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Ⱥ. ɂ. ɏɢɬɪɨɜ, Ⱥ. Ⱥ. ɏɢɬɪɨɜ
ɈȻɓȿɉɊɈɆɕɒɅȿɇɇɕȿ
ȺɋɂɇɏɊɈɇɇɕȿ ɗɅȿɄɌɊɈȾȼɂȽȺɌȿɅɂ
ɋ ɄɈɊɈɌɄɈɁȺɆɄɇɍɌɕɆ ɊɈɌɈɊɈɆ
ɋɩɪɚɜɨɱɧɢɤ
2-ɟ ɢɡɞɚɧɢɟ, ɩɟɪɟɪɚɛɨɬɚɧɧɨɟ ɢ ɞɨɩɨɥɧɟɧɧɨɟ
Ɇɨɫɤɜɚ ȼɨɥɨɝɞɚ
«ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ»
2024
ɍȾɄ 621.313.333.2
ȻȻɄ 31.261.63
ɏ52
ɡɚɫɥɭɠɟɧɧɵɣ ɪɚɛɨɬɧɢɤ ɜɵɫɲɟɣ ɲɤɨɥɵ ɊɎ, ɞ. ɬ. ɧ., ɩɪɨɮɟɫɫɨɪ ɂɧɫɬɢɬɭɬɚ ɷɧɟɪɝɟɬɢɤɢ
ɋɚɧɤɬ-ɉɟɬɟɪɛɭɪɝɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ ɉɟɬɪɚ ȼɟɥɢɤɨɝɨ ȼ. ɇ. Ɂɚɛɨɢɧ;
ɤ. ɬ. ɧ., ɞɨɰɟɧɬ ɂɧɫɬɢɬɭɬɚ ɷɧɟɪɝɟɬɢɤɢ ɋɚɧɤɬ-ɉɟɬɟɪɛɭɪɝɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ
Ɋɟɰɟɧɡɟɧɬɵ:
ɉɟɬɪɚ ȼɟɥɢɤɨɝɨ ȼ. ȼ. ɋɭɯɚɧɨɜ
ɏɢɬɪɨɜ, Ⱥ. ɂ.
ɏ52 Ɉɛɳɟɩɪɨɦɵɲɥɟɧɧɵɟ ɚɫɢɧɯɪɨɧɧɵɟ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɢ ɫ ɤɨɪɨɬɤɨɡɚ-
ɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ : ɫɩɪɚɜɨɱɧɢɤ / Ⱥ. ɂ. ɏɢɬɪɨɜ. Ⱥ. Ⱥ. ɏɢɬɪɨɜ. – 2-ɟ ɢɡɞ.,
ɩɟɪɟɪɚɛ. ɢ ɞɨɩ. – Ɇɨɫɤɜɚ ; ȼɨɥɨɝɞɚ : ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ, 2024. – 104 ɫ. : ɢɥ.,
ɬɚɛɥ.
ISBN 978-5-9729-2052-5
ɉɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɧɚɛɨɪ ɫɜɟɞɟɧɢɣ ɩɨ ɩɚɪɚɦɟɬɪɚɦ ɚɫɢɧɯɪɨɧɧɵɯ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɣ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ. Ɉɫɧɨɜɭ ɫɩɪɚɜɨɱɧɢɤɚ ɫɨɫɬɚɜɥɹɸɬ ɞɜɢɝɚɬɟɥɢ ɫɟɪɢɢ 4Ⱥ.
ɐɢɮɪɨɜɵɟ ɞɚɧɧɵɟ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɢ ɩɪɨɜɟɞɟɧɢɢ ɪɚɫɱɺɬɨɜ, ɧɚɫɬɪɨɣɤɟ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɣ ɱɚɫɬɨɬɵ ɞɥɹ ɭɩɪɚɜɥɟɧɢɹ ɚɫɢɧɯɪɨɧɧɵɦɢ ɞɜɢɝɚɬɟɥɹɦɢ ɨɬɟɱɟɫɬɜɟɧɧɵɯ ɢ ɡɚɪɭɛɟɠɧɵɯ ɩɪɨɢɡɜɨɞɢɬɟɥɟɣ, ɩɪɢ ɫɨɫɬɚɜɥɟɧɢɢ ɦɨɞɟɥɟɣ ɜ ɫɪɟɞɚɯ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ.
Ⱦɥɹ ɫɬɭɞɟɧɬɨɜ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɞɝɨɬɨɜɤɢ 13.03.02 ɢ 13.04.02 «ɗɥɟɤɬɪɨɷɧɟɪɝɟɬɢɤɚ ɢ
ɷɥɟɤɬɪɨɬɟɯɧɢɤɚ».
ɍȾɄ 621.313.333.2
ȻȻɄ 31.261.63
ISBN 978-5-9729-2052-5 ɏɢɬɪɨɜ Ⱥ. ɂ., ɏɢɬɪɨɜ Ⱥ. Ⱥ., 2024
ɎȽȻɈɍ ȼɈ «ɉɫɤɨɜɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ», 2024
ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2024
Ɉɮɨɪɦɥɟɧɢɟ. ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2024
ɋɈȾȿɊɀȺɇɂȿ
ɉɊȿȾɂɋɅɈȼɂȿ
........................................................................................................................... 5
ȼȼȿȾȿɇɂȿ ..................................................................................................................................... 7
1. ɆȿɌɈȾɂɄȺ ɊȺɋɑ ȿɌȺ ȺȻɋɈɅɘɌɇɕɏ ɉȺɊȺɆȿɌɊɈȼ
ɗɅȿɄɌɊɈɆȿɏȺɇɂɑȿɋɄɈɃ ɆɈȾȿɅɂ ȺɋɂɇɏɊɈɇɇɕɏ
ɆȺɒɂɇ
......................................................................................................................................... 17
2. ɌȺȻɅɂɐɕ ɉȺɊȺɆȿɌɊɈȼ ȺȾ ........................................................................................ 21
2.1. Ɍɚɛɥɢɰɵ ɫɩɪɚɜɨɱɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɫɟɪɢɣ ȺȾ ................................................... 21
2.2. Ɋɚɫɱɟɬɧɵɟ ɬɚɛɥɢɰɵ ɛɚɡɨɜɵɯ ɩɚɪɚɦɟɬɪɨɜ ȺȾ ɫɟɪɢɢ 4Ⱥ ................................. 30
2.2.1. Ȼɚɡɨɜɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ
ɫɟɪɢɢ 4A ɫ p = 1 ......................................................................................................... 30
2.2.2. Ɋɚɫɱɟɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ 4A ɫ p = 1 ........................ 31
2.2.3. Ȼɚɡɨɜɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ
ɫɟɪɢɢ 4A c p = 2 ......................................................................................................... 36
2.2.4. Ɋɚɫɱɟɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ 4A ɫ p = 2 ........................ 37
2.2.5. Ȼɚɡɨɜɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ
ɫɟɪɢɢ 4A c p = 3 ......................................................................................................... 41
2.2.6. Ɋɚɫɱɟɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ 4A ɫ p = 3 ........................ 42
2.2.7. Ȼɚɡɨɜɵɟ ɩɚɪɚɦɟɬɪɵ
ɚɫɢɧɯɪɨɧɧɵɯ
ɞɜɢɝɚɬɟɥɟɣ
ɫɟɪɢɢ 4A c p = 4 ......................................................................................................... 46
2.2.8. Ɋɚɫɱɟɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ 4A ɫ p = 4 ........................ 47
2.3. Ɋɚɫɱɟɬɧɵɟ ɬɚɛɥɢɰɵ ɛɚɡɨɜɵɯ ɚɛɫɨɥɸɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ
T- ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ȺȾ
ɫɟɪɢɢ 4A ..................................................................................................................... 52
2.3.1. Ɋɚɫɱɟɬɧɵɟ ɚɛɫɨɥɸɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ
4A ɫ p = 1 .................................................................................................................... 52
2.3.2. Ɋɚɫɱɟɬɧɵɟ ɚɛɫɨɥɸɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ
4A c p = 2 .................................................................................................................... 58
2.3.3. Ɋɚɫɱɟɬɧɵɟ ɚɛɫɨɥɸɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ
4A c p = 3 .................................................................................................................... 64
2.3.4. Ɋɚɫɱɟɬɧɵɟ ɚɛɫɨɥɸɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ
4A c p = 4 .................................................................................................................... 70
3. ɉɊɂɆȿɊɕ ɊȺɋɑȿɌɈȼ ɋ
ȾȺɇɇɕɏ ɋɉɊȺȼɈɑɇɂɄȺ
ɂɋɉɈɅɖɁɈȼȺɇɂȿɆ ɐɂɎɊɈȼɕɏ
................................................................................................... 76
3.1. Ɋɚɫɱɟɬ ɩɚɪɚɦɟɬɪɨɜ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ, ɩɨɫɬɨɹɧɧɵɯ
ɢ ɩɟɪɟɦɟɧɧɵɯ ɩɨɬɟɪɶ
................................................................................................................. 76
3
3.2. Ɋɚɫɱɟɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ȺȾɄɊ ɩɪɢ ɫɤɚɥɹɪɧɨɦ
ɱɚɫɬɨɬɧɨɦ ɭɩɪɚɜɥɟɧɢɢ
............................................................................................................... 83
3.2.1. Ɋɚɫɱɟɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɱɚɫɬɨɬɧɨɦ
ɭɩɪɚɜɥɟɧɢɢ ɩɨ ɭɩɪɨɳɟɧɧɨɣ ɦɟɬɨɞɢɤɟ
................................................................................. 84
3.2.2. Ɋɚɫɱɟɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɱɚɫɬɨɬɧɨɦ
ɭɩɪɚɜɥɟɧɢɢ ɩɨ ɭɬɨɱɧɟɧɧɨɣ ɮɨɪɦɭɥɟ Ʉɥɨɫɫɚ
.................................................................... 86
3.3. Ɋɚɫɱɟɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɱɚɫɬɨɬɧɨɦ
ɭɩɪɚɜɥɟɧɢɢ ɩɨ ɦɟɬɨɞɢɤɟ Ƚ.Ƚ. ɋɨɤɨɥɨɜɫɤɨɝɨ
....................................................................... 90
3.4. Ɋɚɫɱɟɬ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɪɟɨɫɬɚɬɧɨɦ
ɩɭɫɤɟ ȺȾɄɊ
................................................................................................................................... 96
ɁȺɄɅɘɑȿɇɂȿ ............................................................................................................................ 99
ɅɂɌȿɊȺɌɍɊȺ ............................................................................................................................. 100
ȾɅə ɁȺɆȿɌɈɄ ......................................................................................................................... 102
4
ɉɊȿȾɂɋɅɈȼɂȿ
ɋɩɪɚɜɨɱɧɵɟ ɞɚɧɧɵɟ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɜ ɞɚɧɧɨɦ ɩɨɫɨɛɢɢ, ɩɪɟɞɧɚɡɧɚɱɟɧɵ
ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɞɝɨɬɨɜɤɢ 13.03.02 ɢ 13.04.02 «ɗɥɟɤɬɪɨɷɧɟɪɝɟɬɢɤɚ
ɢ ɷɥɟɤɬɪɨɬɟɯɧɢɤɚ», ɢɡɭɱɚɸɳɢɯ ɚɫɢɧɯɪɨɧɧɵɟ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɦɚɲɢɧɵ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɢ ɢɯ ɩɪɢɦɟɧɟɧɢɟ.
Ⱦɚɧɧɵɟ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɜ ɩɨɫɨɛɢɢ, ɩɨɡɜɨɥɹɸɬ ɧɚɣɬɢ ɩɚɪɚɦɟɬɪɵ ɦɨɞɟɥɟɣ
ɚɫɢɧɯɪɨɧɧɵɯ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɣ (ȺȾ), ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɪɚɫɱɟɬɚ ɢɯ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɫɩɨɫɨɛɧɵɟ ɭɩɪɨɫɬɢɬɶ ɧɚɫɬɪɨɣɤɭ ɱɚɫɬɨɬɧɨ-ɪɟɝɭɥɢɪɭɟɦɵɯ ɷɥɟɤɬɪɨɩɪɢɜɨɞɨɜ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ.
Ɇɟɬɨɞɢɤɚ ɪɚɫɱɟɬɚ ɩɚɪɚɦɟɬɪɨɜ ɢ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɫɨɨɬɧɨɲɟ-
ɧɢɹ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɞɚɧɧɨɦ ɩɨɫɨɛɢɢ.
Ɉɞɧɚɤɨ ɬɨɬ, ɤɨɦɭ ɧɟɨɛɯɨɞɢɦɵ ɬɨɥɶɤɨ ɞɚɧɧɵɟ, ɦɨɠɟɬ ɩɪɨɫɬɨ ɢɯ ɧɚɣɬɢ ɜ ɫɨ-
ɨɬɜɟɬɫɬɜɭɸɳɟɣ ɬɚɛɥɢɰɟ ɢ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɨ ɧɚɡɧɚɱɟɧɢɸ.
ȼɵɪɚɠɚɸ ɫɜɨɸ ɢɫɤɪɟɧɧɸɸ ɛɥɚɝɨɞɚɪɧɨɫɬɶ ɜɫɟɦ, ɤɬɨ ɩɪɢɧɹɥ ɭɱɚɫɬɢɟ ɜ
ɩɪɨɜɟɞɟɧɢɢ ɪɚɫɱɟɬɨɜ ɢ ɜɟɪɢɮɢɤɚɰɢɢ ɩɨɥɭɱɟɧɧɵɯ ɞɚɧɧɵɯ.
Ɉɫɨɛɭɸ
ɛɥɚɝɨɞɚɪɧɨɫɬɶ ɜɵɪɚɠɚɸ ɭɜɚɠɚɟɦɵɦ ɪɟɰɟɧɡɟɧɬɚɦ. Ɋɟɰɟɧɡɢɹ
ȼ.ȼ. ɋɭɯɚɧɨɜɚ ɧɚ ɞɚɧɧɨɟ ɦɟɬɨɞɢɱɟɫɤɨɟ ɩɨɫɨɛɢɟ ɛɵɥɚ ɩɨɫɥɟɞɧɟɣ ɟɝɨ ɭɱɟɛɧɨɦɟɬɨɞɢɱɟɫɤɨɣ ɪɚɛɨɬɨɣ.
ɉɟɪɜɨɟ ɢɡɞɚɧɢɟ ɩɨɫɨɛɢɹ ɜɵɲɥɨ ɜ ɫɜɟɬ ɜ 2021 ɝɨɞɭ ɢ ɩɨɫɜɹɳɚɥɨɫɶ ɫɬɨɥɟɬɢɸ ɢɡɞɚɧɢɹ «Ɍɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɬɚɛɥɢɰ» (ɜɩɟɪɜɵɟ ɢɡɞɚɧɵ ɜ
1921 ɝɨɞɭ) ɫɨɜɟɬɫɤɢɦ ɦɚɬɟɦɚɬɢɤɨɦ, ɱɥɟɧɨɦ-ɤɨɪɪɟɫɩɨɧɞɟɧɬɨɦ Ⱥɉɇ ɋɋɋɊ, ɭɪɨɠɟɧɰɟɦ ɝ. ɉɫɤɨɜɚ ȼɥɚɞɢɦɢɪɨɦ Ɇɨɞɟɫɬɨɜɢɱɟɦ
Ȼɪɚɞɢɫɨɦ (23.12.1890 – 23.05.1975).
ȼ.Ɇ. Ȼɪɚɞɢɫ ɭɱɢɥɫɹ ɜ ɉɫɤɨɜɫɤɨɣ ɝɢɦɧɚɡɢɢ,
ɛɵɥ ɢɫɤɥɸɱɟɧ ɜ 1907 ɝɨɞɭ ɡɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ
ɧɟɥɟɝɚɥɶɧɨɣ ɥɢɬɟɪɚɬɭɪɵ, ɛɵɥ ɫɨɫɥɚɧ ɜ ɋɢɛɢɪɶ ɜ
Ɍɨɛɨɥɶɫɤɭɸ ɝɭɛɟɪɧɢɸ ɜ 1909 ɝɨɞɭ ɧɚ 3 ɝɨɞɚ.
ȼ 1915 ɝɨɞɭ ɨɤɨɧɱɢɥ ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɣ ɮɚɤɭɥɶɬɟɬ ɋɚɧɤɬ-ɉɟɬɟɪɛɭɪɝɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ.
ȼ 1921 ɝɨɞɭ ɜɩɟɪɜɵɟ ɜɵɲɟɥ ɟɝɨ ɬɪɭɞ
«Ɍɚɛɥɢɰɵ ɱɟɬɵɪɟɯɡɧɚɱɧɵɯ ɥɨɝɚɪɢɮɦɨɜ ɢ ɧɚɬɭɪɚɥɶɧɵɯ
ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ
ɜɟɥɢɱɢɧ», ɩɨɡɞɧɟɟ «ɑɟɬɵɪɟɯɡɧɚɱɧɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɬɚɛɥɢɰɵ»
(1928 ɝ.).
Ⱦɚɧɧɨɟ ɢɡɞɚɧɢɟ ɫɩɪɚɜɨɱɧɨɝɨ ɩɨɫɨɛɢɹ ɩɨ
ɩɚɪɚɦɟɬɪɚɦ ɚɫɢɧɯɪɨɧɧɵɯ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɣ ɫ
ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ (ȺȾɄɊ) ɹɜɥɹɟɬɫɹ
ɜɬɨɪɵɦ – ɩɟɪɟɪɚɛɨɬɚɧɧɵɦ ɢ ɞɨɩɨɥɧɟɧɧɵɦ, ɜ ɤɨɬɨɪɨɦ ɭɬɨɱɧɟɧɵ ɧɟɤɨɬɨɪɵɟ ɰɢɮɪɨɜɵɟ ɞɚɧɧɵɟ,
5
ɢɫɤɥɸɱɟɧ ɪɹɞ ɢɡɛɵɬɨɱɧɵɯ ɩɨ ɦɧɟɧɢɸ ɚɜɬɨɪɨɜ ɬɚɛɥɢɰ, ɚ ɬɚɤɠɟ ɞɨɛɚɜɥɟɧɚ ɝɥɚɜɚ 3,
ɜɤɥɸɱɚɸɳɚɹ ɩɪɢɦɟɪɵ ɪɚɫɱɟɬɨɜ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɰɢɮɪɨɜɵɯ ɞɚɧɧɵɯ ɞɚɧɧɨɝɨ
ɫɩɪɚɜɨɱɧɢɤɚ:
ɉɚɪɚɦɟɬɪɵ Ɍ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ;
Ɉɩɪɟɞɟɥɟɧɢɟ ɩɨɫɬɨɹɧɧɵɯ ɢ ɩɟɪɟɦɟɧɧɵɯ ɩɨɬɟɪɶ ȺȾɄɊ;
Ɋɚɫɱɟɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ȺȾɄɊ ɩɪɢ
ɪɟɨɫɬɚɬɧɨɦ ɩɭɫɤɟ ɢ ɩɪɢ ɱɚɫɬɨɬɧɨɦ ɭɩɪɚɜɥɟɧɢɢ.
6
ȼȼȿȾȿɇɂȿ
ɗɥɟɤɬɪɨɩɪɢɜɨɞ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɧɚ ɨɫɧɨɜɟ ɚɫɢɧɯɪɨɧɧɵɯ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɣ (ȺȾ) ɫ ɭɩɪɚɜɥɹɟɦɵɦɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹɦɢ ɱɚɫɬɨɬɵ (ɉɑ) ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ
ɹɜɥɹɟɬɫɹ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦ [1].
ɉɪɨɢɡɜɨɞɢɬɟɥɹɦɢ ɉɑ ɹɜɥɹɸɬɫɹ ɜɟɞɭɳɢɟ ɷɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɢɟ ɮɢɪɦɵ:
ABB (ɒɜɟɰɢɹ, ɒɜɟɣɰɚɪɢɹ), Control Techniques (Ⱥɧɝɥɢɹ), Delta Electronics (Ɍɚɣɜɚɧɶ), Emotron (ɒɜɟɰɢɹ), Fuji Electric (əɩɨɧɢɹ), Hitachi (əɩɨɧɢɹ), KEB (Ƚɟɪɦɚɧɢɹ), Leroy Somer (Ɏɪɚɧɰɢɹ), Mitsubishi Electric (əɩɨɧɢɹ), Omron (əɩɨɧɢɹ),
Prostar (Ʉɢɬɚɣ), Sɫhneider Electric (Ɏɪɚɧɰɢɹ), Siemens (Ƚɟɪɦɚɧɢɹ) ɢ ɞɪ.
ȼ Ɋɨɫɫɢɢ ɩɪɨɢɡɜɨɞɹɬɫɹ ɉɑ ɫ
ɦɚɪɤɚɦɢ «ȼɟɫɩɟɪ», «Ɉɜɟɧ», «Ʉɗɍ», «ɍɧɢ-
ɜɟɪɫɚɥ», «ɉɑȺ», «ɋɚɩɮɢɪ» ɢ ɪɹɞ ɞɪɭɝɢɯ.
Ɂɧɚɧɢɟ ɚɛɫɨɥɸɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ȺȾ ɪɚɡɥɢɱɧɵɯ ɫɟɪɢɣ ɨɬɟɱɟɫɬɜɟɧɧɵɯ ɢ ɡɚɪɭɛɟɠɧɵɯ ɩɪɨɢɡɜɨɞɢɬɟɥɟɣ ɞɥɹ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɩɪɨɰɟɞɭɪ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɢɧɚɦɢɱɟɫɤɢɯ ɪɟɠɢɦɨɜ, ɧɚɫɬɪɨɣɤɢ ɩɚɪɚɦɟɬɪɨɜ ɪɟɝɭɥɹɬɨɪɨɜ ɤɨɨɪɞɢɧɚɬ ɜ ɫɢɫɬɟɦɚɯ
ɜɟɤɬɨɪɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ȺȾ ɧɟɨɛɯɨɞɢɦɨ. ɇɨ ɬɚɤɢɟ ɩɚɪɚɦɟɬɪɵ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ
ɩɪɟɞɨɫɬɚɜɥɹɸɬɫɹ ɡɚɜɨɞɚɦɢ-ɢɡɝɨɬɨɜɢɬɟɥɹɦɢ. ɉɪɢɜɨɞɢɦɵɯ ɜ
ɤɚɬɚɥɨɝɟ ȺȾ ɞɚɧɧɵɯ
ɨɛɵɱɧɨ ɧɟɞɨɫɬɚɬɨɱɧɨ, ɱɬɨɛɵ ɩɨ ɧɢɦ ɨɩɪɟɞɟɥɢɬɶ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɩɚɪɚɦɟɬɪɵ.
Ʉ ɬɚɤɢɦ ɩɚɪɚɦɟɬɪɚɦ ɦɨɠɧɨ ɨɬɧɟɫɬɢ:
ɤɪɢɬɢɱɟɫɤɨɟ ɫɤɨɥɶɠɟɧɢɟ – S
ɝɥɚɜɧɨɟ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ – ɏ
[%];
k
[Ɉɦ];
m
ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɦɨɬɤɢ ɫɬɚɬɨɪɚ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ – R
[Ɉɦ];
ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɫɫɟɹɧɢɹ ɨɛɦɨɬɤɢ ɫɬɚɬɨɪɚ ɜ ɧɨɦɢɧɚɥɶɧɨɦ
ɪɟɠɢɦɟ – X
[Ɉɦ];
sq
ɩɪɢɜɟɞɟɧɧɨɟ ɤ ɨɛɦɨɬɤɟ ɫɬɚɬɨɪɚ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɦɨɬɤɢ ɪɨɬɨ-
ɪɚ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ – R
[Ɉɦ];
r
ɩɪɢɜɟɞɟɧɧɨɟ ɤ ɨɛɦɨɬɤɟ ɫɬɚɬɨɪɚ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɫɫɟɹɧɢɹ
ɨɛɦɨɬɤɢ ɪɨɬɨɪɚ ɜ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ – X
[Ɉɦ];
rq
ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɫɟɹɧɢɹ – Q;
ɢɧɞɭɤɬɢɜɧɨɫɬɢ ɤɨɧɬɭɪɚ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ – L
, ɫɬɚɬɨɪɚ – Ls, ɪɨɬɨɪɚ – Lr
m
[ɦȽɧ];
ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɭɸ ɩɨɫɬɨɹɧɧɭɸ ɜɪɟɦɟɧɢ – Ɍ
ɨɛɦɨɬɤɢ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ – Ɍ
, TR [ɦc] ɢ ɪɹɞ ɞɪɭɝɢɯ ɧɟɨɛɯɨɞɢɦɵɯ ɪɚɫɱɟɬɧɵɯ
S
ɢ ɩɨɫɬɨɹɧɧɵɟ ɜɪɟɦɟɧɢ
ɗ
ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ȺȾ.
ɉɪɨɦɵɲɥɟɧɧɨɫɬɶɸ Ɋɨɫɫɢɢ ɜɵɩɭɫɤɚɸɬɫɹ ȺȾ ɫ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɵɦ ɪɨɬɨɪɨɦ (ȺȾɄɊ) ɨɛɳɟɩɪɨɦɵɲɥɟɧɧɨɝɨ ɧɚɡɧɚɱɟɧɢɹ ɫɟɪɢɣ 4Ⱥ, ȺɂɊ, 5Ⱥ, 6Ⱥ, RA,
ȺȾɑɊ. Ⱦɨɫɬɨɜɟɪɧɨ ɢɡɜɟɫɬɧɵ ɬɨɥɶɤɨ ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ Ƚ-ɨɛɪɚɡɧɨɣ ɫɯɟ-
s
7
ɦɵ ɡɚɦɟɳɟɧɢɹ (ɋɁ) (ɪɢɫ. ȼ1) ɞɥɹ ɫɟɪɢɢ 4Ⱥ [2]. ȼ ɬɚɛɥɢɰɟ ȼ.1 ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟɤɨɬɨɪɵɟ ɛɚɡɨɜɵɟ ɩɚɪɚɦɟɬɪɵ ɨɬɟɱɟɫɬɜɟɧɧɵɯ ȺȾɄɊ.
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ ȼ.1
Ɉɬɟɱɟɫɬɜɟɧɧɵɟ ȺȾɄɊ
ȼɵɫɨɬɚ ɨɫɟɣ
ɋɟɪɢɹ
4Ⱥ 50–355 0,06–400
ȺɂɊ 50–355 0,19–315
5Ⱥ 71–355 0,37–400
6Ⱥ 315 90–200
RA 71–280 0,37–100
ȺȾɑɊ 56–355 0,18–250
ɜɪɚɳɟɧɢɹ
(ɦɦ)
Ⱦɢɚɩɚɡɨɧ
ɦɨɳɧɨɫɬɟɣ
(ɤȼɬ)
ɋɢɧɯɪɨɧɧɵɟ
ɱɚɫɬɨɬɵ
ɜɪɚɳɟɧɢɹ
(ɨɛ/ɦɢɧ)
500, 600, 750,
1000, 1500,
3000
750, 1000,
1500, 3000
750, 1000,
1500, 3000
750, 1000,
1500, 3000
750, 1000,
1500, 3000
750, 1000,
1500, 3000
ɇɨɦɢɧɚɥɶɧɵɟ
ɧɚɩɪɹɠɟɧɢɹ
(ȼ)
220/380
380/660
220/380
380/660
220/380
380/660
220/380
380/660
220/380
380/660
220/380
380/660
Ʉɨɷɮɮɢɰɢɟɧɬ
ɄɉȾ
(%)
50–94,5 0,60–0,92
53–94,5 0,61–0,93
60–95,6 0,62–0,93
92,2–93,7 0,83–0,92
48–92 0,70–0,89
ɇɟɬ
ɞɚɧɧɵɯ
ɦɨɳɧɨɫɬɢ
(ɨ.ɟ.)
0,60–0,93
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ ȼ.2
Ɂɚɪɭɛɟɠɧɵɟ ȺȾɄɊ
ɋɟɪɢɹ
M2
(ABB)
1LA
(Siemens)
LS, FLS
(Leroy
Somer)
TIK
(Toshiba)
ȼɵɫɨɬɚ
ɨɫɟɣ
ɜɪɚɳɟɧɢɹ
(ɦɦ)
56–400 0,055–630
56–160 0,06–18,5
56–450 0,09–750 320–4000 320–480 38–97 0,48–0,92
71–160 0,37–18,5
Ⱦɢɚɩɚɡɨɧ
ɦɨɳɧɨɫɬɟɣ
(ɤȼɬ)
ɋɢɧɯɪɨɧɧɵɟ
ɱɚɫɬɨɬɵ
ɜɪɚɳɟɧɢɹ
(ɨɛ/ɦɢɧ)
750, 1000,
1500, 3000
750, 1000,
1500, 3000
1000, 1500,
3000
ɇɨɦɢɧɚɥɶɧɵɟ
ɧɚɩɪɹɠɟɧɢɹ
(ȼ)
400 38–97 0,48–0,92
380 39–91 0,66–0,91
220, 380, 415 71–91 0,78–0,88
ɄɉȾ
(%)
Ʉɨɷɮɮɢɰɢɟɧɬ
ɦɨɳɧɨɫɬɢ
(ɨ.ɟ.)
8
ɉɪɨɜɟɞɟɧɧɵɣ ɚɧɚɥɢɡ ɩɚɫɩɨɪɬɧɵɯ ɞɚɧɧɵɯ ɫɟɪɢɣ ɨɬɟɱɟɫɬɜɟɧɧɵɯ ȺȾ – ȺɂɊ,
5Ⱥ, RA ɢ ɡɚɪɭɛɟɠɧɵɯ M2ɏɏeff2 (ɮɢɪɦɚ ABB), 1LXX (SIEMENS), FLSES IE2
(Leroy Somer) ɩɨɤɚɡɵɜɚɟɬ ɢɯ ɛɥɢɡɨɫɬɶ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɜ ɬɚɛɥɢɰɟ ȼ.3 ɞɥɹ 4 ɬɢɩɨ-
ɪɚɡɦɟɪɨɜ.
ɋɭɳɟɫɬɜɭɸɳɢɟ ɦɟɬɨɞɢɤɢ ɪɚɫɱɟɬɚ ɚɛɫɨɥɸɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ȺȾ ɧɚ ɨɫɧɨɜɟ
ɩɚɫɩɨɪɬɧɵɯ ɞɚɧɧɵɯ ɢɧɨɝɞɚ ɞɚɸɬ ɩɪɨɬɢɜɨɪɟɱɢɜɵɟ ɡɧɚɱɟɧɢɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɧɵɯ
ɩɚɪɚɦɟɬɪɨɜ [3–9]. ȼ [5], ɜ ɱɚɫɬɧɨɫɬɢ, ɭɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɫɭɳɟɫɬɜɭɸɳɢɟ ɦɟɬɨɞɢɤɢ
ɪɚɫɱɟɬɚ
ɩɚɪɚɦɟɬɪɨɜ
ɋɁ ȺȾ ɧɟ ɢɦɟɸɬ ɨɞɧɨɡɧɚɱɧɨɝɨ ɪɟɲɟɧɢɹ, ɥɢɛɨ ɝɪɨɦɨɡɞɤɢ,
ɢɥɢ ɪɟɲɚɸɬ ɡɚɞɚɱɭ ɫ ɛɨɥɶɲɨɣ ɩɨɝɪɟɲɧɨɫɬɶɸ ɞɥɹ ɨɬɞɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ.
Ɋɢɫɭɧɨɤ ȼ1. Ƚ-ɨɛɪɚɡɧɚɹ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ȺȾ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ ȼ.3
Ȼɚɡɨɜɵɟ ɩɚɪɚɦɟɬɪɵ ɚɫɢɧɯɪɨɧɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɫɟɪɢɣ 4Ⱥ, ȺɂɊ, RA, 5A,
M2XXeff2 (ABB), 1LXx (Siemens), FLSES IE2 (Leroy Somer).
ɋɢɧɯɪɨɧɧɚɹ ɫɤɨɪɨɫɬɶ 3000 ɨɛ/ɦɢɧ
ʋ Ɍɂɉ ȺȾ Ɋ
4Ⱥ100S2
ȺɂɊ100S2
1
RA112M2
M2AA112M
1LA6112M
FLSES112M
4Ⱥ100L2
ȺɂɊ100L2
2
RA132SA2
M2AA132SA
1LA6132S
FLSES132S
ɤȼɬ ɄɉȾ ɫosij n
2ɧ,
0,89
0,88
0,80
0,91
0,86
0,91
0,91
0,89
0,89
0,88
0,89
0,90
4,0
5,5
0,865
0,87
0,84
0,86
0,86
0,867
0,875
0,88
0,89
0,86
0,865
0,881
9
K
ɧɨɦ
2880
2850
2895
2850
2905
2915
2880
2850
2880
2855
2925
2915
max
2,2
2,2
3,3
3,0
2,9
3,3
2,2
2,2
3,0
3,6
2,8
2,6
ʋ Ɍɂɉ ȺȾ Ɋ
4Ⱥ112M2
ȺɂɊ112M2
3
RA132SB2
M2AA132SB
1LA6132S
FLSES132S
Ɉ ɤ ɨ ɧ ɱ ɚ ɧ ɢ ɟ ɬ ɚ ɛ ɥ ɢ ɰ ɵ ȼ.3
ɤȼɬ ɄɉȾ ɫosij n
2ɧ,
0,88
0,88
0,89
0,90
0,89
0,91
7,5
0,875
0,875
0,89
0,87
0,88
0,881
K
ɧɨɦ
2900
2895
2890
2855
2929
2920
max
2,2
2,2
3,2
3,8
3,0
2,9
4Ⱥ132M2
ȺɂɊ132M2
4
RA160MA2
M2AA160MA
11,0
1LA6160M
FLSES160M
0,88
0,88
0,875
0,884
0,895
0,895
0,90
0,90
0,89
0,89
0,88
0,90
2900
2910
2940
2915
2940
2940
2,2
2,2
3,3
2,5
2,9
3,1
ȼ [2] ɩɪɟɞɫɬɚɜɥɟɧɵ ɫɜɟɞɟɧɢɹ ɨɛ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɚɯ Ƚ-ɨɛɪɚɡɧɨɣ
ɋɁ ɞɥɹ ȺȾ ɫɟɪɢɢ 4Ⱥ. ɗɬɚ ɩɭɛɥɢɤɚɰɢɹ ɭɧɢɤɚɥɶɧɚ ɬɟɦ, ɱɬɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ ɋɁ ȺȾ. ɉɪɢɧɢɦɚɹ ɝɢɩɨɬɟɡɭ, ɱɬɨ ɞɚɧɧɵɟ, ɩɪɢɜɟɞɟɧɧɵɟ ɜ ɧɟɣ
ɚɛɫɨɥɸɬɧɨ ɞɨɫɬɨɜɟɪɧɵ, ɛɵɥɢ ɩɪɨɜɟɞɟɧɵ ɪɚɫɱɟɬɵ ɛɚɡɨɜɵɯ ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ȺȾ (ɭɤɚɡɚɧɵ ɜɵɲɟ). ȼ ɞɚɧɧɨɦ ɩɨɫɨɛɢɢ ɪɚɫɱɟɬɵ ɩɪɟɞɫɬɚɜɥɟɧɵ
ɜ ɜɢɞɟ ɬɚɛɥɢɰ (ɩɨ ɤɨɬɨɪɵɦ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɢ ɝɪɚɮɢɤɢ).
ȼ ɬɚɛɥɢɰɟ ȼ.4 ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟɤɨɬɨɪɵɟ ɪɚɫɱɟɬɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɚɛɫɨɥɸɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ȺȾ ɫɟɪɢɢ 4Ⱥ. ȼ ɬɚɛɥɢɰɟ ȼ.4 ɭɤɚɡɵɜɚɸɬɫɹ ɡɧɚɱɟɧɢɹ ɞɥɹ ɦɨɳɧɨɫɬɟɣ ɨɬ 1,1 ɤȼɬ ɞɨ 200 ɤȼɬ ɢ ɱɢɫɥɚ ɩɚɪ ɩɨɥɸɫɨɜ 1, 2, 3, 4.
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ ȼ.4
ɉɚɪɚɦɟɬɪɵ ȺȾ ɫɟɪɢɢ 4
ʋ
ɩ/ɩ
1
Ⱥɛɫɨɥɸɬɧɵɣ ɩɚɪɚɦɟɬɪ ȺȾ
ɢ ɟɝɨ ɪɚɡɦɟɪɧɨɫɬɶ
ɇɨɦɢɧɚɥɶɧɚɹ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ – Ȧ
(ɪɚɞ/ɫ)
ɇɈɆ
Ⱥ
ɑɢɫɥɨ ɩɚɪ
ɩɨɥɸɫɨɜ
,
ɪ = 1
ɪ = 2
ɪ = 3
ɪ = 4
1,1 ɤȼɬ 200 ɤȼɬ
294,1
148,6
96,3
73,3
310,9
154,9
103,1
–
Ɇɨɞɭɥɶ ɠɟɫɬɤɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɨɣ
2
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚ ɥɢɧɟɣɧɨɦ
ɭɱɚɫɬɤɟ – G (ɇ ā ɦ/(ɪɚɞ/ɫ))
10
ɪ = 1
ɪ = 2
ɪ = 3
ɪ = 4
0,1993
0,9342
1,4456
3,103
212,19
657,94
1314,97
–
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