉɪɢ ɪɚɛɨɬɟ ɧɚ ɷɬɨɦ ɭɱɚɫɬɤɟ ɢɡ-ɡɚ ɧɚɫɵɳɟɧɢɹ ɡɭɛɰɨɜ ɫɧɢɠɚɟɬɫɹ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɫɫɟɹɧɢɹ ɪɨɬɨɪɚ ɯc2, ɡɚ ɫɱɟɬ ɜɵɬɟɫɧɟɧɢɹ ɬɨɤɚ ɪɨɬɨɪɚ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɱɚɫɬɨɬɵ ɪɚɫɬɟɬ ɟɝɨ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ rc2. Ⱦɥɹ ɭɫɩɟɲɧɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɞɜɢɝɚɬɟɥɹ ɜɫɟɝɞɚ ɠɟɥɚɬɟɥɶɧɨ ɭɜɟɥɢɱɟɧɢɟ ɩɭɫɤɨɜɨɝɨ ɦɨɦɟɧɬɚ Ɇɉ ɢ ɫɧɢɠɟɧɢɟ ɩɭɫɤɨɜɨɝɨ ɬɨɤɚ Iɉ. ɍɜɟɥɢɱɟɧɢɸ ɷɬɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɫɩɨɫɨɛɫɬɜɭɟɬ ɢɡɦɟɧɟɧɢɟ ɮɨɪɦɵ ɩɚɡɚ, ɩɪɢ ɪɚɫɬɟɬ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ, ɪɚɫɬɟɬ ɚɤɬɢɜɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɬɨɤɚ ɪɨɬɨɪɚ, ɪɚɫɬɟɬ ɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ. ɇɚ ɪɢɫ. 3.60 ɩɪɢɜɟɞɟɧɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ. ɏɚɪɚɤɬɟɪɢɫɬɢɤɚ 1 ɩɨɫɬɪɨɟɧɚ ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɧɨɪɦɚɥɶɧɨɝɨ ɢɫɩɨɥɧɟɧɢɹ. ɍ ɞɜɢɝɚɬɟɥɟɣ ɫ ɝɥɭɛɨɤɢɦ ɩɚɡɨɦ ɭɜɟɥɢɱɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɡɚ ɫɱɟɬ ɜɵɬɟɫɧɟɧɢɹ ɬɨɤɚ ɪɨɬɨɪɚ ɩɪɢɜɨɞɢɬ ɤ Ȧ

~

Ȧɇ Ȧɇ2 1

3

Ɇ 2 Ɇɉ2 Ɇɇ

4 Ɇɉ4

Ɋɢɫ. 3.60. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾɄɁ

127

Ɇ

ɭɜɟɥɢɱɟɧɢɸ ɩɭɫɤɨɜɨɝɨ ɦɨɦɟɧɬɚ ɞɨ ɡɧɚɱɟɧɢɹ Ɇɉ2 – ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ 2. Ɍɚɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɨɛɥɚɞɚɟɬ ɞɜɢɝɚɬɟɥɶ ɫ ɩɨɜɵɲɟɧɧɵɦ ɫɤɨɥɶɠɟɧɢɟɦ. ɇɨ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɦɨɦɟɧɬɟ ɭɦɟɧɶɲɚɟɬɫɹ ɞɨ ɡɧɚɱɟɧɢɹ Ȧɇ2 ɢ ɫɧɢɠɚɟɬɫɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɦɟɯɚɧɢɡɦɚ. ɏɨɬɹ ɩɭɫɤɨɜɵɟ ɦɨɦɟɧɬ ɢ ɬɨɤ ɫɧɢɡɢɥɢɫɶ, ɧɨ ɜɨɡɪɚɫɬɚɸɬ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɰɟɩɢ ɪɨɬɨɪɚ. Ɉɫɨɛɚɹ ɤɨɧɫɬɪɭɤɰɢɹ ɩɚɡɨɜ, ɨɛɟɫɩɟɱɢɜɚɸɳɚɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɷɮɮɟɤɬɚ ɜɵɬɟɫɧɟɧɢɹ ɬɨɤɚ ɪɨɬɨɪɚ ɩɪɢ ɪɨɫɬɟ ɟɝɨ ɱɚɫɬɨɬɵ, ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɬɚɤɨɣ ɠɟ ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ Ɇɉ1 ɩɪɢ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɢɡɦɟɧɧɨɣ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ. ɇɚ ɪɢɫ. 3.60 ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ 3 ɨɛɥɚɞɚɟɬ ɞɜɢɝɚɬɟɥɶ ɫ ɝɥɭɛɨɤɢɦ ɩɚɡɨɦ, ɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ 4 – ɞɜɢɝɚɬɟɥɶ ɫ ɞɜɨɣɧɨɣ ɛɟɥɢɱɶɟɣ ɤɥɟɬɤɨɣ. ɇɚ ɪɚɛɨɱɢɯ ɭɱɚɫɬɤɚɯ r2 ɧɟɜɟɥɢɤɨ, ɠɟɫɬɤɨɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜɵɫɨɤɚɹ, ɩɪɢɥɢɱɧɵɣ ɄɉȾ, ɩɨɤɚɡɚɬɟɥɢ ɛɥɢɡɤɢ ɤ ɩɨɤɚɡɚɬɟɥɹɦ ɞɜɢɝɚɬɟɥɹ ɧɨɪɦɚɥɶɧɨɝɨ ɢɫɩɨɥɧɟɧɢɹ. ɉɨ ɦɟɪɟ ɪɨɫɬɚ ɫɤɨɥɶɠɟɧɢɹ s ɪɚɫɬɟɬ r2, ɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ Ɇɉ, ɫɧɢɠɚɟɬɫɹ ɩɭɫɤɨɜɨɣ ɬɨɤ Iɉ. ȼ ɤɚɬɚɥɨɝɚɯ ɩɪɢɜɨɞɹɬɫɹ ɡɧɚɱɟɧɢɹ ɩɭɫɤɨɜɨɝɨ ɬɨɤɚ Iɉ / I1ɇ ɢ ɩɭɫɤɨɜɨɝɨ ɦɨɦɟɧɬɚ Ɇɉ / Ɇɇ ɞɜɢɝɚɬɟɥɹ. Ⱥɧɚɥɢɬɢɱɟɫɤɢɣ ɪɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ȺȾɄɁ ɫɥɨɠɟɧ. Ɉɧɢ ɧɟ ɨɩɢɫɵɜɚɸɬɫɹ ɮɨɪɦɭɥɚɦɢ Ʉɥɨɫɫɚ, ɢ ɩɪɢɯɨɞɢɬɫɹ ɩɨɥɶɡɨɜɚɬɶɫɹ ɤɚɬɚɥɨɠɧɵɦɢ ɤɪɢɜɵɦɢ Ɇ(s), I1(s), cos ĳ1(s), ɤɨɬɨɪɵɟ ɩɪɢɜɨɞɹɬɫɹ ɞɚɥɟɤɨ ɧɟ ɞɥɹ ɤɚɠɞɨɝɨ ɞɜɢɝɚɬɟɥɹ. ɉɪɢɛɥɢɠɟɧɧɵɣ ɪɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ȺȾɄɁ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ. ɇɚ ɫɨɜɪɟɦɟɧɧɨɦ ɷɬɚɩɟ ɪɚɡɜɢɬɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɛɨɥɶɲɨɟ ɜɧɢɦɚɧɢɟ ɨɤɚɡɵɜɚɟɬɫɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚɦ ɫ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹɦɢ ɱɚɫɬɨɬɵ. Ɂɚɞɚɱɚ ɪɚɫɱɟɬɚ ɫɬɚɬɢɤɢ ɢ ɞɢɧɚɦɢɤɢ ɬɚɤɢɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɫɬɚɧɨɜɢɬɫɹ ɚɤɬɭɚɥɶɧɨɣ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɪɚɫɩɨɥɚɝɚɸɬ ɥɢɲɶ ɤɚɬɚɥɨɠɧɵɦɢ ɞɚɧɧɵɦɢ Ɋɇ, nɇ, I1ɇ, Șɇ, cos ĳ1ɇ (ɫɦ. ɩ. 3.5). Ʉɚɬɚɥɨɠɧɵɟ ɤɪɢɜɵɟ Ɇ(s), I1(s), cos ĳ1(s) ɨɛɵɱɧɨ ɧɟ ɩɪɢɜɨɞɹɬɫɹ. Ɋɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɨ ɦɟɬɨɞɢɤɟ, ɢɡɥɨɠɟɧɧɨɣ ɜ ɪɚɡɞɟɥɚɯ 3.5.2. ɢ 3.5.3, ɩɪɢɜɨɞɢɬ ɤ ɫɭɳɟɫɬɜɟɧɧɵɦ ɩɨɝɪɟɲɧɨɫɬɹɦ, ɨɫɨɛɟɧɧɨ ɩɪɢ s > sɄ. Ɋɚɛɨɱɢɣ ɭɱɚɫɬɨɤ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɦɨɠɟɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧ ɩɪɢɛɥɢɠɟɧɧɨ ɩɨ ɞɜɭɦ ɬɨɱɤɚɦ: Ɇ = 0, Ȧ = Ȧ0ɇ ɢ Ɇ = Ɇɇ, Ȧ = Ȧɇ. ɉɨɝɪɟɲɧɨɫɬɶ ɪɚɫɱɟɬɚ ɪɚɫɬɟɬ ɩɨ ɦɟɪɟ ɭɜɟɥɢɱɟɧɢɹ ɦɨɦɟɧɬɚ ɩɪɢ Ɇ > Ɇɇ, ɧɨ ɞɥɹ ɤɚɱɟɫɬɜɟɧɧɨɝɨ ɚɧɚɥɢɡɚ ɫɬɚɬɢɱɟɫɤɢɯ ɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɪɟɝɭɥɢɪɭɟɦɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɬɚɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɚ. ɉɪɢ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɱɚɫɬɨɬɵ ɨɧɚ ɩɟɪɟɧɨɫɢɬɫɹ ɩɚɪɚɥɥɟɥɶɧɨ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɰɟɩɟɣ ɦɚɲɢɧɵ. ɉɨɫɥɟɞɧɢɟ ɥɢɲɶ ɢɡɪɟɞɤɚ ɩɪɢɜɨɞɹɬɫɹ ɜ ɫɩɪɚɜɨɱɧɢɤɚɯ ɞɚɥɟɤɨ ɧɟ ɞɥɹ ɜɫɟɯ ɞɜɢɝɚɬɟɥɟɣ. Ɉɫɨɛɟɧɧɨɫɬɶɸ ɪɚɫɱɟɬɚ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɞɥɹ ȺȾɄɁ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ȺȾɎɊ ɹɜɥɹɟɬɫɹ ɧɚɥɢɱɢɟ ɷɮɮɟɤɬɚ ɜɵɬɟɫɧɟɧɢɹ ɬɨɤɚ ɪɨɬɨɪɚ ɢ ɨɬɫɭɬɫɬɜɢɟ ɧɚɩɪɹɠɟɧɢɹ ȿ2Ɉ. Ɋɚɫɱɟɬ ɜɵɩɨɥɧɢɦ ɛɟɡ ɭɱɟɬɚ ɜɵɬɟɫɧɟɧɢɹ ɬɨɤɚ ɞɥɹ ɧɨɦɢɧɚɥɶɧɨɣ ɬɨɱɤɢ, ɨɛɥɚɞɚɸɳɟɣ ɞɨɫɬɚɬɨɱɧɵɦɢ ɤɚɬɚɥɨɠɧɵɦɢ ɞɚɧɧɵɦɢ. Ⱦɨɩɭɳɟɧɢɹ, ɩɪɢɧɢɦɚɟɦɵɟ ɩɪɢ ɪɚɫɱɟɬɟ ɫɨɩɪɨɬɢɜɥɟɧɢɣ, ɫ ɭɱɟɬɨɦ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜ ɪɚɡɞɟɥɟ 3.5.2: – ɦɨɦɟɧɬ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɞɜɢɝɚɬɟɥɹ ǻɆɏ = 0,05ǜɆɇ; – ɬɨɤ ɪɨɬɨɪɚ ɫɨɜɩɚɞɚɟɬ ɩɨ ɮɚɡɟ ɫ ɗȾɋ ɪɨɬɨɪɚ; ɉɪɢɜɟɞɟɧɧɵɣ ɧɨɦɢɧɚɥɶɧɵɣ ɬɨɤ ɪɨɬɨɪɚ (ɜ ɧɨɦɢɧɚɥɶɧɨɣ ɬɨɱɤɟ ɫɤɨɥɶɠɟɧɢɟ ɦɚɥɨ, ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɫɫɟɹɧɢɹ ɪɨɬɨɪɚ ɬɚɤɠɟ ɦɚɥɨ ɢ ɦɨɠɧɨ ɩɪɢɧɹɬɶ cos·ĳ2 = 1) ɪɚɜɟɧ ɚɤɬɢɜɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɬɨɤɚ ɫɬɚɬɨɪɚ Ic2 H I1H cos ĳ 1H . (3.79)

128

ɉɪɢɜɟɞɟɧɧɨɟ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ ɛɟɡ ɭɱɟɬɚ ɜɵɬɟɫɧɟɧɢɹ ɬɨɤɚ ɪɨɬɨɪɚ r2c

1,05 Pɇ 10 3 sɇ . 3 Ic2ɇ2 (1 sɇ )

(3.80)

Ⱥɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɬɚɬɨɪɚ r1 ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɱɟɪɟɡ ɆɄ ɢɥɢ ɩɪɢɧɹɬɶ r1 = rc2 (ɫɦ. ɩ.3.5.3). ɂɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɚɫɫɟɹɧɢɹ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ r2c xK x1 xc2 1 a 2 sK2 . 2 2 sK ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ xμ

Ic2ɇ rc ( 2 )2 xc22 . Iμɇ sɇ

ɉɪɢɜɟɞɟɧɧɨɟ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ ɫ ɭɱɟɬɨɦ ɜɵɬɟɫɧɟɧɢɹ ɬɨɤɚ ɩɪɢɛɥɢɠɟɧɧɨ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɱɟɪɟɡ ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ Ɇɉ ɢ ɩɭɫɤɨɜɨɣ ɬɨɤ Iɉ: Mɉ Ȧ0ɇ c r2ɉ . 3 Iɉ2 ɉɨɥɭɱɟɧɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɥɟɞɭɟɬ ɩɪɨɜɟɪɢɬɶ, ɪɚɫɫɱɢɬɚɜ ɬɨɤɢ ɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɜ ɧɨɦɢɧɚɥɶɧɨɣ ɬɨɱɤɟ ɞɥɹ Ɍ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ɩɨ ɮɨɪɦɭɥɚɦ (3.67). ɉɨɝɪɟɲɧɨɫɬɶ ɪɚɫɱɟɬɚ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɩɨ ɩɪɢɜɟɞɟɧɧɵɦ ɜɵɲɟ ɫɨɨɬɧɨɲɟɧɢɹɦ ɫɨɫɬɚɜɥɹɟɬ 10…20% ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɚɫɩɨɪɬɧɵɦɢ ɞɚɧɧɵɦɢ. 3.5.8. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ

Ⱦɨ ɫɢɯ ɩɨɪ ɪɚɫɫɦɚɬɪɢɜɚɥɢɫɶ ɪɟɠɢɦɵ ɪɚɛɨɬɵ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɪɚɛɨɬɟ ɨɬ ɢɫɬɨɱɧɢɤɚ ɗȾɋ (U1 = const). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪɟ U1 ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɝɪɭɡɤɢ, ɩɨɬɨɤ ɜ ɦɚɲɢɧɟ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ (ɢɡɦɟɧɹɟɬɫɹ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɫɬɚɬɨɪɚ), ɱɚɫɬɨɬɚ ɩɢɬɚɸɳɟɣ ɫɟɬɢ ɨɩɪɟɞɟɥɹɟɬ ɫɤɨɪɨɫɬɶ ɩɨɥɹ ɞɜɢɝɚɬɟɥɹ. ȼ ɫɜɹɡɢ ɫ ɪɚɡɜɢɬɢɟɦ ɪɟɝɭɥɢɪɭɟɦɨɝɨ U =const 1 ɚɫɢɧɯɪɨɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɱɚɫɬɨɬ~ ɧɵɦ ɭɩɪɚɜɥɟɧɢɟɦ ɢɧɬɟɪɟɫ ɩɪɟɞɫɬɚɜɥɹɟɬ f1=const ɢɡɭɱɟɧɢɟ ɫɜɨɣɫɬɜ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɂɌ. Ɂɧɚɱɢɬɟɥɶɧɚɹ ɱɚɫɬɶ ɩɪɟUɁɌ ɂɌ ɨɛɪɚɡɨɜɚɬɟɥɟɣ ɱɚɫɬɨɬɵ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɚɦɢ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ, ɬ.ɟ. ɮɨɪɦɢɪɭɸɬɫɹ UɁɑ ɬɨɤɢ, ɧɟ ɡɚɜɢɫɹɳɢɟ ɨɬ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɢ I1=f(UɁɌ)=const ɩɚɪɚɦɟɬɪɨɜ ɞɜɢɝɚɬɟɥɹ, ɚ ɨɩɪɟɞɟɥɹɸɳɢɟɫɹ ɬɨɥɶɤɨ ɧɚɩɪɹɠɟɧɢɟɦ ɡɚɞɚɧɢɹ ɬɨɤɚ UɁɌ. f1=f(UɁɑ)=const ɑɚɫɬɨɬɚ ɩɢɬɚɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɚɩɪɹɠɟM ɧɢɟɦ ɡɚɞɚɧɢɹ ɱɚɫɬɨɬɵ UɁɑ. ȼ ɫɢɫɬɟɦɟ ɂɌ – ȺȾ (ɪɢɫ. 3.61) ɫɬɚɬɨɪ ɞɜɢɝɚɬɟɥɹ ɩɨɥɭɱɚɟɬ ɩɢɬɚɧɢɟ ɨɬ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɱɚɫɬɨɬɵ ɫ ɝɥɭɛɨɤɨɣ ɜɧɭɬɪɟɧɧɟɣ Ɋɢɫ. 3.61. ɋɢɫɬɟɦɚ ɂɌ – ȺȾ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɨɛɪɚɬɧɨɣ ɫɜɹɡɶɸ ɩɨ ɬɨɤɭ 129

Įx1

r1

Ic2

I1=const U1=var f1=var

ĮE

Įxc2

Įxμ

Iμ rc2/s

Ɋɢɫ. 3.62. ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ

ɫɬɚɬɨɪɚ, ɩɨɞɞɟɪɠɢɜɚɸɳɟɣ ɩɨɫɬɨɹɧɧɨɣ ɚɦɩɥɢɬɭɞɭ ɬɨɤɚ ɫɬɚɬɨɪɚ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ ɡɚ ɫɱɟɬ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɬɚɬɨɪɟ U1. ɉɪɢ ɬɚɤɨɦ ɩɢɬɚɧɢɢ ɢɫɤɥɸɱɚɟɬɫɹ ɜɥɢɹɧɢɟ ɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɬɚɬɨɪɚ ɧɚ ɜɢɞ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. ɇɚ ɪɢɫ. 3.62 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɂɌ, ɢɡ ɤɨɬɨɪɨɣ ɜɢɞɧɨ, ɱɬɨ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɬɨɤɚ ɫɬɚɬɨɪɚ I1 ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɫɬɚɬɨɪɚ r1 ɢ Įɯ1 ɩɨɫɬɨɹɧɧɨ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɨɤɚ ɪɨɬɨɪɚ Ic2, ɤɨɬɨɪɵɣ ɢɡɦɟɧɹɟɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɝɪɭɡɤɢ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ.

ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɢɡɦɟɧɟɧɢɟ ɬɨɤɚ ɪɨɬɨɪɚ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɬɨɤɚ ɫɬɚɬɨɪɚ ɧɟɢɡɛɟɠɧɨ ɩɪɢɜɨɞɢɬ ɤ ɢɡɦɟɧɟɧɢɸ ɬɨɤɚ -E1 I1 ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Iμ. ɇɚ ɜɟɤɬɨɪɧɨɣ ɞɢɚɝɪɚɦɦɟ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 3.63) ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɧɚɝɪɭɡɤɢ ɬɨɤ ɫɬɚIc2 ɬɨɪɚ I1 ɪɚɜɟɧ ɬɨɤɭ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Iμ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɝɪɭɡɤɢ – ɩɟɪɟɯɨɞ ɨɬ Ic2 Iμ ɫɩɥɨɲɧɵɯ ɜɟɤɬɨɪɨɜ ɤ ɩɭɧɤɬɢɪɧɵɦ – ɬɨɤ ɪɨɬɨɪɚ Ic2 ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɩɨ ɚɦɩɥɢɬɭɞɟ ɢ ɫɞɜɢɝɚɟɬɫɹ ɩɨ ɮɚɡɟ ɨɬɧɨɫɢɬɟɥɶɧɨ Ec2 ɗȾɋ ȿ. ȼɟɤɬɨɪ ɬɨɤɚ ɫɬɚɬɨɪɚ ɫɨɜɟɪɲɚɟɬ ɩɨɜɨɪɨɬ ɫ ɩɨɫɬɨɹɧɧɨɣ ɚɦɩɥɢɬɭɞɨɣ. Ɍɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Iμ ɩɪɢ ɷɬɨɦ Ɋɢɫ. 3.63. ȼɟɤɬɨɪɧɚɹ ɭɦɟɧɶɲɚɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɨ, ɚ ɫɥɟɞɨɜɚɞɢɚɝɪɚɦɦɚ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɬɟɥɶɧɨ ɭɦɟɧɶɲɚɟɬɫɹ ɢ ɩɨɬɨɤ ɦɚɲɢɧɵ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ Ɏ. ȼ ɥɢɬɟɪɚɬɭɪɟ ɷɬɨɬ ɷɮɮɟɤɬ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɪɟɚɤɰɢɟɣ ɹɤɨɪɹ (ɩɨ ɚɧɚɥɨɝɢɢ ɫ ɪɟɚɤɰɢɟɣ ɹɤɨɪɹ Ⱦɇȼ). Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɂɌ – ȺȾ. ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɫɢɫɬɟɦɵ ɂɌ – ȺȾ (ɪɢɫ. 3.62) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɜɢɝɚɬɟɥɶ ɜ ɡɚɬɨɪɦɨɠɟɧɧɨɦ ɪɟɠɢɦɟ ɩɪɢ Ȧ = 0 ɢ ɱɚɫɬɨɬɟ f1 = f1ɇ. ɂɡɦɟɧɟɧɢɟ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɭɱɢɬɵɜɚɟɬɫɹ ɫɤɨɥɶɠɟɧɢɟɦ s ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɱɚɫɬɨɬɨɣ Į. Ɍɚɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɩɨɡɜɨɥɹɟɬ ɪɚɫɫɱɢɬɚɬɶ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɱɟɪɟɡ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɭɸ ɦɨɳɧɨɫɬɶ ɊɗɆ, ɩɟɪɟɞɚɜɚɟɦɭɸ ɢɡ ɫɬɚɬɨɪɚ ɜ ɪɨɬɨɪ, ɢ ɫɢɧɯɪɨɧɧɭɸ ɫɤɨɪɨɫɬɶ Ȧ0.

130

ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɩɨɥɭɱɢɦ ɩɨ ɮɨɪɦɭɥɟ 3 Ic2 2 r2c /s Į Ȧ0ɇ

PɗɆ Ȧ0

M

3 Ic2 2 r2c /Įs . Ȧ0ɇ

(3.81)

ɉɪɢ I1 = const ɩɨ ɡɚɤɨɧɭ ɪɚɡɞɟɥɟɧɢɹ ɬɨɤɨɜ ɜ ɩɚɪɚɥɥɟɥɶɧɵɯ ɰɟɩɹɯ ɧɚɣɞɟɦ ɬɨɤ ɪɨɬɨɪɚ I1 xμ

Ic2

rc /Ds xc 2

2

2

xμ

(3.82)

2

ɢ ɩɨɞɫɬɚɜɢɦ ɜ ɮɨɪɦɭɥɭ ɦɨɦɟɧɬɚ 3 I12 x μ2 r2c /Ds

M

2

2

.

(3.83)

Ȧ0ɇ [ r2c /Ds xc2 x μ ]

ɉɪɢ Įs ĺ 0 ɢ ɩɪɢ Įs ĺ f ɦɨɦɟɧɬ ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ Ɇ ĺ 0. Ⱦɚɧɧɚɹ ɮɭɧɤɰɢɹ ɢɦɟɟɬ ɷɤɫɬɪɟɦɭɦ, ɩɨɷɬɨɦɭ ɬɪɟɛɭɟɬɫɹ ɜɡɹɬɶ ɩɪɨɢɡɜɨɞɧɭɸ dM / d(Įs) ɢ ɩɪɢɪɚɜɧɹɬɶ ɟɟ ɧɭɥɸ. ɇɟ ɩɪɢɜɨɞɹ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɜɵɜɨɞɨɜ (ɫɬɭɞɟɧɬ ɦɨɠɟɬ ɜɵɩɨɥɧɢɬɶ ɢɯ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ – ɩɨ ɚɧɚɥɨɝɢɢ ɫ ɜɵɜɨɞɨɦ ɜ ɩ. 3.5.2), ɩɪɢɜɟɞɟɦ ɮɨɪɦɭɥɭ ɤɪɢɬɢɱɟɫɤɨɝɨ ɫɤɨɥɶɠɟɧɢɹ ĮsɄɌ

r

r2c , xc2 xμ

(3.84)

ɩɪɢ ɤɨɬɨɪɨɦ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɚɥɶɧɨɝɨ (ɤɪɢɬɢɱɟɫɤɨɝɨ) ɡɧɚɱɟɧɢɹ: MɄɌ

3 I12 xμ2 2 Ȧ0ɇ (xc2 xμ )

.

(3.85)

ɉɪɢɜɟɞɟɦ ɜɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤ ɮɨɪɦɭɥɟ Ʉɥɨɫɫɚ, ɪɚɡɞɟɥɢɜ (3.83) ɧɚ (3.85). M

2 MɄɌ . Įs ĮsɄɌ ĮsɄɌ Įs

(3.86)

ɉɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɧɚɩɨɦɢɧɚɟɬ ɭɩɪɨɳɟɧɧɭɸ ɮɨɪɦɭɥɭ Ʉɥɨɫɫɚ ɫ ɬɨɣ ɥɢɲɶ ɪɚɡɧɢɰɟɣ, ɱɬɨ ɧɟ ɛɵɥɨ ɫɞɟɥɚɧɨ ɧɢɤɚɤɢɯ ɞɨɩɭɳɟɧɢɣ (ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢɧɢɦɚɥɢ r1 = 0). ɉɨ (3.86) ɫ ɭɱɟɬɨɦ (3.84) ɢ (3.85) ɫɬɪɨɢɬɫɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ. ɋɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ Ȧ ɭɱɢɬɵɜɚɟɬɫɹ ɚɛɫɨɥɸɬɧɵɦ ɫɤɨɥɶɠɟɧɢɟɦ Į Ȧ0ɇ Ȧ Įs , ɨɬɤɭɞɚ Ȧ0ɇ Ȧ

Ȧ0 Įs Ȧ0ɇ

Į Ȧ0ɇ 1 s

Ȧ0ɇ Į Įs .

ɇɚ ɪɢɫ. 3.64 ɩɨɫɬɪɨɟɧɚ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ, ɩɪɨɯɨɞɹɳɚɹ ɱɟɪɟɡ ɬɨɱɤɢ Ȧ = Ȧ0ɇ, Ɇ = 0 ɢ Ȧ = ȦɄɌ, Ɇ = ɆɄɌ. 131

Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɩɪɢ ɚɛɫɨɥɸɬɧɨɦ ɫɤɨɥɶɠɟɧɢɢ Įs ɜ ɜɵɪɚɠɟɧɢɹɯ ɞɥɹ ɆɄɌ ɢ ĮsɄɌ ɢɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟf1ɇ ɧɢɹ ɯc2 ɢ ɯμ ɫɬɚɧɨɜɹɬɫɹ ɩɨɫɬɨɹɧɧɵɦɢ, ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɱɚɫɬɨɬɵ (ɨɧɢ ɨɩɪɟɞɟɥɟɧɵ ȦɄɌ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ f1ɇ ɢ ɧɨɦɢf1 ĮsɄɌ, r2c r2c > ĮsɄɌ r , sK r xc2 xμ r12 xK2 Ȧ Ȧ0ɇ

ɬɚɤ ɤɚɤ ɯɄ << ɯμ. Ʉɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɂɌ ɆɄɌ < ɆɄ ɢɡ-ɡɚ ɯμ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɜ ɡɧɚɦɟɧɚɬɟɥɟ 3 I12 xμ2 3 U12 . ! MɄɌ MK 2 Ȧ0ɇ (xc2 xμ ) 2 Ȧ0 r1 r r12 xɄ2 Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɂɌ ɨɛɥɚɞɚɟɬ ɦɟɧɶɲɢɦ ɤɪɢɬɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ ɆɄɌ < ɆɄ, ɧɨ ɛɨɥɶɲɟɣ ɤɪɢɬɢɱɟɫɤɨɣ ɫɤɨɪɨɫɬɶɸ ȦɄɌ > ȦɄ, ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɨɧɚ ɞɨɥɠɧɚ ɛɵɬɶ ɡɧɚɱɢɬɟɥɶɧɨ ɠɟɫɬɱɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɂɇ. ɇɚ ɜɢɞ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɂɌ ɫɭɳɟɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɨɤɚɡɵɜɚɟɬ ɜɟɥɢɱɢɧɚ ɬɨɤɚ ɫɬɚɬɨɪɚ I1, ɬɚɤ ɤɚɤ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɆɄ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɤɜɚɞɪɚɬɭ ɬɨɤɚ I1, ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ĮsɄɌ. ɉɪɢ ɜɜɟɞɟɧɢɢ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɶ ɪɨɬɨɪɚ R2ȾɈȻ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɟɦɭ ɢɡɦɟɧɹɟɬɫɹ ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ ĮsɄɌ, ɢɡɦɟɧɹɹ ɠɟɫɬɤɨɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɧɟɢɡɦɟɧɧɨɣ ɜɟɥɢɱɢɧɟ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɆɄɌ. Ɋɚɫɫɦɨɬɪɟɧɧɵɟ ɜɵɲɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɟ ɭɱɢɬɵɜɚɥɢ ɢɡɦɟɧɟɧɢɟ ɯμ, ɩɪɢɧɢɦɚɥɨɫɶ ɯμ = const.

132

Ɉɬɧɨɫɢɬɟɥɶɧɨ ɦɚɥɨɟ ɡɧɚɱɟɧɢɟ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɆɄɌ ɩɨɛɭɠɞɚɟɬ ɭɜɟɥɢɱɢɜɚɬɶ Ȧ0 ɬɨɤ ɫɬɚɬɨɪɚ ɞɨ 2…4ǜI1ɇ, ɱɬɨ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɂɇ ȦɄɌ ɩɪɢɜɨɞɢɬ ɤ ɧɚɫɵɳɟɧɢɸ ɞɜɢɝɚɬɟɥɹ ɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɭɱɟɬɚ ɢɡɦɟɧɟɧɢɹ ɢɧɞɭɤɬɢɜɧɨɝɨ ȦɄ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɯμ = var. ɂɌ ɍɜɟɥɢɱɟɧɢɟ I1 ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɯμ, ɢ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɜɨɡɆ ɪɚɫɬɟɬ ɜ ɦɟɧɶɲɟɣ ɫɬɟɩɟɧɢ, ɱɟɦ ɨɠɢɞɚɜɲɟɟɫɹ ɟɝɨ ɭɜɟɥɢɱɟɧɢɟ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɆɄɌ ɆɄ ɤɜɚɞɪɚɬɭ ɬɨɤɚ. ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɭɦɟɧɶɊɢɫ. 3.65. ɋɪɚɜɧɟɧɢɟ ɲɟɧɢɟ ɯμ ɭɜɟɥɢɱɢɜɚɟɬ ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɜɢɝɚɬɟɥɹ ɠɟɧɢɟ ĮsɄɌ, ɱɬɨ ɭɜɟɥɢɱɢɜɚɟɬ ɧɚɤɥɨɧ ɯɚɪɚɤɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɂɌ ɢ ɂɇ ɬɟɪɢɫɬɢɤɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɱɟɬ ɯμ ɩɪɢɜɨɞɢɬ ɤ ɩɪɚɤɬɢɱɟɫɤɨɦɭ ɜɢɞɭ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɟɝɨ ɨɬ ɂɌ. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɪɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜɵɩɨɥɧɹɟɬɫɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ Ɍ–ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ɫ ɭɱɟɬɨɦ ɢɡɦɟɧɟɧɢɹ ɯμ ɩɨ ɭɪɚɜɧɟɧɢɹɦ (3.70) ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ «harad».

Ȧ

ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɂɌ – ȺȾ. ɂɡ ɜɟɤɬɨɪɧɨɣ ɞɢɚɝɪɚɦɦɵ (ɪɢɫ. 3.63) ɜɢɞɟɧ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ ɬɨɤɨɜ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɫɤɨɪɨɫɬɢ ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫɤɨɥɶɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ. ɉɪɢ s = 0 ɬɨɤ ɫɬɚɬɨɪɚ ɪɚɜɟɧ ɬɨɤɭ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ I1 = Iμ, ɚ ɬɨɤ ɪɨɬɨɪɚ ɪɚɜɟɧ ɧɭɥɸ Ic2= 0. ɉɪɢ ɪɨɫɬɟ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ ɪɚɫɬɭɬ ɫɤɨɥɶɠɟɧɢɟ s, ɗȾɋ ɢ ɬɨɤ ɪɨɬɨɪɚ Ic2. Ɍɨɤ ɫɬɚɬɨɪɚ I1 = const ɢ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɬɨɤɚ ɪɨɬɨɪɚ ɢɡɦɟɧɹɟɬɫɹ ɩɨ ɮɚɡɟ ɩɨ ɞɭɝɟ ɨɤɪɭɠɧɨɫɬɢ. ɋ ɪɨɫɬɨɦ ɬɨɤɚ ɪɨɬɨɪɚ ɭɦɟɧɶɲɚɟɬɫɹ ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. ɉɨ ɡɚɤɨɧɭ ɪɚɡɞɟɥɟɧɢɹ ɬɨɤɨɜ ɜ ɩɚɪɚɥɥɟɥɶɧɵɯ ɰɟɩɹɯ ɧɚɣɞɟɦ ɬɨɤ ɪɨɬɨɪɚ

I1 xμ

Ic2

rc /Ds xc 2

2

2

xμ

(3.87)

2

ɢ ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ

rc /Ds xc rc /Ds xc x 2

Iμ

I1

2

2

2

2

2

2

2

.

(3.88)

μ

ɉɪɢ sĺf ɬɨɤɢ ɫɬɪɟɦɹɬɫɹ ɤ ɩɪɟɞɟɥɶɧɵɦ ɡɧɚɱɟɧɢɹɦ: Ic2 ɉɊȿȾ

I1

xμ xμ xc2

# I1; IPɉɊȿȾ

133

I1

xc2 # 0. xμ xc2

Ɋɚɫɫɦɨɬɪɟɧɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3.66. ɋɬɪɟɦɥɟɧɢɟ ɤ ɧɭɥɸ Iμ ɨɡɧɚɱɚɟɬ ɬɚɤɠɟ, ɱɬɨ ɤ ɧɭɥɸ ɫɬɪɟɦɢɬɫɹ ɢ ɩɨɬɨɤ ɦɚɲɢɧɵ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɪɚɡɜɢɜɚɟɦɵɣ ɟɸ ɦɨɦɟɧɬ. ɗɬɨ ɞɨɤɚɡɵɜɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɯμ = var. ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ ɬɚɤɠɟ ɜɵɫɨɤɭɸ ɠɟɫɬɤɨɫɬɶ ɪɚɛɨɱɟɝɨ ɭɱɚɫɬɤɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɤɨɬɨɪɚɹ ɧɟ ɩɨɡɜɨɥɹɟɬ ɞɜɢɝɚɬɟɥɸ ɭɫɬɨɣɱɢɜɨ ɪɚɛɨɬɚɬɶ ɩɪɢ ɤɨɥɟɛɚɧɢɹɯ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ ɢ ɫɤɨɪɨɫɬɢ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɪɢ ɩɢɬɚɧɢɢ ȺȾ ɨɬ ɂɌ ɩɪɢɯɨɞɢɬɫɹ ɩɪɢɦɟɧɹɬɶ ɨɬɪɢɰɚɬɟɥɶɧɭɸ ɨɛɪɚɬɧɭɸ ɫɜɹɡɶ ɩɨ ɫɤɨɪɨɫɬɢ.

Ȧ

Ȧ0ɇ I1 Iμ

I2|

Ec2

I, Ec2

Ɋɢɫ. 3.66. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɂɌ

3.5.9. ɉɭɫɤ ȺȾ

ɋɩɨɫɨɛɵ ɩɭɫɤɚ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ: – ɩɪɹɦɨɣ ɩɭɫɤ – ɩɪɢ ɩɢɬɚɧɢɢ ɞɜɢɝɚɬɟɥɹ ɨɬ ɫɟɬɢ ɧɟɢɡɦɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ, ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪ ɩɨɞɚɟɬɫɹ ɫɤɚɱɤɨɦ. ɉɭɫɤ ɩɪɨɢɡɜɨɞɢɬɫɹ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ (ɫɦ. ɩ. 3.5.7). ɉɪɢ ɩɭɫɤɨɜɨɦ (s = 1) ɦɨɦɟɧɬɟ Ɇɉ = 0,8…1,8 Ɇɇ ɩɭɫɤɨɜɨɣ ɬɨɤ ɫɬɚɬɨɪɚ I1ɉ ɞɨɫɬɢɝɚɟɬ ɡɧɚɱɟɧɢɹ 5…7·I 1ɇ. ɉɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɫɟɬɢ, ɩɢɬɚɸɳɟɣ ɞɜɢɝɚɬɟɥɶ, ɩɪɢ ɩɭɫɤɟ ɦɨɠɟɬ ɩɪɟɜɵɫɢɬɶ ɞɨɩɭɫɤɚɟɦɨɟ ɩɨ ɭɫɥɨɜɢɹɦ ɷɤɫɩɥɭɚɬɚɰɢɢ –10% Uɇ. – ɪɟɚɤɬɨɪɧɵɣ (ɪɟɠɟ ɚɜɬɨɬɪɚɧɫɮɨɪɦɚɬɨɪɧɵɣ) – ɜ ɰɟɩɶ ɫɬɚɬɨɪɚ ɧɚ ɜɪɟɦɹ ɩɭɫɤɚ ɜɤɥɸɱɚɸɬ ɥɢɛɨ ɪɟɚɤɬɨɪɵ, ɥɢɛɨ ɚɜɬɨɬɪɚɧɫɮɨɪɦɚɬɨɪ ɫ ɰɟɥɶɸ ɨɝɪɚɧɢɱɟɧɢɹ ɩɭɫɤɨɜɨɝɨ ɬɨɤɚ ɢ ɞɨɫɬɢɠɟɧɢɹ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɜ ɫɟɬɢ ɞɨɩɭɫɤɚɟɦɨɝɨ ɡɧɚɱɟɧɢɹ. ɉɪɢ ɩɭɫɤɟ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɫ ɮɚɡɧɵɦ ɪɨɬɨɪɨɦ ɫ ɰɟɥɶɸ ɨɛɟɫɩɟɱɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɣ, ɩɪɟɞɴɹɜɥɹɟɦɵɯ ɤ ɩɭɫɤɭ (ɮɨɪɫɢɪɨɜɚɧɧɵɣ, ɫ ɨɝɪɚɧɢɱɟɧɢɟɦ ɩɨ ɭɫɤɨɪɟɧɢɸ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ, ɧɨɪɦɚɥɶɧɵɣ ɩɭɫɤ – ɫɦ. ɩ. 3.1.6) ɜ ɰɟɩɶ ɪɨɬɨɪɚ ɜɤɥɸɱɚɸɬ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R2ȾɈȻ. ɍɜɟɥɢɱɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɨɬɨɪɚ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɬɨɤɚ ɪɨɬɨɪɚ I2 ɩɪɢ ɨɞɧɨɜɪɟɦɟɧɧɨɦ ɪɨɫɬɟ ɟɝɨ ɚɤɬɢɜɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ I2Ⱥ ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɤ ɭɜɟɥɢɱɟɧɢɸ ɩɭɫɤɨɜɨɝɨ ɦɨɦɟɧɬɚ Ɇɉ. Ɋɟɨɫɬɚɬɧɵɣ ɩɭɫɤ ȺȾɎɊ. ɇɚ ɪɢɫ. 3.67 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɫɢɥɨɜɵɯ ɰɟɩɟɣ ɪɟɨɫɬɚɬɧɨɝɨ ɩɭɫɤɚ ɞɜɢɝɚɬɟɥɹ. Ɋɟɨɫɬɚɬɧɵɣ ɩɭɫɤ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬ ɩɪɢ ɩɨɞɚɱɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɬɚɬɨɪ ɜɜɟɞɟɧɢɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɨɝɪɚɧɢɱɢɜɚɸɳɟɝɨ ɜɟɥɢɱɢɧɭ ɬɨɤɚ ɪɨɬɨɪɚ ɞɨɩɭɫɬɢɦɵɦ ɡɧɚɱɟɧɢɟɦ ɩɨ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦ ɭɫɥɨɜɢɹɦ ɩɭɫɤɚ. ɇɚ ɪɢɫ. 3.68 ɩɪɢɜɟɞɟɧɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɩɭɫɤ ɞɜɢɝɚɬɟɥɹ. ɉɪɢ ɡɚɦɵɤɚɧɢɢ ɤɨɧɬɚɤɬɨɜ ɥɢɧɟɣɧɨɝɨ ɤɨɧɬɚɤɬɨɪɚ ɄɅ ɢ ɨɞɧɨɝɨ ɢɡ ɤɨɧɬɚɤɬɨɪɨɜ ɧɚɩɪɚɜɥɟɧɢɹ Ʉȼ (ɢɥɢ Ʉɇ) ɬɨɤ ɪɨɬɨɪɚ I2 ɩɪɨɬɟɤɚɟɬ ɱɟɪɟɡ ɨɛɦɨɬɤɭ ɪɨɬɨɪɚ ɢ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R1ȾɈȻ ɢ R2ȾɈȻ, ɫɨɡɞɚɟɬɫɹ ɦɨɦɟɧɬ Ɇ1. Ʉɨɧɬɚɤɬɨɪ ɪɟɠɢɦɚ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ Ʉɉȼ ɜɨ ɜɪɟɦɹ ɩɭɫɤɚ ɜɤɥɸɱɟɧ, ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ Rɉȼ ȾɈȻ ɡɚɲɭɧɬɢɪɨɜɚɧɨ. Ⱦɜɢɝɚɬɟɥɶ ɪɚɡɝɨɧɹɟɬɫɹ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɫ R1ȾɈȻ + R2ȾɈȻ , ɬɨɤ ɪɨɬɨɪɚ ɫɧɢɠɚɟɬɫɹ, ɢ ɦɨɦɟɧɬɟ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 ɜɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ Ʉɍ1, ɲɭɧɬɢɪɭɹ R1ȾɈȻ. Ⱦɜɢɝɚɬɟɥɶ ɩɟɪɟɜɨɞɢɬɫɹ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɫ R2ȾɈȻ. Ɍɨɤ 134

ɪɨɬɨɪɚ ɜɧɨɜɶ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɦɨɦɟɧɬ ɧɚɪɚɫɬɚɟɬ ɞɨ ɡɧɚɱɟɧɢɹ Ɇ1. ɉɪɨɢɫɯɨɞɢɬ ɪɚɡɝɨɧ ɞɨ ɫɤɨɪɨɫɬɢ, ɝɞɟ ɩɪɢ ɦɨɦɟɧɬɟ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 ɜɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ Ʉɍ2, ɩɟɪɟɜɨɞɹ ɞɜɢɝɚɬɟɥɶ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ. ɇɚ ɷɬɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɩɪɨɞɨɥɠɚɟɬɫɹ ɪɚɡɝɨɧ ɞɨ ɫɤɨɪɨɫɬɢ Ȧɋ, ɝɞɟ ɩɪɢ Ɇ = Ɇɋ ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɯɨɞɢɬ ɜ ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ ɪɟɠɢɦ ɪɚɛɨɬɵ (ɬɨɱɤɚ 1). ȼ ɩɪɨɰɟɫɫɟ ɪɚɡɝɨɧɚ ɞɜɢɝɚɬɟɥɹ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɭɦɟɧɶɲɚɸɬ ɩɨ ɜɟɥɢɱɢɧɟ, ɨɛɟɫɩɟɱɢɜɚɹ ɩɟɪɟɤɥɸɱɟɧɢɟ ɫɬɭɩɟɧɟɣ ɩɭɫɤɨɜɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɩɨ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɟ. ɉɟɪɟɤɥɸɱɟɧɢɟ ɫɬɭɩɟɧɟɣ ɜɵɩɨɥɧɹɟɬɫɹ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɜ ɮɭɧɤɰɢɢ ɜɪɟɦɟɧɢ, ɬɨɤɚ, ɫɤɨɪɨɫɬɢ. ɉɪɚɜɢɥɶɧɚɹ ɩɭɫɤɨɜɚɹ ɞɢɚɝɪɚɦɦɚ ɫɬɪɨɢɬɫɹ ɢɡ ɭɫɥɨɜɢɹ ɩɨɞɞɟɪɠɚɧɢɹ ɩɨɫɬɨɹɧɫɬɜɚ ɫɪɟɞɧɟɝɨ ~ ɩɭɫɤɨɜɨɝɨ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ, ɨɛɟɫɩɟɱɢɜɚɹ ɪɚɜɟɧɫɬɜɨ ɦɚɤɫɢɦɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ Ɇ1 ɧɚ ɤɚɠɞɨɣ ɢɡ ɩɭɫɤɨɜɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɚ ɬɚɤɠɟ ɪɚɜɟɧɄȼ. ɫɬɜɨ ɦɨɦɟɧɬɨɜ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 (ɪɢɫ. 3.68). Ʉɇ ɉɭɫɤɨɜɵɟ ɪɟɡɢɫɬɨɪɵ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɚɧɚɥɨɝɢɱɧɨ ɪɚɫɫɦɨɬɪɟɧɧɨɦɭ ɜɵɲɟ ɪɚɫɱɟɬɭ ɞɥɹ ɄɅ Ⱦɇȼ (ɫɦ. ɩ. 3.1.6): – ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɥɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɪɨɬɨɪɚ ɩɪɢ ɩɭɫɤɟ R2; – ɜɵɩɨɥɧɹɟɬɫɹ ɪɚɡɛɢɟɧɢɟ R2 ɧɚ ɫɬɭɩɟɧɢ, Ɇ ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɩɪɚɜɢɥɶɧɭɸ ɩɭɫɤɨɜɭɸ ɞɢɚɝɪɚɦɦɭ. Ʉɍ2 Ȧ R2ȾɈȻ Ȧ0ɇ 1 3 Ʉɍ1 ɟɫɬ ɉȼ R2ȾɈȻ ɆɄɁ R1ȾɈȻ Ɇ Ɇ C Ɇ Ɇ 2 1 4 Ʉɉȼ R1ȾɈȻ R1ȾɈȻ+ ɉȼ RɉȼȾɈȻ +R2ȾɈȻ +R2ȾɈȻ +RɉȼȾɈȻ - Ȧ0ɇ 2 Ɋɢɫ. 3.67. ɋɯɟɦɚ ɩɭɫɤɚ ɢ ɪɟɜɟɪɫɚ ɫ ɬɨɪɦɨɠɟɧɢɟɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ

Ɋɢɫ. 3.68. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɜ ɪɟɠɢɦɟ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ

ɋ ɭɱɟɬɨɦ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɜ ɫɟɬɢ ɩɪɢ ɩɭɫɤɟ (ǻU1 = 0,1ǜU1ɇ) ɩɪɢɧɢɦɚɸɬ ɦɚɤɫɢɦɚɥɶɧɵɣ ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ Ɇ1 d ɆɆȺɄɋ = 0,8ǜɆɄ. Ɇɨɦɟɧɬ ɩɟɪɟɤɥɸɱɟɧɢɹ ɜɵɛɢɪɚɸɬ Ɇ2 t 1,2ǜMC ɞɥɹ ɢɫɤɥɸɱɟɧɢɹ ɡɚɫɬɪɟɜɚɧɢɹ ɧɚ ɩɪɨɦɟɠɭɬɨɱɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ. 135

ȼ ɫɜɹɡɢ ɫ ɧɟɥɢɧɟɣɧɨɫɬɶɸ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɬɨɱɧɵɟ ɚɧɚɥɢɬɢɱɟɫɤɢɟ ɪɚɫɱɟɬɵ ɫɥɨɠɧɵ ɢ ɩɪɚɤɬɢɱɟɫɤɢ ɢɦɢ ɧɟ ɩɨɥɶɡɭɸɬɫɹ. ɉɪɢɦɟɧɹɸɬɫɹ ɩɪɢɛɥɢɠɟɧɧɵɟ ɫɩɨɫɨɛɵ, ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɧɟɨɛɯɨɞɢɦɨɣ ɬɨɱɧɨɫɬɢ, ɭɱɢɬɵɜɚɸɳɢɟ ɢɥɢ ɧɟ ɭɱɢɬɵɜɚɸɳɢɟ ɤɪɢɜɢɡɧɭ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. ɉɪɢɦɟɪ 3.9. Ɋɚɫɫɱɢɬɚɬɶ ɢ ɩɨɫɬɪɨɢɬɶ ɩɪɚɜɢɥɶɧɭɸ ɩɭɫɤɨɜɭɸ ɞɢɚɝɪɚɦɦɭ, ɨɛɟɫɩɟɱɢɜɚɸɳɭɸ ɩɭɫɤ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ (ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ ɫɦ. ɜ ɩɪɢɦɟɪɟ 3.5) ɩɪɢ Ɇɋ = 0,5 ɡɚ ɦɢɧɢɦɚɥɶɧɨɟ ɜɪɟɦɹ. ɉɪɢɧɹɬɶ ɱɢɫɥɨ ɫɬɭɩɟɧɟɣ m = 3. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɦɢɧɢɦɚɥɶɧɨɝɨ ɜɪɟɦɟɧɢ ɩɭɫɤɚ ɞɜɢɝɚɬɟɥɶ ɞɨɥɠɟɧ ɪɚɛɨɬɚɬɶ ɫ ɩɪɟɞɟɥɶɧɵɦ ɦɨɦɟɧɬɨɦ ɆȾɈɉ = 0,8ǜɆɄ = 0,8·3·198 = 475 ɇɦ. 3.9.1. ɉɪɢ ɪɚɫɱɟɬɟ ɛɟɡ ɭɱɟɬɚ ɤɪɢɜɢɡɧɵ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢɧɢɦɚɸɬ ɡɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɟɟ ɩɪɹɦɨɥɢɧɟɣɧɵɣ ɭɱɚɫɬɨɤ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ ɬɨɱɤɢ (Ȧ = Ȧ0ɇ, Ɇ = 0) ɢ (Ȧ = Ȧɇ, Ɇ = Ɇɇ). Ɋɚɫɱɟɬ ɦɨɠɧɨ ɜɵɩɨɥɧɢɬɶ ɩɨ ɦɟɬɨɞɢɤɟ ɪɚɫɱɟɬɚ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɫ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ (ɫɦ. ɩ. 3.1.5). Ɇɚɤɫɢɦɚɥɶɧɵɣ ɦɨɦɟɧɬ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ Ɇ1 = ɆȾɈɉ. Ɉɩɪɟɞɟɥɢɦ ɦɨɦɟɧɬ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ Ɇ1 1 1 3 m Ɇ1 ɆȾɈɉ 2,4; Ȝ 2,28; Ɇ2 Ɇ1 sH 2,4 0,035 Ɇ2 Ɇ1/Ȝ 2,4/2,28 1,05. Ɋɚɫɫɱɢɬɚɟɦ ɩɨɥɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɢ ɪɨɬɨɪɚ ɧɚ ɤɚɠɞɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ: R1 1/ M1 1/2,4 0,417; R1 R1 R2H 0,417 7,42 3,094 Ɉɦ;

R2

R1/Ȝ

0,417/2,28

0,183; R 2

R2 R 2H

0,183 7,42 1,358 Ɉɦ;

R3 R2 /Ȝ 0,183/2,28 0,08; R3 R3 R2H 0,08 7,42 0,534 Ɉɦ. ɉɪɨɜɟɪɢɦ ɩɪɚɜɢɥɶɧɨɫɬɶ ɪɚɫɱɟɬɚ – ɧɚ ɩɨɫɥɟɞɧɟɣ ɫɬɭɩɟɧɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɞɨɥɠɧɨ ɛɵɬɶ ɪɚɜɧɨ ɧɟɜɵɤɥɸɱɚɟɦɨɦɭ. R 4 = R3 /Ȝ = 0,08/2,28 = 0,035; R4 = r2c = sɇ; r2c = r2c 7,42 = 0,26 Ɉɦ. ȼɟɥɢɱɢɧɵ ɫɬɭɩɟɧɟɣ ɫɨɩɪɨɬɢɜɥɟɧɢɣ: R1ȾɈȻ = R1 – R2 = 3,094 – 1,358 = 1,736 Ɉɦ; R2ȾɈȻ = R2 – R3 = 1,358 – 0,534 = 0,824 Ɉɦ; R3ȾɈȻ = R3 – rc2 = 0,534 – 0,26 = 0,274 Ɉɦ. ɇɚ ɪɢɫ. 3.69,ɚ ɩɪɢɜɟɞɟɧɵ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɪɚɫɱɟɬɚ. Ɍɨɱɤɚɦɢ 1…7 ɨɬɦɟɱɟɧɵ ɪɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɢ ɦɨɦɟɧɬɨɜ. ȼɢɞɧɨ, ɱɬɨ ɦɚɤɫɢɦɚɥɶɧɵɟ ɦɨɦɟɧɬɵ (ɬɨɱɤɢ 1,3,5) ɧɟ ɩɨɩɚɥɢ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɬɨɝɞɚ ɤɚɤ ɦɨɦɟɧɬɵ ɩɟɪɟɤɥɸɱɟɧɢɹ (ɬɨɱɤɢ 2,4,6) ɫɨɜɩɚɥɢ ɫ ɪɚɫɱɟɬɧɵɦɢ. Ɂɧɚɱɢɬ, ɩɪɢ ɪɚɫɱɟɬɟ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ ɧɟɨɛɯɨɞɢɦ ɭɱɟɬ ɧɟɥɢɧɟɣɧɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. 3.9.2. ɉɨɪɹɞɨɤ ɪɚɫɱɟɬɚ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ ɫ ɭɱɟɬɨɦ ɤɪɢɜɢɡɧɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɦɟɬɨɞɨɦ ɥɭɱɟɜɨɣ ɞɢɚɝɪɚɦɦɵ: – ɫɬɪɨɢɬɫɹ ɟɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ; – ɚɧɚɥɨɝɢɱɧɨ ɡɚɞɚɱɟ 3.9.1 ɩɨ ɡɚɞɚɧɧɨɦɭ ɫɩɨɫɨɛɭ ɩɭɫɤɚ (ɮɨɪɫɢɪɨɜɚɧɧɵɣ, ɫ ɞɨɩɭɫɬɢɦɵɦ ɭɫɤɨɪɟɧɢɟɦ, ɧɨɪɦɚɥɶɧɵɣ) ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɦɚɤɫɢɦɚɥɶɧɵɣ ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ Ɇ1 (ɢɥɢ Ɇ2); – ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ (ɫɦ. ɪɢɫ. 3.69,ɛ) ɨɬɦɟɱɚɸɬ ɬɨɱɤɨɣ ”b” ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɦɨɦɟɧɬɟ Ɇ1;

136

– ɡɚɞɚɸɬɫɹ ɦɨɦɟɧɬɨɦ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 ɢ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɨɬɦɟɱɚɸɬ ɬɨɱɤɨɣ “a” ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɦɨɦɟɧɬɟ Ɇ2; – ɱɟɪɟɡ ɬɨɱɤɢ “a” ɢ ”b” ɩɪɨɜɨɞɹɬ ɩɪɹɦɭɸ ɞɨ ɩɟɪɟɫɟɱɟɧɢɹ ɫ ɝɨɪɢɡɨɧɬɚɥɶɸ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɬɨɱɤɭ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ0ɇ; – ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ “Ɉ” ɹɜɥɹɟɬɫɹ ɩɨɥɸɫɨɦ ɥɭɱɟɜɨɣ ɞɢɚɝɪɚɦɦɵ; – ɫɨɟɞɢɧɹɸɬ ɬɨɱɤɭ “Ɉ” ɫ ɬɨɱɤɨɣ Ɇ1 ɩɪɢ ɫɤɨɪɨɫɬɢ Ȧ = 0; – ɩɪɢ ɩɟɪɟɫɟɱɟɧɢɢ ɩɨɥɭɱɟɧɧɨɣ ɩɪɹɦɨɣ ɫ ɦɨɦɟɧɬɨɦ Ɇ2 ɜɵɩɨɥɧɹɸɬ ɩɟɪɟɯɨɞ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɫɤɨɪɨɫɬɢ ɤ ɦɨɦɟɧɬɭ Ɇ1; – ɩɨɥɭɱɟɧɧɭɸ ɬɨɱɤɭ ɜɧɨɜɶ ɫɨɟɞɢɧɹɸɬ ɫ “Ɉ” ɢ ɬ.ɞ. ɉɪɢ ɩɪɚɜɢɥɶɧɨ ɜɵɛɪɚɧɧɨɦ ɡɧɚɱɟɧɢɢ Ɇ2 ɜɵɯɨɞ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɩɨɥɭɱɚɸɬ ɩɪɢ ɦɨɦɟɧɬɟ Ɇ1 ɢ ɩɪɚɜɢɥɶɧɚɹ ɩɭɫɤɨɜɚɹ ɞɢɚɝɪɚɦɦɚ ɩɨɫɬɪɨɟɧɚ. ȿɫɥɢ ɩɪɚɜɢɥɶɧɚɹ ɩɭɫɤɨɜɚɹ ɞɢɚɝɪɚɦɦɚ ɧɟ ɩɨɥɭɱɟɧɚ, ɬɨ ɢɡɦɟɧɹɸɬ Ɇ2 ɢ ɩɨɜɬɨɪɹɸɬ ɩɨɫɬɪɨɟɧɢɟ ɞɨ ɟɟ ɩɨɥɭɱɟɧɢɹ. ɉɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɦɨɦɟɧɬɚ ɫɤɨɥɶɠɟɧɢɟ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɫɨɩɪɨɬɢɜɥɟɧɢɸ ɜ ɰɟɩɢ ɪɨɬɨɪɚ, ɩɨɷɬɨɦɭ ɢɡɦɟɪɹɸɬ ɨɬɪɟɡɤɢ ɩɪɢ Ɇ = Ɇ2 (ɫɦ. ɪɢɫ. 3.69,ɛ) ɢ ɩɨ ɫɨɨɬɧɨɲɟɧɢɹɦ ɨɬɪɟɡɤɨɜ ɨɩɪɟɞɟɥɹɸɬ ɩɨɥɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɢ ɪɨɬɨɪɚ: R1 = r2 ·(ce / ca); R2 = r2 (cd / ca), ɝɞɟ r2 – ɧɟɜɵɤɥɸɱɚɟɦɨɟ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɮɚɡɵ ɪɨɬɨɪɚ. Ɂɧɚɱɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɢɫɩɨɥɶɡɭɸɬ ɩɪɢ ɪɚɫɱɟɬɟ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɜɢɝɚɬɟɥɹ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɪɢɫ. 3.69, ɩɨɥɭɱɢɥɫɹ ɩɭɫɤ ɜ ɞɜɟ ɫɬɭɩɟɧɢ ɩɪɢ ɨɞɢɧɚɤɨɜɵɯ ɫ ɩɪɟɞɵɞɭɳɢɦ ɪɚɫɱɟɬɨɦ ɡɧɚɱɟɧɢɹɯ Ɇ1 ɢ Ɇ2. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɥɹ ɷɬɨɝɨ ɪɚɫɱɟɬɚ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3.69,ɛ. Ȧ

Ȧ 6

7

4

5

0

ɫ a d

Ȧ0ɇ b

e

Mɋ

2

3

M2

1 M1

M

M Mɋ

ɚ)

M2

M1

ɛ)

Ɋɢɫ.3.69. ɉɨɫɬɪɨɟɧɢɟ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ ȺȾ ɚ) ɛɟɡ ɭɱɟɬɚ ɢ ɛ) ɫ ɭɱɟɬɨɦ ɤɪɢɜɢɡɧɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

137

3.5.10. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ȺȾ

ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ȺȾ ɫɬɪɨɢɬɫɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɪɶ ɦɨɳɧɨɫɬɢ ɜ ɩɪɨɰɟɫɫɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɧɟɪɝɢɢ, ɨɰɟɧɤɢ ɫɨɫɬɚɜɥɹɸɳɢɯ ɩɨɬɟɪɶ ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ – ɄɉȾ ɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɦɨɳɧɨɫɬɢ. Ɋɚɫɫɦɨɬɪɢɦ ɷɧɟɪɝɟɬɢɱɟɫɤɭɸ ɞɢɚɝɪɚɦɦɭ ɞɜɢɝɚɬɟɥɶɧɨɊ1=3ǜU1ǜI1ǜcosĳ1 ɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ȺȾ (Ɇ > 0, Ȧ > 0), ɩɪɢɜɟɞɟɧɧɭɸ ɧɚ ɪɢɫ. 2 3.70. ǻɊ1=3ǜI1 ǜr1 Ɇɨɳɧɨɫɬɶ Ɋ1, ɩɨɬɪɟɛɥɹɟɊɗɆ=ɆɗɆǜȦ0 2 ǻɊ1ɉɈɋɌ=3ǜI1 ǜrμ ɦɚɹ ɢɡ ɫɟɬɢ, ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɫɨɡɞɚɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ 2 ɦɨɳɧɨɫɬɢ Ɋ ɗɆ, ɩɟɪɟɞɚɜɚɟɦɨɣ ǻɊ2=3ǜI2 ǜr2 ɜ ɪɨɬɨɪ, ɡɚ ɜɵɱɟɬɨɦ ɩɟɪɟɦɟɧɧɵɯ ɩɨɬɟɪɶ ɜ ɚɤɬɢɜɧɨɦ ɫɨɩɪɨɊɆȿɏ= ɆɗɆǜȦ ǻɊ2ȾɈȻ=3ǜI22ǜR2ȾɈȻ ɬɢɜɥɟɧɢɢ ɫɬɚɬɨɪɚ ǻɊ1 ɢ ɩɨɫɬɨɹɧɧɵɯ, ɧɟ ɡɚɜɢɫɹɳɢɯ ɨɬ ɧɚɝɪɭɡɤɢ, ɩɨɬɟɪɶ ɜ ɫɬɚɥɢ ɫɬɚɬɨɪɚ Ɋȼ=ɆȼǜȦ ǻɊɆȿɏ=ɊɆȿɏ–Ɋȼ ǻɊ1ɉɈɋɌ. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɦɨɳɧɨɫɬɶ ɊɗɆ ɩɪɟɨɛɪɚɡɭɟɬɫɹ, ɡɚ ɜɵɱɟɬɨɦ ɩɨɬɟɪɶ ɦɨɳɧɨɫɬɢ ɜ Ɋɢɫ. 3.70. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɚɤɬɢɜɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɪɨɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ȺȾ ɬɨɪɚ ǻɊ2, ɜ ɦɟɯɚɧɢɱɟɫɤɭɸ ɦɨɳɧɨɫɬɶ ɊɆȿɏ, ɜɵɞɚɜɚɟɦɭɸ ɧɚ ɜɚɥ Ɋȼ, ɡɚ ɜɵɱɟɬɨɦ ɦɟɯɚɧɢɱɟɫɤɢɯ ɩɨɬɟɪɶ ɜɧɭɬɪɢ ɞɜɢɝɚɬɟɥɹ ǻɊɆȿɏ. Ɉɰɟɧɤɭ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɧɟɪɝɢɢ ɜɵɩɨɥɧɹɸɬ ɫ ɩɨɦɨɳɶɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ ɄɉȾ Ș = Ɋȼ / Ɋɋ. ɇɚ ɪɢɫ. 3.71 ɩɪɢɜɟɞɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ Ș = f (Pȼ), ɩɨɫɬɪɨɟɧɧɚɹ ɩɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ. ɄɉȾ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ ɪɚɜɟɧ Șɇ = 0,75…0,95, ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɧɨɦɢɧɚɥɶɧɨɣ ɦɨɳɧɨɫɬɢ Ɋɇ ɞɜɢɝɚɬɟɥɹ ɄɉȾ ɪɚɫɬɟɬ. ɉɪɢ ɧɚɪɚɫɬɚɧɢɢ ɧɚɝɪɭɡɤɢ Școs ĳ1 ȘȘ ɧɚ ɜɚɥɭ ɄɉȾ ɪɚɫɬɟɬ ɜ ɫɜɹɡɢ ɫ cos ĳ1ɇ ɪɨɫɬɨɦ ɩɨɥɟɡɧɨɣ ɦɨɳɧɨɫɬɢ, Șɇ ɩɪɢ Ɋȼ § Ɋɇ ɄɉȾ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɭɦɚ, ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɪɨɫɬɟ Ɋȼ ɄɉȾ ɫɧɢɠɚɟɬɫɹ ɜ ɫɜɹɡɢ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɩɨɬɟɪɶ cos ĳ10 ɦɨɳɧɨɫɬɢ ɜɧɭɬɪɢ ɦɚɲɢɧɵ. Ɋ Ɋ Ⱦɪɭɝɢɦ ɩɨɤɚɡɚɬɟɥɟɦ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦ ɦɚɲɢɧɭ ɩɟɊɇ Ɋɇ ɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɤɚɤ ɩɪɢɟɦɧɢɤ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ, ɹɜɥɹɊɢɫ. 3.71. ɗɧɟɪɝɟɬɢɱɟɫɤɢɟ ɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ, ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɭɱɢɬɵɜɚɸɳɢɣ ɷɮɮɟɤɬɢɜɧɨɫɬɶ 138

ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɚɤɬɢɜɧɨɣ ɷɧɟɪɝɢɢ. ɉɪɢ ɫɢɧɭɫɨɢɞɚɥɶɧɨɣ ɮɨɪɦɟ ɧɚɩɪɹɠɟɧɢɹ ɢ ɬɨɤɚ ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɨɬɧɨɲɟɧɢɟ ɚɤɬɢɜɧɨɣ ɦɨɳɧɨɫɬɢ P ɤ ɩɨɥɧɨɣ ɦɨɳɧɨɫɬɢ S, ɱɢɫɥɟɧɧɨ ɪɚɜɧɨɟ ɞɥɹ ɬɪɟɯɮɚɡɧɨɣ ɫɟɬɢ 3 PCɎ P cos ĳ1 . (3.89) S 3 U1Ɏ I1Ɏ ɇɚ ɪɢɫ. 3.71 ɩɨɤɚɡɚɧɚ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ cos ĳ1 = f (Pȼ). ɉɪɢ ɪɚɛɨɬɟ ɜ ɪɟɠɢɦɚɯ, ɛɥɢɡɤɢɯ ɤ ɧɨɦɢɧɚɥɶɧɨɦɭ, ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ ɞɨɫɬɢɝɚɟɬ ɡɧɚɱɟɧɢɣ cos ĳ1 = 0,7…0,85. ȼ ɪɟɠɢɦɟ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɞɜɢɝɚɬɟɥɶ ɩɨɬɪɟɛɥɹɟɬ ɜ ɨɫɧɨɜɧɨɦ ɪɟɚɤɬɢɜɧɭɸ ɷɧɟɪɝɢɸ, cos ĳ10 = 0,05…0,15 ɭɱɢɬɵɜɚɟɬ ɩɨɬɪɟɛɥɟɧɢɟ ɚɤɬɢɜɧɨɣ ɷɧɟɪɝɢɢ ɧɚ ɩɨɤɪɵɬɢɟ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɜ ɞɜɢɝɚɬɟɥɟ. ɉɪɢ Ɋȼ > Ɋɇ ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ ɫɧɢɠɚɟɬɫɹ ɡɚ ɫɱɟɬ ɪɨɫɬɚ ɪɟɚɤɬɢɜɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɬɨɤɚ ɪɨɬɨɪɚ. 3.5.10.

Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ

Ⱥɫɢɧɯɪɨɧɧɵɣ ɞɜɢɝɚɬɟɥɶ ɹɜɥɹɟɬɫɹ ɨɛɪɚɬɢɦɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɦɚɲɢɧɨɣ, ɫɩɨɫɨɛɧɨɣ ɪɚɛɨɬɚɬɶ ɤɚɤ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ, ɬɚɤ ɢ ɜ ɝɟɧɟɪɚɬɨɪɧɨɦ ɪɟɠɢɦɟ. ɉɪɢ ɩɨɹɜɥɟɧɢɢ ɧɚ ɜɚɥɭ ɢɡɛɵɬɨɱɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɯɨɞɢɬ ɜ ɝɟɧɟɪɚɬɨɪɧɵɣ ɪɟɠɢɦ. ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɩɨɬɪɟɛɥɟɧɢɹ ɢɡɛɵɬɨɱɧɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ȺȾ ɪɚɛɨɬɚɟɬ ɜ ɬɚɤɢɯ ɠɟ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɚɯ, ɤɚɤ ɢ ɪɚɫɫɦɨɬɪɟɧɧɵɣ ɪɚɧɟɟ ɞɜɢɝɚɬɟɥɶ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ: ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ, ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɢ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ. Ɋɟɤɭɩɟɪɚɬɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ (ɊɌ) ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ – ɢɡɛɵɬɨɱɧɚɹ ɚɤɬɢɜɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɫɟɬɶ ɡɚ ɜɵɱɟɬɨɦ ɩɨɬɟɪɶ ɜ ɫɬɚɬɨɪɧɵɯ ɢ ɪɨɬɨɪɧɵɯ ɰɟɩɹɯ ɦɚɲɢɧɵ. ɂɡɛɵɬɨɱɧɚɹ ɦɨɳɧɨɫɬɶ ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɊ1=3ǜU1ǜI1ǜcosĳ1 ǻɊ1=3ǜI12ǜr1 ɥɹ ɭɜɟɥɢɱɢɜɚɟɬ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɞɨ ɡɧɚɱɟɧɢɣ, ɩɪɟɜɵɲɚɸɳɢɯ ɫɤɨɪɨɫɬɶ ǻɊ1ɉɈɋɌ=3ǜI12ǜrμ ɜɪɚɳɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ (ɫɢɧɯɪɨɧɧɭɸ ɫɤɨɪɨɫɬɶ). ɉɪɨɜɨɞɧɢɤɢ ɪɨɬɨɪɚ ɊɗɆ=ɆɗɆǜȦ0 ǻɊ2=3ǜI22ǜr2 ɨɩɟɪɟɠɚɸɬ ɩɨɥɟ ɫɬɚɬɨɪɚ ɢ ɜ ɧɢɯ ɧɚɜɨɞɢɬɫɹ ɗȾɋ, ɜɟɤ2 ǻɊ2ȾɈȻ=3ǜI2 ǜR2ȾɈȻ ɬɨɪ ɤɨɬɨɪɨɣ ɦɟɧɹɟɬ ɧɚɩɪɚɜɥɟɧɢɟ ɧɚ ɨɛɪɚɬɧɨɟ ɩɨ ǻɊɆȿɏ=Ɋȼ–ɊȼɆȿɏ ɨɬɧɨɲɟɧɢɸ ɤ ɞɜɢɝɚɬɟɥɶɊɆȿɏ= ɆɗɆǜȦ ɧɨɦɭ ɪɟɠɢɦɭ. ɉɨɹɜɥɹɟɬɫɹ ɬɨɤ ɪɨɬɨɪɚ, ɨɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɨɤɚ ɪɨɬɨɪɚ ɫ ɩɨɬɨɤɨɦ ɜɨɡɧɢɤɚɟɬ ɬɨɪɦɨɡɧɨɣ Ɋȼ=ɆȼǜȦ ɦɨɦɟɧɬ. ɇɚ ɪɢɫ. 3.72 ɩɪɢɜɟɞɟɧɚ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ Ɋɢɫ. 3.72. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɞɢɚɝɪɚɦɦɚ ɪɟɠɢɦɚ ɪɟɤɭɪɟɠɢɦɚ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. ɇɚɩɪɚɜɥɟɧɢɟ ɩɨɬɨɤɚ ɦɨɳ 139

ɧɨɫɬɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɜɢɝɚɬɟɥɶɧɵɦ ɪɟɠɢɦɨɦ – ɨɛɪɚɬɧɨɟ, ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɜ ɫɟɬɶ. ɉɪɢ ɩɟɪɟɯɨɞɟ ɜ ɪɟɠɢɦ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɶ ɩɪɨɯɨɞɢɬ ɯɚɪɚɤɬɟɪɧɵɟ ɬɨɱɤɢ: 1) ɯɨɥɨɫɬɨɣ ɯɨɞ (Ɋȼ = 0) – ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɦɚɲɢɧɟ ɩɨɤɪɵɜɚɸɬɫɹ ɫɨ ɫɬɨɪɨɧɵ ɫɟɬɢ; 2) ɢɞɟɚɥɶɧɵɣ ɯɨɥɨɫɬɨɣ ɯɨɞ – ɗȾɋ ɢ ɬɨɤ ɪɨɬɨɪɚ ɪɚɜɧɵ ɧɭɥɸ, ɆɗɆ = 0, ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɨɬɟɪɢ ɩɨɤɪɵɜɚɸɬɫɹ ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ, ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɰɟɩɢ ɫɬɚɬɨɪɚ ɩɨɬɪɟɛɥɹɸɬɫɹ ɢɡ ɫɟɬɢ; 3) ɚɤɬɢɜɧɚɹ ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɢɡ ɫɟɬɢ, ɪɚɜɧɚ ɧɭɥɸ Ɋ1 = 0, ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɰɟɩɹɯ ɦɚɲɢɧɵ ɩɨɤɪɵɜɚɸɬɫɹ ɫɨ ɫɬɨɪɨɧɵ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ. Ɋɟɠɢɦ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɧɚɱɢɧɚɟɬɫɹ ɩɪɢ ɫɤɨɪɨɫɬɢ Ȧ > Ȧ0ɇ, ɤɨɝɞɚ ɦɟɧɹɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɚɤɬɢɜɧɨɣ ɦɨɳɧɨɫɬɢ Ɋ1 < 0. ȼɚɪɢɚɧɬɵ ɨɛɟɫɩɟɱɟɧɢɹ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɩɨɯɨɠɢ ɧɚ ɚɧɚɥɨɝɢɱɧɵɟ ɞɥɹ Ⱦɇȼ, ɟɫɥɢ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɪɚɛɨɱɢɣ ɭɱɚɫɬɨɤ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (ɫɦ. ɪɢɫ. 3.19): 1) ɢɡɦɟɧɟɧɢɟ ɡɧɚɤɚ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɨɬ Ɇɋ ɧɚ Ɇɋ1 < 0, ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɯɨɞɢɬ ɢɡ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɜ ɪɟɠɢɦ ɪɟɤɭɩɟɪɚɰɢɢ ɱɟɪɟɡ ɬɨɱɤɭ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ0; 2) ɫɩɭɫɤ ɝɪɭɡɚ – ɩɪɢ ɧɟɢɡɦɟɧɧɨɦ ɡɧɚɤɟ Ɇɋ ɞɜɢɝɚɬɟɥɶ ɜɪɚɳɚɟɬɫɹ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ, ɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɝɪɭɡɚ ɩɟɪɟɯɨɞɢɬ ɜ ɪɟɠɢɦ ɪɟɤɭɩɟɪɚɰɢɢ ɫɨ ɫɤɨɪɨɫɬɶɸ ɜɵɲɟ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ (Ȧ > Ȧ0ɇ); 3) ɩɪɢ ɫɧɢɠɟɧɢɢ ɱɚɫɬɨɬɵ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɬɚɬɨɪɟ (ɜɚɪɢɚɧɬ ɩɢɬɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɨɬ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɱɚɫɬɨɬɵ) ɫɧɢɠɚɟɬɫɹ ɫɢɧɯɪɨɧɧɚɹ ɫɤɨɪɨɫɬɶ Ȧ0 < Ȧ0ɇ. Ⱦɜɢɝɚɬɟɥɶ ɨɫɭɳɟɫɬɜɥɹɟɬ ɩɟɪɟɯɨɞ ɢɡ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɜ ɪɟɠɢɦ ɪɟɤɭɩɟɪɚɰɢɢ. ɇɚ ɭɱɚɫɬɤɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɨɬ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɞɨ Ȧ0 – ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɪɟɠɢɦɟ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɪɢ ɊɌ ɹɜɥɹɟɬɫɹ ɩɪɨɞɨɥɠɟɧɢɟɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɜɨ ɜɬɨɪɨɣ (ɢɥɢ ɱɟɬɜɟɪɬɵɣ) ɤɜɚɞɪɚɧɬ. ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (3.61) ɧɟ ɢɡɦɟɧɹɟɬɫɹ, ɢɡɦɟɧɹɟɬɫɹ ɥɢɲɶ ɡɧɚɤ ɫɤɨɥɶɠɟɧɢɹ. Ⱦɨɫɬɨɢɧɫɬɜɚ ɪɟɠɢɦɚ ɊɌ ɚɧɚɥɨɝɢɱɧɵ ɪɟɠɢɦɭ ɊɌ Ⱦɇȼ: 1) ɠɺɫɬɤɢɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ; 2) ɜɵɫɨɤɚɹ ɷɤɨɧɨɦɢɱɧɨɫɬɶ, ɢɡɛɵɬɨɱɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɫɟɬɶ. 3) ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɧɚɥɢɱɢɹ ɩɨɬɪɟɛɢɬɟɥɹ ɷɧɟɪɝɢɢ ɪɟɤɭɩɟɪɚɰɢɢ ɨɬɩɚɞɚɟɬ ɩɪɢ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɧɚ ɩɟɪɟɦɟɧɧɨɦ ɬɨɤɟ. ɇɟɞɨɫɬɚɬɤɨɦ ɪɟɠɢɦɚ ɊɌ ɹɜɥɹɟɬɫɹ ɩɨɬɪɟɛɥɟɧɢɟ ɢɡ ɫɟɬɢ ɪɟɚɤɬɢɜɧɨɣ ɷɧɟɪɝɢɢ ɩɪɢ ɜɨɡɜɪɚɳɟɧɢɢ ɜ ɫɟɬɶ ɚɤɬɢɜɧɨɣ ɷɧɟɪɝɢɢ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɬɨɤɨɜɚɹ ɧɚɝɪɭɡɤɚ ɫɟɬɢ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɫɧɢɠɚɟɬɫɹ; Ɉɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɨɝɪɚɧɢɱɟɧɚ ɝɪɭɡɨɩɨɞɴɟɦɧɵɦɢ ɦɟɯɚɧɢɡɦɚɦɢ (ɤɪɚɧɵ, ɥɢɮɬɵ ɢ ɬ.ɩ.) ɢ ɫɢɫɬɟɦɚɦɢ ɫ ɢɧɞɢɜɢɞɭɚɥɶɧɵɦɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹɦɢ (ɉɑ – ȺȾ). Ɍɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ (ɉȼ). Ɋɟɠɢɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ – ɬɨɪɦɨɡɧɨɣ ɪɟɠɢɦ, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɜɤɥɸɱɟɧ ɞɥɹ ɨɞɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɜɪɚɳɟɧɢɹ, ɧɨ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɢɯ ɫɢɥ ɜɪɚɳɚɟɬɫɹ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɫɬɨɪɨɧɭ. Ⱦɜɢɝɚɬɟɥɶ ɩɨɥɭɱɚɟɬ ɢɡɛɵɬɨɱɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɫ ɜɚɥɚ, ɩɪɟɨɛɪɚɡɭɟɬ ɟɟ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ. ɋɬɚɬɨɪ ɞɜɢɝɚɬɟɥɹ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɟɠɢɦɚ ɉȼ 140

ɩɨɞɤɥɸɱɟɧ ɤ ɫɟɬɢ, ɢɡ ɫɟɬɢ ɩɨɬɪɟɛɥɹɟɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɡɛɵɬɨɱɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫ ɜɚɥɚ, ɩɪɟɨɛɪɚɡɨɜɚɧɧɚɹ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ, ɢ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɢɡ ɫɟɬɢ ɪɚɫɫɟɢɜɚɸɬɫɹ ɧɚ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɇɚ ɪɢɫ. 3.67 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ. ɇɚ ɪɢɫ. 3.68 ɩɨɤɚɡɚɧɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɬɢɯ ɪɟɠɢɦɨɜ. Ɋɟɠɢɦ ɉȼ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ: – ɩɪɢ ɚɤɬɢɜɧɨɦ ɫɬɚɬɢɱɟɫɤɨɦ ɦɨɦɟɧɬɟ Ɇɋ ɩɭɬɟɦ ɭɜɟɥɢɱɟɧɢɹ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɢ ɪɨɬɨɪɚ ɞɨ ɡɧɚɱɟɧɢɹ R1ȾɈȻ+R2ȾɈȻ+RɉȼȾɈȻ, ɤɨɝɞɚ ɦɨɦɟɧɬ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɆɄɁ ɫɬɚɧɟɬ ɦɟɧɶɲɟ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇɋ (ɆɄɁ < Ɇɋ) – ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ 2; – ɞɥɹ ɨɫɬɚɧɨɜɤɢ ɞɜɢɝɚɬɟɥɹ ɩɨ ɨɤɨɧɱɚɧɢɢ ɞɜɢɠɟɧɢɹ ɜ ɨɞɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɪɟɜɟɪɫɢɪɭɟɬɫɹ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪɟ (Ʉȼ – ɨɬɤɥɸɱɚɟɬɫɹ, Ʉɇ – ɜɤɥɸɱɚɟɬɫɹ), ɚ ɜ ɰɟɩɶ ɪɨɬɨɪɚ ɜɜɨɞɹɬɫɹ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R1ȾɈȻ+R2ȾɈȻ+RɉȼȾɈȻ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɷɬɢɯ ɩɟɪɟɤɥɸɱɟɧɢɣ ɞɜɢɝɚɬɟɥɶ ɢɡ ɬɨɱɤɢ 1 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɩɟɪɟɯɨɞɢɬ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ 3 ɪɟɠɢɦɚ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɢ ɫɧɢɠɚɟɬ ɫɤɨɪɨɫɬɶ ɞɨ ɨɫɬɚɧɨɜɤɢ ɜ ɬɨɱɤɟ 4. ȼ ɬɨɱɤɟ 4 ɫɥɟɞɭɟɬ ɨɬɤɥɸɱɢɬɶ ɞɜɢɝɚɬɟɥɶ ɨɬ ɫɟɬɢ (ɤɨɧɬɚɤɬɨɪɚɦɢ Ʉɇ ɢ ɄɅ) ɜɨ ɢɡɛɟɠɚɧɢɟ ɪɚɡɝɨɧɚ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ. ɉɪɢ ɪɟɜɟɪɫɟ ɞɜɢɝɚɬɟɥɹ ɨɬ ɬɨɱɤɢ 4 ɧɚɱɧɟɬɫɹ ɩɭɫɤ ɜ ɨɛɪɚɬɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ȼ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɪɨɬɨɪ ɜɪɚɳɚɟɬɫɹ ɩɪɨɬɢɜ ɩɨɥɹ ɫɬɚɬɨɪɚ Ȧ < 0, ɫɤɨɥɶɠɟɧɢɟ s > 1, ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɤɨɥɶɰɚɯ ɪɨɬɨɪɚ ɛɨɥɶɲɟ ȿ20, ɫɭɳɟɫɬɜɟɧɧɨ ɭɜɟɥɢɱɢɜɚɸɬɫɹ ɬɨɤɢ ɪɨɬɨɪɚ ɢ ɫɬɚɬɨɪɚ. ɍ ɞɜɢɝɚɬɟɥɹ ɫ ɮɚɡɧɵɦ ɪɨɬɨɪɨɦ ɬɨɤɢ ɨɝɪɚɧɢɱɢɜɚɸɬ ɜɜɟɞɟɧɢɟɦ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɶ ɪɨɬɨɪɚ, ɜɵɧɨɫɹ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɢɡ ɞɜɢɝɚɬɟɥɹ ɢ ɨɛɟɫɩɟɱɢɜɚɹ ɧɟɨɛɯɨɞɢɦɵɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɪɟɠɢɦɵ ɪɚɛɨɬɵ. ɍ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɨɝɨ ȺȾ ɬɨɤɢ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɨɝɪɚɧɢɱɢɜɚɸɬɫɹ, ɱɬɨ ɜɵɡɵɜɚɟɬ ɡɧɚɱɢɬɟɥɶɧɵɟ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɞɜɢɝɚɬɟɥɟ ɢ ɟɝɨ ɧɚɝɪɟɜ. ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɢ ɧɟ ɢɡɦɟɧɹɟɬɫɹ (3.61), ɥɢɲɶ ɢɡɦɟɧɹɟɬɫɹ ɡɧɚɱɟɧɢɟ ɫɤɨɥɶɠɟɧɢɹ. ɉɪɢ ɪɟɜɟɪɫɟ ɢɡɦɟɧɹɟɬɫɹ ɡɧɚɤ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ0ɇ. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɪɟɠɢɦɚ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 3.73, ɢɡ ɤɨɬɨɪɨɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ ɦɨɳɧɨɫɬɶ ɩɨɬɪɟɛɥɹɟɬɫɹ ɢɡ ɫɟɬɢ ɢ ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɢ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɪɨɬɨɪɧɨɣ ɰɟɩɢ.

ɊɗɆ=Ɋɋ–ǻɊ1

ɊɆȿɏ= ɊɗɆǜ(1–s)

Ɋɋ=3ǜU1ǜI1ǜcosĳ1

Ɋȼ=ɆȼǜȦ

ǻɊ2=ɊɗɆǜs+ɊɆȿɏ ǻɊɆȿɏ=Ɋȼ–ɊɆȿɏ

ǻɊ1=3ǜI12ǜr1 ǻɊ1ɉɈɋɌ=3ǜI12ǜrμ ǻɊ2ȾɈȻ=3ǜI22ǜR2ȾɈȻ

ǻɊ2=3ǜI22ǜr2

Ɋɢɫ. 3.73. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɪɟɠɢɦɚ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ȺȾ 141

Ⱦɨɫɬɨɢɧɫɬɜɚ ɪɟɠɢɦɚ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ (ɢɧɬɟɧɫɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ ɞɨ ɩɨɥɧɨɣ ɨɫɬɚɧɨɜɤɢ, ɩɪɨɫɬɨɬɚ ɨɫɭɳɟɫɬɜɥɟɧɢɹ) ɢ ɟɝɨ ɧɟɞɨɫɬɚɬɤɢ (ɧɟɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɚɹ ɷɧɟɪɝɟɬɢɤɚ, ɦɹɝɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɨɬɤɥɸɱɟɧɢɹ ɩɪɢɜɨɞɚ ɩɪɢ ɫɤɨɪɨɫɬɢ, ɛɥɢɡɤɨɣ ɤ ɧɭɥɸ) ɨɩɪɟɞɟɥɹɸɬ ɨɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɪɟɠɢɦɚ. Ɉɧɚ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɧɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ, ɝɞɟ ɩɨɬɟɪɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɜɟɥɢɤɢ, ɚ ɩɪɨɫɬɨɬɚ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɪɟɠɢɦɚ ɢɦɟɟɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ. Ɋɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (ȾɌ). Ɋɟɠɢɦɨɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɧɚɡɵɜɚɸɬ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɢɡɛɵɬɨɱɧɭɸ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɪɚɫɫɟɢɜɚɟɬ ɧɚ ɨɬɞɟɥɶɧɨ ɜɤɥɸɱɺɧɧɵɣ ɪɟɡɢɫɬɨɪ. ɉɪɢ ɷɬɨɦ ɨɛɦɨɬɤɚ ɫɬɚɬɨɪɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɨɬɨɤ ɜ ɦɚɲɢɧɟ, ɚ ɪɨɬɨɪɧɵɟ ɨɛɦɨɬɤɢ ɡɚɦɵɤɚɸɬɫɹ ɧɚ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ. Ⱦɥɹ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɪɚɡɪɚɛɨɬɚɧɨ ɧɟɫɤɨɥɶɤɨ ɜɚɪɢɚɧɬɨɜ ɫɯɟɦ. ɂɯ ɨɫɧɨɜɧɨɟ ɨɬɥɢɱɢɟ – ɨɛɟɫɩɟɱɟɧɢɟ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɢɥɢ ɫɨɡɞɚɧɢɟ ɭɫɥɨɜɢɣ ɞɥɹ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɞɜɢɝɚɬɟɥɹ. ɇɚ ɪɢɫ. 3.74 ɩɪɢɜɟɞɟɧɵ ɧɟɤɨɬɨɪɵɟ ɢɡ ɧɢɯ. ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦɢ ɹɜɥɹɸɬɫɹ ɫɯɟɦɵ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ, ɤɨɝɞɚ ɨɛɦɨɬɤɢ ɫɬɚɬɨɪɚ ɩɨɞɤɥɸɱɚɸɬɫɹ ɤ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ: – ɤ ɫɟɬɢ ɱɟɪɟɡ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ RȾɌ (ɫɯɟɦɚ ɚ); – ɱɟɪɟɡ ɩɨɧɢɠɚɸɳɢɣ ɬɪɚɧɫɮɨɪɦɚɬɨɪ TV ɢ ɜɵɩɪɹɦɢɬɟɥɶ VT (ɫɯɟɦɚ ɛ). ȼ ɫɯɟɦɚɯ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɨɬɨɤ ɨɫɬɚɬɨɱɧɨɝɨ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɫ ɩɨɫɥɟɞɭɸɳɢɦ ɪɨɫɬɨɦ ɩɨɬɨɤɚ ɡɚ ɫɱɟɬ ɩɨɞɤɥɸɱɟɧɢɹ ɗȾɋ ɪɨɬɨɪɚ ɤ ɨɛɦɨɬɤɚɦ ɫɬɚɬɨɪɚ (ɫɯɟɦɚ ɜ) ɢɥɢ ɡɚ ɫɱɟɬ ɫɨɡɞɚɧɢɹ ɤɨɥɟɛɚɬɟɥɶɧɨɝɨ ɤɨɧɬɭɪɚ ɢɧɞɭɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɨɛɦɨɬɨɤ ɫ ɩɨɞɤɥɸɱɟɧɧɵɦɢ ɤ ɨɛɦɨɬɤɚɦ ɫɬɚɬɨɪɚ ɟɦɤɨɫɬɹɦɢ ɋ. Ɋɚɫɫɦɨɬɪɢɦ ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ (ɫɯɟɦɵ ɚ, ɛ). ɉɨ ɨɛɦɨɬɤɚɦ ɫɬɚɬɨɪɚ ɩɪɨɬɟɤɚɟɬ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ, ɫɨɡɞɚɜɚɹ ɧɟɩɨɞɜɢɠɧɨɟ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. ȼ ɨɛɦɨɬɤɟ ɪɨɬɨɪɚ ɧɚɜɨɞɢɬɫɹ ɗȾɋ, ɚɦɩɥɢɬɭɞɚ ɢ ɱɚɫɬɨɬɚ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɪɨɬɨɪɚ. ȼ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɨɦ ɪɨɬɨɪɟ (ɩɪɢ ɡɚɦɵɤɚɧɢɢ ɮɚɡɧɨɝɨ ɪɨɬɨɪɚ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ) ɩɪɨɬɟɤɚɟɬ ɬɨɤ, ɨɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɤɨɬɨɪɨɝɨ ɫ ɩɨɬɨɤɨɦ ɫɨɡɞɚɟɬɫɹ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɝɨ ɦɨɦɟɧɬɚ Ɇ ɢ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇɋ ɫɤɨɪɨɫɬɶ ɪɨɬɨɪɚ ɫɧɢɠɚɟɬɫɹ, ɭɦɟɧɶɲɚɟɬɫɹ ɗȾɋ, ɚ ɜɦɟɫɬɟ ɫ ɧɟɣ – ɬɨɤ ɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ. ɉɪɢ Ȧ = 0 ɗȾɋ, ɬɨɤ ɪɨɬɨɪɚ ɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɨɬɫɭɬɫɬɜɭɸɬ. ɋɯɟɦɵ ɩɨɞɤɥɸɱɟɧɢɹ ɢɫɬɨɱɧɢɤɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɤ ɨɛɦɨɬɤɚɦ ɫɬɚɬɨɪɚ, ɫɨɟɞɢɧɟɧɧɵɯ ɜ ɡɜɟɡɞɭ ɢ ɬɪɟɭɝɨɥɶɧɢɤ, ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 3.75. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɫɯɟɦ, ɫɢɦɦɟɬɪɢɱɧɨ ɩɨɞɤɥɸɱɢɬɶ ɨɛɦɨɬɤɢ ɛɟɡ ɪɚɡɪɵɜɚ ɧɭɥɟɜɨɣ ɬɨɱɤɢ ɧɟ ɭɞɚɟɬɫɹ. Ⱦɪɭɝɚɹ ɡɚɞɚɱɚ – ɤɚɤ ɪɚɫɫɱɢɬɚɬɶ ɦɚɝɧɢɬɨɞɜɢɠɭɳɭɸ ɫɢɥɭ Fɉ, ɫɨɡɞɚɜɚɟɦɭɸ ɩɨɫɬɨɹɧɧɵɦ ɬɨɤɨɦ, ɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ, ɫɨɡɞɚɜɚɟɦɵɣ ɜ ɬɚɤɢɯ ɫɯɟɦɚɯ ɜɤɥɸɱɟɧɢɹ. ɉɪɢ ɪɚɫɱɟɬɚɯ ɡɚɦɟɧɹɸɬ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ ɨɛɦɨɬɨɤ Iɉ cɬɚɬɨɪɚ ɷɤɜɢɜɚɥɟɧɬɧɵɦ ɬɪɟɯɮɚɡɧɵɦ ɬɨɤɨɦ I1 ɢɡ ɭɫɥɨɜɢɹ ɪɚɜɟɧɫɬɜɚ ɆȾɋ ɩɨɫɬɨɹɧɧɨɝɨ Fɉ ɢ ɩɟɪɟɦɟɧɧɨɝɨ F~ ɬɨɤɨɜ. Ɋɟɡɭɥɶɬɢɪɭɸɳɚɹ ɆȾɋ ɬɪɟɯɮɚɡɧɨɝɨ ɬɨɤɚ 3 F~ = 2 I1 w 1 . 2 ɆȾɋ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɞɥɹ ɫɨɟɞɢɧɟɧɢɹ ɨɛɦɨɬɨɤ ɜ ɡɜɟɡɞɭ Fɉ 3 Iɉ w 1 .

142

ɂɡ ɭɫɥɨɜɢɹ ɪɚɜɟɧɫɬɜɚ ɆȾɋ ɩɨɥɭɱɚɟɦ ɞɟɣɫɬɜɭɸɳɟɟ ɡɧɚɱɟɧɢɟ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ: I1

2 Iɉ 3

k ɋɏ Iɉ .

(3.90)

Ʉɨɷɮɮɢɰɢɟɧɬ ɫɯɟɦɵ kɋɏ ɡɚɜɢɫɢɬ ɨɬ ɫɯɟɦɵ ɩɨɞɤɥɸɱɟɧɢɹ ɨɛɦɨɬɨɤ ɤ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. Ⱦɥɹ ɩɪɢɜɟɞɟɧɧɨɝɨ ɜɵɲɟ ɪɚɫɱɟɬɚ ɞɥɹ ɫɨɟɞɢɧɟɧɢɹ ɨɛɦɨɬɨɤ ɜ ɡɜɟɡɞɭ kɋɏ = 0,816, ɞɥɹ ɫɨɟɞɢɧɟɧɢɹ ɨɛɦɨɬɨɤ ɜ ɬɪɟɭɝɨɥɶɧɢɤ (ɫɦɨɬɪɢ ɪɢɫ. 3.75) kɋɏ = 0,47.

~

+

~

–

~ TV

ɄȾ

ɄɅ

ɄɅ

ɄȾ

RȾɌ

VT Ɇ

ɚ

Ɇ ɛ

~ ~ ɄɅ ɄɅ

ɄȾ

Ɇ Ɇ

ɄȾ

ɋ ɝ

R2ȾɈȻ

Ɋɢɫ. 3.74. ɋɯɟɦɵ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ȺȾ: ɚ – ɨɬ ɫɟɬɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ; ɛ – ɫ ɜɵɩɪɹɦɢɬɟɥɟɦ; ɜ – ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ; ɝ – ɫ ɤɨɧɞɟɧɫɚɬɨɪɚɦɢ ȼ

ɜ 143

ɉɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ ɩɨɡɜɨɥɹɟɬ ɩɪɢɦɟɧɢɬɶ ɞɥɹ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ȺȾ ɜ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɨɬɪɚɛɨɬɚɧɧɭɸ ɜɵɲɟ ɦɟɬɨɞɢɤɭ ɪɚɫɱɟɬɚ ɞɥɹ ɫɢɦɦɟɬɪɢɱɧɵɯ ɰɟɩɟɣ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ. + Iɉ

Iɉ w1

3 Iɉ w 1

Iɉǜw1 – 2 Iɉ w 1 3

+

1 Iɉ w1 3

Iɉ

Iɉǜw1 1 Iɉ w1 3

– Ɋɢɫ. 3.75. ɋɯɟɦɵ ɩɨɞɤɥɸɱɟɧɢɹ ɨɛɦɨɬɨɤ ɫɬɚɬɨɪɚ ɩɪɢ ɧɟɡɚɜɢɫɢɦɨɦ ɩɢɬɚɧɢɢ Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫɬɚɧɨɜɢɬɫɹ ɱɚɫɬɧɵɦ ɫɥɭɱɚɟɦ ɩɢɬɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɩɪɢ ɱɚɫɬɨɬɟ ɬɨɤɚ f1 = 0, ɤɨɝɞɚ ɫɢɧɯɪɨɧɧɚɹ ɫɤɨɪɨɫɬɶ Ȧ0 = 0, ɚ ɚɛɫɨɥɸɬɧɨɟ ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ r2c ĮsɄɌ r , (3.91) xc2 xμ ɢ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ MKT

3 I12 x P2 2 Ȧ0H ( xc2 x P )

(3.92)

ɨɫɬɚɸɬɫɹ ɩɨɫɬɨɹɧɧɵɦɢ. Ɋɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜɵɩɨɥɧɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ M

2 MɄɌ , ĮsɄɌ Įs ĮsɄɌ Įs

(3.93)

Į Ȧ 0H Ȧ Ȧ . Ȧ 0H Ȧ 0H ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ I1 = const ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ: – ɬɨɤ ɪɨɬɨɪɚ ɝɞɟ ɫɤɨɥɶɠɟɧɢɟ Įs

144

I1 xμ

Ic2

rc

2

/ Įs xc2 xμ

2

;

2

(3.94)

– ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Iμ

I1

rc

2

rc

2

2

/ Įs xc2

2

2

/ Įs xc2 xμ

2

.

(3.95)

ɇɚ ɪɢɫ. 3.76 ɩɨɫɬɪɨɟɧɵ ɦɟɯɚɧɢɱɟɫɤɚɹ Ȧ(Ɇ) ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ Ȧ(I1), Ȧ(Ic2), Ȧ(Iμ) ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɜ Ȧ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. Iμ ɉɪɢ Įs = 0 ɬɨɤ ɫɬɚɬɨɪɚ ɪɚɜɟɧ ɬɨɤɭ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ I1 = Iμ, Ic2 ɚ ɬɨɤ ɪɨɬɨɪɚ ɪɚɜɟɧ ɧɭɥɸ Ic2 = 0. ɉɪɢ ɪɨɫɬɟ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ M ɪɚɫɬɭɬ ɫɤɨɥɶɠɟɧɢɟ Įs, ɗȾɋ ɪɨȦɄɌ ɬɨɪɚ ȿc2 ɢ ɬɨɤ ɪɨɬɨɪɚ Ic2. Ɍɨɤ Ec2 ɫɬɚɬɨɪɚ I1 = const. ɋ ɪɨɫɬɨɦ ɬɨI, Ec2, M ɤɚ ɪɨɬɨɪɚ ɭɦɟɧɶɲɚɟɬɫɹ ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ, ɤ ɧɭɥɸ ɫɬɪɟɦɢɬɆɄɌ I1 ɫɹ ɢ ɩɨɬɨɤ ɦɚɲɢɧɵ, ɚ ɫɥɟɞɨɜɚɊɢɫ. 3.76. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɬɟɥɶɧɨ, ɢ ɪɚɡɜɢɜɚɟɦɵɣ ɟɸ ɦɨɜ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɦɟɧɬ. Ɇɚɤɫɢɦɚɥɶɧɵɣ ɦɨɦɟɧɬ ɆɄɌ ɡɚɜɢɫɢɬ ɨɬ ɤɜɚɞɪɚɬɚ ɷɤɜɢ2 ɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ I1 (3.83), ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɨɬ ɤɜɚɞɪɚɬɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɜ ɰɟɩɢ ɫɬɚɬɨɪɚ. Ʉɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ ĮsɄɌ (ɫɤɨɪɨɫɬɶ ȦɄɌ) ɡɚɜɢɫɢɬ ɨɬ ɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɢ ɪɨɬɨɪɚ rc2. ɉɪɢ ɜɜɟɞɟɧɢɢ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɶ ɪɨɬɨɪɚ R2ȾɈȻ ɤɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ, ɚ ɫɤɨɪɨɫɬɶ ȦɄɌ ɭɜɟɥɢɱɢɜɚɟɬɫɹ. ɀɟɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ǻM 2 MKT ȕ ǻȦ Ȧ0H ĮsKT ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɜɚɞɪɚɬɭ ɬɨɤɚ ɫɬɚɬɨɪɚ ɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɩɪɢ ɟɝɨ ɪɨɫɬɟ, ɢ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɸ ɰɟɩɢ ɪɨɬɨɪɚ, ɫɧɢɠɚɹɫɶ ɩɪɢ ɜɜɟɞɟɧɢɢ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ. ɉɪɢ ɪɚɫɱɟɬɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɜɢɝɚɬɟɥɹ ɜ ɪɟɠɢɦɟ ȾɌ: – ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɤɪɢɜɭɸ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɦɚɲɢɧɵ, ɬɚɤ ɤɚɤ ɬɨɤ Iμ ɢ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɯμ ɢɡɦɟɧɹɸɬɫɹ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ (ɜɨɡɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɭɧɢɜɟɪɫɚɥɶɧɨɣ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɥɹ ɦɚɲɢɧ ɞɚɧɧɨɣ ɫɟɪɢɢ). ȿɫɥɢ ɭɫɬɪɚɢɜɚɟɬ ɬɨɱɧɨɫɬɶ ɪɚɫɱɟɬɨɜ, ɬɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɯμ = const; – ɡɚɞɚɸɬɫɹ ɆɄɌ (ɩɨ ɬɪɟɛɨɜɚɧɢɹɦ ɬɟɯɧɨɥɨɝɢɢ ɢɡɜɟɫɬɧɵ ɞɨɩɭɫɬɢɦɨɟ ɭɫɤɨɪɟɧɢɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɢɥɢ ɦɢɧɢɦɚɥɶɧɨɟ ɜɪɟɦɹ ɬɨɪɦɨɠɟɧɢɹ);

145

– ɩɨ ɮɨɪɦɭɥɟ (3.90) ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɷɤɜɢɜɚɥɟɧɬɧɵɣ ɬɨɤ I1, ɩɪɢ ɷɬɨɦ ɟɝɨ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɧɟ ɞɨɥɠɧɨ ɩɪɟɜɵɲɚɬɶ 4ǜI1ɇ ɢɡ-ɡɚ ɡɧɚɱɢɬɟɥɶɧɨɝɨ ɧɚɫɵɳɟɧɢɹ ɦɚɲɢɧɵ; – ɡɚɞɚɸɬɫɹ ɤɪɢɬɢɱɟɫɤɢɦ ɫɤɨɥɶɠɟɧɢɟɦ ĮsɄɌ = 0,3…0,5 ɢɡ ɭɫɥɨɜɢɹ ɩɨɥɭɱɟɧɢɹ ɦɚɤɫɢɦɚɥɶɧɨɣ ɩɥɨɳɚɞɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (ɨɧɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɦɨɳɧɨɫɬɢ); – ɩɨ ɮɨɪɦɭɥɟ (3.91) ɪɚɫɫɱɢɬɵɜɚɸɬ ɜɟɥɢɱɢɧɭ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɢ ɪɨɬɨɪɚ, ɩɪɢ ɷɬɨɦ ɜɵɛɢɪɚɸɬ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R2ȾɈȻ ɢɡ ɩɭɫɤɨɜɵɯ ɪɟɡɢɫɬɨɪɨɜ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɩɭɫɤ ɞɜɢɝɚɬɟɥɹ ɢ ɭɬɨɱɧɹɸɬ ĮsɄɌ; – ɩɪɢ ɪɚɫɫɱɢɬɚɧɧɵɯ ĮsɄɌ ɢ ɆɄɌ ɜɵɩɨɥɧɹɸɬ ɪɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɨ ɮɨɪɦɭɥɚɦ (3.93), (3.94). Ⱦɥɹ ɪɚɫɱɟɬɚ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɝɨɬɨɜɵɟ ɩɪɨɝɪɚɦɦɵ ɪɚɫɱɟɬɚ, ɩɨɹɜɢɜɲɢɟɫɹ ɜ ɩɨɫɥɟɞɧɟɟ ɜɪɟɦɹ, ɥɢɛɨ ɫɨɫɬɚɜɢɬɶ ɫɜɨɸ ɩɪɨɝɪɚɦɦɭ, ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ Matlab ɢɥɢ Mathcad. 3.5.11. Ɋɚɫɱɟɬ ɫɯɟɦ ɜɤɥɸɱɟɧɢɹ ȺȾ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɪɚɛɨɬɭ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ

Ɉɛɟɫɩɟɱɟɧɢɟ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɫ ɡɚɞɚɧɧɨɣ ɬɟɯɧɨɥɨɝɚɦɢ ɫɤɨɪɨɫɬɶɸ ȦɁȺȾ ɩɪɢ ɡɚɞɚɧɧɨɣ ɜɟɥɢɱɢɧɟ ɦɨɦɟɧɬɚ ɆɁȺȾ ɪɟɲɚɟɬɫɹ ɞɥɹ ȺȾ ɜɜɟɞɟɧɢɟɦ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɢ ɪɨɬɨɪɚ ɢ ɫɬɚɬɨɪɚ, ɩɪɢɦɟɧɟɧɢɟɦ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɣ ɱɚɫɬɨɬɵ ɢ ɧɚɩɪɹɠɟɧɢɹ. Ⱦɥɹ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɩɟɪɟɯɨɞ ɨɬ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ ɆɁȺȾ ɤ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɦɭ ɦɨɦɟɧɬɭ ɞɜɢɝɚɬɟɥɹ Ɇ ɭɫɥɨɠɧɹɟɬɫɹ ɨɬɫɭɬɫɬɜɢɟɦ ɞɨɫɬɭɩɧɨɣ ɞɨɤɭɦɟɧɬɚɰɢɢ ɞɥɹ ɪɚɫɱɟɬɚ ɩɨɬɟɪɶ ɦɨɦɟɧɬɚ ǻɆɏɏ ɞɜɢɝɚɬɟɥɹ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ. ȼ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɩɪɢɯɨɞɢɬɫɹ ɩɪɢɧɢɦɚɬɶ ǻɆɏɏ = 0, ɆɗɆ ɁȺȾ = Ɇɋ = ɆɁȺȾ. ɉɨ ɡɚɞɚɧɧɨɦɭ ɦɨɦɟɧɬɭ ɆɁȺȾ ɢ ɡɚɞɚɧɧɨɣ ɫɤɨɪɨɫɬɢ ȦɁȺȾ ɬɪɟɛɭɟɬɫɹ ɜɵɛɪɚɬɶ ɫɯɟɦɭ ɜɤɥɸɱɟɧɢɹ, ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɭɸ ɞɥɹ ɡɚɞɚɧɧɨɝɨ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɢ ɪɚɫɫɱɢɬɚɬɶ ɢɥɢ ɧɚɩɪɹɠɟɧɢɟ U1, ɢɥɢ ɱɚɫɬɨɬɭ f1, ɢɥɢ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R2ȾɈȻ, ɏ2ȾɈȻ, ɏ1ȾɈȻ ,R1ȾɈȻ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɪɚɛɨɬɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. Ʉɪɨɦɟ ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɨɛɵɱɧɨ ɪɚɫɫɱɢɬɵɜɚɸɬ ɦɟɯɚɧɢɱɟɫɤɭɸ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɩɪɨɯɨɞɹɳɢɟ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ, ɄɉȾ ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ. ɉɪɢɦɟɪ 3.10. Ɋɚɫɫɱɢɬɚɬɶ ɜɟɥɢɱɢɧɭ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɢ ɪɨɬɨɪɚ R2ȾɈȻ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 4AK200M8ɍ3 (ɫɦ. ɩɪɢɦɟɪ 3.7), ɨɛɟɫɩɟɱɢɜɚɸɳɟɝɨ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: MɁȺȾ = ± 0,8, ȦɁȺȾ = 0,4. Ɋɚɫɫɱɢɬɚɬɶ ɢ ɩɨɫɬɪɨɢɬɶ ɦɟɯɚɧɢɱɟɫɤɢɟ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɩɪɨɯɨɞɹɳɢɟ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɢ. Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ ɢ ɪɚɫɫɱɢɬɚɬɶ ɤɩɞ ɢ cosĳ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɩɨɫɬɚɜɥɟɧɧɨɣ ɡɚɞɚɱɢ ɢɫɩɨɥɶɡɭɟɦ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɰɟɩɢ ɪɨɬɨɪɚ R2 ɢ ɫɤɨɥɶɠɟɧɢɟɦ s, ɫɩɪɚɜɟɞɥɢɜɭɸ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ r2 R2 . sȿɋɌ sɂɋɄ Ɋɚɫɱɟɬ ɞɥɹ ɬɨɱɤɢ MɁȺȾ = 0,8, ȦɁȺȾ = 0,4, ɪɟɠɢɦ ɪɚɛɨɬɵ – ɞɜɢɝɚɬɟɥɶɧɵɣ. 146

ɋɯɟɦɚ ɪɚɫɱɟɬɚ: – ɩɨ ɡɚɞɚɧɧɨɣ ɜɟɥɢɱɢɧɟ ɆɁȺȾ ɧɚɯɨɞɢɦ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɢ ɨɩɪɟɞɟɥɹɟɦ sȿɋɌ = ¨ȦȿɋɌ / Ȧ0; ǻȦȿɋɌ = sȿɋɌ = sɇ, ¨ȦȿɋɌ = Ȧ0 – ȦȿɋɌ ɆɁȺȾ = 0,035·0,8 = 0,028; – ɡɧɚɱɟɧɢɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R2ȾɈȻ ɪɚɫɫɱɢɬɵɜɚɟɦ ɩɨ ɮɨɪɦɭɥɟ: s 0,6 0,268 0,268 = 5,475 Ɉɦ, R 2 ȾɈȻ = R 2 r2 = ɂɋɄ r2 r2 = sȿɋɌ 0,028 ɝɞɟ r2 = 0,268 Ɉɦ. ȼɵɪɚɠɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɩɪɨɯɨɞɹɳɢɯ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ, ɩɨɥɭɱɢɦ, ɩɨɞɫɬɚɜɥɹɹ ɜ ɮɨɪɦɭɥɵ Ʉɥɨɫɫɚ (3.62) ɢ ɒɭɛɟɧɤɨ ȼ.Ⱥ. (3.69, 3.70) ɡɧɚɱɟɧɢɹ ɤɪɢɬɢɱɟɫɤɨɝɨ ɢ ɧɨɦɢɧɚɥɶɧɨɝɨ ɫɤɨɥɶɠɟɧɢɣ: sɄ 0,21 sɄɂ R2 5,734 4,5; r2 0,268 sɇɂ

sɇ R2 r2

0,035 5,734 0,268

0,75.

Ɂɧɚɱɟɧɢɹ ɬɨɤɨɜ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɩɪɢ sɂɋɄ = 0,6: I1ɁȺȾ

2 Iμ2 (I1ɧ Iμ2 )

ɆɁȺȾ s ɁȺȾ Ɇɇ sɇɂ

22,58 2 (37,8 2 22,58 2 ) I2ɁȺȾ

I2ɇ

ɆɁȺȾ sɁȺȾ Ɇɇ sɇɂ

28

0,8 198 0,6 198 0,75 0,8 198 0,6 198 0,75

33,26 Ⱥ, 22,4 Ⱥ.

Ɋɚɫɱɟɬ ɞɥɹ ɬɨɱɤɢ MɁȺȾ = – 0,8, ȦɁȺȾ = 0,4. Ɋɟɠɢɦ ɪɚɛɨɬɵ – ɬɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɚɛɨɬɵ ɜɨ ɜɬɨɪɨɦ ɤɜɚɞɪɚɧɬɟ ɧɟɨɛɯɨɞɢɦɨ ɢɡɦɟɧɢɬɶ ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɩɟɪɟɤɥɸɱɢɬɶ ɞɜɟ ɮɚɡɵ ɫɬɚɬɨɪɚ), ɩɪɢ ɷɬɨɦ Ȧ0ɇ= – 1. ǻȦȿɋɌ = sȿɋɌ = sɇ, MɁȺȾ = 0,035·0,8 = 0,028;

R 2ȾɈȻ

SɂɋɄ = Ȧ0ɇ ȦɁȺȾ = (– 1 – 0,4) / ( – 1) = 1,4. s 1,4 = R 2 r2 = ɂɋɄ r2 r2 = 0,268 0,268 13,4 0,268 = 13,13 Ɉɦ. sȿɋɌ 0,028

Ⱦɥɹ ɪɟɠɢɦɚ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ sɄɂ= 10,5; sɇɂ= 1,75. Ɂɧɚɱɟɧɢɹ ɬɨɤɨɜ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɩɪɢ sɂɋɄ = 1,4 ɪɚɜɧɵ ɪɚɫɫɱɢɬɚɧɧɵɦ ɞɥɹ ɬɨɱɤɢ sɂɋɄ = 0,6, ɬɚɤ ɤɚɤ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɦɨɦɟɧɬɚ ɨɬɧɨɲɟɧɢɟ ɫɤɨɥɶɠɟɧɢɣ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɸ ɫɨɩɪɨɬɢɜɥɟɧɢɣ. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɜɜɟɞɟɧɢɢ ɜ ɰɟɩɶ ɪɨɬɨɪɚ R2ȾɈȻ, ɩɪɨɯɨɞɹɳɢɟ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ, ɩɨɫɬɪɨɟɧɵ ɜ ɩɪɨɝɪɚɦɦɟ «harad» ɢ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3.77. Ɂɧɚɱɟɧɢɹ ɬɨɤɨɜ ɜ ɨɬɦɟɱɟɧɧɵɯ ɬɨɱɤɚɯ ɪɚɜɧɵ ɪɚɫɫɱɢɬɚɧɧɵɦ ɜɵɲɟ ɡɧɚɱɟɧɢɹɦ.

147

Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ ɞɜɢɝɚɬɟɥɹ sɂɋɄ = 0,6: ɆɁȺȾ ȦɁȺȾ PɉɈɅ ȘɁȺȾ ɊɁȺɌɊ ɆɁȺȾ ȦɁȺȾ 3 I12ɁȺȾ r1 3 I22ɁȺȾ r2

ɜ

ɡɚɞɚɧɧɨɣ

0,8 198 0,4 78,5 0,8 198 0,4 78,5 3 33,26 2 0,22 3 22,4 2 5,743

ɬɨɱɤɟ

4973,76 14348,7

ɩɪɢ

0,347.

ȼ ɩɪɢɜɟɞɟɧɧɨɦ ɪɚɫɱɟɬɟ ɧɟ ɭɱɬɟɧɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɞɜɢɝɚɬɟɥɟ, ɤɨɬɨɪɵɟ ɬɪɚɞɢɰɢɨɧɧɨ ɨɬɧɨɫɹɬ ɤ ɩɨɬɟɪɹɦ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. Ʉɪɨɦɟ ɬɨɝɨ, ɧɟ ɭɱɬɟɧɵ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɤɨɧɬɭɪɟ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ, ɬ.ɤ. ɚɤɬɢɜɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɤɨɧɬɭɪɚ ɜ ɪɚɫɱɟɬɚɯ ɨɛɵɱɧɨ ɩɪɟɧɟɛɪɟɝɚɸɬ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɡɚɬɪɚɱɟɧɧɚɹ ɦɨɳɧɨɫɬɶ ɊɁȺɌɊ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɚɤɬɢɜɧɭɸ ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɭɸ ɢɡ ɫɟɬɢ. Ʉɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɊɁȺɌɊ 14348,7 cosĳ ɁȺȾ 0,654. 3 U1Ɏ I1ɁȺȾ 3 220 33,26 Ɇɟɯɚɧɢɱɟɫɤɢɟ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɟɠɢɦɚ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɝɨ ɪɚɛɨɬɭ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ, ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3.77.

Ɋɢɫ. 3.77. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ, ɩɪɨɯɨɞɹɳɢɟ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ, ɩɪɢ ɜɜɟɞɟɧɢɢ R2ȾɈȻ ɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ ȼ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɪɟɠɢɦɟ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ, ɢɡɛɵɬɨɱɧɚɹ ɷɧɟɪɝɢɹ ɫ ɜɚɥɚ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɧɚɝɪɟɜ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɢ ɪɨɬɨɪɚ. Ʉɪɨɦɟ ɬɨɝɨ, ɦɨɳɧɨɫɬɶ ɩɨɬɪɟɛɥɹɟɬɫɹ ɢ ɢɡ ɫɟɬɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜ ɫɟɬɶ ɧɟ ɜɨɡɜɪɚɳɚɟɬɫɹ, ɢ ɩɨɥɟɡɧɚɹ ɪɚɛɨɬɚ ɜ ɷɬɨɦ ɪɟɠɢɦɟ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɩɢɬɚɸɳɟɣ ɫɟɬɢ ɪɚɜɧɚ ɧɭɥɸ. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ Ș ɞɜɢɝɚɬɟɥɹ ɜ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɪɚɜɟɧ ɧɭɥɸ. 148

Ʉɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ sɂɋɄ = 1,4 3 I12 r1 3 I22 r2 3 I22 R 2ȾɈȻ ɆɁȺȾ ȦɁȺȾ Ɋɋ cos ĳɁȺȾ 3 U1Ɏ I1ɁȺȾ 3 U1Ɏ I1ɁȺȾ 3 33,26 2 0,22 3 22,4 2 0,268 3 22,4 2 13,13 0,8 198 1,4 78,5 3 220 33,26

0,159.

ɉɪɢɦɟɪ 3.11. Ɋɚɫɫɱɢɬɚɬɶ ɱɚɫɬɨɬɭ ɢ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪɟ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 4AK200M8ɍ3 (ɫɦ. ɩɪɢɦɟɪ 3.7), ɨɛɟɫɩɟɱɢɜɚɸɳɟɝɨ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: MɁȺȾ = 0,8, ȦɁȺȾ = 0,4. Ɋɚɫɫɱɢɬɚɬɶ ɦɟɯɚɧɢɱɟɫɤɢɟ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɩɪɨɯɨɞɹɳɢɟ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ. Ɋɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ – ɞɜɢɝɚɬɟɥɶɧɵɣ. Ⱦɜɢɝɚɬɟɥɶ ɩɨɥɭɱɚɟɬ ɩɢɬɚɧɢɟ ɨɬ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɱɚɫɬɨɬɵ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɝɨ ɧɟɡɚɜɢɫɢɦɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɱɚɫɬɨɬɵ ɢ ɚɦɩɥɢɬɭɞɵ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɬɚɬɨɪɟ. Ⱦɥɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ ɪɚɫɱɟɬɚ ɱɚɫɬɨɬɵ ɜɵɩɨɥɧɢɦ ɩɚɪɚɥɥɟɥɶɧɵɣ ɩɟɪɟɧɨɫ ɟɫɬɟɫɬɜɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ Ȧ0 ȦɁȺȾ ǻȦȿɋɌ ȦɁȺȾ sɇ ɆɁȺȾ .

Ɉɬɧɨɫɢɬɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɱɚɫɬɨɬɵ ɪɚɜɧɨ Į = Ȧ0 = 0,428. ɂɫɩɨɥɶɡɭɹ ɬɢɩɨɜɨɟ ɨɬɧɨɲɟɧɢɟ U1ɇ / fɇ = 4,4 , ɜɵɛɢɪɚɟɦ U1ɁȺȾ= 4,4·D·f1ɇ= 4,4·0,428·50 = 94,16 ȼ. f1ɁȺȾ = D·f1ɇ = 0,428·50 = 21,4 Ƚɰ. Ⱦɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɪɚɫɱɟɬɚ ɫɥɟɞɭɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɨɝɪɚɦɦɭ «harad», ɭɱɢɬɵɜɚɸɳɭɸ ɢɡɦɟɧɟɧɢɟ ɢɧɞɭɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɯμ (ɤɪɢɜɭɸ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ). ȿɫɥɢ ɞɜɢɝɚɬɟɥɶ ɧɟ ɩɨɩɚɥ ɜ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ, ɨɩɪɟɞɟɥɹɸɬ ɪɚɡɧɢɰɭ ɦɟɠɞɭ ɡɚɞɚɧɧɨɣ ɢ ɪɚɫɫɱɢɬɚɧɧɨɣ ɫɤɨɪɨɫɬɹɦɢ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ 'Ȧ = 0,2 ɪɚɞ/ɫ, 'Ȧ = 0,00255), ɧɚ ɷɬɭ ɜɟɥɢɱɢɧɭ ɢɡɦɟɧɹɸɬ ɱɚɫɬɨɬɭ (D = 0,428 + 0,00255 = 0,4305, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ f1 = 21,53 Ƚɰ), ɧɚɩɪɹɠɟɧɢɟ U1 ɢ ɩɨɜɬɨɪɹɸɬ ɪɚɫɱɟɬ ɜ ɩɪɨɝɪɚɦɦɟ «harad». ɉɪɢ ɪɚɛɨɬɟ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ U1 = 101,67 ȼ, f1 = 21,4 Ƚɰ, ɩɪɢɜɟɞɟɧɧɨɣ ɧɚ ɪɢɫ. 3.77, ɢ ɡɚɞɚɧɧɨɦ ɦɨɦɟɧɬɟ ɆɁȺȾ = 0,8·Ɇɇ = 0,8·198 = 158,4 ɇɦ ɩɪɨɝɪɚɦɦɚ «harad» ɜɵɞɚɥɚ ɫɥɟɞɭɸɳɢɟ ɪɟɡɭɥɶɬɚɬɵ: Ȧ = 31,6 ɪɚɞ/c ( ȦɁȺȾ = 0,4·78,5 = 31,4 ɪɚɞ/ɫ ), Ɇ = 159,5 ɇɦ, I1 = 38,56 Ⱥ, I2 = 19,9 Ⱥ, IP = 31,7 Ⱥ, ȿ = 90 ȼ. Ɋɚɫɫɱɢɬɚɧɧɵɟ ɡɧɚɱɟɧɢɹ U1 ɢ f1 ɨɛɟɫɩɟɱɢɜɚɸɬ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɫ ɞɨɫɬɚɬɨɱɧɨɣ ɬɨɱɧɨɫɬɶɸ. Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ U1 / f1 = 4,75 4,4. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ ɫɥɟɞɭɟɬ ɩɪɨɞɨɥɠɢɬɶ ɪɚɫɱɟɬ ɡɚ ɫɱɟɬ ɭɜɟɥɢɱɟɧɢɹ ɱɚɫɬɨɬɵ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɭɫɬɨɣɱɢɜɨɣ ɪɚɛɨɬɵ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɭɫɬɚɧɚɜɥɢɜɚɸɬ ɡɚɩɚɫ ɩɨ ɩɟɪɟɝɪɭɡɨɱɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɆɄ 2·ɆɁȺȾ, ɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɪɚɫɱɟɬɚ ɫɥɟɞɹɬ ɡɚ ɟɝɨ ɨɛɟɫɩɟɱɟɧɢɟɦ. ɉɪɢɦɟɪ 3.12. Ɋɚɫɫɱɢɬɚɬɶ ɱɚɫɬɨɬɭ ɢ ɬɨɤ ɫɬɚɬɨɪɚ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 4AK200M8ɍ3 (ɫɦ. ɩɪɢɦɟɪ 3.7), ɨɛɟɫɩɟɱɢɜɚɸɳɟɝɨ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: MɁȺȾ = 0,8, ȦɁȺȾ = 0,4. ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ.

149

ɉɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ (ɂɌ) ɜɟɥɢɱɢɧɚ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɬɚɬɨɪɚ, ɩɨɷɬɨɦɭ ɞɥɹ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢɦɟɧɹɸɬ ɭɩɪɨɳɟɧɧɭɸ ɮɨɪɦɭɥɭ Ʉɥɨɫɫɚ, ɤɨɬɨɪɚɹ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɹɜɥɹɟɬɫɹ ɭɬɨɱɧɟɧɧɨɣ. 2 ɆɄɌ . Ɇ ĮsɄɌ Įs Įs ĮsɄɌ Ɉɞɧɚɤɨ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɹɟɬɫɹ ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ, ɢ ɞɚɠɟ ɩɪɢɛɥɢɠɟɧɧɵɣ ɪɚɫɱɟɬ ɩɪɢ ɢɡɜɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɞɜɢɝɚɬɟɥɹ ɞɚɟɬ ɛɨɥɶɲɭɸ ɩɨɝɪɟɲɧɨɫɬɶ ɜ ɨɛɟɫɩɟɱɟɧɢɢ ɪɚɛɨɬɵ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ. ɉɪɢɧɢɦɚɟɦ ɡɧɚɱɟɧɢɟ ɆɄɌ=2·ɆɁȺȾ, ɨɛɟɫɩɟɱɢɜɚɹ ɧɟɨɛɯɨɞɢɦɭɸ ɩɟɪɟɝɪɭɡɨɱɧɭɸ ɫɩɨɫɨɛɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ. Ɋɚɫɫɱɢɬɵɜɚɟɦ ɚɛɫɨɥɸɬɧɨɟ ɫɤɨɥɶɠɟɧɢɟ DsɄɌ ɩɨ ɢɡɜɟɫɬɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦ ɪɨɬɨɪɚ rc2 ɢ ɯc2 ɢ ɢɧɞɭɤɬɢɜɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɯP =ɯPɧ: DsɄɌ = rc2 / (xP + xc2) = 0,268 / (12,8+0,7) = 0,02. ɉɨɞɫɬɚɜɥɹɹ ɩɪɢɧɹɬɵɟ ɡɧɚɱɟɧɢɹ ɜ ɮɨɪɦɭɥɭ Ʉɥɨɫɫɚ, ɨɩɪɟɞɟɥɢɦ ɡɧɚɱɟɧɢɟ ɚɛɫɨɥɸɬɧɨɝɨ ɫɤɨɥɶɠɟɧɢɹ DsɁȺȾ ɩɪɢ ɡɚɞɚɧɧɨɦ ɦɨɦɟɧɬɟ ɞɜɢɝɚɬɟɥɹ P = ɆɄɌ / ɆɁȺȾ. ĮsɁȺȾ ĮsɄɌ /(μ r μ2 1) 0,02/(2 r 22 1) 0,00536. ɂɡ ɮɨɪɦɭɥɵ ɚɛɫɨɥɸɬɧɨɝɨ ɫɤɨɥɶɠɟɧɢɹ ɩɨɥɭɱɢɦ ɡɧɚɱɟɧɢɹ ɡɚɞɚɧɧɨɣ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ0ɁȺȾ, ɱɚɫɬɨɬɵ f1ɁȺȾ, ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɫɤɨɥɶɠɟɧɢɹ sɁȺȾ: Ȧ0ɁȺȾ ȦɁȺȾ ĮsɁȺȾ ; Ȧ0ɁȺȾ ĮsɁȺȾ Ȧ0ɇ ȦɁȺȾ (ĮsɁȺȾ ȦɁȺȾ ) Ȧ0ɇ Ȧ0ɇ (0,00536 0,4) 78,5

31,82 ɪɚɞ/ɫ;

f 1ɁȺȾ Į f1ɇ sɁȺȾ

Į

0,40536 50

Ȧ0ɁȺȾ ȦɁȺȾ ȦɁȺȾ

ĮsɁȺȾ ȦɁȺȾ

0,00536 0,4

0,40536.

20,27 Ƚɰ;

Į sɁȺȾ Į

0,00536 0,40536

0,013.

ɇɚɯɨɞɢɦ ɬɨɤ ɫɬɚɬɨɪɚ I1 ɢɡ ɮɨɪɦɭɥɵ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇɤɬ ɩɪɢ ɯP=ɯPɧ, ɬɚɤ ɤɚɤ ɡɧɚɱɟɧɢɟ ɯP ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɩɨɤɚ ɧɟ ɨɩɪɟɞɟɥɟɧɨ. 2 MɄɌ Ȧ0ɇ (ɯμ ɯc2 ) 2 2 0,8 198 78,5 (12,8 0,7) 36,95 Ⱥ. I1 2 3 xμ 3 12,8 2 Ⱦɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ ɫɥɟɞɭɟɬ ɜɵɩɨɥɧɹɬɶ ɜ ɩɪɨɝɪɚɦɦɟ «harad», ɬɚɤ ɤɚɤ ɩɪɢɯɨɞɢɬɫɹ ɭɱɢɬɵɜɚɬɶ ɢɡɦɟɧɟɧɢɟ ɯμ. Ɋɚɫɱɟɬ ɫ ɭɱɟɬɨɦ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɚɟɬ ɪɟɡɭɥɶɬɚɬɵ ɧɟɭɬɟɲɢɬɟɥɶɧɵɟ ɩɪɢ ȦɁȺȾ = 0,4 ɦɨɦɟɧɬ Ɇ = 0,24·ɆɁȺȾ. ɉɪɢ ɡɚɞɚɧɧɨɦ ɡɧɚɱɟɧɢɢ ɦɨɦɟɧɬ, ɚ ɆɁȺȾ = 0,8, ɫɤɨɪɨɫɬɶ ɫɨɫɬɚɜɢɥɚ Ȧ = 0,38. ɑɬɨɛɵ ɫɤɨɪɨɫɬɶ ɩɨɞɧɹɬɶ ɞɨ ɡɚɞɚɧɧɨɣ, ɭɜɟɥɢɱɢɜɚɟɦ ɱɚɫɬɨɬɭ ɧɚ 'Ȧ = 0,02, ɬɨɝɞɚ ɧɨɜɵɟ ɡɧɚɱɟɧɢɹ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ ɢ ɱɚɫɬɨɬɵ ɫɨɫɬɚɜɹɬ D = 0,40536+0,02 = 0,425 ɢ f1ɁȺȾ = 21,3 Ƚɰ. ɉɨɜɬɨɪɹɟɦ ɪɚɫɱɟɬ ɩɪɢ ɧɨɜɨɦ ɡɧɚɱɟɧɢɢ ɱɚɫɬɨɬɵ ɢ ɩɨɥɭɱɚɟɦ, ɱɬɨ ɩɪɢ Ȧ=0,4 ɦɨɦɟɧɬ ɫɨɫɬɚɜɢɥ Ɇ = 0,984·ɆɁȺȾ, ɬɨɤ ɪɨɬɨɪɚ – Ic2 =19,9 Ⱥ, ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ IP =29,8 Ⱥ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɨɥɶɤɨ ɭɱɟɬ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɚɟɬ ɞɨɫɬɨɜɟɪɧɵɟ ɪɟɡɭɥɶɬɚɬɵ. 150

ɉɪɢɦɟɪ 3.13. Ɋɚɫɫɱɢɬɚɬɶ ɜɟɥɢɱɢɧɭ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɜ ɰɟɩɢ ɫɬɚɬɨɪɚ Iɉ ɢ ɜɟɥɢɱɢɧɭ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɢ ɪɨɬɨɪɚ R2ȾɈȻ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 4AK200M8ɍ3 (ɫɦ. ɩɪɢɦɟɪ 3.7), ɨɛɟɫɩɟɱɢɜɚɸɳɟɝɨ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: MɁȺȾ = – 0,8, Ȧ ɁȺȾ = 0,4 ɜ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. Ɋɚɫɫɱɢɬɚɬɶ ɢ ɩɨɫɬɪɨɢɬɶ ɦɟɯɚɧɢɱɟɫɤɢɟ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɩɪɨɯɨɞɹɳɢɟ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ. Ɋɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ – ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ, ɩɢɬɚɧɢɟ ɰɟɩɢ ɫɬɚɬɨɪɚ – ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ. Ɉɛɦɨɬɤɢ ɫɬɚɬɨɪɚ ɫɨɟɞɢɧɟɧɵ ɜ ɡɜɟɡɞɭ, ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ ɩɨɞɤɥɸɱɟɧ ɤ ɞɜɭɦ ɮɚɡɚɦ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɭɫɬɨɣɱɢɜɨɣ ɪɚɛɨɬɵ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɭɫɬɚɧɨɜɢɦ ɡɚɩɚɫ ɩɨ ɩɟɪɟɝɪɭɡɨɱɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɆɄ = 2·ɆɁȺȾ. Ɍɨɝɞɚ ɜɟɥɢɱɢɧɚ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ (ɩɪɢ ɯP=ɯPɇ = const) ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ I1ɁȺȾ

2ɆɄȺɌ Ȧ 0ɇ (ɯ μ ɯc2 )

2 2 0,8 198 78,5 (12,8 0,7) 3 12,8 2

2 3 ɯ μ

36,96Ⱥ ,

ɚ ɜɟɥɢɱɢɧɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɪɢ ɫɯɟɦɟ ɫɨɟɞɢɧɟɧɢɹ – ɡɜɟɡɞɚ Iɉ= I1ɁȺȾ / 0,816 = 36,96 / 0,816 = 45,3 Ⱥ. ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɢɦɟɟɬ ɜɢɞ Ȧ Ȧ 2Ɇ 0 ɤɬ , ɝɞɟ Įs , Ɇ Įs Ȧ Įs 0ɧ ɤɬ Įs Įs ɤɬ Įs

rc 2

ĮsȿɋɌ

r

r

0,268 12,8 0,7

r0,02. c x ɯ μ 2 ȼ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ Ȧ0 = 0, ɆɄɌ = 2·ɆɁȺȾ = 2·0,8·198 = 316,8 ɇɦ. Ɂɚɞɚɜɚɹɫɶ ɚɛɫɨɥɸɬɧɵɦ ɫɤɨɥɶɠɟɧɢɟɦ Ds, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɫɤɨɪɨɫɬɶɸ ɞɜɢɝɚɬɟɥɹ Ȧ = Ds·Ȧ0ɇ, ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɢ ɫɬɪɨɢɬɫɹ ɟɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɰɟɩɢ ɪɨɬɨɪɚ). Ⱦɥɹ ɪɚɫɱɟɬɚ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɢ ɪɨɬɨɪɚ ɨɩɪɟɞɟɥɢɦ ɚɛɫɨɥɸɬɧɨɟ ɫɤɨɥɶɠɟɧɢɟ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɩɪɢ μ = ɆɄɌ / ɆɁȺȾ: ɤɬ

ĮsɄɌ /(μ r (μ2 1)

0,02/(2 r (22 1) 0,00536. Ⱦɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɪɨɬɨɪɚ (ɢɡ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɫɤɨɥɶɠɟɧɢɣ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɣ), ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɪɚɛɨɬɭ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ, ĮsɂɋɄ 0,4 Rc2ȾɈȻ r2c r2c 0,268 0,268 19,736 Ɉɦ. ĮsȿɋɌ 0,00536 Ⱦɥɹ ɪɚɫɱɟɬɚ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢɫɩɨɥɶɡɭɸɬ ɡɚɤɨɧ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɬɨɤɨɜ ɜ ɩɚɪɚɥɥɟɥɶɧɵɯ ɰɟɩɹɯ. Ɂɚɞɚɸɬɫɹ ɚɛɫɨɥɸɬɧɵɦ ɫɤɨɥɶɠɟɧɢɟɦ ɢ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɬɨɤɚ ɫɬɚɬɨɪɚ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɬɨɤ ɪɨɬɨɪɚ ɢ ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. 151

Ɍɨɤ ɪɨɬɨɪɚ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɯμ 12,8 36,96 Ic2 I1 2 2 § 0,268 19,736 · § R2 · 2 2 ¸ (12,8 0,7) ¸¸ (xμ xc2 ) ¨ ¨¨ 0,4 ¹ © © ĮsɂɋɄ ¹

9,13 Ⱥ.

Ɍɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ

Iμ

I1

§ Rc2 ¨ ¨ ĮsɂɋɄ © 2

2

· ¸ xc22 ¸ ¹

2

36,96

§ 0,268 19,732 · 2 ¸ 0,7 ¨ 0,4 ¹ © 2

35,68 A .

§ 0,268 19,732 · § Rc2 · 2 ¨ ¸ (12,8 0,7) ¸ (xμ xc2 )2 ¨ 0,4 ¨ ĮsɂɋɄ ¸ © ¹ ¹ © Ɋɚɫɱɟɬɵ ɜɵɩɨɥɧɹɥɢɫɶ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɢɧɞɭɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ, ɬɨɝɞɚ ɤɚɤ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɬɨɤ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɹɟɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɬɨɤɚ ɪɨɬɨɪɚ (ɩɨ ɚɧɚɥɨɝɢɢ ɫ ɞɜɢɝɚɬɟɥɟɦ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ – ɪɟɚɤɰɢɹ ɹɤɨɪɹ). ɇɟɭɱɺɬ ɢɡɦɟɧɟɧɢɹ ɏP ɩɪɢɜɨɞɢɬ ɤ ɡɧɚɱɢɬɟɥɶɧɵɦ ɩɨɝɪɟɲɧɨɫɬɹɦ, ɚ ɭɱɟɬ – ɜɟɞɟɬ ɤ ɭɫɥɨɠɧɟɧɢɸ ɪɚɫɱɟɬɚ. ɉɪɢɦɟɧɟɧɢɟ ɗȼɆ ɩɨɡɜɨɥɹɟɬ ɭɬɨɱɧɢɬɶ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɣ ɪɚɫɱɟɬ ɫ ɭɱɟɬɨɦ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ (ɩɪɨɝɪɚɦɦɚ «harad» [5]). ɍɱɟɬ ɢɡɦɟɧɟɧɢɹ ɯP ɩɪɢ ɪɚɫɱɟɬɧɵɯ ɩɚɪɚɦɟɬɪɚɯ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (R2 = 20 Ɉɦ ɢ I1 = 36,95 Ⱥ) ɩɨɡɜɨɥɢɥ ɨɩɪɟɞɟɥɢɬɶ ɩɪɢ ɫɤɨɪɨɫɬɢ ȦɁȺȾ = 0,4 ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ = 0,24·ɆɁȺȾ. ɉɟɪɟɪɚɫɱɺɬ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ – ɭɦɟɧɶɲɟɧɢɟ R2ȾɈȻ ɜ 1 / 0,24 ɪɚɡɚ ɢɡ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɫɤɨɥɶɠɟɧɢɹ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ – ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɦɨɦɟɧɬɚ. ɇɚ ɪɢɫ. 3.78 ɩɪɢ ɡɚɞɚɧɧɨɣ ɫɤɨɪɨɫɬɢ ȦɁȺȾ = 0,4 (ɬɨɱɤɚ 2) ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ, ɪɚɫɫɱɢɬɚɧɧɚɹ ɫ ɭɱɟɬɨɦ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɢ R2 = 5,745 Ɉɦ, ɨɛɟɫɩɟɱɢɜɚɟɬ ɦɨɦɟɧɬ Ɇ = 0,75·ɆɁȺȾ.

Ɋɢɫ. 3.78. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɨɜ, ɩɪɨɯɨɞɹɳɢɟ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ

ȼɵɜɨɞ: ɞɚɠɟ ɞɥɹ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɪɚɫɱɟɬɚ ɪɟɠɢɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ, ɤɚɤ ɢ ɥɸɛɨɝɨ ɪɟɠɢɦɚ ɩɪɢ ɩɢɬɚɧɢɢ ȺȾ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ, ɧɭɠɧɨ ɭɱɢɬɵɜɚɬɶ ɢɡɦɟɧɟɧɢɟ ɢɧɞɭɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɯP ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɬɨɤɚ ɪɨɬɨɪɚ. 3.5.4. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ȺȾ

Ⱦɥɹ ɪɚɫɱɺɬɚ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɩɪɢ ɧɟɥɢɧɟɣɧɵɯ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ ɢɫɩɨɥɶɡɭɸɬ ɦɟɬɨɞɵ ɭɫɪɟɞɧɟɧɢɹ ɢɥɢ ɥɢɧɟɚɪɢɡɚɰɢɢ (ɫɦ. ɩ. 3.2.5). Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɧɟɥɢɧɟɣɧɵ. Ⱦɥɹ ɩɪɢɛɥɢɠɟɧɧɵɯ ɪɚɫɱɟɬɨɜ ɢɧɨɝɞɚ ɩɪɢɦɟɧɹɸɬ ɪɚɫɱɟɬɵ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ ɫ ɩɪɹɦɨɥɢɧɟɣɧɵɦɢ ɦɟɯɚɧɢɱɟɫɤɢɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɪɚɛɨɱɟɝɨ ɭɱɚɫɬɤɚ. ɉɪɢ ɧɟɥɢɧɟɣɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɱɢɫɥɟɧɧɵɟ ɦɟɬɨɞɵ ɪɚɫɱɟɬɚ ɧɚ ɗȼɆ. Ⱦɥɹ ɪɚɫɱɺɬɚ ɦɟɯɚɧɢɱɟɫɤɢɯ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ȺȾ ɢɫɩɨɥɶɡɭɸɬ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɢ ɭɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ dȦ ; Ɇ = ȕ·(Ȧ0ɇ – Ȧ). M MC J dt Ⱦɥɹ ɪɚɫɱɟɬɨɜ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ ɫ ɭɱɟɬɨɦ ɤɪɢɜɢɡɧɵ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɤɨɧɬɪɨɥɶɧɵɯ ɡɚɞɚɧɢɣ ɢ ɜ ɤɭɪɫɨɜɨɦ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɩɪɨɝɪɚɦɦɨɣ READ, ɤɨɬɨɪɚɹ ɪɟɲɚɟɬ ɫɢɫɬɟɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɚɫɢɧɯɪɨɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɩɪɨɰɟɞɭɪɟ Ɋɭɧɝɟ-Ʉɭɬɬɚ. Ɋɚɫɱɟɬ ɬɨɤɨɜ ɜɨ ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɜɵɩɨɥɧɹɟɬɫɹ ɜ ɩɪɨɝɪɚɦɦɟ «harad». ɉɪɢɦɟɪ 3.14. Ɋɚɫɫɱɢɬɚɬɶ ɢ ɩɨɫɬɪɨɢɬɶ ɧɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ Ɇ(t) ɢ Ȧ(t) ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 4ȺɄ200Ɇ8 (ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ – ɜ ɩɪɢɦɟɪɟ 3.7) ɩɪɢ Ɇɋ = 0,5 ɢ J = 2·JȾȼ ɡɚ ɦɢɧɢɦɚɥɶɧɨɟ ɜɪɟɦɹ. ɉɪɚɜɢɥɶɧɚɹ ɩɭɫɤɨɜɚɹ ɞɢɚɝɪɚɦɦɚ ɪɚɫɫɱɢɬɚɧɚ ɩɨ ɦɟɬɨɞɢɤɟ 3.5.9: – Ɇɚɤɫɢɦɚɥɶɧɵɣ ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ Ɇ1 = 2,4·Ɇɇ = 475,2 ɇɦ; – Ɇɨɦɟɧɬ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 = 1,05·Ɇɇ = 207,9 ɇɦ; – Ɇɨɦɟɧɬ ɫɬɚɬɢɱɟɫɤɢɣ Ɇɋ = 0,5·Ɇɇ = 99 ɇɦ; – ɉɨɥɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɨɬɨɪɧɨɣ ɰɟɩɢ ɞɥɹ ɩɭɫɤɚ ɩɨ ɫɬɭɩɟɧɹɦ: R1 = 3,094 Ɉɦ, R2 = 1,358 Ɉɦ, R3 = 0,534 Ɉɦ, r2 = 0,268 Ɉɦ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɬɨɪɦɨɡɧɨɝɨ ɪɟɠɢɦɚ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɦɚɤɫɢɦɚɥɶɧɵɦ ɬɨɪɦɨɡɧɵɦ ɦɨɦɟɧɬɨɦ. – ɇɚɱɚɥɶɧɵɣ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ Ɇ = – 2,4·Ɇɇ = – 475,2 ɇɦ; – ɇɚɱɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ȦɌɇȺɑ = 0,9825·Ȧ0ɇ = 77,13 ɪɚɞ/ɫ; – Ɇɨɦɟɧɬ ɫɬɚɬɢɱɟɫɤɢɣ Ɇɋ = 0,5·Ɇɇ= 99 ɇɦ; – ɉɨɥɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɮɚɡɵ ɪɨɬɨɪɧɨɣ ɰɟɩɢ R2ɉȼ = 6,325 Ɉɦ. Ɋɚɫɱɟɬ ɜɵɩɨɥɧɟɧ ɜ ɩɪɨɝɪɚɦɦɟ READ ɫ ɭɱɟɬɨɦ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ Ɍɗ. ɇɚ ɪɢɫ. 3.79 ɩɪɢɜɟɞɟɧɵ ɧɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ ɢ ɢɧɬɟɝɪɚɥɶɧɵɟ ɩɨɤɚɡɚɬɟɥɢ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɞɜɢɝɚɬɟɥɹ 4ȺɄ200Ɇ8. ɉɭɫɤ ɞɜɢɝɚɬɟɥɹ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɬɪɢ ɫɬɭɩɟɧɢ. ɂɡ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɜɪɟɦɹ ɪɚɛɨɬɵ ɧɚ ɤɚɠɞɨɣ ɫɬɭɩɟɧɢ, ɜɪɟɦɹ ɩɭɫɤɚ tɉ = 0,45 ɫ. Ɉɬɤɥɨɧɟɧɢɹ ɦɨɦɟɧɬɨɜ Ɇ1 ɢ Ɇ2 ɨɬ ɡɚɞɚɧɧɵɯ ɡɧɚɱɟɧɢɣ ɧɟɡɧɚɱɢɬɟɥɶɧɨ, ɜɥɢɹɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ Ɍɗ ɜɢɞɧɨ ɧɚ ɩɟɪɜɨɣ ɫɬɭɩɟɧɢ, ɝɞɟ ɬɨɤ ɢ ɦɨɦɟɧɬ ɧɚɪɚɫɬɚɸɬ ɧɟ ɫɤɚɱɤɨɦ, ɢ ɩɪɢ ɜɵɯɨɞɟ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ, ɝɞɟ ɬɨɤ ɢ ɦɨɦɟɧɬ ɧɟ ɭɫɩɟɜɚɸɬ ɞɨɫɬɢɱɶ ɡɚɞɚɧɧɵɯ ɪɚɫɱɟɬɧɵɯ ɡɧɚɱɟɧɢɣ.

Ɍɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɩɪɨɢɡɜɟɞɟɧɨ ɡɚ ɜɪɟɦɹ tɉȼ = 0,21 ɫ ɢ ɨɫɭɳɟɫɬɜɥɟɧɨ ɧɚ ɧɚɱɚɥɶɧɵɯ ɭɱɚɫɬɤɚɯ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɯ ɡɚɜɢɫɢɦɨɫɬɟɣ Ɇ(t) ɢ I(t). Ⱦɥɹ ɪɚɫɱɟɬɚ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɡɚ ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɢɧɬɟɝɪɚɥɶɧɵɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ ɢɡ ɩɪɨɝɪɚɦɦɵ «READ» (ɫɦ. ɪɢɫ. 3.79).

Ɋɢɫ. 3.79. ɇɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ ɪɟɨɫɬɚɬɧɨɝɨ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ȺȾ Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɡɚ ɰɢɤɥ Kɰ = Ⱥ / Ɋ = 3073,24 / 17818,94 = 0,172. Ʉɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ ɡɚ ɰɢɤɥ P 17818,94 cosĳɐ 0,835. P2 Q2 17818,94 2 11759,47 2 ɋɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɵɣ ɬɨɤ ɞɜɢɝɚɬɟɥɹ I1Ʉȼt t 1568,2 IɋɊɄȼ 46,83 Ⱥ. t 0,715

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3.5.4. ɍɩɪɚɠɧɟɧɢɹ ɞɥɹ ɫɚɦɨɩɪɨɜɟɪɤɢ (ɪɚɫɱɟɬɵ ɜɵɩɨɥɧɹɸɬɫɹ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ)

3.5.4.1. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ȺȾ ɩɪɢ Ɇɋ = 1 ɢ R2 = 1. 3.5.4.2. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ȺȾ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɩɪɢ Ɇɋ = 2. ɉɪɢɧɹɬɶ Sɇ = 0,05. 3.5.4.3. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ȺȾ ɩɪɢ ɜɜɟɞɟɧɢɢ ɜ ɰɟɩɶ ɪɨɬɨɪɚ R2ȾɈȻ = 0,5. ɉɪɢɧɹɬɶ Sɇ = 0,05, Ɇɋ = 1. 3.5.4.4. Ɉɩɪɟɞɟɥɢɬɶ ɜɟɥɢɱɢɧɭ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɢ ɪɨɬɨɪɚ ȺȾ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɝɨ ɩɭɫɤɨɜɨɣ ɦɨɦɟɧɬ Ɇ = 2. 3.5.4.5. Ɉɩɪɟɞɟɥɢɬɶ R2 ȺȾ, ɱɬɨɛɵ ɩɪɢ Ɇɋ = 1 ɩɨɥɭɱɢɬɶ Ȧ = 0,7. 3.5.4.6. ȺȾ ɪɚɛɨɬɚɟɬ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ. Ɉɩɪɟɞɟɥɢɬɶ R2, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɦɨɦɟɧɬ ɩɟɪɟɤɥɸɱɟɧɢɹ ɜ ɪɟɠɢɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ, ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ = 2. 3.5.4.7. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɫɤɨɪɨɫɬɶ ȺȾ, ɟɫɥɢ ɭɜɟɥɢɱɢɬɶ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɧɨɣ ɰɟɩɢ ɜ 5 ɪɚɡ. ɉɪɢɧɹɬɶ Ɇɋ = 1, Sɇ = 0,1. 3.5.4.8. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ, ɟɫɥɢ ɩɪɢ ɪɚɛɨɬɟ ȺȾ ɫ Ɇɋ = 1 ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ (ɆɄ / Ɇɇ = 3) ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪɟ ɫɧɢɡɢɥɨɫɶ ɜɞɜɨɟ. 3.5.4.9. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɠɟɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ, ɟɫɥɢ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪɟ ɫɧɢɡɢɥɨɫɶ ɜɞɜɨɟ? 3.5.4.10. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɠɟɫɬɤɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɟɫɥɢ ɩɪɢ ɩɢɬɚɧɢɢ ȺȾ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɬɨɤ ɫɬɚɬɨɪɚ ɜɨɡɪɨɫ ɜɞɜɨɟ? 3.5.4.11. Ɉɩɪɟɞɟɥɢɬɶ ɱɚɫɬɨɬɭ ɢ ɧɚɩɪɹɠɟɧɢɟ ȺȾ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɟɝɨ ɪɚɛɨɬɭ ɜ ɬɨɱɤɟ Ɇɋ = 0,5 ɢ Ȧɋ = 0,2, ɟɫɥɢ Sɇ = 0,1. 3.5.4.12. Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ ȺȾ, ɫɤɨɪɨɫɬɶ ɢ ɦɨɦɟɧɬ, ɟɫɥɢ ɱɚɫɬɨɬɚ ɫɟɬɢ Į = – 0,5, Ɇɋ = 1, Sɇ = 0,1. ɉɪɢɧɹɬɶ U / f = const. 3.5.4.13. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ȺȾ, ɟɫɥɢ ɩɪɢ Ɇɋ = 1 ɢ Ȧɋ = 0,8 ɱɚɫɬɨɬɚ ɬɨɤɚ ɫɟɬɢ ɫɧɢɡɢɥɚɫɶ ɧɚ 0,1 ɩɪɢ U / f = const. 3.5.4.14. ɉɪɢ ɪɚɛɨɬɟ ȺȾ ɫ Ɇɋ = 1, Į = 0,5, U1 = 0,5 ɦɨɦɟɧɬ ɜɨɡɪɨɫ ɜɞɜɨɟ. Ɉɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɹ f1 ɢ U1, ɱɬɨɛɵ ɜɨɫɫɬɚɧɨɜɢɬɶ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ. ɉɪɢɧɹɬɶ Sɇ = 0,1. 3.5.4.15. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɹɬɫɹ ɫɤɨɪɨɫɬɶ ɫɩɭɫɤɚ ɢ ɬɨɤ ɪɨɬɨɪɚ ɩɪɢ ɪɚɛɨɬɟ ȺȾ ɜ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ, ɟɫɥɢ: – ɬɨɤ ɫɬɚɬɨɪɚ ɭɜɟɥɢɱɢɬɶ ɜɞɜɨɟ? – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ ɭɜɟɥɢɱɢɬɶ ɜɞɜɨɟ? 3.5.4.16. ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɪɨɬɨɪɚ ɭɜɟɥɢɱɢɥɢ ɜɞɜɨɟ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɜɪɟɦɹ ɩɭɫɤɚ? 3.5.4.17. ȺȾ ɪɚɛɨɬɚɟɬ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ, ɟɫɥɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɨɬɨɪɚ ɭɦɟɧɶɲɢɬɶ ɜɞɜɨɟ ɜ ɪɟɠɢɦɚɯ: – ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ? – ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ?

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3.6. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 3.6.1. Ɉɫɨɛɟɧɧɨɫɬɢ ɋȾ ɋɢɧɯɪɨɧɧɵɣ ɞɜɢɝɚɬɟɥɶ (ɋȾ) ɛɥɚɝɨɞɚɪɹ ɯɨɪɨɲɢɦ ɷɧɟɪɝɟɬɢɱɟɫɤɢɦ ɩɨɤɚɡɚɬɟɥɹɦ ɩɨ ɄɉȾ ɢ ɤɨɷɮɮɢɰɢɟɧɬɭ ɦɨɳɧɨɫɬɢ ɢ ɩɨɜɵɲɟɧɧɨɣ ɧɚɞɟɠɧɨɫɬɢ ɜ ɫɜɹɡɢ ɫɨ ɡɧɚɱɢɬɟɥɶɧɵɦ ɜɨɡɞɭɲɧɵɦ ɡɚɡɨɪɨɦ ɦɟɠɞɭ ɫɬɚɬɨɪɨɦ ɢ ɪɨɬɨɪɨɦ ɜɫɟ ɛɨɥɶɲɟ ɜɵɬɟɫɧɹɸɬ ɚɫɢɧɯɪɨɧɧɵɟ ɞɜɢɝɚɬɟɥɢ ɜ ɦɨɳɧɵɯ ɭɫɬɚɧɨɜɤɚɯ ɫ ɞɥɢɬɟɥɶɧɵɦ ɪɟɠɢɦɨɦ ɪɚɛɨɬɵ. ɋȾ ɫɬɚɥ ɦɨɧɨɩɨɥɶɧɵɦ ɞɥɹ ɤɪɭɩɧɵɯ ɤɨɦɩɪɟɫɫɨɪɨɜ ɢ ɧɚɫɨɫɨɜ, ɞɥɹ ɝɥɚɜɧɵɯ ɩɪɢɜɨɞɨɜ ɧɟɩɪɟɪɵɜɧɵɯ ɧɟɪɟɝɭɥɢɪɭɟɦɵɯ ɩɪɨɤɚɬɧɵɯ ɫɬɚɧɨɜ, ɞɥɹ ɩɪɢɜɨɞɨɜ ɛɨɥɶɲɨɣ ɢ ɫɪɟɞɧɟɣ ɦɨɳɧɨɫɬɢ ɜ ɰɟ~ ~ ɦɟɧɬɧɨɣ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ. ɋɢɧɯɪɨɧɧɵɣ ɞɜɢɝɚɬɟɥɶ – ɦɚɲɢɧɚ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ, ɭ ɤɨɬɨɪɨɣ ɨɛɦɨɬɤɚ ɫɬɚɬɨɪɚ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ, ɤɚɤ ɭ ȺȾ. M M ɉɪɢ ɩɨɞɤɥɸɱɟɧɢɢ ɫɬɚɬɨɪɚ ɤ ɫɟɬɢ ɬɪɟɯɮɚɡɧɨɝɨ ɬɨɤɚ ɫɨɡɞɚɟɬɫɹ ɜɪɚɳɚɸɳɟɟɫɹ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. Ɉɛɦɨɬɤɚ Iȼ ɪɨɬɨɪɚ – ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ, ɪɚɡɦɟɳɚ+ + ɟɬɫɹ ɧɚ ɩɨɥɸɫɚɯ – ɭ ɋȾ ɫ ɹɜɧɨɩɨɥɸɫɚ) ɛ) ɧɵɦ ɪɨɬɨɪɨɦ ɢɥɢ ɭɥɨɠɟɧɚ ɜ ɩɚɡɵ ɪɨɊɢɫ. 3.80. ɍɫɥɨɜɧɨɟ ɨɛɨɡɧɚɱɟɧɢɟ ɬɨɪɚ – ɭ ɧɟɹɜɧɨɩɨɥɸɫɧɵɯ ɋȾ. ɉɨɞɚɱɚ ɹɜɧɨɩɨɥɸɫɧɨɝɨ (ɚ) ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɜ ɰɟɩɶ ɪɨɬɨɪɚ ɱɚɳɟ ɢ ɧɟɹɜɧɨɩɨɥɸɫɧɨɝɨ (ɛ) ɋȾ ɜɫɟɝɨ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɟɪɟɡ ɤɨɧɬɚɤɬɧɵɟ ɤɨɥɶɰɚ (ɪɢɫ.3.80). Ɉɫɨɛɟɧɧɨɫɬɢ ɋȾ: – ɫɢɧɯɪɨɧɧɵɣ ɞɜɢɝɚɬɟɥɶ ɨɛɥɚɞɚɟɬ ɚɛɫɨɥɸɬɧɨ ɠɺɫɬɤɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ. ɋɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɚɫɬɨɬɨɣ ɩɢɬɚɸɳɟɣ ɫɟɬɢ f1. ɢ ɱɢɫɥɨɦ ɩɚɪ ɩɨɥɸɫɨɜ pɉ

2ʌ f 1. ɨ p ɩ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɝɪɭɡɤɢ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɧɚɦɟɬɢɥɚɫɶ ɜɨɡɦɨɠɧɨɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɋȾ ɜ ɪɟɝɭɥɢɪɭɟɦɨɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ, ɞɥɹ ɢɡɦɟɧɟɧɢɹ ɫɤɨɪɨɫɬɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɱɚɫɬɨɬɵ. – ɜɚɠɧɵɦ ɩɪɟɢɦɭɳɟɫɬɜɨɦ ɤɨɧɫɬɪɭɤɰɢɢ ɋȾ ɹɜɥɹɟɬɫɹ ɛɨɥɶɲɨɣ ɜɨɡɞɭɲɧɵɣ ɡɚɡɨɪ, ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɟɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢ ɫɜɨɣɫɬɜɚ ɦɚɥɨ ɡɚɜɢɫɹɬ ɨɬ ɢɡɧɨɫɚ ɩɨɞɲɢɩɧɢɤɨɜ ɢ ɧɟɬɨɱɧɨɫɬɢ ɦɨɧɬɚɠɚ ɪɨɬɨɪɚ. – ɜɵɫɨɤɢɣ ɄɉȾ ɫɨɜɪɟɦɟɧɧɵɯ ɋȾ, ɫɨɫɬɚɜɥɹɸɳɢɣ 96…98%, ɱɬɨ ɧɚ 1… 1,5% ɜɵɲɟ ɄɉȾ ȺȾ ɬɟɯ ɠɟ ɝɚɛɚɪɢɬɨɜ ɢ ɫɤɨɪɨɫɬɢ. – ɜɨɡɦɨɠɧɨɫɬɶ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɩɟɪɟɝɪɭɡɨɱɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɋȾ ɡɚ ɫɱɺɬ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɢ ɦɟɧɶɲɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɷɬɨɝɨ ɩɨɤɚɡɚɬɟɥɹ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɫɟɬɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ȺȾ. – ɜɨɡɦɨɠɧɨɫɬɶ ɢɡɝɨɬɨɜɥɟɧɢɹ ɧɚ ɛɨɥɶɲɢɟ ɦɨɳɧɨɫɬɢ (ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɞɟɫɹɬɤɨɜ ɦɟɝɚɜɚɬɬ). Ȧ

156

– ɜɨɡɦɨɠɧɨɫɬɶ ɪɚɛɨɬɵ ɫ ɜɵɫɨɤɢɦ ɢ ɞɚɠɟ ɨɩɟɪɟɠɚɸɳɢɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɦɨɳɧɨɫɬɢ cos ĳ. Ⱦɚɠɟ ɩɪɢ ɪɚɛɨɬɟ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɋȾ ɦɨɠɟɬ ɝɟɧɟɪɢɪɨɜɚɬɶ ɜ ɫɟɬɶ ɪɟɚɤɬɢɜɧɭɸ ɷɧɟɪɝɢɸ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɩɪɢ ɬɨɤɟ ɪɨɬɨɪɚ Iȼ = 0, ɧɚɩɪɹɠɟɧɢɟ ɫɟɬɢ U1 ɫɨɡɞɚɺɬ ɬɨɤ ɫɬɚɬɨɪɚ I1, ɤɨɬɨɪɵɣ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɫɨɡɞɚɺɬ ɩɨɬɨɤ Ɏ1, ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɨɹɜɥɹɟɬɫɹ ɗȾɋ ɞɜɢɝɚɬɟɥɹ E1, ɤɨɬɨɪɚɹ ɢ ɭɪɚɜɧɨɜɟɲɢɜɚɟɬ ɩɪɢɥɨɠɟɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɫɟɬɢ U1. ȿɫɥɢ ɩɪɟɧɟɛɪɟɱɶ ɚɤɬɢɜɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɰɟɩɢ ɫɬɚɬɨɪɚ ɜ ɜɢɞɭ ɟɝɨ ɦɚɥɨɫɬɢ, ɬɨ ɞɜɢɝɚɬɟɥɶ ɩɨɬɪɟɛɥɹɟɬ ɢɡ ɫɟɬɢ ɱɢɫɬɨ ɪɟɚɤɬɢɜɧɭɸ ɷɧɟɪɝɢɸ, ɬɨ ɟɫɬɶ ĳ § 900. ɉɪɢ ɩɨɜɵɲɟɧɢɢ Iȼ ɗȾɋ ɫɬɚɬɨɪɚ E1, ɭɪɚɜɧɨɜɟɲɢɜɚɸɳɚɹ ɧɚɩɪɹɠɟɧɢɟ ɫɟɬɢ U1, ɫɨɡɞɚɟɬɫɹ ɬɨɤɨɦ ɪɨɬɨɪɚ Iȼ ɢ ɬɨɤɨɦ ɫɬɚɬɨɪɚ I1. ɉɨ ɦɟɪɟ ɪɨɫɬɚ ɬɨɤɚ ɪɨɬɨɪɚ ɞɨɥɹ ɬɨɤɚ ɫɬɚɬɨɪɚ ɜ I1 Ɇ3 ɫɨɡɞɚɧɢɢ ȿ1 ɫɧɢɠɚɟɬɫɹ, ɩɨɬɪɟɛɥɟɧɢɟ ɪɟɚɤɬɢɜɧɨɣ ɷɧɟɪɝɢɢ ɢɡ ɫɟɬɢ ɫɨɤɪɚɳɚɟɬɫɹ, ɱɬɨ ɜɵɡɵɜɚɟɬ ɩɨɜɵɲɟɧɢɟ cos ĳ. ɉɪɢ ɞɚɥɶɧɟɣɆ2 ɲɟɦ ɭɜɟɥɢɱɟɧɢɢ Iȼ (ɩɪɢ ɩɟɪɟɜɨɡɛɭɠɞɟɧɢɢ ɞɜɢɝɚɬɟɥɹ) ɗȾɋ ɞɜɢɝɚɬɟɥɹ ɫɬɚɧɨɜɢɬɫɹ Ɇ1 ɛɨɥɶɲɟ ɧɚɩɪɹɠɟɧɢɹ ɫɟɬɢ, ɧɨ ɨɧɚ ɧɟ ɦɨɠɟɬ ĳ<0 ĳ>0 ɩɪɟɜɵɫɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɫɟɬɢ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɗȾɋ ɫɬɚɧɨɜɢɬɫɹ ɨɩɟɪɟɠɚɸɳɟɣ, ɞɜɢɝɚɬɟɥɶ IB ɧɚɱɢɧɚɟɬ ɩɨɬɪɟɛɥɹɬɶ ɢɡ ɫɟɬɢ ɬɨɤ, ɨɩɟɪɟɠɚɸɳɢɣ ɧɚɩɪɹɠɟɧɢɟ, ɭɝɨɥ ĳ > 0 – ɬɚɤɠɟ Ɋɢɫ. 3.81. U – ɨɛɪɚɡɧɵɟ ɨɩɟɪɟɠɚɸɳɢɣ. ɇɚ ɪɢɫ. 3.81 ɩɪɢɜɟɞɟɧɵ U – ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɋȾ ɨɛɪɚɡɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɩɨɤɚɡɵɜɚɸɳɢɟ ɢɡɦɟɧɟɧɢɟ ɬɨɤɚ ɫɬɚɬɨɪɚ I1 ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɬɨɤɚ ɪɨɬɨɪɚ Iȼ. ɉɭɧɤɬɢɪɧɚɹ ɥɢɧɢɹ ɧɚ ɪɢɫ.3.81 ɫɨɨɬɜɟɬɫɬɜɭɟɬ cos ĳ = 1. 3.6.2. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ

ɉɨɫɥɟ ɜɯɨɠɞɟɧɢɹ ɋȾ ɜ ɫɢɧɯɪɨɧɢɡɦ ɟɝɨ ɫɤɨɪɨɫɬɶ ɩɪɢ ɢɡɦɟɧɟɧɢɹɯ ɦɨɦɟɧɬɚ ɧɚɝɪɭɡɤɢ ɧɚ ɜɚɥɭ ɞɨ ɧɟɤɨɬɨɪɨɝɨ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ MMAX ɨɫɬɚɺɬɫɹ ɩɨɫɬɨɹɧɧɨɣ ɢ ɪɚɜɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ Ȧ0 (ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ). ɉɨɷɬɨɦɭ ɟɝɨ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɢɦɟɟɬ ɜɢɞ ɩɪɹɦɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɥɢɧɢɢ, ɩɨɤɚɡɚɧɧɨɣ ɧɚ ɪɢɫ. 3.82. ȿɫɥɢ ɦɨɦɟɧɬ ɧɚɝɪɭɡɤɢ ɩɪɟɜɵɫɢɬ ɡɧɚɱɟɧɢɟ MMAX, ɬɨ ɋȾ ɜɵɩɚɞɚɟɬ ɢɡ ɫɢɧɯɪɨɧɢɡɦɚ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ Ȧ ɋȾ MMAX, ɞɨ ɤɨɬɨɪɨɝɨ ɫɨɯɪɚɧɹɟɬɫɹ ɫɢɧɯɪɨɧɧɚɹ Ȧ0 ɪɚɛɨɬɚ ɋȾ ɫ ɫɟɬɶɸ, ɫɥɭɠɢɬ ɭɝɥɨɜɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɋȾ. Ɉɧɚ ɨɬɪɚɠɚɟɬ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɦɟɧɬɚ Ƚɟɧɟɪɚɬɨɪ- ȾɜɢɝɚɬɟɥɶɆ ɨɬ ɭɝɥɚ Ĭ – ɭɝɥɚ ɫɞɜɢɝɚ ɦɟɠɞɭ ɗȾɋ ɫɬɚɬɨɪɚ ɧɵɣ ɪɟɠɢɦ ɧɵɣ ɪɟɠɢɦ ȿ1 ɢ ɧɚɩɪɹɠɟɧɢɟɦ ɫɟɬɢ U1. M ɉɨɥɭɱɢɦ ɭɝɥɨɜɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɞɥɹ ɧɟ0 ɆɇɈ MMAX ɹɜɧɨɩɨɥɸɫɧɨɝɨ ɋȾ ɩɪɢ ɩɪɟɧɟɛɪɟɠɟɧɢɢ ɚɤɬɢɜɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɨɛɦɨɬɤɢ ɫɬɚɬɨɪɚ. Ɋɢɫ. 3.82. Ɇɟɯɚɧɢɱɟɫɤɚɹ ȼɟɤɬɨɪɧɚɹ ɞɢɚɝɪɚɦɦɚ ɞɥɹ ɷɬɨɝɨ ɫɥɭɱɚɹ ɩɨɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɋȾ ɤɚɡɚɧɚ ɧɚ ɪɢɫ. 3.83, ɝɞɟ ɨɛɨɡɧɚɱɟɧɨ: xC – ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɮɚɡɵ ɨɛɦɨɬɤɢ ɫɬɚɬɨɪɚ; I1 – ɬɨɤ ɫɬɚɬɨɪɚ ɋȾ. 157

ɉɨɞɜɨɞɢɦɚɹ ɤ ɋȾ ɦɨɳɧɨɫɬɶ ɦɨɠɟɬ ɛɵɬɶ ɩɪɢɧɹɬɚ ɪɚɜɧɨɣ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɦɨɳɧɨɫɬɢ P1

PɗɆ

M Ȧ0

3 UɎ I cosĳ ,

ɝɞɟ UɎ – ɮɚɡɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɫɟɬɢ; ĳ – ɭɝɨɥ ɫɞɜɢɝɚ ɦɟɠɞɭ ɧɚɩɪɹɠɟɧɢɟɦ ɢ ɬɨɤɨɦ ɋȾ. Ɉɬɫɸɞɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ PɗɆ 3 UɎ I1 cos ĳ . M Ȧ0 Ȧ0

(3.96)

(3.97)

ɂɡ ɜɟɤɬɨɪɧɨɣ ɞɢɚɝɪɚɦɦɵ ɫɥɟɞɭɟɬ

UɎ cos ĳ

E1 cos(ĳ 4) .

(3.98)

Ɋɚɫɫɦɨɬɪɟɧɢɟ ɬɪɟɭɝɨɥɶɧɢɤɚ Ⱥȼɋ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ, ɱɬɨ cos(ĳ 4)

UɎ sin4 , I xɋ

(3.99)

ɬɨɝɞɚ (3.98) ɡɚɩɢɲɟɬɫɹ ɤɚɤ UɎ cos ĳ

E UɎ sin4 . I xɋ

(3.100)

ɉɨɞɫɬɚɧɨɜɤɚ (3.100) ɜ (3.97) ɞɚɺɬ ɜɵɪɚɠɟɧɢɟ ɦɨɦɟɧɬɚ: M

3 UɎ E sin4 Ȧ0 x ɋ

MɆȺɄɋ sin4,

(3.101)

3 UɎ E – ɦɚɤɫɢɦɚɥɶɧɵɣ ɦɨɦɟɧɬ ɋȾ. Ȧ0 x ɋ ɂɡ ɜɵɪɚɠɟɧɢɹ (3.101) ɜɢɞɧɨ, ɱɬɨ ɦɨɦɟɧɬ ɋȾ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɢɧɭɫɨɢA I1xC ɞɚɥɶɧɭɸ ɮɭɧɤɰɢɸ ɭɝɥɚ Ĭ ɦɚɲɢɧɵ. ɗɬɨ ɜɵɪɚɠɟɧɢɟ ɫɩɪɚɜɟɞɥɢɜɨ ɬɨɥɶɤɨ ɞɥɹ ɦɚU1 ĳ–Ĭ ɲɢɧ ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ. ɑɬɨɛɵ ɩɨɥɭɱɢɬɶ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɹɜɧɨB ɩɨɥɸɫɧɨɣ ɦɚɲɢɧɵ, ɧɟɨɛɯɨɞɢɦɨ ɭɱɟɫɬɶ C Ĭ ɪɟɚɤɬɢɜɧɵɣ ɦɨɦɟɧɬ, ɜɵɡɵɜɚɟɦɵɣ ɫɬɪɟɦE1 ɥɟɧɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ ɡɚɦɤɧɭɬɶɫɹ ɩɨ ɩɭɬɢ ɧɚɢɦɟɧɶɲɟɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ (ɪɢɫ. ĳ 3.84). ɉɪɢ ɨɬɫɬɚɜɚɧɢɢ ɩɨɥɸɫɚ ɨɬ ɨɫɢ ɩɨɬɨɤɚ ɩɨɫɥɟɞɧɢɣ ɫɬɪɟɦɢɬɫɹ ɜɵɩɪɹɦɢɬɶɫɹ, ɢ ɷɬɨ ɫɬɪɟɦɥɟɧɢɟ ɩɨɪɨɠɞɚɟɬ ɞɨɩɨɥɧɢɬɟɥɶI1 ɧɵɣ ɦɨɦɟɧɬ ɦɚɲɢɧɵ ɆɊȿȺɄɌ. Ɋɢɫ. 3.83. ȼɟɤɬɨɪɧɚɹ ɉɨɷɬɨɦɭ ɞɥɹ ɹɜɧɨɩɨɥɸɫɧɨɣ ɦɚɲɢɧɵ ɞɢɚɝɪɚɦɦɚ ɋȾ ɩɪɢ r1=0 ɜɵɪɚɠɟɧɢɟ (3.101) ɡɚɦɟɧɢɬɫɹ ɧɚ ɜɵɪɚɠɟɧɢɟ (3.102).

ɝɞɟ MɆȺɄɋ

158

M

3 UɎ E 3 UɎ2 §¨ 1 1 ·¸ sin(2 4) , sin( 4) Ȧ0 x1d 2 Ȧ0 ¨© x1q x1d ¸¹ MɊȿȺɄɌɂȼɇɕɃ

(3.102)

ɝɞɟ ɯ1q – ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɨ ɩɪɨɞɨɥɶɧɨɣ ɨɫɢ ɞɜɢɝɚɬɟɥɹ; ɯ1d – ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɨ ɩɨɩɟɪɟɱɧɨɣ ɨɫɢ. ɇɚ ɪɢɫ. 3.85 ɩɨɤɚɡɚɧɚ ɭɝɥɨɜɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɹɜɧɨɩɨɥɸɫɧɨɝɨ ɋȾ. ɉɪɢ ɪɚɛɨɬɟ ɫ Ĭ > 90ɨ ɭɜɟɥɢɱɟɧɢɟ ɧɚɝɪɭɡɤɢ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ, ɩɨɹɜɥɟɧɢɸ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ ɆȾɂɇ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɋȾ ɜɵɩɚɞɚɟɬ ɢɡ ɫɢɧɯɪɨɧɢɡɦɚ.

Ɇ

N

MɆȺɄɋ

Ɇɋɂɇ+ɆɊȿȺɄɌ

ɆɊȿȺɄɌ Ɇɋɂɇ

Ɇɇ

ɆɊȿȺɄɌ

S 0 Ɋɢɫ. 3.84. Ⱦɟɣɫɬɜɢɟ ɪɟɚɤɬɢɜɧɨɝɨ ɦɨɦɟɧɬɚ

șɇɈɆ

ʌ/2

ʌ

ș

Ɋɢɫ. 3.85. ɍɝɥɨɜɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɹɜɧɨɩɨɥɸɫɧɨɝɨ ɋȾ.

3.6.3. ȼɥɢɹɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɧɚ ɜɢɞ ɦɟɯɚɧɢɱɟɫɤɢɯ ɢ ɭɝɥɨɜɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ

ȼɵɪɚɠɟɧɢɟ ɭɝɥɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɋȾ (3.102) M

3 UɎ E 3 UɎ2 §¨ 1 1 ·¸ sin(2 4) sin( 4) Ȧ0 x1d 2 Ȧ0 ¨© x1q x1d ¸¹ MɊȿȺɄɌɂȼɇɕɃ

ɩɪɢ ɜɵɞɟɥɟɧɢɢ ɬɨɥɶɤɨ ɪɟɝɭɥɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ 2

M

§U · U I A Ɏ ȼ sin4 B ¨¨ 1 ¸¸ sin 2 4 , f1 © f1 ¹

ɝɞɟ Ⱥ ɢ ȼ – ɩɨɫɬɨɹɧɧɵɟ ɜɟɥɢɱɢɧɵ. Ⱦɥɹ ɧɟɹɜɧɨɩɨɥɸɫɧɨɝɨ ɞɜɢɝɚɬɟɥɹ (ɜɬɨɪɨɣ ɱɥɟɧ ɨɬɫɭɬɫɬɜɭɟɬ) M

A

UɎ Iȼ sin4 . f1 159

ɂɡ ɩɪɢɜɟɞɟɧɧɨɝɨ ɜɵɪɚɠɟɧɢɹ ɫɥɟɞɭɟɬ, ɱɬɨ ɦɚɤɫɢɦɚɥɶɧɵɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɢ ɱɚɫɬɨɬɵ ɩɢɬɚɸɳɟɣ ɫɟɬɢ ɢ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ. ɍɜɟɥɢɱɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɫɟɬɢ U1, ɬɨɤɚ Iȼ ɢ ɭɦɟɧɶɲɟɧɢɟ ɱɚɫɬɨɬɵ ɫɟɬɢ f1 ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɆɆȺɄɋ (ɪɢɫ. 3.86). ɇɚ ɫɤɨɪɨɫɬɶ ɋȾ ɜɥɢɹɟɬ ɬɨɥɶɤɨ ɱɚɫɬɨɬɚ ɫɟɬɢ. Ɇ

U1Ĺ,IȼĹ,f1Ļ

U1=var IB=var

Ȧ Ȧ0

MMAX U1Ļ,IȼĻ,f1Ĺ f1=var

Ɇɇ 0

ș

ʌ

șɇ ʌ/2

M MMAX1

MMAX3 MMAX2

Ɋɢɫ.3.86. ɍɝɥɨɜɵɟ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɋȾ

ɉɪɢ ɩɨɫɬɨɹɧɫɬɜɟ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɢ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɢɜɨɞɢɬ ɤ ɨɝɪɚɧɢɱɟɧɢɸ ɆɆȺɄɋ. ɇɚ ɪɢɫ. 3.86 ɩɨɤɚɡɚɧɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. ɉɪɢ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɱɚɫɬɨɬɵ ɩɪɨɢɫɯɨɞɢɬ ɢɡɦɟɧɟɧɢɟ ɫɤɨɪɨɫɬɢ, ɚ ɨɝɪɚɧɢɱɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɧɚ ɤɚɠɞɨɣ ɢɡ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɪɚɡɥɢɱɧɨ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɥɟɝɤɨ ɭɩɪɚɜɥɹɬɶ ɜɟɥɢɱɢɧɨɣ ɦɨɦɟɧɬɚ, ɢɡɦɟɧɹɹ ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ. ɗɬɢɦ ɩɨɥɶɡɭɸɬɫɹ ɩɪɢ ɩɭɫɤɟ ɢ ɩɪɢ ɪɟɡɤɨɦ ɧɚɛɪɨɫɟ ɧɚɝɪɭɡɤɢ, ɩɪɢɦɟɧɹɹ ɜ ɷɬɢɯ ɪɟɠɢɦɚɯ ɭɜɟɥɢɱɟɧɢɟ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ (ɮɨɪɫɢɪɨɜɤɭ ɜɨɡɛɭɠɞɟɧɢɹ). 3.6.4. ɍɩɪɨɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɋȾ

MMAX

ɇɚ ɪɢɫ. 3.87 ɢɡɨɛɪɚɠɟɧɚ ɭɝɥɨɜɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɋȾ. Ⱦɥɹ ɫɨɫɬɚɜɥɟɧɢɹ ɭɩɪɨɳɟɧɧɨɣ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ ɥɢɧɟɚɪɢɡɢɪɭɟɦ ɪɚɛɨɱɢɣ ɭɱɚɫɬɨɤ ɢ ɡɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ ɩɨɥɭɱɟɧɧɨɣ ɩɪɹɦɨɣ Ɇ=f(ș) ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɧɚɤɥɨɧɚ b:

Ɇ

Ɇɇ

0

Ĭɇ ʌ/2

ʌ

Ĭ

Mɋɂɇ

b4.

(3.103)

ɉɪɨɞɢɮɮɟɪɟɧɰɢɪɭɟɦ ɨɛɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (3.103) ɩɨ dt

Ɋɢɫ. 3.87. Ɉɩɪɟɞɟɥɟɧɢɟ b dɆɋɂɇ dt

MɇɈɆ 4 4ɇɈɆ

b

d4 dt

b Ȧ0 Ȧ .

160

(3.104)

ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɫ ɜɵɯɨɞɨɦ ɩɨ ɫɢɧɯɪɨɧɧɨɦɭ ɦɨɦɟɧɬɭ: Mɋɂɇ Ȧ0 Ȧ

Wɋɂɇ (p)

b . p

ɇɚ ɪɨɬɨɪɟ ɞɜɢɝɚɬɟɥɹ, ɤɪɨɦɟ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɪɚɡɦɟɳɚɟɬɫɹ ɩɭɫɤɨɜɚɹ ɨɛɦɨɬɤɚ (ɞɥɹ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ – ɷɬɨ ɞɟɦɩɮɟɪɧɚɹ ɨɛɦɨɬɤɚ). ɉɪɢ ɭɱɟɬɟ ɞɟɦɩɮɟɪɧɨɣ ɨɛɦɨɬɤɢ ɜ ɞɜɢɝɚɬɟɥɟ ɜɨɡɧɢɤɚɟɬ ɚɫɢɧɯɪɨɧɧɵɣ ɦɨɦɟɧɬ MȺɋɂɇ

2 MK 2 MK # s s/sK sK /s sK 2 MK Ȧ0 Ȧ sK Ȧ0

2 MK Ȧ0 Ȧ sK Ȧ0

ȕ (Ȧ0 Ȧ).

ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɫ ɜɵɯɨɞɨɦ ɩɨ ɚɫɢɧɯɪɨɧɧɨɦɭ ɦɨɦɟɧɬɭ: MAɋɂɇ Ȧ0 Ȧ

WȺɋɂɇ p

ȕ.

ɋ ɭɱɟɬɨɦ ɨɫɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ dȦ dȦ MC ȕ TɆ dt dt ɢ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ M MC J

WɆȿɏ p

Ȧp M MC

1 Jp

1 ȕ TɆ p

ɩɨɫɬɪɨɟɧɚ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɋȾ (ɪɢɫ. 3.88). Ⱥɧɚɥɢɡ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɪɢ ȕ = 0 ɜ ɩɪɹɦɨɦ ɤɚɧɚɥɟ ɫɢɫɬɟɦɵ ɪɚɫɩɨɥɨɠɟɧɵ ɞɜɚ ɢɧɬɟɝɪɢɪɭɸɳɢɯ ɡɜɟɧɚ, ɫɢɫɬɟɦɚ ɢɦɟɟɬ ɚɫɬɚɬɢɡɦ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ, ɡɚɩɚɫ ɩɨ ɮɚɡɟ ǻĳ = 180°. ɉɪɢ ɡɚɦɵɤɚɧɢɢ ɬɚɤɨɣ ɫɢɫɬɟɦɵ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɨɛɪɚɬɧɨɣ ɫɜɹɡɶɸ ɩɨɥɭɱɢɦ ɫɢɫɬɟɦɭ ɧɚ ɝɪɚɧɢɰɟ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɤɨɥɟɛɚɬɟɥɶɧɭɸ ɫɢɫɬɟɦɭ (ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨ ɢɡɦɟɧɹɟɬɫɹ ɜɨɤɪɭɝ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ ɩɨɥɹ ɦɚɲɢɧɵ). Ɇɋ Ȧ0

b p

Ɇɋɂɇ

1 ȕ TM

+ ȕ

ɆȺɋɂɇ

Ɋɢɫ. 3.88. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɋȾ

161

Ȧ

3.6.5. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɋȾ ɩɪɢ ɩɭɫɤɟ

Ɉɞɧɢɦ ɢɡ ɧɟɞɨɫɬɚɬɤɨɜ ɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɨɫɬɶ ɟɝɨ ɩɭɫɤɚ ɨɬ ɫɟɬɢ ɜ ɧɟɪɟɝɭɥɢɪɭɟɦɨɦ ɩɪɢɜɨɞɟ. ȿɫɥɢ ɩɪɢ ɩɭɫɤɟ ɜɤɥɸɱɟɧɚ ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ, ɬɨ ɛɵɫɬɪɨɜɪɚɳɚɸɳɟɟɫɹ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɫɬɚɬɨɪɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɩɨɞɜɢɠɧɨɝɨ ɪɨɬɨɪɚ ɫɨɡɞɚɟɬ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɫ ɧɭɥɟɜɵɦ ɫɪɟɞɧɢɦ ɡɧɚɱɟɧɢɟɦ. Ɋɨɬɨɪ ɨɫɬɚɟɬɫɹ ɧɟɩɨɞɜɢɠɧɵɦ. ȿɫɥɢ ɪɨɬɨɪ ɪɚɡɨȦ Ɇ ɝɧɚɬɶ ɞɨ ɫɤɨɪɨɫɬɢ, ɛɥɢɡɤɨɣ ɤ ɫɢɧɯɪɨɧɧɨɣ, ɢ ȼɏ2 Ɇȼɏ1 ɧɚ ɷɬɨɣ ɫɤɨɪɨɫɬɢ ɩɨɞɤɥɸɱɢɬɶ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ, ɬɨ ɪɨɬɨɪ ɛɭɞɟɬ ɭɫɩɟɜɚɬɶ ɡɚ ɩɨɬɨɤɨɦ Ȧȼɏ ɫɬɚɬɨɪɚ, ɢ ɞɜɢɝɚɬɟɥɶ ɜɬɹɝɢɜɚɟɬɫɹ ɜ ɫɢɧɯɪɨɧɢɡɦ. Ⱦɥɹ ɪɚɡɝɨɧɚ ɞɜɢɝɚɬɟɥɹ ɞɨ ɩɨɞɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ (0,95·Ȧ0ɇ) ɧɚ ɪɨɬɨɪɟ ɞɜɢɝɚɬɟɥɹ, M ɤɪɨɦɟ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɪɚɡɦɟɳɚɟɬɫɹ Ɇɉ1 Ɇɉ2 ɩɭɫɤɨɜɚɹ ɨɛɦɨɬɤɚ ɬɢɩɚ ɛɟɥɢɱɶɟɝɨ ɤɨɥɟɫɚ. ɉɭɫɤɨɜɚɹ ɨɛɦɨɬɤɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɭɫɤ ɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ, ɤɚɤ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɊɢɫ. 3.89. ɉɭɫɤɨɜɵɟ ɬɟɥɹ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ. Ɇɟɯɚɧɢɱɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɋȾ ɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɋȾ ɩɪɢ ɩɭɫɤɟ (ɪɢɫ. 3.89) ɨɛɥɚɞɚɸɬ ɪɚɡɥɢɱɧɵɦɢ ɩɭɫɤɨɜɵɦɢ ɦɨɦɟɧɬɚɦɢ: – ɩɪɢ ɩɭɫɤɟ ɫ ɦɚɥɵɦ ɦɨɦɟɧɬɨɦ ɧɚɝɪɭɡɤɢ (ɜɟɧɬɢɥɹɬɨɪ) ɢɫɩɨɥɶɡɭɟɬɫɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɫ ɦɚɥɵɦ ɩɭɫɤɨɜɵɦ ɦɨɦɟɧɬɨɦ Ɇɉ1 < Ɇɉ2; – ɩɪɢ ɩɭɫɤɟ ɫ ɛɨɥɶɲɢɦ ɦɨɦɟɧɬɨɦ ɧɚɝɪɭɡɤɢ (ɲɚɪɨɜɚɹ ɦɟɥɶɧɢɰɚ) ɢɫɩɨɥɶɡɭɸɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɫ ɨɬɧɨɫɢɬɟɥɶɧɨ ɛɨɥɶɲɢɦ ɩɭɫɤɨɜɵɦ ɦɨɦɟɧɬɨɦ Ɇɉ2. ɉɨ ɨɤɨɧɱɚɧɢɢ ɩɭɫɤɚ ɩɪɢ ɫɤɨɪɨɫɬɢ ȦȼɌ ɋȾ ɞɨɥɠɟɧ ɪɚɡɜɢɜɚɬɶ ɦɨɦɟɧɬ, ɩɪɟɨɞɨɥɟɜɚɸɳɢɣ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɢ ɞɨɫɬɚɬɨɱɧɵɣ ɞɥɹ ɜɬɹɝɢɜɚɧɢɹ ɜ ɫɢɧɯɪɨɧɢɡɦ ɩɪɢ ɩɨɞɚɱɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ (Ɇȼɏ2 > Ɇȼɏ1). Ʉɨ ɜɪɟɦɟɧɢ ɩɭɫɤɚ ɩɪɟɞɴɹɜɥɹɸɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɠɟɫɬɤɢɟ ɬɪɟɛɨɜɚɧɢɹ, ɬɚɤ ɤɚɤ ɩɭɫɤɨɜɚɹ ɨɛɦɨɬɤɚ ɧɚɯɨɞɢɬɫɹ ɩɨɞ ɬɨɤɨɦ ɬɨɥɶɤɨ ɜɨ ɜɪɟɦɹ ɩɭɫɤɚ, ɜɵɩɨɥɧɹɟɬɫɹ ɩɨ ɦɢɧɢɦɭɦɭ ɪɚɫɯɨɞɚ ɦɟɞɢ ɢ ɧɚɝɪɟɜɚɟɬɫɹ ɩɪɢ ɩɭɫɤɟ ɞɨ ɩɪɟɞɟɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ. Ɂɚɬɹɝɢɜɚɧɢɟ ɩɭɫɤɚ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɜɵɯɨɞɭ ɢɡ ɫɬɪɨɹ ɩɭɫɤɨɜɨɣ ɨɛɦɨɬɤɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɞɜɢɝɚɬɟɥɹ. ɉɭɫɤ ɋȾ ɦɨɠɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɪɚɡɥɢɱɧɵɦɢ ɫɩɨɫɨɛɚɦɢ: 1) ɩɪɹɦɨɣ ɩɭɫɤ (ɞɥɹ ɦɚɲɢɧ ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɫɨɬɟɧ ɤɢɥɨɜɚɬɬ); 2) ɩɪɢ ɩɭɫɤɟ ɋȾ ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ (ɧɟɫɤɨɥɶɤɨ ɬɵɫɹɱ ɤɢɥɨɜɚɬɬ) ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɨɝɪɚɧɢɱɟɧɢɹ ɩɭɫɤɨɜɵɯ ɬɨɤɨɜ ɩɨɧɢɠɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ, ɱɬɨ ɞɨɫɬɢɝɚɟɬɫɹ ɱɚɳɟ ɜɫɟɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɪɟɚɤɬɨɪɨɜ ɢɥɢ ɚɜɬɨɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ; Ʌɟɝɤɢɣ ɩɭɫɤ ɋȾ ɧɚɱɢɧɚɸɬ ɫ ɪɟɚɤɬɨɪɨɦ ɜ ɰɟɩɢ ɫɬɚɬɨɪɚ, ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɫɬɚɬɨɪɟ ɩɨɧɢɠɚɸɬ, ɡɚɬɟɦ ɪɟɚɤɬɨɪ ɨɬɤɥɸɱɚɸɬ, ɢ ɞɜɢɝɚɬɟɥɶ ɨɤɚɡɵɜɚɟɬɫɹ ɩɨɞɤɥɸɱɺɧɧɵɦ ɧɚ ɩɨɥɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɫɟɬɢ, ɩɨɫɥɟ ɱɟɝɨ ɩɨɞɤɥɸɱɚɸɬ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ; 3) ɩɪɢ ɬɹɠɺɥɨɦ ɩɭɫɤɟ ɋȾ ɫ ɩɨɦɨɳɶɸ ɪɟɚɤɬɨɪɚ ɩɨɧɢɠɚɸɬ ɧɚɩɪɹɠɟɧɢɟ, ɡɚɬɟɦ ɩɨɞɤɥɸɱɚɸɬ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ, ɩɨɫɥɟ ɱɟɝɨ ɨɬɤɥɸɱɚɸɬ ɪɟɚɤɬɨɪ, ɢ ɞɜɢɝɚɬɟɥɶ ɨɤɚɡɵɜɚɟɬɫɹ ɩɨɞɤɥɸɱɺɧɧɵɦ ɧɚ ɩɨɥɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɫɟɬɢ ɫ ɩɨɞɤɥɸɱɟɧɧɨɣ ɨɛɦɨɬɤɨɣ ɜɨɡɛɭɠɞɟɧɢɹ, ɩɪɢ ɚɫɢɧɯɪɨɧɧɨɦ ɩɭɫɤɟ ɋȾ ɪɨɬɨɪɧɚɹ ɨɛɦɨɬɤɚ ɡɚɦɵɤɚɟɬɫɹ ɧɚ ɪɚɡɪɹɞɧɵɣ ɪɟɡɢɫɬɨɪ (ɪɢɫ.3.90,ɚ), ɤɨɬɨɪɵɣ ɨɝɪɚɧɢɱɢɜɚɟɬ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɨɛɦɨɬɤɟ ɪɨɬɨɪɚ ɩɪɢ ɩɭɫɤɟ, ɭɥɭɱɲɚɟɬ ɩɭɫɤɨɜɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɞɜɢɝɚɬɟɥɹ ɢ ɝɚɫɢɬ ɷɧɟɪɝɢɸ ɩɨɥɹ ɩɪɢ ɤɨɪɨɬɤɨɦ ɡɚɦɵɤɚɧɢɢ ɜ ɰɟɩɢ ɫɬɚɬɨɪɚ. 162

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Ɋɢɫ. 3.90. ɋɯɟɦɵ ɩɭɫɤɚ ɋȾ ɫ ɪɚɡɪɹɞɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ (ɚ), ɪɟɨɫɬɚɬɧɵɣ ɩɭɫɤ ɫ ɝɥɭɯɨɩɨɞɤɥɸɱɺɧɧɵɦ ɜɨɡɛɭɞɢɬɟɥɟɦ (ɛ), ɫ ɜɨɡɛɭɞɢɬɟɥɟɦ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ (ɜ) ȿɫɥɢ ɨɫɬɚɜɢɬɶ ɩɪɢ ɩɭɫɤɟ ɞɜɢɝɚɬɟɥɹ ɧɢɡɤɨɜɨɥɶɬɧɭɸ ɨɛɦɨɬɤɭ ɪɨɬɨɪɚ ɪɚɡɨɦɤɧɭɬɨɣ, ɬɨ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɧɚ ɧɟɣ ɩɨɹɜɢɬɫɹ ɧɟɞɨɩɭɫɬɢɦɨ ɜɵɫɨɤɨɟ ɧɚɩɪɹɠɟɧɢɟ, ɢ ɨɛɦɨɬɤɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɛɢɬɚ. ȿɫɥɢ ɨɛɦɨɬɤɭ ɪɨɬɨɪɚ ɡɚɦɤɧɭɬɶ ɧɚɤɨɪɨɬɤɨ, ɬɨ ɞɜɢɝɚɬɟɥɶ ɩɨɥɭɱɢɬ ɩɪɨɜɚɥ ɦɨɦɟɧɬɚ ɩɪɢ ɩɨɥɨɜɢɧɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ, ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɷɮɮɟɤɬ «ɨɞɧɨɨɫɧɨɝɨ ɜɤɥɸɱɟɧɢɹ». ɉɪɢ ɡɚɦɵɤɚɧɢɢ ɨɛɦɨɬɤɢ ɪɨɬɨɪɚ ɧɚɤɨɪɨɬɤɨ ɩɪɢ ɩɭɫɤɟ ɋȾ ɜ ɧɟɣ ɧɚɜɨɞɢɬɫɹ ɨɞɧɨɮɚɡɧɚɹ ɗȾɋ ɫ ɱɚɫɬɨɬɨɣ ɫɤɨɥɶɠɟɧɢɹ, ɩɪɨɬɟɤɚɟɬ ɬɨɤ, ɜɨɡɧɢɤɚɟɬ ɨɞɧɨɮɚɡɧɨɟ ɩɨɥɟ. ɗɬɨ ɩɨɥɟ ɦɨɠɧɨ ɪɚɡɥɨɠɢɬɶ ɧɚ ɩɨɥɟ ɩɪɹɦɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ, ɜɪɚɳɚɸɳɟɟɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ Ȧɉɉ, ɢ ɩɨɥɟ ɨɛɪɚɬɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ, ɜɪɚɳɚɸɳɟɟɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ Ȧ0ɉ. ɋɤɨɪɨɫɬɶ ɩɨɥɹ ɪɨɬɨɪɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɪɨɬɨɪɚ Ȧ2 = Ȧ0·s. ɉɪɢɱɺɦ ɩɨɥɟ ɩɪɹɦɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ Ȧɉɉ

ȦɊɈɌ Ȧ 2

Ȧ 0 (1 s) Ȧ 0 s

Ȧ0

ɜɪɚɳɚɟɬɫɹ ɫ ɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɶɸ Ȧ0 ɢ ɪɚɡɜɢɜɚɟɬ ɦɨɦɟɧɬ Ɇɉɉ (ɪɢɫ. 3.91), ɚ ɩɨɥɟ ɨɛɪɚɬɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɜɪɚɳɚɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ Ȧ0ɉ

ȦɊɈɌ Ȧ2

Ȧ0 (1 s) Ȧ0 s

Ȧ0 (1 2 s) ,

ɫɜɹɡɚɧɧɨɣ ɫ ɭɞɜɨɟɧɧɨɣ ɜɟɥɢɱɢɧɨɣ ɫɤɨɥɶɠɟɧɢɹ ɢ ɫɨɡɞɚɟɬ ɦɨɦɟɧɬ ɆɈɉ. ɉɪɢ s = 0,5 ɫɤɨɪɨɫɬɶ Ȧ0ɉ = 0, ɗȾɋ, ɬɨɤ ɢ ɦɨɦɟɧɬ ɷɬɨɝɨ ɩɨɥɹ ɬɚɤɠɟ ɪɚɜɧɵ ɧɭɥɸ. ɉɪɢ s < 0,5 ɩɨɥɟ ɨɛɪɚɬɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɫɨɡɞɚɟɬ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɦɨɦɟɧɬ ɆɈɉ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ, ɧɚɩɪɚɜɥɟɧɧɵɣ ɧɚɜɫɬɪɟɱɭ ɦɨɦɟɧɬɭ ɆɉɈ, ɪɚɡɜɢɜɚɟɦɨɦɭ ɩɭɫɤɨɜɨɣ ɨɛɦɨɬɤɨɣ. ɉɪɢ s > 0,5 – ɦɨɦɟɧɬ ɆɈɉ ɫɨɜɩɚɞɚɟɬ ɫ ɦɨɦɟɧɬɨɦ Ɇɉɉ. 163

Ɋɟɡɭɥɶɬɢɪɭɸɳɢɣ ɦɨɦɟɧɬ ɆɊȿɁ ɨɬ ɫɭɦɦɵ ɬɪɟɯ ɦɨɦɟɧɬɨɜ ɩɪɢ s = 0,5 ɫɨɡȦ ɆɉɈ ɞɚɟɬ ɩɪɨɜɚɥ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɢ ɟɫɥɢ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɩɨMɈɉ ɩɚɞɚɟɬ ɜ ɷɬɨɬ ɩɪɨɜɚɥ, ɬɨ ɞɚɥɶɧɟɣɲɢɣ MɊȿɁ ɪɚɡɝɨɧ ɞɜɢɝɚɬɟɥɹ ɫɬɚɧɨɜɢɬɫɹ ɧɟɜɨɡɦɨɠɧɵɦ, ɞɜɢɝɚɬɟɥɶ «ɡɚɫɬɪɟɜɚɟɬ». Ⱦɥɹ ɢɫɤɥɸɱɟɧɢɹ ɷɬɨɝɨ ɷɮɮɟɤɬɚ ɨɛM ɦɨɬɤɭ ɪɨɬɨɪɚ ɧɟ ɡɚɤɨɪɚɱɢɜɚɸɬ, ɚ ɩɨɞɤɥɸɱɚɸɬ ɧɚ ɪɚɡɪɹɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ RɊ = 10·rɈȼ. ȿɝɨ ɜɤɥɸɱɟɧɢɟ ɫɧɢɠɚɟɬ Ɇɉɉ ɩɪɨɜɚɥɵ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɨɞɧɨɨɫɧɨɟ ɜɤɥɸɱɟɧɢɟ ɜ ɦɟɧɶɲɟɣ ɫɬɟɩɟɧɢ ɜɥɢɹɟɬ ɧɚ ɩɭɫɤ. Ɋɢɫ. 3.91. ɉɭɫɤɨɜɵɟ ɇɟɞɨɫɬɚɬɨɤ – ɪɚɡɪɹɞɧɨɟ ɫɨɩɪɨɬɢɜɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɷɮɮɟɤɬɟ ɥɟɧɢɟ ɧɟɨɛɯɨɞɢɦɨ ɨɬɤɥɸɱɚɬɶ, ɫɧɢɠɚɟɬɨɞɧɨɨɫɧɨɝɨ ɜɤɥɸɱɟɧɢɹ ɫɹ ɧɚɞɟɠɧɨɫɬɶ. ȼ ɫɯɟɦɟ ɫ ɝɥɭɯɨɩɨɞɤɥɸɱɟɧɧɵɦ ɜɨɡɛɭɞɢɬɟɥɟɦ (ɪɢɫ. 3.90,ɛ) ɜɨ ɢɡɛɟɠɚɧɢɟ ɡɚɫɬɪɟɜɚɧɢɹ ɧɚ ɩɨɥɨɜɢɧɧɨɣ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɶ ɡɚɩɭɫɤɚɸɬ ɩɪɢ ɨɝɪɚɧɢɱɟɧɧɨɦ ɦɨɦɟɧɬɟ ɧɚɝɪɭɡɤɢ Ɇɋ < 0,4·Ɇɇ (ɩɭɫɤ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɧɚɫɨɫɚ ɫ ɡɚɤɪɵɬɨɣ ɦɚɝɢɫɬɪɚɥɶɸ). ɋɬɪɟɦɥɟɧɢɟ ɤ ɭɫɬɪɨɣɫɬɜɚɦ ɛɟɫɤɨɧɬɚɤɬɧɨɝɨ ɩɭɫɤɚ (ɢɫɤɥɸɱɟɧɢɟ ɳɟɬɨɱɧɨɝɨ ɤɨɧɬɚɤɬɚ) ɩɪɢɜɟɥɨ ɤ ɫɨɡɞɚɧɢɸ ɢ ɩɪɢɦɟɧɟɧɢɸ ɜɨɡɛɭɞɢɬɟɥɟɣ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ (ɪɢɫ. 3.90,ɜ). ɉɟɪɟɦɟɧɧɵɣ ɬɨɤ ɩɨɞɚɟɬɫɹ ɜ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ ɱɟɪɟɡ ɞɢɨɞɧɵɣ ɜɵɩɪɹɦɢɬɟɥɶ, ɜɪɚɳɚɸɳɢɣɫɹ ɧɚ ɜɚɥɭ ɋȾ. ɍɩɪɚɜɥɟɧɢɟ ɬɨɤɨɦ ɜɨɡɛɭɠɞɟɧɢɹ ɋȾ ɜɟɞɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɜɨɡɛɭɞɢɬɟɥɹ, ɪɚɡɦɟɳɟɧɧɨɣ ɧɚ ɫɬɚɬɨɪɟ ɜɨɡɛɭɞɢɬɟɥɹ. 3.6.6. Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ ɋȾ

ɋɢɧɯɪɨɧɧɵɣ ɞɜɢɝɚɬɟɥɶ ɹɜɥɹɟɬɫɹ ɨɛɪɚɬɢɦɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɦɚɲɢɧɨɣ, ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɡɧɚɤɚ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ ɨɧ ɩɟɪɟɯɨɞɢɬ ɜ ɝɟɧɟɪɚɬɨɪɧɵɣ ɪɟɠɢɦ. ɋȾ ɫɜɨɣɫɬɜɟɧɧɵ ɬɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ, ɪɚɫɫɦɨɬɪɟɧɧɵɟ ɪɚɧɟɟ ɞɥɹ ɞɪɭɝɢɯ ɞɜɢɝɚɬɟɥɟɣ: ɪɟɤɭɩɟɪɚɬɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ, ɬɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ, ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ. ɉɪɢ ɪɟɤɭɩɟɪɚɬɢɜɧɨɦ ɬɨɪɦɨɠɟɧɢɢ, ɤɨɝɞɚ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ < 0, ɪɨɬɨɪ ɞɜɢɝɚɬɟɥɹ ɨɩɟɪɟɠɚɟɬ ɩɨɥɟ ɧɚ ɭɝɨɥ ș, ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɹɜɥɹɟɬɫɹ ɩɪɨɞɨɥɠɟɧɢɟɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɜɨ ɜɬɨɪɨɣ ɤɜɚɞɪɚɧɬ. ɉɪɢɦɟɧɹɟɬɫɹ ɪɟɤɭɩɟɪɚɰɢɹ ɜ ɫɢɫɬɟɦɟ Ƚ-Ⱦ, ɝɞɟ ɫɢɧɯɪɨɧɧɵɣ ɞɜɢɝɚɬɟɥɶ ɹɜɥɹɟɬɫɹ ɩɪɢɜɨɞɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɝɟɧɟɪɚɬɨɪɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ȼ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɚɯ ɢɡɛɵɬɨɱɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɩɟɪɟɜɨɞɢɬ ɝɟɧɟɪɚɬɨɪ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɜ ɞɜɢɝɚɬɟɥɶɧɵɣ ɪɟɠɢɦ, ɢ ɫɢɧɯɪɨɧɧɨɦɭ ɞɜɢɝɚɬɟɥɸ ɩɪɢɯɨɞɢɬɫɹ ɪɚɛɨɬɚɬɶ ɝɟɧɟɪɚɬɨɪɨɦ, ɨɬɞɚɜɚɹ ɷɧɟɪɝɢɸ ɜ ɫɟɬɶ. Ⱦɥɹ ɋȾ ɜɨɡɦɨɠɟɧ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ, ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɟɦɵɣ ɞɥɹ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ. ɂ ɋȾ ɪɚɛɨɬɚɟɬ ɩɪɢ ɬɨɪɦɨɠɟɧɢɢ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɜ ɚɫɢɧɯɪɨɧɧɨɦ ɪɟɠɢɦɟ, ɢɫɩɨɥɶɡɭɹ ɩɭɫɤɨɜɭɸ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɭɸ ɨɛɦɨɬɤɭ ɪɨɬɨɪɚ. Ⱦɥɹ ɟɝɨ ɨɫɭɳɟɫɬɜɥɟɧɢɹ, ɤɚɤ ɭ ȺȾ, ɩɟɪɟɤɥɸɱɚɸɬ ɞɜɟ ɮɚɡɵ ɧɚɫɬɚɬɨɪɟ, ɢɡɦɟɧɹɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɹ ɩɨɬɨɤɚ ɜ ɦɚɲɢɧɟ, ɩɪɨɢɫɯɨɞɢɬ ɬɨɪ164

ɦɨɠɟɧɢɟ ɧɚ ɜɵɛɟɝɟ. Ɉɞɧɚɤɨ, ɜ ɫɜɹɡɢ ɫ ɦɚɥɵɦɢ ɬɨɪɦɨɡɧɵɦɢ ɦɨɦɟɧɬɚɦɢ ɢ ɡɧɚɱɢɬɟɥɶɧɵɦɢ ɬɨɤɚɦɢ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɞɥɹ ɋȾ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɩɪɢɦɟɧɹɟɬɫɹ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɫ ɰɟɥɶɸ ɨɫɬɚɧɨɜɤɢ ɩɪɢɦɟɧɹɸɬ ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ. Ɉɛɦɨɬɤɭ ɫɬɚɬɨɪɚ ɨɬɤɥɸɱɚɸɬ ɨɬ ɫɟɬɢ ɢ ɩɨɞɤɥɸɱɚɸɬ ɧɚ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ (ɪɢɫ. 3.92). Ɉɛɦɨɬɤɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ (ɨɛɦɨɬɤɚ ɪɨɬɨɪɚ) ɨɛɬɟɤɚɟɬɫɹ ɬɨɤɨɦ, ɫɨɡɞɚɜɚɹ ɩɨɬɨɤ ɜ ɦɚɲɢɧɟ. ɗȾɋ, ɧɚɜɨɞɢɦɚɹ ɜ ɫɬɚɬɨɪɟ, ɨɩɪɟɞɟɥɹɟɬ ɬɨɤɢ ɫɬɚɬɨɪɚ, ɩɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɤɨɬɨɪɵɯ ɫ ɩɨɬɨɤɨɦ ɫɨɡɞɚɟɬɫɹ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ. Ⱦɥɹ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɜɵɤɥɸɱɢɬɶ ɦɚɫɥɹɧɵɣ ɜɵɤɥɸɱɚɬɟɥɶ ȼɆ1 ɢ ɜɤɥɸɱɢɬɶ ȼɆ2. ȼɢɞ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɡɚɜɢɫɢɬ ɨɬ ɫɩɨɫɨɛɚ ɜɨɡɛɭɠɞɟɧɢɹ:

~

Ȧ

ȼɆ1 Ȧ0ɇ 3

ȼɆ2 1

M

2 Ɇ

R + -

0 Ɋɢɫ. 3.92. ɋɯɟɦɚ ɋȾ ɞɥɹ ɪɟɠɢɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

1) ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɩɨɥɭɱɚɟɬ ɩɢɬɚɧɢɟ ɨɬ ɧɟɡɚɜɢɫɢɦɨɝɨ ɢɫɬɨɱɧɢɤɚ, ɬɨɤ Iȼ = const; 2) ɩɢɬɚɧɢɟ ɨɬ ɜɨɡɛɭɞɢɬɟɥɹ, ɪɚɡɦɟɳɺɧɧɨɝɨ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ, ɩɨɫɬɨɹɧɟɧ ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ ɜɨɡɛɭɞɢɬɟɥɹ Iȼȼ = const. ɉɪɢ ɫɧɢɠɟɧɢɢ ɫɤɨɪɨɫɬɢ ɭɦɟɧɶɲɚɟɬɫɹ ɗȾɋ ɫɬɚɬɨɪɚ; 3) ɜɨɡɛɭɞɢɬɟɥɶ ɧɚ ɜɚɥɭ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ, ɩɪɢ ɫɧɢɠɟɧɢɢ ɫɤɨɪɨɫɬɢ ɭɦɟɧɶɲɚɟɬɫɹ ɢ ɗȾɋ ɜɨɡɛɭɞɢɬɟɥɹ, ɢ ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ ɜɨɡɛɭɞɢɬɟɥɹ. ɇɚɢɥɭɱɲɢɣ ɷɮɮɟɤɬ – ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɧɟɡɚɜɢɫɢɦɨɝɨ ɢɫɬɨɱɧɢɤɚ. ɇɟɞɨɫɬɚɬɨɤ ɬɪɚɞɢɰɢɨɧɧɵɣ ɞɥɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ – ɭɦɟɧɶɲɟɧɢɟ ɦɨɦɟɧɬɚ ɩɪɢ ɫɧɢɠɟɧɢɢ ɫɤɨɪɨɫɬɢ. Ƚɥɚɜɚ ɱɟɬɜɟɪɬɚɹ

ɗɇȿɊȽȿɌɂɄȺ ɗɅȿɄɌɊɈɉɊɂȼɈȾȺ. ȼɕȻɈɊ ɗɅȿɄɌɊɈȾȼɂȽȺɌȿɅȿɃ ɉɈ ɆɈɓɇɈɋɌɂ ɗɧɟɪɝɟɬɢɤɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɫɥɟɞɭɸɳɢɟ ɜɨɩɪɨɫɵ: – ɪɚɫɱɺɬɵ ɡɚɬɪɚɬ ɧɚ ɜɵɩɨɥɧɟɧɢɟ ɡɚɞɚɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɪɚɛɨɬɵ; – ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɩɪɢ ɟɺ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɢ; – ɨɩɪɟɞɟɥɟɧɢɟ ɧɟɨɛɯɨɞɢɦɨɣ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɟɣ ɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɣ; – ɚɧɚɥɢɡ ɪɟɠɢɦɨɜ ɩɨɬɪɟɛɥɟɧɢɹ ɧɚ ɷɬɚɩɚɯ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ; – ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɚɤɬɢɜɧɨɣ ɢ ɪɟɚɤɬɢɜɧɨɣ ɷɧɟɪɝɢɢ. 165

4.1. ɗɧɟɪɝɟɬɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɗɧɟɪɝɢɹ WC, ɩɨɬɪɟɛɥɹɟɦɚɹ ɢɡ ɫɟɬɢ, ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ WɆȿɏ, ɪɚɫɯɨɞɭɟɦɚɹ ɧɚ ɜɚɥɭ, ɩɨɬɟɪɢ ɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ ǻW ɨɩɪɟɞɟɥɹɸɬ ɜɚɠɧɵɟ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɩɨɤɚɡɚɬɟɥɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɄɉȾ ƾ ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ cos ĳ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɦɢ ɜɵɪɚɠɟɧɢɹɦɢ: P Ɋ Ș = ȼ , cos ĳ = C , Ɋɋ S ɝɞɟ Ɋȼ – ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ; Ɋɋ – ɚɤɬɢɜɧɚɹ ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɦ ɢɡ ɫɟɬɢ; S – ɩɨɥɧɚɹ ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɢɡ ɫɟɬɢ. ɉɨɜɵɲɟɧɢɟ Ș ɢ cos ĳ ɩɨɡɜɨɥɹɟɬ ɩɨɥɧɟɟ ɢɫɩɨɥɶɡɨɜɚɬɶ ɷɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɹ ɢ ɫɧɢɡɢɬɶ ɟɝɨ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɟ ɪɚɫɯɨɞɵ. ɄɉȾ Ș ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ cos ĳ ɫɭɳɟɫɬɜɟɧɧɨ ɡɚɜɢɫɹɬ ɨɬ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇɋ, ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ Ȧ, ɧɚɩɪɹɠɟɧɢɹ U ɢ ɱɚɫɬɨɬɵ ɫɟɬɢ f. ɗɤɨɧɨɦɢɱɧɨɫɬɶ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɢɡɜɟɫɬɧɨɦ ɰɢɤɥɟ ɟɫɬɶ ɨɬɧɨɲɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɪɚɛɨɬɵ ɤ ɩɨɬɪɟɛɥɟɧɧɨɣ ɡɚ ɷɬɨ ɜɪɟɦɹ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ, ɤɨɬɨɪɨɟ ɧɚɡɵɜɚɸɬ ɰɢɤɥɨɜɵɦ ɄɉȾ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɩɪɢ ɷɬɨɦ ɨɬɪɟɡɤɢ ɜɪɟɦɟɧɢ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɪɢɧɢɦɚɸɬɫɹ ɬɚɤɢɦɢ, ɤɨɝɞɚ ɡɚɩɚɫ ɷɧɟɪɝɢɢ ɜ ɷɥɟɦɟɧɬɚɯ ɫɢɫɬɟɦɵ ɨɞɢɧɚɤɨɜ. tɐ

Șɐ

WɆȿɏ Wɋ

³ MPO (t) ȦPO (t) dt

0

.

tɐ

(4.1)

³ PC (t) dt

0

ɇɚɩɪɢɦɟɪ, ɞɥɹ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɟɦɚ ɡɚ ɜɪɟɦɹ ɪɚɫɱɟɬɚ ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶ ɜɪɟɦɹ ɩɨɞɴɟɦɚ ɢ ɨɩɭɫɤɚɧɢɹ ɝɪɭɡɚ, ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɜ ɧɚɱɚɥɟ ɢ ɤɨɧɰɟ ɪɚɛɨɬɵ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɛɭɞɟɬ ɨɞɢɧɚɤɨɜɚ. Ș

cos ĳ

Șɇ

cos ĳɇ

P

P

Pɇ

Pɇ

Ɋɢɫ. 4.1. ɗɧɟɪɝɟɬɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

166

ȿɫɥɢ ɧɚ ɭɱɚɫɬɤɟ ɪɚɫɱɟɬɚ ɦɟɯɚɧɢɱɟɫɤɚɹ ɦɨɳɧɨɫɬɶ ɊɆȿɏ ɢ ɦɨɳɧɨɫɬɶ Ɋɋ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɢɡ ɫɟɬɢ, ɩɨɫɬɨɹɧɧɵ, ɬɨ ɝɨɜɨɪɹɬ ɨ ɦɝɧɨɜɟɧɧɨɦ ɄɉȾ Ș = ɊɊɈ / Ɋɋ. ɂɫɯɨɞɧɵɦ ɩɚɪɚɦɟɬɪɨɦ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦ ɤɚɠɞɨɟ ɭɫɬɪɨɣɫɬɜɨ, ɹɜɥɹɟɬɫɹ ɧɨɦɢɧɚɥɶɧɵɣ ɄɉȾ Șɇ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɧɨɦɢɧɚɥɶɧɨɣ ɧɚɝɪɭɡɤɟ ɢ ɫɤɨɪɨɫɬɢ. ɄɉȾ – ɷɬɨ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ, ɹɜɥɹɸɳɚɹɫɹ ɦɟɪɨɣ ɷɤɨɧɨɦɢɱɧɨɫɬɢ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɧɟɪɝɢɢ, ɦɟɪɨɣ ɩɨɥɟɡɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨɬɪɟɛɥɹɟɦɨɣ ɷɧɟɪɝɢɢ. ɍɧɢɜɟɪɫɚɥɶɧɚɹ ɨɰɟɧɤɚ ɄɉȾ – ɩɨ ɰɢɤɥɨɜɨɦɭ ɄɉȾ Șɐ. ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɧɟɦɚɥɨɜɚɠɧɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɷɤɨɧɨɦɢɱɧɨɫɬɶ ɩɨɬɪɟɛɥɟɧɢɹ ɷɧɟɪɝɢɢ ɨɬ ɫɟɬɢ ɢɥɢ ɚɜɬɨɧɨɦɧɨɝɨ ɢɫɬɨɱɧɢɤɚ, ɬ.ɟ. ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɤɚɤ ɩɪɢɟɦɧɢɤɚ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ. ɗɤɨɧɨɦɢɱɧɨɫɬɶ ɩɨɬɪɟɛɥɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɬɟɯɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɷɥɟɦɟɧɬɨɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. Ɍɚɤ, ɞɜɢɝɚɬɟɥɶ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɨɬɪɟɛɥɹɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɷɧɟɪɝɢɸ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ, ɤɨɬɨɪɚɹ ɢɞɟɬ ɧɚ ɩɨɬɟɪɢ. ɍ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɬɨɤɢ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɫɭɳɟɫɬɜɟɧɧɨ ɜɵɲɟ, ɢ ɷɤɨɧɨɦɢɱɧɨɫɬɶ ɩɨɬɪɟɛɥɟɧɢɹ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɷɬɢɦ ɞɜɢɝɚɬɟɥɟɦ ɡɧɚɱɢɬɟɥɶɧɨ ɧɢɠɟ. ɉɪɢ ɩɨɬɪɟɛɥɟɧɢɢ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɧɚ ɩɟɪɟɦɟɧɧɨɦ ɬɨɤɟ ɞɥɹ ɩɟɪɟɞɚɱɢ ɚɤɬɢɜɧɨɣ ɦɨɳɧɨɫɬɢ Ɋ = UǜIǜcos ĳ ɧɟɨɛɯɨɞɢɦ ɬɨɤ Iǜcosĳ. ɇɨ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɢɫɬɨɱɧɢɤɚ Rɂ, ɥɢɧɢɢ RɅ ɢ ɩɪɢɟɦɧɢɤɚ RɉɊ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨɥɧɵɦ ɬɨɤɨɦ I = P / (Uǜcos ĳ). ɉɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɩɪɢɟɦɧɢɤɟ: 2

ǻɊ

2

I RɉɊ

§ · Ɋ ¨¨ ¸¸ RɉɊ © U cos ĳ ¹

2

1 §P· ¨ ¸ R cos 2 ĳ ©U¹

ǻPɉɊ , cos2 ĳ

(4.2)

ɝɞɟ ǻɊɉɊ – ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɩɪɢ ɩɟɪɟɞɚɱɟ ɧɚ ɩɨɫɬɨɹɧɧɨɦ ɬɨɤɟ. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɩɪɢ ɩɟɪɟɞɚɱɟ ɩɟɪɟɦɟɧɧɵɦ ɬɨɤɨɦ ɜ 1 / cos2ĳ ɜɵɲɟ, ɱɟɦ ɩɪɢ ɩɟɪɟɞɚɱɟ ɩɨɫɬɨɹɧɧɵɦ ɬɨɤɨɦ, ɢ ɹɫɧɨ ɫɬɪɟɦɥɟɧɢɟ ɤ ɜɫɟɦɟɪɧɨɦɭ ɩɨɜɵɲɟɧɢɸ cos ĳ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, cos ĳ ɟɫɬɶ ɦɟɪɚ ɷɤɨɧɨɦɢɱɧɨɫɬɢ ɩɨɬɪɟɛɥɟɧɢɹ ɚɤɬɢɜɧɨɣ ɦɨɳɧɨɫɬɢ. ɉɪɢ ɧɟɫɢɧɭɫɨɢɞɚɥɶɧɵɯ ɬɨɤɚɯ (ɩɢɬɚɧɢɟ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɣ) ɷɤɨɧɨɦɢɱɧɨɫɬɶ ɩɨɬɪɟɛɥɟɧɢɹ ɨɰɟɧɢɜɚɸɬ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɦɨɳɧɨɫɬɢ Ɋ . U I ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɵɫɲɢɯ ɝɚɪɦɨɧɢɤ ɤɆ=cos ĳ, ɜ ɨɫɬɚɥɶɧɵɯ ɫɥɭɱɚɹɯ ɤɆ

ɤɆ

ɤ ɂ cos ĳ 1 ,

(4.3)

(4.4)

ɝɞɟ ɤɂ = I1 / I – ɤɨɷɮɮɢɰɢɟɧɬ ɢɫɤɚɠɟɧɢɣ; I1 – ɞɟɣɫɬɜɭɸɳɟɟ ɡɧɚɱɟɧɢɟ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɢ ɧɟɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɬɨɤɚ; I – ɞɟɣɫɬɜɭɸɳɟɟ ɡɧɚɱɟɧɢɟ ɧɟɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɬɨɤɚ; ĳ1 – ɭɝɨɥ ɫɞɜɢɝɚ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɢ ɧɟɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɬɨɤɚ.

4.2. ɗɧɟɪɝɟɬɢɤɚ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɨɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɗɧɟɪɝɟɬɢɤɚ ɭɫɬɚɧɨɜɢɜɲɢɯɫɹ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɛɵɥɚ ɪɚɫɫɦɨɬɪɟɧɚ ɜɵɲɟ ɩɪɢ ɢɡɭɱɟɧɢɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɤɨɧɤɪɟɬɧɵɯ ɞɜɢɝɚɬɟɥɟɣ. Ȼɚɥɚɧɫ ɷɧɟɪɝɢɣ, ɭɱɚɫɬɜɭɸɳɢɯ ɜ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɢ, ɨɛɴɟɞɢɧɹɟɬ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɜɪɚɳɚɸɳɢɯɫɹ ɱɚɫɬɟɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ WɄ, ɷɥɟɤ167

ɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɫɢɥɨɜɵɯ ɨɛɦɨɬɨɤ Wɋ ɢ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɷɬɢɯ ɨɛɦɨɬɤɚɯ ǻW. ɏɨɬɹ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ǻɊ

ǻɊɉɈɋɌ ǻɊɉȿɊ .

ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɭɦɦɨɣ ɩɨɫɬɨɹɧɧɵɯ ǻɊɉɈɋɌ ɢ ɩɟɪɟɦɟɧɧɵɯ ǻɊɉȿɊ ɩɨɬɟɪɶ, ɧɨ ǻɊɉɈɋɌ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɧɚɝɪɭɡɤɢ ɢ ɧɚ ɤɚɱɟɫɬɜɟɧɧɵɟ ɩɨɤɚɡɚɬɟɥɢ ɷɧɟɪɝɟɬɢɤɢ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɫɭɳɟɫɬɜɟɧɧɨ ɧɟ ɫɤɚɡɵɜɚɸɬɫɹ. Ɍɟɦ ɛɨɥɟɟ, ɱɬɨ ɢɯ ɦɨɠɧɨ ɨɬɧɟɫɬɢ ɤ ɫɬɚɬɢɱɟɫɤɨɦɭ ɦɨɦɟɧɬɭ Ɇɋ. 4.2.1. ɗɧɟɪɝɟɬɢɤɚ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɨɜ Ⱦɇȼ.

Ɋɚɫɫɦɨɬɪɢɦ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɞɜɢɝɚɬɟɥɟɦ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɰɟɯɨɜɨɣ ɫɟɬɢ (ɪɢɫ.4.2). ȼ ɭɪɚɜɧɟɧɢɢ ɪɚɜɧɨɜɟɫɢɹ ɧɚɩɪɹɠɟɧɢɣ dI (4.5) dt ɭɦɧɨɠɢɦ ɨɛɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ ɧɚ ɬɨɤ ɹɤɨɪɹ I ɢ ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɪɚɜɟɧɫɬɜɚ ɦɨɳɧɨɫɬɟɣ U = E +IR +L

U I E I I2 R L I

dI , dt

(4.6)

PC = PɆȿɏ + ǻP + PL ,

(4.7)

ɝɞɟ UǜI = Ɋɋ – ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɢɡ ɫɟɬɢ; U kɎ Ȧ Ɇ E I Ɇ Ȧ ɊɆȿɏ – ɦɟɯɚɧɢLM kɎ ɱɟɫɤɚɹ ɦɨɳɧɨɫɬɶ; I2ǜR = ǻɊ – ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɫɨɩɪɨR ɬɢɜɥɟɧɢɹɯ ɹɤɨɪɧɨɣ ɰɟɩɢ; Ɇ dI 1 d(I2 ) d 1 L I L ( L I2 ) PL – dt 2 dt dt 2 ɦɨɳɧɨɫɬɶ, ɪɚɫɯɨɞɭɟɦɚɹ ɧɚ ɢɡɦɟɧɟɧɢɟ ɡɚɊɢɫ. 4.2. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ ɩɚɫɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ ɨɛɦɨɬɤɢ Ⱦɇȼ ɹɤɨɪɹ. ɗɧɟɪɝɢɹ ɟɫɬɶ ɢɧɬɟɝɪɚɥ ɡɚ ɨɩɪɟɞɟɥɟɧɧɵɣ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ, ɩɨɷɬɨɦɭ ɩɟɪɟɣɞɟɦ ɤ ɛɚɥɚɧɫɭ ɷɧɟɪɝɢɣ.

³ Pɋ dt

³ PɆȿɏ dt ³ ǻɊ dt L

I2 , 2

(4.8)

ɢɥɢ WC = WɆȿɏ + ǻWə + WL. ɋɪɚɜɧɢɦ ɷɧɟɪɝɢɸ WL, ɪɚɫɯɨɞɭɟɦɭɸ ɧɚ ɢɡɦɟɧɟɧɢɟ ɡɚɩɚɫɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ ɨɛɦɨɬɤɢ ɹɤɨɪɹ, ɫ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɩɪɢɜɨɞɚ WɄ.

168

I2 2 2 L 2 2 2 WL 2 = L R I kɎɇ R = L kɎɇ R I = = R J R Ȧ02 kɎɇ 2 WK Ȧ02 R J Ȧ02 kɎɇ 2 R J 2 1 R 2 2 ȉ ə ǿ2 = Ɍə ǿ = 2 . ɌM U2 ɌM ǿɄɁ

(4.9)

Ɍɚɤ ɤɚɤ IɄɁ / I § 10, ɚ Ɍə / ɌɆ < 1, ɬɨ WL < 0,01. Ⱦɚɠɟ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ R ɬɨɤ IɄɁ ɭɦɟɧɶɲɚɟɬɫɹ, ɡɚɬɨ ɌɆ ɪɚɫɬɟɬ, ɢ ɩɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɢɡɦɟɧɢɬɫɹ ɧɟɫɭɳɟɫɬɜɟɧɧɨ. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɷɧɟɪɝɟɬɢɤɢ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɜɟɥɢɱɢɧɨɣ WL ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɢ ɩɪɢɧɹɬɶ WL § 0. Ȼɚɥɚɧɫ ɷɧɟɪɝɢɣ ɩɪɢ ɷɬɨɦ ɩɪɢɧɢɦɚɟɬ ɜɢɞ WC

WɆȿɏ ǻW .

(4.10)

Ɋɚɫɫɦɨɬɪɢɦ ɫɨɫɬɚɜɥɹɸɳɢɟ ɷɬɨɝɨ ɛɚɥɚɧɫɚ: t

WɆȿɏ

t

Ȧ

t

t ɄɈɇ dȦ = ³ PC dt = ³ M(t) Ȧ(t) dt = ³ (MC J ) Ȧ dt = ³ MC dt ³ J Ȧ dȦ = dt 0 0 0 0 ȦɇȺɑ 2 2 ȦɄɈɇ ȦɇȺɑ Ȧ2 ȦɄɈɇ t J ; = ³ MC dt J = ³ MC dt J 2 2 2 ȦɇȺɑ 0 0 t

Wɫ

t

t

³ Pɫ dt

³ U I dt

0

0

t

dȦ

U

§ · ³ E E I dt ³ M Ȧ0 dt ³ ¨ MC J dt ¸ Ȧ0 dt © ¹ 0

(4.11)

³ MC Ȧ0 dt J Ȧ0 ȦɄɈɇ ȦɇȺɑ ; ǻW

§

Ȧ

·

§

Ȧ

·

ɄɈɇ ɇȺɑ ³ MC Ȧ0 Ȧ dt J ȦɄɈɇ ¨ Ȧ0 2 ¸ J ȦɇȺɑ ¨ Ȧ0 2 ¸. ¹ © ¹ ©

ɉɨɥɭɱɢɥɢ ɜɵɪɚɠɟɧɢɹ (4.11) ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɜ ɨɛɳɟɦ ɜɢɞɟ ɞɥɹ ɜɫɟɯ ɜɢɞɨɜ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ. Ɂɞɟɫɶ ɧɟ ɭɱɢɬɵɜɚɸɬɫɹ ɩɨɬɟɪɢ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ǻWȼɈɁȻ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɨɬɟɪɢ ǻWɏɏ, ɪɚɜɧɵɟ ɩɨɬɟɪɹɦ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ. Ɉɛɳɢɟ ɩɨɬɟɪɢ ɜ ɦɚɲɢɧɟ ǻWɆȺɒ

ǻW ǻWȼɈɁȻ ǻWXX

ǻW ³ U I dt ³ ǻPXX dt.

(4.12)

ɉɪɢɦɟɧɢɦ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɨɧɤɪɟɬɧɵɯ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ. 1. ɉɭɫɤ Ⱦɇȼ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ. ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ MC = 0; ȦɇȺɑ = 0; ȦɄɈɇ = Ȧ0 ɩɨɞɫɬɚɜɥɹɟɦ ɜ (4.11).. ɗɧɟɪɝɢɹ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɢɡ ɫɟɬɢ WC = J Ȧ02

Ȧ2 2 = J 0 2 = 2 WɄɂɇ . 2 2

(4.13)

Ɇɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ WɆȿɏ

Ȧ02 = WɄɂɇ . = J 2

169

(4.14)

ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɰɟɩɢ ɹɤɨɪɹ Ȧ

ǻW = WɄɂɇ .

Ȧ0

ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢ ɬɨɤɚ ɹɤɨɪɧɨɣ ɰɟɩɢ, ɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɩɪɢɜɨɞɚ, ɬ.ɟ. ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ ɢ ɤɜɚɞɪɚɬɨɦ ɫɤɨɪɨɫɬɢ Ȧ02 . Ɋɚɫɫɦɨɬɪɢɦ ɩɨɬɟɪɢ ɩɪɢ ɩɭɫɤɟ ɫ ɪɚɡɧɵɦɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦɢ ɜ ɰɟɩɢ ɹɤɨɪɹ (ɪɢɫ. 4.3). ɉɭɫɬɶ ɆɄ1 = 2ǜɆɄ2, ɬɨɝɞɚ ɩɪɢ ɥɸɛɨɣ ɫɤɨɪɨɫɬɢ Ɇ1 = 2ǜɆ2, ɚ I1 = 2ǜI2, R1 = R2 / 2, ɜɪɟɦɹ ɩɭɫɤɚ tɉ1 = tɉ2 / 2.

1 2 Ɇ ɆɄ2

ɆɄ1

Ɋɢɫ. 4.3. ɉɭɫɤ Ⱦɇȼ ɫ ɪɚɡɧɵɦɢ R ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 1 ǻW1

2 1

I R1 t ɉ1

2 I2 2 R2 tɉ2

2

I2 R 2 t ɉ2

ǻW2 2 2 ɪɚɜɧɵ ɩɨɬɟɪɹɦ ɷɧɟɪɝɢɢ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 2. Ʉɨɧɟɱɧɨ, ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɪɚɡɥɢɱɧɵ, ɢ ɜɪɟɦɟɧɚ ɩɭɫɤɚ ɪɚɡɥɢɱɚɸɬɫɹ, ɧɨ ɟɫɬɶ ɭɜɟɥɢɱɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ, ɢ ɤɚɤ ɜɢɞɧɨ ɢɡ ɷɬɨɝɨ ɩɪɢɦɟɪɚ, ɞɥɹ ɪɨɫɬɚ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɩɪɢɯɨɞɢɬɫɹ ɭɜɟɥɢɱɢɜɚɬɶ ɦɨɳɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ. 2. ɉɭɫɤ ɩɨɞ ɧɚɝɪɭɡɤɨɣ ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ (ɪɢɫ. 4.4): MC 0; ȦɇȺɑ = 0; ȦɄɈɇ = Ȧɋ ɩɨɞɫɬɚɜɥɹɟɦ ɜ (4.11). ɋɨɫɬɚɜɥɹɸɳɢɟ ɛɚɥɚɧɫɚ ɷɧɟɪɝɢɣ: Ȧ Wɋ = ³ Ɇɋ Ȧ0 dt J Ȧ0 ȦC ;

Ȧ0 Ȧɋ

(4.15)

2

WɆȿɏ

Ȧ = ³ Ɇɋ Ȧɋ dt J C ; 2

Ɇ

(4.16) 2

Ȧ (4.17) ǻW = ³ Ɇɋ Ȧ0 dt J Ȧ0 ȦC J C . 2 Ɇɋ ɆȾɂɇ ɉɪɢ ɫɬɚɬɢɱɟɫɤɨɣ ɫɤɨɪɨɫɬɢ, ɛɥɢɡɤɨɣ ɤ ɫɤɨɪɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Ȧɋ § Ȧ0, ɫɨɫɬɚɜɊɢɫ. 4.4. ɉɭɫɤ Ⱦɇȼ ɥɹɸɳɚɹ ɩɨɬɟɪɶ, ɡɚɜɢɫɹɳɚɹ ɨɬ J, ɛɥɢɡɤɚ ɤ WɄ, ɚ ɩɨɞ ɧɚɝɪɭɡɤɨɣ ɩɨɬɟɪɢ ɜɨɡɪɚɫɬɚɸɬ ɡɚ ɫɱɟɬ Ɇɋ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɭɫɤɨɦ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ ɭɦɟɧɶɲɢɥɫɹ ɆȾɂɇ, ɜɨɡɪɨɫɥɨ ɜɪɟɦɹ ɩɭɫɤɚ, ɜɵɪɨɫɥɢ ɢ ɩɨɬɟɪɢ ǻW. ɇɨ ɨɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɜ ɩɪɨɰɟɫɫɟ ɪɚɡɝɨɧɚ ɜɵɩɨɥɧɹɥɚɫɶ ɢ ɩɨɥɟɡɧɚɹ ɪɚɛɨɬɚ. 3. Ɍɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ MC = 0; ȦɇȺɑ = Ȧ0; ȦɄɈɇ = 0;Ȧ0 = - Ȧ0 ɩɨɞɫɬɚɜɥɹɟɦ ɜ ɮɨɪɦɭɥɵ (4.11). WC = J Ȧ02

Ȧ2 2 = J 0 2 = 2 WK . 2 2

170

(4.18)

Ȧ Ȧ0

WɆȿɏ

Ȧɋ

Ȧ 02 - J = - WK 2

(4.19)

Ȧ 02 (4.20) ) 3 WɄ . 2 Ɇ ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɤɪɚɣɧɟ ɜɟɥɢɤɢ, ɧɟ ɡɚɜɢɫɹɬ ɨɬ Ɇɋ ɜɢɞɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɫɨɩɪɨɬɢɜɥɟɧɢɹ R, ɜɪɟɦɟɧɢ ɬɨɪɦɨɠɟɧɢɹ, ɚ ɡɚɜɢɫɹɬ ɨɬ ɡɚɩɚɫɚ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. ɉɪɢ Ɇɋ > 0 (ɪɢɫ. 4.5) ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɧɟɫɤɨɥɶ- Ȧ0 ɤɨ ɫɧɢɠɚɸɬɫɹ, ɬɚɤ ɤɚɤ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ ɩɨɦɨɝɚɟɬ ɬɨɪɦɨɡɢɬɶ ɩɪɢɜɨɞ, ɡɧɚɤ ɩɨɞɢɧɬɟɝɪɚɥɶɧɨɝɨ ɜɵɪɚɠɟɧɢɹ - Ȧɋ 2 ȦC ǻW = Ɇ Ȧ Ȧ dt J Ȧ Ȧ J . – Ɋɢɫ. 4.5. Ɍɨɪɦɨɠɟɧɢɟ ³ ɋ 0 ɋ 0 C 2 ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɨɬɪɢɰɚɬɟɥɶɧɵɣ. ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɩɪɢ ɪɟɜɟɪɫɟ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ ɩɪɢ ɬɨɪɦɨɠɟɧɢɢ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɢ ɩɭɫɤɟ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ ɫɨɫɬɚɜɥɹɸɬ ǻW = 4ǜWɄ, ɩɪɢ ɞɢɧɚɦɢɱɟɫɤɨɦ ɬɨɪɦɨɠɟɧɢɢ – ǻW = WɄ. ǻW = J (Ȧ 02

4.2.2. Ɉɛ ɷɧɟɪɝɟɬɢɤɟ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɨɜ Ⱦɇȼ ɢ Ⱦɉȼ

ɗɧɟɪɝɟɬɢɤɭ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɉȼ) ɪɚɫɫɦɨɬɪɢɦ ɧɚ ɨɫɧɨɜɚɧɢɢ ɩɪɟɞɵɞɭɳɟɝɨ ɪɚɡɞɟɥɚ ɢ ɜɵɹɜɢɦ ɨɫɧɨɜɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɷɧɟɪɝɟɬɢɤɢ Ⱦɉȼ. ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɰɟɩɢ ɹɤɨɪɹ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɟ M

ǻW = ³ I2 R dt

Ⱦɉȼ Ⱦɇȼ

1

ɢ ɡɚɜɢɫɹɬ ɨɬ ɤɜɚɞɪɚɬɚ ɬɨɤɚ I2 ɢ ɜɪɟɦɟɧɢ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ tɉɉ, ɚ ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɩɨ ɨɫɧɨɜɧɨɦɭ ɭɪɚɜɧɟɧɢɸ ɞɜɢɠɟɧɢɹ ǻt

I 1 Ɋɢɫ. 4.6. Ɂɚɜɢɫɢɦɨɫɬɢ Ɇ(I) ɞɥɹ Ⱦɉȼ ɢ Ⱦɇȼ

(4.21)

J ǻȦ MȾɂɇ

(4.22)

Ɇɨɦɟɧɬ Ⱦɇȼ Ɇ = ɤ·Ɏɇ·I Ł I ɬɨɤɭ ɹɤɨɪɹ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɩɨɬɨɤɟ. Ɇɨɦɟɧɬ Ⱦɉȼ Ɇ = ɤɎ(I)ǜI Ł I, Ɏ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɬɨɤɭ ɹɤɨɪɹ ɢ ɩɨɬɨɤɭ. ɉɨɷɬɨɦɭ ɩɪɢ ɬɨɤɚɯ ɹɤɨɪɹ I > Iɇ (ɫɦ. ɪɢɫ. 4.6): ɆȾɉȼ ! ɆȾɇȼ , t ɉɉ Ⱦɉȼ t ɉɉ Ⱦɇȼ , ǻWȾɉȼ ǻWȾɇȼ .

171

ɉɪɢ I < Iɇ ɡɧɚɤɢ ɧɟɪɚɜɟɧɫɬɜɚ ɜ ɩɪɢɜɟɞɟɧɧɵɯ ɫɨɨɬɧɨɲɟɧɢɹɯ ɢɡɦɟɧɹɬɫɹ ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ. Ɉɬɫɸɞɚ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɜɵɜɨɞ, ɱɬɨ ɜ ɮɨɪɫɢɪɨɜɚɧɧɵɯ ɪɟɠɢɦɚɯ ɷɤɨɧɨɦɢɱɧɟɟ Ⱦɉȼ, ɚ ɩɪɢ ɧɚɝɪɭɡɤɚɯ, ɦɟɧɶɲɢɯ ɧɨɦɢɧɚɥɶɧɨɣ, ɫɥɟɞɭɟɬ ɨɬɞɚɬɶ ɩɪɟɞɩɨɱɬɟɧɢɟ Ⱦɇȼ. 4.2.3. ɗɧɟɪɝɟɬɢɤɚ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɨɜ ɚɫɢɧɯɪɨɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɢɦɟɸɬ ɧɟɫɤɨɥɶɤɨ ɫɨɫɬɚɜɥɹɸɳɢɯ: ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɫɬɚɬɨɪɟ ǻW1, ɜ ɪɨɬɨɪɟ ǻW2, ɩɨɬɟɪɢ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ǻWɏɏ. ɉɨɬɟɪɢ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ǻW ɏɏ ³ ǻP ɏɏ dt – ɧɚ ɬɪɟɧɢɟ, ɧɚ ɩɟɪɟɦɚɝɧɢɱɢɜɚɧɢɟ – ɬɟɨɪɟɬɢɱɟɫɤɢ ɡɚɜɢɫɹɬ ɨɬ ɫɤɨɪɨɫɬɢ, ɧɨ ɡɚɜɢɫɢɦɨɫɬɶ ɫɥɨɠɧɚ, ɢ ɩɪɚɤɬɢɱɟɫɤɢ ɢɯ ɫɱɢɬɚɸɬ ɩɨɫɬɨɹɧɧɵɦɢ ɢ ɪɚɜɧɵɦɢ ɩɨɬɟɪɹɦ ɦɨɳɧɨɫɬɢ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ ǻɊɏɏɇ. Ɍɨɝɞɚ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ǻWɏɏ = ǻɊɏɏɇ·tɉ. ɉɪɢ ɩɢɬɚɧɢɢ ɞɜɢɝɚɬɟɥɹ ɨɬ ɰɟɯɨɜɨɣ ɫɟɬɢ ɫɢɧɯɪɨɧɧɚɹ ɫɤɨɪɨɫɬɶ ɩɨɫɬɨɹɧɧɚ Ȧ0= Ȧ0ɇ = const. Ȼɭɞɟɦ ɫɱɢɬɚɬɶ ɩɨɫɬɨɹɧɧɵɦ ɢ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ J = const. ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɰɟɩɢ ɪɨɬɨɪɚ s

2

2 ³ 3 Ic2 Rc2 dt s ³ PɗɆ s dt

ǻW2 = ³ ǻP2 dt = ³ 3 I2 R 2 dt

dȦ ·

§

³ M Ȧ0 s dt ³ M Ȧ0 Ȧ dt ³ ¨ MC J dt ¸ Ȧ0 Ȧ dt ¹ ©

(4.23)

dZ ³ MC Ȧ0 Ȧ dt ³ J Ȧ0 Ȧ dt dt § Ȧ ȦɇȺɑ · § Ȧ0 ȦɄɈɇ · ¸. ¸ J ȦɇȺɑ ¨ 0 ³ MC Ȧ0 Ȧ dt J ȦɄɈɇ ¨ 2 2 © ¹ © ¹

ɉɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɩɨɥɧɨɫɬɶɸ ɩɨɜɬɨɪɹɟɬ 4.11, ɩɨɥɭɱɟɧɧɨɟ ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɉɨɬɟɪɢ ɜ ɪɨɬɨɪɟ ɧɟ ɡɚɜɢɫɹɬ ɧɢ ɨɬ ɬɨɤɚ, ɧɢ ɨɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɡɚɩɚɫɨɦ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ. ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ ɢ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɩɪɢ ɩɭɫɤɟ ɫɨɫɬɚɜɥɹɸɬ ǻW2 = WɄ, ɩɪɢ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɢ – ǻW2 = 3ǜWɄ, ɩɪɢ ɞɢɧɚɦɢɱɟɫɤɨɦ ɬɨɪɦɨɠɟɧɢɢ (ɛɟɡ ɭɱɟɬɚ ɩɨɬɟɪɶ ɜ ɫɬɚɬɨɪɟ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ) – ǻW2 = WɄ. ɉɪɢ ɧɚɥɢɱɢɢ Ɇɋ – ɫɨɨɬɧɨɲɟɧɢɹ ɚɧɚɥɨɝɢɱɧɵ. ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɰɟɩɢ ɫɬɚɬɨɪɚ ǻW1

2 ³ ǻP1 dt ³ 3 I1 r1 dt .

(4.24)

Ɍɨɤ ɫɬɚɬɨɪɚ I1 ɨɩɪɟɞɟɥɹɟɬɫɹ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɫɭɦɦɨɣ ɬɨɤɚ ɪɨɬɨɪɚ Ic2 ɢ ɬɨɤɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ Iμ. ɇɨ ɜ ɩɟɪɟɯɨɞɧɨɦ ɩɪɨɰɟɫɫɟ ɬɨɤɢ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ ɞɨɫɬɢɝɚɸɬ 5…7 – ɤɪɚɬɧɨɝɨ ɡɧɚɱɟɧɢɹ ɧɨɦɢɧɚɥɶɧɨɝɨ ɬɨɤɚ, ɜɟɥɢɤɨ ɫɤɨɥɶɠɟɧɢɟ, ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ Iμ ɢ ɩɪɢɧɹɬɶ I1 § Ic2. Ɍɨɝɞɚ ǻW1

Rc

2 2 ³ 3 Ic2 r1 dt Rc

2

r

r

1 1 ³ ǻP2 Rc dt ǻW2 Rc . 2

172

2

(4.25)

ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɫɬɚɬɨɪɟ ɡɚɜɢɫɹɬ ɨɬ ɫɨɩɪɨɬɢɜɥɟɧɢɣ r1 ɢ Rc2. ɉɨɥɧɵɟ ɩɨɬɟɪɢ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɜ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ ɫ ɞɨɩɭɳɟɧɢɟɦ, ɱɬɨ Rc2 =const

§ r · ǻW2 ¨¨1 1 ¸¸ . © Rc2 ¹

ǻW

(4.26)

Ⱦɥɹ ȺȾ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ ɦɨɠɧɨ ɩɪɢɧɹɬɶ r1 § Rc2, ɬɨɝɞɚ ǻW = 2ǜǻW2. ɉɪɚɤɬɢɱɟɫɤɢ ɩɨɥɭɱɚɟɬɫɹ, ɱɬɨ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ ɚɫɢɧɯɪɨɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜɞɜɨɟ ɛɨɥɶɲɟ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɜ ɞɜɢɝɚɬɟɥɟ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ȼɜɟɞɟɧɢɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɶ ɪɨɬɨɪɚ R2| ɫɧɢɠɚɟɬ ɨɛɳɢɟ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ǻW ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɢ ɫɧɢɠɚɟɬ ɩɨɬɟɪɢ ɜɧɭɬɪɢ ɦɚɲɢɧɵ. ɍ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɨɝɨ ȺȾ ɜɫɟ ɩɨɬɟɪɢ ɜɵɞɟɥɹɸɬɫɹ ɜɧɭɬɪɢ ɞɜɢɝɚɬɟɥɹ, ɜ ɤɚɬɚɥɨɝɚɯ ɩɪɢɜɨɞɢɬɫɹ ɞɨɩɭɫɬɢɦɨɟ ɱɢɫɥɨ ɜɤɥɸɱɟɧɢɣ ɜ ɱɚɫ. ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ ȺȾ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ ɩɪɢ Ɇɋ 0 ɢ ɢɡɜɟɫɬɧɨɣ ɜɟɥɢɱɢɧɟ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ ǻW20 ɦɨɠɧɨ ɨɰɟɧɢɬɶ, ɟɫɥɢ ɩɪɢɧɹɬɶ, ɱɬɨ ɞɜɢɝɚɬɟɥɶ ɪɚɡɝɨɧɹɟɬɫɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɪɟɞɧɟɝɨ ɦɨɦɟɧɬɚ Ɇ = ɆɋɊ = (Ɇɉ + ɆɄ) / 2 = const ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɦɨɦɟɧɬɟ ɢɧɟɪɰɢɢ J = const. ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɰɟɩɢ ɪɨɬɨɪɚ ǻW 2

³ M Ȧ 0 s dt .

ɂɡ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɆɋɊ = Ɇɋ + JǜdȦ / dt ɨɩɪɟɞɟɥɢɦ dt

J dȦ MCP MC

ɢ ɩɨɞɫɬɚɜɢɦ ɜ ɜɵɪɚɠɟɧɢɟ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ǻW2

J dȦ CP MC

³ MCP Ȧ0 s M

MCP CP MC

³ J Ȧ0 Ȧ dȦ M

MCP . ǻW20 MCP MC

(4.27)

ɉɨɬɟɪɢ ɜ ɪɨɬɨɪɟ ɩɪɢ ɩɭɫɤɟ ɫ Ɇɋ 0 ǻW 2ɉ

ǻW 2ɉɈ Ɇ § ¨¨1 ɋ © ɆɋɊ

· ¸¸ ¹

. (4.28)

ɉɨɥɧɵɟ ɩɨɬɟɪɢ ɩɪɢ ɩɭɫɤɟ ɢ r1 = Rc2 ɫɨɫɬɚɜɥɹɸɬ ǻWɉ = 2ǜǻW2ɉ. ɉɨɥɧɵɟ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɩɪɢ ɬɨɪɦɨɠɟɧɢɢ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ 'Wɉȼ

'WɉȼɈ § Ɇ · ¨¨1 ɋ ¸¸ © ɆɋɊ ¹

173

. (4.29)

4.2.4. ɉɭɬɢ ɭɥɭɱɲɟɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ ɡɚɜɢɫɹɬ ɨɬ ɡɚɩɚɫɚ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ WɄ. 1. Ⱦɥɹ ɭɦɟɧɶɲɟɧɢɹ ɩɨɬɟɪɶ ɧɭɠɧɨ ɫɧɢɠɚɬɶ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ 2

J Ȧ0 . 2

ǻWɄ

(4.30)

ɡɚ ɫɱɟɬ ɫɧɢɠɟɧɢɹ ɦɨɦɟɧɬɚ ɢɧɟɪɰɢɢ J ɢ ɫɧɢɠɟɧɢɹ ɫɤɨɪɨɫɬɢ Ȧ0 (ɩɪɢɦɟɧɹɬɶ ɞɜɢɝɚɬɟɥɢ ɫ ɦɟɧɶɲɢɦ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ JȾȼ ɢ ɫ ɦɟɧɶɲɟɣ ɫɤɨɪɨɫɬɶɸ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ). ȿɫɥɢ Ȧ = ȦɁȺȾ ɢ ɫɧɢɡɢɬɶ ɟɟ ɧɟ ɭɞɚɟɬɫɹ, ɬɨ ɞɥɹ ɫɧɢɠɟɧɢɹ JȾȼ ɩɪɢɦɟɧɹɸɬ ɞɜɢɝɚɬɟɥɢ ɫ ɹɤɨɪɟɦ ɛɨɥɶɲɟɣ ɞɥɢɧɵ ɢ ɦɟɧɶɲɟɝɨ ɞɢɚɦɟɬɪɚ – ɤɪɚɧɨɜɵɟ ɞɜɢɝɚɬɟɥɢ, ɢɧɨɝɞɚ ɭɫɬɚɧɚɜɥɢɜɚɸɬ ɞɜɚ ɞɜɢɝɚɬɟɥɹ ɩɨɥɨɜɢɧɧɨɣ ɦɨɳɧɨɫɬɢ. 2. ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ ɡɚɜɢɫɹɬ ɨɬ ɫɩɨɫɨɛɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ǻW

§ Ȧ0 ȦɄɈɇ · § Ȧ ȦɇȺɑ · ¸ J ȦɇȺɑ ¨ 0 ¸. 2 2 © ¹ © ¹

³ MC Ȧ0 Ȧ dt J ȦɄɈɇ ¨

(4.31)

Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɩɪɢ Ɇɋ 0 ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ǻW Ł (Ȧ0 – Ȧ). ɇɚ ɪɢɫ. 4.7 ɩɪɢɜɟɞɟɧɵ ɧɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɢ ɧɚ ɨɫɧɨɜɚɧɢɢ ɮɨɪɦɭɥɵ ɩɨɬɟɪɶ ǻW ɫɥɟɞɭɟɬ, ɱɬɨ ɧɚ ɞɢɚɝɪɚɦɦɟ 1 ɪɚɡɧɨɫɬɶ ɫɤɨɪɨɫɬɟɣ (Ȧ0 – Ȧ) ɦɟɧɟɟ ɬɚɤɨɜɨɣ ɧɚ ɞɢɚɝɪɚɦɦɟ 2. ɂ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɩɟɪɟɯɨɞɧɨɦ ɩɪɨɰɟɫɫɟ ɩɨ ɤɪɢɜɨɣ 1 ɛɭɞɭɬ ɦɟɧɶɲɟ, ɱɟɦ ɧɚ ɞɪɭɝɢɯ ɤɪɢɜɵɯ ǻW1 ǻW2 ǻW3 , ɩɪɢɱɟɦ ɤɚɤ ɩɪɢ ɩɭɫɤɟ, ɬɚɤ ɢ ɩɪɢ ɬɨɪɦɨɠɟɧɢɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɡɚɤɨɧ ɭɩɪɚɜɥɟɧɢɹ ɩɭɫɤɨɦ ɢ ɬɨɪɦɨɠɟɧɢɟɦ ɧɟ ɛɟɡɪɚɡɥɢɱɟɧ ɤ ɩɨɬɟɪɹɦ. 3. ɋɧɢɠɟɧɢɹ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɦɨɠɧɨ ɞɨɛɢɬɶɫɹ ɩɪɢɦɟɧɟɧɢɟɦ ɪɟɝɭɥɢɪɭɟɦɵɯ ɫɢɫɬɟɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ (Ɍɉ – Ⱦ, Ƚ – Ⱦ, ɉɑ – ȺȾ ɢ ɞɪ.), ɤɨɬɨɪɵɟ ɨɛɟɫɩɟɱɢɜɚɸɬ ɩɥɚɜɧɵɣ ɩɭɫɤ ɢ ɪɟɤɭɩɟɪɚɬɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɨɬɞɚɱɟɣ ɷɧɟɪɝɢɢ ɬɨɪɦɨɠɟɧɢɹ ɜ ɫɟɬɶ, ɱɬɨ ɧɟɜɨɡɦɨɠɧɨ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɫɟɬɢ. ɇɚ ɪɢɫ. 4.8 ɩɨɤɚɡɚɧɵ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɫɩɨɫɨɛɚɯ ɩɭɫɤɚ. ɉɪɢ ɩɭɫɤɟ ɨɬ ɫɟɬɢ ɫ U = const ɩɥɨɳɚɞɶ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ ɪɚɡɛɢɜɚɟɬɫɹ ɧɚ S1 Ł WɆȿɏ ɢ S2 Ł ǻW, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɵɜɨɞɚɦ 4.2. ɉɪɢ ɩɥɚɜɧɨɦ ɩɭɫɤɟ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɭɦɟɧɶɲɚɸɬɫɹ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɩɥɨɳɚɞɢ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦɚ ǻWɉɅ. 4. ɉɪɢ ɩɭɫɤɟ ɞɜɭɯ ɞɜɢɝɚɬɟɥɟɣ ɨɬ ɫɟɬɢ ɩɨɹɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɫɧɢɠɟɧɢɹ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɡɚ ɫɱɟɬ ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɫɟɬɢ ɫɧɚɱɚɥɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫɨɟɞɢɧɟɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ, ɚ ɩɪɢ ɞɨɫɬɢɠɟɧɢɢ ɩɨɥɨɜɢɧɧɨɣ ɫɤɨɪɨɫɬɢ – ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɩɨɞɤɥɸɱɟɧɢɹ ɢɯ ɤ ɫɟɬɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɩɪɢ ɩɭɫɤɟ ɫɧɢɠɚɸɬɫɹ ɜɞɜɨɟ (ɫɦ. ɪɢɫ. 4.8). Ɍɚɤɨɣ ɫɩɨɫɨɛ ɩɪɢɦɟɧɢɦ ɢ ɞɥɹ ɩɭɫɤɚ ɞɜɭɯɫɤɨɪɨɫɬɧɨɝɨ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɨɝɨ ȺȾ.

174

4.2.5. ɗɧɟɪɝɨɫɛɟɪɟɠɟɧɢɟ ɫɪɟɞɫɬɜɚɦɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɜ ɪɚɡɜɢɬɵɯ ɫɬɪɚɧɚɯ ɩɨɬɪɟɛɥɹɟɬ ɞɨ 65% Ȧ0 ɜɫɟɣ ɜɵɪɚɛɚɬɵɜɚɟɦɨɣ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ, ɢ ɷɧɟɪɝɨɫɛɟɪɟɠɟȦC ɧɢɟ ɫɬɚɧɨɜɢɬɫɹ ɨɞɧɨɣ ɢɡ ɨɫ1 3 ɧɨɜɧɵɯ ɩɪɨɛɥɟɦ. Ɋɚɫɫɦɚɬɪɢ2 3 ɜɚɸɬ ɞɜɚ ɧɚɩɪɚɜɥɟɧɢɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɩɪɨɛɥɟɦɵ. 2 1 1. ɗɧɟɪɝɨɫɛɟɪɟɠɟɧɢɟ ɫɨɛɫɬɜɟɧɧɨ ɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ ɜɵt ɩɨɥɧɹɟɬɫɹ ɩɭɬɟɦ ɫɧɢɠɟɧɢɹ ɩɨɬɟɪɶ ɷɧɟɪɝɢɢ ɜ ɩɪɨɰɟɫɫɟ ɩɪɟɊɢɫ. 4.7. ɋɩɨɫɨɛɵ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɛɪɚɡɨɜɚɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɷɧɟɪɝɢɢ ɜ ɦɟɯɚɧɢɱɟɫɤɭɸ, ɩɨɜɵɲɟɧɢɟ ɄɉȾ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ JǜȦ ɡɚ ɫɱɟɬ: ǻWɉɅ U=const – ɩɪɚɜɢɥɶɧɨɝɨ ɜɵɛɨɪɚ ȦɄɈɇ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨS2Ł ǻW ɫɬɢ. ɉɪɢɦɟɧɟɧɢɟ ɞɜɢɝɚɬɟɥɹ Ȧ/2 ɡɚɜɵɲɟɧɧɨɣ ɦɨɳɧɨɫɬɢ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɄɉȾ ɢ cos ĳ; S1ŁWɆȿɏ – ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɪɟɝɭɥɢȦ ɪɭɟɦɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ (Ɍɉ – Ⱦ, ɉɑ – ȺȾ ɢ ɞɪ.), ɨɛɟɫɩɟɱɢȦ0/2 Ȧ0 ɜɚɸɳɟɝɨ ɪɚɛɨɬɭ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɆɁȺȾ, ȦɁȺȾ ɫ ɦɢɧɢɦɚɥɶɊɢɫ. 4.8. ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɧɵɦɢ ɩɨɬɟɪɹɦɢ; ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɫɩɨɫɨɛɚɯ ɩɭɫɤɚ – ɨɬɤɚɡ ɨɬ ɪɟɨɫɬɚɬɧɵɯ ɫɩɨɫɨɛɨɜ ɪɟɝɭɥɢɪɨɜɚɧɢɹ; – ɩɪɢɦɟɧɟɧɢɟ ɮɢɥɶɬɪɨɤɨɦɩɟɧɫɢɪɭɸɳɢɯ ɭɫɬɪɨɣɫɬɜ ɞɥɹ ɭɜɟɥɢɱɟɧɢɹ ɤɨɷɮɢɰɢɟɧɬɚ ɦɨɳɧɨɫɬɢ ɢ ɮɢɥɶɬɪɚɰɢɢ ɜɵɫɲɢɯ ɝɚɪɦɨɧɢɤ ɬɨɤɚ. 2. ɋɨɡɞɚɧɢɟ ɷɧɟɪɝɨɫɛɟɪɟɝɚɸɳɢɯ ɬɟɯɧɨɥɨɝɢɣ ɧɚ ɛɚɡɟ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɨɩɬɢɦɢɡɚɰɢɢ ɫɚɦɢɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ, ɨɛɟɫɩɟɱɢɜɚɹ ɜɵɛɨɪ ɬɪɟɛɭɟɦɨɣ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɪɚɛɨɱɢɯ ɨɪɝɚɧɨɜ ɢɯ ɧɨɦɢɧɚɥɶɧɚɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɜɵɛɢɪɚɟɬɫɹ ɫ ɛɨɥɶɲɢɦ ɡɚɩɚɫɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɧɚɫɨɫɚ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɨɫɧɨɜɧɨɦ ɝɢɞɪɚɜɥɢɱɟɫɤɢɟ ɫɩɨɫɨɛɵ: – ɞɪɨɫɫɟɥɢɪɨɜɚɧɢɟ – ɭɫɬɚɧɨɜɤɚ ɡɚɞɜɢɠɤɢ 1 ɧɚ ɩɢɬɚɸɳɟɣ ɦɚɝɢɫɬɪɚɥɢ; – ɪɟɰɢɪɤɭɥɹɰɢɹ – ɪɚɛɨɬɚ ɧɚɫɨɫɚ ɧɚ ɩɟɪɟɩɭɫɤ, ɜɨɡɜɪɚɬ ɠɢɞɤɨɫɬɢ ɜɨ ɜɫɚɫɵɜɚɸɳɭɸ ɦɚɝɢɫɬɪɚɥɶ (ɡɚɞɜɢɠɤɚ 2). ɇɚ ɪɢɫ. 4.9 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ, ɚ ɬɚɤɠɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚɫɨɫɚ ɢ ɦɚɝɢɫɬɪɚɥɢ ɜ ɤɨɨɪɞɢɧɚɬɚɯ ɇ – ɧɚɩɨɪ, Q – ɪɚɫɯɨɞ. ɉɪɢ ɨɬɤɪɵɬɨɣ ɡɚɞɜɢɠɤɟ 1 ɢ ɡɚɤɪɵɬɨɣ 2 ɧɚɫɨɫ ɪɚɛɨɬɚɟɬ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɇ0 – 2 – 1 – 3 ɜ ɬɨɱɤɟ 1 ɩɟɪɟɫɟ Ȧ

175

ɱɟɧɢɹ ɫ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɦɚɝɢɫɬɪɚɥɢ ɇȽ – 4 – 1, ɫɨɡɞɚɜɚɹ ɧɚɩɨɪ ɇ1 ɢ ɨɛɟɫɩɟɱɢɜɚɹ ɪɚɫɯɨɞ Q1. Ⱦɥɹ ɫɧɢɠɟɧɢɹ ɪɚɫɯɨɞɚ ɞɨ Q2 ɩɪɢɤɪɵɜɚɸɬ ɡɚɞɜɢɠɤɭ 1, ɧɚɫɨɫ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ 2, ɚ ɧɚɩɨɪ ɜ ɦɚɝɢɫɬɪɚɥɢ ɫɧɢɠɟɧ ɞɨ ɇ3. ɉɥɨɳɚɞɶ ɇ2 – 2 – 4 – ɇ3 ɨɬɪɚɠɚɟɬ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɧɚ ɩɪɟɨɞɨɥɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɡɚɞɜɢɠɤɢ. ȿɫɥɢ ɩɪɢ ɨɬɤɪɵɬɨɣ ɡɚɞɜɢɠɤɟ 1 ɩɪɢɨɬɤɪɵɬɶ ɡɚɞɜɢɠɤɭ 2, ɬɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɚɝɢɫɬɪɚɥɢ ɩɟɪɟɣɞɟɬ ɜ ɬɨɱɤɭ 3 ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚɫɨɫɚ, ɜ ɦɚɝɢɫɬɪɚɥɶ ɩɨɣɞɟɬ ɪɚɫɯɨɞ Q2, ɚ ɪɚɫɯɨɞ (Q3 – Q2) ɛɭɞɟɬ ɩɟɪɟɯɨɞɢɬ ɧɚ ɜɫɚɫɵɜɚɸɳɭɸ ɦɚɝɢɫɬɪɚɥɶ. ɉɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɧɚɫɨɫɚ ɜ ɷɬɨɦ ɫɥɭɱɚɟ H H0 H2 Ɂɚɞɜ.1

2 1

H1

H01 ɇɚɫɨɫ

3

4

H3 HȽ

Ɂɚɞɜ.2

Q Q2

Q1

Q3

Ɋɢɫ. 4.9. Ƚɢɞɪɚɜɥɢɱɟɫɤɚɹ ɫɯɟɦɚ ɧɚɫɨɫɧɨɣ ɭɫɬɚɧɨɜɤɢ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ: ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɧɚɫɨɫɚ (ɇ0 – 2 – 1 – 3) ɢ ɝɢɞɪɚɜɥɢɱɟɫɤɨɣ ɫɟɬɢ (ɇȽ – 4 – 1) ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɩɥɨɳɚɞɢ Q3 – Q2 – 4 – 1. ɉɪɢɦɟɧɟɧɢɟ ɪɟɝɭɥɢɪɭɟɦɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɩɨɡɜɨɥɢɬ ɫɧɢɡɢɬɶ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ, ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɚɫɨɫɚ ɩɪɨɣɞɟɬ ɱɟɪɟɡ ɬɨɱɤɭ 4 ɢ ɨɛɟɫɩɟɱɢɬ ɬɪɟɛɭɟɦɭɸ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ Q2. Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɟ ɩɨɬɟɪɢ, ɫɜɹɡɚɧɧɵɟ ɫ ɪɟɝɭɥɢɪɨɜɚɧɢɟɦ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɧɚɫɨɫɚ, ɩɪɢ ɷɬɨɦ ɧɟ ɜɨɡɧɢɤɧɭɬ. ɉɟɪɟɯɨɞ ɤ ɪɟɝɭɥɢɪɭɟɦɨɦɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ ɧɚɫɨɫɨɜ, ɤɚɤ ɩɨɤɚɡɵɜɚɟɬ ɨɩɵɬ, ɞɚɟɬ ɞɨ 30% ɷɤɨɧɨɦɢɢ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ [10].

4.3. ȼɵɛɨɪ ɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨɫɬɢ 4.3.1. Ɉɛɳɢɟ ɩɨɥɨɠɟɧɢɹ ɩɨ ɜɵɛɨɪɭ ɞɜɢɝɚɬɟɥɟɣ

ɇɚ ɧɚɱɚɥɶɧɨɦ ɷɬɚɩɟ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɢɡɭɱɚɟɬɫɹ ɦɟɫɬɨ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɜ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ, ɟɟ ɨɫɧɨɜɧɵɟ ɮɭɧɤɰɢɢ ɢ ɡɚɞɚɱɢ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɷɬɨɝɨ ɢɡɭɱɟɧɢɹ ɮɨɪɦɭɥɢɪɭɸɬɫɹ ɬɪɟɛɨɜɚɧɢɹ ɤ ɪɚɛɨɱɟɣ ɦɚɲɢɧɟ ɫɨ ɫɬɨɪɨɧɵ ɬɟɯɧɨɥɨɝɢɢ. ɉɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɢɥɢ ɟɟ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɢɡɭɱɚɟɬɫɹ ɩɨ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɟ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɢɡɭɱɟɧɢɹ ɩɪɢɧɰɢɩɚ ɞɟɣɫɬɜɢɹ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɬɪɟɛɨɜɚɧɢɹ ɤ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ. 176

Ɉɫɧɨɜɧɵɦɢ ɬɪɟɛɨɜɚɧɢɹɦɢ, ɤɨɬɨɪɵɟ ɞɨɥɠɧɵ ɛɵɬɶ ɛɟɡɭɫɥɨɜɧɨ ɜɵɩɨɥɧɟɧɵ ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɹɜɥɹɸɬɫɹ ɬɪɟɛɨɜɚɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ: – ɧɚɞɺɠɧɨɫɬɶ – ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɨɛɹɡɚɧ ɜɵɩɨɥɧɢɬɶ ɡɚɞɚɧɧɵɟ ɮɭɧɤɰɢɢ ɜ ɨɝɨɜɨɪɟɧɧɵɯ ɭɫɥɨɜɢɹɯ ɜ ɬɟɱɟɧɢɟ ɨɩɪɟɞɟɥɺɧɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɜɪɟɦɟɧɢ. ȿɫɥɢ ɷɬɨ ɧɟ ɨɛɟɫɩɟɱɟɧɨ, ɜɫɟ ɨɫɬɚɥɶɧɵɟ ɤɚɱɟɫɬɜɚ ɨɤɚɠɭɬɫɹ ɛɟɫɩɨɥɟɡɧɵɦɢ. ɇɟɭɱɺɬ ɧɚɞɺɠɧɨɫɬɢ ɩɪɢɜɨɞɢɬ ɤ ɬɹɠɺɥɵɦ ɩɨɫɥɟɞɫɬɜɢɹɦ;– ɞɨɥɠɧɚ ɛɵɬɶ ɨɛɟɫɩɟɱɟɧɚ ɡɚɞɚɧɧɚɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɦɟɯɚɧɢɡɦɚ, ɧɢɤɨɝɞɚ ɫɧɢɠɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɧɟ ɨɤɭɩɚɟɬɫɹ ɫɧɢɠɟɧɢɟɦ ɫɬɨɢɦɨɫɬɢ ɨɛɨɪɭɞɨɜɚɧɢɹ; – ɩɟɪɟɦɟɳɟɧɢɟ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɜ ɩɪɟɞɟɥɚɯ ɡɚɞɚɧɧɨɝɨ ɜɪɟɦɟɧɢ; – ɭɫɤɨɪɟɧɢɟ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɧɟ ɞɨɥɠɧɨ ɩɪɟɜɵɲɚɬɶ ɡɚɞɚɧɧɨɝɨ (ɞɨɩɭɫɬɢɦɨɝɨ) ɡɧɚɱɟɧɢɹ; – ɨɬɤɥɨɧɟɧɢɟ ɫɤɨɪɨɫɬɢ ɭɫɬɚɧɨɜɢɜɲɟɝɨ ɪɟɠɢɦɚ ɧɟ ɞɨɥɠɧɨ ɩɪɟɜɵɲɚɬɶ ɡɚɞɚɧɧɨɝɨ ɡɧɚɱɟɧɢɹ (ɡɚɞɚɧɧɨɝɨ ɫɬɚɬɢɡɦɚ); – ɩɨ ɬɪɟɛɨɜɚɧɢɸ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɞɨɥɠɟɧ ɨɛɟɫɩɟɱɢɜɚɬɶ ɪɟɜɟɪɫ. ȼɵɛɨɪ ɪɨɞɚ ɬɨɤɚ ɢ ɬɢɩɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɨɢɡɜɨɞɢɬɶ ɧɚ ɨɫɧɨɜɟ ɪɚɫɫɦɨɬɪɟɧɢɹ ɢ ɫɪɚɜɧɟɧɢɹ ɬɟɯɧɢɤɨ-ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɪɹɞɚ ɜɚɪɢɚɧɬɨɜ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ ɬɟɯɧɢɱɟɫɤɢɦ ɬɪɟɛɨɜɚɧɢɹɦ ɞɚɧɧɨɣ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢ ɬɪɟɛɨɜɚɧɢɣ, ɩɪɟɞɴɹɜɥɹɟɦɵɯ ɤ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ, ɧɟɨɛɯɨɞɢɦɨ ɜɵɛɪɚɬɶ ɜɚɪɢɚɧɬ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɫɩɨɫɨɛɧɵɣ ɩɨɥɧɨɫɬɶɸ ɜɵɩɨɥɧɢɬɶ ɬɪɟɛɨɜɚɧɢɹ ɢ ɛɵɬɶ ɨɞɧɨɜɪɟɦɟɧɧɨ ɦɚɤɫɢɦɚɥɶɧɨ ɷɤɨɧɨɦɢɱɧɵɦ. "ɉɪɚɜɢɥɚ ɭɫɬɪɨɣɫɬɜɚ ɷɥɟɤɬɪɨɭɫɬɚɧɨɜɨɤ" >3@ ɪɟɤɨɦɟɧɞɭɸɬ ɧɚɱɢɧɚɬɶ ɩɪɨɰɟɫɫ ɜɵɛɨɪɚ ɪɨɞɚ ɬɨɤɚ ɫ ɞɜɢɝɚɬɟɥɟɣ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ. "…V – 3 – 11. Ⱦɥɹ ɩɪɢɜɨɞɚ ɦɟɯɚɧɢɡɦɨɜ, ɧɟ ɬɪɟɛɭɸɳɢɯ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ, ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɢɯ ɦɨɳɧɨɫɬɢ, ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɦɟɧɹɬɶ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɢ ɫɢɧɯɪɨɧɧɵɟ ɢɥɢ ɚɫɢɧɯɪɨɧɧɵɟ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ. Ⱦɥɹ ɩɪɢɜɨɞɚ ɦɟɯɚɧɢɡɦɨɜ, ɢɦɟɸɳɢɯ ɬɹɠɟɥɵɟ ɭɫɥɨɜɢɹ ɩɭɫɤɚ ɢɥɢ ɪɚɛɨɬɵ ɥɢɛɨ ɬɪɟɛɭɸɳɢɯ ɢɡɦɟɧɟɧɢɹ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ, ɫɥɟɞɭɟɬ ɩɪɢɦɟɧɹɬɶ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɢ ɫ ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɵɦɢ ɢ ɷɤɨɧɨɦɢɱɧɵɦɢ ɦɟɬɨɞɚɦɢ ɩɭɫɤɚ ɢɥɢ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ, ɜɨɡɦɨɠɧɵɦɢ ɜ ɞɚɧɧɨɣ ɭɫɬɚɧɨɜɤɟ… V – 3 – 14. ɗɥɟɤɬɪɨɞɜɢɝɚɬɟɥɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɞɨɩɭɫɤɚɟɬɫɹ ɩɪɢɦɟɧɹɬɶ ɬɨɥɶɤɨ ɜ ɬɟɯ ɫɥɭɱɚɹɯ, ɤɨɝɞɚ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɢ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɧɟ ɨɛɟɫɩɟɱɢɜɚɸɬ ɬɪɟɛɭɟɦɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɦɟɯɚɧɢɡɦɚ ɥɢɛɨ ɧɟ ɷɤɨɧɨɦɢɱɧɵ..." Ⱦɥɹ ɧɟɪɟɝɭɥɢɪɭɟɦɨɝɨ ɩɪɢɜɨɞɚ ɜɵɛɨɪ ɬɢɩɚ ɞɜɢɝɚɬɟɥɹ ɩɪɨɫɬ. Ⱦɜɢɝɚɬɟɥɢ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɩɪɨɳɟ ɩɨ ɤɨɧɫɬɪɭɤɰɢɢ, ɫɬɨɢɦɨɫɬɶ ɢɯ ɧɢɠɟ, ɨɛɫɥɭɠɢɜɚɧɢɟ ɬɨɠɟ ɬɪɟɛɭɟɬ ɦɟɧɶɲɢɯ ɡɚɬɪɚɬ. ɉɪɢ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɫ ɱɚɫɬɵɦɢ ɩɭɫɤɚɦɢ ɢ ɬɨɪɦɨɠɟɧɢɹɦɢ ɪɚɰɢɨɧɚɥɶɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɜɢɝɚɬɟɥɢ ɩɨɜɵɲɟɧɧɨɝɨ ɫɤɨɥɶɠɟɧɢɹ. Ⱦɥɹ ɪɟɝɭɥɢɪɭɟɦɨɝɨ ɩɪɢɜɨɞɚ ɡɚɞɚɱɚ ɜɵɛɨɪɚ ɬɢɩɚ ɩɪɢɜɨɞɚ ɪɟɲɚɟɬɫɹ ɫɥɨɠɧɟɟ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɢɚɩɚɡɨɧɚ ɢ ɩɥɚɜɧɨɫɬɢ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ, ɬɪɟɛɨɜɚɧɢɣ ɤ ɤɚɱɟɫɬɜɭ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɦɨɝɭɬ ɛɵɬɶ ɩɪɢɦɟɧɟɧɵ ɤɚɤ ɫɢɫɬɟɦɵ ɪɟɨɫɬɚɬɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ, ɬɚɤ ɢ ɫɢɫɬɟɦɵ ɫ ɢɧɞɢɜɢɞɭɚɥɶɧɵɦɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹɦɢ. ɉɪɢ ɝɥɭɛɨɤɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɫɤɨɪɨɫɬɢ ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɜɨɩɪɨɫ ɪɟɲɚɟɬɫɹ ɜ ɩɨɥɶɡɭ ɩɪɢɜɨɞɨɜ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. Ɉɞɧɚɤɨ ɤɨɧɤɭɪɟɧɬɧɵɦɢ ɩɨ ɫɜɨɢɦ ɫɜɨɣɫɬɜɚɦ ɹɜɥɹɸɬɫɹ ɩɪɢɜɨɞɵ ɫ ɱɚɫɬɨɬɧɵɦ ɢ ɱɚɫɬɨɬɧɨ-ɬɨɤɨɜɵɦ ɭɩɪɚɜɥɟɧɢɟɦ. ɉɪɟɢɦɭɳɟɫɬɜɚ ɩɪɢɜɨɞɨɜ ɫ ɚɫɢɧɯɪɨɧɧɵɦɢ ɞɜɢɝɚɬɟɥɹɦɢ - ɩɪɨɫɬɨɬɚ ɤɨɧɫɬɪɭɤɰɢɢ ɢ ɩɨɜɵɲɟɧɧɚɹ 177

ɧɚɞɟɠɧɨɫɬɶ ɞɜɢɝɚɬɟɥɟɣ, ɜɨɡɦɨɠɧɨɫɬɶ ɢɯ ɢɡɝɨɬɨɜɥɟɧɢɹ ɜ ɩɨɬɨɱɧɨɦ ɩɪɨɢɡɜɨɞɫɬɜɟ >7@. ɉɪɟɩɹɬɫɬɜɢɟɦ ɤ ɛɵɫɬɪɨɦɭ ɜɧɟɞɪɟɧɢɸ ɱɚɫɬɨɬɧɨ-ɪɟɝɭɥɢɪɭɟɦɵɯ ɩɪɢɜɨɞɨɜ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɨɫɬɶ ɫɢɫɬɟɦ ɭɩɪɚɜɥɟɧɢɹ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɧɟɞɨɫɬɚɬɨɱɧɨɣ ɧɚɞɟɠɧɨɫɬɢ ɢɯ ɪɚɛɨɬɵ ɢ ɩɨɜɵɲɟɧɧɨɣ ɫɬɨɢɦɨɫɬɢ. ȼɵɛɨɪ ɞɜɢɝɚɬɟɥɹ ɞɥɹ ɩɪɨɟɤɬɢɪɭɟɦɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ: – ɜɵɛɨɪ ɤɨɧɫɬɪɭɤɰɢɢ (ɢɫɩɨɥɧɟɧɢɹ) ɞɜɢɝɚɬɟɥɹ; – ɜɵɛɨɪ ɞɜɢɝɚɬɟɥɹ ɩɨ ɫɤɨɪɨɫɬɢ; – ɜɵɛɨɪ ɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨɫɬɢ. ɉɪɢ ɜɵɛɨɪɟ ɞɜɢɝɚɬɟɥɹ ɩɨ ɤɨɧɫɬɪɭɤɬɢɜɧɨɦɭ ɢɫɩɨɥɧɟɧɢɸ ɭɱɢɬɵɜɚɟɬɫɹ ɪɟɠɢɦ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɢ ɭɫɥɨɜɢɹ ɷɤɫɩɥɭɚɬɚɰɢɢ ɨɛɨɪɭɞɨɜɚɧɢɹ, ɩɨɞ ɤɨɬɨɪɵɦɢ ɫɥɟɞɭɟɬ ɩɨɧɢɦɚɬɶ ɭɫɥɨɜɢɹ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ (ɫɨɞɟɪɠɚɧɢɟ ɩɵɥɢ, ɤɨɪɪɨɡɢɨɧɧɨ-ɚɤɬɢɜɧɵɯ ɷɥɟɦɟɧɬɨɜ, ɜɡɪɵɜɨ- ɢ ɩɨɠɚɪɨɨɩɚɫɧɵɯ ɫɦɟɫɟɣ ɢ ɬ.ɩ.), ɜɨɡɞɟɣɫɬɜɢɟ ɤɥɢɦɚɬɢɱɟɫɤɢɯ ɮɚɤɬɨɪɨɜ ɢ ɬ.ɞ. Ⱦɜɢɝɚɬɟɥɢ ɜɵɩɭɫɤɚɸɬɫɹ ɫ ɭɱɟɬɨɦ ɤɥɢɦɚɬɢɱɟɫɤɢɯ ɮɚɤɬɨɪɨɜ ɫɪɟɞɵ, ɜ ɤɨɬɨɪɵɯ ɨɧɢ ɛɭɞɭɬ ɷɤɫɩɥɭɚɬɢɪɨɜɚɬɶɫɹ, ɜ ɩɪɟɞɟɥɚɯ ɤɨɬɨɪɵɯ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɜɵɩɨɥɧɟɧɢɟ ɮɚɤɬɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɣ ɤ ɞɜɢɝɚɬɟɥɹɦ. Ʉɥɢɦɚɬɢɱɟɫɤɨɟ ɢɫɩɨɥɧɟɧɢɟ ɭɤɚɡɵɜɚɟɬɫɹ ɜ ɩɚɫɩɨɪɬɟ ɢ ɬɚɛɥɢɱɤɟ ɞɜɢɝɚɬɟɥɹ ɜ ɜɢɞɟ ɭɫɥɨɜɧɨɝɨ ɨɛɨɡɧɚɱɟɧɢɹ: ɍ3, ɍɏɅ1. Ȼɭɤɜɵ ɜ ɨɛɨɡɧɚɱɟɧɢɢ ɨɛɨɡɧɚɱɚɸɬ ɤɥɢɦɚɬɢɱɟɫɤɨɟ ɢɫɩɨɥɧɟɧɢɟ: ɍ – ɞɥɹ ɭɦɟɪɟɧɧɨɝɨ ɤɥɢɦɚɬɚ; Ɍ – ɞɥɹ ɬɪɨɩɢɱɟɫɤɨɝɨ ɤɥɢɦɚɬɚ; ɍɏɅ – ɞɥɹ ɭɦɟɪɟɧɧɨɝɨ ɢ ɯɨɥɨɞɧɨɝɨ ɤɥɢɦɚɬɚ; Ɇ – ɞɥɹ ɦɨɪɫɤɨɝɨ ɤɥɢɦɚɬɚ. ɐɢɮɪɚ ɨɛɨɡɧɚɱɚɟɬ ɪɚɡɦɟɳɟɧɢɟ ɨɛɨɪɭɞɨɜɚɧɢɹ: 1 – ɧɚ ɨɬɤɪɵɬɨɦ ɜɨɡɞɭɯɟ; 2 – ɩɨɞ ɧɚɜɟɫɨɦ; 3 – ɜ ɡɚɤɪɵɬɵɯ ɩɨɦɟɳɟɧɢɹɯ ɫ ɟɫɬɟɫɬɜɟɧɧɨɣ ɜɟɧɬɢɥɹɰɢɟɣ; 4 – ɜ ɩɨɦɟɳɟɧɢɹɯ ɫ ɪɟɝɭɥɢɪɭɟɦɵɦɢ ɤɥɢɦɚɬɢɱɟɫɤɢɦɢ ɭɫɥɨɜɢɹɦɢ; 5 – ɜ ɩɨɦɟɳɟɧɢɹɯ ɫ ɩɨɜɵɲɟɧɧɨɣ ɜɥɚɠɧɨɫɬɶɸ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɫɬɟɩɟɧɢ ɡɚɳɢɬɵ ɷɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɹ ɩɪɢɦɟɧɹɸɬɫɹ ɛɭɤɜɵ IP ɢ ɫɥɟɞɭɸɳɢɟ ɡɚ ɧɢɦɢ ɞɜɟ ɰɢɮɪɵ (ɧɚɩɪɢɦɟɪ, IP23). ɉɟɪɜɚɹ ɰɢɮɪɚ ɨɡɧɚɱɚɟɬ ɫɬɟɩɟɧɶ ɡɚɳɢɬɵ ɨɬ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɹ ɫ ɞɜɢɠɭɳɢɦɢɫɹ ɱɚɫɬɹɦɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɦɢ ɜɧɭɬɪɢ ɞɜɢɝɚɬɟɥɹ, ɚ ɬɚɤɠɟ ɫɬɟɩɟɧɶ ɡɚɳɢɬɵ ɞɜɢɝɚɬɟɥɹ ɨɬ ɩɨɩɚɞɚɧɢɹ ɜɧɭɬɪɶ ɬɜɟɪɞɵɯ ɩɨɫɬɨɪɨɧɧɢɯ ɬɟɥ. ɋɬɟɩɟɧɶ ɡɚɳɢɬɵ, ɨɩɪɟɞɟɥɟɧɧɵɟ ɩɟɪɜɨɣ ɰɢɮɪɨɣ, ɭɤɚɡɵɜɚɸɬ: 0 – ɡɚɳɢɬɚ ɨɬɫɭɬɫɬɜɭɟɬ; 1 – ɡɚɳɢɬɚ ɨɬ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɜɧɭɬɪɶ ɬɜɟɪɞɵɯ ɬɟɥ ɪɚɡɦɟɪɨɦ ɛɨɥɟɟ 50 ɦɦ; 2 – ɡɚɳɢɬɚ ɨɬ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɬɜɟɪɞɵɯ ɬɟɥ ɪɚɡɦɟɪɨɦ ɛɨɥɟɟ 12 ɦɦ, ɚ ɬɚɤɠɟ ɩɚɥɶɰɟɜ ɢ ɩɪɟɞɦɟɬɨɜ ɞɥɢɧɨɣ ɛɨɥɟɟ 80 ɦɦ; 3 – ɡɚɳɢɬɚ ɨɬ ɬɜɟɪɞɵɯ ɬɟɥ – ɢɧɫɬɪɭɦɟɧɬɨɜ, ɩɪɨɜɨɥɨɤɢ ɞɢɚɦɟɬɪɨɦ ɢɥɢ ɬɨɥɳɢɧɨɣ ɛɨɥɟɟ 2,5 ɦɦ; 4 – ɡɚɳɢɬɚ ɨɬ ɩɪɨɜɨɥɨɤɢ, ɬɜɟɪɞɵɯ ɬɟɥ ɪɚɡɦɟɪɨɦ 1 ɦɦ; 5 – ɡɚɳɢɬɚ ɨɬ ɩɵɥɢ, ɤɨɥɢɱɟɫɬɜɨ ɩɪɨɧɢɤɚɸɳɟɣ ɩɵɥɢ ɧɟ ɧɚɪɭɲɚɟɬ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ; 6– ɩɵɥɟɧɟɩɪɨɧɢɰɚɟɦɨɫɬɶ. ȼɬɨɪɚɹ ɰɢɮɪɚ ɨɡɧɚɱɚɟɬ ɫɬɟɩɟɧɶ ɡɚɳɢɬɵ ɨɬ ɩɨɩɚɞɚɧɢɹ ɜɨɞɵ: 0 – ɡɚɳɢɬɚ ɨɬɫɭɬɫɬɜɭɟɬ; 178

1 – ɡɚɳɢɬɚ ɨɬ ɤɚɩɟɥɶ ɜɨɞɵ; 2 – ɡɚɳɢɬɚ ɨɬ ɤɚɩɟɥɶ ɜɨɞɵ ɩɪɢ ɧɚɤɥɨɧɟ ɞɨ 15º; 3 – ɡɚɳɢɬɚ ɨɬ ɞɨɠɞɹ; 4 – ɡɚɳɢɬɚ ɨɬ ɛɪɵɡɝ; 5 – ɡɚɳɢɬɚ ɨɬ ɜɨɞɹɧɵɯ ɫɬɪɭɣ; 6 – ɡɚɳɢɬɚ ɨɬ ɜɨɥɧ ɜɨɞɵ; 7 – ɡɚɳɢɬɚ ɩɪɢ ɩɨɝɪɭɠɟɧɢɢ ɜ ɜɨɞɭ; 8 – ɡɚɳɢɬɚ ɩɪɢ ɞɥɢɬɟɥɶɧɨɦ ɩɨɝɪɭɠɟɧɢɢ ɜ ɜɨɞɭ. Ɋɚɡɦɟɳɟɧɢɟ ɞɜɢɝɚɬɟɥɹ ɜ ɩɨɦɟɳɟɧɢɢ ɞɨɩɭɫɤɚɟɬ IP00 – IP20, ɧɚ ɨɬɤɪɵɬɨɦ ɜɨɡɞɭɯɟ – ɧɟ ɧɢɠɟ IP44. ȼɵɛɨɪ ɞɜɢɝɚɬɟɥɹ ɩɨ ɤɨɧɫɬɪɭɤɬɢɜɧɨɦɭ ɢɫɩɨɥɧɟɧɢɸ ɫɨɫɬɨɢɬ ɜ ɩɪɢɦɟɧɟɧɢɢ ɜ ɩɪɨɟɤɬɢɪɭɟɦɨɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ ɞɜɢɝɚɬɟɥɹ, ɩɨɞɯɨɞɹɳɟɝɨ ɩɨ ɫɩɨɫɨɛɭ ɡɚɳɢɬɵ ɨɬ ɜɨɡɞɟɣɫɬɜɢɹ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ (ɡɚɤɪɵɬɵɣ, ɡɚɳɢɳɟɧɧɵɣ ɢ ɬ.ɞ.), ɫɩɨɫɨɛɭ ɜɟɧɬɢɥɹɰɢɢ (ɫ ɫɚɦɨɜɟɧɬɢɥɹɰɢɟɣ, ɫ ɧɟɡɚɜɢɫɢɦɨɣ ɜɟɧɬɢɥɹɰɢɟɣ ɢ ɬ.ɞ.), ɩɨ ɧɚɥɢɱɢɸ ɜɫɬɪɨɟɧɧɨɝɨ ɬɚɯɨɝɟɧɟɪɚɬɨɪɚ ɢ ɞɪɭɝɢɦ ɤɨɧɫɬɪɭɤɬɢɜɧɵɦ ɨɫɨɛɟɧɧɨɫɬɹɦ. ȼɵɛɨɪ ɞɜɢɝɚɬɟɥɹ ɩɨ ɫɤɨɪɨɫɬɢ ɞɨɥɠɟɧ ɩɪɢ ɢɡɜɟɫɬɧɨɣ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɟ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɨɛɟɫɩɟɱɢɬɶ ɬɪɟɛɭɟɦɵɟ ɫɤɨɪɨɫɬɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ. ɉɪɢ ɷɬɨɦ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɞɨɥɠɟɧ ɛɵɬɶ ɧɚɦɟɱɟɧ ɫɩɨɫɨɛ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɣ ɧɚɢɥɭɱɲɢɟ ɬɟɯɧɢɤɨ-ɷɤɨɧɨɦɢɱɟɫɤɢɟ ɩɨɤɚɡɚɬɟɥɢ. ȿɫɥɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɪɚɛɨɬɚɟɬ ɜ ɪɟɠɢɦɟ ɱɚɫɬɵɯ ɩɭɫɤɨɜ ɢ ɬɨɪɦɨɠɟɧɢɣ, ɫɥɟɞɭɟɬ ɜɵɛɢɪɚɬɶ ɞɜɢɝɚɬɟɥɶ ɬɢɯɨɯɨɞɧɨɝɨ ɢɫɩɨɥɧɟɧɢɹ. 4.3.2. Ɉɫɧɨɜɧɵɟ ɤɪɢɬɟɪɢɢ ɜɵɛɨɪɚ ɞɜɢɝɚɬɟɥɟɣ ɩɨ ɦɨɳɧɨɫɬɢ

Ɂɚɞɚɱɚ ɩɪɚɜɢɥɶɧɨɝɨ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɫɜɹɡɚɧɚ, ɫ ɨɞɧɨɣ ɫɬɨɪɨɧɵ, ɫ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ ɛɟɡɭɫɥɨɜɧɨɝɨ ɨɛɟɫɩɟɱɟɧɢɹ ɬɪɟɛɨɜɚɧɢɣ ɬɟɯɧɨɥɨɝɢɢ, ɫ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ – ɫ ɨɛɟɫɩɟɱɟɧɢɟɦ ɧɚɞɟɠɧɨɫɬɢ ɟɝɨ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɣ ɪɚɛɨɬɵ, ɚ ɬɚɤɠɟ ɫ ɜɵɩɨɥɧɟɧɢɟɦ ɩɪɨɛɥɟɦ ɷɧɟɪɝɨɫɛɟɪɟɠɟɧɢɹ. ɉɪɢ ɜɵɛɨɪɟ ɞɜɢɝɚɬɟɥɹ ɡɚɧɢɠɟɧɧɨɣ ɦɨɳɧɨɫɬɢ: – ɧɚɪɭɲɚɟɬɫɹ ɧɨɪɦɚɥɶɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ; – ɫɧɢɠɚɟɬɫɹ ɟɟ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ; – ɜɨɡɧɢɤɚɸɬ ɚɜɚɪɢɢ; – ɞɜɢɝɚɬɟɥɶ ɩɪɟɠɞɟɜɪɟɦɟɧɧɨ ɜɵɯɨɞɢɬ ɢɡ ɫɬɪɨɹ. Ⱦɜɢɝɚɬɟɥɶ ɩɨɜɵɲɟɧɧɨɣ ɦɨɳɧɨɫɬɢ: – ɢɦɟɟɬ ɡɚɧɢɠɟɧɧɵɟ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɩɨɤɚɡɚɬɟɥɢ Ș ɢ cos ĳ; – ɭɜɟɥɢɱɢɜɚɟɬ ɤɚɩɢɬɚɥɶɧɵɟ ɡɚɬɪɚɬɵ; – ɩɨɜɵɲɚɟɬ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ; – ɩɪɟɠɞɟɜɪɟɦɟɧɧɨ ɜɵɜɨɞɢɬ ɢɡ ɫɬɪɨɹ ɦɟɯɚɧɢɡɦ; – ɭɜɟɥɢɱɢɜɚɟɬ ɡɚɬɪɚɬɵ ɧɚ ɪɟɦɨɧɬ. ȿɫɥɢ ɞɥɢɬɟɥɶɧɚɹ ɧɚɝɪɭɡɤɚ ɞɜɢɝɚɬɟɥɹ ɛɨɥɶɲɟ ɧɨɦɢɧɚɥɶɧɨɣ, ɜɵɲɟ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ, ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɝɪɟɜɚɟɬɫɹ, ɫɧɢɠɚɟɬɫɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɩɪɨɱɧɨɫɬɶ ɢɡɨɥɹɰɢɢ ɨɛɦɨɬɨɤ ɢ, ɤɚɤ ɫɥɟɞɫɬɜɢɟ, ɫɧɢɠɚɟɬɫɹ ɢɯ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɱɧɨɫɬɶ, ɩɨɜɵɲɚɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɨɛɨɹ ɢɡɨɥɹɰɢɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɨɫɧɨɜɧɵɦ ɤɪɢɬɟɪɢɟɦ ɜɵɛɨɪɚ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨɫɬɢ ɹɜɥɹɟɬɫɹ ɬɟɦɩɟɪɚɬɭɪɚ ɟɝɨ ɨɛɦɨɬɨɤ, ɟɝɨ ɧɚɝɪɟɜ. ɇɨɦɢɧɚɥɶɧɚɹ ɧɚɝɪɭɡɤɚ ɞɜɢɝɚɬɟɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɚɜɨɞɨɦ-ɢɡɝɨɬɨɜɢɬɟɥɟɦ ɢɡ ɭɫɥɨɜɢɣ ɧɚɝɪɟɜɚ. ɋɭɳɟɫɬɜɭɟɬ «ɜɨɫɶɦɢɝɪɚɞɭɫɧɨɟ ɩɪɚɜɢɥɨ» – ɩɨɜɵɲɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɢɡɨɥɹɰɢɢ ɨɬ ɧɨɦɢɧɚɥɶɧɨɣ ɧɚ 8 – 10 ɝɪɚɞɭɫɨɜ ɫɨɤɪɚɳɚɟɬ ɫɪɨɤ ɫɥɭɠɛɵ ɢɡɨɥɹɰɢɢ ɜ ɞɜɚ ɪɚɡɚ. 179

Ɂɚɞɚɱɚ ɜɵɛɨɪɚ ɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨɫɬɢ ɨɫɥɨɠɧɹɟɬɫɹ ɬɟɦ, ɱɬɨ ɧɚɝɪɭɡɤɚ ɧɚ ɟɝɨ ɜɚɥɭ ɜ ɩɪɨɰɟɫɫɟ ɪɚɛɨɬɵ, ɤɚɤ ɩɪɚɜɢɥɨ, ɢɡɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ ɊɊɆ = f(t), ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɢɡɦɟɧɹɸɬɫɹ ɝɪɟɸɳɢɟ ɩɨɬɟɪɢ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ. ȿɫɥɢ ɜɵɛɪɚɬɶ ɞɜɢɝɚɬɟɥɶ ɊȾȼ = ɊɆȺɄɋ ɊɆ, ɬɨ ɩɪɢ ɫɧɢɠɟɧɢɢ ɧɚɝɪɭɡɤɢ ɞɜɢɝɚɬɟɥɶ ɧɟ ɛɭɞɟɬ ɢɫɩɨɥɶɡɨɜɚɧ ɩɨ ɦɨɳɧɨɫɬɢ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɧɟɞɨɩɭɫɬɢɦɨ ɜɵɛɢɪɚɬɶ ɧɨɦɢɧɚɥɶɧɭɸ ɦɨɳɧɨɫɬɶ ɊȾȼ = ɊɆɂɇ ɊɆ. Ⱦɥɹ ɨɛɨɫɧɨɜɚɧɢɹ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɧɭɠɧɨ ɡɧɚɬɶ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ ɧɚɝɪɭɡɤɢ ɜɨ ɜɪɟɦɟɧɢ. Ⱦɥɹ ɪɚɛɨɱɢɯ ɦɚɲɢɧ, ɪɚɛɨɬɚɸɳɢɯ ɜ ɰɢɤɥɢɱɟɫɤɢɯ ɪɟɠɢɦɚɯ, ɫɬɪɨɢɬɫɹ ɧɚɝɪɭɡɨɱɧɚɹ ɞɢɚɝɪɚɦɦɚ ɊɊɆ = f(t) ɢɥɢ Ɇɋ = f(t) ɡɚ ɰɢɤɥ ɪɚɛɨɬɵ, ɤɨɬɨɪɚɹ ɩɨɡɜɨɥɹɟɬ ɫɭɞɢɬɶ ɨɛ ɢɡɦɟɧɟɧɢɢ ɩɨɬɟɪɶ ɜ ɞɜɢɝɚɬɟɥɟ, ɱɬɨ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɬɶ ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɭ ɩɪɢ ɢɡɜɟɫɬɧɨɦ ɯɚɪɚɤɬɟɪɟ ɩɪɨɰɟɫɫɚ ɧɚɝɪɟɜɚ. Ɍɚɤɨɣ ɩɨɞɯɨɞ ɩɨɡɜɨɥɹɟɬ ɜɵɛɪɚɬɶ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɶ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɦɚɤɫɢɦɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɢɡɨɥɹɰɢɢ ɨɛɦɨɬɨɤ ɧɟ ɩɪɟɜɵɫɢɥɚ ɞɨɩɭɫɬɢɦɨɝɨ ɡɧɚɱɟɧɢɹ. ɗɬɨ ɭɫɥɨɜɢɟ ɹɜɥɹɟɬɫɹ ɨɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɤɪɢɬɟɪɢɟɜ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɧɚɞɟɠɧɨɣ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɬɟɱɟɧɢɟ ɜɫɟɝɨ ɫɪɨɤɚ ɟɝɨ ɷɤɫɩɥɭɚɬɚɰɢɢ. ȼɬɨɪɨɟ ɭɫɥɨɜɢɟ ɜɵɛɨɪɚ ɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨɫɬɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɟɝɨ ɩɟɪɟɝɪɭɡɨɱɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɞɨɥɠɧɚ ɛɵɬɶ ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɭɫɬɨɣɱɢɜɨɣ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɩɟɪɢɨɞɵ ɦɚɤɫɢɦɚɥɶɧɨɣ ɧɚɝɪɭɡɤɢ. 4.3.3. Ɉɫɧɨɜɵ ɬɟɨɪɢɢ ɧɚɝɪɟɜɚ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɲɢɧ

ȼɵɞɟɥɟɧɢɟ ɬɟɩɥɨɜɵɯ ɩɨɬɟɪɶ ɩɪɢɜɨɞɢɬ ɤ ɧɚɝɪɟɜɚɧɢɸ ɞɜɢɝɚɬɟɥɹ, ɧɚɤɥɚɞɵɜɚɹ ɷɬɢɦ ɨɝɪɚɧɢɱɟɧɢɹ ɧɚ ɪɟɠɢɦɵ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɦɚɲɢɧɚ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɵɦ ɨɛɴɟɤɬɨɦ ɧɚɝɪɟɜɚ, ɜɫɟ ɨɫɨɛɟɧɧɨɫɬɢ ɤɨɬɨɪɨɝɨ ɜ ɪɚɫɱɟɬɚɯ ɩɨ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɦɭ ɜɵɛɨɪɭ ɞɜɢɝɚɬɟɥɹ ɭɱɟɫɬɶ ɬɪɭɞɧɨ. Ʉɨɧɫɬɪɭɤɰɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɲɢɧ ɫɨɞɟɪɠɢɬ ɷɥɟɦɟɧɬɵ, ɜɵɩɨɥɧɟɧɧɵɟ ɢɡ ɦɚɬɟɪɢɚɥɨɜ, ɢɦɟɸɳɢɯ ɫɭɳɟɫɬɜɟɧɧɨ ɪɚɡɥɢɱɧɵɟ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ ɢ ɬɟɩɥɨɟɦɤɨɫɬɶ. Ɇɟɞɶ ɢ ɚɥɸɦɢɧɢɣ (ɨɛɦɨɬɨɱɧɵɣ ɩɪɨɜɨɞ) ɯɨɪɨɲɨ ɩɪɨɜɨɞɹɬ ɬɟɩɥɨ. ɏɭɠɟ ɩɪɨɜɨɞɢɬ ɬɟɩɥɨ ɫɬɚɥɶ (ɦɚɝɧɢɬɨɩɪɨɜɨɞ ɢ ɫɬɚɧɢɧɚ). ɉɥɨɯɨ ɩɪɨɜɨɞɹɬ ɬɟɩɥɨ ɢɡɨɥɹɰɢɨɧɧɵɟ ɦɚɬɟɪɢɚɥɵ, ɨɤɪɭɠɚɸɳɢɟ ɩɪɨɜɨɞɧɢɤɢ – ɢɫɬɨɱɧɢɤɢ ɬɟɩɥɚ. ɉɪɟɩɹɬɫɬɜɭɸɬ ɯɨɪɨɲɟɦɭ ɨɬɜɨɞɭ ɬɟɩɥɚ ɧɟɰɢɪɤɭɥɢɪɭɸɳɢɟ ɫɥɨɢ ɜɨɡɞɭɯɚ, ɚ ɬɚɤɠɟ ɧɟɩɥɨɬɧɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɤɨɧɬɚɤɬɚ. ɋɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɸɬ ɧɚ ɧɚɝɪɟɜ ɢ ɫɩɨɫɨɛ ɨɯɥɚɠɞɟɧɢɹ ɩɨɥɨɠɟɧɢɟ ɱɚɫɬɟɣ ɦɚɲɢɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɭɬɟɣ ɩɪɨɬɟɤɚɧɢɹ ɨɯɥɚɠɞɚɸɳɟɝɨ ɜɨɡɞɭɯɚ. Ɋɚɡɥɢɱɧɵ ɩɭɬɢ ɬɟɩɥɨɩɟɪɟɞɚɱɢ: – ɨɬ ɨɛɦɨɬɨɤ ɤ ɨɯɥɚɠɞɚɸɳɟɦɭ ɜɨɡɞɭɯɭ – ɩɪɢ ɯɨɪɨɲɟɣ ɜɟɧɬɢɥɹɰɢɢ; – ɨɬ ɨɛɦɨɬɨɤ ɤ ɫɬɚɧɢɧɟ ɫ ɪɚɡɜɢɬɨɣ ɡɚ ɫɱɟɬ ɨɪɟɛɪɟɧɢɹ ɧɚɪɭɠɧɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ. ȼ ɰɟɥɹɯ ɭɩɪɨɳɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɨɪɚ ɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨɫɬɢ ɩɪɢɦɟɧɹɸɬ ɬɟɨɪɢɸ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɧɚɝɪɟɜɚ. ȿɟ ɨɫɧɨɜɧɵɟ ɞɨɩɭɳɟɧɢɹ: – ɞɜɢɝɚɬɟɥɶ – ɫɩɥɨɲɧɨɟ ɨɞɧɨɪɨɞɧɨɟ ɬɟɥɨ ɫ ɛɟɫɤɨɧɟɱɧɨ ɛɨɥɶɲɨɣ ɜɧɭɬɪɟɧɧɟɣ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶɸ (ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɨɞɢɧɚɤɨɜɚ), ɬɨ ɟɫɬɶ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɪɚɜɧɚ ɛɟɫɤɨɧɟɱɧɨɫɬɢ; – ɬɟɦɩɟɪɚɬɭɪɚ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ – ɩɨɫɬɨɹɧɧɚ, ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɩɥɚ, ɨɬɞɚɜɚɟɦɨɝɨ ɞɜɢɝɚɬɟɥɟɦ, ɬɨ ɟɫɬɶ ɩɨɦɟɳɟɧɢɟ ɨɛɥɚɞɚɟɬ ɛɟɫɤɨɧɟɱɧɨɣ ɬɟɩɥɨɟɦɤɨɫɬɶɸ (tºɈɋ = 40ºɋ); – ɬɟɩɥɨɬɚ, ɨɬɞɚɜɚɟɦɚɹ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɩɟɪɜɨɣ ɫɬɟɩɟɧɢ ɪɚɡɧɨɫɬɢ ɬɟɦɩɟɪɚɬɭɪ ɞɜɢɝɚɬɟɥɹ ɢ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ; 180

– ɬɟɩɥɨɜɵɟ ɩɨɬɟɪɢ, ɬɟɩɥɨɟɦɤɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɬɟɩɥɨɨɬɞɚɱɢ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɞɜɢɝɚɬɟɥɹ. ɉɪɢ ɭɤɚɡɚɧɧɵɯ ɭɫɥɨɜɢɹɯ ɬɟɩɥɨɜɵɟ ɩɪɨɰɟɫɫɵ ɧɚɝɪɟɜɚ ɢ ɨɯɥɚɠɞɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɨɩɢɫɵɜɚɸɬɫɹ ɭɪɚɜɧɟɧɢɟɦ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ. ɉɭɫɬɶ ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɫ ɧɚɝɪɭɡɤɨɣ Ɋ ɧɚ ɜɚɥɭ ɢ ɜɵɞɟɥɹɟɬ ɩɨɬɟɪɢ ǻɊ

Ɋ

1 Ș .

(4.32)

Ș

Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɚ ǻɊ·dt (Ⱦɠ), ɜɵɞɟɥɟɧɧɨɟ ɜ ɞɜɢɝɚɬɟɥɟ ɡɚ ɜɪɟɦɹ dt –ɚɤɬɢɜɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ. Ɂɚ ɫɱɟɬ ɩɨɬɟɪɶ ǻɊ·dt ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ Ĭ ɡɚ ɜɪɟɦɹ dt ɜɨɡɪɚɫɬɟɬ ɧɚ dĬ. ȼɵɞɟɥɟɧɧɨɟ ɬɟɩɥɨ ɪɚɫɯɨɞɭɟɬɫɹ ɩɨ ɞɜɭɦ ɧɚɩɪɚɜɥɟɧɢɹɦ: – ɨɬɞɚɟɬɫɹ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ (ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ, ɤɨɧɜɟɧɰɢɹ, ɥɭɱɟɢɫɩɭɫɤɚɧɢɟ) Ⱥ 4 4Ɉɋ dt

A Ĳ dt,

(4.33)

ɝɞɟ Ⱥ [Ⱦɠ / (ºɋǜɫ)] – ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɨɬɞɚɱɢ – ɷɬɨ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɚ, ɨɬɞɚɜɚɟɦɨɟ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ ɡɚ 1 ɫ ɩɪɢ ɪɚɡɧɨɫɬɢ ɬɟɦɩɟɪɚɬɭɪ Ĳ = 1ºɋ. Ⱥ ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɫɬɪɭɤɬɢɜɧɨɝɨ ɢɫɩɨɥɧɟɧɢɹ ɦɚɲɢɧɵ (ɡɚɤɪɵɬɨɟ, ɡɚɳɢɳɟɧɧɨɟ, ɨɬɤɪɵɬɨɟ) ɢ ɨɬ ɬɢɩɚ ɜɟɧɬɢɥɹɰɢɢ (ɧɟɜɟɧɬɢɥɢɪɭɟɦɵɣ, ɫɚɦɨɜɟɧɬɢɥɢɪɭɟɦɵɣ, ɩɪɢɧɭɞɢɬɟɥɶɧɨ ɜɟɧɬɢɥɢɪɭɟɦɵɣ); – ɢɞɟɬ ɧɚ ɭɜɟɥɢɱɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɞɜɢɝɚɬɟɥɹ, ɩɪɢɪɚɳɟɧɢɟ ɬɟɩɥɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɩɪɢɪɚɳɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɵ ɋǜdĲ, ɝɞɟ ɋ [Ⱦɠ / ºɋ]– ɬɟɩɥɨɟɦɤɨɫɬɶ ɞɜɢɝɚɬɟɥɹ – ɷɬɨ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɚ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɧɚɝɪɟɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɧɚ 1ºɋ. ɍɪɚɜɧɟɧɢɟ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɩɪɢɧɢɦɚɟɬ ɜɢɞ ǻɊ dt A Ĳ dt ɋ dW. (4.34) Ɂɚɞɚɱɚ – ɨɩɪɟɞɟɥɢɬɶ ɡɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɩɪɟɜɵɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɞɜɢɝɚɬɟɥɹ ɜɨ ɜɪɟɦɟɧɢ Ĳ(t). Ɋɚɡɞɟɥɢɦ (6.34) ɧɚ Ⱥǜdt: C dĲ ǻP . (4.35) A dt A ɉɨɥɭɱɢɥɢ ɥɢɧɟɣɧɨɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɫ ɩɪɚɜɨɣ ɱɚɫɬɶɸ. ɉɪɢ ǻɊ = const – ɩɪɚɜɚɹ ɱɚɫɬɶ ɩɨɫɬɨɹɧɧɚ – ɢɦɟɟɦ ɭɪɚɜɧɟɧɢɟ ɫ ɪɚɡɞɟɥɹɸɳɢɦɢɫɹ ɩɟɪɟɦɟɧɧɵɦɢ. Ɋɚɡɞɟɥɢɦ ɩɟɪɟɦɟɧɧɵɟ

Ĳ

ǻP Ĳ A

C dĲ , A dt

dt

C/A dĲ , Ĳ ǻP/A

t

³ dt

0

Ĳ

C/A

dĲ ³ ĲɇȺɑ Ĳ ǻP/A

(4.36)

ɢ ɜɨɡɶɦɟɦ ɢɧɬɟɝɪɚɥ: t

C Ĳ ǻP / A ln . A ĲɇȺɑ ǻP / A

(4.37)

Ɉɛɨɡɧɚɱɢɦ ɋ / Ⱥ = [(Ⱦɠ / ºɋ)ǜ(ºɋǜɫ / Ⱦɠ)] = [c] = ɌɌ ɢ ɧɚɡɨɜɟɦ ɬɟɩɥɨɜɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ.

181

Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɢɦɟɟɬ ɜɢɞ Ĳ(t)

t ǻP §¨ TɌ 1 e A ¨ ©

t · TɌ ¸Ĳ . e ¸ ɇȺɑ ¹

(4.38)

ɉɪɢ ĲɇȺɑ = 0 ɭɪɚɜɧɟɧɢɟ (4.38) ɭɩɪɨɳɚɟɬɫɹ Ĳ(t)

t ǻP §¨ TɌ 1 e A ¨ ©

· ¸, ¸ ¹

(4.39)

ɢ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɨɩɢɫɵɜɚɟɬɫɹ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɫ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ ɌɌ. ȼ ɧɚɱɚɥɟ ɩɪɨɰɟɫɫɚ (ɪɢɫ. 4.10) ɬɟɩɥɨ ɢɞɟɬ ɧɚ ɧɚɝɪɟɜ ɞɜɢɝɚɬɟɥɹ, ɬɟɩɥɨɨɬɞɚɱɚ ɧɟɡɧɚɱɢĲ Ĳɍ= ǻɊ/Ⱥ ɬɟɥɶɧɚ ɢɡ-ɡɚ ɦɚɥɨɣ ɪɚɡɧɨɫɬɢ ɬɟɦɩɟɪɚɬɭɪ ɞɜɢɝɚɬɟɥɹ ɢ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ. ɋ ɪɨɫɬɨɦ ɬɟɦɩɟɪɚɬɭɪɵ ɞɜɢɝɚɬɟɥɹ ɪɚɫɬɟɬ ɬɟɩɥɨɨɬɞɚɱɚ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɞɨɫɬɢɝɚɟɬ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ Ĳɍ. ȼ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɩɪɨɰɟɫɫɟ ɤɨɥɢɱɟɫɬɜɨ t ɬɟɩɥɚ, ɜɵɞɟɥɹɟɦɨɝɨ ɜ ɞɜɢɝɚɬɟɥɟ, ɪɚɜɧɨ ɤɨɥɢɌɇ ɱɟɫɬɜɭ ɬɟɩɥɚ, ɨɬɞɚɜɚɟɦɨɦɭ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ. Ɋɢɫ. 4.10. ɉɟɪɟɯɨɞɧɵɣ ɍɫɬɚɧɨɜɢɜɲɢɣɫɹ ɩɟɪɟɝɪɟɜ Ĳɍ = ǻɊ / Ⱥ ɩɪɨɰɟɫɫ ɧɚɝɪɟɜɚ ɞɜɢɝɚɬɟɥɹ ɡɚɜɢɫɢɬ ɨɬ ɬɟɩɥɨɜɵɯ ɩɨɬɟɪɶ ɜ ɞɜɢɝɚɬɟɥɟ ǻɊ ɢ ɟɝɨ ɬɟɩɥɨɨɬɞɚɱɢ Ⱥ, ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɩɥɨɟɦɤɨɫɬɢ. ɑɟɦ ɛɨɥɶɲɟ ɧɚɝɪɭɡɤɚ ɞɜɢɝɚɬɟɥɹ, ɬɟɦ ɛɨɥɶɲɟ ɩɨɬɟɪɢ ǻɊ, ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ Ĭ, ɜɵɲɟ ɟɝɨ ɩɟɪɟɝɪɟɜ Ĳɍ = Ĭ – ĬɈɋ. Ⱦɥɹ ɫɧɢɠɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɞɜɢɝɚɬɟɥɹ ɩɨɬɪɟɛɭɟɬɫɹ ɫɧɢɡɢɬɶ ɩɨɬɟɪɢ ǻɊ (ɭɦɟɧɶɲɢɬɶ ɧɚɝɪɭɡɤɭ), ɭɜɟɥɢɱɢɬɶ ɬɟɩɥɨɨɬɞɚɱɭ Ⱥ (ɭɫɢɥɢɬɶ ɜɟɧɬɢɥɹɰɢɸ, ɭɫɬɚɧɨɜɢɬɶ ɜɟɧɬɢɥɹɬɨɪ). Ɇɨɠɧɨ ɭɜɟɥɢɱɢɬɶ ɧɚɝɪɭɡɤɭ ɞɜɢɝɚɬɟɥɹ ɡɚ ɫɱɟɬ ɭɜɟɥɢɱɟɧɢɹ Ĳɍ, ɩɪɢɦɟɧɢɜ ɛɨɥɟɟ ɜɵɫɨɤɢɣ ɤɥɚɫɫ ɧɚɝɪɟɜɨɫɬɨɣɤɨɫɬɢ ɢɡɨɥɹɰɢɢ. ɉɭɫɬɶ Ⱥǜ Ĳǜdt = 0 (ɨɬɫɭɬɫɬɜɭɟɬ ɬɟɩɥɨɨɬɞɚɱɚ – ɚɞɢɚɛɚɬɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ). ɍɪɚɜɧɟɧɢɟ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ (4.3) ɩɪɢɦɟɬ ɜɢɞ: ǻɊ dt C dĲ ɢɥɢ ǻɊ t C Ĳ . ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɬɟɦɩɟɪɚɬɭɪ, ɚ ɜɨ ɜɪɟɦɟɧɢ ɛɭɞɟɬ ɧɚɪɚɫɬɚɬɶ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ Ĳ = (ǻɊ / ɋ) ǜt ɢ ɫɬɪɟɦɢɬɶɫɹ ɤ ɛɟɫɤɨɧɟɱɧɨɫɬɢ. ȼɪɟɦɹ, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɬɟɦɩɟɪɚɬɭɪɚ ɞɨɫɬɢɝɧɟɬ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ Ĳ = Ĳɍ, C ɋ ǻɊ ɋ Ĳ ɍ ɌɌ , (4.40) ǻP ǻɊ Ⱥ Ⱥ ɪɚɜɧɨ ɬɟɩɥɨɜɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɬɟɩɥɨɜɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ ɌɌ – ɷɬɨ ɜɪɟɦɹ, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɞɜɢɝɚɬɟɥɶ ɜ ɚɞɢɚɛɚɬɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ (ɛɟɡ ɨɬɞɚɱɢ ɬɟɩɥɚ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ) ɞɨɫɬɢɝɧɟɬ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɩɟɪɟɝɪɟɜɚ Ĳɍ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɧɨɪɦɚɥɶɧɵɦ ɭɫɥɨɜɢɹɦ ɬɟɩɥɨɨɬɞɚɱɢ. Ɍɟɩɥɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɌɌ ɡɚɜɢɫɢɬ ɨɬ ɝɚɛɚɪɢɬɚ ɦɚɲɢɧɵ, ɫ ɪɨɫɬɨɦ ɤɨɬɨɪɨɝɨ ɨɧɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ. ȼɟɥɢɱɢɧɚ ɌɌ ɢɡɦɟɪɹɟɬɫɹ ɨɬ ɞɟɫɹɬɤɨɜ ɦɢɧɭɬ ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɱɚɫɨɜ. t

182

Ɉɩɪɟɞɟɥɹɟɬɫɹ ɌɌ ɤɚɤ ɩɪɚɜɢɥɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɩɭɬɟɦ: – ɫɧɢɦɚɟɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɚɹ ɌɌ1 ɌɌ2 ɌɌ3 ɤɪɢɜɚɹ Ĳ(t); Ĳɍ – ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ Ĳɍ, ɤɨɬɨɪɨɟ ɱɚɫɬɨ ɧɟɢɡĲ(t) ɜɟɫɬɧɨ, ɪɚɡɛɢɜɚɸɬ ɤɪɢɜɭɸ Ĳ(t) ɧɚ ɭɱɚɫɬkǜǻĲ ɤɢ ɜɪɟɦɟɧɢ ǻti (ɪɢɫ. 4.11) ɢ ɩɨɥɭɱɟɧɧɵɟ ɧɚ ɤɚɠɞɨɦ ɭɱɚɫɬɤɟ ɩɪɢɪɚɳɟɧɢɹ ǻĲi ɨɬǻĲi ɤɥɚɞɵɜɚɸɬ ɜɥɟɜɨ ɨɬ ɨɫɢ Ĳ. ɑɟɪɟɡ ɩɨɥɭɱɟɧɧɵɟ ɬɨɱɤɢ ɩɪɨɜɨɞɹɬ ɭɫɪɟɞɧɟɧɧɭɸ ɩɪɹɦɭɸ ɤ·ǻĲ ɞɨ ɩɟɪɟɫɟɱɟɧɢɹ ɫ ɨɫɶɸ Ĳ ɢ t ɩɪɢ t = 0 ɧɚɯɨɞɹɬ ɭɫɬɚɧɨɜɢɜɲɟɟɫɹ ɡɧɚǻti ɱɟɧɢɟ Ĳɍ; – ɩɪɨɜɨɞɹɬ ɤɚɫɚɬɟɥɶɧɭɸ ɤ ɤɪɢɜɨɣ ɢ ɩɪɢ Ĳɍ ɧɚɯɨɞɹɬ ɬɟɩɥɨɜɭɸ ɩɨɫɬɨɹɧɧɭɸ Ɋɢɫ. 4.11. Ɉɩɪɟɞɟɥɟɧɢɟ ɌɌ ɜɪɟɦɟɧɢ ɌɌ. Ɇɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɌɌ ɩɪɢ ɢɡɜɟɫɬɧɨɦ ɡɧɚɱɟɧɢɢ Ĳɍ ɩɨ ɜɪɟɦɟɧɢ ɞɨɫɬɢɠɟɧɢɹ ɤɨɧɤɪɟɬɧɵɯ ɡɧɚɱɟɧɢɣ ɬɟɦɩɟɪɚɬɭɪɵ Ĳ ɩɨ ɮɨɪɦɭɥɟ ɷɤɫɩɨɧɟɧɬɵ: – Ĳ = 0,632·Ĳɍ ɩɪɢ t = ɌɌ; – Ĳ = 0,85·Ĳɍ ɩɪɢ t = 2·ɌɌ; – Ĳ = 0,95·Ĳɍ ɩɪɢ t =3·ɌɌ. Ɉɛɚ ɦɟɬɨɞɚ ɹɜɥɹɸɬɫɹ ɬɨɱɧɵɦɢ ɞɥɹ ɷɤɫɩɨɬɟɧɰɢɚɥɶɧɵɯ ɡɚɜɢɫɢɦɨɫɬɟɣ. Ɉɞɧɚɤɨ ɬɟɨɪɢɹ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɧɚɝɪɟɜɚ, ɩɪɢɧɹɬɚɹ ɞɥɹ ɪɚɫɱɟɬɨɜ, ɭɱɢɬɵɜɚɟɬ ɞɚɥɟɤɨ ɧɟ ɜɫɟ ɨɫɨɛɟɧɧɨɫɬɢ ɬɟɩɥɨɜɵɯ ɩɪɨɰɟɫɫɨɜ, ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɚɹ ɤɪɢɜɚɹ – ɞɚɥɟɤɨ ɧɟ ɷɤɫɩɨɧɟɧɬɚ. ɉɪɢɯɨɞɢɬɫɹ ɨɩɪɟɞɟɥɹɬɶ ɌɌ ɦɟɬɨɞɨɦ ɭɫɪɟɞɧɟɧɢɹ, ɩɭɬɟɦ ɨɩɪɟɞɟɥɟɧɢɹ ɌɌ ɜ ɧɟɫɤɨɥɶɤɢɯ ɬɨɱɤɚɯ (ɫɦ. ɪɢɫ. 4.11): Ĳ

ɌɌ

Ɍ Ɍ1 Ɍ Ɍ 2 Ɍ Ɍ 3 . 3

(4.41)

4.3.4. Ɉɯɥɚɠɞɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɲɢɧ

ɉɪɢ ɨɫɬɚɧɨɜɤɟ ɧɚɝɪɟɬɨɣ ɦɚɲɢɧɵ ɩɪɨɰɟɫɫ ɨɯɥɚɠɞɟɧɢɹ ɢɞɟɬ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɬɟɩɥɨɨɬɞɚɱɢ, ɬɟɩɥɨɜɵɟ ɩɨɬɟɪɢ ɨɬɫɭɬɫɬɜɭɸɬ ǻɊ = 0, ɭɫɬɚɧɨɜɢɜɲɚɹɫɹ ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɤɨɧɰɟ ɩɪɨɰɟɫɫɚ ɨɯɥɚɠɞɟɧɢɹ Ĳɍ = ǻɊ / Ⱥ = 0 ɢ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɩɪɢ ɨɯɥɚɠɞɟɧɢɢ ɢɦɟɟɬ ɜɢɞ: Ĳt

ĲɇȺɑ e

t TɌɈ

.

(4.42)

ȼ ɧɚɱɚɥɟ ɩɪɨɰɟɫɫɚ – ɢɧɬɟɧɫɢɜɧɚɹ ɬɟɩɥɨɨɬɞɚɱɚ, ɜɟɥɢɤɚ ɪɚɡɧɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪ ɞɜɢɝɚɬɟɥɹ ɢ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ. ɉɪɢ ɭɦɟɧɶɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɞɜɢɝɚɬɟɥɹ ɢɯ ɪɚɡɧɨɫɬɶ ɫɧɢɠɚɟɬɫɹ ɢ ɬɟɩɥɨɨɬɞɚɱɚ ɩɚɞɚɟɬ. Ɍɟɩɥɨɨɬɞɚɱɚ ɡɚɜɢɫɢɬ ɨɬ ɫɩɨɫɨɛɚ ɜɟɧɬɢɥɹɰɢɢ ɦɚɲɢɧɵ. ɉɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɶ ɝɨɧɢɬ ɱɟɪɟɡ ɫɟɛɹ ɨɯɥɚɠɞɚɸɳɢɣ ɜɨɡɞɭɯ, ɭɜɟɥɢɱɢɜɚɹ ɬɟɩɥɨɨɬɞɚɱɭ. ɍ ɨɫɬɚɧɨɜɥɟɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɫɚɦɨɜɟɧɬɢɥɹɰɢɹ ɨɬɫɭɬɫɬɜɭɟɬ, ɬɟɩɥɨɨɬɞɚɱɚ ɩɚɞɚɟɬ, ɨɫɬɚɟɬɫɹ ɬɨɥɶɤɨ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɨɬɞɚɱɢ ɫɧɢɠɚɟɬɫɹ Ⱥ = Ⱥ0, ɬɟɩɥɨ183

ɜɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɩɪɢ ɨɯɥɚɠɞɟɧɢɢ ɌɌɈ = ɋ / ȺɈ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɢ ɫɬɚɧɨɜɢɬɫɹ ɛɨɥɶɲɟ ɬɟɩɥɨɜɨɣ ɩɨɫɬɨɹɧɧɨɣ ɩɪɢ ɪɚɛɨɬɟ: ɌɌ < ɌɌɈ. ĲɇȺɑ ɇɚ ɩɪɚɤɬɢɤɟ ɩɨɥɶɡɭɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɯɭɞɲɟɧɢɹ ɭɫɥɨɜɢɣ ɬɟɩɥɨɨɬɞɚɱɢ ȕ0 = Ⱥ / Ⱥ0 = ɌɌ / ɌɌɈ, ɤɨɬɨɪɵɣ ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɫɬɪɭɤɰɢɢ ɞɜɢɝɚɬɟɥɹ ɢ ɫɩɨɫɨɛɚ ɟɝɨ ɜɟɧɬɢɥɹɰɢɢ. ɉɪɢɦɟɪɧɵɟ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ȕ0 ɞɥɹ ɞɜɢt ɝɚɬɟɥɟɣ ɪɚɡɥɢɱɧɨɝɨ ɢɫɩɨɥɧɟɧɢɹ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ.4.1. Ⱦɥɹ ɬɨɱɧɵɯ ɪɚɫɱɟɬɨɜ ɭɯɭɞɲɟɧɢɟ ɭɫɥɨɜɢɣ ɨɯɥɚɊɢɫ. 4.12. ɉɟɪɟɯɨɞɧɵɣ ɠɞɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɜ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɚɯ ɭɱɢɬɵɜɚɩɪɨɰɟɫɫ ɨɯɥɚɠɞɟɧɢɹ ɸɬ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɯɭɞɲɟɧɢɹ ɬɟɩɥɨɨɬɞɚɱɢ ɩɪɢ ɞɜɢɝɚɬɟɥɹ ɢɡɦɟɧɟɧɢɢ ɫɤɨɪɨɫɬɢ ȕi = Ⱥi / Ⱥ = ɌɌ / ɌɌi. Ɉɞɧɚɤɨ ɤɨɯ ɷɮɮɢɰɢɟɧɬ ȕi Ł Ȧ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɫɤɨɪɨɫɬɢ, ɝɞɟ ɯ > 1, ɢ ɞɥɹ ɤɚɠɞɨɣ ɫɟɪɢɢ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɲɢɧ ɷɬɨɬ ɩɨɤɚɡɚɬɟɥɶ ɫɜɨɣ. Ⱦɨɩɭɫɬɢɦɨ ɩɪɢɦɟɧɹɬɶ ɜ ɪɚɫɱɟɬɚɯ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ȕi. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɨɧ ɩɪɢɧɢɦɚɟɬ ɡɧɚɱɟɧɢɹ: Ĳ

0 Ȧ d 0,2 ȦH

ȕi

0,2 ȦH Ȧ d 0,8 ȦH

ȕi

Ȧ ! 0,8 ȦH

ȕi

ȕ0 ;

1 ȕ0 ; 2

1.

Ⱦɥɹ ɞɜɢɝɚɬɟɥɟɣ, ɪɚɛɨɬɚɸɳɢɯ ɜ ɪɟɠɢɦɚɯ ɱɚɫɬɵɯ ɩɭɫɤɨɜ ɢ ɬɨɪɦɨɠɟɧɢɣ, ɧɟɭɱɺɬ ɭɯɭɞɲɟɧɢɹ ɭɫɥɨɜɢɣ ɬɟɩɥɨɨɬɞɚɱɢ ɩɪɢɜɨɞɢɬ ɤ ɩɟɪɟɝɪɟɜɭ ɞɜɢɝɚɬɟɥɹ ɢ ɩɪɟɠɞɟɜɪɟɦɟɧɧɨɦɭ ɜɵɯɨɞɭ ɟɝɨ ɢɡ ɫɬɪɨɹ. Ɍɚɛɥɢɰɚ 4.1 Ʉɨɷɮɮɢɰɢɟɧɬ ɭɯɭɞɲɟɧɢɹ ɭɫɥɨɜɢɣ ɨɯɥɚɠɞɟɧɢɹ ȕ 0 ɂɫɩɨɥɧɟɧɢɟ ɞɜɢɝɚɬɟɥɹ ȕ0 Ɂɚɤɪɵɬɵɣ ɫ ɧɟɡɚɜɢɫɢɦɨɣ ɜɟɧɬɢɥɹɰɢɟɣ

1

Ɂɚɤɪɵɬɵɣ ɛɟɡ ɩɪɢɧɭɞɢɬɟɥɶɧɨɝɨ ɨɯɥɚɠɞɟɧɢɹ

0,95…0,98

Ɂɚɤɪɵɬɵɣ ɫ ɫɚɦɨɜɟɧɬɢɥɹɰɢɟɣ

0,45…0,55

Ɂɚɳɢɳɟɧɧɵɣ ɫ ɫɚɦɨɜɟɧɬɢɥɹɰɢɟɣ

0,25…0,35

4.3.5. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɟɣ ɩɨ ɭɫɥɨɜɢɹɦ ɧɚɝɪɟɜɚ

ȼ ɩɪɨɰɟɫɫɟ ɪɚɛɨɬɵ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɢ ɱɟɪɟɡ t = (3…4)ǜɌɌ ɞɨɫɬɢɝɧɟɬ ɭɫɬɚɧɨɜɢɜɲɟɝɨ ɡɧɚɱɟɧɢɹ Ĳ = Ĳɍ, ɤɨɝɞɚ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɚ, ɜɵɞɟɥɟɧɧɨɝɨ ɜ ɞɜɢɝɚɬɟɥɟ, ɪɚɜɧɨ ɤɨɥɢɱɟɫɬɜɭ ɬɟɩɥɚ, ɨɬɞɚɜɚɟɦɨɝɨ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ. ɗɬɨ ɜɨɡɦɨɠɧɨ ɩɪɢ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɫ ɩɨɫɬɨɹɧɧɨɣ ɧɚɝɪɭɡɤɨɣ. 184

Ɋɚɡɥɢɱɚɸɬ ɩɨ ɬɪɟɛɨɜɚɧɢɹɦ ɫɬɚɧɞɚɪɬɨɜ ɜɨɫɟɦɶ ɧɨɦɢɧɚɥɶɧɵɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɟɣ. ɉɨɞ ɧɨɦɢɧɚɥɶɧɵɦ ɪɟɠɢɦɨɦ ɪɚɛɨɬɵ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɦɚɲɢɧɵ ɩɨɧɢɦɚɸɬ ɪɟɠɢɦ, ɞɥɹ ɤɨɬɨɪɨɝɨ ɨɧɚ ɩɪɟɞɧɚɡɧɚɱɟɧɚ ɩɪɟɞɩɪɢɹɬɢɟɦ-ɢɡɝɨɬɨɜɢɬɟɥɟɦ. Ⱦɥɹ ɷɬɨɝɨ ɪɟɠɢɦɚ ɜ ɤɚɬɚɥɨɝɟ ɢ ɩɚɫɩɨɪɬɟ ɞɜɢɝɚɬɟɥɹ ɭɤɚɡɵɜɚɸɬɫɹ ɧɨɦɢɧɚɥɶɧɵɟ ɞɚɧɧɵɟ: Ɋɇ, Uɇ, Iɇ, I2ɇ, Iȼɇ,nɇ, Șɇ, cos ĳɇ ɢ ɞɪɭɝɢɟ. Ɋɟɠɢɦɵ ɪɚɛɨɬɵ ɨɛɨɡɧɚɱɚɸɬ S1…S8. S1 – ɩɪɨɞɨɥɠɢɬɟɥɶɧɵɣ ɧɨɦɢɧɚɥɶɧɵɣ ɪɟɠɢɦ – ɪɟɠɢɦ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 4.13, ɚ) ɩɪɢ ɧɟɢɡɦɟɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɧɚɝɪɭɡɤɟ, ɤɨɝɞɚ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɞɨɫɬɢɝɚɟɬ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ (ɞɜɢɝɚɬɟɥɢ ɜɟɧɬɢɥɹɬɨɪɨɜ, ɧɚɫɨɫɨɜ, ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɨɤ ɢ ɬ.ɩ.) S2 – ɤɪɚɬɤɨɜɪɟɦɟɧɧɵɣ ɧɨɦɢɧɚɥɶɧɵɣ ɪɟɠɢɦ – ɪɟɠɢɦ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 4.13, ɛ), ɤɨɝɞɚ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɡɚ ɜɪɟɦɹ ɪɚɛɨɬɵ ɫ ɩɨɫɬɨɹɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɧɚɝɪɭɡɤɨɣ ɧɟ ɞɨɫɬɢɝɚɟɬ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ, ɚ ɡɚ ɜɪɟɦɹ ɩɚɭɡɵ, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɨɬɤɥɸɱɚɟɬɫɹ ɨɬ ɫɟɬɢ, ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɭɫɩɟɜɚɟɬ ɞɨɫɬɢɱɶ ɬɟɦɩɟɪɚɬɭɪɵ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ. ɏɚɪɚɤɬɟɪɢɡɭɸɳɚɹ ɜɟɥɢɱɢɧɚ – ɜɪɟɦɹ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɣ ɪɚɛɨɬɵ tɊ: 10, 30, 60, 90 ɦɢɧ. ȼɪɟɦɹ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɣ ɪɚɛɨɬɵ tɊ = 60 ɦɢɧ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɱɚɫɨɜɨɣ ɦɨɳɧɨɫɬɶɸ. S3 – ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɵɣ ɧɨɦɢɧɚɥɶɧɵɣ ɪɟɠɢɦ – ɪɟɠɢɦ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 4.13, ɜ), ɩɪɢ ɤɨɬɨɪɨɦ ɤɪɚɬɤɨɜɪɟɦɟɧɧɵɟ ɩɟɪɢɨɞɵ ɩɨɫɬɨɹɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɧɚɝɪɭɡɤɢ (ɪɚɛɨɱɢɟ ɩɟɪɢɨɞɵ – tɊ) ɱɟɪɟɞɭɸɬɫɹ ɫ ɩɟɪɢɨɞɚɦɢ ɨɬɤɥɸɱɟɧɢɹ ɦɚɲɢɧɵ (ɩɚɭɡɚɦɢ – tɈ), ɩɪɢɱɟɦ ɤɚɤ ɩɪɢ ɪɚɛɨɬɟ, ɬɚɤ ɢ ɜ ɩɚɭɡɟ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɧɟ ɭɫɩɟɜɚɟɬ ɞɨɫɬɢɱɶ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ. Ɋɇ,ǻɊɇ,Ĳ

Ɋɇ,ǻɊɇ,Ĳ

Ɋɇ,ǻɊɇ,Ĳ

Ɋɇ

Ɋɇ

Ɋɇ Ĳɍ= ĲȾɈɉ

Ĳ

Ĳ

ǻɊɇ t ɚ

t

tɊ ǻɊɇ

tɐ

ɛ

ǻɊɇ

t0

tɊ

ɜ

t

Ɋɢɫ. 4.13. ɇɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ ɢ ɝɪɚɮɢɤɢ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɝɨ (ɚ), ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ (ɛ) ɢ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ (ɜ) ɧɨɦɢɧɚɥɶɧɵɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɏɚɪɚɤɬɟɪɢɡɭɸɳɚɹ ɜɟɥɢɱɢɧɚ – ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɜɤɥɸɱɟɧɢɹ İ = tɊ / (tɊ + t0) = tɊ / tɐ. ȼ ɤɚɬɚɥɨɝɚɯ ɩɪɢɜɨɞɹɬɫɹ ɞɚɧɧɵɟ ɞɜɢɝɚɬɟɥɟɣ ɩɪɢ ɉȼ(%) = İ·100%. Ɂɚɜɨɞ-ɢɡɝɨɬɨɜɢɬɟɥɶ ɩɪɢɜɨɞɢɬ ɞɚɧɧɵɟ ɞɨɩɭɫɤɚɟɦɨɣ ɧɚɝɪɭɡɤɢ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɉȼ = 15, 25, 40, 60, 100%. ɉɪɢ ɷɬɨɦ ɨɝɨɜɚɪɢɜɚɟɬɫɹ, ɱɬɨ ɜɪɟɦɹ ɰɢɤɥɚ ɧɟ ɞɨɥɠɧɨ ɩɪɟɜɵɲɚɬɶ tɐ 10 ɦɢɧ. Ɋɟɠɢɦɵ S1–S3 ɹɜɥɹɸɬɫɹ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɨɫɧɨɜɧɵɦɢ, ɧɨɦɢɧɚɥɶɧɵɟ ɞɚɧɧɵɟ ɧɚ ɤɨɬɨɪɵɟ ɜɤɥɸɱɚɸɬɫɹ ɜ ɩɚɫɩɨɪɬ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɢ ɤɚɬɚɥɨɝɢ. ɇɨɦɢɧɚɥɶɧɵɟ ɪɟɠɢɦɵ S4 – S8 ɜɜɟɞɟɧɵ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɜɩɨɫɥɟɞɫɬɜɢɢ ɭɩɪɨɫɬɢɬɶ ɡɚɞɚɱɭ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɪɟɠɢɦɚ, ɪɚɫɲɢɪɢɜ ɧɨɦɟɧɤɥɚɬɭɪɭ ɩɨɫɥɟɞɧɢɯ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɷɬɢ ɪɟɠɢɦɵ ɧɟ ɧɨɪɦɢɪɭɸɬɫɹ. 185

Ɂɚɞɚɱɚ ɜɵɛɨɪɚ ɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨɫɬɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨɛɵ ɩɪɚɜɢɥɶɧɨ ɫɨɩɨɫɬɚɜɢɬɶ ɟɝɨ ɪɚɛɨɱɢɣ ɪɟɠɢɦ ɫ ɧɨɦɢɧɚɥɶɧɵɦ, ɨɛɟɫɩɟɱɢɜ ɦɚɤɫɢɦɚɥɶɧɨɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɜɵɛɪɚɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɩɨ ɭɫɥɨɜɢɹɦ ɧɚɝɪɟɜɚ. 4.3.6. Ɇɟɬɨɞɵ ɷɤɜɢɜɚɥɟɧɬɢɪɨɜɚɧɢɹ ɩɨ ɧɚɝɪɟɜɭ

ɉɪɚɜɢɥɶɧɨ ɜɵɛɪɚɧɧɵɣ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɶ ɞɨɥɠɟɧ ɛɵɬɶ ɩɨɥɧɨɫɬɶɸ ɢɫɩɨɥɶɡɨɜɚɧ ɩɨ ɧɚɝɪɟɜɭ. Ⱥ ɟɫɥɢ ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɢɡɦɟɧɹɟɬɫɹ? Ɋɋ(t) = var? Ɍɨɝɞɚ ɧɭɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɦɚɤɫɢɦɚɥɶɧɭɸ ɬɟɦɩɟɪɚɬɭɪɭ ĲɆȺɄɋ ɡɚ ɜɪɟɦɹ ɪɚɛɨɬɵ ɢ ɫɪɚɜɧɢɬɶ ɫ ɞɨɩɭɫɬɢɦɨɣ ĲȾɈɉ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ĲɆȺɄɋ ĲȾɈɉ. ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɢɡɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ (ɩɟɪɟɦɟɠɚɸɳɢɣɫɹ ɪɟɠɢɦ), ɢɡɦɟɧɹɸɬɫɹ ɩɨɬɟɪɢ ǻɊ ɢ ɬɟɦɩɟɪɚɬɭɪɚ Ĭ ɞɜɢɝɚɬɟɥɹ. Ƚɪɚɮɢɤ ɧɚɝɪɭɡɤɢ ɪɚɡɨɛɶɟɦ ɧɚ ɭɱɚɫɬɤɢ, ɝɞɟ ɦɨɳɧɨɫɬɶ ɩɨɫɬɨɹɧɧɚ. ɗɬɨɦɭ ɭɫɥɨɜɢɸ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ (4.38) ɢ ɞɥɹ ɤɚɠɞɨɝɨ ɭɱɚɫɬɤɚ ɫɩɪɚɜɟɞɥɢɜɨ ɜɵɪɚɠɟɧɢɟ Ĳ (t)

t § TɌ ¨ Ĳɍ 1 e ¨ ©

t · TɌ ¸Ĳ , e ¸ ɇȺɑ ¹

ɚ ɭɱɚɫɬɤɨɜ – ɧɟɫɤɨɥɶɤɨ. ɉɪɢɜɟɞɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ Ĳ(t) ɢɫɩɨɥɶɡɨɜɚɬɶ ɦɨɠɧɨ, ɧɨ ɞɥɹ ɷɬɨɝɨ ɡɧɚɬɶ Ĳɍ = ǻɊ / Ⱥ, ɌɌ = ɋ / Ⱥ, ȕ, ɚ ɭ ɧɚɫ ɧɟɬ ɞɚɠɟ ɞɜɢɝɚɬɟɥɹ, ɢ ɩɨɷɬɨɦɭ ɞɚɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɩɪɨɜɟɪɤɢ ɩɨ ɧɚɝɪɟɜɭ ɩɪɢ ɢɡɜɟɫɬɧɨɣ ɦɨɳɧɨɫɬɢ ɢ ɬɢɩɟ ɞɜɢɝɚɬɟɥɹ. Ʉɫɬɚɬɢ, ɜ ɤɚɬɚɥɨɝɚɯ ɧɚ ɩɪɢɜɨɞɹɬɫɹ Ĳɍ, ɌɌ, ȕ, ɢɯ ɧɭɠɧɨ ɨɩɪɟɞɟɥɹɬɶ ɨɩɵɬɧɵɦ ɩɭɬɟɦ. ɂɫɩɨɥɶɡɭɟɬɫɹ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɩɪɢ ɪɚɫɱɟɬɚɯ, ɤɨɝɞɚ ɧɚ ɢɡɜɟɫɬɧɨɦ ɞɜɢɝɚɬɟɥɟ ɢɡɦɟɧɹɟɬɫɹ ɧɚɝɪɭɡɤɚ ɪɚɛɨɱɟɣ ɦɚɲɢɧɵ ɢɥɢ ɩɪɢ ɪɟɤɨɧɫɬɪɭɤɰɢɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɩɨɥɭɱɢɊ, Ĳ ɥɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɚɧɚɥɢɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɪɚɫɱɟɬɚ ɦɨɳɧɨɫɬɢ, ĲɆȺɄɋ ɤɨɝɞɚ ɪɟɚɥɶɧɵɣ ɝɪɚɮɢɤ ɫ ɢɡɦɟɧɹɸɳɟɣɫɹ ɧɚɝɪɭɡɤɨɣ ɡɚɦɟɧɹɸɬ Ɋɋ(t) Ɋɗ ɝɪɚɮɢɤɨɦ ɫ ɧɟɢɡɦɟɧɧɨɣ (ɷɤɜɢɜɚɥɟɧɬɧɨɣ) ɧɚɝɪɭɡɤɨɣ. ɗɤɜɢɜɚɥɟɧɬɧɚɹ ɧɚɝɪɭɡɤɚ ɜɵɛɢɪɚɟɬɫɹ ɢɡ ɭɫɥɨɜɢɹ, ɱɬɨ ɦɚɤɫɢɦɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɪɟɚɥɶɧɨɦ Ɋɋ(t) ɢ ɷɤt Ɋ4 Ɋ4 Ɋ1 Ɋ2 Ɋ3 Ɋ1 ɜɢɜɚɥɟɧɬɧɨɦ Ɋɗ ɝɪɚɮɢɤɚɯ ɨɞɢɧɚɤɨɜɚ (ɫɦ. ɪɢɫ. 4.14). ȼɫɟ ɷɤɜɢt4 t1 t2 t3 ɜɚɥɟɧɬɧɵɟ ɦɟɬɨɞɵ ɫɩɪɚɜɟɞɥɢɜɵ ɞɥɹ ɰɢɤɥɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɢ ɩɪɢ Ɋɢɫ. 4.14. ɇɚɝɪɭɡɨɱɧɚɹ ɞɢɚɝɪɚɦɦɚ ɜɪɟɦɟɧɢ ɰɢɤɥɚ tɐ 10 ɦɢɧ. ɋɱɢɊɋ(t)=var ɢ ɝɪɚɮɢɤ ɬɟɦɩɟɪɚɬɭɪɵ Ĳ(t). ɬɚɟɬɫɹ, ɱɬɨ ɡɚ ɷɬɨ ɜɪɟɦɹ ɬɟɩɥɨɜɨɟ ɫɨɫɬɨɹɧɢɟ ɞɜɢɝɚɬɟɥɹ (ɬɟɦɩɟɪɚɬɭɪɚ, ɬɟɩɥɨɜɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ) ɫɭɳɟɫɬɜɟɧɧɨ ɧɟ ɢɡɦɟɧɹɟɬɫɹ. Ɇɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɩɨɬɟɪɶ. ɉɪɢ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɦ ɱɢɫɥɟ ɰɢɤɥɨɜ ɝɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚɱɢɧɚɟɬ ɩɨɜɬɨɪɹɬɶɫɹ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɜ ɧɚɱɚɥɟ ɢ ɤɨɧɰɟ ɰɢɤɥɚ ɨɤɚɡɵɜɚɟɬɫɹ ɨɞɢɧɚɤɨɜɨɣ. 186

ɇɚ ɪɢɫ. 4.14 ɩɪɢɜɟɞɟɧ ɝɪɚɮɢɤ Ɋɋ(t), ɪɚɡɛɢɬɵɣ ɧɚ n ɭɱɚɫɬɤɨɜ, ɧɚ ɤɚɠɞɨɦ ɢɡ ɤɨɬɨɪɵɯ Ɋɋ = const. ɉɨɷɬɨɦɭ ɩɪɢɦɟɧɢɦɨ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ Ĳi

t § TɌi ¨ Ĳ ɍi 1 e ¨ ©

t · TɌi ¸Ĳ e . ¸ ɇȺɑi ¹

(4.43)

ɇɚ ɤɚɠɞɨɦ ɭɱɚɫɬɤɟ ɫɜɨɟ ɡɧɚɱɟɧɢɟ ɭɫɬɚɧɨɜɢɜɲɟɣɫɹ ɬɟɦɩɟɪɚɬɭɪɵ: Ĳɍi = ǻɊi / Ai. Ʉɨɧɟɱɧɨɟ ɡɧɚɱɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ ɩɟɪɜɨɦ ɭɱɚɫɬɤɟ: Ĳ ɄɈɇ1 ĲɇȺɑ1 e

t 1 TɌ1

t § 1 · TɌ1 ¸ ¨ . Ĳ ɍ1 1 e ¨ ¸ © ¹

(4.44)

Ʉɨɧɟɱɧɨɟ ɡɧɚɱɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ ɜɬɨɪɨɦ ɭɱɚɫɬɤɟ: Ĳ ɄɈɇ2 ĲɇȺɑ2 e

t 2 TɌ2

t § 2 TɌ2 ¨ Ĳ ɍ2 1 e ¨ ©

· ¸. ¸ ¹

(4.45)

ɇɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɤɚɠɞɨɝɨ ɭɱɚɫɬɤɚ ɪɚɜɧɨ ɤɨɧɟɱɧɨɦɭ ɡɧɚɱɟɧɢɸ ɩɪɟɞɵɞɭɳɟɝɨ ɭɱɚɫɬɤɚ ĲɇȺɑ2 = ĲɄɈɇ1. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɩɨɞɫɬɚɜɥɹɹ ɜ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɡɧɚɱɟɧɢɹ ĲɄɈɇi = ĲɇȺɑ(I-1), ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ n-ɨɝɨ ɭɱɚɫɬɤɚ Ĳ ɄɈɇn ĲɇȺɑ1 e

n t ¦( i ) T i 1 Ɍi

n

t t § ¦( i ) 1 · Ti TɌ1 ¸ ¨ e i 2 Ĳ ɍ1 1 e ¸ ¨ ¹ ©

(4.46) n t t t § § ¦( i ) 2 · n · Ti Ĳ ɍ2 ¨1 e TɌ2 ¸ e i 3 .... Ĳ ɍn ¨1 e TTn ¸. ¨ ¸ ¨ ¸ © ¹ © ¹ ȿɫɥɢ ɩɪɢɧɹɬɶ, ɱɬɨ ɡɧɚɱɟɧɢɟ ĲɆȺɄɋ ɩɨɥɭɱɚɟɦ ɜ ɧɚɱɚɥɟ ɰɢɤɥɚ ĲɇȺɑ1, ɚ ɨɧɨ ɪɚɜɧɨ ɤɨɧɟɱɧɨɦɭ ɡɧɚɱɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ n – ɨɦ ɭɱɚɫɬɤɟ ĲɄɈɇn. Ĳ ɄɈɇn ĲɇȺɑ1 ĲɆȺɄɋ n

t t t § § ¦( i ) 1 · 2 Ti T T Ĳ ɍ1 ¨1 e Ɍ1 ¸ e i 2 Ĳ ɍ2 ¨1 e Ɍ2 ¨ ¸ ¨ © ¹ ©

n

t · ¦ ( ti ) § n Ti T ¸ e i 3 .... Ĳ ¨1 e Tn ɍn ¨ ¸ ¹ ©

n t ¦( i ) T i 1 Ɍi

· ¸ ¸ ¹.

(4.47)

1 e ȼɨɫɩɨɥɶɡɭɟɦɫɹ ɪɚɡɥɨɠɟɧɢɟɦ ɜ ɪɹɞ Ɇɚɤɥɨɪɟɧɚ ɮɭɧɤɰɢɢ eɍ | 1

y y2 .... , ɫɩɪɚɜɟɞɥɢɜɨɣ ɞɥɹ y << 1. 1! 2!

ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ, ɜɪɟɦɹ ɰɢɤɥɚ tɐ 10 ɦɢɧ << TT – ɬɟɩɥɨɜɨɣ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ, ɨɬɧɨɲɟɧɢɟ y = tɐ / TT << 1. Ɉɬɫɸɞɚ ɦɨɠɧɨ ɩɪɢɧɹɬɶ:

e ɍ | 1; 1 ɟ ɍ | ɭ .

187

ɇɚɣɞɟɦ ɦɚɤɫɢɦɚɥɶɧɭɸ ɬɟɦɩɟɪɚɬɭɪɭ ĲɆȺɄɋ ɪɟɚɥɶɧɨɝɨ ɝɪɚɮɢɤɚ ɫ ɭɱɟɬɨɦ ɩɪɢɧɹɬɵɯ ɞɨɩɭɳɟɧɢɣ Ĳ ɍ1 ĲɆȺɄɋ

ti · ¸ TTi ¸¹ 1© . n § t · ¦ ¨¨ i ¸¸ i 1 © TTi ¹

n

t1 t t Ĳ ɍ2 2 ... Ĳ ɍn n TT1 TT2 TTn n § t · ¦ ¨¨ i ¸¸ i 1 © TTi ¹

§

¦ ¨¨ Ĳ ɍi i

(4.48)

Ɇɚɤɫɢɦɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ĲɆȺɄɋ ɪɟɚɥɶɧɨɝɨ ɝɪɚɮɢɤɚ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɚ ɦɚɤɫɢɦɚɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɢ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɝɪɚɮɢɤɚ § · ¨ 'Pi ti ¸ ¦¨ C ¸¸ i 1¨ Ai Ai ¹ © · § n ¨ t ¸ i ¦¨ C ¸ i 1¨ ¸ © Ai ¹ n

ĲɆȺɄɋ

'Ɋɗ Ⱥ

n

¦ 'Pi t i i 1 n

d Ĳ ȾɈɉ

¦ A i t i

ǻPɇ . Ⱥ

(4.49)

i 1

ɉɨɬɟɪɢ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɝɪɚɮɢɤɚ n

n

i 1 n

i 1 n

¦ ('Ɋi t i ) ¦ ('Pi t i ) ǻPɗ

Ⱥ

¦ (A i t i ) i 1

d 'PH

(4.50)

¦ (ȕi t i ) i 1

ɫɪɚɜɧɢɜɚɸɬɫɹ ɫ ɧɨɦɢɧɚɥɶɧɵɦɢ ɩɨɬɟɪɹɦɢ ǻɊɇ. ɉɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ (4.50) ɹɜɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ ɦɟɬɨɞɚ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɩɨɬɟɪɶ. ɉɨ ɧɟɣ ɨɩɪɟɞɟɥɹɸɬ ɩɪɚɜɢɥɶɧɨɫɬɶ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɜ ɱɢɫɥɢɬɟɥɟ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫɭɦɦɚɪɧɚɹ ɷɧɟɪɝɢɹ ɬɟɩɥɨɜɵɯ ɩɨɬɟɪɶ ɞɜɢɝɚɬɟɥɹ ɜ ɰɢɤɥɟ, ɚ ɡɧɚɦɟɧɚɬɟɥɶ ɭɱɢɬɵɜɚɟɬ ɭɯɭɞɲɟɧɢɟ ɭɫɥɨɜɢɣ ɨɯɥɚɠɞɟɧɢɹ ȕi, ɭɦɟɧɶɲɚɹ ɜɪɟɦɹ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ, ɩɪɢɜɨɞɹ ɭɫɥɨɜɢɹ ɨɬɞɚɱɢ ɬɟɩɥɚ ɩɪɢ ɩɨɧɢɠɟɧɧɵɯ ɫɤɨɪɨɫɬɹɯ ɤ ɭɫɥɨɜɢɹɦ ɨɬɞɚɱɢ ɬɟɩɥɚ ɞɜɢɝɚɬɟɥɟɦ, ɪɚɛɨɬɚɸɳɢɦ ɧɚ ɧɨɦɢɧɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ. ɉɪɚɜɢɥɶɧɵɣ ɜɵɛɨɪ ɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨɫɬɢ ɛɭɞɟɬ ɜɵɩɨɥɧɟɧ ɩɪɢ ĲɆȺɄɋ ĲȾɈɉ, ǻɊɗ ǻɊɇ. Ⱦɨɩɭɫɤɚɟɦɵɣ ɩɟɪɟɝɪɟɜ ĲȾɈɉ = ĬȾɈɉ – ĬɈɋ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɥɚɫɫɨɦ ɧɚɝɪɟɜɨɫɬɨɣɤɨɫɬɢ ɢɡɨɥɹɰɢɢ (Ⱥ, ȿ, ȼ, F, H, C), ɚ ɬɟɦɩɟɪɚɬɭɪɚ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɨɣ ĬɈɋ = 40 ºɋ. ɉɪɢ Ȧ § const ɦɨɠɧɨ ɩɪɢɧɹɬɶ ȕi = 1, ɬɨɝɞɚ ɮɨɪɦɭɥɚ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɩɨɬɟɪɶ (4.50) ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɮɨɪɦɭɥɭ ɫɪɟɞɧɢɯ ɩɨɬɟɪɶ, ɧɟ ɭɱɢɬɵɜɚɸɳɭɸ ɢɡɦɟɧɟɧɢɟ ɭɫɥɨɜɢɣ ɨɯɥɚɠɞɟɧɢɹ. ǻPɗ

1 n ¦ ( ǻPi t i ) tɐ i 1

ǻɊɋɊ .

Ⱦɨɫɬɨɢɧɫɬɜɚ ɦɟɬɨɞɚ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɩɨɬɟɪɶ: – ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɚɹ ɬɨɱɧɨɫɬɶ; – ɭɧɢɜɟɪɫɚɥɶɧɨɫɬɶ – ɩɪɢɦɟɧɢɦ ɞɥɹ ɥɸɛɨɝɨ ɬɢɩɚ ɞɜɢɝɚɬɟɥɹ. 188

(4.51)

ɇɟɞɨɫɬɚɬɤɢ ɦɟɬɨɞɚ: – ɞɥɹ ɪɚɫɱɟɬɚ ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɬɶ ɩɨɬɟɪɢ ǻɊ ɧɚ ɤɚɠɞɨɦ ɭɱɚɫɬɤɟ, ɚ ɷɬɨ ɜɨɡɦɨɠɧɨ ɥɢɲɶ ɩɪɢ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɜɵɛɪɚɧɧɨɦ ɞɜɢɝɚɬɟɥɟ – ɦɟɬɨɞ ɩɨɜɟɪɨɱɧɵɣ; – ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɫɥɨɠɧɨɫɬɶ ɪɚɫɱɟɬɨɜ, ǻɊ = f (I, Ș), ɧɭɠɧɨ ɡɧɚɬɶ ɬɨɤɢ ɢ ɄɉȾ ɧɚ ɤɚɠɞɨɦ ɭɱɚɫɬɤɟ. Ɇɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ. Ɋɚɫɱɟɬ ɩɨɬɟɪɶ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɫɥɨɠɧɵɦ ɢ ɜɵɡɵɜɚɟɬ ɫɬɪɟɦɥɟɧɢɟ ɧɚɣɬɢ ɦɟɬɨɞ, ɤɨɬɨɪɵɣ ɧɟ ɬɪɟɛɨɜɚɥ ɛɵ ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɪɶ ɧɚ ɤɚɠɞɨɦ ɭɱɚɫɬɤɟ. ɇɭɠɟɧ ɤɨɫɜɟɧɧɵɣ ɦɟɬɨɞ ɨɰɟɧɤɢ ɩɨɬɟɪɶ. Ɇɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ ɨɫɧɨɜɚɧ ɧɚ ɡɚɦɟɧɟ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɩɪɨɬɟɤɚɸɳɟɝɨ ɜ ɞɜɢɝɚɬɟɥɟ ɢ ɢɡɦɟɧɹɸɳɟɝɨɫɹ ɜɨ ɜɪɟɦɟɧɢ ɬɨɤɚ ɬɨɤɨɦ ɷɤɜɢɜɚɥɟɧɬɧɵɦ, ɤɨɬɨɪɵɣ ɜɵɡɜɚɥ ɛɵ ɜ ɞɜɢɝɚɬɟɥɟ ɬɚɤɢɟ ɠɟ ɩɨɬɟɪɢ, ɤɚɤ ɢ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɩɪɨɬɟɤɚɸɳɢɣ ɬɨɤ. ɉɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɞɜɢɝɚɬɟɥɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɭɦɦɨɣ ɩɨɫɬɨɹɧɧɵɯ ɩɨɬɟɪɶ, ɧɟ ɡɚɜɢɫɹɳɢɯ ɨɬ ɧɚɝɪɭɡɤɢ, ɢ ɩɟɪɟɦɟɧɧɵɯ ɩɨɬɟɪɶ, ɫɜɹɡɚɧɧɵɯ ɫ ɤɜɚɞɪɚɬɨɦ ɬɨɤɚ: ǻɊ = ǻɊɉɈɋɌ + b·I2.

(4.52)

ɉɨɞɫɬɚɜɢɦ ɜ ɮɨɪɦɭɥɭ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɩɨɬɟɪɶ n

¦ ('Pi t i ) ǻPɗ

i 1 n

d 'PH .

¦ (ȕi t i ) i 1

ɉɨɥɭɱɢɦ ɮɨɪɦɭɥɭ ɦɟɬɨɞɚ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɩɨɫɬɨɹɧɧɵɟ ɩɨɬɟɪɢ ɧɟ ɢɡɦɟɧɹɸɬɫɹ: n

¦ Ii2 t i Iɗ

i 1 n

¦ ȕi t i

d IH .

(4.53)

i 1

ɗɤɜɢɜɚɥɟɧɬɧɵɣ ɬɨɤ ɫɨɡɞɚɟɬ ɬɚɤɢɟ ɠɟ ɩɨɬɟɪɢ ɜ ɞɜɢɝɚɬɟɥɟ, ɤɚɤ ɢ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɩɪɨɬɟɤɚɸɳɢɣ ɬɨɤ. ǻɊɗ ǻɊɇ; ǻɊɉɈɋɌ + b·Iɗ2 ǻɊɉɈɋɌ + b·Iɇ2; Iɗ Iɇ. ɉɪɢ Iɗ << Iɇ – ɞɜɢɝɚɬɟɥɶ ɧɟɞɨɝɪɭɠɟɧ, ɩɪɢ Iɗ > Iɇ – ɩɟɪɟɝɪɭɠɟɧ, ɜ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ɩɪɟɞɫɬɨɢɬ ɜɵɛɨɪ ɧɨɜɨɝɨ ɞɜɢɝɚɬɟɥɹ. Ⱦɜɢɝɚɬɟɥɶ ɜɵɛɪɚɧ ɩɨ ɦɨɳɧɨɫɬɢ ɩɪɚɜɢɥɶɧɨ, ɟɫɥɢ Iɗ = (0,85…0,9)·Iɇ. ȿɫɥɢ ɭɫɥɨɜɢɹ ɨɯɥɚɠɞɟɧɢɹ ɧɟ ɢɡɦɟɧɹɸɬɫɹ (ȕi = 1), ɩɨɥɭɱɚɟɦ ɮɨɪɦɭɥɭ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɝɨ ɬɨɤɚ, ɧɟ ɭɱɢɬɵɜɚɸɳɭɸ ɢɡɦɟɧɟɧɢɟ ɭɫɥɨɜɢɣ ɨɯɥɚɠɞɟɧɢɹ: Iɗ

1 n 2 ¦ Ii t i tɐ i 1

IɋɊɄȼ .

(4.54)

ȿɫɥɢ ɝɪɚɮɢɤ ɬɨɤɚ ɩɥɚɜɧɵɣ (ɪɢɫ.4.15), ɬɨ ɜɵɩɨɥɧɹɸɬ ɥɢɧɟɚɪɢɡɚɰɢɸ ɢ ɨɩɪɟɞɟɥɹɸɬ ɷɤɜɢɜɚɥɟɧɬɧɵɣ ɬɨɤ Iɗ ɧɚ ɭɱɚɫɬɤɚɯ. Ⱦɥɹ ɥɢɧɟɣɧɨ (ɜɨ ɜɪɟɦɟɧɢ) ɢɡɦɟɧɹɸɳɟ189

ɝɨɫɹ ɬɨɤɚ I(t) = I1 + (I2 – I1)ǜt / tɈ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɟ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɧɚ ɭɱɚɫɬɤɟ I12 I1 I2 I22 . 3

IɋɊɄȼ

(4.55)

ɉɪɢ I1 = 0 ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɟ ɡɧɚɱɟɧɢɟ I I IɋɊɄȼ = 2 > IɋɊ = 2 . 2 3 ɋɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɵɣ ɬɨɤ ɛɨɥɶɲɟ ɫɪɟɞɧɟɝɨ ɬɨɤɚ, ɩɨɷɬɨɦɭ ɩɪɨɜɟɪɤɭ ɧɚɝɪɟɜɚ ɜɫɟɝɞɚ ɫɥɟɞɭɟɬ ɜɟɫɬɢ ɩɨ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɦɭ ɬɨɤɭ. Ⱦɨɫɬɨɢɧɫɬɜɚ ɦɟɬɨɞɚ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ: – ɦɟɬɨɞ ɭɧɢɜɟɪɫɚɥɶɧɵɣ, ɦɨɠɟɬ ɩɪɢɦɟɧɹɬɶɫɹ ɞɥɹ ɥɸɛɨɝɨ ɬɢɩɚ ɞɜɢɝɚɬɟɥɹ. Ɍɟɨɪɟɬɢɱɟɫɤɢ ɧɟ ɦɨɠɟɬ ɩɪɢɦɟɧɹɬɶɫɹ ɬɨɝɞɚ, I ɤɨɝɞɚ ɩɨɬɟɪɢ ɧɟ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɬɨɤɭ (ɞɥɹ ɝɥɭɛɨɤɨɩɚɡɧɨɝɨ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɨɝɨ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ǻɊ Ł I2·r, ɚ ɧɟ I2) ɢ ɤɨɝɞɚ ɧɟɨɛI2 ɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɢɡɦɟɧɟɧɢɟ ɩɨɫɬɨɹɧɧɵɯ ɩɨI1 ɬɟɪɶ (ɜ ɫɬɚɥɢ, ɧɚ ɩɟɪɟɦɚɝɧɢɱɢɜɚɧɢɟ, ɧɚ ɬɪɟtO t ɧɢɟ); – ɦɟɬɨɞ ɩɪɨɳɟ, ɝɪɚɮɢɤ ɬɨɤɨɜ ɪɚɫɫɱɢɬɚɬɶ t1 t2 t3 t4 t5 t6 t7 ɥɟɝɱɟ, ɱɟɦ ɝɪɚɮɢɤ ɩɨɬɟɪɶ. Ʉ ɧɟɞɨɫɬɚɬɤɚɦ ɦɟɬɨɞɚ ɫɥɟɞɭɟɬ ɨɬɧɟɫɬɢ Ɋɢɫ. 4.15. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ ɜɵɛɨɪɚ ɩɪɨɬɟɤɚɸɳɢɣ ɬɨɤ I =f (t) ɞɜɢɝɚɬɟɥɹ, ɬɚɤ ɤɚɤ ɦɟɬɨɞ ɹɜɥɹɟɬɫɹ ɩɨɜɟɪɨɱɧɵɦ. Ɇɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɦɨɦɟɧɬɚ. ɉɪɚɤɬɢɱɟɫɤɢ ɞɥɹ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɩɪɢɯɨɞɢɬɫɹ ɩɨɥɶɡɨɜɚɬɶɫɹ ɧɚɝɪɭɡɨɱɧɨɣ ɞɢɚɝɪɚɦɦɨɣ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ Ɇ = f(t). ȿɫɥɢ ɦɨɦɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɬɨɤɭ Ɇ Ł I, ɬɨ ɩɨɥɭɱɚɟɦ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɦɨɦɟɧɬɚ n

¦ Mi2 t i Mɗ

i 1 n

¦ ȕi t i

d Ɇɇ .

(4.56)

i 1

Ɇɟɬɨɞ ɯɨɪɨɲ ɬɟɦ, ɱɬɨ ɧɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɪɚɫɫɱɢɬɵɜɚɬɶ ɬɨɤ I = f(t), ɞɨɫɬɚɬɨɱɧɨ ɡɧɚɬɶ Ɇ = f(t). ɇɨ ɧɚɝɪɭɡɨɱɧɭɸ ɞɢɚɝɪɚɦɦɭ Ɇ = f(t) ɛɟɡ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɜɵɛɪɚɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɪɚɫɫɱɢɬɚɬɶ ɧɟɜɨɡɦɨɠɧɨ, ɬɚɤ ɤɚɤ Ɇ = Ɇɋ + ɆȾɂɇ, ɩɪɢɱɟɦ ɦɨɦɟɧɬ ɫɬɚɬɢɱɟɫɤɢɣ Ɇɋ ɢɡɜɟɫɬɟɧ ɢɡ ɪɚɫɱɟɬɨɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ, ɚ ɦɨɦɟɧɬ ɞɢɧɚɦɢɱɟɫɤɢɣ ɆȾɂɇ = f(JȾȼ) ɧɟɢɡɜɟɫɬɟɧ. ɇɚɝɪɭɡɨɱɧɭɸ ɞɢɚɝɪɚɦɦɭ Ɇ(t) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ, ɟɫɥɢ: – ɩɨɫɬɨɹɧɧɚ ɫɤɨɪɨɫɬɶ Ȧ = const, ɬɨ dȦ / dt = 0, ɆȾɂɇ = 0, ɬɨɝɞɚ Ɇ(t) = Ɇɋ(t); – JɊɈ >> JȾȼ – ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɜɚɥɭ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɦɨɦɟɧɬɚ ɢɧɟɪɰɢɢ ɞɜɢɝɚɬɟɥɹ (ɭɪɚɜɧɨɜɟɲɟɧɧɵɟ ɥɢɮɬɵ, ɦɚɯɨɜɢɱɧɵɟ ɩɪɢɜɨɞɵ, ɛɵɫɬɪɨɯɨɞɧɵɟ ɩɨɞɴɟɦɧɢɤɢ). 190

ɇɨ ɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɬɨɤɭ ɬɨɥɶɤɨ ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ. ɍ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɩɪɢ Ɇ = 0 ɬɨɤ ɫɬɚɬɨɪɚ ɪɚɜɟɧ ɬɨɤɭ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɢ ɧɚɝɪɟɜ ɩɪɨɞɨɥɠɚɟɬɫɹ. ɂɧɨɝɞɚ ɩɪɢɦɟɧɹɸɬ ɦɟɬɨɞ Ɇɗ ɞɥɹ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ, ɧɨ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ ɜ ɞɢɚɩɚɡɨɧɟ 0,5·Ɇɇ Ɇ 0,75·ɆɄ, ɨɬɞɚɜɚɹ ɫɟɛɟ ɨɬɱɟɬ ɜ ɬɨɦ, ɱɬɨ ɩɨɝɪɟɲɧɨɫɬɶ ɛɭɞɟɬ ɛɨɥɶɲɨɣ. ɉɪɢɦɟɧɹɸɬ ɦɟɬɨɞ Ɇɗ ɢ ɞɥɹ ɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ, ɧɨ ɩɪɢ ɧɚɝɪɭɡɤɚɯ, ɛɥɢɡɤɢɯ ɤ ɧɨɦɢɧɚɥɶɧɵɦ. Ɉɛɵɱɧɨ ɦɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɦɨɦɟɧɬɚ ɢɫɩɨɥɶɡɭɸɬ ɬɨɥɶɤɨ ɞɥɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɢɡ-ɡɚ ɟɝɨ ɧɟɞɨɫɬɚɬɤɚ – ɨɝɪɚɧɢɱɟɧɧɚɹ ɨɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ (ɢ ɬɢɩɵ ɞɜɢɝɚɬɟɥɟɣ, ɢ ɞɢɚɩɚɡɨɧ ɢɡɦɟɧɟɧɢɹ ɧɚɝɪɭɡɤɢ). Ɇɟɬɨɞ Ɇɗ ɧɟɥɶɡɹ ɢɫɩɨɥɶɡɨɜɚɬɶ, ɤɨɝɞɚ ɧɟ ɩɪɢɦɟɧɢɦ ɦɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ ɢ ɤɨɝɞɚ ɦɨɦɟɧɬ ɧɟ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɬɨɤɭ (ɟɫɥɢ ɢɡɦɟɧɹɟɬɫɹ ɩɨɬɨɤ). Ɇɟɬɨɞ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɣ ɦɨɳɧɨɫɬɢ. ɇɚɝɪɟɜ ɞɜɢɝɚɬɟɥɹ ɜɵɡɵɜɚɸɬ ɬɟɩɥɨɜɵɟ ɩɨɬɟɪɢ ɜɧɭɬɪɢ ɦɚɲɢɧɵ ǻɊ, ɢ ɪɚɫɱɟɬ ɦɟɬɨɞɨɦ ǻɊɗ ɞɚɟɬ ɛɨɥɟɟ ɬɨɱɧɵɟ ɪɟɡɭɥɶɬɚɬɵ. ȼɨ ɦɧɨɝɢɯ ɫɥɭɱɚɹɯ ǻɊɗ Ł Iɗ2, ɢ ɦɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ ɩɪɢɦɟɧɹɸɬ ɱɚɳɟ ɞɪɭɝɢɯ ɦɟɬɨɞɨɜ. ɋɚɦɵɣ ɩɪɨɫɬɨɣ ɦɟɬɨɞ Ɇɗ ɞɥɹ ɩɪɨɜɟɪɤɢ ɞɜɢɝɚɬɟɥɹ ɩɨ ɧɚɝɪɟɜɭ ɢɫɩɨɥɶɡɭɸɬ ɤɪɚɣɧɟ ɪɟɞɤɨ, ɚ ɞɥɹ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɫ ɱɚɫɬɵɦɢ ɩɭɫɤɚɦɢ ɢ ɬɨɪɦɨɠɟɧɢɹɦɢ ɩɪɢɦɟɧɹɸɬ ɥɢɲɶ ɞɥɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ. Ʉɨɝɞɚ ɠɟ ɩɨɬɟɪɢ ɜ ɞɜɢɝɚɬɟɥɟ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɦɨɳɧɨɫɬɢ? Ɇɨɳɧɨɫɬɶ ɦɚɲɢɧ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ Ɋ= = U·I·Ș ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɬɨɤɭ ɩɪɢ U = const ɢ Ș = const. ȿɫɥɢ U = const ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɩɪɢ ɩɢɬɚɧɢɢ ɞɜɢɝɚɬɟɥɹ ɨɬ ɰɟɯɨɜɨɣ ɫɟɬɢ, ɬɨ Ș § const ɦɨɠɧɨ ɝɪɭɛɨ ɩɪɢɧɹɬɶ ɩɪɢ 0,5·Ɋɇ < Ɋ < 2·Ɋɇ. Ɇɨɳɧɨɫɬɶ ɦɚɲɢɧ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ Ɋ~ = 3 ·U·I·cosĳ·Ș ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɬɨɤɭ ɩɪɢ ɩɨɫɬɨɹɧɫɬɜɟ Ș ɢ cos ĳ. ȿɫɥɢ ɨ Ș § const ɝɨɜɨɪɢɥɨɫɶ ɜɵɲɟ, ɬɨ ɨ cos ĳ § const ɦɨɠɧɨ ɝɪɭɛɨ ɝɨɜɨɪɢɬɶ ɩɪɢ 0,5·Ɋɇ < Ɋ < 1,5·Ɋɇ. ɇɨ ɞɚɠɟ ɟɫɥɢ Ɋ Ł I, ɬɨ ɬɚɤɠɟ Ɋ = Ɇ·Ȧ, ɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɶ Ɋ Ł Ɇ Ł I ɜɨɡɦɨɠɧɚ ɥɢɲɶ ɩɪɢ Ȧ = const ɢ ȕi = const. Ɉɬɫɸɞɚ ɜɵɜɨɞ, ɱɬɨ ɨɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɷɬɨɝɨ ɦɟɬɨɞɚ ɤɪɚɣɧɟ ɨɝɪɚɧɢɱɟɧɚ, ɢ ɮɨɪɦɭɥɚ ɦɨɳɧɨɫɬɢ, ɝɪɭɛɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚɹ ɩɨɬɟɪɹɦ, ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɚ ɥɢɲɶ ɢɡ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɝɨ ɬɨɤɚ IɋɊɄȼ

1 n 2 ¦ (Ii t i ) , ɬɨɝɞɚ PɋɊɄȼ tɐ i 1

1 n 2 ¦ (Pi t i ) . tɐ i 1

(4.57)

ȼɵɩɚɞɚɟɬ ɪɟɠɢɦ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ, ɬɚɤ ɤɚɤ ɩɪɢ Ȧ = 0 ɦɨɳɧɨɫɬɶ ɪɚɜɧɚ Ɋ = 0, ɚ ɬɨɤ I 0, ɢ ɧɚɝɪɟɜ ɩɪɨɞɨɥɠɚɟɬɫɹ. Ɇɟɬɨɞ ɊɋɊɄȼ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɩɪɢɛɥɢɠɟɧɧɵɣ ɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ, ɤɨɝɞɚ ɦɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɦɨɦɟɧɬɚ ɧɟ ɩɪɢɦɟɧɢɦ (ɞɜɢɝɚɬɟɥɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɢ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ). ɗɬɨɬ ɦɟɬɨɞ ɨɛɹɡɚɬɟɥɶɧɨ ɧɭɠɞɚɟɬɫɹ ɜ ɭɬɨɱɧɟɧɢɢ ɞɪɭɝɢɦɢ ɦɟɬɨɞɚɦɢ. Ɇɟɬɨɞ ɊɋɊɄȼ ɧɟ ɩɪɢɦɟɧɢɦ ɬɨɝɞɚ, ɤɨɝɞɚ ɧɟ ɩɪɢɦɟɧɹɸɬɫɹ ɦɟɬɨɞɵ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ ɢ ɦɨɦɟɧɬɚ, ɚ ɬɚɤɠɟ ɬɚɦ, ɝɞɟ ɢɡɦɟɧɹɟɬɫɹ ɫɤɨɪɨɫɬɶ, ɬɚɤ ɤɚɤ ɜ ɷɬɢɯ ɪɟɠɢɦɚɯ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ ɦɨɳɧɨɫɬɢ ɧɟ ɨɬɪɚɠɚɟɬ ɭɫɥɨɜɢɹ ɧɚɝɪɟɜɚ ɞɜɢɝɚɬɟɥɹ.

191

4.3.7. ȼɵɛɨɪ ɩɨ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɟɣ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ

ɊĲ

Ɋ ĲɆȺɄɋ Ĳ

tɊ

ĲɆɂɇ

tɈ

t

tɐ Ɋɢɫ. 4.16. ɇɚɝɪɟɜ ɢ ɨɯɥɚɠɞɟɧɢɟ ɞɜɢɝɚɬɟɥɹ

ɉɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɵɣ ɧɨɦɢɧɚɥɶɧɵɣ ɪɟɠɢɦ S3 – ɪɟɠɢɦ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 4.16), ɩɪɢ ɤɨɬɨɪɨɦ ɤɪɚɬɤɨɜɪɟɦɟɧɧɵɟ ɩɟɪɢɨɞɵ ɪɚɛɨɬɵ tɊ ɫ ɩɨɫɬɨɹɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɧɚɝɪɭɡɤɨɣ ɱɟɪɟɞɭɸɬɫɹ ɫ ɩɚɭɡɚɦɢ t0, ɩɪɢɱɟɦ ɤɚɤ ɩɪɢ ɪɚɛɨɬɟ, ɬɚɤ ɢ ɜ ɩɚɭɡɟ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ Ĳ(t) ɧɟ ɭɫɩɟɜɚɟɬ ɞɨɫɬɢɱɶ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ Ĳɍ. Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɜɤɥɸtP tP ɱɟɧɢɹ H , ɉȼ(%) = İ·100%. tP t 0 tɐ Ⱦɨɩɭɫɤɚɟɦɚɹ ɧɚɝɪɭɡɤɚ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɩɪɢɜɨɞɢɬɫɹ ɩɪɢ ɤɚɬɚɥɨɠɧɵɯ ɉȼ = 15, 25, 40, 60, 100%.

ɇɚɝɪɟɜ ɢ ɨɯɥɚɠɞɟɧɢɟ ɞɜɢɝɚɬɟɥɹ. ɉɨ ɩɪɨɲɟɫɬɜɢɢ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɜɪɟɦɟɧɢ ɪɚɛɨɬɵ ɩɨɥɭɱɢɦ ɪɟɝɭɥɹɪɧɵɣ ɝɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ, ɦɚɤɫɢɦɚɥɶɧɵɟ ɬɟɦɩɟɪɚɬɭɪɵ ĲɆȺɄɋ ɜ ɰɢɤɥɚɯ ɛɭɞɭɬ ɪɚɜɧɵ, ɛɭɞɭɬ ɩɨɜɬɨɪɹɬɶɫɹ ɢ ɦɢɧɢɦɚɥɶɧɵɟ ɬɟɦɩɟɪɚɬɭɪɵ ĲɆɂɇ. ȼ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɦ ɪɟɠɢɦɟ (ɉɄɊ) ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ Ĳ(t): – ɞɥɹ ɜɪɟɦɟɧɢ ɪɚɛɨɬɵ tɊ Ĳ ɆȺɄɋ

t § Ɋ TɌ ¨ Ĳɍ 1 e ¨ ©

t · Ɋ TɌ ¸Ĳ e ; ¸ Ɇɂɇ ¹

– ɞɥɹ ɩɚɭɡɵ t0 Ĳ Ɇɂɇ ĲɆȺɄɋ e

t 0 TɌɈ

.

Ɂɞɟɫɶ ɧɟɨɛɯɨɞɢɦɨ ɭɱɟɫɬɶ ɭɫɥɨɜɢɹ ɬɟɩɥɨɨɬɞɚɱɢ ɪɚɛɨɬɚɸɳɟɝɨ ɢ ɨɫɬɚɧɨɜɥɟɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ. ɇɚɣɞɟɦ ɦɚɤɫɢɦɚɥɶɧɭɸ ɬɟɦɩɟɪɚɬɭɪɭ Ĳ ɆȺɄɋ

t § Ɋ TɌ ¨ Ĳ ɍ 1 e ¨ ©

t t · 0 Ɋ TɌɈ TɌ ¸Ĳ e , ɆȺɄɋ e ¸ ¹

ɨɬɤɭɞɚ Ĳ ɆȺɄɋ Ĳ ɍ

1 e 1 e

t Ɋ TɌ

§t t ¨¨ Ɋ 0 © TɌ TTO

192

· ¸¸ ¹

.

ȼɵɱɢɬɚɟɦɨɟ ɜ ɡɧɚɦɟɧɚɬɟɥɟ ɦɟɧɶɲɟ ɜɵɱɢɬɚɟɦɨɝɨ ɜ ɱɢɫɥɢɬɟɥɟ, ɩɨɷɬɨɦɭ ĲɆȺɄɋ < Ĳɍ. ȿɫɥɢ ɫɨɡɞɚɬɶ ɜ ɉɄɊ ɧɚɝɪɭɡɤɭ, ɪɚɜɧɭɸ ɧɨɦɢɧɚɥɶɧɨɣ ɞɥɢɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ, ɬɨ ɞɜɢɝɚɬɟɥɶ ɛɭɞɟɬ ɧɟɞɨɝɪɭɠɟɧ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɭɠɧɨ ɫɨɡɞɚɜɚɬɶ ɧɚɝɪɭɡɤɭ ɛɨɥɶɲɭɸ ɧɨɦɢɧɚɥɶɧɨɣ, ɱɬɨɛɵ ɦɚɤɫɢɦɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɰɢɤɥɟ ɞɨɫɬɢɝɚɥɚ ɞɨɩɭɫɬɢɦɨɝɨ ɡɧɚɱɟɧɢɹ ɩɨ ɭɫɥɨɜɢɹɦ ɧɚɝɪɟɜɚ: ĲɆȺɄɋ = ĲȾɈɉ. ɉɪɢɪɚɜɧɹɟɦ ĲɆȺɄɋ = ĲȾɈɉ: Ĳ ɆȺɄɋ

1 e

ǻPɉɄ Ⱥ

t Ɋ TɌ

§t t ¨¨ Ɋ 0 © TɌ TTO

ǻɊɇ . Ⱥ

Ĳ ȾɈɉ

· ¸¸ ¹

1 e Ɉɬɫɸɞɚ ɧɚɣɞɟɦ ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɪɦɢɱɟɫɤɨɣ ɩɟɪɟɝɪɭɡɤɢ (ɩɨ ɩɨɬɟɪɹɦ, ɩɨ ɬɟɩɥɭ) ǻPɉɄ ǻPɇ

kT

1 e

§t t · ¨¨ Ɋ 0 ¸¸ © TɌ TTO ¹

1 e

t Ɋ TɌ

.

ȼɵɩɨɥɧɢɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ: tP t t + 0 = P TT TTɈ TT

§ t T · t ¨¨1 + 0 T ¸¸ = P © TTɈ tP ¹ TT

§ ȕ t · t ¨¨1 + 0 0 ¸¸ = P tP ¹ TT ©

§ t + ȕ0 t 0 · t ¸¸ = P . ¨¨ P tP © ¹ İc TT

ȼ ɩɨɥɭɱɟɧɧɨɦ ɜɵɪɚɠɟɧɢɢ: – ȕ0 ɭɦɟɧɶɲɚɟɬ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɩɚɭɡɵ ɜɨ ɫɬɨɥɶɤɨ ɪɚɡ, ɜɨ ɫɤɨɥɶɤɨ ɪɚɡ ɯɭɠɟ ɬɟɩɥɨɨɬɞɚɱɚ ɨɫɬɚɧɨɜɥɟɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ; – ȕ0t0 – ɷɬɨ ɜɪɟɦɹ ɩɚɭɡɵ, ɡɚ ɤɨɬɨɪɨɟ ɞɜɢɝɚɬɟɥɶ ɭɫɩɟɥ ɛɵ ɫɧɢɡɢɬɶ ɬɟɦɩɟɪɚɬɭɪɭ, ɟɫɥɢ ɛɵ ɧɟ ɢɡɦɟɧɢɥɢɫɶ ɭɫɥɨɜɢɹ ɬɟɩɥɨɨɬɞɚɱɢ; – İc – ɩɪɢɜɟɞɟɧɧɚɹ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɜɤɥɸɱɟɧɢɹ. Ɉɧɚ ɩɪɢɜɟɞɟɧɚ ɤ ɬɚɤɢɦ ɠɟ ɭɫɥɨɜɢɹɦ ɨɯɥɚɠɞɟɧɢɹ ɜ ɩɚɭɡɟ, ɤɚɤ ɩɪɢ ɜɪɚɳɟɧɢɢ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɍɩɪɨɫɬɢɦ ɤɌ ɢɡ ɭɫɥɨɜɢɹ, ɱɬɨ tɐ / ɌɌ < 0,1. ɂɫɩɨɥɶɡɭɹ ɪɚɡɥɨɠɟɧɢɟ ɜ ɪɹɞ Ɇɚɤɥɨɪɟɧɚ ɮɭɧɤɰɢɢ (1 – ɟ– y) = 1 – (1 – y + y2 /2! – y 3 / 3! + +….) = y + y2 /2! – y3 / 3!… § y, ɩɨɥɭɱɢɦ kT

ǻPɉɄ ǻPɇ

1 e

§t t ¨¨ Ɋ 0 © TɌ TTO t Ɋ TɌ

· ¸¸ ¹

1 e

tɊ İ c TɌ t Ɋ TɌ

tɊ T T İc TɌ tɊ

1 . İc

1 e 1 e Ɍɟɪɦɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɝɪɭɡɤɢ ɩɨɤɚɡɵɜɚɟɬ, ɜɨ ɫɤɨɥɶɤɨ ɪɚɡ ɦɨɝɭɬ ɛɵɬɶ ɭɜɟɥɢɱɟɧɵ ɩɨɬɟɪɢ ɩɪɨɬɢɜ ɧɨɦɢɧɚɥɶɧɵɯ. ɇɚɩɪɢɦɟɪ, ɟɫɥɢ İ = 0,25, ȕ0 =0,5, ɬɨ ɩɪɢɜɟɞɟɧɧɚɹ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɜɤɥɸɱɟɧɢɹ ɪɚɜɧɚ tɊ tɐ tɊ İ 0,25 İc 0,4 . t Ɋ ȕ0 t 0 t Ɋ t ɐ ȕ0 t 0 t ɐ İ ȕ0 1 İ 0,25 0,5 1 0,25

Ɍɟɪɦɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɝɪɭɡɤɢ ɫɨɫɬɚɜɢɬ

193

ǻPɉɄ ǻPɇ

kT

1 İc

1 0,4

2,5 .

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɚɝɪɭɡɤɭ ɧɚ ɞɜɢɝɚɬɟɥɶ ɦɨɠɧɨ ɭɜɟɥɢɱɢɬɶ ɧɚ ɫɬɨɥɶɤɨ, ɱɬɨɛɵ ɩɨɬɟɪɢ ɭɜɟɥɢɱɢɥɢɫɶ ɜ 2,5 ɪɚɡɚ !? Ɇɧɨɝɨ ɷɬɨ ɢɥɢ ɦɚɥɨ? Ʌɭɱɲɟ ɨɰɟɧɢɬɶ ɩɟɪɟɝɪɭɡɤɭ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɟɪɟɝɪɭɡɤɢ ɩɨ ɬɨɤɭ ɤi.(ɟɝɨ ɧɚɡɵɜɚɸɬ ɬɚɤɠɟ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɩɟɪɟɝɪɭɡɤɢ). kT

ǻPɉɄ ǻɊɇ

2 ǻPɉɈɋɌ ɉɄ b IɉɄ

ǻPɉɈɋɌ ɇ b Iɇ2

.

IɉɄ ɤ Ɍ . ȼ ɩɪɟɞɵɞɭɳɟɦ Iɇ ɩɪɢɦɟɪɟ ɤɌ = 2,5, ɬɨɝɞɚ ɤi § 1,6. Ⱦɥɹ ɩɨɥɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨ ɧɚɝɪɟɜɭ ɞɜɢɝɚɬɟɥɹ ɞɥɢɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɜ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɦ ɪɟɠɢɦɟ ɟɝɨ ɷɤɜɢɜɚɥɟɧɬɧɵɣ ɬɨɤ ɞɨɥɠɟɧ ɛɵɬɶ ɭɜɟɥɢɱɟɧ ɜ ɤi ɪɚɡ. ȿɫɥɢ ɩɨɫɬɨɹɧɧɵɟ ɩɨɬɟɪɢ ɧɟ ɢɡɦɟɧɹɸɬɫɹ, ɬɨ k i

IȾɈɉ ɉɄ

Iɇ k i

Iɇ k T

Iɇ / İc .

ȼ ɩɪɢɦɟɪɟ ɩɨɥɭɱɢɥɢ ɤi = 1,6. Ⱥ ɟɫɥɢ İc = 0,25, ɬɨɝɞɚ IȾɈɉ = 2ǜIɇ. Ⱦɥɹ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɧɭɠɧɵ ɞɪɭɝɢɟ ɞɜɢɝɚɬɟɥɢ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɛɨɥɟɟ ɜɵɫɨɤɢɟ ɬɟɩɥɨɜɵɟ ɪɟɠɢɦɵ. Ⱦɜɢɝɚɬɟɥɢ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ. Ⱦɥɹ ɩɨɜɬɨɪɧɨɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ (ɪɟɠɢɦ ɪɚɛɨɬɵ S3) ɜɵɩɭɫɤɚɸɬɫɹ ɞɜɢɝɚɬɟɥɢ ɫɩɟɰɢɚɥɶɧɵɯ ɫɟɪɢɣ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɯ ɞɥɹ ɷɬɨɝɨ ɪɟɠɢɦɚ. ɇɚɢɛɨɥɟɟ ɢɡɜɟɫɬɧɚ ɤɪɚɧɨɜɨ-ɦɟɬɚɥɥɭɪɝɢɱɟɫɤɚɹ ɫɟɪɢɹ, ɜ ɤɨɬɨɪɨɣ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɜɢɝɚɬɟɥɹɦɢ ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɣ ɫɟɪɢɢ: – ɭɫɢɥɟɧɵ ɛɵɫɬɪɨɧɚɝɪɟɜɚɸɳɢɟɫɹ ɱɚɫɬɢ (ɤɨɥɥɟɤɬɨɪ – ɜ ɞɜɢɝɚɬɟɥɹɯ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ, ɭɫɢɥɟɧɵ ɨɛɦɨɬɤɢ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ – ɜɵɞɟɪɠɢɜɚɸɬ ɬɨɤɢ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ); – ɡɚ ɫɱɟɬ ɭɦɟɧɶɲɟɧɢɹ ɞɢɚɦɟɬɪɚ ɪɨɬɨɪɚ (ɹɤɨɪɹ) ɫɧɢɠɟɧɵ ɦɨɦɟɧɬɵ ɢɧɟɪɰɢɢ; – ɭɜɟɥɢɱɟɧɚ ɩɟɪɟɝɪɭɡɨɱɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɞɜɢɝɚɬɟɥɟɣ ɞɨ 3 – 4 ɡɧɚɱɟɧɢɣ ɧɨɦɢɧɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ. Ⱦɜɢɝɚɬɟɥɢ ɷɬɨɣ ɫɟɪɢɢ (ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ – ɬɢɩɚ Ⱦ, ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ - ɬɢɩɚ 4MTF(H)) ɢɦɟɸɬ ɢ ɞɪɭɝɨɣ ɫɩɨɫɨɛ ɧɨɪɦɢɪɨɜɚɧɢɹ, ɩɪɢ ɤɨɬɨɪɨɦ ɜ ɤɚɬɚɥɨɝɟ ɭɤɚɡɵɜɚɟɬɫɹ ɞɨɩɭɫɤɚɟɦɚɹ ɧɚɝɪɭɡɤɚ ɧɚ ɜɚɥɭ ɊȾɈɉ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɉȼɄȺɌ =15, 25, 40, 60, 100%. Ⱦɥɹ ɩɪɢɦɟɪɚ ɜ ɬɚɛɥ. 4.2 ɩɪɢɜɟɞɟɧɵ ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ ɞɜɢɝɚɬɟɥɹ MTF412-6. Ɍɚɛɥɢɰɚ 4.2 Ʉɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ MTF412-6 ɉȼ,% 25 40 60 100 30 ɦɢɧ 60 ɦɢɧ Ɋ, ɤȼɬ 36 30 25 18 25 18 I1,Ⱥ 87 76 69,5 60,5 69,5 60,5 n, ɨɛ/ɦɢɧ 955 965 970 980 970 980 cos ĳ 0,75 0,71 0,65 0,55 0,65 0,55 Ș 83,5 84,5 84 82 84 82 I2,Ⱥ 88 73 61 42 61 42 2 MK = 932 ɇɦ, U2ɇ (ȿ2Ɉ) = 255 ȼ, J = 2,7 ɤɝɦ , m = 345 ɤɝ 194

ɉɪɢɜɨɞɹɬɫɹ ɜ ɤɚɬɚɥɨɝɚɯ ɬɚɤɠɟ ɢ ɤɚɬɚɥɨɠɧɵɟ ɤɪɢɜɵɟ Ɇ, I, cos M1 = f (S) – ɞɥɹ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɢ Ɇ, n, K f(I) – ɞɥɹ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɇɚ ɪɢɫ. 4.17 ɧɚ ɤɚɬɚɥɨɠɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɩɨɤɚɡɚɧɵ ɡɧɚɱɟɧɢɹ ɦɨɦɟɧɬɨɜ ɢ ɫɤɨɪɨɫɬɟɣ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɉȼ, ɢɡ ɤɨɬɨɪɨɣ ɜɢɞɧɨ, ɱɬɨ ɞɜɢɝɚɬɟɥɶ ɨɛɥɚɞɚɟɬ ɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ, ɚ ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ ɉȼ ɩɪɢɜɨɞɹɬɫɹ ɞɥɹ ɨɞɧɨɣ ɢɡ ɬɨɱɟɤ ɷɬɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. Ɇ ɇɨɦɢɧɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɞɥɹ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɜɢɝɚɬɟɥɹ ɹɜɥɹɸɬɫɹ ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ ɩɪɢ ɉȼ = 40%. Ɉɛɪɚɬɢɬɟ Ɋɢɫ. 4.17. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɩɟɪɟɝɪɭɡɨɱɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɆɄ / Ɇɇ= 3 ɩɪɢɜɟɞɟɧɧɨɝɨ ɜ ɬɚɛɥɢɰɟ 4.1 ɢ ɤɚɬɚɥɨɠɧɵɟ ɬɨɱɤɢ ɞɜɢɝɚɬɟɥɹ ɩɨɥɭɱɟɧɚ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɦɨɦɟɧɬɟ Ɇɇ ɞɥɹ ɉȼ = 40%, ɤɨɬɨɪɵɣ ɫɚɦ ɜɞɜɨɟ ɛɨɥɶɲɟ ɦɨɦɟɧɬɚ ɩɪɢ ɉȼ = 100%. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɜɢɝɚɬɟɥɹɦɢ ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɣ ɫɟɪɢɢ ɩɟɪɟɝɪɭɡɨɱɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɞɜɢɝɚɬɟɥɟɣ ɤɪɚɧɨɜɨɦɟɬɚɥɥɭɪɝɢɱɟɫɤɨɣ ɫɟɪɢɢ ɜ 2…2,5 ɪɚɡɚ ɛɨɥɶɲɟ. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɉȼ ɫɧɢɠɚɸɬɫɹ ɞɨɩɭɫɤɚɟɦɵɟ ɩɨɬɟɪɢ ǻɊ, ɞɨɩɭɫɤɚɟɦɚɹ ɩɨ ɧɚɝɪɟɜɭ ɦɨɳɧɨɫɬɶ Ɋ, ɬɨɤɢ ɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ, ɪɚɫɬɟɬ ɫɤɨɪɨɫɬɶ. ɇɨ ɩɪɢ ɷɬɨɦ ɫɧɢɠɚɸɬɫɹ ɢ ɄɉȾ, ɢ cos ĳ, ɱɬɨ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɬɨɦ, ɤɚɤɨɣ ɰɟɧɨɣ ɩɨɥɭɱɟɧɨ ɭɜɟɥɢɱɟɧɢɟ ɩɟɪɟɝɪɭɡɨɱɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ. Ɉɩɪɟɞɟɥɟɧɢɟ ɞɨɩɭɫɤɚɟɦɨɣ ɧɚɝɪɭɡɤɢ ɩɪɢ ɉȼ, ɨɬɥɢɱɧɨɣ ɨɬ ɤɚɬɚɥɨɠɧɨɣ. ɉɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɫ ɉȼɎȺɄɌ = ɉȼɄȺɌ ɜ ɤɚɬɚɥɨɝɟ ɭɤɚɡɚɧɵ ɞɨɩɭɫɤɚɟɦɵɟ ɧɚɝɪɭɡɤɢ. ɉɪɨɜɟɪɤɚ ɞɜɢɝɚɬɟɥɹ ɩɨ ɧɚɝɪɟɜɭ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɚ. ɇɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɢɬɶ ɞɥɹ ɪɟɚɥɶɧɨɝɨ ɝɪɚɮɢɤɚ ɪɚɫɱɟɬ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɩɨɬɟɪɶ ǻɊɗ ɢɥɢ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ Iɗ (ɢɥɢ ɞɪɭɝɢɯ ɩɪɢɟɦɥɟɦɵɯ ɜɟɥɢɱɢɧ) ɢ ɫɨɩɨɫɬɚɜɢɬɶ ɢɯ ɫ ɤɚɬɚɥɨɠɧɵɦɢ. Ⱦɜɢɝɚɬɟɥɢ ɜɵɛɢɪɚɸɬɫɹ ɩɨ ɤɚɬɚɥɨɝɭ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɡɧɚɱɟɧɢɟ ɟɝɨ ɦɨɳɧɨɫɬɢ ɊɄȺɌ ɩɪɢ ɉȼɄȺɌ ɛɵɥɨ ɛɵ ɪɚɜɧɨ ɢ ɧɟɫɤɨɥɶɤɨ ɛɨɥɶɲɟ ɪɚɫɫɱɢɬɚɧɧɨɣ ɦɨɳɧɨɫɬɢ ɊȾȼ. Ɂɚɞɚɱɚ ɭɫɥɨɠɧɹɟɬɫɹ, ɟɫɥɢ ɉȼ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɤɚɬɚɥɨɠɧɨɣ, ɩɪɢ ɉȼɎȺɄɌ ɉȼɄȺɌ. Ɋɟɲɢɬɶ ɬɚɤɭɸ ɡɚɞɚɱɭ ɦɨɠɧɨ ɝɪɚɮɢɱɟɫɤɢɦ ɢɥɢ ɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɚɦɢ. 1. Ƚɪɚɮɢɱɟɫɤɢɣ ɦɟɬɨɞ ɩɪɟɞɩɨɥɚɝɚɟɬ ɩɨɫɬɪɨɟɧɢɟ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ (ɫɦ. ɬɚɛɥ.4.1) ɡɚɜɢɫɢɦɨɫɬɢ IȾɈɉ = f(ɉȼ) ɢ ɧɚɯɨɠɞɟɧɢɟ ɞɨɩɭɫɤɚɟɦɨɣ ɧɚɝɪɭɡɤɢ ɩɪɢ ɉȼ = ɉȼɎȺɄɌ. ɉɪɢɦɟɪ ɬɚɤɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ. 4.18. 2. ɑɚɳɟ ɷɬɭ ɡɚɞɚɱɭ ɪɟɲɚɸɬ ɚɧɚɥɢɬɢɱɟɫɤɢ. Ⱦɥɹ ɷɬɨɝɨ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɦɟɬɨɞɨɦ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɩɨɬɟɪɶ. ɉɭɫɬɶ ɢɦɟɟɦ ɞɜɚ ɝɪɚɮɢɤɚ ɧɚɝɪɭɡɤɢ (ɪɢɫ. 4.19) ɫ ɨɞɢɧɚɤɨɜɵɦ ɜɪɟɦɟɧɟɦ ɰɢɤɥɚ tɐ1 = tɐ2 = tɐ, ɧɨ ɜɪɟɦɹ ɪɚɛɨɬɵ ɜ ɰɢɤɥɚɯ ɪɚɡɥɢɱɧɨ. ɉɭɫɬɶ ɞɥɹ ɝɪɚɮɢɤɚ 1 ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɜɤɥɸɱɟɧɢɹ ɪɚɜɧɚ ɤɚɬɚɥɨɠɧɨɣ İ1 = İɄȺɌ, ɞɥɹ ɝɪɚɮɢɤɚ 2 – İ2 = İɎȺɄɌ. ɇɭɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɞɨɩɭɫɤɚɟɦɭɸ ɧɚɝɪɭɡɤɭ ɩɪɢ ɮɚɤɬɢɱɟɫɤɨɣ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɜɤɥɸɱɟɧɢɹ İɎȺɄɌ. Ȧ

100 60 40 25 15 ɉȼ,%

195

ǻɊ

IȾɈɉ

1 IȾɈɉ.ɎȺɄɌ

tɊ1

IɄȺɌ İɄȺɌ

t01 t 2

tɊ2 15 25 40

60

100

ɉȼ,%

IɎȺɄɌ İɎȺɄɌ

t02 t

tɐ

ɉȼɎȺɄɌ Ɋɢɫ. 4.18. Ɉɩɪɟɞɟɥɟɧɢɟ ɞɨɩɭɫɤɚɟɦɨɣ ɧɚɝɪɭɡɤɢ ɝɪɚɮɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ

Ɋɢɫ. 4.19. Ƚɪɚɮɢɤɢ ɩɨɬɟɪɶ ɦɨɳɧɨɫɬɢ ɩɪɢ İɎȺɄɌ İɄȺɌ

Ɉɫɧɨɜɧɨɟ ɭɫɥɨɜɢɟ – ɦɚɤɫɢɦɚɥɶɧɵɟ ɬɟɦɩɟɪɚɬɭɪɵ ɞɨɥɠɧɵ ɛɵɬɶ ɨɞɢɧɚɤɨɜɵ ɞɥɹ ɨɛɨɢɯ ɝɪɚɮɢɤɨɜ ĲɆȺɄɋ1 = ĲɆȺɄɋ2, ɷɤɜɢɜɚɥɟɧɬɧɵɟ ɩɨɬɟɪɢ n

¦ ( ǻPi t i ) ǻPɗ

i 1 n

¦ (Ei t i ) i 1

ɨɛɨɢɯ ɝɪɚɮɢɤɨɜ ɞɨɥɠɧɵ ɛɵɬɶ ɪɚɜɧɵ: ǻɊɗ1=ǻɊɗ2; ǻPɄȺɌ t Ɋ1 ǻPɎȺɄɌ t Ɋ2 ; t Ɋ1 ȕ0 t 01 t Ɋ2 ȕ0 t 02 ǻɊɄȺɌǜİcɄȺɌ = ǻɊɎȺɄɌǜİcɎȺɄɌ; 2 (ǻ PɉɈɋɌ Ʉ b IɄȺɌ ) İcɄȺɌ (ǻ PɉɈɋɌ ɎȺɄɌ b I2ȾɈɉ ) İcɎȺɄɌ . 2 Ɋɚɡɞɟɥɢɦ ɨɛɟ ɱɚɫɬɢ ɧɚ b IɄȺɌ

§ ǻPɉɈɋɌ ɄȺɌ · ¨ ¸ İcɄȺɌ 1 ¨ b I2 ¸ © ¹ ɄȺɌ

2 § ǻPɉɈɋɌ ɎȺɄɌ IɄȺɌ · ¨ ¸ İcɎȺɄɌ . 2 ¨ b I2 ¸ IɄȺɌ © ¹ ɄȺɌ

Ɍɨɝɞɚ 2 IȾɈɉ

ǻPɉɈɋɌ ɎȺɄɌ § ǻPɉɈɋɌ ɄȺɌ · İcɄȺɌ ¨ ¸ 1 , 2 2 ¨ b I ¸ İc b I © ¹ ɎȺɄɌ ɄȺɌ ɄȺɌ ɚ ɞɨɩɭɫɤɚɟɦɵɣ ɬɨɤ ɩɪɢ İɎȺɄɌ ɪɚɜɟɧ: 2 IɄȺɌ

IȾɈɉ

IɄȺɌ

ǻPɉɈɋɌ ɄȺɌ İcɄȺɌ İc ɄȺɌ 2 İcɎȺɄɌ İcɎȺɄɌ b IɄȺɌ

196

ǻPɉɈɋɌ ɎȺɄɌ 2 b IɄȺɌ

,

(4.58)

İcɄȺɌ ǻPɉɈɋɌ ɄȺɌ – ɩɪɢɜɟɞɟɧɢɟ ɩɨɫɬɨɹɧɧɵɯ ɩɨɬɟɪɶ ɤɚɬɚɥɨɠɧɨɝɨ ɝɪɚɮɢɤɚ ɤ İcɎȺɄɌ ɮɚɤɬɢɱɟɫɤɨɦɭ ɉȼ. Ɋɚɡɧɨɫɬɶ ɩɪɢɜɟɞɟɧɧɵɯ ɩɨɫɬɨɹɧɧɵɯ ɩɨɬɟɪɶ ɤɚɬɚɥɨɠɧɨɝɨ ɝɪɚɮɢɤɚ ɢ ɩɨɫɬɨɹɧɧɵɯ ɩɨɬɟɪɶ ɮɚɤɬɢɱɟɫɤɨɝɨ ɝɪɚɮɢɤɚ ɦɚɥɚ, ɢ ɟɸ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. Ɍɨɝɞɚ ɞɨɩɭɫɤɚɟɦɵɣ ɬɨɤ ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɪɚɜɧɵɦ:

ɝɞɟ

IȾɈɉ

IɄȺɌ

İcɄȺɌ . İcɎȺɄɌ

ȼ ɩɚɫɩɨɪɬɧɵɯ ɞɚɧɧɵɯ ɭɱɬɟɧɵ ɭɫɥɨɜɢɹ ɨɯɥɚɠɞɟɧɢɹ ɞɥɹ ɤɚɬɚɥɨɠɧɨɝɨ ɉȼ. Ʉɚɤ ɭɱɢɬɵɜɚɬɶ ɢɡɦɟɧɟɧɢɟ ɭɫɥɨɜɢɣ ɨɯɥɚɠɞɟɧɢɹ ɦɟɠɞɭ ɤɚɬɚɥɨɠɧɵɦɢ ɉȼ? ȿɫɥɢ ɉȼ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɬɨ ɩɪɢ ɨɞɢɧɚɤɨɜɨɣ ɧɚɝɪɭɡɤɟ ɪɚɫɬɭɬ ɩɨɫɬɨɹɧɧɵɟ ɩɨɬɟɪɢ (ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ), ɪɚɫɬɟɬ ɬɟɦɩɟɪɚɬɭɪɚ, ɧɨ ɨɞɧɨɜɪɟɦɟɧɧɨ ɪɚɫɬɟɬ ɬɟɩɥɨɨɬɞɚɱɚ ɡɚ ɫɱɟɬ ɭɜɟɥɢɱɟɧɢɹ ɜɪɟɦɟɧɢ ɪɚɛɨɬɵ, ɱɬɨ ɡɚɫɬɚɜɥɹɟɬ ɬɟɦɩɟɪɚɬɭɪɭ ɭɦɟɧɶɲɚɬɶɫɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɮɚɤɬɨɪɵ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɜɡɚɢɦɧɨ ɤɨɦɩɟɧɫɢɪɭɸɬɫɹ, ɢ ɷɬɨ ɦɨɠɧɨ ɭɱɟɫɬɶ ɜ IȾɈɉ ɞɥɹ ɨɛɥɟɝɱɟɧɢɹ ɪɚɫɱɟɬɨɜ ɡɚ ɫɱɟɬ ɧɟɡɧɚɱɢɬɟɥɶɧɨɝɨ ɫɧɢɠɟɧɢɹ ɬɨɱɧɨɫɬɢ IȾɈɉ

IɄȺɌ

İ ɄȺɌ . İ ɎȺɄɌ

(4.59)

ɇɨ ɩɪɢ ɷɬɨɦ ɞɥɹ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɧɢɦɚɬɶ ɡɧɚɱɟɧɢɹ IɄȺɌ ɢ ɉȼ, ɛɥɢɠɚɣɲɢɟ ɤ ɉȼɄȺɌ. Ɍɚɤɨɟ ɜɵɪɚɠɟɧɢɟ ɫɩɪɚɜɟɞɥɢɜɨ ɩɪɢ ɜɵɛɨɪɟ ɫɩɟɰɢɚɥɶɧɨɣ ɤɪɚɧɨɜɨɦɟɬɚɥɥɭɪɝɢɱɟɫɤɨɣ ɫɟɪɢɢ. ȿɫɥɢ ɜ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɦ ɪɟɠɢɦɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɜɢɝɚɬɟɥɶ ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɣ ɫɟɪɢɢ, ɬɚɤɨɟ ɭɩɪɨɳɟɧɢɟ ɧɟɞɨɩɭɫɬɢɦɨ, ɢ ɪɚɫɱɟɬ ɜɟɞɭɬ ɩɨ ɩɨɥɧɨɣ ɮɨɪɦɭɥɟ (4.58). ɉɪɢ ɧɚɝɪɭɡɤɚɯ, ɛɥɢɡɤɢɯ ɤ ɧɨɦɢɧɚɥɶɧɵɦ, ɤɨɝɞɚ ɦɨɳɧɨɫɬɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɬɨɤɭ (cos ĳ ɢ Ș ɦɚɥɨ ɢɡɦɟɧɹɸɬɫɹ ɜ ɷɬɨɦ ɫɥɭɱɚɟ) ɞɨɩɭɫɬɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɦɟɬɨɞ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɣ ɦɨɳɧɨɫɬɢ PȾɈɉ

ɊɄȺɌ

İ ɄȺɌ . İ ɎȺɄɌ

ȿɫɥɢ ɜɪɟɦɹ ɰɢɤɥɚ tɐ > 10 ɦɢɧ, ɬɨ ɪɚɫɱɟɬ ɜɵɩɨɥɧɹɸɬ ɤɚɤ ɞɥɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ. ȼɵɛɨɪ ɩɨ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜɵɛɨɪɚ ɞɜɢɝɚɬɟɥɹ ɩɨ ɦɨɳɧɨɫɬɢ ɞɥɹ ɩɨɜɬɨɪɧɨɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɩɨɞɪɨɛɧɨ ɢɡɥɨɠɟɧɚ ɜ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɩɨ ɤɭɪɫɨɜɨɦɭ ɩɪɨɟɤɬɢɪɨɜɚɧɢɸ [26]. ȼ ɷɬɨɦ ɪɚɡɞɟɥɟ ɩɟɪɟɱɢɫɥɢɦ ɥɢɲɶ ɨɫɧɨɜɧɵɟ ɷɬɚɩɵ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ. 1. ɇɚ ɨɫɧɨɜɚɧɢɢ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɦɟɯɚɧɢɡɦɚ (ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ) ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɫɬɚɬɢɱɟɫɤɢɟ ɦɨɳɧɨɫɬɢ ɢɥɢ ɫɬɚɬɢɱɟɫɤɢɟ ɦɨɦɟɧɬɵ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɧɚ ɤɚɠɞɨɦ ɭɱɚɫɬɤɟ ɪɚɛɨɬɵ ɢ ɫɬɪɨɹɬɫɹ ɧɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ ɊɊɈ ɋɌ(t) ɢɥɢ ɆɊɈ ɋɌ(t); 2. ȿɫɥɢ ɡɚɞɚɧɨ ɞɨɩɭɫɬɢɦɨɟ ɭɫɤɨɪɟɧɢɟ ɚȾɈɉ, ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɞɢɧɚɦɢɱɟɫɤɢɟ ɦɨɦɟɧɬɵ ɆɊɈ Ⱦɂɇ ɧɚ ɭɱɚɫɬɤɚɯ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ, ɩɪɢ ɪɚɫɱɟɬɟ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ ɦɨɳɧɨɫɬɢ ɪɚɫɫɱɢɬɵɜɚɸɬ 197

ɊȾɂɇ = ɆɊɈ ȾɂɇǜȦɊɈ ɋɊ ɢ ɫ ɭɱɟɬɨɦ ɡɧɚɤɚ ɨɩɪɟɞɟɥɹɸɬ ɦɨɳɧɨɫɬɢ ɧɚ ɭɱɚɫɬɤɚɯ ɊɊɈ = ɊɊɈ ɋɌ + ɊȾɂɇ. ȿɫɥɢ ɚȾɈɉ ɧɟ ɡɚɞɚɧɚ, ɬɨ ɫɥɟɞɭɟɬ ɟɝɨ ɡɧɚɱɟɧɢɟ ɩɨɢɫɤɚɬɶ ɜ ɬɟɯɧɢɱɟɫɤɨɣ ɥɢɬɟɪɚɬɭɪɟ ɞɥɹ ɫɜɨɟɝɨ ɢɥɢ ɚɧɚɥɨɝɢɱɧɨɝɨ ɦɟɯɚɧɢɡɦɚ ɢ ɩɪɢɧɹɬɶ ɩɪɢɛɥɢɠɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɩɨ ɢɧɬɭɢɰɢɢ. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɞɚɧɧɵɯ ɩɨ ɚȾɈɉ ɧɟɬ ɜɨɡɦɨɠɧɨɫɬɢ ɞɥɹ ɪɚɫɱɟɬɚ ɞɢɧɚɦɢɱɟɫɤɢɯ ɦɨɦɟɧɬɨɜ; 3. ȼɪɟɦɟɧɚ ɪɚɛɨɬɵ ɢ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ ɧɚ ɭɱɚɫɬɤɚɯ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɨ ɢɡɜɟɫɬɧɨɦɭ ɚȾɈɉ ɢ ɪɚɛɨɱɟɣ ɫɤɨɪɨɫɬɢ vɍ: tɉ

tɌ

vɍ ; Lɉ ɚ ȾɈɉ

LT

a ȾɈɉ t 2 ; 2

ȼɪɟɦɟɧɚ ɪɚɛɨɬɵ ɜ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɪɟɠɢɦɟ – ɩɨ ɡɚɞɚɧɧɨɦɭ ɩɭɬɢ ɩɟɪɟɦɟɳɟL ɍ L (Lɉ L Ɍ ) . ɧɢɹ L ɢ ɩɭɬɢ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɪɟɠɢɦɚ Lɍ: t ɍ vɍ vɍ ȿɫɥɢ ɚȾɈɉ ɧɟ ɡɚɞɚɧɨ, ɩɪɢɯɨɞɢɬɫɹ ɫɬɪɨɢɬɶ ɧɚɝɪɭɡɨɱɧɭɸ ɞɢɚɝɪɚɦɦɭ ɬɨɥɶɤɨ ɞɥɹ L ; ɫɬɚɬɢɤɢ ɢ ɪɚɫɫɱɢɬɵɜɚɬɶ ɬɨɥɶɤɨ ɜɪɟɦɹ ɪɚɛɨɬɵ ɧɚ ɭɱɚɫɬɤɟ tɊ vɍ 4. ɉɨ ɩɨɫɬɪɨɟɧɧɨɣ ɧɚɝɪɭɡɨɱɧɨɣ ɞɢɚɝɪɚɦɦɟ Ɇ(t) ɪɚɫɫɱɢɬɵɜɚɸɬ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɵɣ ɦɨɦɟɧɬ ɆɋɊ Ʉȼ (ɩɨ ɞɢɚɝɪɚɦɦɟ Ɋ(t) – ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɭɸ ɦɨɳɧɨɫɬɶ ɊɋɊ Ʉȼ) ɆɋɊɄȼ

1 n 2 ¦ Mi t i ; PɋɊ Ʉȼ tɐ i 1

1 n 2 ¦ Pi t i tɐ i 1

ɢ ɨɩɪɟɞɟɥɹɸɬ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɜɤɥɸɱɟɧɢɹ ɉȼ = tɊ / tɐ; 5. ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɪɚɫɫɱɢɬɵɜɚɸɬ ɦɨɳɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ, ɩɪɢɜɟɞɟɧɧɭɸ ɤ ɉȼɄȺɌ: PȾȼ ɉɊȿȾ

ɤɁ

3 ɆɋɊɄȼ ȦɊɈ ɉȼ 10 , ɤȼɬ, Șɉ ɉȼɄȺɌ

ɝɞɟ ɤɁ – ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ ɧɚ ɧɟɭɱɬɟɧɧɵɟ ɦɚɯɨɜɵɟ ɦɚɫɫɵ ɞɜɢɝɚɬɟɥɹ ɢ ɩɟɪɟɞɚɱɢ, ɢɧɬɭɢɬɢɜɧɨ ɜɵɛɢɪɚɟɦɵɣ ɪɚɜɧɵɦ ɤɁ = 1,1…1,5. ɉɪɢ ɷɬɨɦ ɞɥɹ ɨɬɧɨɲɟɧɢɹ tɉ / tɍ 0,05 ɩɪɢɧɢɦɚɸɬ ɦɟɧɶɲɢɟ ɡɧɚɱɟɧɢɹ ɤɁ, ɞɥɹ tɉ / tɍ > 0.2…0,3 – ɛɨɥɶɲɢɟ ɡɧɚɱɟɧɢɹ ɤɁ. ɉɪɢ tɍ , ɛɥɢɡɤɨɦ ɤ ɧɭɥɸ (ɫɥɟɞɹɳɢɟ ɫɢɫɬɟɦɵ), ɤɁ ɦɨɠɟɬ ɩɪɢɧɢɦɚɬɶ ɨɱɟɧɶ ɛɨɥɶɲɢɟ ɡɧɚɱɟɧɢɹ, ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɪɚɫɱɟɬ ɩɨ 5.13 ɫɬɚɧɨɜɢɬɫɹ ɨɱɟɧɶ ɝɪɭɛɵɦ; Șɉ – ɄɉȾ ɩɟɪɟɞɚɱɢ, ɧɚ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɫɬɚɞɢɢ ɦɨɠɧɨ ɩɪɢɧɹɬɶ Șɉ § 0,8. ɇɚ ɨɫɧɨɜɟ ɪɚɫɱɟɬɚ ɩɨ 5.13 ɜɵɛɢɪɚɸɬ ɢɡ ɤɚɬɚɥɨɝɚ ɦɨɳɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɊɄȺɌ ɩɪɢ ɉȼɄȺɌ, ɪɚɜɧɭɸ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɛɨɥɶɲɭɸ ɊȾȼ ɉɊȿȾ: ɊȾȼ ɉɊȿȾ ɊɄȺɌ. 6. ȼɵɛɢɪɚɸɬ ɪɟɞɭɤɬɨɪ ɫ ɩɟɪɟɞɚɬɨɱɧɵɦ ɱɢɫɥɨɦ, ɪɚɜɧɵɦ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɦɟɧɶɲɢɦ ɪɚɫɫɱɢɬɚɧɧɨɝɨ ɩɨ ɮɨɪɦɭɥɟ 198

Ȧɇ ȦɊɈ

iɊ

Ȧɇ D , 2 vɍ

ɩɪɢ ɷɬɨɦ ɧɨɦɢɧɚɥɶɧɵɣ ɦɨɦɟɧɬ Ɇɇ ɊȿȾ ɧɚ ɛɵɫɬɪɨɯɨɞɧɨɦ ɜɚɥɭ ɪɟɞɭɤɬɨɪɚ ɞɨɥɠɟɧ ɛɵɬɶ ɪɚɜɟɧ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɛɨɥɶɲɟ ɧɨɦɢɧɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ Ɇɇ Ⱦȼ Ɇɇ ɊȿȾ Ɇɇ Ⱦȼ. 7. ɉɪɢɜɨɞɹɬ ɫɬɚɬɢɱɟɫɤɢɟ ɦɨɦɟɧɬɵ ɆC ɢ ɦɨɦɟɧɬɵ ɢɧɟɪɰɢɢ J ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ; 8. ȼɵɛɢɪɚɸɬ ɫɢɫɬɟɦɭ ɭɩɪɚɜɥɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ (Ɍɉ-Ⱦ, ɉɑ-ȺȾ, ɪɟɨɫɬɚɬɧɨɟ ɭɩɪɚɜɥɟɧɢɟ ɢ ɬ.ɩ.) ɢ ɜɵɛɢɪɚɸɬ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɢ ɢɥɢ ɩɚɧɟɥɶ ɭɩɪɚɜɥɟɧɢɹ; 9. ȼɵɩɨɥɧɹɟɬɫɹ ɪɚɫɱɟɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɢɫɬɟɦɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ; 10. Ɋɚɫɫɱɢɬɵɜɚɸɬɫɹ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɢ ɫɬɪɨɹɬɫɹ ɧɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ Ȧ(t), M(t), I(t), L(t) ɢ ɞɪɭɝɢɟ; 11. ȼɵɩɨɥɧɹɟɬɫɹ ɩɪɨɜɟɪɤɚ ɞɜɢɝɚɬɟɥɹ ɩɨ ɧɚɝɪɟɜɭ ɩɪɢɟɦɥɟɦɵɦ ɦɟɬɨɞɨɦ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɜɟɥɢɱɢɧ, ɱɚɳɟ ɜɫɟɝɨ – ɦɟɬɨɞɨɦ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ n

¦ Ii2 ti i 1 n

Iɗ

¦ ti Ei2

d IȾɈɉ ,

(4.53)

i 1

ɩɪɢ ɷɬɨɦ ȕiǜti – ɭɱɢɬɵɜɚɟɬ ɬɨɥɶɤɨ ɜɪɟɦɹ ɪɚɛɨɬɵ, ɜɪɟɦɹ ɩɚɭɡɵ t0 ɭɱɬɟɧɨ ɡɚɜɨɞɨɦɢɡɝɨɬɨɜɢɬɟɥɟɦ ɢ ɜ ɪɚɫɱɟɬɟ ɩɨ (4.53) ɧɟ ɭɱɚɫɬɜɭɟɬ. ȼɟɥɢɱɢɧɚ ɞɨɩɭɫɬɢɦɨɝɨ ɬɨɤɚ IȾɈɉ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɪɢ ɮɚɤɬɢɱɟɫɤɨɦ ɉȼ S tɉ S t ɍ S t T , tɐ

ɉȼɎȺɄɌ

ɩɨ ɮɨɪɦɭɥɟ IȾɈɉ

IɄȺɌ

ɉȼɄȺɌ . ɉȼɎȺɄɌ

Ɂɧɚɱɟɧɢɟ ɤɚɬɚɥɨɠɧɨɝɨ ɬɨɤɚ IɄȺɌ ɧɚɯɨɞɹɬ ɜ ɤɚɬɚɥɨɝɟ ɩɪɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɉȼɄȺɌ. Ⱦɨɩɭɫɬɢɦɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɷɤɜɢɜɚɥɟɧɬɧɵɦ ɢ ɞɨɩɭɫɬɢɦɵɦ ɬɨɤɚɦɢ Iɗ = (0,85…0,9)ǜ IȾɈɉ. 12. ɉɪɨɜɟɪɤɚ ɜɵɩɨɥɧɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɣ: – ɩɨ ɞɨɩɭɫɬɢɦɨɦɭ ɭɫɤɨɪɟɧɢɸ ɚȾɈɉ; – ɩɨ ɨɛɟɫɩɟɱɟɧɢɸ ɡɚɞɚɧɧɵɯ ɫɤɨɪɨɫɬɟɣ ȦɊɈ; – ɩɨ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɜɵɩɨɥɧɹɟɬɫɹ ɫɪɚɜɧɟɧɢɟɦ ɡɚɞɚɧɧɨɝɨ tɊ ɁȺȾ ɢ ɪɚɫɱɟɬɧɨɝɨ ɜɪɟɦɟɧɢ ɪɚɛɨɬɵ ɩɪɢɜɨɞɚ ɜ ɰɢɤɥɟ tɊ ɊȺɋɑ: tɊ ɁȺȾ tɊ ɊȺɋɑ. 13. ɉɪɨɜɟɪɤɨɣ ɧɚ ɤɪɚɬɤɨɜɪɟɦɟɧɧɵɟ ɩɟɪɟɝɪɭɡɤɢ ɞɜɢɝɚɬɟɥɹ ɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɫɪɚɜɧɢɜɚɸɬ ɜɪɟɦɹ ɢ ɜɟɥɢɱɢɧɭ ɩɟɪɟɝɪɭɡɨɤ ɜ ɫɢɫɬɟɦɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɞɨɩɭɫɬɢɦɵɦɢ ɩɪɟɞɟɥɶɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɩɨ ɤɚɬɚɥɨɠɧɵɦ ɞɚɧɧɵɦ;

199

14. ɉɪɢ ɪɟɨɫɬɚɬɧɨɦ ɭɩɪɚɜɥɟɧɢɢ ɩɪɨɢɡɜɨɞɹɬ ɜɵɛɨɪ ɩɭɫɤɨ-ɬɨɪɦɨɡɧɵɯ ɪɟɡɢɫɬɨɪɨɜ ɢ ɩɪɨɜɟɪɤɭ ɢɯ ɩɨ ɧɚɝɪɟɜɭ; 15. Ɋɚɫɱɟɬ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɡɚ ɜɪɟɦɹ ɰɢɤɥɚ: – ɰɢɤɥɨɜɵɣ ɄɉȾ Șɐ = Ⱥ/Ɋ, – ɰɢɤɥɨɜɵɣ cos ĳɐ = cos (arctg Q/P), n

ɝɞɟ

Ⱥ=

¦ Mi Zi t i – ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɧɚ ɜɚɥɭ ɡɚ ɜɪɟɦɹ ɰɢɤɥɚ;

i 1 n

P= ¦ 3 Ui Ii cos Mi t i – ɚɤɬɢɜɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɢɡ ɫɟɬɢ; i 1 n

Q = ¦ 3 Ui Ii sin Mi t i – ɪɟɚɤɬɢɜɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɢɡ ɫɟɬɢ. i 1

16. ɉɪɨɜɨɞɢɬɫɹ ɚɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɢ ɫɪɚɜɧɟɧɢɟ ɢɯ ɫ ɚɧɚɥɨɝɢɱɧɵɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ ɢɡ ɥɢɬɟɪɚɬɭɪɧɵɯ ɢɫɬɨɱɧɢɤɨɜ. 4.3.8. ȼɵɛɨɪ ɩɨ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ

Ʉɪɚɬɤɨɜɪɟɦɟɧɧɵɦ ɪɟɠɢɦɨɦ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɧɚɡɵɜɚɸɬ ɬɚɤɨɣ ɪɟɠɢɦ (ɪɢɫ. 4.20), ɤɨɝɞɚ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɡɚ ɜɪɟɦɹ ɪɚɛɨɬɵ t = tɊ ɧɟ ɞɨɫɬɢɝɚɟɬ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ (Ĳ < Ĳɍ), ɚ ɡɚ ɜɪɟɦɹ ɩɚɭɡɵ t = t0, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɨɬɤɥɸɱɚɟɬɫɹ ɨɬ ɫɟɬɢ, ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɭɫɩɟɜɚɟɬ ɞɨɫɬɢɱɶ ɬɟɦɩɟɪɚɬɭɪɵ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ (Ĳ = 0). ȼ ɤɚɬɚɥɨɝɚɯ ɪɟɠɢɦ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɜɪɟɦɟɧɟɦ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɣ ɪɚɛɨɬɵ tɊ: 10, 30, 60, 90 ɦɢɧ. Ɂɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧ ɧɚ ɨɫɧɨɜɚɧɢɢ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ Ĳ(t)

t · TɌ ¸Ĳ . e ¸ ɇȺɑ ¹

t ǻP §¨ TɌ 1 e A ¨ ©

(4.60)

ɉɪɢ ĲɇȺɑ = 0 ɢ t = tɊ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɞɨɫɬɢɝɧɟɬ ĲɆȺɄɋ

t § Ɋ TɌ ¨ Ĳɍ 1 e ¨ ©

· ¸Ĳ , ɍ ¸ ¹

(4.61)

ɤɨɬɨɪɚɹ ɦɟɧɶɲɟ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ Ĳɍ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɟɫɥɢ ɧɚɝɪɭɡɤɚ ɞɜɢɝɚɬɟɥɹ ɛɭɞɟɬ ɪɚɜɧɚ ɧɨɦɢɧɚɥɶɧɨɣ ɞɥɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ, ɬɨ ɞɜɢɝɚɬɟɥɶ ɧɟ ɧɚɝɪɟɟɬɫɹ ɞɨ ɞɨɩɭɫɬɢɦɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ĲȾɈɉ ɢ ɧɟ ɛɭɞɟɬ ɢɫɩɨɥɶɡɨɜɚɧ ɩɨ ɧɚɝɪɟɜɭ. Ⱦɥɹ ɩɨɥɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɩɨ ɧɚɝɪɟɜɭ ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ĲɆȺɄɋ = ĲȾɈɉ. Ɍɨɝɞɚ t § Ɋ TɌ ¨ Ĳɍ 1 e ¨ ©

ǻPK A

· ¸ ¸ ¹

t § Ɋ TɌ ¨ 1 e ¨ ©

Ĳ ȾɈɉ , · ¸ ¸ ¹

ǻPH , A

200

(4.62)

(4.63)

ɢ ɬɟɪɦɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɝɪɭɡɤɢ (ɩɨ ɩɨɬɟɪɹɦ) kT

ǻPK ǻPH

1 § ¨1 e ¨ ©

tɊ TɌ

· ¸ ¸ ¹

. (4.64)

ɉɪɢ t / TT < 0,1, ɢɫɩɨɥɶɡɭɹ ɪɚɡɥɨɠɟɧɢɟ e – y ɜ ɪɹɞ Ɇɚɤɥɨɪɟɧɚ (ɫɦ. 4.3.6), ɩɨɥɭɱɢɦ ɤɌ § TT / tɊ. Ɍɟɪɦɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɝɪɭɡɤɢ ɩɪɢ tɊ / TT =0,1 ɛɭɞɟɬ ɪɚɜɟɧ ɤɌ § 10. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɝɪɭɡɤɢ ɩɨ ɬɨɤɭ (ɫɦ. ɩ. 4.3.7) ɩɪɢ ɷɬɨɦ ɫɨɫɬɚɜɢɬ k i k T § 3. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɶ ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɣ ɫɟɪɢɢ ɦɨɠɧɨ ɩɟɪɟɝɪɭɡɢɬɶ ɩɨ ɩɨɬɟɪɹɦ ɜ 10 ɪɚɡ?, ɩɨ ɬɨɤɭ – ɜ 3 ɪɚɡɚ?! ɇɨ ɦɵ ɩɨɦɧɢɦ, ɱɬɨ ɤɪɨɦɟ ɧɚɝɪɟɜɚ ɫɭɳɟɫɬɜɭɸɬ ɞɪɭɝɢɟ ɮɚɤɬɨɪɵ, ɨɝɪɚɧɢɱɢɜɚɸɳɢɟ Ɋɇ,ǻɊɇ, Ĳ ɜɨɡɦɨɠɧɨɫɬɶ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɟɣ (ɭɫɥɨɜɢɹ Ɋɇ ɤɨɦɦɭɬɚɰɢɢ – ɞɥɹ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ, ɜɟɥɢɱɢɧɚ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ – ɞɥɹ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ). ɉɨ ɭɫɥɨɜɢɹɦ ɧɚĲ (t) ɝɪɟɜɚ ɦɨɝɭɬ ɫɨɡɞɚɜɚɬɶɫɹ ɧɚɝɪɭɡɤɢ, ɤɨɬɨɪɵɟ ɧɟ ɩɪɨɯɨɞɹɬ ɩɨ ɞɪɭɝɢɦ ɭɫɥɨɜɢɹɦ. Ɉɬɫɸɞɚ, ǻɊ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɞɜɢɝɚɬɟɥɟɣ ɧɨɪɦɚɥɶɧɨɝɨ ɢɫɇ t ɩɨɥɧɟɧɢɹ (ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɣ ɫɟɪɢɢ) ɞɥɹ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɧɟɜɵɝɨɞɧɨ, ɧɟtɊ ɜɨɡɦɨɠɧɨ ɢɯ ɪɚɰɢɨɧɚɥɶɧɨɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ. Ⱦɥɹ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ Ɋɢɫ. 4.20. ɇɚɝɪɟɜ ɩɪɢɦɟɧɹɸɬ ɞɜɢɝɚɬɟɥɢ ɫɩɟɰɢɚɥɶɧɨɣ ɤɪɚɧɨɜɨɢ ɨɯɥɚɠɞɟɧɢɟ ɞɜɢɝɚɬɟɥɹ ɦɟɬɚɥɥɭɪɝɢɱɟɫɤɨɣ ɫɟɪɢɢ (ɫɦ. ɩ. 4.3.7). ȼ ɤɚɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɬɚɥɨɝɚɯ ɩɪɢɜɨɞɹɬɫɹ ɡɧɚɱɟɧɢɹ ɞɨɩɭɫɤɚɟɦɨɣ ɪɚɛɨɬɵ ɧɚɝɪɭɡɤɢ ɊȾɈɉ, IȾɈɉ ɩɪɢ ɤɚɬɚɥɨɠɧɨɦ ɜɪɟɦɟɧɢ ɪɚɛɨɬɵ: tɄȺɌ = 30 ɦɢɧ., 60 ɦɢɧ. ȿɫɥɢ tɊ = tɄȺɌ ɢ ɧɚɝɪɭɡɤɚ ɩɨɫɬɨɹɧɧɚ I ɊC = const – ɜɵɛɨɪ ɦɨɳɧɨɫɬɢ ɩɪɨɫɬ. ɇɭɠɧɨ Iɗ ɎȺɄɌ ɫɨɩɨɫɬɚɜɢɬɶ ɞɨɩɭɫɤɚɟɦɵɟ ɧɚɝɪɭɡɤɢ ɪɟɚɥɶɧɨɝɨ ɢ ɤɚɬɚɥɨɠɧɨɝɨ ɝɪɚɮɢɤɨɜ. Iɗ ȿɫɥɢ tɊ tɄȺɌ ɢ ɧɚɝɪɭɡɤɚ ɩɟɪɟɦɟɧɧɚɹ ɊC = var, ɬɨ ɪɚɫɫɱɢɬɵɜɚɸɬ ɩɪɢɟɦɥɟɦɵɦ ɦɟɬɨɞɨɦ ɷɤɜɢɜɚɥɟɧɬɢɪɨɜɚɧɢɹ (ǻɊɗ, Iɗ, Ɇɗ) ɞɨɩɭɫɤɚɟɦɭɸ ɷɤɜɢɜɚɥɟɧɬɧɭɸ ɧɚɝɪɭɡɤɭ ɪɟɚɥɶɧɨɝɨ ɝɪɚɮɢɤɚ (ɧɚɩɪɢɦɟɪ, Iɗ ɎȺɄɌ) ɩɨ ɦɟɬɨɞɢɤɟ, ɢɡɥɨt ɠɟɧɧɨɣ ɜ ɩ. 4.3.7, ɡɚ ɮɚɤɬɢɱɟɫɤɨɟ ɜɪɟɦɹ ɪɚtɎȺɄɌ tɄȺɌ ɛɨɬɵ tɎȺɄɌ. Ⱦɚɥɟɟ ɫɱɢɬɚɸɬ, ɱɬɨ ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜɪɟɦɹ tɎȺɄɌ ɫ ɧɚɝɪɭɡɤɨɣ Iɗ ɎȺɄɌ, ɚ ɜɪɟɦɹ (tɄȺɌ – tɎȺɄɌ) – ɫ ɧɚɝɪɭɡɤɨɣ I = 0. Ɇɟɬɨɞɨɦ ɷɤɊɢɫ. 4.21. Ɉɩɪɟɞɟɥɟɧɢɟ ɞɨɩɭɫɤɚɟɦɨɣ ɧɚɝɪɭɡɤɢ ɞɜɢɝɚɬɟɥɹ ɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ ɪɚɫɫɱɢɬɵɜɚɸɬ Iɗ ɡɚ ɜɪɟɦɹ tɄȺɌ ɢ ɫɪɚɜɧɢɜɚɸɬ ɫ ɞɨɩɭɫɬɢɦɵɦ ɤɚɬɚɥɨɠɧɵɦ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɬɨɤɨɦ IȾɈɉ. ɪɚɛɨɬɵ

201

4.3.9. ȼɵɛɨɪ ɩɨ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ

ɉɪɨɞɨɥɠɢɬɟɥɶɧɵɦ ɪɟɠɢɦɨɦ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɧɚɡɵɜɚɸɬ ɪɟɠɢɦ, ɜ ɤɨɬɨɪɨɦ ɡɚ ɜɪɟɦɹ ɪɚɛɨɬɵ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ ɞɨɫɬɢɝɚɟɬ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ. Ⱦɥɹ ɷɬɨɝɨ ɪɟɠɢɦɚ ɩɪɢɦɟɧɹɸɬ ɞɜɢɝɚɬɟɥɢ ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɣ ɫɟɪɢɢ (ȺɄ, ȺɈ, 4Ⱥ, ɉ, 2ɉ, ɋȾ ɢ ɞɪɭɝɢɟ ɬɢɩɵ). ȼɫɟ ɞɜɢɝɚɬɟɥɢ ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɣ ɫɟɪɢɢ ɧɨɪɦɢɪɭɸɬɫɹ ɨɞɢɧɚɤɨɜɨ: Ɋɇ, Iɇ, nɇ, Ⱦɜɢɝɚɬɟɥɢ ɪɚɡɜɢɜɚɸɬ ɧɨɦɢɧɚɥɶɧɭɸ ɦɨɳɧɨɫɬɶ Ɋɇ ɜ ɬɟɱɟɧɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨ ɞɥɢɬɟɥɶɧɨɝɨ ɜɪɟɦɟɧɢ, ɜɵɞɟɪɠɢɜɚɸɬ ɧɨɦɢɧɚɥɶɧɵɣ ɬɨɤ Iɇ ɬɚɤɨɟ ɠɟ ɜɪɟɦɹ. ɗɬɢ ɞɜɢɝɚɬɟɥɢ ɪɚɫɫɱɢɬɚɧɵ ɬɚɤ, ɱɬɨɛɵ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɬɨɤɟ ɬɟɦɩɟɪɚɬɭɪɚ ɞɜɢɝɚɬɟɥɹ Ĳɍ ɛɵɥɚ ɪɚɜɧɚ ɞɨɩɭɫɬɢɦɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ĲȾɈɉ. Ĳɍ ĲȾɈɉ. ɉɪɢ ɩɨɫɬɨɹɧɧɨɣ ɦɨɳɧɨɫɬɢ Ɋɋ = const ɢ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɢ Ȧ = const ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɞɜɢɝɚɬɟɥɟ 1 Ș ǻP P d 'Ɋɇ (4.65) Ș ɧɟ ɩɪɟɜɵɲɚɸɬ ɧɨɦɢɧɚɥɶɧɵɯ, ɨɬɫɸɞɚ ɫɥɟɞɭɟɬ ɭɫɥɨɜɢɟ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɩɨ ɤɚɬɚɥɨɝɭ Ɋɋ Ɋɇ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɪɨɢɡɜɨɞɢɬɶ ɩɪɨɜɟɪɤɭ ɞɜɢɝɚɬɟɥɹ ɩɨ ɧɚɝɪɟɜɭ, ɬɚɤ ɤɚɤ ɷɬɨɬ ɪɚɫɱɟɬ ɜɵɩɨɥɧɟɧ ɡɚɜɨɞɨɦ-ɢɡɝɨɬɨɜɢɬɟɥɟɦ. ɉɪɢ ɩɭɫɤɟ ɩɨɬɟɪɢ ǻɊ ɜɵɲɟ, ɧɨ ɬɚɤ ɤɚɤ ɩɭɫɤ ɩɪɨɢɡɜɨɞɢɬɫɹ ɪɟɞɤɨ, ɬɨ ɩɨɬɟɪɢ ɩɪɢ ɩɭɫɤɟ ɧɟ ɭɱɢɬɵɜɚɸɬɫɹ. ɉɪɢ ɩɟɪɟɦɟɧɧɨɣ ɫɬɚɬɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɟ ɫɬɪɨɢɬɫɹ ɧɚɝɪɭɡɨɱɧɚɹ ɞɢɚɝɪɚɦɦɚ Ɋɋ = f(t), ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɚɹ ɦɨɳɧɨɫɬɶ 1 n 2 PɋɊɄȼ ¦ Pi t i (4.66) tɐ i 1

ɢɥɢ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɵɣ ɦɨɦɟɧɬ 1 n 2 ¦ Mi t i tɐ i 1

MɋɊɄȼ

(4.67)

ɢ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɜɵɛɢɪɚɟɬɫɹ ɞɜɢɝɚɬɟɥɶ ɦɨɳɧɨɫɬɶɸ ɊȾȼ = ɊɋɊɄȼ ɢɥɢ ɊȾȼ = ɆɋɊɄȼǜȦ. Ⱦɚɥɟɟ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɧɚɝɪɭɡɨɱɧɵɟ ɞɢɚɝɪɚɦɦɵ I(t), M(t), Ȧ(t) ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɢɟɦɥɟɦɵɦ ɦɟɬɨɞɨɦ ɷɤɜɢɜɚɥɟɧɬɧɚɹ ɧɚɝɪɭɡɤɚ ɞɜɢɝɚɬɟɥɹ ɞɥɹ ɪɟɚɥɶɧɨɝɨ ɝɪɚɮɢɤɚ. ȿɫɥɢ ɢɫɩɨɥɶɡɨɜɚɧ ɦɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ, ɬɨ ɩɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ Iɗ ɫɪɚɜɧɢɜɚɟɬɫɹ ɫ ɧɨɦɢɧɚɥɶɧɵɦ ɬɨɤɨɦ Iɇ n

¦ Ii2 ti Iɗ

i 1 n

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d IH .

i 1

202

(4.68)

4.3.10. ɉɪɨɜɟɪɤɚ ɞɜɢɝɚɬɟɥɹ ɧɚ ɤɪɚɬɤɨɜɪɟɦɟɧɧɭɸ ɩɟɪɟɝɪɭɡɤɭ

ɇɚɝɪɟɜ ɨɩɪɟɞɟɥɹɟɬ ɞɥɢɬɟɥɶɧɭɸ ɧɚɝɪɭɡɨɱɧɭɸ ɫɩɨɫɨɛɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɭɸ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɬɟɱɟɧɢɟ ɧɨɪɦɚɬɢɜɧɨɝɨ ɫɪɨɤɚ ɷɤɫɩɥɭɚɬɚɰɢɢ (20 ɥɟɬ). ɋɭɳɟɫɬɜɭɸɬ ɮɚɤɬɨɪɵ, ɨɝɪɚɧɢɱɢɜɚɸɳɢɟ ɧɚɝɪɭɡɤɭ ɜ ɬɟɱɟɧɢɟ ɧɟɩɪɨɞɨɥɠɢɬɟɥɶɧɨɝɨ ɜɪɟɦɟɧɢ (ɤɪɚɬɤɨɜɪɟɦɟɧɧɵɟ ɩɟɪɟɝɪɭɡɤɢ). ɗɬɨ – ɜɬɨɪɨɣ ɤɪɢɬɟɪɢɣ ɩɪɚɜɢɥɶɧɨɫɬɢ ɜɵɛɨɪɚ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ Ⱦɥɹ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɣ ɫɟɪɢɢ ɤɪɚɬɤɨɜɪɟɦɟɧɧɵɟ ɩɟɪɟɝɪɭɡɤɢ ɨɝɪɚɧɢɱɟɧɵ ɭɫɥɨɜɢɹɦɢ ɤɨɦɦɭɬɚɰɢɢ IɆȺɄɋ ȾɈɉ = (2…2,5)·Iɇ. Ʉɪɚɬɤɨɜɪɟɦɟɧɧɵɟ ɩɟɪɟɝɪɭɡɤɢ ɞɜɢɝɚɬɟɥɟɣ ɤɪɚɧɨɜɨ-ɦɟɬɚɥɥɭɪɝɢɱɟɫɤɨɣ ɫɟɪɢɢ ɨɝɨɜɚɪɢɜɚɸɬɫɹ ɜ ɤɚɬɚɥɨɝɟ ɢ ɫɨɫɬɚɜɥɹɸɬ IɆȺɄɋ ȾɈɉ = (3…4)· Iɇ. ɉɪɢ ɪɚɛɨɬɟ ɜ ɪɟɠɢɦɟ ɨɫɥɚɛɥɟɧɢɹ ɩɨɥɹ, ɤɨɝɞɚ Ȧ > ȦȿɋɌ ɭɫɥɨɜɢɹ ɤɨɦɦɭɬɚɰɢɢ ɭɯɭɞɲɚɸɬɫɹ, ɢ ɦɚɤɫɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɬɨɤ ɩɪɢɯɨɞɢɬɫɹ ɫɧɢɠɚɬɶ. ȼɟɥɢɱɢɧɭ ɦɚɤɫɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɨɝɨ ɬɨɤɚ ɩɪɢ Ȧ > ȦȿɋɌ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɩɨ ɮɨɪɦɭɥɟ: Ȧ IɆȺɄɋ ȾɈɉ IɆȺɄɋ ȾɈɉ ɉɊɂ Zɇ 3 ɇ . Ȧ ɉɪɢ Ȧ = 2ǜȦɇ ɢ IɆȺɄɋȾɈɉ IɆȺɄɋȾɈɉ(ɉɊɂ Z ) (2...2,5) Iɇ ɜɟɥɢɱɢɧɚ ɦɚɤɫɢɦɚɥɶɧɨ ɧ

ɞɨɩɭɫɬɢɦɨɝɨ ɬɨɤɚ ɫɨɫɬɚɜɢɬ Ȧɇ 2...2,5 Iɇ 0,8 1,6...2 Iɇ . Ȧ Ⱦɥɹ ɛɟɫɤɨɥɥɟɤɬɨɪɧɵɯ ɦɚɲɢɧ ɬɨɤ ɧɟ ɹɜɥɹɟɬɫɹ ɮɚɤɬɨɪɨɦ, ɨɝɪɚɧɢɱɢɜɚɸɳɢɦ ɦɚɤɫɢɦɚɥɶɧɭɸ ɧɚɝɪɭɡɤɭ ɞɜɢɝɚɬɟɥɹ. Ⱦɥɹ ɚɫɢɧɯɪɨɧɧɵɯ ɢ ɫɢɧɯɪɨɧɧɵɯ ɦɚɲɢɧ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɩɪɟɞɟɥ ɩɨ ɦɨɦɟɧɬɭ. Ʉɪɢɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɨɛɵɱɧɨ ɢɦɟɟɬ ɡɧɚɱɟɧɢɟ ɆɄ = (1,8…2,5)ǜɆɇ, ɩɪɢ ɷɬɨɦ ɦɚɤɫɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɦɨɦɟɧɬ ɢɡ-ɡɚ ɤɨɥɟɛɚɧɢɣ ɧɚɩɪɹɠɟɧɢɹ ɩɢɬɚɧɢɹ ɩɪɢɧɢɦɚɸɬ ɪɚɜɧɵɦ ɆɆȺɄɋ= 0,8·ɆɄ. ɋɢɧɯɪɨɧɧɵɣ ɞɜɢɝɚɬɟɥɶ ɪɚɡɜɢɜɚɟɬ ɦɚɤɫɢɦɚɥɶɧɵɣ ɦɨɦɟɧɬ ɆɆȺɄɋ = (2,5…3,5)·Ɇɇ. ɉɪɢ ɷɬɨɦ ɜɟɥɢɱɢɧɚ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɋȾ ɦɨɠɟɬ ɪɟɝɭɥɢɪɨɜɚɬɶɫɹ ɢɡɦɟɧɟɧɢɟɦ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ (ɮɨɪɫɢɪɨɜɤɨɣ ɜɨɡɛɭɠɞɟɧɢɹ), ɱɬɨ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɪɢ ɩɭɫɤɟ ɢ ɩɪɢ ɫɧɢɠɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɬɚɬɨɪɟ. Ʉɪɚɬɤɨɜɪɟɦɟɧɧɵɟ ɩɟɪɟɝɪɭɡɤɢ ɞɜɢɝɚɬɟɥɟɣ ɨɩɪɟɞɟɥɹɸɬɫɹ ɭɫɥɨɜɢɹɦɢ ɩɭɫɤɚ, ɬɨɪɦɨɠɟɧɢɹ, ɧɚɛɪɨɫɚ ɧɚɝɪɭɡɤɢ ɢ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɧɚ ɫɬɚɞɢɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɩɪɢ ɜɵɛɨɪɟ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ. IɆȺɄɋ ȾɈɉ

IɆȺɄɋ ȾɈɉZɧ 3

4.3.11. ɉɪɨɜɟɪɤɚ ɞɜɢɝɚɬɟɥɹ ɩɨ ɭɫɥɨɜɢɹɦ ɩɭɫɤɚ

ȿɫɥɢ ɭɫɥɨɜɢɹ ɩɭɫɤɚ ɞɜɢɝɚɬɟɥɟɣ ɫ ɪɟɨɫɬɚɬɧɵɦ ɭɩɪɚɜɥɟɧɢɟɦ (RȾɈȻ) ɢ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɧɞɢɜɢɞɭɚɥɶɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ (f = var, U = var) ɡɚɤɥɚɞɵɜɚɸɬɫɹ ɩɪɢ ɪɚɫɱɟɬɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ, ɬɨ ɩɪɢ ɜɵɛɨɪɟ ɦɨɳɧɨɫɬɢ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ ɢ ɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɧɟɨɛɯɨɞɢɦɚ ɞɨɩɨɥɧɢɬɟɥɶɧɚɹ ɩɪɨɜɟɪɤɚ ɩɨ ɭɫɥɨɜɢɹɦ ɩɭɫɤɚ. 203

1. ɉɭɫɤɨɜɨɣ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɞɨɥɠɟɧ ɛɵɬɶ ɛɨɥɶɲɟ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɩɪɢ Ȧ = 0. 2. Ɇɨɦɟɧɬ ɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɧɚ ɩɨɞɫɢɧɯɪɨɧɧɨɣ ɫɤɨɪɨɫɬɢ ɞɥɹ ɧɚɞɟɠɧɨɝɨ ɜɬɹɝɢɜɚɧɢɹ ɜ ɫɢɧɯɪɨɧɢɡɦ ɞɨɥɠɟɧ ɛɵɬɶ ɛɨɥɶɲɟ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɧɚ ɷɬɨɣ ɫɤɨɪɨɫɬɢ. 3. Ⱦɥɹ ɤɪɭɩɧɵɯ ɚɫɢɧɯɪɨɧɧɵɯ ɢ ɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɨɜɟɪɤɚ ɜɟɥɢɱɢɧɵ ɩɪɢɫɨɟɞɢɧɟɧɧɨɝɨ ɦɨɦɟɧɬɚ ɢɧɟɪɰɢɢ ɦɟɯɚɧɢɡɦɚ JɉɊɂɋɈȿȾ JɆȺɄɋ.ɉɊɂɋɈȿȾ. ɇɟɫɨɛɥɸɞɟɧɢɟ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɩɪɢɜɨɞɢɬ ɤ ɡɚɬɹɝɢɜɚɧɢɸ ɩɭɫɤɚ, ɩɪɨɯɨɞɹɳɟɝɨ ɩɪɢ ɛɨɥɶɲɢɯ ɬɨɤɚɯ, ɢ ɜɵɯɨɞɭ ɞɜɢɝɚɬɟɥɹ ɢɡ ɫɬɪɨɹ. ȼɟɥɢɱɢɧɚ JɆȺɄɋ.ɉɊɂɋɈȿȾ ɩɪɢɜɨɞɢɬɫɹ ɜ ɤɚɬɚɥɨɝɚɯ.

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5. ȻɂȻɅɂɈȽɊȺɎɂɑȿɋɄɂɃ ɋɉɂɋɈɄ

Ɉɫɧɨɜɧɚɹ ɥɢɬɟɪɚɬɭɪɚ 1. Ʉɥɸɱɟɜ ȼ.ɂ. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 2001. – 698 ɫ. 2. Ʉɨɜɱɢɧ ɋ.Ⱥ., ɋɚɛɢɧɢɧ ɘ.Ⱥ. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ. – ɋɉɛ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1994.– 496 ɫ. 3. Ɇɨɫɤɚɥɟɧɤɨ ȼ.ȼ. Ⱥɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ: ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1986. – 416 ɫ. Ⱦɨɩɨɥɧɢɬɟɥɶɧɚɹ ɥɢɬɟɪɚɬɭɪɚ 4. Ȼɚɲɚɪɢɧ Ⱥ.ȼ., ɉɨɫɬɧɢɤɨɜ ɘ.ȼ. ɉɪɢɦɟɪɵ ɪɚɫɱɟɬɚ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɧɚ ɗȼɆ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ. – Ʌ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1990. – 512 ɫ.,ɢɥ. 5. ȼɟɲɟɧɟɜɫɤɢɣ ɋ.ɇ. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɟɣ ɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ. – Ɇ.: ɗɧɟɪɝɢɹ, 1977. – 432 ɫ. 6. ȼɨɥɶɞɟɤ Ⱥ.ɂ. ɗɥɟɤɬɪɢɱɟɫɤɢɟ ɦɚɲɢɧɵ. ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ. Ʌ.: “ɗɧɟɪɝɢɹ”, 1974. – 840 ɫ. 7. ɂɥɶɢɧɫɤɢɣ ɇ.Ɏ. Ɉɫɧɨɜɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ɂɡɞɚɬɟɥɶɫɬɜɨ Ɇɗɂ, 2003. – 224 ɫ. 8. Ʉɚɩɭɧɰɨɜ ɘ.Ⱦ., ȿɥɢɫɟɟɜ ȼ.Ⱥ., ɂɥɶɹɲɟɧɤɨ Ʌ.Ⱥ. ɗɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɟ ɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɩɪɨɦɵɲɥɟɧɧɵɯ ɭɫɬɚɧɨɜɨɤ: ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ȼɵɫɲ. ɲɤɨɥɚ, 1979. – 359 ɫ. 9. Ɇɢɯɚɣɥɨɜ Ɉ.ɉ. Ⱥɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ ɫɬɚɧɤɨɜ ɢ ɩɪɨɦɵɲɥɟɧɧɵɯ ɪɨɛɨɬɨɜ: ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, 1990. – 304 ɫ. 10. Ɉɧɢɳɟɧɤɨ Ƚ.Ȼ. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɩɪɢɜɨɞ: ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ɊȺɋɏɇ, 2003.– 320 ɫ. 11. Ɉɫɧɨɜɵ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ/ Ɇ.Ƚ.ɑɢɥɢɤɢɧ, Ɇ.Ɇ.ɋɨɤɨɥɨɜ, ȼ.Ɇ.Ɍɟɪɟɯɨɜ, Ⱥ.ȼ.ɒɢɧɹɧɫɤɢɣ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ɗɧɟɪɝɢɹ, 1974.– 568 ɫ. 12. Ɍɟɪɟɯɨɜ ȼ.Ɇ. ɗɥɟɦɟɧɬɵ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1987. – 224 ɫ. 13. ɑɢɥɢɤɢɧ Ɇ.Ƚ., Ʉɥɸɱɟɜ ȼ.ɂ., ɋɚɧɞɥɟɪ Ⱥ.ɋ. Ɍɟɨɪɢɹ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: ɗɧɟɪɝɢɹ, 1979. – 616 ɫ. ɋɩɪɚɜɨɱɧɚɹ ɥɢɬɟɪɚɬɭɪɚ 14. Ⱥɫɢɧɯɪɨɧɧɵɟ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɢ ɫɟɪɢɢ 4Ⱥ: ɋɩɪɚɜɨɱɧɢɤ / Ⱥ.ɗ. Ʉɪɚɜɱɢɤ, Ɇ.ɇ. ɒɥɚɮ, ȼ.ɂ. Ⱥɮɨɧɢɧ ɢ ɞɪ. – Ɇ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1982. 15. Ⱦɜɢɝɚɬɟɥɢ ɚɫɢɧɯɪɨɧɧɵɟ ɬɪɟɯɮɚɡɧɵɟ ɤɪɚɧɨɜɵɟ ɢ ɦɟɬɚɥɥɭɪɝɢɱɟɫɤɢɟ ɫɟɪɢɣ ɆɌF, MTH, MTKF, MTKH. ɇɄ 01.30.01-82. ɗɥɟɤɬɪɨɬɟɯɧɢɤɚ ɋɋɋɊ. – Ɇ.: ɂɧɮɨɪɦɷɥɟɤɬɪɨ, 1985. 16. Ⱦɜɢɝɚɬɟɥɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɤɪɚɧɨɜɵɟ ɢ ɦɟɬɚɥɥɭɪɝɢɱɟɫɤɢɟ ɫɟɪɢɢ Ⱦ. ɇɄ 01.19.01-82. ɗɥɟɤɬɪɨɬɟɯɧɢɤɚ ɋɋɋɊ. – Ɇ.: ɂɧɮɨɪɦɷɥɟɤɬɪɨ, 1985. 17. Ʉɪɚɧɨɜɨɟ ɷɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɟ: ɋɩɪɚɜɨɱɧɢɤ / ɉɨɞ ɪɟɞ. Ⱥ.Ⱥ. Ɋɚɛɢɧɨɜɢɱɚ.– Ɇ.: ɗɧɟɪɝɢɹ, 1979. 205

18. Ʉɨɦɩɥɟɤɬɧɵɟ ɬɢɪɢɫɬɨɪɧɵɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɵ: ɋɩɪɚɜɨɱɧɢɤ / ɉɨɞ ɪɟɞ. Ⱥ.Ⱥ. ɉɟɪɟɥɶɦɭɬɟɪɚ. – Ɇ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1988. – 319 ɫ. 19. ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɦɚɲɢɧɚɦ / ɉɨɞ ɪɟɞ. ɂ.ɉ. Ʉɨɩɵɥɨɜɚ ɢ ȼ.ȼ. Ʉɥɨɤɨɜɚ. – Ɇ.:ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1988.– Ɍ.1.– 456 ɫ. 20. ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɦɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ / ɉɨɞ ɪɟɞ. ȿɥɢɫɟɟɜɚ ȼ.Ⱥ., ɒɢɧɹɧɫɤɨɝɨ Ⱥ.ȼ. – Ɇ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1983. – 616 ɫ. 21. ɗɥɟɤɬɪɨɩɪɢɜɨɞɵ ɫɟɪɢɢ ɗɄɌɁ. Ɉɬɪɚɫɥɟɜɨɣ ɤɚɬɚɥɨɝ 08.35.03 – 96. – Ɇ.: ɂɧɮɨɪɦɷɥɟɤɬɪɨ, 1996. 22. ɗɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɢɣ ɫɩɪɚɜɨɱɧɢɤ. – Ɇ.: ɗɧɟɪɝɨɢɡɞɚɬ, 1982. – Ɍ.3, ɤɧ.2. – 560 ɫ. 23. əɭɪɟ Ⱥ.Ƚ. , ɉɟɜɡɧɟɪ ȿ.Ɇ. Ʉɪɚɧɨɜɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ: Cɩɪɚɜɨɱɧɢɤ. – Ɇ.: ɗɧɟɪɝɨɚɬɨɦɢɡɞɚɬ, 1988. – 344 ɫ Ɇɟɬɨɞɢɱɟɫɤɚɹ ɥɢɬɟɪɚɬɭɪɚ 24. Ƚɟɥɶɦɚɧ Ɇ.ȼ. ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ ɬɢɪɢɫɬɨɪɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɣ ɞɥɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ – ɑɟɥɹɛɢɧɫɤ: ɂɡɞ.ɑȽɌɍ, 1996. – 91 ɫ. 25. Ƚɟɥɶɦɚɧ Ɇ.ȼ. Ɋɚɫɱɟɬ ɜɟɧɬɢɥɶɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɣ ɞɥɹ ɱɚɫɬɨɬɧɨɪɟɝɭɥɢɪɭɟɦɵɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ. – ɑɟɥɹɛɢɧɫɤ: ɂɡɞ. ɑȽɌɍ, 1997. – 37 ɫ. 26. Ⱦɪɚɱɟɜ Ƚ.ɂ. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɤ ɤɭɪɫɨɜɨɦɭ ɩɪɨɟɤɬɢɪɨɜɚɧɢɸ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɡɚɨɱɧɨɝɨ ɨɛɭɱɟɧɢɹ. – ɑɟɥɹɛɢɧɫɤ: ɂɡɞ. ɘɍɪȽɍ, 2002. – 137 ɫ. 27. Ⱦɪɚɱɟɜ Ƚ.ɂ. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɤ ɤɭɪɫɨɜɨɦɭ ɩɪɨɟɤɬɢɪɨɜɚɧɢɸ. – ɑɟɥɹɛɢɧɫɤ: ɂɡɞ. ɘɍɪȽɍ, 1998. – 160 ɫ. 28. Ⱦɪɚɱɟɜ Ƚ.ɂ. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɩɨ ɬɢɩɨɜɵɦ ɪɚɫɱɟɬɚɦ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɡɚɨɱɧɨɝɨ ɨɛɭɱɟɧɢɹ. – ɑɟɥɹɛɢɧɫɤ: ɂɡɞ. ɘɍɪȽɍ, 2002. – 85 ɫ. 29. Ʌɟɜɢɧɬɨɜ ɋ.Ⱦ. Ⱥɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɤ ɤɭɪɫɨɜɨɦɭ ɩɪɨɟɤɬɢɪɨɜɚɧɢɸ. ɉɨɞ ɪɟɞ. Ƚ.ɂ.Ⱦɪɚɱɺɜɚ. – ɑɟɥɹɛɢɧɫɤ: ɂɡɞ. ɑȽɌɍ, 1996. – 35 ɫ. 30. Ɉɫɢɩɨɜ Ɉ.ɂ., ɍɫɵɧɢɧ ɘ.ɋ., Ⱦɪɚɱɟɜ Ƚ.ɂ. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɤ ɥɚɛɨɪɚɬɨɪɧɵɦ ɪɚɛɨɬɚɦ. ȼ 4-ɯ ɱɚɫɬɹɯ. – ɑɟɥɹɛɢɧɫɤ: ɂɡɞ. ɘɍɪȽɍ, 1998. 31. Ɍɟɨɪɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ: Ɋɚɛɨɱɚɹ ɩɪɨɝɪɚɦɦɚ, ɡɚɞɚɧɢɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɪɚɛɨɬɵ, ɤɨɧɬɪɨɥɶɧɵɟ ɡɚɞɚɱɢ / ɋɨɫɬɚɜɢɬɟɥɢ: Ƚ.ɂ.Ⱦɪɚɱɟɜ, ɋ.Ɇ.Ȼɭɬɚɤɨɜ, ȼ.Ⱥ.Ʉɢɫɥɸɤ; ɉɨɞ ɪɟɞɚɤɰɢɟɣ Ƚ.ɂ.Ⱦɪɚɱɟɜɚ.– ɑɟɥɹɛɢɧɫɤ: ɂɡɞ. ɘɍɪȽɍ, 2000. – 46 ɫ.

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ɈȽɅȺȼɅȿɇɂȿ ɉɪɟɞɢɫɥɨɜɢɟ…………………………………………….…………………………………..3 Ƚɥɚɜɚ ɩɟɪɜɚɹ. ȼȼȿȾȿɇɂȿ. ɈɋɇɈȼɇɕȿ ɉɈɇəɌɂə ɂ ɈɉɊȿȾȿɅȿɇɂə 1.1. ɂɫɬɨɪɢɹ ɪɚɡɜɢɬɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ………………………………….…….…..4 1.2. Ɏɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɫɨɜɪɟɦɟɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ…………..……….7 1.3. Ɇɟɫɬɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɫɨɜɪɟɦɟɧɧɨɣ ɬɟɯɧɨɥɨɝɢɢ……………….….…….7 1.4. ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɢ ɫɨɜɪɟɦɟɧɧɚɹ ɷɧɟɪɝɟɬɢɤɚ…………………………..………9 1.5. Ɉɛɳɢɟ ɬɪɟɛɨɜɚɧɢɹ ɤ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ………………………………..……….9 1.6. ɋɜɹɡɶ Ɍɗɉ ɫ ɞɪɭɝɢɦɢ ɞɢɫɰɢɩɥɢɧɚɦɢ……………………………..…………10 Ƚɥɚɜɚ ɜɬɨɪɚɹ. ɆȿɏȺɇɂɑȿɋɄȺə ɑȺɋɌɖ ɗɅȿɄɌɊɈɉɊɂȼɈȾȺ 2.1. Ʉɢɧɟɦɚɬɢɱɟɫɤɢɟ ɫɯɟɦɵ ɪɚɛɨɱɢɯ ɨɪɝɚɧɨɜ………………………..………….11 2.2. Ɋɚɫɱɟɬɧɵɟ ɫɯɟɦɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ……………..….14 2.3. ɍɱɟɬ ɩɨɬɟɪɶ ɜ ɩɟɪɟɞɚɱɚɯ……………………………………………………....17 2.4. ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ……………………………………....21 2.5. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɤɚɤ ɨɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ………..…23 2.6. ɉɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ…….…..…24 2.7. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɭɩɪɭɝɨɣ ɫɜɹɡɶɸ……….…….…...31 2.7.1. ɉɪɢɜɟɞɟɧɢɟ ɭɩɪɭɝɨɫɬɢ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ………………………….….…32 2.7.2. ɉɪɢɜɟɞɟɧɢɟ ɦɧɨɝɨɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɤ ɞɜɭɯɦɚɫɫɨɜɨɣ……..33 2.7.3. ɍɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɢ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ………………………………………………………………………………………34 2.7.4. ɉɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ…………….35 2.7.5. ɉɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ ɫ ɡɚɡɨɪɨɦ.38 2.8. Ɉɛɨɛɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ.39 2.9. ɍɩɪɚɠɧɟɧɢɹ ɞɥɹ ɫɚɦɨɩɪɨɜɟɪɤɢ ………………………………………………40 Ƚɥɚɜɚ ɬɪɟɬɶɹ. ɗɅȿɄɌɊɈɆȿɏȺɇɂɑȿɋɄɂȿ ɋȼɈɃɋɌȼȺ ɂ ɏȺɊȺɄɌȿɊɂɋɌɂɄɂ ȾȼɂȽȺɌȿɅȿɃ 3.1. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɚɪɚɥɥɟɥɶɧɨɝɨ (ɧɟɡɚɜɢɫɢɦɨɝɨ) ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɇȼ) 3.1.1. ɍɪɚɜɧɟɧɢɹ ɢ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɇȼ……………….…………………...42 3.1.2. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ……...………47 3.1.3 Ɂɨɧɵ ɞɨɩɭɫɬɢɦɵɯ ɧɚɝɪɭɡɨɤ…………………………………………………49 3.1.4. ȿɫɬɟɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɇȼ ɢ ɢɯ ɪɚɫɱɟɬ……………………….49 3.1.5. ɂɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɇȼ ɢ ɢɯ ɪɚɫɱɟɬ……………………...54 3.1.6. Ɋɟɨɫɬɚɬɧɵɣ ɩɭɫɤ Ⱦɇȼ…………………...………………………………….57 3.1.7. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ Ⱦɇȼ………………..………………………..61 3.1.8. Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ Ⱦɇȼ…………………………………………………..62 3.1.9. Ɋɚɫɱɟɬ ɫɯɟɦ ɜɤɥɸɱɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɪɚɛɨɬɭ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ……………………………………………………………………68 3.1.10. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɫ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɰɟɯɨɜɨɣ ɫɟɬɢ……………………………………………………………………..74 3.1.11 ɍɩɪɚɠɧɟɧɢɹ ɞɥɹ ɫɚɦɨɩɪɨɜɟɪɤɢ………………………………………….80 3.2. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɉȼ)…………………………………………82 3.2.1. ɍɪɚɜɧɟɧɢɹ ɢ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɉȼ………………………………...82 207

3.2.2. ȿɫɬɟɫɬɜɟɧɧɵɟ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɉȼ……………..83 3.2.3.Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ Ⱦɉȼ………………………………………………..84 3.2.4. Ɋɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ Ⱦɉȼ…………………………………………….88 3.2.5. Ɋɟɨɫɬɚɬɧɵɣ ɩɭɫɤ Ⱦɉȼ…………………………………………………...92 3.3. Ɉɫɨɛɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɞɜɢɝɚɬɟɥɟɣ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɋȼ)……………………………………………………………..95 3.4. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ………………………………………….…………………………………………96 3.5. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɚɫɢɧɯɪɨɧɧɨɝɨ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ 3.5.1. Ɉɫɧɨɜɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ (ȺȾ)……...98 3.5.2. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ…………………………………..101 3.5.3. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ…………………………110 3.5.4. Ɏɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɜɢɞɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ………...115 3.5.5. ɍɩɪɨɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ȺȾ…………………………………116 3.5.6. ɂɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɢ ɢɯ ɪɚɫɱɟɬ…………………..117 3.5.7. ȿɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ…………………………………..127 3.5.8. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ȺȾ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ………………………………………………129 3.5.9. ɉɭɫɤ ȺȾ…………………………………………………………………..134 3.5.10. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ȺȾ …………………………………….138 3.5.11. Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ ȺȾ……………………………………………….139 3.5.12. Ɋɚɫɱɟɬ ɫɯɟɦ ɜɤɥɸɱɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɪɚɛɨɬɭ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ……………………………………………………………….146 3.5.13. Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ȺȾ………………………..153 3.5.14. ɍɩɪɚɠɧɟɧɢɹ ɞɥɹ ɫɚɦɨɩɪɨɜɟɪɤɢ…………………………………….155 3.6 ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ 3.6.1 Ɉɫɨɛɟɧɧɨɫɬɢ ɋȾ…………………………………………………………156 3.6.2 Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ…………157 3.6.3 ȼɥɢɹɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɧɚ ɜɢɞ ɦɟɯɚɧɢɱɟɫɤɢɯ ɢ ɭɝɥɨɜɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ…………………………..159 3.6.4 ɍɩɪɨɳɟɧɧɚɹ cɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɋȾ …………………………………160 3.6.5 Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɋȾ ɩɪɢ ɩɭɫɤɟ………………………162 3.6.6 Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ ɋȾ………………………………………………...164 Ƚɥɚɜɚ ɱɟɬɜɟɪɬɚɹ. ɗɇȿɊȽȿɌɂɄȺ ɗɅȿɄɌɊɈɉɊɂȼɈȾȺ. ȼɕȻɈɊ ɗɅȿɄɌɊɈȾȼɂȽȺɌȿɅȿɃ ɉɈ ɆɈɓɇɈɋɌɂ 4.1. ɗɧɟɪɝɟɬɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ………………..…….166 4.2. ɗɧɟɪɝɟɬɢɤɚ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɨɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ…………..………...167 4.2.1.ɗɧɟɪɝɟɬɢɤɚ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɨɜ Ⱦɇȼ…………………………..168 4.2.2. Ɉɛ ɷɧɟɪɝɟɬɢɤɟ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɨɜ Ⱦɇȼ ɢ Ⱦɉȼ……………...171 4.2.3. ɗɧɟɪɝɟɬɢɤɚ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɨɜ ɚɫɢɧɯɪɨɧɧɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ……………………………………………………………..172 4.2.4. ɉɭɬɢ ɭɥɭɱɲɟɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ………………………………………………..174 4.2.5. ɗɧɟɪɝɨɫɛɟɪɟɠɟɧɢɟ ɫɪɟɞɫɬɜɚɦɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ………………175 4.3. ȼɵɛɨɪ ɞɜɢɝɚɬɟɥɟɣ ɩɨ ɦɨɳɧɨɫɬɢ 4.3.1. Ɉɛɳɢɟ ɩɨɥɨɠɟɧɢɹ ɩɨ ɜɵɛɨɪɭ ɞɜɢɝɚɬɟɥɟɣ ………………………176 208

4.3.2. Ɉɫɧɨɜɧɵɟ ɤɪɢɬɟɪɢɢ ɜɵɛɨɪɚ ɞɜɢɝɚɬɟɥɟɣ ɩɨ ɦɨɳɧɨɫɬɢ………..179 4.3.3. Ɉɫɧɨɜɵ ɬɟɨɪɢɢ ɧɚɝɪɟɜɚ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɲɢɧ………..………..180 4.3.4. Ɉɯɥɚɠɞɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɦɚɲɢɧ…………...…………………..183 4.3.5. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɟɣ ɩɨ ɭɫɥɨɜɢɹɦ ɧɚɝɪɟɜɚ………………………………………………………………………...184 4.3.6. Ɇɟɬɨɞɵ ɷɤɜɢɜɚɥɟɧɬɢɪɨɜɚɧɢɹ ɩɨ ɧɚɝɪɟɜɭ………………………...186 4.3.7. ȼɵɛɨɪ ɩɨ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɟɣ ɩɨɜɬɨɪɧɨ-ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ……………………………………………………….……..192 4.3.8. ȼɵɛɨɪ ɩɨ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ………………………………………………………………200 4.3.9. ȼɵɛɨɪ ɩɨ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ…………………………………………………………………………...202 4.3.10. ɉɪɨɜɟɪɤɚ ɞɜɢɝɚɬɟɥɹ ɧɚ ɤɪɚɬɤɨɜɪɟɦɟɧɧɭɸ ɩɟɪɟɝɪɭɡɤɭ……….203 4.3.11. ɉɪɨɜɟɪɤɚ ɞɜɢɝɚɬɟɥɹ ɩɨ ɭɫɥɨɜɢɹɦ ɩɭɫɤɚ………………………..203

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