PTO_uchebnoe_posobie

Ɂɜɟɡɞɨɱɤɢ – ɞɟɬɚɥɢ, ɜɵɩɨɥɧɟɧɧɵɟ ɜ ɮɨɪɦɟ ɞɢɫɤɚ ɫ ɡɭɛɶɹɦɢ (ɝɧɟɡɞɚɦɢ) ɧɚ ɨɛɪɚɡɭɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɟ ɞɥɹ ɢɡɦɟɧɟɧɢɹ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ ɰɟɩɢ ɢɥɢ ɩɟɪɟɞɚɱɢ ɧɚ ɧɟɟ ɬɹɝɨɜɵɟ ɭɫɢɥɢɹ. ɂɯ ɜɵɩɨɥɧɹɸɬ ɥɢɬɵɦɢ ɢɡ ɱɭɝɭɧɚ ɢɥɢ ɫɬɚɥɢ (ɞɥɹ ɤɪɭɝɥɨɡɜɟɧɧɵɯ ɫɜɚɪɧɵɯ ɰɟɩɟɣ), ɢɡ ɩɪɨɤɚɬɚ ɢɥɢ ɥɢɬɟɣɧɨɣ ɫɬɚɥɢ (ɞɥɹ ɩɥɚɫɬɢɧɱɚɬɵɯ ɰɟɩɟɣ). Ɂɜɟɡɞɨɱɤɢ ɞɥɹ ɩɥɚɫɬɢɧɱɚɬɵɯ ɰɟɩɟɣ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɡɭɛɱɚɬɵɟ ɤɨɥɟɫɚ, ɡɭɛɶɹ ɤɨɬɨɪɵɯ ɜɯɨɞɹɬ ɦɟɠɞɭ ɩɥɚɫɬɢɧɚɦɢ ɰɟɩɟɣ, ɫɨɩɪɢɤɚɫɚɹɫɶ ɫ ɜɚɥɢɤɚɦɢ ɲɚɪɧɢɪɨɜ.

Ɋɢɫ.2.14. Ɂɜɟɡɞɨɱɤɢ: ɚ —ɞɥɹ ɫɜɚɪɧɨɣ; ɛ – ɞɥɹ ɩɥɚɫɬɢɧɱɚɬɨɣ ɰɟɩɟɣ

ɉɨɥɢɫɩɚɫɬɵ. Ƚɢɛɤɢɟ ɬɹɝɨɜɵɟ ɨɪɝɚɧɵ ɢ ɛɥɨɤɢ ɢɫɩɨɥɶɡɭɸɬ ɤɚɤ ɩɪɨɫɬɟɣɲɢɟ ɝɪɭɡɨɩɨɞɴɟɦɧɵɟ ɭɫɬɪɨɣɫɬɜɚ.

ɉɪɢ ɩɨɞɴɟɦɟ ɝɪɭɡɚ ɱɟɪɟɡ ɧɟɩɨɞɜɢɠɧɨ ɡɚɤɪɟɩɥɟɧɧɵɣ ɛɥɨɤ (ɪɢɫ. 2.15) ɧɚɬɹɠɟɧɢɟ ɫɛɟɝɚɸɳɟɣ ɜɟɬɜɢ Fc ɤɚɧɚɬɚ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɭɫɢɥɢɹ, ɧɟɨɛɯɨɞɢɦɨɝɨ ɞɥɹ ɩɨɞɴɟɦɚ ɝɪɭɡɚ Gɝ , ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɨɬ ɠɟɫɬɤɨɫɬɢ ɤɚɧɚɬɚ Fk ɚ ɬɚɤɠɟ ɫɨɩɪɨɬɢɜɥɟɧɢɣ Fɛ ɨɬ ɬɪɟɧɢɹ ɩɨɞɲɢɩɧɢɤɨɜ ɛɥɨɤɚ: Fc = G ɝɪ + F k + Fɛ .

ɀɟɫɬɤɨɫɬɶ ɤɚɧɚɬɚ ɩɪɢ ɫɝɢɛɚɧɢɢ ɧɚ ɛɥɨɤɟ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɨɫɢ ɪɭɱɶɹ ɛɥɨɤɚ ɞɨ ɫɪɟɞɧɟɣ ɥɢɧɢɢ ɤɚɧɚɬɚ ɧɚ ɧɟɫɝɢɛɚɸɳɟɣ ɜɟɬɜɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɚ ɧɚ ɫɛɟɝɚɸɳɟɣ ɭɦɟɧɶɲɚɟɬɫɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɧɨɦɢɧɚɥɶɧɵɦ ɪɚɞɢɭɫɨɦ ɛɥɨɤɚ ɛ ʹ ; ɧɚɬɹɠɟɧɢɟ ɫɛɟɝɚɸɳɟɣ ɜɟɬɜɢ ɤɚɧɚɬɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɧɚ F k = G ɝ (b /

a – 1) G ɝ (0,01…0,02).

61

Ɋɢɫ. 2.15. ɚ – ɛɥɨɤ ɫ ɧɟɩɨɞɜɢɠɧɨɣ ɨɫɶɸ; ɛ – ɫɯɟɦɚ ɧɚɛɟɝɚɧɢɹ ɤɚɧɚɬɚ ɧɚ ɛɥɨɤ; ɜ

– ɫɤɨɪɨɫɬɶ ɤɚɧɚɬɚ ɧɚ ɧɟɩɨɞɜɢɠɧɨɦ ɛɥɨɤɟ; ɝ – ɫɤɨ ɪɨɫɬɶ ɤɚɧɚɬɚ ɧɚ ɩɨɞɜɢɠɧɨɦ ɛɥɨɤɟ

ɉɪɢ ɨɬɧɨɲɟɧɢɢ ɞɢɚɦɟɬɪɚ ɨɫɢ ɤ ɞɢɚɦɟɬɪɭ ɪɭɱɶɹ ɛɥɨɤɚ ɛ = 1/6 ɢ ɤɨ-

ɷɮɮɢɰɢɟɧɬɚɯ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ f = 0,1 ɢ f = 0,02, ɫɢɥɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɨɬ ɬɪɟɧɢɹ ɜ ɩɨɞɲɢɩɧɢɤɚɯ ɛɥɨɤɚ F ɛ = 2 G ɝ f k d / ɛ G ɝ (0,03…0,006).

ɄɉȾ ɛɥɨɤɚ ɫ ɩɨɞ ɲɢɩɧɢɤɚɦɢ ɤɚɱɟɧɢɹ Ș ɩ = 0,97…0,98, ɫɤɨɥɶɠɟɧɢɹ Ș ɩ = 0,94…0,96.

ɇɚɩɪɹɠɟɧɢɟ ɩɟɪɟɤɢɧɭɬɨɝɨ ɱɟɪɟɡ ɧɟɩɨɞɜɢɠɧɵɣ ɛɥɨɤ ɤɚɧɚɬɚ Fc = G ɝ / Ș ɩ ɉɪɢɦɟɧɟɧɢɟ ɫɢɫɬɟɦ ɵ ɛɥɨɤɚ (ɫ ɩɨɞɜɢɠɧɵɦɢ ɢ ɧɟɩɨɞɜɢɠɧɵɦɢ ɨɫɹɦɢ) ɫɜɹ-

ɡɚɧɧɵɯ ɝɢɛɤɢɦɢ ɬɹɝɨɜɵɦ ɢ ɨɪɝɚɧɚɦɢ, ɩɪɢɜɟɥɨ ɤ ɫɨɡɞɚɧɢɸ ɩɨɥɢɫɩɚɫɬɨɜ. ɉɨɥɢɫɩɚɫɬɵ ɦɨɝɭɬ ɛɵɬɶ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɦɢ ɝɪɭɡɨɩɨɞɴɟɦɧɵɦɢ ɭɫɬɪɨɣɫɬɜɚɦɢ ɢɥɢ ɜɯɨɞɢɬɶ ɜ ɫɨɫɬɚɜ ɦɟɯɚɧɢɡɦɨɜ ɝɪɭɡɨɩɨɞɴɟɦɧɵɯ ɦɚɲɢɧ.

62

ɉɨɥɢɫɩɚɫɬ – ɭɫɬɪɨɣɫɬɜɨ ɞɥɹ ɩɨɞɴɟɦɚ ɢɥɢ ɩɨɞɬɹɝɢɜɚɧɢɹ ɝɪɭɡɨɜ, ɫɨɫɬɨɹɳɟɟ ɢɡ ɧɟɩɨɞɜɢɠɧɵɯ ɢ ɩɨɞɜɢɠɧɵɯ ɛɥɨɤɨɜ, ɨɝɢɛɚɟɦɵɯ ɝɢɛɤɢɦ ɬɹɝɨɜɵɦ ɨɪɝɚɧɨɦ, ɫɦɨɧɬɢɪɨɜɚɧɧɵɯ ɜ ɨɛɨɣɦɚɯ. Ƚɪɭɡ ɤɪɟɩɹɬ ɤ ɤɪɸɤɭ ɧɢɠɧɟɣ ɩɨɞɜɢɠɧɨɣ ɨɛɨɣɦɵ, ɤɨɬɨɪɭɸ ɨɛɵɱɧɨ ɧɚɡɵɜɚɸɬ ɤɪɸɤɨɜɨɣ ɩɨɞɜɟɫɤɨɣ.

Ɋɢɫ. 2.16. ɋɯɟɦɚ ɫɬɟɩɟɧɧɨɝɨ (ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ) ɩɨɥɢɫɩɚɫɬɚ ɫ ɬɪɟɦɹ ɩɨɞɜɢɠɧɵɦɢ ɢ ɨɞɧɢɦ ɧɟɩɨɞɜɢɠɧɵɦ ɛɥɨɤɨɦ

Ɉɫɧɨɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɩɨɥɢɫɩɚɫɬɚ ɹɜɥɹɟɬɫɹ ɤɪɚɬɧɨɫɬɶ i ɉ. ȿɟ ɨɩɪɟɞɟɥɹɸɬ ɩɪɢ ɨɞɢɧɚɪɧɨɦ ɛɚɪɚɛɚɧɟ ɩɨ ɱɢɫɥɭ ɜɟɬɜɟɣ ɤɚɧɚɬɚ, ɧɚ ɤɨɬɨɪɵɯ ɩɨɞɜɟɲɟɧ ɝɪɭɡ.

ɉɪɢ ɫɞɜɨɟɧɧɨɦ ɛɚɪɚɛɚɧɟ ɤɪɚɬɧɨɫɬɶ ɩɨɥɢɫɩɚɫɬɚ ɪɚɜɧɚ ɩɨɥɨɜɢɧɟ ɱɢɫɥɚ ɜɟɬɜɟɣ ɤɚɧɚɬɚ, ɧɚ ɤɨɬɨɪɵɯ ɩɨɞɜɟɲɟɧ ɝɪɭɡ.

63

ɉɨɥɢɫɩɚɫɬ ɢɫɩɨɥɶɡɭɸɬ ɞɥɹ ɜɵɢɝɪɵɲɚ ɜ ɫɢɥɟ ɢ ɪɟɠɟ – ɞɥɹ ɜɵɢɝɪɵɲɚ ɜ ɫɤɨɪɨɫɬɢ.

ɝ ݖɛ ɩ (ɩɪɢ ɧɟɩɨɞɜɢɠɧɨɦ ɝɪɭɡɟ),

ɝɞɟ - ɧɚɬɹɠɟɧɢɟ ɤɚɧɚɬɨɜ; ɝ - ɜɟɫ ɝɪɭɡɚ; ݖɛ - ɱɢɫɥɨ ɪɚɛɨɱɢɯ ɭɱɚɫɬɤɨɜ ɧɚ ɛɚɪɚɛɚɧɟ (Z = 2 ɞɥɹ ɫɞɜɨɟɧɧɨɝɨ).

ɉɪɢ ɩɨɞɴɟɦɟ ɝɪɭɡɚ ɡɚ ɫɱɟɬ ɩɨɬɟɪɶ ɜ ɛɥɨɤɚɯ ɧɚɬɹɠɟɧɢɟ ɤɚɧɚɬɨɜ ɭɜɟɥɢɱɢɬɫɹ, ɨɧɨ ɦɚɤɫɢɦɚɥɶɧɨ ɜ ɦɟɫɬɟ ɧɚɛɟɝɚɧɢɹ ɤɚɧɚɬɚ ɧɚ ɛɚɪɚɛɚɧ.

ɦɨɦɟɧɬ ɧɚ ɜɚɥɭ ɜ ɬɹɝɨɜɨɟ ɭɫɢɥɢɟ ɜ ɤɚɧɚɬɟ (ɜɪɚɳɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɛɚɪɚɛɚɧɚ ɜ ɩɨɫɬɭɩɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɤɚɧɚɬɚ).

Ȼɚɪɚɛɚɧɵ ɢɦɟɸɬ ɰɢɥɢɧɞɪɢɱɟɫɤɭɸ ɮɨɪɦɭ ɢ ɢɯ ɢɡɝɨɬɚɜɥɢɜɚɸɬ ɥɢɬɵɦɢ, ɫɜɚɪɧɨ-ɥɢɬɵɦɢ ɢɥɢ ɫɜɚɪɧɨ-ɜɚɥɶɰɨɜɚɧɧɵɦɢ ɢɡ ɫɬɚɥɟɣ 35Ʌ ɢ 55Ʌ ɩɨ ȽɈɋɌ 97775 ɢɥɢ ɱɭɝɭɧɚ ɋɑ15, ɋɑ18 ɢ ɋɑ24.

ɉɨ ɧɚɡɧɚɱɟɧɢɸ ɪɚɡɥɢɱɚɸɬ ɛɚɪɚɛɚɧɵ ɞɥɹ ɦɧɨɝɨɫɥɨɣɧɨɣ ɧɚɜɢɜɤɢ ɤɚɧɚɬɚ ɛɨɥɶɲɨɣ ɞɥɢɧɵ ɢ ɨɞɧɨɫɥɨɣɧɨɣ. Ɇɧɨɝɨɫɥɨɣɧɵɟ ɛɚɪɚɛɚɧɵ ɢɦɟɸɬ ɝɥɚɞɤɭɸ ɪɚɛɨɱɭɸ ɩɨɜɟɪɯɧɨɫɬɶ, ɨɞɧɨɫɥɨɣɧɵɟ ɛɚɪɚɛɚɧɵ (ɪɢɫ. 2.17) ɜɫɟɝɞɚ ɜɵɩɨɥɧɹɸɬ ɧɚɪɟɡɧɵɦɢ (ɜ ɦɨɫɬɨɜɵɯ ɤɪɚɧɚɯ).

64

Ɋɢɫ. 2.17. Ȼɚɪɚɛɚɧ ɫ ɧɚɪɟɡɚɧɧɨɣ ɜɢɧɬɨɜɨɣ ɤɚɧɚɜɤɨɣ ɞɥɹ ɤɚɧɚɬɚ Ʉɚɧɚɜɤɢ, ɧɚɪɟɡɚɧɧɵɟ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɛɚɪɚɛɚɧɚ ɩɨ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ, ɭɩɨɪɹɞɨɱɢɜɚɸɬ ɭɤɥɚɞɤɭ ɜɢɬɤɨɜ ɤɚɧɚɬɚ ɧɚ ɛɚɪɚɛɚɧɟ, ɭɜɟɥɢɱɢɜɚɸɬ ɩɥɨɳɚɞɶ ɤɨɧɬɚɤɬɚ ɫ ɛɚɪɚɛɚɧɨɦ, ɭɦɟɧɶɲɚɸɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɜɧɭɬɪɟɧɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɩɪɨɜɨɥɨɤɚɯ ɤɚɧɚɬɚ, ɭɫɬɪɚɧɹɸɬ ɬɪɟɧɢɟ ɦɟɠɞɭ ɫɨɫɟɞɧɢɦɢ ɜɢɬɤɚɦɢ ɤɚɧɚɬɚ ɢ ɭɦɟɧɶɲɚɸɬ

ɟɝɨ ɢɡɧɨɫ. Ⱦɥɹ ɷɬɨɝɨ ɲɚɝ ɧɚɪɟɡɤɢ ɤɚɧɚɜɨɤ

ǡ ; ǡ ; ǡ͵ ; .

ɂɡ ɭɫɥɨɜɢɹ ɩɪɨɱɧɨɫɬɢ ɢ ɬɟɯɧɨɥɨɝɢɱɧɨɫɬɢ ɢɡɝɨɬɨɜɥɟɧɢɹ ɬɨɥɳɢɧɚ ɫɬɟɧɤɢ ɛɚɪɚɛɚɧɚ δ = 0,02DɛǤ

ɋ ɰɟɥɶɸ ɩɨɜɵɲɟɧɢɹ ɫɪɨɤɚ ɫɥɭɠɛɵ ɫɬɚɥɶɧɵɯ ɤɚɧɚɬɨɜ ɧɚɢɦɟɧɶɲɢɣ ɞɨɩɭɫɤɚɟɦɵɣ ɞɢɚɦɟɬɪ ɛɚɪɚɛɚɧɚ ɞɨɥɠɟɧ ɛɵɬɶ e, ɝɞɟ ɟ – ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɬɢɩɚ ȽɉɆ ɢ ɪɟɠɢɦɚ ɟɝɨ ɪɚɛɨɬɵ (ɥɟɛɟɞɤɢ ɝɪɭɡɨɜɵɟ – ɟ = 20). Ⱦɢɚɦɟɬɪ ɪɟɛɨɪɞɵ (ɛɨɪɬɢɤɚ) ɪ ʹ .

ɉɪɢ ɨɞɧɨɫɥɨɣɧɨɣ ɧɚɜɢɜɤɟ ɤɚɧɚɬɚ ɧɚ ɛɚɪɚɛɚɧ ɞɥɢɧɚ ɩɨɫɥɟɞɧɟɝɨ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɬɪɟɯ ɭɱɚɫɬɤɨɜ, ɧɚ ɤɨɬɨɪɵɯ ɪɚɡɦɟɳɟɧɵ 1) ɜɢɬɤɢ ɤɚɧɚɬɚ ɧɚ ɛɚɪɚɛɚɧɟ, ɧɚɯɨɞɹɳɢɟɫɹ ɩɨɞ ɩɪɢɠɢɦɧɵɦɢ ɩɥɚɧɤɚɦɢ, 2) ɧɟɩɪɢɤɨɫɧɨɜɟɧɧɵɟ (ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ) ɜɢɬɤɢ ɢ 3) ɪɚɛɨɱɢɟ ɜɢɬɤɢ ɤɚɧɚɬɚ, ɧɚɜɢɜɚɟɦɨɝɨ ɜ ɩɪɨɰɟɫɫɟ ɩɨɞɴɟɦɚ ɝɪɭɡɚ.

65

Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɦɢ ɧɚɡɵɜɚɸɬ ɜɢɬɤɢ ɤɚɧɚɬɚ, ɤɨɬɨɪɵɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɪɟɛɨɜɚɧɢɹɦɢ ɉɪɚɜɢɥ ɩɨ ɤɪɚɧɚɦ ɜɫɟɝɞɚ ɞɨɥɠɧɵ ɨɫɬɚɜɚɬɶɫɹ ɧɚɜɢɬɵɦɢ ɧɚ ɛɚɪɚɛɚɧ ɥɟɛɟɞɤɢ ɞɚɠɟ ɩɪɢ ɫɚɦɨɦ ɧɢɡɤɨɦ ɪɚɛɨɱɟɦ ɩɨɥɨɠɟɧɢɢ ɤɪɸɤɨɜɨɣ ɩɨɞɜɟɫɤɢ, ɢɯ ɞɨɥɠɧɨ ɛɵɬɶ ɧɟ ɦɟɧɟɟ 1,5; ɧɚɡɧɚɱɟɧɢɟ ɢɯ – ɭɦɟɧɶɲɢɬɶ ɡɚ ɫɱɟɬ ɫɢɥ ɬɪɟɧɢɹ ɩɨ ɡɚɤɨɧɭ ɗɣɥɟɪɚ ɧɚɬɹɠɟɧɢɟ ɤɚɧɚɬɚ ɜ ɦɟɫɬɟ ɟɝɨ ɤɪɟɩɥɟɧɢɹ –

ɤɪ ɟ ,

ɝɞɟ - ɦɚɤɫɢɦɚɥɶɧɨɟ ɪɚɛɨɱɟɟ ɧɚɬɹɠɟɧɢɟ; =0,16 – ɦɢɧɢɦɚɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ; = 3ʌ – ɦɢɧɢɦɚɥɶɧɵɣ ɭɝɨɥ ɨɛɯɜɚɬɚ.

ȿɫɥɢ – ɪɚɛɨɱɚɹ ɞɥɢɧɚ ɤɚɧɚɬɚ, ɧɚɦɚɬɵɜɚɟɦɨɝɨ ɧɚ ɛɚɪɚɛɚɧ, ɬɨ ɞɥɢɧɚ ɪɚɛɨɱɟɝɨ ɭɱɚɫɬɤɚ ɧɚɪɟɡɧɨɣ ɱɚɫɬɢ ɛɚɪɚɛɚɧɚ ɛɟɡ ɭɱɟɬɚ ɦɟɫɬɚ ɞɥɹ ɡɚɤɪɟɩɥɟɧɢɹ ɤɚɧɚɬɚ ɧɚ ɛɚɪɚɛɚɧɟ

ɛ ǡ ǥʹ Ǥ

ɱɟɧɢɹ ɢ ɫɠɚɬɢɹ.

ɍ ɛɚɪɚɛɚɧɨɜ ɞɥɢɧɨɣ ɦɟɧɟɟ ɬɪɟɯ ɞɢɚɦɟɬɪɨɜ ɧɚɩɪɹɠɟɧɢɟ ɨɬ ɢɡɝɢɛɚ ɢ ɤɪɭɱɟɧɢɹ ɧɟ ɩɪɟɜɵɲɚɟɬ (0…15 %) ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɫɠɚɬɢɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɫɬɟɧɤɢ ɛɚɪɚɛɚɧɚ ɪɚɫɫɱɢɬɵɜɚɸɬ ɧɚ ɫɠɚɬɢɟ ɩɨ ɮɨɪɦɭɥɚɦ ɞɥɹ ɪɚɫɱɟɬɚ ɬɨɥɫɬɨɫɬɟɧɧɵɯ ɫɨɫɭɞɨɜ, ɧɚɯɨɞɹɳɢɯɫɹ ɩɨɞ ɜɧɟɲɧɢɦ ɪɚɜɧɨɦɟɪɧɵɦ ɞɚɜɥɟɧɢɟɦ.

2.2. 2. Ɍɨɪɦɨɡɧɵɟ ɭɫɬɪɨɣɫɬɜɚ Ɉɫɬɚɧɨɜɵ

Ⱦɥɹ ɧɚɞɟɠɧɨɣ ɪɚɛɨɬɵ ȽɉɆ ɧɟɨɛɯɨɞɢɦɵ ɭɫɬɪɨɣɫɬɜɚ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɭɞɟɪɠɚɧɢɟ ɩɨɞɧɹɬɨɝɨ ɝɪɭɡɚ ɧɚ ɜɟɫɭ, ɚ ɬɚɤɠɟ ɩɥɚɜɧɨɟ ɨɩɭɫɤɚɧɢɟ ɟɝɨ ɫ ɪɟɝɭɥɢɪɭɟɦɨɣ ɫɤɨɪɨɫɬɶɸ. Ⱦɥɹ ɭɞɟɪɠɚɧɢɹ ɩɨɞɧɹɬɨɝɨ ɝɪɭɡɚ ɧɚ ɜɟɫɭ ɢɫɩɨɥɶɡɭɸɬ ɯɪɚɩɨɜɵɟ ɢ ɮɪɢɤɰɢɨɧɧɵɟ ɨɫɬɚɧɨɜɵ.

ɏɪɚɩɨɜɨɣ ɨɫɬɚɧɨɜ ɫɨɫɬɨɢɬ ɢɡ ɡɭɛɱɚɬɨɝɨ ɯɪɚɩɨɜɨɝɨ ɤɨɥɟɫɚ ɢ ɫɨɛɚɱɤɢ. ɉɪɢ ɩɨɞɴɟɦɟ ɝɪɭɡɚ ɯɪɚɩɨɜɨɟ ɤɨɥɟɫɨ ɫɜɨɛɨɞɧɨ ɩɨɜɨɪɚɱɢɜɚɟɬɫɹ ɜɦɟɫɬɟ ɫ ɜɚɥɨɦ. ɉɪɢ ɫɩɭɫɤɟ ɝɪɭɡɚ ɫɨɛɚɱɤɚ ɜɯɨɞɢɬ ɜɨ ɜɩɚɞɢɧɵ ɯɪɚɩɨɜɨɝɨ ɤɨɥɟɫɚ ɢ ɩɪɟɩɹɬɫɬɜɭɟɬ ɟɝɨ ɨɛɪɚɬɧɨɦɭɩɨɜɨɪɨɬɭ. Ɋɚɫɱɟɬ ɯɪɚɩɨɜɨɝɨɨɫɬɚɧɨɜɚ ɧɚɩɪɨɱɧɨɫɬɶ ɚɧɚɥɨɝɢɱɟɧɪɚɫɱɟɬɭɡɭɛɱɚɬɵɯ ɤɨɥɟɫ. Ɂɭɛɯɪɚɩɨɜɨɝɨɤɨɥɟɫɚ ɪɚɫɫɱɢɬɵɜɚɸɬɧɚɢɡɝɢɛɢɩɪɨɜɟɪɹɸɬɧɚɫɦɹɬɢɟ.

ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɯɪɚɩɨɜɵɯ ɦɟɯɚɧɢɡɦɨɜ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɭɦɟɧɶɲɟɧɢɹ ɫɢɥ ɵ ɭɞɚɪɚ ɜɨ ɜɪɟɦɹ ɢɯ ɨɫɬɚɧɨɜɤɢ. Ⱦɥɹ ɷɬɨɝɨ ɯɪɚɩɨɜɵɟ ɤɨɥɟɫɚ ɞɟɥɚɸɬ ɦɚɥɨɝɨ ɞɢɚɦɟɬɪɚ (ɜ ɰɟɥɹɯ ɭɦɟɧɶɲɟɧɢɹ ɨɤɪɭɠɧɨɣ ɫɤɨɪɨɫɬɢ) ɫ ɧɟɛɨɥɶɲɢɦ ɲɚɝɨɦ ɢ ɱɢɫɥɨɦ ɡɭɛɶɟɜ z = 10…24.

Ɋɢɫ.2.18. ɋɯɟɦɚ ɯɪɚɩɨɜɨ ɝɨ ɨɫɬɚɧɨɜɚ: ɚ — ɩɨɥɨɠɟɧɢɟ ɫɨɛɚɱɤɢ ɜ ɡɚɰɟɩɥɟɧɢɢ; ɛ — ɪɚɫɱɟɬɧɨɟ ɩɨɥɨɠɟɧɢɟ ɫɨɛɚɱɤɢ

67

Ɏɪɢɤɰɢɨɧɧɵɟ ɨɫɬɚɧɨɜɵ ɪɚɛɨɬɚɸɬ ɛɟɫɲɭɦɧɨ ɢ ɧɟ ɞɚɸɬ ɬɨɥɱɤɨɜ. ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɵɦɢ ɢ ɫɨɜɟɪɲɟɧɧɵɦɢ ɮɪɢɤɰɢɨɧɧɵɦɢ ɨɫɬɚɧɨɜɚɦɢ ɹɜɥɹɸɬɫɹ ɪɨɥɢɤɨɜɵɟ.

Ɋɨɥɢɤɨɜɵɣ ɨɫɬɚɧɨɜ ɫɨɫɬɨɢɬ ɢɡ ɤɨɪɩɭɫɚ, ɜɬɭɥɤɢ, ɫɨɟɞɢɧɟɧɧɨɣ ɫ ɜɚɥɨɦ ɦɟɯɚɧɢɡɦɚ, ɢ ɪɨɥɢɤɨɜ. ɉɪɢ ɜɪɚɳɟɧɢɢ ɜɬɭɥɤɢ ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ (ɩɪɢ ɧɟɩɨɞɜɢɠɧɨɦ ɤɨɪɩɭɫɟ) ɪɨɥɢɤɢ ɭɜɥɟɤɚɸɬɫɹ ɫɢɥɚɦɢ ɬɪɟɧɢɹ ɜ ɧɚɢɛɨɥɟɟ ɲɢɪɨɤɭɸ ɱɚɫɬɶ ɤɥɢɧɨɜɨɝɨ ɩɚɡɚ, ɱɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɫɜɨɛɨɞɧɨɟ ɜɪɚɳɟɧɢɟ ɜɬɭɥɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɪɩɭɫɚ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɚɜɥɟɧɢɹ ɜɪɚɳɟɧɢɹ ɜɬɭɥɤɢ ɪɨɥɢɤɢ ɡɚɯɨɞɹɬ ɜ ɭɡɤɭɸ ɱɚɫɬɶ ɤɥɢɧɨɜɨɝɨ ɩɚɡɚ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɡɚɤɥɢɧɢɜɚɧɢɸ.

ȼ ɤɨɧɫɬɪɭɤɰɢɸ ɨɫɬɚɧɨɜɚ ɜɤɥɸɱɟɧɵ ɩɪɭɠɢɧɵ, ɨɬɠɢɦɚɸɳɢɟ ɪɨɥɢɤɢ ɜ ɭɡɤɢɣ ɭɝɨɥ ɩɚɡɚ.

ȡ > tg ן ,

ɝɞɟ ן - ɭɝɨɥ ɪɨɥɢɤɨɜɨɝɨ ɨɫɬɚɧɨɜɚ, cos ן = (2a + d) / D - d; a – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɨɫɢ ɜɪɚɳɟɧɢɹ ɞɨ ɩɥɨɫɤɨɫɬɢ ɜɬɭɥɤɢ; d – ɞɢɚɦɟɬɪ ɪɨɥɢɤɚ.

Ⱦɥɢɧɭ ɪɨɥɢɤɚ ( ɩɪɢ ǡ ɩɪɢɛɥɢɠɟɧɧɨ ɨɩɪɟɞɟɥɹɸɬ ɩɨ ɞɨɩɭɫɤɚɟɦɨ-

ɦɭ ɥɢɧɟɣɧɨɦɭ ɞɚɜɥɟɧɢɸ ǡ ɝɞɟ = 4,6 ɤɇ/ɫɦ – ɞɨɩɭɫɤɚɟɦɨɟ ɥɢɧɟɣɧɨɟ

ɞɚɜɥɟɧɢɟ ɞɥɹ ɰɟɦɟɧɬɢɪɨɜɚɧɧɨɣ ɢ ɡɚɤɚɥɟɧɧɨɣ ɭɝɥɟɪɨɞɢɫɬɨɣ ɫɬɚɥɢ.

Ɍɨɪɦɨɡɚ

Ɍɨɪɦɨɡɚ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɭɞɟɪɠɚɧɢɹ ɝɪɭɡɚ ɜ ɧɟɩɨɞɜɢɠɧɨɦ ɫɨɫɬɨɹɧɢɢ, ɞɥɹ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɨɩɭɫɤɚɧɢɹ ɝɪɭɡɚ, ɚ ɬɚɤɠɟ ɞɥɹ ɩɨɝɥɨɳɟɧɢɹ ɢɧɟɪɰɢɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨ ɞɜɢɠɭɳɢɯɫɹ ɦɚɫɫ ɬɟɥɟɠɤɢ ɫ ɝɪɭɡɨɦ ɢɥɢ ɤɪɚɧɚ.

ɗɬɚ ɭɧɢɜɟɪɫɚɥɶɧɨɫɬɶ ɩɪɢɜɟɥɚ ɤ ɫɨɡɞɚɧɢɸ ɛɨɥɶɲɨɝɨ ɱɢɫɥɚ ɪɚɡɧɨɨɛɪɚɡɧɵɯ ɬɨɪɦɨɡɨɜ; ɫɬɨɩɨɪɧɵɯ, ɫɩɭɫɤɧɵɯ ɢ ɤɨɦɛɢɧɢɪɨɜɚɧɧɵɯ; ɩɨɫɥɟɞɧɢɟ ɫɥɭɠɚɬ ɨɞɧɨɜɪɟɦɟɧɧɨ ɞɥɹ ɨɫɬɚɧɨɜɤɢ ɝɪɭɡɚ ɢ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɤɨɪɨɫɬɢ ɨɩɭɫɤɚɧɢɹ. Ɍɨɪɦɨɡɚ ɞɟɥɹɬ ɧɚ ɞɜɟ ɨɫɧɨɜɧɵɟ ɝɪɭɩɩɵ:

-ɫ ɪɚɞɢɚɥɶɧɵɦ ɧɚɠɚɬɢɟɦ (ɤɨɥɨɞɨɱɧɵɟ ɢ ɥɟɧɬɨɱɧɵɟ);

-ɫ ɨɫɟɜɵɦ ɧɚɠɚɬɢɟɦ (ɞɢɫɤɨɜɵɟ ɢ ɤɨɧɢɱɟɫɤɢɟ).

ȼɝɪɭɡɨɩɨɞɴɟɦɧɵɯ ɭɫɬɪɨɣɫɬɜɚɯ ɫ ɦɚɲɢɧɧɵɦ ɩɪɢɜɨɞɨɦ ɩɪɢɦɟɧɹɸɬ ɞɢɫɬɚɧɰɢɨɧɧɨ ɭɩɪɚɜɥɹɟɦɵɟ ɬɨɪɦɨɡɚ, ɤɨɬɨɪɵɟ ɡɚɬɨɪɦɚɠɢɜɚɸɬɫɹ ɝɪɭɡɨɦ ɢɥɢ ɩɪɭɠɢɧɨɣ, ɚ ɪɚɫɬɨɪɦɚɠɢɜɚɸɬɫɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɨɦ ɢɥɢ ɷɥɟɤɬɪɨɝɢɞɪɨɬɨɥɤɚɬɟɥɟɦ.

Ɍɨɪɦɨɡ ɧɚɯɨɞɢɬɫɹ ɜ ɧɨɪɦɚɥɶɧɨ ɡɚɦɤɧɭɬɨɦ ɫɨɫɬɨɹɧɢɢ, ɱɬɨɛɵ ɝɪɭɡ ɧɟ ɭɩɚɥ, ɩɪɢ ɜɤɥɸɱɟɧɧɨɦ ɞɜɢɝɚɬɟɥɟ ɬɨɪɦɨɡ ɪɚɫɬɨɪɦɚɠɢɜɚɟɬɫɹ.

ȼɝɪɭɡɨɩɨɞɴɟɦɧɵɯ ɦɚɲɢɧɚɯ ɲɢɪɨɤɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥɢ ɤɨɥɨɞɨɱɧɵɟ ɬɨɪɦɨɡɚ. Ɉɧɢ ɫɨɫɬɨɹɬ ɢɡ ɪɵɱɚɝɨɜ ɢ ɨɞɧɨɣ ɢɥɢ ɞɜɭɯ ɤɨɥɨɞɨɤ.

69

Ɍɨɪɦɨɠɟɧɢɟ ɦɟɯɚɧɢɡɦɚ ɤɨɥɨɞɨɱɧɵɦ ɬɨɪɦɨɡɨɦ ɩɪɨɢɫɯɨɞɢɬ ɡɚ ɫɱɟɬ ɫɢɥ ɬɪɟɧɢɹ ɦɟɠɞɭ ɬɨɪɦɨɡɧɵɦ ɲɤɢɜɨɦ, ɫɜɹɡɚɧɧɵɦ ɫ ɨɞɧɢɦ ɢɡ ɜɚɥɨɜ ɦɟɯɚɧɢɡɦɚ, ɢ ɬɨɪɦɨɡɧɨɣ ɤɨɥɨɞɤɨɣ, ɫɨɟɞɢɧɟɧɧɨɣ ɩɨɫɪɟɞɫɬɜɨɦ ɪɵɱɚɠɧɨɣ ɫɢɫɬɟɦɵ ɫ ɧɟɩɨɞɜɢɠɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ ɤɨɧɫɬɪɭɤɰɢɢ.

ȼ ɞɜɭɯɤɨɥɨɞɨɱɧɨɦ ɬɨɪɦɨɡɟ (ɪɢɫ.2.20) ɬɨɪɦɨɡɧɨɣ ɲɤɢɜ1 ɡɚɤɪɟɩɥɺɧ ɲɩɨɧɤɨɣ ɧɚ ɜɚɥɭ2 ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ. Ʉ ɫɬɨɣɤɚɦ 3 ɲɚɪɧɢɪɧɨ ɩɪɢɤɪɟɩɥɟɧɵ ɤɨɥɨɞɤɢ 4 ɫ ɮɪɢɤɰɢɨɧɧɵɦɢ ɧɚɤɥɚɞɤɚɦɢ 5.

Ɋɢɫ. 2 .20.: 1 – ɬɨɪɦɨɡɧɨɣɲɤɢɜ; 2 – ɜɚɥ; 3 - ɫɬɨɣɤɢ; 4 – ɤɨɥɨɞɤɢ; 5– ɮɪɢɤɰɢɨɧɧɵɟɧɚɤɥɚɞɤɢ.

ɉɪɢ ɫɛɥɢɠɟɧɢɢ ɫɬɨɟɤ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɨɞɢɧɚɤɨɜɵɯ ɭɫɢɥɢɣ Fɤ , ɫɨɡɞɚɜɚɟɦɵɯ ɫɢɫɬɟɦɨɣ ɩɪɭɠɢɧ ɢɥɢ ɞɪ. ɭɫɬɪɨɣɫɬɜ, ɤɨɥɨɞɤɢ ɩɪɢɠɢɦɚɸɬɫɹ ɤ ɲɤɢɜɭ ɭɫɢɥɢɹɦɢ

Fɧ1 ɢ Fɧ2 .Ɋɚɫɬɨɪɦɚɠɢɜɚɟɬɫɹ ɲɤɢɜ ɩɪɢ ɨɬɯɨɞɟ ɬɨɪɦɨɡɧɵɯ ɤɨɥɨɞɨɤ, ɫɨ ɫɬɨɣɤɚɦɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɨɞɢɧɚɤɨɜɵɯ ɭɫɢɥɢɣ FH ɜɨ ɜɧɟɲɧɢɟ ɨɬ ɲɤɢɜɚ ɫɬɨɪɨɧɵ. ɗɬɢ ɭɫɢ-

ɥɢɹ ɫɨɡɞɚɸɬɫɹ ɫ ɩɨɦɨɳɶɸ ɷɥɟɤɬɪɨɦɚɝɧɢɬɚ ɢɥɢ ɷɥɟɤɬɪɨɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɬɨɥɤɚɬɟɥɹ. Ɍɨɪɦɨɡɧɨɣ ɲɤɢɜ ɡɚɬɨɪɦɚɠɢɜɚɟɬɫɹ ɫɢɥɚɦɢ ɬɪɟɧɢɹ

Ȼɨɥɟɟ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɸɬ ɞɜɭɯɤɨɥɨɞɨɱɧɵɟ ɬɨɪɦɨɡɚ, ɤɨɬɨɪɵɟ ɧɟ ɢɦɟɸɬ ɧɟɞɨɫɬɚɬɤɚ ɨɞɧɨɤɨɥɨɞɨɱɧɨɝɨ ɬɨɪɦɨɡɚ, ɬɚɤ ɤɚɤ ɩɪɢ ɨɞɧɨɜɪɟɦɟɧɧɨɦ ɩɪɢɠɚɬɢɢ ɞɜɭɯ ɞɢɚɦɟɬɪɚɥɶɧɨ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɤɨɥɨɞɨɤ ɩɨɱɬɢ ɤɨɦɩɟɧɫɢɪɭɸɬɫɹ ɪɚɞɢɚɥɶɧɵɟ ɫɢɥɵ ɧɚ ɲɤɢɜɟ, ɢ ɜɚɥ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɡɝɪɭɠɟɧɧɵɦ ɨɬ ɪɚɞɢɚɥɶɧɨɣ ɧɚɝɪɭɡ-

70