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Файл:Расчет переходных процессов в электроэнергетических системах методом интеграла Дюамеля. Учебное пособие
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Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪ ɩɪɢɦɟɧɟɧɢɹ ɢɧɬɟɝɪɚɥɚ Ⱦɸɚɦɟɥɹ ɤ
ܣ
ɪɚɫɱɟɬɭ ɬɨɤɚ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɜ ɟɦɤɨɫɬɢ ɰɟɩɢ
(ɫɦ. ɪɢɫ. 1.12), ɟɫɥɢ ɧɚ ɟɟ ɜɯɨɞɟ ɜɨɡɧɢɤɚɟɬ ɧɚɩɪɹɠɟɧɢɟ
(ɪɢɫ. 1.16)
ሽ
=
+ ܤ
ሾܪሺݐሻ
ݐെɒ
൬
െܪሺݐെɒ
ଶ
൰
ɒ
ଶ
ܪሺݐെɒ
ݑሼݐ
ሻሿ
+
ଵ
ሻ
.
ଶ
(1.85)
Ɋɢɫ. 1.16
ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɫɬɭɩɟɧɱɚɬɚɹ ɢ ɢɦɩɭɥɶɫɧɚɹ ɩɟɪɟɯɨɞ-
ɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɥɭɱɟɧɵ ɪɚɧɟɟ ɢ ɢɦɟɸɬ ɜɢɞ
ሼݐሽ
௨
=
ܴ
݄
1
௧
ି
ோʬ
݁
ଵ
ήܪሺݐ
ሻ
(1.86)
ɢ
ή݁
௧
ି
ோʬ
ήܪሺݐ
1
ሻ
+
ܴ
ଵ
Ɂሺݐ
ሻ
(1.87)
.
ሼݐሽ
݇
௨
= െ
ܴଵܴʬܥ
1
ɉɨɥɭɱɢɦ ɪɟɲɟɧɢɹ ɨɬɞɟɥɶɧɨ ɧɚ ɤɚɠɞɨɦ ɢɡ ɢɧɬɟɪɜɚɥɨɜ ɫɭ-
ɳɟɫɬɜɨɜɚɧɢɹ ɜɨɡɞɟɣɫɬɜɢɹ.
41
I. ȼ ɢɧɬɟɪɜɚɥɟ 0…IJ1 ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɜɵɡɜɚɧ ɩɨɞɚɱɟɣ
ܣ
ܣ
ܣ
݂
ܣ
ɧɚ ɜɯɨɞ ɰɟɩɢ ɫɬɭɩɟɧɱɚɬɨɝɨ ɧɚɩɪɹɠɟɧɢɹ
ݑሼݐ
ሽ
=
ήܪሺݐ
ሻ
,
(1.88)
ɢ ɩɨɷɬɨɦɭ ɪɟɲɟɧɢɟ ɡɚɩɢɫɵɜɚɟɬɫɹ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ
௧
ି
ሺݐሻ
݅
=
0<ݐ< ɒ
ோʬ
݁
ܴ
ଵ
ଵ
ήܪሺݐ
.
ሻ
,
(1.89)
II. ȼ ɢɧɬɟɪɜɚɥɟ IJ1…IJ2 ɩɪɨɰɟɫɫ ɜɵɡɵɜɚɟɬɫɹ ɩɪɹɦɨɭɝɨɥɶ-
ɧɵɦ ɧɚɩɪɹɠɟɧɢɟɦ
ሽ
ݑሼݐ
=
ሾܪሺݐሻ
െܪሺݐെ߬
ሻሿ
.
ଵ
(1.90)
ɉɨɷɬɨɦɭ ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɫɱɢɬɚɧ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɨ ɦɟɬɨɞɭ ɧɚɥɨɠɟɧɢɹ ɫ ɭɱɟɬɨɦ ɡɚɩɚɡɞɵɜɚɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɜɪɟɦɹ IJ1. Ɂɚɦɟɬɢɦ, ɱɬɨ ɡɞɟɫɶ ɧɟɬ
ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜ ɩɪɢɦɟɧɟɧɢɢ ɢɧɬɟɝɪɚɥɚ Ⱦɸɚɦɟɥɹ.
III. Ɍɨɤ ɜ ɢɧɬɟɪɜɚɥɟ IJ2…t ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɫɱɢɬɚɧ ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɱɟɬɜɟɪɬɨɣ ɮɨɪɦɵ ɡɚɩɢɫɢ ɢɧɬɟɝɪɚɥɚ Ⱦɸɚɦɟɥɹ (1.75).
ȼɯɨɞɹɳɢɟ ɜ ɧɟɝɨ ɜɟɥɢɱɢɧɵ ɢɦɟɸɬ ɜɢɞ
˒˓ˋ 0<ݐ< ɒ
ሺɒሻ
=
0 ˒˓ˋ ɒଵ< ݐ< ɒ
൞
ɒെɒ
ܤ
൬
ɒ
ଶ
ଶ
˒˓ˋ ɒଶ< ݐ< ݐ;
൰
,
ଵ
,
ଶ
(1.91)
݄
ሺ0ሻ
=
1
;
ܴ
ଵ
(1.92)
42
ܣ
ܣ
݇ሺݐെɒሻ= െ
ܴ
ଵܴʬ
1
௧ିத
ି
ோ
ʬ
ή݁
.
(1.93)
ܥ
ɇɚ ɜɫɟɦ ɢɧɬɟɪɜɚɥɟ 0…t ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɜɨɡɞɟɣɫɬɜɢɹ
ɢɦɟɸɬ ɦɟɫɬɨ ɞɜɟ ɬɨɱɤɢ ɧɚɪɭɲɟɧɢɹ ɝɥɚɞɤɨɫɬɢ. ɉɨɷɬɨɦɭ ɢɧɬɟɝɪɚɥ (1.75) ɪɚɡɨɛɶɟɬɫɹ ɧɚ ɬɪɢ ɢɧɬɟɝɪɚɥɚ
த
భ
1
ݐെɒ
ሺݐሻ
݅
=
ܤ
൬
ܴ
ଵ
௧
+ නܤ
த
మ
ɒ
ɒെɒ
൬
ଶ
+ න
൰
ଶ
ɒ
ଶ
ଶ
൰ή൬
െ
ܴଵܴʬܥ
െ
൬
1
1
ܴଵܴʬܥ
ି
݁
௧ିத
ோʬ
௧ିத
ି
ோ
ʬ
݁
൰
݀ɒ
݀ɒ
+
൰
(1.94)
,
ɒଶ< ݐ.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɜ ɩɨɥɭɱɟɧɧɨɦ ɜɵɪɚɠɟɧɢɢ ɨɩɭɳɟɧ ɢɧɬɟɝɪɚɥ
ɜ ɩɪɟɞɟɥɚɯ IJ1…IJ2, ɬ. ɤ. ɧɚ ɷɬɨɦ ɢɧɬɟɪɜɚɥɟ ɩɨɞɵɧɬɟɝɪɚɥɶɧɚɹ
ɮɭɧɤɰɢɹ f (IJ) ɪɚɜɧɚ ɧɭɥɸ.
Ɍɨɝɞɚ ɦɨɠɧɨ ɧɚɩɢɫɚɬɶ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɬɨɤɚ
௧
ି
1
ݐെɒ
௧
ଵ
ோʬ
ଵ
݁
ɒ
ଶ
ݐ݁
௧
ܴʬܥ൬݁
௧
ି
ோʬ
ܴ
ଵ
ଶ
െ
൰
௧
ோ
ʬ
+ ܤ
ோ
݁
൬
ሺݐሻ
݅
=
ܤ
൬
ܴ
ଵ
ି
ோʬ
ܤ
݁
െ
ɒ
ܴ
ଶ
ି
ܤ
݁
+
ɒ
ܴ
ଶ
+ܤ
ோʬ
݁
ܴ
ଵ
ି
ோʬ
݁
ܴ
௧
ோ
ʬ
െ݁
௧
ʬ
െ݁
௧
ଵ
த
ோʬ
൬
ோʬ
మ
த
భ
ோʬ
݁
െ1
+
൰
த
మ
ோʬ
݁
+
(1.95)
த
మ
+
൰
,
൰
ɒଶ< ݐ,
43
ɢɥɢ, ɨɤɨɧɱɚɬɟɥɶɧɨ
ܣ
݂
݂
݂
ܣ
த
ሺݐሻ
1
=
݅
ܤ
+
ɒ
ଶ
ܴ
ܴʬܥ
ή
ଵ
ܴ
1 െ݁
൬
ଵ
൬
ோʬ
1 െ݁
భ
ି
൰
௧ିத
ோʬ
௧
ି
ோ
ʬ
݁
+
మ
,
൰
(1.96)
ɒଶ< ݐ.
IV. Ⱦɥɹ ɪɚɫɱɟɬɚ ɬɨɤɚ ɜ ɢɧɬɟɪɜɚɥɟ IJ2…t ɦɨɠɧɨ ɬɚɤɠɟ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɩɟɪɜɨɣ ɮɨɪɦɨɣ ɡɚɩɢɫɢ ɢɧɬɟɝɪɚɥɚ Ⱦɸɚɦɟɥɹ
(1.81). ȼɯɨɞɹɳɢɟ ɜ ɢɧɬɟɝɪɚɥ ɜɟɥɢɱɢɧɵ ɩɪɢɦɭɬ ɜɢɞ
0 ˒˓ˋ 0<ݐ< ɒ
=
ܤ
ቐ
ɒ
ଶ
˒˓ˋ ɒଶ< ݐ
ሻ
Ԣሺɒ
,
ଶ
;
(1.97)
௧ିத
1
ି
݄ሺݐെɒ
ሻ
=
ோʬ
; (1.98)
݁
ܴ
ଵ
ሺ0ሻ
ο
=ܣ;
(1.99)
݄ሺݐ
ሻ
=
ܴ
1
௧
ି
ோʬ
; (1.100)
݁
ଵ
ሺ
ሻ
ο
ɒ
= െ
ଵ
;
(1.101)
௧ିத
1
݄ሺݐെɒ
ሻ
=
ଵ
ܴ
ଵ
భ
ି
ோʬ
݁
.
(1.102)
44
ɉɨɞɫɬɚɜɥɹɹ ɢɯ ɜ ɢɧɬɟɝɪɚɥ (1.81), ɩɨɥɭɱɢɦ
ܣ
ܣ
ܣ
௧
1
ି
ோ
ሺݐሻ
݅
=
ܴ
௧
+ න
த
మ
ʬ
݁
ଵ
ܤ
ɒ
ଶ
െ
௧ିத
1
ି
ή
ோʬ
݁
ܴ
ଵ
ܴ
1
ଵ
݀ɒ
௧ିத
భ
ି
ோʬ
݁
+
(1.103)
,
ɒଶ< ݐ.
ȼɵɩɨɥɧɢɜ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ, ɨɤɨɧɱɚɬɟɥɶɧɨ ɦɨɠɟɦ ɧɚɩɢɫɚɬɶ
த
ሺݐሻ
1
݅
=
ܤ
+
ɒ
ଶ
ܴ
ܴʬܥ
ή
ଵ
ܴ
1 െ݁
൬
൬
ଵ
ோʬ
1 െ݁
భ
ି
൰
௧ିத
ோʬ
௧
ି
ோʬ
݁
+
మ
൰
(1.104)
,
ɒଶ< ݐ.
ɂɬɚɤ, ɩɪɨɰɟɞɭɪɚ ɪɚɫɱɟɬɚ ɩɨ ɩɟɪɜɨɣ ɮɨɪɦɟ ɡɚɩɢɫɢ ɢɧɬɟɝɪɚɥɚ Ⱦɸɚɦɟɥɹ ɨɤɚɡɚɥɚɫɶ ɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɨɣ, ɬ. ɤ. ɩɨɞɵɧɬɟɝɪɚɥɶɧɨɟ ɜɵɪɚɠɟɧɢɟ ɩɪɢ ɜɵɛɨɪɟ ɞɚɧɧɨɣ ɮɨɪɦɵ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɨɳɟ.
45
Ƚɥɚɜɚ 2
ɉɊɂɅɈɀȿɇɂə
ɆȿɌɈȾȺ ɂɇɌȿȽɊȺɅȺ ȾɘȺɆȿɅə
2.1. Ɋɚɛɨɬɚ ɜɵɩɪɹɦɢɬɟɥɹ ɜ ɫɯɟɦɚɯ ɫɪɚɜɧɟɧɢɹ
ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ ɧɚ ɟɦɤɨɫɬɧɭɸ ɧɚɝɪɭɡɤɭ
ȼ ɬɟɯɧɢɤɟ ɪɟɥɟɣɧɨɣ ɡɚɳɢɬɵ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɫɯɟɦɵ ɫɪɚɜɧɟɧɢɹ ɩɟɪɟɦɟɧɧɵɯ ɬɨɤɨɜ, ɧɚɩɪɹɠɟɧɢɣ ɥɢɛɨ ɢɯ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɫɭɦɦ. ɉɟɪɟɦɟɧɧɵɟ ɧɚɩɪɹɠɟɧɢɹ (ɬɨɤɢ) ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɜɵɩɪɹɦɥɹɸɬ. Ⱦɥɹ ɷɬɨɝɨ ɜ ɫɯɟɦɭ ɫɪɚɜɧɟɧɢɹ ɜɯɨɞɹɬ
ɜɵɩɪɹɦɢɬɟɥɢ (ɪɢɫ. 2.1), ɪɚɛɨɬɚɸɳɢɟ ɧɚ ɟɦɤɨɫɬɧɭɸ ɧɚɝɪɭɡɤɭ.
Ɋɢɫ. 2.1
ȼɟɫɶ ɩɪɨɰɟɫɫ ɭɫɬɚɧɨɜɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɜɵɯɨɞɟ ɜɵɩɪɹɦɢɬɟɥɹ ɜ ɩɟɪɟɯɨɞɧɨɦ ɪɟɠɢɦɟ ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɛɢɬ ɧɚ ɞɜɟ
ɱɚɫɬɢ: ɡɚɪɹɞ ɢ ɪɚɡɪɹɞ ɤɨɧɞɟɧɫɚɬɨɪɚ.
46
ȿɫɥɢ ɦɝɧɨɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɜɯɨɞɟ ɜɵɩɪɹɦɢɬɟɥɹ ɫ ɭɱɟɬɨɦ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɞɢɨɞɚɯ ɜɵɲɟ
ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɤɨɧɞɟɧɫɚɬɨɪɟ, ɩɪɨɢɫɯɨɞɢɬ ɟɝɨ ɡɚɪɹɞ. ȼ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɜɯɨɞɟ ɜɵɩɪɹɦɢɬɟɥɹ ɧɢɠɟ, ɞɢɨɞɵ
ɜɵɩɪɹɦɢɬɟɥɹ ɡɚɤɪɵɬɵ ɢ ɤɨɧɞɟɧɫɚɬɨɪ ɪɚɡɪɹɠɚɟɬɫɹ.
Ɉɬɦɟɬɢɦ, ɱɬɨ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɤɨɧɞɟɧɫɚɬɨɪɟ ɡɚ ɜɪɟɦɹ ɪɚɡɪɹɞɚ ɫɭɳɟɫɬɜɟɧɧɨ ɧɟ ɢɡɦɟɧɹɟɬɫɹ, ɬ. ɤ. ɩɭɥɶɫɚɰɢɹ
ɧɚɩɪɹɠɟɧɢɹ ɜ ɫɯɟɦɚɯ ɫɪɚɜɧɟɧɢɹ ɧɟɞɨɩɭɫɬɢɦɚ ɢ ɨɛɵɱɧɨ ɧɟ ɩɪɟɜɨɫɯɨɞɢɬ ɟɞɢɧɢɰ ɩɪɨɰɟɧɬɨɜ.
Ɋɚɫɫɦɨɬɪɢɦ ɩɪɨɰɟɫɫ ɡɚɪɹɞɚ ɤɨɧɞɟɧɫɚɬɨɪɚ ɜ ɧɟɫɤɨɥɶɤɨ
ɭɩɪɨɳɟɧɧɨɣ ɦɨɞɟɥɢ ɜɵɩɪɹɦɢɬɟɥɹ (ɪɢɫ. 2.2, ɚ).
Ɋɢɫ. 2.2
ɉɭɫɬɶ ɜ ɦɨɦɟɧɬ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɭɝɥɭ ș1, ɧɚ ɤɨɧɞɟɧɫɚɬɨɪɟ ɢɦɟɥɨɫɶ ɧɟɤɨɬɨɪɨɟ ɧɚɩɪɹɠɟɧɢɟ U0, ɪɚɜɧɨɟ ɧɚɩɪɹɠɟɧɢɸ ɧɚ ɜɯɨɞɟ ɜɵɩɪɹɦɢɬɟɥɹ. Ⱦɚɥɟɟ ɧɚɱɢɧɚɟɬɫɹ ɡɚɪɹɞ ɤɨɧɞɟɧɫɚɬɨɪɚ, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɟɪɟɤɥɸɱɟɧɢɸ ɤɥɸɱɚ K ɜ ɩɨɥɨɠɟɧɢɟ 1. ȼ ɦɨɦɟɧɬ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɭɝɥɭ ș
, ɡɚɪɹɞ ɩɪɟɤɪɚ-
2
ɬɢɬɫɹ ɢ ɤɥɸɱ ɡɚɣɦɟɬ ɩɨɥɨɠɟɧɢɟ 2.
47
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɯɨɞɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɧɚɩɪɹɠɟɧɢɹ
ɧɚ ɤɨɧɞɟɧɫɚɬɨɪɟ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɩɟɪɜɨɣ ɮɨɪɦɨɣ ɡɚɩɢɫɢ ɢɧɬɟɝɪɚɥɚ Ⱦɸɚɦɟɥɹ (1.81)
ᇱ
ሺɅሻ
ݑ
= ݑ
ሺ0ሻ ݄ሺɅሻ
+ න
݀ݑሺɒ
݀ɒ
ሻ
݄ሺɅെɒሻ݀ɒ
,
(2.1)
ɝɞɟ h(ș), h(ș – IJ) – ɩɟɪɟɯɨɞɧɵɟ ɮɭɧɤɰɢɢ ɩɪɢ ɟɞɢɧɢɱɧɨɦ
ɫɤɚɱɤɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɰɟɩɢ; u(0) – ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɜɯɨɞɟ ɜɵɩɪɹɦɢɬɟɥɹ ɜ ɦɨɦɟɧɬ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ
ɭɝɥɭ ș1.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɜ ɥɟɜɨɣ ɱɚɫɬɢ ɫɨɨɬɧɨɲɟɧɢɹ (2.1) ɩɪɢɫɭɬɫɬɜɭɟɬ ɫɥɚɝɚɟɦɨɟ, ɭɱɢɬɵɜɚɸɳɟɟ ɫɤɚɱɨɤ ɩɪɢɥɨɠɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ.
ɇɚ ɜɯɨɞɟ ɜɵɩɪɹɦɢɬɟɥɹ ɞɟɣɫɬɜɭɟɬ ɧɚɩɪɹɠɟɧɢɟ
ݑሺɒሻ= ܷ
ሺ
sin
ɒ+ Ʌ
ሻ
,
ଵ
(2.2)
ɝɞɟ Um – ɚɦɩɥɢɬɭɞɧɨɟ ɡɧɚɱɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ.
Ɍɨɝɞɚ, ɩɪɨɢɡɜɨɞɧɚɹ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢɧɢɦɚɟɬ ɜɢɞ
ሻ
݀ݑሺɒ
݀ɒ
= ܷ
ሺ
cos
ɒ+ Ʌ
(2.3)
ሻ
.
ଵ
ɉɟɪɟɯɨɞɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɪɢ ɟɞɢɧɢɱɧɨɦ ɫɤɚɱɤɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɜɯɨɞɟ ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɚ ɩɭɬɟɦ ɪɟɲɟɧɢɹ ɫɥɟɞɭɸɳɟɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɧɚɩɪɹɠɟɧɢɹ
48
ሺݐሻ
݀ݑ
ܥή
ܴ
ଵ
݀ݐ
+ ݑ
ሺݐሻ
= ܪሺݐ
(2.4)
ሻ
.
ɉɪɢɦɟɧɹɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ Ʌɚɩɥɚɫɚ, ɩɨɥɭɱɚɟɦ
1
ଵܥݑ
ሺሻ
ܴ
+ ݑ
ሺሻ
=
.
(2.5)
ɂɡɨɛɪɚɠɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɤɨɧɞɟɧɫɚɬɨɪɟ
ݑ
=
ή
ܴଵܥ
ሺሻ
1
ቀ+
1
,
(2.6)
1
ቁ
ܥ
ܴ
ଵ
ɨɬɤɭɞɚ
௧
ି
ሺݐሻ
=1െ݁
ݑ
ோభ
,
(2.7)
ɢɥɢ
ሺɅሻ
ݑ
=1െ݁
ି
னோభ
.
(2.8)
Ɍɨɝɞɚ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɟɪɟɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫ ɪɟɚɤɰɢɟɣ ɜ ɜɢɞɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɤɨɧɞɟɧɫɚɬɨɪɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ
ሼɅሽ
݄
௨௨
= ൫1 െ݁
ିஔ
൯ܪሺɅ
ሻ
,
(2.9)
ɝɞɟ
Ɂ=
ɘܴଵܥ
1
=
2Ɏܴଵܥ
ܶ
.
(2.10)
49
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɮɭɧɤɰɢɸ h(ș – IJ), ɜɵɪɚɠɚɸɳɭɸ ɫɬɭɩɟɧ-
ܣ
ܣ
ܣ
ɱɚɬɭɸ ɩɟɪɟɯɨɞɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɜ (2.1), ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
ሺ
Ʌെɒሻ=1െ݁
݄
ିஔሺିத
ሻ
.
(2.11)
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ
ᇱ
ሺɅሻ
ݑ
= ܷsin Ʌଵ൫1 െ݁
+ܷනcosሺɒ+ Ʌ
ሻ
ଵ
ൣ1 െ݁
ିஔ
ିஔሺିத
൯+
ሻ
൧݀߬
(2.12)
,
ɨɬɤɭɞɚ, ɩɪɨɞɟɥɚɜ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ, ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɪɟɲɟɧɢɟ
ᇱ
ሺɅሻ
ݑ
= ܷ
+
ሾ
ሺ
sin
ሺ
Ʌ+ Ʌ
ሺ
sin
Ʌଵ+ ɔሻെsin Ʌ
ሻ
െ
ଵ
ሺ
sin
Ʌ+ Ʌଵ+ ɔ
ሻ
݁
ଵ
ିஔ
ሻ
+
൧,
(2.13)
ɝɞɟ
1
=
1+Ɂ
ξ
;
ଶ
(2.14)
ɔ=tanିଵɁ;
(2.15)
ܷ
=sin
ିଵ
.
(2.16)
ܷ
Ʌ
ଵ
50
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