EP / Теория ЭП Драчев

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.:

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

Ⱦɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɢ ɹɤɨɪɹ ɩɪɢ ɉȼ:

ɇɚ ɪɢɫ. 3.26 ɩɪɢɜɟɞɟɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ, ɩɪɨɯɨɞɹɳɚɹ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ 2 ɩɪɢ ɜɜɟɞɟɧɢɢ RȾɈȻ = 8,83 Ɉɦ. ɋɨɩɪɨɬɢɜɥɟ-

ɧɢɟ 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 ɬɨɪɦɨɠɟ-

Ⱦɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɢ ɹɤɨɪɹ ɩɪɢ ɞɢɧɚɦɢɱɟɫɤɨɦ ɬɨɪɦɨɠɟɧɢɢ

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.

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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.

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.

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Ɋɟɲɚɟɦ ɤɜɚɞɪɚɬɧɨɟ ɭɪɚɜɧɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɬɨɤɚ

ɉɨɥɭɱɢɥɢ Ɏ1 0,786, Ɏ2 0,047. ɉɪɢɧɢɦɚɟɦ ɢɡ ɮɢɡɢɱɟɫɤɢɯ ɫɨɨɛɪɚɠɟɧɢɣ

Ɏ1 0,786 .

Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɛɚɡɨɜɨɝɨ ɡɧɚɱɟɧɢɹ ɩɨɬɨɤɚ Ɏɇ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɤɚɬɚɥɨɝɚ [16]

ɝɞɟ N = 558 – ɱɢɫɥɨ ɚɤɬɢɜɧɵɯ ɩɪɨɜɨɞɧɢɤɨɜ; ɪɉ = 2 – ɱɢɫɥɨ ɩɚɪ ɩɨɥɸɫɨɜ;

2ɚ = 2 – ɱɢɫɥɨ ɩɚɪɚɥɥɟɥɶɧɵɯ ɜɟɬɜɟɣ ɨɛɦɨɬɤɢ ɹɤɨɪɹ. ɉɪɢ k Ɏɇ = 2,3 ȼ ɫ ɜɟɥɢɱɢɧɚ ɧɨɦɢɧɚɥɶɧɨɝɨ ɩɨɬɨɤɚ

ɉɨ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ Ⱦ32 [16] ɩɨ ɜɟɥɢɱɢɧɟ ɩɨɬɨɤɚ

Ɏ1 Ɏ1 Ɏɇ 0,786 0,01356 0,0107 ȼɛ,

ɨɩɪɟɞɟɥɢɦ ɧɚɦɚɝɧɢɱɢɜɚɸɳɭɸ ɫɢɥɭ

FB iB ȦB 1500 A .

Ɂɧɚɱɟɧɢɟ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɢ ɪɚɛɨɬɟ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ:

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

Ⱦɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ Rȼ ȾɈȻ

ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɢ ɩɢɬɚɧɢɢ ɨɬ ɢɧɞɢɜɢɞɭɚɥɶɧɨɝɨ ɜɨɡɛɭɞɢɬɟɥɹ:

UB IB rOB 1 119 119 B.

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Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɫɬɚɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ:

Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ:

3.1.10.Ɇɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

ɫɩɪɹɦɨɥɢɧɟɣɧɨɣ 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

ɢ ɭɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

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

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

ȼ ɨɛɳɟɦ ɜɢɞɟ ɪɟɲɟɧɢɟ ɷɬɨɝɨ ɥɢɧɟɣɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ:

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

ɉɪɢ t = f – eTM 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

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

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 ɩɭɫ-

ɤɟ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ.3.12. ȼɵɲɟ ɪɚɫɫɦɨɬɪɟɧɚ ɦɟɬɨɞɢɤɚ ɪɚɫɱɟɬɚ ɩɪɚɜɢɥɶɧɨɣ ɩɭɫɤɨɜɨɣ ɞɢɚɝɪɚɦɦɵ.

Ɋɚɫɱɟɬ ɧɚɝɪɭɡɨɱɧɵɯ ɞɢɚɝɪɚɦɦ ɩɪɨɢɡɜɨɞɢɦ ɩɨ ɮɨɪɦɭɥɚɦ (3.43) ɢ (3.44):

t

Ȧ t ȦC ȦɇȺɑ Ȧɋ ɟ TM ,

t

Ɇ t MC MɇȺɑ Mɋ ɟ 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:

ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 1:

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:

t

Ɇ2 MC M1 Mɋ ɟ TM1

76

Ɇ1

Ɇ2

Ɇɋ

t

Ɋɢɫ.3.27. ɉɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɭɫɤɚ Ⱦɇȼ

Ɍɨɝɞɚ

ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 2:

ɆɇȺɑ = Ɇ1, ȦɇȺɑ = Ȧ1, Ȧɋ = Ȧɋ2.

ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 2:

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

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

ɧɨ ɜɪɟɦɹ ɪɚɛɨɬɵ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨ ɮɨɪɦɭɥɟ (3.46) ɪɚɫɫɱɢɬɚɬɶ ɧɟɥɶɡɹ (tɟ=f), ɩɪɢɛɥɢɠɟɧɧɨ ɫɱɢɬɚɸɬ tɟ § 3·Ɍɦɟ.

ȼɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɩɭɫɤɚ ɞɜɢɝɚɬɟɥɹ

tɉɉ t1 t2 te .

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.

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):

t

Ȧ t ȦC ȦɇȺɑ Ȧɋ ɟ TM ,

t

Ɇ t MC MɇȺɑ Mɋ ɟ TM .

ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ:

ɆɇȺɑ = – ɆɌɇȺɑ; ȦɇȺɑ = Ȧɋ; Ȧɋ= – Ȧɋ1.

ɋ ɭɱɟɬɨɦ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ:

t

Ȧ t ȦC1 ȦɇȺɑ Ȧɋ1 ɟ TMɉȼ ,

78

t

Ɇ t MC MɌɇȺɑ Mɋ ɟ TMɉȼ .

ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ

ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɩɭɫɤɨɜɵɯ ɪɟɠɢɦɚɯ ɢɡ-ɡɚ ɡɧɚɱɢɬɟɥɶɧɨɣ ɜɟɥɢɱɢɧɵ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ.

ɉɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɧɚɱɢɧɚɟɬɫɹ ɜ ɬɨɱɤɟ 1 ɜ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɢ ɩɨ

2

-ɆɄɁ

-Ȧ0ɇ

ɟɫɬ

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:

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.

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