EP / Теория ЭП Драчев

ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɫ ɜɵɯɨɞɨɦ ɩɨ ɫɢɧɯɪɨɧɧɨɦɭ ɦɨɦɟɧɬɭ:

Wɋɂɇ(p)	Mɋɂɇ		b	.
	Ȧ0 Ȧ
			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	2 MK		Ȧ0 Ȧ
	s/s	s /s				s
				s				Ȧ	0
	K	K		K		K

2 MK Ȧ0 Ȧ ȕ (Ȧ0 Ȧ).

sK Ȧ0

ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɫ ɜɵɯɨɞɨɦ ɩɨ ɚɫɢɧɯɪɨɧɧɨɦɭ ɦɨɦɟɧɬɭ:

WȺɋɂɇ	p	MAɋɂɇ	ȕ.
		Ȧ0 Ȧ

ɋ ɭɱɟɬɨɦ ɨɫɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

M M J	dȦ	M	ȕ T	dȦ
C	dt C		Ɇ dt

ɢ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ

	WɆȿɏ	p	Ȧ p		1		1
			M MC		J p 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 Ɇɋɂɇ	1	Ȧ

p+ ȕ TM

ɆȺɋɂɇ

ȕ

Ɋɢɫ. 3.88. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɋȾ

161

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. Ɋɨ-

ɬɨɪ ɨɫɬɚɟɬɫɹ ɧɟɩɨɞɜɢɠɧɵɦ. ȿɫɥɢ ɪɨɬɨɪ	ɪɚɡɨ-
ɝɧɚɬɶ ɞɨ ɫɤɨɪɨɫɬɢ, ɛɥɢɡɤɨɣ ɤ ɫɢɧɯɪɨɧɧɨɣ, ɢ		Ȧ
			Ɇȼɏ2
ɧɚ ɷɬɨɣ ɫɤɨɪɨɫɬɢ ɩɨɞɤɥɸɱɢɬɶ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠ-				Ɇȼɏ1
ɞɟɧɢɹ, ɬɨ ɪɨɬɨɪ ɛɭɞɟɬ ɭɫɩɟɜɚɬɶ ɡɚ ɩɨɬɨɤɨɦ		Ȧȼɏ
ɫɬɚɬɨɪɚ, ɢ ɞɜɢɝɚɬɟɥɶ ɜɬɹɝɢɜɚɟɬɫɹ ɜ ɫɢɧɯɪɨ-
ɧɢɡɦ. Ⱦɥɹ ɪɚɡɝɨɧɚ ɞɜɢɝɚɬɟɥɹ ɞɨ ɩɨɞɫɢɧɯɪɨɧ-
ɧɨɣ ɫɤɨɪɨɫɬɢ (0,95·Ȧ0ɇ) ɧɚ ɪɨɬɨɪɟ ɞɜɢɝɚɬɟɥɹ,				M
ɤɪɨɦɟ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɪɚɡɦɟɳɚɟɬɫɹ
ɩɭɫɤɨɜɚɹ ɨɛɦɨɬɤɚ ɬɢɩɚ ɛɟɥɢɱɶɟɝɨ ɤɨɥɟɫɚ.			Ɇɉ1	Ɇɉ2
ɉɭɫɤɨɜɚɹ ɨɛɦɨɬɤɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɭɫɤ	ɫɢɧ-

ɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ, ɤɚɤ ɚɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚ-	Ɋɢɫ. 3.89.
		ɉɭɫɤɨɜɵɟ

ɬɟɥɹ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ. Ɇɟɯɚɧɢɱɟ-
	ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ 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

ɢɧɚɝɪɟɜɚɟɬɫɹ 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

~		~							~

	M			M
			M
		Ʉ
Iȼ	RɊ			ȼ	LMB
		Ʉ
			ȼ
	ȼ
	LMB		LMB
	ɚ		ɛ	ɜ

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 «ɨɞɧɨɨɫɧɨ-

ɝɨ 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 Ȧ2 Ȧ0 (1 s) Ȧ0 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 ɫɨɡ-
	Ȧ
		ɆɉɈ	ɞɚɟɬ ɩɪɨɜɚɥ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟ-
	MɈɉ		ɪɢɫɬɢɤɟ, ɢ ɟɫɥɢ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɩɨ-
			ɩɚɞɚɟɬ ɜ ɷɬɨɬ ɩɪɨɜɚɥ, ɬɨ ɞɚɥɶɧɟɣɲɢɣ
		MɊȿɁ	ɪɚɡɝɨɧ ɞɜɢɝɚɬɟɥɹ ɫɬɚɧɨɜɢɬɫɹ ɧɟɜɨɡ-
			ɦɨɠɧɵɦ, ɞɜɢɝɚɬɟɥɶ «ɡɚɫɬɪɟɜɚɟɬ».
		M	Ⱦɥɹ ɢɫɤɥɸɱɟɧɢɹ ɷɬɨɝɨ ɷɮɮɟɤɬɚ ɨɛ-
			ɦɨɬɤɭ ɪɨɬɨɪɚ ɧɟ ɡɚɤɨɪɚɱɢɜɚɸɬ, ɚ ɩɨɞ-
			ɤɥɸɱɚɸɬ ɧɚ ɪɚɡɪɹɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ
			RɊ = 10·rɈȼ. ȿɝɨ ɜɤɥɸɱɟɧɢɟ ɫɧɢɠɚɟɬ
	Ɇɉɉ		ɩɪɨɜɚɥɵ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢ-
			ɤɟ, ɨɞɧɨɨɫɧɨɟ ɜɤɥɸɱɟɧɢɟ ɜ ɦɟɧɶɲɟɣ
	Ɋɢɫ. 3.91. ɉɭɫɤɨɜɵɟ		ɫɬɟɩɟɧɢ ɜɥɢɹɟɬ ɧɚ ɩɭɫɤ.
			ɇɟɞɨɫɬɚɬɨɤ – ɪɚɡɪɹɞɧɨɟ ɫɨɩɪɨɬɢɜ-
	ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɷɮɮɟɤɬɟ
	ɨɞɧɨɨɫɧɨɝɨ ɜɤɥɸɱɟɧɢɹ		ɥɟɧɢɟ ɧɟɨɛɯɨɞɢɦɨ ɨɬɤɥɸɱɚɬɶ, ɫɧɢɠɚɟɬ-
			ɫɹ ɧɚɞɟɠɧɨɫɬɶ.
			ȼ ɫɯɟɦɟ ɫ ɝɥɭɯɨɩɨɞɤɥɸɱɟɧɧɵɦ ɜɨɡ-
			ɛɭɞɢɬɟɥɟɦ (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 ɬɨɪ-

164

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:

~

	ȼɆ1	Ȧ
		Ȧ0ɇ
	ȼɆ2	3
M	1	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:

Ș = Ɋȼ , cos ij = PC ,

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

	WɆȿɏ		³MPO(t) ȦPO(t) dt
		0		.	(4.1)
Șɐ	Wɋ		tɐ
			³PC(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

RɉɊ

§

Ɋ

·2

§P ·2

1

ǻPɉɊ

I

¨

¸

RɉɊ

¨

¸

R

,

(4.2)

ǻɊ

2

2

¨

¸

©U¹

cos

cos

©U cosij¹

ij

ij

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
ɤɆ		.	(4.3)
	U I
ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɵɫɲɢɯ ɝɚɪɦɨɧɢɤ ɤɆ=cos ij, ɜ ɨɫɬɚɥɶɧɵɯ ɫɥɭɱɚɹɯ
ɤɆ ɤɂ cosij1,			(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, ɷɥɟɤ-

167

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

	U = E + I R + L	dI	(4.5)
		dt

ɭɦɧɨɠɢɦ ɨɛɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ ɧɚ ɬɨɤ ɹɤɨɪɹ I ɢ ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɪɚɜɟɧɫɬɜɚ ɦɨɳɧɨɫɬɟɣ

U I E I I2 R L I	dI	,	(4.6)
	dt
PC = PɆȿɏ + ǻP + PL ,			(4.7)

ɝɞɟ UǜI = Ɋɋ – ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɢɡ

U

ɫɟɬɢ;

kɎ Ȧ Ɇ

LM

E I

Ɇ Ȧ

ɊɆȿɏ –

ɦɟɯɚɧɢ-

kɎ

ɱɟɫɤɚɹ ɦɨɳɧɨɫɬɶ;

I2ǜR = ǻɊ – ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɫɨɩɪɨ-

R

ɬɢɜɥɟɧɢɹɯ ɹɤɨɪɧɨɣ ɰɟɩɢ;

Ɇ

L I

dI

1

L

d(I2 )

d

(

1

L I2 )

P –

dt

2

dt

dt 2

L

Ɋɢɫ. 4.2. ɋɯɟɦɚ ɜɤɥɸɱɟɧɢɹ

ɦɨɳɧɨɫɬɶ, ɪɚɫɯɨɞɭɟɦɚɹ ɧɚ ɢɡɦɟɧɟɧɢɟ ɡɚ-

ɩɚɫɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ

ɷɧɟɪɝɢɢ

ɨɛɦɨɬɤɢ

Ⱦɇȼ

ɹɤɨɪɹ.

ɗɧɟɪɝɢɹ ɟɫɬɶ ɢɧɬɟɝɪɚɥ ɡɚ ɨɩɪɟɞɟɥɟɧɧɵɣ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ, ɩɨɷɬɨɦɭ ɩɟɪɟɣɞɟɦ ɤ ɛɚɥɚɧɫɭ ɷɧɟɪɝɢɣ.

³Pɋ dt ³PɆȿɏ	dt ³ǻɊ dt L	I2	,	(4.8)
	2

ɢɥɢ

WC = WɆȿɏ + ǻWə + WL.

ɋɪɚɜɧɢɦ ɷɧɟɪɝɢɸ WL, ɪɚɫɯɨɞɭɟɦɭɸ ɧɚ ɢɡɦɟɧɟɧɢɟ ɡɚɩɚɫɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ ɨɛɦɨɬɤɢ ɹɤɨɪɹ, ɫ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɩɪɢɜɨɞɚ WɄ.

168

L

I2

2

2

W

L

2

R I kɎɇ

R

L

=

=

2 R

WK

J

Ȧ02

R J Ȧ02 kɎɇ

2

= Ɍə

1

R2

ǿ2 =

ȉə

ǿ2

.

U2

ɌM

ɌM ǿɄɁ2

=	L		kɎɇ 2		R2 I2		=
	R		J R		Ȧ02 kɎɇ	2
						(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 .

Ɋɚɫɫɦɨɬɪɢɦ ɫɨɫɬɚɜɥɹɸɳɢɟ ɷɬɨɝɨ ɛɚɥɚɧɫɚ:

t

t

t

dȦ

t

ȦɄɈɇ

WɆȿɏ = ³PC

dt = ³M(t) Ȧ(t) dt = ³(MC J

) Ȧ dt = ³MC dt

³J Ȧ dȦ =

0

0

0

dt

0

ȦɇȺɑ

t

2

t

2

2

= ³MC

dt J

Ȧ

ȦɄɈɇ = ³MC dt J

ȦɄɈɇ

J

ȦɇȺɑ

;

0

2

ȦɇȺɑ 0

2

2

t

t

t

U

§

dȦ·

Wɫ

³Pɫ dt ³U I dt ³

E I dt ³M

Ȧ0 dt

³¨MC

J

¸

Ȧ0 dt

0

0

0 E

©

dt ¹

³MC Ȧ0 dt J Ȧ0 ȦɄɈɇ ȦɇȺɑ ;

Ȧ0 Ȧ dt

§

ȦɄɈɇ

·

§

ȦɇȺɑ ·

ǻW

³MC

J ȦɄɈɇ

¨Ȧ0

¸

J ȦɇȺɑ ¨

Ȧ0

¸.

2

©

¹

©

2 ¹

(4.10)

(4.11)

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 ³U I dt ³ǻPXX 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

W	= J Ȧ2		2	= J		Ȧ02		2 = 2 W .	(4.13)
C	0	2		2				Ʉɂɇ
Ɇɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ
	WɆȿɏ			= J	Ȧ02			= WɄɂɇ .	(4.14)
				2

169

Ȧ

Ȧ0

1

2

Ɇ

ɆɄ2 ɆɄ1

Ɋɢɫ. 4.3. ɉɭɫɤ Ⱦɇȼ ɫ ɪɚɡɧɵɦɢ R

ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ 1

ɉɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜ ɰɟɩɢ ɹɤɨɪɹ

ǻW = WɄɂɇ .

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.

ǻW I 2	R t		2 I2 2 R2		tɉ2	I	2	R		t		ǻW
		ɉ1							2		ɉ2
1 1	1		2		2	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).

Ȧ

ɋɨɫɬɚɜɥɹɸɳɢɟ ɛɚɥɚɧɫɚ ɷɧɟɪɝɢɣ:

Ȧ0

Wɋ = ³Ɇɋ Ȧ0 dt J Ȧ0 ȦC;

(4.15)

Ȧɋ

WɆȿɏ = ³

Ɇɋ Ȧɋ dt J

ȦC

2

;

(4.16)

Ɇ

2

2

ǻW = ³Ɇɋ Ȧ0

dt J Ȧ0 ȦC J

ȦC

.

(4.17)

2

Ɇɋ ɆȾɂɇ

ɉɪɢ ɫɬɚɬɢɱɟɫɤɨɣ ɫɤɨɪɨɫɬɢ, ɛɥɢɡɤɨɣ ɤ ɫɤɨɪɨ-

Ɋɢɫ. 4.4. ɉɭɫɤ Ⱦɇȼ

ɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Ȧɋ § Ȧ0, ɫɨɫɬɚɜ-

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 ɜɵɩɨɥ-

ɧɹɥɚɫɶ ɢ ɩɨɥɟɡɧɚɹ ɪɚɛɨɬɚ.
3. Ɍɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ
ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ MC = 0; ȦɇȺɑ = Ȧ0; ȦɄɈɇ = 0;Ȧ0 = - Ȧ0							ɩɨɞɫɬɚɜɥɹɟɦ ɜ ɮɨɪ-
ɦɭɥɵ (4.11).
W	= J Ȧ 2		2	= J	Ȧ02	2 = 2 W .	(4.18)
C	0	2		2		K

170