Электрические машины

ɡɨɪ. ɇɚ ɫɟɪɞɟɱɧɢɤ ɩɨɥɸɫɚ ɧɚɞɟɜɚɸɬ ɤɚɬɭɲɤɢ ɨɛɦɨɬɨɤ ɧɟɡɚɜɢɫɢɦɨɝɨ (ɢɥɢ ɩɚɪɚɥɥɟɥɶɧɨɝɨ) 3 ɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ 3ɚ, ɩɨ ɤɨɬɨɪɵɦ ɩɪɨɬɟɤɚɟɬ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ. Ʉɚɬɭɲɤɢ ɧɚɦɚɬɵɜɚɸɬɫɹ ɧɚ ɤɚɪɤɚɫ 4, ɜɵɩɨɥɧɹɟɦɵɣ ɥɢɛɨ ɢɡ ɥɢɫɬɨɜɨɣ ɫɬɚɥɢ ɬɨɥɳɢɧɨɣ 1–2 ɦɦ ɫ ɨɤɥɟɣɤɨɣ ɷɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɢɦ ɤɚɪɬɨɧɨɦ ɧɚ ɬɨɥɳɢɧɭ 2–3 ɦɦ, ɥɢɛɨ ɢɡ ɩɥɚɫɬɦɚɫɫɵ ɢɥɢ ɛɚɤɟɥɢɡɢɪɨɜɚɧɧɨɣ ɛɭɦɚɝɢ. ȼ ɦɚɲɢɧɚɯ ɦɚɥɨɣ ɢ ɫɪɟɞɧɟɣ ɦɨɳɧɨɫɬɢ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɧɟɪɟɞɤɨ ɜɵɩɨɥɧɹɸɬ ɛɟɫɤɚɪɤɚɫɧɵɟ ɤɚɬɭɲɤɢ ɨɫɧɨɜɧɵɯ ɩɨɥɸɫɨɜ. ɋ ɰɟɥɶɸ ɭɦɟɧɶɲɟɧɢɹ ɝɢɝɪɨɫɤɨɩɢɱɧɨɫɬɢ ɢ ɭɜɟɥɢɱɟɧɢɹ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɤɚɬɭɲɤɢ ɤɨɦɩɚɭɧɞɢɪɭɸɬ ɢɥɢ ɩɨɞɜɟɪɝɚɸɬ ɦɧɨɝɨɤɪɚɬɧɨɣ ɩɪɨɩɢɬɤɟ ɜ ɝɨɪɹɱɢɯ ɥɚɤɚɯ ɫ ɩɨɫɥɟɞɭɸɳɟɣ ɫɭɲɤɨɣ ɜ ɩɟɱɚɯ. Ⱦɥɹ ɥɭɱɲɟɝɨ ɨɯɥɚɠɞɟɧɢɹ ɤɚɬɭɲɤɭ ɞɟɥɹɬ ɩɨ ɜɵɫɨɬɟ ɧɚ ɞɜɟ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɱɚɫɬɟɣ, ɦɟɠɞɭ ɤɨɬɨɪɵɦɢ ɨɫɬɚɜɥɹɸɬ ɞɨɫɬɚɬɨɱɧɨɣ ɲɢɪɢɧɵ ɜɟɧɬɢɥɹɰɢɨɧɧɵɟ ɤɚɧɚɥɵ. Ʉɪɟɩɥɟɧɢɟ ɩɨɥɸɫɨɜ ɤ ɫɬɚɧɢɧɟ 5 ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɪɢ ɩɨɦɨɳɢ ɫɩɟɰɢɚɥɶɧɵɯ ɛɨɥɬɨɜ.

Ȼ. Ⱦɨɛɚɜɨɱɧɵɟ ɩɨɥɸɫɵ

Ɋɢɫ. 4.5. Ⱦɨɛɚɜɨɱɧɵɣ ɩɨɥɸɫ:

1 – ɫɟɪɞɟɱɧɢɤ; 2 – ɩɨɥɸɫɧɚɹ ɤɚɬɭɲɤɚ

ȼ. ɋɬɚɧɢɧɚ

Ⱦɨɛɚɜɨɱɧɵɣ ɩɨɥɸɫ (ɪɢɫ. 4.5), ɬɚɤ ɠɟ ɤɚɤ ɢ ɨɫɧɨɜɧɨɣ, ɫɨɫɬɨɢɬ:

–ɢɡ ɫɟɪɞɟɱɧɢɤɚ 1, ɨɤɚɧɱɢɜɚɸɳɟɝɨɫɹ

ɩɨɥɸɫɧɵɦ ɧɚɤɨɧɟɱɧɢɤɨɦ ɬɨɣ ɢɥɢ ɢɧɨɣ ɮɨɪɦɵ,

–ɤɚɬɭɲɤɢ 2, ɧɚɞɟɬɨɣ ɧɚ ɫɟɪɞɟɱɧɢɤ.

Ⱦɨɛɚɜɨɱɧɵɟ ɩɨɥɸɫɵ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɫɬɪɨɝɨ ɩɨɫɟɪɟɞɢɧɟ ɦɟɠɞɭ ɨɫɧɨɜɧɵɦɢ ɩɨɥɸɫɚɦɢ ɢ ɤɪɟɩɹɬɫɹ ɤ ɫɬɚɧɢɧɟ ɛɨɥɬɚɦɢ. Ɉɛɵɱɧɨ ɞɨɛɚɜɨɱɧɵɟ ɩɨɥɸɫɵ ɞɟɥɚɸɬɫɹ ɦɚɫɫɢɜɧɵɦɢ, ɧɨ ɜ ɦɚɲɢɧɚɯ, ɪɚɛɨɬɚɸɳɢɯ ɩɪɢ ɪɟɡɤɨ ɩɟɪɟɦɟɧɧɨɣ ɧɚɝɪɭɡɤɟ, ɨɧɢ ɜɵɩɨɥɧɹɸɬɫɹ ɢɡ ɥɢɫɬɨɜɨɣ ɫɬɚɥɢ.

ɋɬɚɧɢɧɨɣ ɧɚɡɵɜɚɸɬ ɧɟɩɨɞɜɢɠɧɭɸ ɱɚɫɬɶ ɦɚɲɢɧɵ, ɤ ɤɨɬɨɪɨɣ ɤɪɟɩɹɬɫɹ ɨɫɧɨɜɧɵɟ ɢ ɞɨɛɚɜɨɱɧɵɟ ɩɨɥɸɫɵ ɢ ɩɪɢ ɩɨɦɨɳɢ ɤɨɬɨɪɨɣ ɦɚɲɢɧɚ ɤɪɟɩɢɬɫɹ ɤ ɮɭɧɞɚɦɟɧɬɭ. ɑɚɫɬɶ ɫɬɚɧɢɧɵ, ɫɥɭɠɚɳɚɹ ɞɥɹ ɩɪɨɜɟɞɟɧɢɹ ɩɨɬɨɤɚ ɨɫɧɨɜɧɵɯ ɢ ɞɨɛɚɜɨɱɧɵɯ ɩɨɥɸɫɨɜ, ɧɚɡɵɜɚɟɬɫɹ ɹɪɦɨɦ.

ɋɬɚɧɢɧɚ ɢɡɝɨɬɚɜɥɢɜɚɟɬɫɹ ɢɡ ɱɭɝɭɧɚ ɢɥɢ ɫɬɚɥɢ ɫ ɪɚɡɴɟɦɨɦ ɢɥɢ ɛɟɡ ɧɟɝɨ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɢɩɚ ɢ ɦɨɳɧɨɫɬɢ ɦɚɲɢɧɵ. ȿɫɥɢ ɞɢɚɦɟɬɪ ɹɤɨɪɹ ɧɟ ɩɪɟɜɨɫɯɨɞɢɬ 35–45 ɫɦ, ɬɨ ɤɪɨɦɟ ɩɨɥɸɫɨɜ ɤ ɫɬɚɧɢɧɟ ɤɪɟɩɹɬɫɹ ɟɳɟ ɩɨɞɲɢɩɧɢɤɨɜɵɟ ɳɢɬɵ, ɩɨɞɞɟɪɠɢɜɚɸɳɢɟ ɳɢɬɨɜɵɟ ɩɨɞɲɢɩɧɢɤɢ. ȿɫɥɢ ɞɢɚɦɟɬɪ ɳɢɬɚ ɩɪɟɜɵɲɚɟɬ 1 ɦ, ɬɨ ɨɛɵɱɧɨ ɩɟɪɟɯɨɞɹɬ ɧɚ ɫɬɨɹɤɨɜɵɟ ɩɨɞɲɢɩɧɢɤɢ, ɭɫɬɚɧɚɜɥɢɜɚɟɦɵɟ ɨɬɞɟɥɶɧɨ ɨɬ ɫɬɚɧɢɧɵ ɧɚ ɮɭɧɞɚɦɟɧɬɧɨɣ ɩɥɢɬɟ ɦɚɲɢɧɵ. ȼ ɦɚɲɢɧɚɯ ɫ ɛɨɥɶɲɢɦ ɞɢɚɦɟɬɪɨɦ ɹɤɨɪɹ ɤ ɫɬɚɧɢɧɟ ɱɚɫɬɨ ɤɪɟɩɢɬɫɹ ɳɟɬɨɱɧɚɹ ɬɪɚɜɟɪɡɚ.

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Ƚ. ɋɟɪɞɟɱɧɢɤ ɹɤɨɪɹ

ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɩɪɢɦɟɧɹɸɬɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɡɭɛɱɚɬɵɟ ɫɟɪɞɟɱɧɢɤɢ ɹɤɨɪɹ ɛɚɪɚɛɚɧɧɨɝɨ ɬɢɩɚ. ɉɪɢ ɧɨɪɦɚɥɶɧɨɣ ɞɥɹ ɦɚɲɢɧ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɱɚɫɬɨɬɟ ɩɟɪɟɦɚɝɧɢɱɢɜɚɧɢɹ ɹɤɨɪɹ (20–60 Ƚɰ) ɫɟɪɞɟɱɧɢɤɢ ɜɵɩɨɥɧɹɸɬ ɢɡ ɥɢɫɬɨɜɨɣ ɷɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɨɣ ɫɬɚɥɢ ɬɨɥɳɢɧɨɣ 0,5 ɦɦ. Ʌɢɫɬɵ ɫɬɚɥɢ ɧɚɛɢɪɚɸɬ ɜ ɨɫɟɜɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɦɚɲɢɧɵ ɢ ɞɥɹ ɭɦɟɧɶɲɟɧɢɹ ɩɨɬɟɪɶ ɨɬ ɜɢɯɪɟɜɵɯ ɬɨɤɨɜ ɢɡɨɥɢɪɭɸɬ ɞɪɭɝ ɨɬ ɞɪɭɝɚ ɥɚɤɨɦ ɢɥɢ ɨɤɫɢɞɧɨɣ ɩɥɟɧɤɨɣ.

Ɇɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɦɚɥɨɣ ɦɨɳɧɨɫɬɢ ɜɵɩɨɥɧɹɸɬɫɹ ɨɛɵɱɧɨ ɫ ɨɫɟɜɨɣ ɫɢɫɬɟɦɨɣ ɜɟɧɬɢɥɹɰɢɢ (ɪɢɫ. 4.6), ɦɚɲɢɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ ɢɦɟɸɬ ɪɚɞɢɚɥɶɧɭɸ ɫɢɫɬɟɦɭ ɜɟɧɬɢɥɹɰɢɢ.

Ɋɢɫ. 4.6. Ʌɢɫɬ ɫɬɚɥɢ ɛɚɪɚɛɚɧɧɨɝɨ ɹɤɨɪɹ
ɫ ɨɫɟɜɨɣ ɫɢɫɬɟɦɨɣ ɜɟɧɬɢɥɹɰɢɢ	Ɋɢɫ. 4.7. Ɉɬɞɟɥɶɧɚɹ ɫɟɤɰɢɹ ɨɛɦɨɬɤɢ

ȼ ɩɨɫɥɟɞɧɟɦ ɫɥɭɱɚɟ ɫɟɪɞɟɱɧɢɤ ɹɤɨɪɹ ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɢɥɢ ɧɟɫɤɨɥɶɤɢɯ ɩɚɤɟɬɨɜ, ɪɚɡɦɟɪ ɤɚɠɞɨɝɨ ɢɡ ɤɨɬɨɪɵɯ ɜ ɨɫɟɜɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɫɨɫɬɚɜɥɹɟɬ 4–10 ɫɦ; ɲɢɪɢɧɚ ɜɟɧɬɢɥɹɰɢɨɧɧɨɝɨ ɤɚɧɚɥɚ ɦɟɠɞɭ ɩɚɤɟɬɚɦɢ – 8–10 ɦɦ. ɋɟɪɞɟɱɧɢɤ ɹɤɨɪɹ ɫɩɪɟɫɫɨɜɵɜɚɟɬɫɹ ɫ ɨɛɟɢɯ ɫɬɨɪɨɧ ɩɨɫɪɟɞɫɬɜɨɦ ɧɚɠɢɦɧɵɯ ɩɪɢɫɩɨɫɨɛɥɟɧɢɣ, ɤɨɬɨɪɵɟ ɨɫɨɛɵɦ ɨɛɪɚɡɨɦ ɤɪɟɩɹɬɫɹ ɧɚ ɜɚɥɭ ɢɥɢ ɫɬɹɝɢɜɚɸɬɫɹ ɛɨɥɬɚɦɢ. Ⱦɥɹ ɭɥɭɱɲɟɧɢɹ ɨɯɥɚɠɞɟɧɢɹ ɦɚɲɢɧɵ ɦɚɥɨɣ ɦɨɳɧɨɫɬɢ ɫɧɚɛɠɚɸɬɫɹ ɤɪɵɥɵɲɤɚɦɢ; ɜ ɦɚɲɢɧɚɯ ɛɨɥɶɲɟɣ ɦɨɳɧɨɫɬɢ ɧɚ ɜɚɥ ɧɚɫɚɠɢɜɚɸɬ ɜɟɧɬɢɥɹɬɨɪ.

Ⱦ. Ɉɛɦɨɬɤɚ ɹɤɨɪɹ

Ɍɚɤ ɠɟ, ɤɚɤ ɢ ɞɪɭɝɢɟ ɱɚɫɬɢ ɦɚɲɢɧɵ, ɨɛɦɨɬɤɚ ɹɤɨɪɹ ɦɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɪɟɬɟɪɩɟɥɚ ɪɹɞ ɢɡɦɟɧɟɧɢɣ. ɉɪɢɦɟɧɹɟɦɵɟ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɨɛɦɨɬɤɢ ɹɤɨɪɹ ɛɚɪɚɛɚɧɧɨɝɨ ɬɢɩɚ ɫɨɫɬɨɹɬ ɢɡ ɫɟɤɰɢɣ (ɪɢɫ. 4.7), ɢɡɝɨɬɨɜɥɹɟɦɵɯ ɱɚɳɟ ɜɫɟɝɨ ɧɚ ɨɫɨɛɵɯ ɲɚɛɥɨɧɚɯ ɢ ɭɤɥɚɞɵɜɚɟɦɵɯ ɜ ɩɚɡɚɯ ɫɟɪɞɟɱɧɢɤɚ ɹɤɨɪɹ. ɇɚ ɪɢɫ. 4.8, ɚ

ɩɪɟɞɫɬɚɜɥɟɧ ɹɤɨɪɶ ɦɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɧɟɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ ɛɟɡ ɨɛɦɨɬɤɢ, ɚ ɧɚ ɪɢɫ. 4.8, ɛ – ɬɨɬ ɠɟ ɹɤɨɪɶ ɜ ɝɨɬɨɜɨɦ ɜɢɞɟ.

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ɚ

ɛ

Ɋɢɫ. 4.8. əɤɨɪɶ ɦɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ:

ɛɟɡ ɨɛɦɨɬɤɢ (ɚ); ɜ ɝɨɬɨɜɨɦ ɜɢɞɟ (ɛ)

ȿ. Ʉɨɥɥɟɤɬɨɪ

Ɉɛɦɨɬɤɚ ɹɤɨɪɹ ɩɪɢɫɨɟɞɢɧɹɟɬɫɹ ɤ ɤɨɥɥɟɤɬɨɪɭ, ɤɨɬɨɪɵɣ ɢɦɟɟɬ ɪɚɡɥɢɱɧɨɟ ɢɫɩɨɥɧɟɧɢɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ, ɨɬ ɦɨɳɧɨɫɬɢ ɦɚɲɢɧɵ ɢ ɟɟ ɛɵɫɬɪɨɯɨɞɧɨɫɬɢ. ɇɚ ɪɢɫ. 4.9 ɩɨɤɚɡɚɧ ɤɨɥɥɟɤɬɨɪ ɩɪɨɫɬɨɝɨ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɬɢɩɚ. Ɉɛɵɱɧɨ ɤɨɥɥɟɤɬɨɪ ɜɵɩɨɥɧɹɟɬɫɹ ɢɡ ɦɟɞɧɵɯ ɩɥɚɫɬɢɧ ɬɪɚɩɟɰɟɢɞɚɥɶɧɨɣ ɮɨɪɦɵ, ɢɡɨɥɢɪɨɜɚɧɧɵɯ ɞɪɭɝ ɨɬ ɞɪɭɝɚ ɢ ɨɬ ɤɨɪɩɭɫɚ ɩɨɫɪɟɞɫɬɜɨɦ ɦɢɤɚɧɢɬɨɜɵɯ ɩɪɨɤɥɚɞɨɤ ɢ ɦɚɧɠɟɬ. ɉɥɚɫɬɢɧɵ ɡɚɤɪɟɩɥɹɸɬɫɹ ɧɚ ɥɚɫɬɨɱɤɢɧɵɯ ɯɜɨɫɬɚɯ, ɢ ɩɨɫɥɟ ɪɹɞɚ ɡɚɩɪɟɫɫɨɜɨɤ ɜ ɝɨɪɹɱɟɦ ɫɨɫɬɨɹɧɢɢ ɤɨɥɥɟɤɬɨɪ ɨɛɬɚɱɢɜɚɟɬɫɹ, ɱɬɨɛɵ ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɶ ɛɵɥɚ ɫɬɪɨɝɨ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ. ɋɨɟɞɢɧɟɧɢɟ ɨɛɦɨɬɤɢ ɹɤɨɪɹ ɫ ɤɨɥɥɟɤɬɨɪɨɦ ɦɨɠɧɨ ɩɪɨɢɡɜɨɞɢɬɶ ɪɚɡɥɢɱɧɵɦ ɨɛɪɚɡɨɦ. ȿɫɥɢ ɪɚɡɧɢɰɚ ɦɟɠɞɭ ɞɢɚɦɟɬɪɚɦɢ ɹɤɨɪɹ ɢ ɤɨɥɥɟɤɬɨɪɚ ɧɟɜɟɥɢɤɚ, ɬɨ ɤɨɧɰɵ ɫɟɤɰɢɣ ɹɤɨɪɧɨɣ ɨɛɦɨɬɤɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɜɩɚɢɜɚɸɬɫɹ ɜ ɩɥɚɫɬɢɧɵ ɤɨɥɥɟɤɬɨɪɚ. ɉɪɢ ɡɧɚɱɢɬɟɥɶɧɨɣ ɪɚɡɧɢɰɟ ɦɟɠɞɭ ɷɬɢɦɢ ɞɢɚɦɟɬɪɚɦɢ ɬɪɟɛɭɟɦɨɟ ɫɨɟɞɢɧɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɫ ɩɨɦɨɳɶɸ ɫɨɟɞɢɧɢɬɟɥɶɧɵɯ ɡɜɟɧɶɟɜ (ɩɟɬɭɲɤɨɜ), ɨɞɧɚ ɢɡ ɜɨɡɦɨɠɧɵɯ ɮɨɪɦ ɤɨɬɨɪɵɯ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 4.9.

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Ɋɢɫ. 4.9. ɉɪɨɞɨɥɶɧɵɣ ɪɚɡɪɟɡ ɤɨɥɥɟɤɬɨɪɚ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɬɢɩɚ:

1 – ɤɨɥɥɟɤɬɨɪɧɚɹ ɩɥɚɫɬɢɧɚ; 2 – ɧɚɠɢɦɧɵɟ ɤɨɧɭɫɵ; 3 – ɢɡɨɥɢɪɭɸɳɢɟ ɦɚɧɠɟɬɵ; 4 – ɢɡɨɥɢɪɭɸɳɚɹ ɩɪɨɤɥɚɞɤɚ; 5 – ɩɟɬɭɲɨɤ

ɀ. ɓɟɬɨɱɧɵɣ ɚɩɩɚɪɚɬ

Ⱦɥɹ ɨɬɜɨɞɚ ɬɨɤɚ ɨɬ ɜɪɚɳɚɸɳɟɝɨɫɹ ɤɨɥɥɟɤɬɨɪɚ ɜ ɝɟɧɟɪɚɬɨɪɚɯ ɢ ɩɨɞɜɨɞɚ ɤ ɧɟɦɭ ɬɨɤɚ ɜ ɞɜɢɝɚɬɟɥɹɯ ɩɪɢɦɟɧɹɟɬɫɹ ɳɟɬɨɱɧɵɣ ɚɩɩɚɪɚɬ, ɫɨɫɬɨɹɳɢɣ:

ɚ) ɢɡ ɳɟɬɨɤ; ɛ) ɳɟɬɤɨɞɟɪɠɚɬɟɥɟɣ;

ɜ) ɳɟɬɨɱɧɵɯ ɩɚɥɶɰɟɜ; ɝ) ɳɟɬɨɱɧɨɣ ɬɪɚɜɟɪɡɵ; ɞ) ɬɨɤɨɫɨɛɢɪɚɸɳɢɯ ɲɢɧ.

Ɉɞɧɚ ɢɡ ɬɢɩɢɱɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɳɟɬɤɨɞɟɪɠɚɬɟɥɹ ɦɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 4.10. ȼ ɫɨɜɪɟɦɟɧɧɵɯ ɦɚɲɢɧɚɯ ɩɨɱɬɢ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɩɪɢɦɟɧɹɸɬɫɹ ɭɝɨɥɶɧɨ-ɝɪɚɮɢɬɨɜɵɟ ɢɥɢ ɦɟɞɧɨ-ɝɪɚɮɢɬɨɜɵɟ ɳɟɬɤɢ – ɩɨɫɥɟɞɧɢɟ ɜ ɤɨɥɥɟɤɬɨɪɧɵɯ ɦɚɲɢɧɚɯ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɧɢɡɤɨɝɨ ɧɚɩɪɹɠɟɧɢɹ.

ɓɟɬɤɚ ɩɨɦɟɳɚɟɬɫɹ ɜ ɳɟɬɤɨɞɟɪɠɚɬɟɥɟ ɢ ɩɨɫɪɟɞɫɬɜɨɦ ɩɪɭɠɢɧɵ ɩɪɢɠɢɦɚɟɬɫɹ ɤ ɤɨɥɥɟɤɬɨɪɭ. ɓɟɬɤɨɞɟɪɠɚɬɟɥɶ ɡɚɤɪɟɩɥɹɟɬɫɹ ɧɚ ɩɚɥɶɰɟ ɢ ɭɞɟɪɠɢɜɚɟɬ ɳɟɬɤɭ ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɩɨɥɨɠɟɧɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɥɥɟɤɬɨɪɚ. ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧ ɬɢɩ ɳɟɬɤɨɞɟɪɠɚɬɟɥɹ, ɩɪɢɞɚɸɳɢɣ ɳɟɬɤɟ ɪɚɞɢɚɥɶɧɨɟ ɩɨɥɨɠɟɧɢɟ ɢ ɩɨɡɜɨɥɹɸɳɢɣ ɟɣ ɩɟɪɟɦɟɳɚɬɶɫɹ ɜ ɨɛɨɣɦɟ ɳɟɬɤɨɞɟɪɠɚɬɟɥɹ. ɉɟɪɟɞɚɱɚ ɬɨɤɚ ɨɬ ɳɟɬɤɢ ɤ ɩɚɥɶɰɭ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɨɫɪɟɞɫɬɜɨɦ ɝɢɛɤɨɝɨ ɤɚɛɟɥɹ 4 (ɪɢɫ. 4.10). ɇɚ ɤɚɠɞɨɦ ɩɚɥɶɰɟ ɨɛɵɱɧɨ ɩɨɦɟɳɚɸɬ ɞɜɟ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɳɟɬɨɤ, ɪɚɛɨɬɚɸɳɢɯ ɩɚɪɚɥɥɟɥɶɧɨ.

ɉɚɥɶɰɵ ɳɟɬɤɨɞɟɪɠɚɬɟɥɟɣ ɢɦɟɸɬ ɰɢɥɢɧɞɪɢɱɟɫɤɭɸ ɢɥɢ ɩɪɢɡɦɚɬɢɱɟɫɤɭɸ ɮɨɪɦɭ, ɡɚɤɪɟɩɥɹɸɬɫɹ ɜ ɳɟɬɨɱɧɨɣ ɬɪɚɜɟɪɡɟ ɢ ɢɡɨɥɢɪɭɸɬɫɹ ɨɬ ɩɨɫɥɟɞɧɟɣ ɢɡɨɥɹɰɢɨɧɧɵɦɢ ɜɬɭɥɤɚɦɢ.

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	Ɋɢɫ. 4.10. ɓɟɬɤɨɞɟɪɠɚɬɟɥɶ:		Ɋɢɫ. 4.11.
				Ʉɪɟɩɥɟɧɢɟ ɳɟɬɨɱɧɵɯ
1 – ɨɛɨɣɦɚ ɳɟɬɤɨɞɟɪɠɚɬɟɥɹ; 2 – ɳɟɬɤɚ;			ɩɚɥɶɰɟɜ ɜ ɬɪɚɜɟɪɡɟ
3 – ɧɚɠɢɦɧɚɹ ɩɪɭɠɢɧɚ; 4 – ɬɨɤɨɜɟɞɭɳɢɣ
	ɬɪɨɫɢɤ

Ɉɞɢɧ ɢɡ ɫɩɨɫɨɛɨɜ ɤɪɟɩɥɟɧɢɹ ɳɟɬɨɱɧɵɯ ɩɚɥɶɰɟɜ ɤ ɬɪɚɜɟɪɡɟ ɩɨɤɚɡɚɧ ɧɚ

ɪɢɫ. 4.11. Ɍɪɚɜɟɪɡɚ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɧɚ ɩɨɞɲɢɩɧɢɤɨɜɵɯ ɳɢɬɚɯ ɜ ɦɚɲɢɧɚɯ ɦɚɥɨɣ ɢ ɫɪɟɞɧɟɣ ɦɨɳɧɨɫɬɢ (ɪɢɫ. 4.12).

ȼɫɟ ɳɟɬɤɢ ɨɞɧɨɣ ɩɨɥɹɪɧɨɫɬɢ ɫɨɟɞɢɧɹɸɬɫɹ ɦɟɠɞɭ ɫɨɛɨɣ ɫɛɨɪɧɵɦɢ ɲɢɧɚɦɢ, ɨɬ ɤɨɬɨɪɵɯ ɡɚɬɟɦ ɢɞɭɬ ɨɬɜɨɞɵ ɤ ɡɚɠɢɦɚɦ ɦɚɲɢɧɵ.

Ɋɢɫ. 4.12. Ʉɪɟɩɥɟɧɢɟ ɳɟɬɨɱɧɨɣ ɬɪɚɜɟɪɡɵ ɧɚ ɩɨɞɲɢɩɧɢɤɟ

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4.1.4. ɉɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɝɟɧɟɪɚɬɨɪɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ

Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɝɟɧɟɪɚɬɨɪɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɧɚ ɩɪɢɦɟɪɟ ɩɪɨɫɬɟɣɲɟɣ ɦɚɲɢɧɵ, ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ. 4.13. Ɇɚɝɧɢɬɧɚɹ ɫɢɫɬɟɦɚ ɷɬɨɣ ɦɚɲɢɧɵ ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɧɟɩɨɞɜɢɠɧɵɯ ɩɨɥɸɫɨɜ N – S, ɫɨɡɞɚɸɳɢɯ ɩɨɫɬɨɹɧɧɵɣ ɩɨ ɜɟɥɢɱɢɧɟ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ. Ɉɫɧɨɜɧɨɣ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ ɜ ɧɨɪɦɚɥɶɧɵɯ ɦɚɲɢɧɚɯ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫɨɡɞɚɟɬɫɹ ɨɛɦɨɬɤɨɣ ɜɨɡɛɭɠɞɟɧɢɹ, ɤɨɬɨɪɚɹ ɪɚɫɩɨɥɨɠɟɧɚ ɧɚ ɫɟɪɞɟɱɧɢɤɚɯ ɩɨɥɸɫɨɜ ɢ ɩɢɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ ɬɨɤɨɦ. ɉɨ ɨɛɳɟɦɭ ɩɪɚɜɢɥɭ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɦɟɠɞɭ ɩɨɥɸɫɚɦɢ N – S ɧɚɩɪɚɜɥɟɧɵ ɨɬ ɫɟɜɟɪɧɨɝɨ ɩɨɥɸɫɚ N ɤ ɸɠɧɨɦɭ ɩɨɥɸɫɭ S.

ȼ ɩɪɨɫɬɪɚɧɫɬɜɟ ɦɟɠɞɭ ɩɨɥɸɫɚɦɢ ɧɚɯɨɞɢɬɫɹ ɹɤɨɪɶ, ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɬɨɪɨɝɨ ɜ ɞɢɚɦɟɬɪɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɭɥɨɠɟɧ ɜɢɬɨɤ ɨɛɦɨɬɤɢ ɹɤɨɪɹ ab – cd. Ʉɨɧɰɵ ɜɢɬɤɚ ɩɪɢɫɨɟɞɢɧɹɸɬɫɹ ɤ ɞɜɭɦ ɦɟɞɧɵɦ ɫɟɝɦɟɧɬɚɦ – ɩɥɚɫɬɢɧɚɦ ɤɨɥɥɟɤɬɨɪɚ, ɢɡɨɥɢɪɨɜɚɧɧɵɦ ɤɚɤ ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɬɚɤ ɢ ɨɬ ɜɚɥɚ, ɧɚ ɤɨɬɨɪɵɣ ɨɧɢ ɩɨɫɚɠɟɧɵ ɜɝɥɭɯɭɸ. ɇɚ ɩɥɚɫɬɢɧɵ ɧɚɥɨɠɟɧɵ ɧɟɩɨɞɜɢɠɧɵɟ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɳɟɬɤɢ A ɢ B, ɤ ɤɨɬɨɪɵɦ ɩɪɢɫɨɟɞɢɧɹɟɬɫɹ ɜɧɟɲɧɹɹ ɰɟɩɶ, ɫɨɫɬɨɹɳɚɹ ɢɡ ɤɚɤɢɯ-ɥɢɛɨ ɩɪɢɟɦɧɢɤɨɜ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ. Ɋɚɫɩɨɥɨɠɟɧɢɟ ɳɟɬɨɤ ɧɟ ɩɪɨɢɡɜɨɥɶɧɨ, ɚ ɢɦɟɟɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ.

Ɋɢɫ. 4.13. ɉɪɨɫɬɟɣɲɚɹ ɦɚɲɢɧɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ

ɉɪɢɜɟɞɟɦ ɹɤɨɪɶ ɜɨ ɜɪɚɳɟɧɢɟ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ ɜ ɡɚɞɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɧɚɩɪɢɦɟɪ, ɩɪɨɬɢɜ ɜɪɚɳɟɧɢɹ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ. Ɍɚɤ ɤɚɤ ɩɪɨɜɨɞɧɢɤɢ ab ɢ cd ɧɚɯɨɞɹɬɫɹ ɜ ɫɨɜɟɪɲɟɧɧɨ ɨɞɢɧɚɤɨɜɵɯ ɭɫɥɨɜɢɹɯ ɨɞɢɧ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɥɸɫɚ N, ɞɪɭɝɨɣ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɥɸɫɚ S, ɬɨ ɞɨɫɬɚɬɨɱɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ɩɪɨɰɟɫɫ ɧɚɜɟɞɟɧɢɹ ɗȾɋ ɬɨɥɶɤɨ ɜ ɤɚɤɨɦ-ɧɢɛɭɞɶ ɨɞɧɨɦ ɩɪɨɜɨɞɧɢɤɟ, ɧɚɩɪɢɦɟɪ ɜ ɩɪɨɜɨɞɧɢɤɟ ab. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɩɨ ɜɫɟɣ ɞɥɢɧɟ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɩɪɨɜɨɞɧɢɤɚ, ɬ. ɟ. ɬɨɣ ɱɚɫɬɢ ɟɝɨ, ɤɨɬɨɪɚɹ ɩɟɪɟɫɟɤɚɟɬ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɢɧɞɭɤɰɢɹ ȼ ɢɦɟɟɬ ɨɞɧɨ ɢ ɬɨ ɠɟ ɡɧɚɱɟɧɢɟ. ȿɫɥɢ V í ɫɤɨɪɨɫɬɶ ɩɟɪɟɦɟɳɟɧɢɹ ɩɪɨɜɨɞɧɢɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ

65

ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɬɨ ɩɨ ɡɚɤɨɧɭ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɜ ɮɨɪɦɭɥɢɪɨɜɤɟ Ɏɚɪɚɞɟɹ ɦɝɧɨɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɗȾɋ, ɧɚɜɨɞɢɦɨɣ ɜ ɩɪɨɜɨɞɧɢɤɟ ɩɪɢ ɜɪɚɳɟɧɢɢ

ɹɤɨɪɹ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ e = B l V. ȼɟɥɢɱɢɧɵ l ɢ V ɧɟɢɡɦɟɧɧɵ ɜ ɞɚɧɧɵɯ ɭɫɥɨɜɢɹɯ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɗȾɋ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɢɧɞɭɤɰɢɢ:

e # B.

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɭɫɥɨɜɢɹɯ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ ɗȾɋ ɜ ɩɪɨɜɨɞɧɢɤɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɪɟɦɟɧɢ ɰɟɥɢɤɨɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɯɚɪɚɤɬɟɪɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɩɨɞ ɩɨɥɸɫɨɦ.

ɍɫɥɨɜɢɦɫɹ ɧɚɡɵɜɚɬɶ ɥɢɧɢɸ, ɤɨɬɨɪɚɹ ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ ɰɟɧɬɪ ɹɤɨɪɹ ɬɨɱɧɨ ɩɨɫɟɪɟɞɢɧɟ ɦɟɠɞɭ ɩɨɥɸɫɚɦɢ N ɢ S, ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɧɟɣɬɪɚɥɶɸ, ɚ ɱɚɫɬɶ ɨɤ-

ɪɭɠɧɨɫɬɢ ɹɤɨɪɹ W, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɨɞɧɨɦɭ ɩɨɥɸɫɭ, – ɩɨɥɸɫɧɵɦ ɞɟɥɟɧɢɟɦ. Ɇɚɲɢɧɚ ɧɚ ɪɢɫ. 4.13. ɢɦɟɟɬ ɨɞɧɭ ɩɚɪɭ ɩɨɥɸɫɨɜ, ɬ. ɟ. ɞɜɚ ɩɨɥɸɫɧɵɯ ɞɟɥɟɧɢɹ.

Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɪɟɚɥɶɧɨɣ ɦɚɲɢɧɵ ɧɨɫɢɬ ɫɥɨɠɧɵɣ ɯɚɪɚɤɬɟɪ. ɇɨ ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɩɟɪɜɭɸ ɢɥɢ ɨɫɧɨɜɧɭɸ ɝɚɪɦɨɧɢɤɭ ɢ ɫ ɞɨɫɬɚɬɨɱɧɨɣ ɫɬɟɩɟɧɶɸ ɬɨɱɧɨɫɬɢ ɫɱɢɬɚɬɶ, ɱɬɨ ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ɪɚɫɩɪɟɞɟɥɹɟɬɫɹ ɩɨɞ ɩɨɥɸɫɚɦɢ N ɢ S ɫɢɧɭɫɨɢɞɚɥɶɧɨ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚɜɨɞɢɦɚɹ ɜ ɩɪɨɜɨɞɧɢɤɟ ɗȾɋ ɢɡɦɟɧɹɟɬɫɹ ɬɨɠɟ ɫɢɧɭɫɨɢɞɚɥɶɧɨ (ɪɢɫ. 4.14).

Ɋɢɫ. 4.14. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ȼ ɩɨɞ ɩɨɥɸɫɚɦɢ. ɂɡɦɟɧɟɧɢɟ ɗȾɋ ɜɨ ɜɪɟɦɟɧɢ

ɇɚɩɪɚɜɥɟɧɢɟ ɗȾɋ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɩɪɚɜɢɥɭ ɩɪɚɜɨɣ ɪɭɤɢ. ɉɪɢɦɟɧɢɜ ɷɬɨ ɩɪɚɜɢɥɨ, ɨɩɪɟɞɟɥɢɦ ɧɚɩɪɚɜɥɟɧɢɟ ɗȾɋ ɜ ɩɪɨɜɨɞɧɢɤɟ ab ɧɚ ɪɢɫ. 4.13. Ʉɨɝɞɚ ɩɪɨɜɨɞɧɢɤ ɩɪɨɯɨɞɢɬ ɩɨɞ ɫɟɜɟɪɧɵɦ ɩɨɥɸɫɨɦ, ɬɨ ɜ ɧɟɦ ɧɚɜɨɞɢɬɫɹ ɗȾɋ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɤ ɧɚɦ ɢɡ-ɡɚ ɩɥɨɫɤɨɫɬɢ ɱɟɪɬɟɠɚ, ɚ ɤɨɝɞɚ ɨɧ ɩɪɨɯɨɞɢɬ ɩɨɞ ɸɠɧɵɦ ɩɨɥɸɫɨɦ, ɬɨ ɜ ɨɛɪɚɬɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ – ɨɬ ɧɚɫ ɡɚ ɩɥɨɫɤɨɫɬɶ ɱɟɪɬɟɠɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɩɪɨɜɨɞɧɢɤɟ ab ɧɚɜɨɞɢɬɫɹ ɩɟɪɟɦɟɧɧɚɹ ɜɨ ɜɪɟɦɟɧɢ ɗȾɋ, ɢɡɦɟɧɹɸɳɚɹ ɫɜɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɞɜɚ ɪɚɡɚ ɡɚ ɨɞɢɧ ɨɛɨɪɨɬ ɹɤɨɪɹ.

ȼɪɟɦɹ T , ɡɚ ɤɨɬɨɪɨɟ ɩɪɨɢɫɯɨɞɢɬ ɨɞɧɨ ɩɨɥɧɨɟ ɢɡɦɟɧɟɧɢɟ ɗȾɋ, ɧɚɡɵɜɚɟɬɫɹ ɩɟɪɢɨɞɨɦ ɗȾɋ. ɑɢɫɥɨ ɩɟɪɢɨɞɨɜ ɜ ɨɞɧɭ ɫɟɤɭɧɞɭ ɧɚɡɵɜɚɟɬɫɹ ɱɚɫɬɨɬɨɣ ɢ ɢɡɦɟɪɹɟɬɫɹ ɜ ɝɟɪɰɚɯ (Ƚɰ). ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɦɚɲɢɧɚ ɢɦɟɟɬ p ɩɚɪ ɩɥɸɫɨɜ, ɱɚɫɬɨɬɚ ɧɚɜɟɞɟɧɧɨɣ ɗȾɋ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ p, ɬ. ɟ.

66

ɟa=2e .		(5)
p n
f = 60	,	(4)
ɝɞɟ n – ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ, ɢɡɦɟɪɹɟɦɚɹ ɱɢɫɥɨɦ ɨɛɨɪɨɬɨɜ ɜ ɦɢɧɭɬɭ.
ȼ ɨɛɨɢɯ ɩɪɨɜɨɞɧɢɤɚɯ (ab ɢ cd)	ɜɫɥɟɞɫɬɜɢɟ ɫɢɦɦɟɬɪɢɢ ɢɧɞɭɤɬɢɪɭɸɬɫɹ

ɨɞɢɧɚɤɨɜɵɟ ɗȾɋ, ɤɨɬɨɪɵɟ ɩɨ ɤɨɧɬɭɪɭ ɜɢɬɤɚ ɫɤɥɚɞɵɜɚɸɬɫɹ, ɢ ɩɨɷɬɨɦɭ ɩɨɥɧɚɹ ɗȾɋ ɹɤɨɪɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɦɚɲɢɧɵ

Ɋɚɫɫɦɨɬɪɢɦ ɮɨɪɦɭ ɩɨɥɧɨɣ ɗȾɋ ɹɤɨɪɹ ɟa. ɂɡ ɪɢɫ. 4.13. ɜɢɞɧɨ, ɱɬɨ ɩɨɥɩɟɪɢɨɞɚ ɳɟɬɤɚ Ⱥ ɛɭɞɟɬ ɫɨɩɪɢɤɚɫɚɬɶɫɹ ɫ ɤɨɥɥɟɤɬɨɪɧɨɣ ɩɥɚɫɬɢɧɨɣ ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫ ɩɪɨɜɨɞɧɢɤɨɦ ab, ɧɚɯɨɞɹɳɢɦɫɹ ɩɨɞ ɫɟɜɟɪɧɵɦ ɩɨɥɸɫɨɦ. ȼɬɨɪɭɸ ɱɚɫɬɶ ɩɟɪɢɨɞɚ, ɤɨɝɞɚ ɜɢɬɨɤ ɩɨɜɟɪɧɟɬɫɹ ɧɚ 180q, ɳɟɬɤɚ Ⱥ ɛɭɞɟɬ ɫɨɟɞɢɧɟɧɚ ɫ ɩɪɨɜɨɞɧɢɤɨɦ cd, ɧɚɯɨɞɹɳɢɦɫɹ ɬɚɤɠɟ ɩɨɞ ɫɟɜɟɪɧɵɦ ɩɨɥɸɫɨɦ, ɬ. ɟ. ɩɨɞ ɩɨɥɸɫɨɦ ɬɨɣ ɠɟ ɩɨɥɹɪɧɨɫɬɢ. ɓɟɬɤɚ Ⱥ ɜɫɟɝɞɚ ɫɨɩɪɢɤɚɫɚɟɬɫɹ ɬɨɥɶɤɨ ɫ ɬɨɣ ɩɥɚɫɬɢɧɨɣ, ɫ ɤɨɬɨɪɨɣ ɫɨɟɞɢɧɟɧ ɩɪɨɜɨɞɧɢɤ, ɧɚɯɨɞɹɳɢɣɫɹ ɩɨɞ ɫɟɜɟɪɧɵɦ ɩɨɥɸɫɨɦ; ɧɚɨɛɨɪɨɬ, ɳɟɬɤɚ ȼ ɫɨɟɞɢɧɹɟɬɫɹ ɬɨɥɶɤɨ ɫ ɬɟɦ ɩɪɨɜɨɞɧɢɤɨɦ, ɤɨɬɨɪɵɣ ɧɚɯɨɞɢɬɫɹ ɩɨɞ ɸɠɧɵɦ ɩɨɥɸɫɨɦ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɨ ɜɧɟɲɧɟɣ ɰɟɩɢ ɬɨɤ ɛɭɞɟɬ ɩɪɨɬɟɤɚɬɶ ɬɨɥɶɤɨ ɜ ɨɞɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɚ ɢɦɟɧɧɨ, ɨɬ ɳɟɬɤɢ Ⱥ ɤ ɳɟɬɤɟ ȼ. ɉɪɨɢɫɯɨɞɢɬ ɜɵɩɪɹɦɥɟɧɢɟ ɩɟɪɟɦɟɧɧɨɣ ɗȾɋ,

ɧɚɜɨɞɢɦɨɣ ɜ ɜɢɬɤɟ abícd, ɢ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɜ ɩɭɥɶɫɢɪɭɸɳɭɸ ɗȾɋ ɧɚ ɳɟɬɤɚɯ ɢ ɩɭɥɶɫɢɪɭɸɳɢɣ ɬɨɤ ɜɨ ɜɧɟɲɧɟɦ ɭɱɚɫɬɤɟ ɰɟɩɢ (ɪɢɫ. 4.15.).

ea,ia

Ɋɢɫ. 4.15. ȼɵɩɪɹɦɥɟɧɧɵɟ ɗȾɋ ɢ ɬɨɤ

ɉɨɥɹɪɧɨɫɬɶ ɳɟɬɨɤ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɜɨ ɜɧɟɲɧɟɣ ɰɟɩɢ ɨɫɬɚɸɬɫɹ ɧɟɢɡɦɟɧɧɵɦɢ. ɓɟɬɤɚ Ⱥ, ɨɬ ɤɨɬɨɪɨɣ ɬɨɤ ɨɬɜɨɞɢɬɫɹ ɜɨ ɜɧɟɲɧɸɸ ɰɟɩɶ, ɫɱɢɬɚɟɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɢ ɨɛɨɡɧɚɱɚɟɬɫɹ «ɩɥɸɫ», ɚ ɳɟɬɤɚ ȼ ɫɱɢɬɚɟɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɢ ɨɛɨɡɧɚɱɚɟɬɫɹ «ɦɢɧɭɫ».

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɝɟɧɟɪɚɬɨɪɟ ɤɨɥɥɟɤɬɨɪ ɹɜɥɹɟɬɫɹ ɦɟɯɚɧɢɱɟɫɤɢɦ ɜɵɩɪɹ-

ɦɢɬɟɥɟɦ, ɤɨɬɨɪɵɣ ɩɪɟɨɛɪɚɡɨɜɵɜɚɟɬ ɩɟɪɟɦɟɧɧɵɣ ɬɨɤ ɨɛɦɨɬɤɢ ɹɤɨɪɹ ɜ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ ɜɨ ɜɧɟɲɧɟɣ ɰɟɩɢ.

ɓɟɬɤɢ ɧɟɨɛɯɨɞɢɦɨ ɭɫɬɚɧɨɜɢɬɶ ɧɚ ɩɥɚɫɬɢɧɚɯ ɤɨɥɥɟɤɬɨɪɚ ɬɚɤ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.13. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜ ɦɨɦɟɧɬ ɩɟɪɟɯɨɞɚ ɳɟɬɤɢ ɫ ɨɞɧɨɣ ɤɨɥɥɟɤɬɨɪɧɨɣ ɩɥɚɫɬɢɧɵ ɧɚ ɞɪɭɝɭɸ, ɤɨɝɞɚ ɜɢɬɨɤ ɡɚɦɵɤɚɟɬɫɹ ɧɚɤɨɪɨɬɤɨ, ɧɚɜɨɞɢɦɚɹ ɗȾɋ ɪɚɜɧɚ ɧɭɥɸ. ɉɟɪɟɦɟɧɧɚɹ ɗȾɋ ɜɵɩɪɹɦɥɹɟɬɫɹ ɩɨɥɧɨɫɬɶɸ, ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɳɟɬɤɚɯ ɦɚɤ-

ɫɢɦɚɥɶɧɨ.

ɇɚ ɪɢɫ. 4.15. ɜɢɞɧɨ, ɱɬɨ ɬɨɤ ɜɨ ɜɧɟɲɧɟɣ ɰɟɩɢ ɢɡɦɟɧɹɟɬɫɹ ɨɬ ɧɭɥɹ ɞɨ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɬ. ɟ. ɩɭɥɶɫɚɰɢɢ ɬɨɤɚ ɜɟɥɢɤɢ. Ⱦɥɹ ɭɦɟɧɶɲɟɧɢɹ ɩɭɥɶɫɚɰɢɣ ɬɨɤɚ ɫɥɟɞɭɟɬ ɧɚ ɫɟɪɞɟɱɧɢɤɟ ɹɤɨɪɹ ɪɚɡɦɟɫɬɢɬɶ ɧɟɫɤɨɥɶɤɨ ɜɢɬɤɨɜ, ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɩɨ ɟɝɨ ɨɤɪɭɠɧɨɫɬɢ, ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɭɜɟɥɢɱɢɬɶ ɤɨɥɢɱɟɫɬɜɨ

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ɤɨɥɥɟɤɬɨɪɧɵɯ ɩɥɚɫɬɢɧ, ɬ. ɟ. ɩɪɢɦɟɧɢɬɶ ɛɨɥɟɟ ɫɥɨɠɧɭɸ ɩɨ ɭɫɬɪɨɣɫɬɜɭ ɨɛɦɨɬɤɭ ɹɤɨɪɹ ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɛɨɥɟɟ ɫɥɨɠɧɵɣ ɤɨɥɥɟɤɬɨɪ.

ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɡɚɠɢɦɚɯ ɝɟɧɟɪɚɬɨɪɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ

Uɚ = Ea í Iɚ ra ,

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ɝɞɟ Uɚ – ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɡɚɠɢɦɚɯ ɨɛɦɨɬɤɢ ɹɤɨɪɹ; Ea – ɗȾɋ ɨɛɦɨɬɤɢ ɹɤɨɪɹ;

Iɚ – ɬɨɤ ɹɤɨɪɹ;

ra – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɦɨɬɤɢ ɹɤɨɪɹ ɢ ɳɟɬɨɤ.

ɂɡ ɩɪɢɜɟɞɟɧɧɨɝɨ ɜɵɪɚɠɟɧɢɹ ɜɢɞɧɨ, ɱɬɨ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɡɚɠɢɦɚɯ ɹɤɨɪɹ Uɚ ɛɭɞɟɬ ɦɟɧɶɲɟ ɗȾɋ ɹɤɨɪɹ Eɚ ɧɚ ɜɟɥɢɱɢɧɭ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɰɟɩɢ ɨɛɦɨɬɤɢ ɹɤɨɪɹ ra.

ɉɪɨɜɨɞɧɢɤɢ ɨɛɦɨɬɤɢ ɹɤɨɪɹ ɫ ɬɨɤɨɦ Iɚ ɧɚɯɨɞɹɬɫɹ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɩɨɷɬɨɦɭ ɧɚ ɧɢɯ ɛɭɞɭɬ ɞɟɣɫɬɜɨɜɚɬɶ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɫɢɥɵ (ɪɢɫ. 4.16)

Fɷɦ =B Iɚ l.

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Ɋɢɫ. 4.16. Ɋɚɛɨɬɚ ɩɪɨɫɬɟɣɲɟɣ ɦɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɜ ɪɟɠɢɦɟ ɝɟɧɟɪɚɬɨɪɚ

ɗɬɢ ɫɢɥɵ ɫɨɡɞɚɸɬ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ Ɇɷɦ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɪɢɫ. 4.16, ɜ ɪɟɠɢɦɟ ɝɟɧɟɪɚɬɨɪɚ ɷɬɨɬ ɦɨɦɟɧɬ ɞɟɣɫɬɜɭɟɬ ɩɪɨɬɢɜ ɧɚɩɪɚɜɥɟɧɢɹ ɜɪɚɳɟɧɢɹ ɹɤɨɪɹ ɢ ɹɜɥɹɟɬɫɹ ɬɨɪɦɨɡɧɵɦ.

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4.1.5. ɉɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ

Ʉɚɤ ɭɤɚɡɵɜɚɥɨɫɶ ɜɵɲɟ, ɦɚɲɢɧɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɨɛɪɚɬɢɦɚ, ɬ. ɟ. ɦɨɠɟɬ ɪɚɛɨɬɚɬɶ ɤɚɤ ɜ ɪɟɠɢɦɟ ɝɟɧɟɪɚɬɨɪɚ, ɬɚɤ ɢ ɜ ɪɟɠɢɦɟ ɞɜɢɝɚɬɟɥɹ. ɇɚ ɪɢɫ. 4.17 ɢɡɨɛɪɚɠɟɧɵ ɞɜɟ ɩɪɨɫɬɟɣɲɢɟ ɦɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. Ɉɞɧɚ ɢɡ ɧɢɯ ɪɚɛɨɬɚɟɬ ɜ ɪɟɠɢɦɟ ɝɟɧɟɪɚɬɨɪɚ (ȽɉɌ), ɚ ɞɪɭɝɚɹ ɜ ɪɟɠɢɦɟ ɞɜɢɝɚɬɟɥɹ (ȾɉɌ).

Ʉɚɤ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɪɚɧɶɲɟ, ɜ ȽɉɌ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ, ɩɨɞɜɟɞɟɧɧɚɹ ɤ ɜɚɥɭ ɦɚɲɢɧɵ ɩɟɪɜɢɱɧɵɦ ɞɜɢɝɚɬɟɥɟɦ, ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ. Ⱦɜɢɝɚɬɟɥɢ ȾɉɌ ɩɨɬɪɟɛɥɹɸɬ ɢɡ ɫɟɬɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ, ɩɪɟɨɛɪɚɡɭɸɬ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɜ ɦɟɯɚɧɢɱɟɫɤɭɸ ɢ ɩɪɢɜɨɞɹɬ ɜ ɞɜɢɠɟɧɢɟ ɤɨɦɩɪɟɫɫɨɪ, ɜɟɧɬɢɥɹɬɨɪ, ɧɚɫɨɫ, ɤɨɥɟɫɧɵɟ ɩɚɪɵ ɷɥɟɤɬɪɨɜɨɡɚ ɢ ɬ. ɞ.

ɉɨɥɹɪɧɨɫɬɶ ɩɨɥɸɫɨɜ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɦɚɲɢɧɚɯ ɨɞɢɧɚɤɨɜɚ. əɤɨɪɶ ɝɟɧɟɪɚɬɨɪɚ (ɪɢɫ. 4.17, ɚ) ɜɪɚɳɚɟɬɫɹ ɩɟɪɜɢɱɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ. ȼ ɩɪɨɜɨɞɧɢɤɚɯ ɹɤɨɪɹ ɧɚɜɨɞɢɬɫɹ ɗȾɋ – Ea . ɇɚɩɪɚɜɥɟɧɢɟ Ea ɨɩɪɟɞɟɥɟɧɨ ɩɨ ɩɪɚɜɢɥɭ ɩɪɚɜɨɣ ɪɭɤɢ. ɉɪɢ ɩɨɞɤɥɸɱɟɧɢɢ ɧɚɝɪɭɡɤɢ ɤ ɰɟɩɢ ɨɛɦɨɬɤɢ ɹɤɨɪɹ ɩɨ ɨɛɦɨɬɤɟ ɩɨɬɟɱɟɬ ɬɨɤ Ia. ɇɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ Ia ɜ ɝɟɧɟɪɚɬɨɪɟ ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ Ea . ɇɚ ɩɪɨɜɨɞɧɢɤɢ ɫ ɬɨɤɨɦ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɞɟɣɫɬɜɭɸɬ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ

ɫɢɥɵ Fɷɦ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɪɢɫ. 4.17, ɚ, ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɫɢɥɵ ɜ ɪɟɠɢɦɟ ɝɟɧɟɪɚɬɨɪɚ ɹɜɥɹɸɬɫɹ ɬɨɪɦɨɡɧɵɦɢ, ɬɚɤ ɤɚɤ ɧɚɩɪɚɜɥɟɧɵ ɩɪɨɬɢɜ ɧɚɩɪɚɜɥɟɧɢɹ ɜɪɚɳɟɧɢɹ.

Ɋɢɫ.17 Ɋɚɛɨɬɚ ɩɪɨɫɬɟɣɲɟɣ ɦɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ

ɜ ɪɟɠɢɦɟ ɝɟɧɟɪɚɬɨɪɚ (ɚ), ɜ ɪɟɠɢɦɟ ɞɜɢɝɚɬɟɥɹ (ɛ)

Ɋɚɫɫɦɨɬɪɟɧɧɚɹ ɩɪɨɫɬɟɣɲɚɹ ɦɚɲɢɧɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɦɨɠɟɬ ɪɚɛɨɬɚɬɶ ɬɚɤɠɟ ɞɜɢɝɚɬɟɥɟɦ, ɟɫɥɢ ɨɛɦɨɬɤɭ ɹɤɨɪɹ ɩɨɞɤɥɸɱɢɬɶ ɤ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ (ɪɢɫ. 4.17, ɛ). ɇɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɜ ɨɛɦɨɬɤɟ ɹɤɨɪɹ ɡɚɜɢɫɢɬ ɨɬ ɩɨɥɹɪɧɨɫɬɢ

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