EP / Теория ЭП Драчев

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 ɫɨ-

ɩɪɨɬɢɜɥɟɧɢɹ 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.

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 ɬɨɪɦɨ-

ɠɟɧɢɹ 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

ɆȾɋ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɞɥɹ ɫɨɟɞɢɧɟɧɢɹ ɨɛɦɨɬɨɤ ɜ ɡɜɟɡɞɭ

Fɉ 3 Iɉ w1.

142

ɂɡ ɭɫɥɨɜɢɹ ɪɚɜɟɧɫɬɜɚ ɆȾɋ ɩɨɥɭɱɚɟɦ ɞɟɣɫɬɜɭɸɳɟɟ ɡɧɚɱɟɧɢɟ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ:

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.

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.

+

–

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

ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ I1 = const ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ:

– ɬɨɤ ɪɨɬɨɪɚ

144

ɇɚ ɪɢɫ. 3.76 ɩɨɫɬɪɨɟɧɵ ɦɟɯɚɧɢɱɟɫɤɚɹ Ȧ(Ɇ) ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ Ȧ(I1),

ɆɄɌ ɡɚɜɢɫɢɬ ɨɬ ɤɜɚɞɪɚɬɚ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɬɨɤɚ I12 (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

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 ɮɨɪɦɭ-

ɥɚɦ (3.93), (3.94).

Ⱦɥɹ ɪɚɫɱɟɬɚ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɝɨɬɨɜɵɟ ɩɪɨɝɪɚɦɦɵ ɪɚɫɱɟɬɚ, ɩɨɹɜɢɜɲɢɟɫɹ

ɜɩɨɫɥɟɞɧɟɟ 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

Ɋɚɫɱɟɬ ɞɥɹ ɬɨɱɤɢ MɁȺȾ = 0,8, ȦɁȺȾ = 0,4, ɪɟɠɢɦ ɪɚɛɨɬɵ – ɞɜɢɝɚɬɟɥɶɧɵɣ.

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ɋɯɟɦɚ ɪɚɫɱɟɬɚ:

– ɩɨ ɡɚɞɚɧɧɨɣ ɜɟɥɢɱɢɧɟ ɆɁȺȾ ɧɚɯɨɞɢɦ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ

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:

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

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;

SɂɋɄ = Ȧ0ɇ ȦɁȺȾ = (– 1 – 0,4) / ( – 1) = 1,4.

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.

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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

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

ɢɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ

ȼɡɚɞɚɧɧɨɣ 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.

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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.

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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.

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.

ɇɚɯɨɞɢɦ ɬɨɤ ɫɬɚɬɨɪɚ I1 ɢɡ ɮɨɪɦɭɥɵ ɤɪɢɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ Ɇɤɬ ɩɪɢ ɯP=ɯPɧ, ɬɚɤ ɤɚɤ ɡɧɚɱɟɧɢɟ ɯP ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɩɨɤɚ ɧɟ ɨɩɪɟɞɟɥɟɧɨ.

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.

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