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Определение параметров тепловыделения по экспериментальной индикаторной диаграмме дизельного двигателя..pdf

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2. Ʉɨɪɨɥɟɜ ȼ. ɂ. Ɍɪɟɧɚɠɟɪɧɚɹ ɩɨɞɝɨɬɨɜɤɚ ɫɭɞɨɜɵɯ ɦɟɯɚɧɢɤɨɜ. Ɍɪɟɧɚɠɟɪɧɚɹ ɩɨɞɝɨɬɨɜɤɚ ɜɚɯɬɟɧɧɵɯ ɦɟɯɚɧɢɤɨɜ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɬɪɟɧɚɠɟɪɚ ɦɚɲɢɧɧɨɝɨ ɨɬɞɟɥɟɧɢɹ / ȼ. ɂ. Ʉɨɪɨɥɟɜ, Ⱥ. Ƚ. Ɍɚɪɚɧɢɧ. — ɇɨɜɨɪɨɫɫɢɣɫɤ: ɆȽȺ ɢɦ. ɚɞɦ. Ɏ. Ɏ. ɍɲɚɤɨɜɚ, 2011. — ɑ. 2. — 308 ɫ.
ȁDzǸ 621.436
ǹ. ǰ. ȀȡȕȜȐ,
Ȓ-Ȟ Ƞȓȣț. țȎȡȘ, ȝȞȜȢȓȟȟȜȞ,
DZȁǺǾȂ ȖȚȓțȖ ȎȒȚȖȞȎșȎ ǿ. Ǽ. ǺȎȘȎȞȜȐȎ
ɈɉɊȿȾȿɅȿɇɂȿ ɉȺɊȺɆȿɌɊɈȼ ɌȿɉɅɈȼɕȾȿɅȿɇɂə
ɉɈ ɗɄɋɉȿɊɂɆȿɇɌȺɅɖɇɈɃ ɂɇȾɂɄȺɌɈɊɇɈɃ ȾɂȺȽɊȺɆɆȿ
ȾɂɁȿɅɖɇɈȽɈ ȾȼɂȽȺɌȿɅə
DEFINITION OF PARAMETERS OF THE THERMAL EMISSION
UNDER THE EXPERIMENTAL DISPLAY DIAGRAM OF THE DIESEL ENGINE
Ɉɫɧɨɜɵɜɚɹɫɶ ɧɚ ɯɚɪɚɤɬɟɪɟ ɝɟɧɟɪɚɰɢɢ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ ɜ ɰɟɩɧɵɯ ɪɟɚɤɰɢɹɯ, ɩɪɨɰɟɫɫ ɫɝɨɪɚɧɢɹ ɨɩɢɫɚɧ ɫ ɩɨɦɨɳɶɸ ɤɢɧɟɬɢɤɢ ɰɟɩɧɵɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ, ɩɪɟɞɥɨɠɟɧɧɵɯ ɚɤɚɞɟɦɢɤɨɦ ɇ. ɇ. ɋɟɦɟɧɨɜɵɦ. ɂɫɩɨɥɶɡɭɹ
ɷɬɨɬ ɦɟɯɚɧɢɡɦ, ɜ ɫɬɚɬɶɟ ɩɪɢɜɨɞɢɬɫɹ ɦɟɬɨɞɢɤɚ ɨɩɪɟɞɟɥɟɧɢɹ ɨɫɧɨɜɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɝɨɪɚɧɢɹ: ɩɨɤɚɡɚɬɟɥɹ ɫɝɨɪɚɧɢɹ m ɢ ɭɫɥɨɜɧɨɣ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɫɝɨɪɚɧɢɹ ijz ɩɨ ɢɧɞɢɤɚɬɨɪɧɨɣ ɞɢɚɝɪɚɦɦɟ ɞɢɡɟɥɶɧɨɝɨ
ɞɜɢɝɚɬɟɥɹ.
Being based on character of generation of the active centers in chain reactions, combustion process is
described with the help of kinetics of the chain interactions, offered by academician N. N. Semenov. Using this
mechanism, article shows the technique of definition of the basic characteristics of combustion: an indicator of
combustion and conditional duration of combustion by the display diagram of the diesel engine.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɬɟɩɥɨɜɵɞɟɥɟɧɢɟ, ɢɧɞɢɤɚɬɨɪɧɚɹ ɞɢɚɝɪɚɦɦɚ, ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɫɝɨɪɚɧɢɹ.
Key words: thermal emission, the display diagram, duration of combustion.
Выпуск 2
ɂ
62
ɁȼȿɋɌɇɈ, ɱɬɨ ɫɝɨɪɚɧɢɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɥɢɛɨ ɤɢɧɟɬɢɱɟɫɤɢɦɢ ɩɪɨɰɟɫɫɚɦɢ, ɥɢɛɨ ɞɢɮɮɭɡɢɨɧɧɵɦɢ. ɋɝɨɪɚɧɢɟ ɜɨ ɜɫɟɯ ɟɝɨ ɮɚɡɚɯ ɹɜɥɹɟɬɫɹ ɤɨɦɩɥɟɤɫɨɦ ɫɥɨɠɧɵɯ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ
ɮɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ. ȼ ɨɫɧɨɜɟ ɷɬɨɝɨ ɤɨɦɩɥɟɤɫɚ ɥɟɠɢɬ ɯɢɦɢɱɟɫɤɚɹ ɪɟɚɤɰɢɹ
ɬɨɩɥɢɜɚ ɫ ɤɢɫɥɨɪɨɞɨɦ ɜɨɡɞɭɯɚ.
ɋɝɨɪɚɧɢɟ, ɤɚɤ ɪɟɡɭɥɶɬɚɬ ɷɤɡɨɬɟɪɦɢɱɟɫɤɨɣ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɨɫɬɵɦɢ ɬɟɪɦɨɯɢɦɢɱɟɫɤɢɦɢ ɭɪɚɜɧɟɧɢɹɦɢ, ɤɨɬɨɪɵɟ ɞɚɸɬ ɜɨɡɦɨɠɧɨɫɬɶ ɨɩɪɟɞɟɥɢɬɶ ɬɟɨɪɟɬɢɱɟɫɤɢ ɧɟɨɛɯɨɞɢɦɨɟ
ɤɨɥɢɱɟɫɬɜɨ ɜɨɡɞɭɯɚ ɞɥɹ ɫɝɨɪɚɧɢɹ ɡɚɞɚɧɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɬɨɩɥɢɜɚ, ɚ ɬɚɤɠɟ ɫɨɫɬɚɜ ɢ ɨɛɴɟɦ ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ. Ɉɞɧɚɤɨ ɷɬɢ ɭɪɚɜɧɟɧɢɹ ɧɟ ɞɚɸɬ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɞɢɧɚɦɢɤɟ ɩɪɨɰɟɫɫɚ ɫɝɨɪɚɧɢɹ.
ɉɪɨɰɟɫɫ ɫɝɨɪɚɧɢɹ ɦɨɠɟɬ ɛɵɬɶ ɨɩɢɫɚɧ, ɟɫɥɢ ɜ ɨɫɧɨɜɭ ɤɢɧɟɬɢɤɢ ɩɨɥɨɠɢɬɶ ɰɟɩɧɵɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ, ɩɪɟɞɥɨɠɟɧɧɵɟ ɚɤɚɞɟɦɢɤɨɦ ɇ. ɇ. ɋɟɦɟɧɨɜɵɦ. ȼ ɨɫɧɨɜɟ ɷɬɨɝɨ ɭɱɟɧɢɹ ɥɟɠɢɬ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨ ɬɨɦ, ɱɬɨ ɩɪɟɜɪɚɳɟɧɢɟ ɜɟɳɟɫɬɜ (ɬɨɩɥɢɜɨ ɢ ɤɢɫɥɨɪɨɞ ɜɨɡɞɭɯɚ) ɜ ɩɪɨɰɟɫɫɟ ɪɟɚɤɰɢɢ ɩɪɨɯɨɞɢɬ
ɱɟɪɟɡ ɪɹɞ ɫɬɚɞɢɣ, ɜ ɤɨɬɨɪɵɯ ɨɛɪɚɡɭɸɬɫɹ ɯɢɦɢɱɟɫɤɢ ɚɤɬɢɜɧɵɟ ɜɟɳɟɫɬɜɚ, ɢɧɬɟɧɫɢɜɧɨ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɟ ɤɚɤ ɫ ɢɫɯɨɞɧɵɦɢ ɜɟɳɟɫɬɜɚɦɢ, ɬɚɤ ɢ ɞɪɭɝ ɫ ɞɪɭɝɨɦ.
ɉɪɨɦɟɠɭɬɨɱɧɵɟ ɯɢɦɢɱɟɫɤɢ ɚɤɬɢɜɧɵɟ ɜɟɳɟɫɬɜɚ ɧɚɡɵɜɚɸɬɫɹ ɚɤɬɢɜɧɵɦɢ ɰɟɧɬɪɚɦɢ ɫ ɨɞɧɨɣ
ɢɥɢ ɞɜɭɦɹ ɫɜɨɛɨɞɧɵɦɢ ɜɚɥɟɧɬɧɨɫɬɹɦɢ. Ɉɫɧɨɜɵɜɚɹɫɶ ɧɚ ɯɚɪɚɤɬɟɪɟ ɝɟɧɟɪɚɰɢɢ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ ɜ
ɰɟɩɧɵɯ ɪɟɚɤɰɢɹɯ, ɨɱɟɜɢɞɧɨ, ɱɬɨ ɤɨɥɢɱɟɫɬɜɨ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ dn ɡɚ ɜɪɟɦɹ dt ɫɜɹɡɚɧɨ ɫ ɤɨɥɢɱɟɫɬɜɨɦ ɫɝɨɪɟɜɲɟɝɨ ɡɚ ɷɬɨ ɜɪɟɦɹ ɬɨɩɥɢɜɚ dM, ɬɨ ɟɫɬɶ dM = Kdn.
ɋɤɨɪɨɫɬɶ ɜɵɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ ɢ ɫɤɨɪɨɫɬɶ ɝɟɧɟɪɚɰɢɢ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ ɫɜɹɡɚɧɵ ɦɟɠɞɭ ɫɨɛɨɣ
ɡɚɜɢɫɢɦɨɫɬɶɸ
(1)
ɝɞɟ Ʉ — ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ.
Ɉɬɫɸɞɚ ɜɢɞɧɨ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɜɵɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɫɤɨɪɨɫɬɢ ɨɛɪɚɡɨɜɚɧɢɹ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ. ȼɜɟɞɟɦ ɩɨɧɹɬɢɟ «ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ»:
,
(2)
ɤɨɬɨɪɨɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɤɨɪɨɫɬɶ ɝɟɧɟɪɚɰɢɢ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ ɜ ɟɞɢɧɢɰɟ ɦɚɫɫɵ ɢɫɯɨɞɧɨɝɨ
ɬɨɩɥɢɜɚ. Ɉɬɧɨɫɢɬɟɥɶɧɨɟ ɢɡɦɟɧɟɧɢɟ ɦɚɫɫɵ ɬɨɩɥɢɜɚ ɩɪɢ ɟɝɨ ɫɝɨɪɚɧɢɢ ɫɜɹɡɚɧɨ ɫ ɨɬɧɨɫɢɬɟɥɶɧɨɣ
ɩɥɨɬɧɨɫɬɶɸ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ ɫɨɨɬɧɨɲɟɧɢɟɦ
(3)
ɇɚ ɪɢɫ. 1, ɚ ɩɪɢɜɟɞɟɧ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ ɫɤɨɪɨɫɬɢ ɫɝɨɪɚɧɢɹ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ, ɜɵɝɨɪɚɧɢɹ
ɦɚɫɫɵ ɬɨɩɥɢɜɚ — ɪɢɫ. 1, ɛ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɩɥɨɬɧɨɫɬɢ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ ɩɨ ɜɪɟɦɟɧɢ — ɪɢɫ. 1, ɜ —
ɜ ɤɚɦɟɪɟ ɫɝɨɪɚɧɢɹ ɞɜɢɝɚɬɟɥɹ.
Ɋɢɫ. 1. ɉɥɨɬɧɨɫɬɶ ɝɟɧɟɪɚɰɢɢ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ
Ⱥɧɚɥɢɡɢɪɭɹ ɩɪɢɜɟɞɟɧɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ, ɜɢɞɧɨ, ɱɬɨ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ (ɩɪɢ t = 0)
ɜɟɥɢɱɢɧɚ
ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɚ, ɚ ɢɫɯɨɞɧɚɹ ɦɚɫɫɚ ɜɟɥɢɤɚ, ɬɨ ɟɫɬɶ
. ȼ ɤɨɧɰɟ ɩɪɨɰɟɫɫɚ
ɫɝɨɪɚɧɢɹ ɬɨɩɥɢɜɨ ɭɠɟ ɢɡɪɚɫɯɨɞɨɜɚɧɨ, ɬɨ ɟɫɬɶ M ĺ 0, ɚ ɜɟɥɢɱɢɧɚ
ɟɳɟ ɧɟ ɪɚɜɧɚ ɧɭɥɸ (ɚɤɬɢɜ-
ɧɵɟ ɰɟɧɬɪɵ ɩɨɤɚ ɧɟ ɢɫɱɟɡɥɢ). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ t ĺ tmax ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɚɤɬɢɜɧɵɯ
Выпуск 2
ɰɟɧɬɪɨɜ
ĺ ’ ɪɟɡɤɨ ɜɨɡɪɚɫɬɚɟɬ.
63
Ɂɚɜɢɫɢɦɨɫɬɶ ȡ = f(t) ɦɨɠɟɬ ɛɵɬɶ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɧɚ ɜɵɪɚɠɟɧɢɟɦ
ȡ = ct ,
m
ɝɞɟ ɫ — ɦɧɨɠɢɬɟɥɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ, m — ɩɨɤɚɡɚɬɟɥɶ ɫɬɟɩɟɧɢ.
ȿɫɬɟɫɬɜɟɧɧɨ, ɱɬɨ ɫ ɢ m — ɷɦɩɢɪɢɱɟɫɤɢɟ ɤɨɷɮɮɢɰɢɟɧɬɵ.
ɉɨɞɫɬɚɜɥɹɹ ɜ ɭɪɚɜɧɟɧɢɟ (3) ɜɦɟɫɬɨ ȡ ɜɵɪɚɠɟɧɢɟ (4) ɩɨɥɭɱɢɦ
(4)
.
(5)
ɉɪɨɢɧɬɟɝɪɢɪɭɟɦ ɟɝɨ ɨɬ ɧɚɱɚɥɚ ɫɝɨɪɚɧɢɹ t = 0 ɞɨ ɬɟɤɭɳɟɝɨ ɦɨɦɟɧɬɚ ɜɪɟɦɟɧɢ t:
ɝɞɟ M0 — ɦɚɫɫɚ ɬɨɩɥɢɜɚ ɜ ɧɚɱɚɥɟ ɫɝɨɪɚɧɢɹ ɩɪɢ t = 0.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɨɥɭɱɢɦ
.
(6)
ɉɨɬɟɧɰɢɪɭɹ, ɩɨɥɭɱɚɟɦ
.
ȼɟɥɢɱɢɧɚ
ɱɬɨ
(7)
. Ɉɬɧɢɦɟɦ ɨɬ ɟɞɢɧɢɰɵ ɩɪɚɜɭɸ ɢ ɥɟɜɭɸ ɱɚɫɬɢ ɜɵɪɚɠɟɧɢɹ (7). ɂɦɟɹ ɜ ɜɢɞɭ,
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɨɬɧɨɫɢɬɟɥɶɧɭɸ ɞɨɥɸ ɫɝɨɪɟɜɲɟɝɨ ɬɨɩɥɢɜɚ ɤ ɦɨɦɟɧɬɭ
ɜɪɟɦɟɧɢ t, ɨɛɨɡɧɚɱɢɦ ɟɟ ɡɚ x, ɬɨɝɞɚ
.
(8)
Ɏɨɪɦɭɥɚ (8) ɨɩɢɫɵɜɚɟɬ ɞɢɧɚɦɢɤɭ ɫɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ ɜ ɞɜɢɝɚɬɟɥɟ. Ɉɞɧɚɤɨ ɩɪɚɤɬɢɱɟɫɤɨɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɟɟ ɡɚɬɪɭɞɧɟɧɨ ɢɡ-ɡɚ ɨɬɫɭɬɫɬɜɢɹ ɡɧɚɧɢɹ ɩɨɫɬɨɹɧɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ Ʉ ɢ ɫ.
ɉɪɟɨɛɪɚɡɭɟɦ ɷɬɭ ɮɨɪɦɭɥɭ ɩɪɢ ɭɫɥɨɜɢɢ t ĺ ’. ȼ ɷɬɨɦ ɫɥɭɱɚɟ x ĺ 1, ɬɨ ɟɫɬɶ ɬɨɩɥɢɜɨ ɩɨɥɧɨɫɬɶɸ ɜɵɝɨɪɚɟɬ, ɧɨ ɩɪɢ ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ ɞɥɢɬɟɥɶɧɨɫɬɢ ɩɪɨɰɟɫɫɚ tz ɬɨɩɥɢɜɨ ɜɵɝɨɪɚɟɬ ɜ ɤɨɥɢɱɟɫɬɜɟ
xz, ɤɨɬɨɪɨɟ ɜɫɟɝɞɚ ɧɟɫɤɨɥɶɤɨ ɦɟɧɶɲɟ ɟɞɢɧɢɰɵ.
ɉɟɪɟɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ (8) ɞɥɹ ɞɜɭɯ ɦɨɦɟɧɬɨɜ ɜɪɟɦɟɧɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵɯ t ɢ tz:
,
(9)
.
Ʌɨɝɚɪɢɮɦɢɪɭɹ ɟɝɨ ɢ ɩɨɱɥɟɧɧɨ ɞɟɥɹ ɪɟɡɭɥɶɬɚɬ, ɩɨɥɭɱɢɦ
.
(10)
Выпуск 2
ɍɪɚɜɧɟɧɢɟ (8) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɪɨɰɟɫɫ ɜɵɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ ɧɨɫɢɬ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɣ ɯɚɪɚɤɬɟɪ. ɉɭɫɬɶ tz ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɟɥɢɱɢɧɟ xz = 0,999, ɬɨɝɞɚ: ln(1 – xz ) = ln(1 – 0,999) = –6,908.
64
ɉɨɞɫɬɚɜɥɹɹ ɜ ɜɵɪɚɠɟɧɢɟ (10) ɜɦɟɫɬɨ ln(1 x z ) ɢ ɩɨɬɟɧɰɢɪɭɹ ɪɟɡɭɥɶɬɚɬ, ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ
,
(11)
ɩɨɥɭɱɟɧɧɨɟ ɩɪɨɮɟɫɫɨɪɨɦ ɂ. ɂ. ȼɢɛɟ ɞɥɹ ɜɵɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ ɜ ɞɜɢɝɚɬɟɥɟ [1]. ȼ ɷɬɨɦ ɭɪɚɜɧɟɧɢɢ
m — ɩɨɤɚɡɚɬɟɥɶ ɩɪɨɰɟɫɫɚ ɫɝɨɪɚɧɢɹ, tz — ɭɫɥɨɜɧɚɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɫɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ.
Ɏɨɪɦɭɥɚ ȼɢɛɟ ɮɨɪɦɚɥɶɧɨ ɨɬɪɚɠɚɟɬ ɤɢɧɟɬɢɤɭ ɫɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ, ɬɨ ɟɫɬɶ ɨɫɧɨɜɵɜɚɟɬɫɹ ɧɚ
ɩɪɟɞɫɬɚɜɥɟɧɢɹɯ ɨ ɫɤɨɪɨɫɬɢ ɝɟɧɟɪɚɰɢɢ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ ɩɪɢ ɰɟɩɧɨɦ ɦɟɯɚɧɢɡɦɟ ɪɟɚɤɰɢɢ. Ⱦɥɹ ɟɟ
ɞɚɥɶɧɟɣɲɟɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɡɚɦɟɧɢɬɶ ɜ ɧɟɣ ɜɪɟɦɹ t ɧɚ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɤɨɥɟɧɱɚɬɨɝɨ
ɜɚɥɚ, ɨɬɫɱɢɬɵɜɚɟɦɵɣ ɨɬ ɬɨɱɤɢ ɧɚɱɚɥɚ ɜɢɞɢɦɨɝɨ ɫɝɨɪɚɧɢɹ, ɬɨ ɟɫɬɶ ɨɬ
, ɬɨɝɞɚ
,
(12)
ɝɞɟ ij, ijz — ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɬɟɤɭɳɚɹ ɢ ɭɫɥɨɜɧɚɹ ɞɥɢɬɟɥɶɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɫɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ, ɜɵɪɚɠɟɧɧɵɟ ɜ ɭɝɥɚɯ ɩɨɜɨɪɨɬɚ ɤɨɥɟɧɱɚɬɨɝɨ ɜɚɥɚ ɨɬ ɧɚɱɚɥɚ ɜɢɞɢɦɨɝɨ ɫɝɨɪɚɧɢɹ.
Ⱦɢɮɮɟɪɟɧɰɢɪɭɹ ɭɪɚɜɧɟɧɢɟ (12), ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɫɝɨɪɚɧɢɹ
ɬɨɩɥɢɜɚ:
.
(13)
ɋ ɭɱɟɬɨɦ ɧɟɞɨɫɬɚɬɨɱɧɨɣ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɦɟɯɚɧɢɡɦɚ ɰɟɩɧɵɯ ɪɟɚɤɰɢɣ ɜ ɩɪɨɰɟɫɫɟ ɫɝɨɪɚɧɢɹ
ɫɥɨɠɧɨɝɨ ɭɝɥɟɜɨɞɨɪɨɞɧɨɝɨ ɬɨɩɥɢɜɚ ɨɩɪɟɞɟɥɟɧɢɟ ɨɫɧɨɜɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɝɨɪɚɧɢɹ m ɢ ijz ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɩɭɬɟɦ. ɂɫɩɨɥɶɡɭɹ ɢɧɞɢɤɚɬɨɪɧɭɸ ɞɢɚɝɪɚɦɦɭ p = f(ij), ɩɨɥɭɱɟɧɧɭɸ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɩɭɬɟɦ, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɭɤɚɡɚɧɧɵɟ ɨɫɧɨɜɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɝɨɪɚɧɢɹ.
Ⱦɥɹ ɷɬɨɝɨ ɜɵɞɟɥɢɦ ɜ ɢɧɞɢɤɚɬɨɪɧɨɣ ɞɢɚɝɪɚɦɦɟ ɡɚɜɢɫɢɦɨɫɬɶ ɜɵɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ ɜɢɞɚ x = f(ij). Ɂɞɟɫɶ
ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɱɚɫɬɶ ɩɪɨɰɟɫɫɚ, ɚ ɢɦɟɧɧɨ ɨɬ ɧɚɱɚɥɚ ɜɢɞɢɦɨɝɨ ɫɝɨɪɚɧɢɹ ɞɨ ɨɬɤɪɵɬɢɹ ɜɵɩɭɫɤɧɵɯ ɤɥɚɩɚɧɨɜ, ɝɞɟ ɨɧ ɩɪɨɬɟɤɚɟɬ ɩɪɢ M = const.
Ⱦɥɹ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɨɛɴɟɦɚ ɩɟɪɟɦɟɳɟɧɢɹ ɩɨɪɲɧɹ ɜɵɪɚɠɟɧɢɟ ɩɟɪɜɨɝɨ ɡɚɤɨɧɚ ɬɟɪɦɨɞɢɧɚɦɢɤɢ
ɡɚɩɢɲɟɦ ɜ ɜɢɞɟ
dQ = Mdu + pdv + dQw ,
ɝɞɟ
(14)
dQ — ɷɥɟɦɟɧɬɚɪɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɩɨɞɜɟɞɟɧɧɨɣ ɬɟɩɥɨɬɵ;
du — ɢɡɦɟɧɟɧɢɟ ɭɞɟɥɶɧɨɣ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɪɚɛɨɱɟɝɨ ɬɟɥɚ;
p — ɞɚɜɥɟɧɢɟ ɪɚɛɨɱɟɝɨ ɬɟɥɚ;
dv — ɢɡɦɟɧɟɧɢɟ ɪɚɛɨɱɟɝɨ ɨɛɴɟɦɚ ɰɢɥɢɧɞɪɚ;
dQw — ɷɥɟɦɟɧɬɚɪɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɨɬɜɟɞɟɧɧɨɣ ɨɬ ɪɚɛɨɱɟɝɨ ɬɟɥɚ.
ɉɪɢ ɫɝɨɪɚɧɢɢ ɰɢɤɥɨɜɨɣ ɩɨɞɚɱɢ qɰ ɜɵɞɟɥɹɟɬɫɹ ɬɟɩɥɨɬɚ:
dQ = qɰ Â QH Â dx,
(15)
ɝɞɟ dx — ɷɥɟɦɟɧɬɚɪɧɚɹ ɞɨɥɹ ɫɝɨɪɟɜɲɟɝɨ ɬɨɩɥɢɜɚ.
ȿɫɥɢ ɫɱɢɬɚɬɶ, ɱɬɨ ɪɚɛɨɱɟɟ ɬɟɥɨ ɜ ɰɢɥɢɧɞɪɟ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɚɦɢ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, PV = MRT,
ɚ du = CV dT, ɬɨ, ɩɨɞɫɬɚɜɥɹɹ ɜ (14) ɜɵɪɚɠɟɧɢɟ (15) ɢ ɪɚɡɞɟɥɢɜ ɩɪɚɜɭɸ ɢ ɥɟɜɭɸ ɱɚɫɬɢ ɩɨɥɭɱɟɧɧɨɝɨ
ɭɪɚɜɧɟɧɢɹ ɧɚ ɜɧɭɬɪɟɧɧɸɸ ɷɧɟɪɝɢɸ ɪɚɛɨɱɟɝɨ ɬɟɥɚ, ɩɨɥɭɱɢɦ
qɰ Â QH
(16)
Выпуск 2
ɍɱɢɬɵɜɚɹ, ɱɬɨ
.
, ɩɨɥɭɱɚɟɦ
qɰ Â QH
.
(17)
ȼɵɪɚɠɚɹ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɢɡɦɟɧɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɫɨɫɬɨɹɧɢɹ ɢɡ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ, ɩɨɥɭɱɢɦ
.
(18)
65
ɋɨɩɨɫɬɚɜɥɹɹ ɭɪɚɜɧɟɧɢɹ (17) (18) ɢ ɪɟɲɚɹ ɢɯ ɨɬɧɨɫɢɬɟɥɶɧɨ
dx
dM
ɝɞɟ
, ɧɚɣɞɟɦ
M ˜ CV ˜ T § d ln P
dQ ·
1
d ln v
K
˜ w ¸,
¨
QHH © d M
qɰ Q
dM
M ˜ CV ˜ T d M ¹
(19)
— ɫɤɨɪɨɫɬɶ ɫɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ;
— ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ;
— ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɛɴɟɦɚ.
Ɉɬɫɸɞɚ ɫɤɨɪɨɫɬɶ ɬɟɩɥɨɨɬɜɨɞɚ ɨɬ ɪɚɛɨɱɟɝɨ ɬɟɥɚ
ɪɚɜɧɚ
(20)
ɝɞɟ Į(ij) — ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɟɩɥɨɨɬɞɚɱɢ, ɨɫɪɟɞɧɟɧɧɨɟ ɩɨ ɦɝɧɨɜɟɧɧɨɣ ɬɟɩɥɨɜɨɫɩɪɢɧɢɦɚɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ F(ij);
T(ij) — ɬɟɦɩɟɪɚɬɭɪɚ ɪɚɛɨɱɟɝɨ ɬɟɥɚ;
Tw — ɬɟɦɩɟɪɚɬɭɪɚ ɩɨɜɟɪɯɧɨɫɬɟɣ ɤɚɦɟɪɵ ɫɝɨɪɚɧɢɹ;
n — ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɤɨɥɟɧɱɚɬɨɝɨ ɜɚɥɚ.
ȼɟɥɢɱɢɧɵ Ɇ ɢ qɰ ɢɡɦɟɪɹɸɬɫɹ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɧɚ ɫɬɟɧɞɟ, ɬɚɤ ɤɚɤ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɜɨɡɞɭɲɧɵɣ ɡɚɪɹɞ ɢ ɰɢɤɥɨɜɭɸ ɩɨɞɚɱɭ ɬɨɩɥɢɜɚ. ɇɢɡɲɚɹ ɬɟɩɥɨɬɚ ɫɝɨɪɚɧɢɹ Qɇ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɚɪɤɨɣ
ɬɨɩɥɢɜɚ.
ɇɚ ɨɫɧɨɜɟ ɤɢɧɟɦɚɬɢɤɢ ɤɪɢɜɨɲɢɩɧɨ-ɲɚɬɭɧɧɨɝɨ ɦɟɯɚɧɢɡɦɚ ɜɵɱɢɫɥɹɟɬɫɹ ɜɟɥɢɱɢɧɚ
.
Ɉɛɪɚɛɚɬɵɜɚɹ ɢɧɞɢɤɚɬɨɪɧɭɸ ɞɢɚɝɪɚɦɦɭ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ,
ɧɚɯɨɞɢɦ
, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢɫɬɢɧɧɨɟ ɡɧɚɱɟɧɢɟ ɢɡɨɯɨɪɧɨɣ
ɬɟɩɥɨɟɦɤɨɫɬɢ CV ɢ ɩɨɤɚɡɚɬɟɥɹ ɚɞɢɚɛɚɬɵ Ʉ.
ɂɦɟɹ ɢɧɞɢɤɚɬɨɪɧɭɸ ɞɢɚɝɪɚɦɦɭ ɜ ɜɢɞɟ ɤɪɢɜɨɣ P = f ( ij ) ɢɥɢ ɜ ɬɚɛɥɢɱɧɨɣ ɮɨɪɦɟ, ɧɚɯɨɞɢɦ
Выпуск 2
ɨɬɧɨɫɢɬɟɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɞɚɜɥɟɧɢɹ ɜ ɰɢɥɢɧɞɪɟ:
66
.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ (19) ɧɟɨɛɯɨɞɢɦɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɧɚɱɚɥɶɧɵɟ
ɭɫɥɨɜɢɹ. ȼ ɧɚɱɚɥɟ ɜɢɞɢɦɨɝɨ ɝɨɪɟɧɢɹ (ɜ ɬɨɱɤɟ ɨɬɪɵɜɚ ɤɪɢɜɨɣ ɝɨɪɟɧɢɹ ɨɬ ɤɪɢɜɨɣ ɫɠɚɬɢɹ) ɢɡɜɟɫɬɧɵ
ij0, Ɋ0, Ɍ0, ɩɪɢ ɷɬɨɦ x = 0, ɚ ij = ij0.
ɑɢɫɥɟɧɧɨ ɢɧɬɟɝɪɢɪɭɹ ɭɪɚɜɧɟɧɢɟ (19) ɦɟɬɨɞɨɦ Ɋɭɧɝɟ–Ʉɭɬɬɚ, ɧɚɯɨɞɢɦ ɡɚɜɢɫɢɦɨɫɬɶ ɜɵɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ x = f(ij).
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɩɭɬɟɦ ɩɨɥɭɱɟɧɚ ɤɪɢɜɚɹ ɜɵɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ ɤɚɤ ɮɭɧɤɰɢɹ ɭɝɥɚ ɩɨɜɨɪɨɬɚ ɤɨɥɟɧɱɚɬɨɝɨ ɜɚɥɚ, ɤɨɬɨɪɚɹ ɩɨɡɜɨɥɹɟɬ ɜɵɱɢɫɥɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɝɨɪɟɧɢɹ: ɭɫɥɨɜɧɭɸ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɫɝɨɪɚɧɢɹ ijz ɢ ɩɨɤɚɡɚɬɟɥɶ ɫɝɨɪɚɧɢɹ m. ɉɨɫɥɟɞɧɟɟ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ
ɫɞɟɥɚɬɶ ɧɟɤɨɬɨɪɵɟ ɨɛɨɛɳɟɧɢɹ ɢ ɭɫɬɚɧɨɜɢɬɶ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɫɜɹɡɚɧɧɵɟ ɫ ɜɵɞɟɥɟɧɢɟɦ ɬɟɩɥɨɬɵ
ɩɪɢ ɫɝɨɪɚɧɢɢ ɬɨɩɥɢɜɚ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɢɫɩɨɥɶɡɭɟɦ ɭɪɚɜɧɟɧɢɟ (11). ɉɪɟɨɛɪɚɡɭɟɦ ɟɝɨ ɢ
ɩɪɨɥɨɝɚɪɢɮɦɢɪɭɟɦ
,
(21)
ɩɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɩɨɥɭɱɢɦ
(22)
ɉɨɫɥɟ ɜɬɨɪɢɱɧɨɝɨ ɥɨɝɚɪɢɮɦɢɪɨɜɚɧɢɹ:
(23)
ɉɪɟɞɫɬɚɜɢɦ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɜ ɜɢɞɟ
.
(24)
ȼɟɥɢɱɢɧɚ, ɫɬɨɹɳɚɹ ɜ ɤɜɚɞɪɚɬɧɵɯ ɫɤɨɛɤɚɯ, ɟɫɬɶ ɮɭɧɤɰɢɹ ɞɨɥɢ ɜɵɝɨɪɟɜɲɟɝɨ ɬɨɩɥɢɜɚ x. Ɉɛɨɡɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɨɛɨɡɧɚɱɢɦ Y = lg ij ɢ Yz = lg ijz, ɬɨɝɞɚ
ɧɚɱɢɦ ɟɟ ɤɚɤ
(25)
ȼ ɢɬɨɝɟ ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɟ ɩɪɹɦɨɣ, ɝɞɟ ɦɧɨɠɢɬɟɥɶ
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɭɝɥɨɜɨɣ ɤɨ-
ɷɮɮɢɰɢɟɧɬ (ɪɢɫ. 2).
Ɉɬɪɟɡɤɢ Xz ɢ Yz ɮɢɤɫɢɪɭɸɬɫɹ ɧɚ
ɨɫɹɯ ɤɨɨɪɞɢɧɚɬ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ
tg tg
,
(26)
ɨɬɤɭɞɚ
ɢ
. (27)
ȕ
Выпуск 2
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɫɩɨɥɶɡɭɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɨɥɭɱɟɧɧɭɸ ɢɧɞɢɤɚɬɨɪɧɭɸ ɞɢɚɝɪɚɦɦɭ P = f (ij), ɨɩɪɟɞɟɥɹɟɦ ɭɫɥɨɜɧɭɸ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ
ɫɝɨɪɚɧɢɹ ij z ɢ ɩɨɤɚɡɚɬɟɥɶ ɯɚɪɚɤɬɟɪɢɫɊɢɫ. 2. ɍɪɚɜɧɟɧɢɟ ɩɪɹɦɨɣ
ɬɢɤɢ ɫɝɨɪɚɧɢɹ m. Ɉɞɧɚɤɨ ɨɧɢ ɫɜɨɣɫɬɜɟɧɧɵ ɬɨɥɶɤɨ ɬɨɣ ɮɨɪɦɟ ɤɚɦɟɪɟ ɫɝɨɪɚɧɢɹ ɢ ɪɟɠɢɦɭ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ, ɧɚ
ɤɨɬɨɪɨɦ ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɢɧɞɢɤɚɬɨɪɧɚɹ
ɞɢɚɝɪɚɦɦɚ. ɂɡɦɟɧɟɧɢɟ ɪɟɠɢɦɚ ɪɚɛɨɬɵ, ɤɨɧɫɬɪɭɤɰɢɢ ɤɚɦɟɪɵ ɫɝɨɪɚɧɢɹ ɢ ɞɚɠɟ ɬɨɩɥɢɜɨɩɨɞɚɱɢ
ɩɪɢɜɨɞɢɬ ɢ ɤ ɢɡɦɟɧɟɧɢɸ ɷɬɢɯ ɩɨɤɚɡɚɬɟɥɟɣ.
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɞɢɡɟɥɹɯ ɫɤɨɪɨɫɬɶ ɩɪɨɬɟɤɚɧɢɹ ɯɢɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɜɵɲɟ ɫɤɨɪɨɫɬɢ ɮɢɡɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫɨɜ, ɩɨɷɬɨɦɭ ɜɧɚɱɚɥɟ ɫɝɨɪɚɟɬ ɩɨɪɰɢɹ ɬɨɩɥɢɜɚ, ɩɨɞɝɨɬɨɜɥɟɧɧɚɹ ɡɚ ɜɪɟɦɹ
ɡɚɞɟɪɠɤɢ ɫɚɦɨɜɨɫɩɥɚɦɟɧɟɧɢɹ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɪɚɡɜɢɬɢɟ ɪɟɚɤɰɢɢ ɫɝɨɪɚɧɢɹ ɩɨɞɱɢɧɹɟɬɫɹ ɡɚɤɨɧɚɦ
ɤɢɧɟɬɢɤɢ. ɉɨɫɥɟ ɜɵɝɨɪɚɧɢɹ ɩɟɪɜɢɱɧɨɣ ɩɨɪɰɢɢ ɬɨɩɥɢɜɚ ɫɤɨɪɨɫɬɶ ɩɪɨɬɟɤɚɧɢɹ ɪɟɚɤɰɢɢ ɫɞɟɪɠɢɜɚɟɬɫɹ ɫɤɨɪɨɫɬɶɸ ɞɢɮɮɭɡɢɢ ɩɚɪɨɨɛɪɚɡɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ ɬɨɩɥɢɜɚ, ɱɬɨ ɩɨɞɬɜɟɪɠɞɚɟɬ ɢ ɷɤɫɩɟɪɢɦɟɧɬ.
ɇɚ ɪɢɫ. 3 ɩɪɢɜɟɞɟɧ ɬɢɩɢɱɧɵɣ ɝɪɚɮɢɤ ɫɤɨɪɨɫɬɢ ɫɝɨɪɚɧɢɹ ɞɢɡɟɥɹ.
67
ȼ ɨɬɥɢɱɢɟ ɨɬ ɫɝɨɪɚɧɢɹ ɝɨɦɨɝɟɧɧɵɯ ɫɢɫɬɟɦ ɜ
ɰɢɥɢɧɞɪɚɯ ɤɚɪɛɸɪɚɬɨɪɧɵɯ ɢ ɝɚɡɨɜɵɯ ɞɜɢɝɚɬɟɥɟɣ,
ɝɞɟ ɤɪɢɜɚɹ ɫɤɨɪɨɫɬɢ ɜɵɞɟɥɟɧɢɹ ɬɟɩɥɨɬɵ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɨɞɧɢɦ ɦɚɤɫɢɦɭɦɨɦ, ɭ ɞɢɡɟɥɟɣ ɢɯ ɞɜɚ.
ɉɪɢɪɨɞɚ ɩɟɪɜɨɝɨ ɦɚɤɫɢɦɭɦɚ ɨɛɴɹɫɧɹɟɬɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɤɢɧɟɬɢɱɟɫɤɢɦ ɦɟɯɚɧɢɡɦɨɦ ɫɝɨɪɚɧɢɹ:
ɩɪɨɢɫɯɨɞɢɬ ɫɝɨɪɚɧɢɟ ɭɠɟ ɩɨɞɝɨɬɨɜɥɟɧɧɨɣ ɬɨɩɥɢɜɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ, ɤɨɬɨɪɚɹ ɨɛɪɚɡɨɜɚɥɚɫɶ ɩɪɢ ɢɫɩɚɪɟɧɢɢ ɬɨɩɥɢɜɧɨɝɨ ɮɚɤɟɥɚ ɜ ɩɪɨɰɟɫɫɟ ɩɪɨɞɜɢɠɟɧɢɹ ɟɝɨ ɩɨ ɤɚɦɟɪɟ ɫɝɨɪɚɧɢɹ. Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɞɨɥɹ
ɬɨɩɥɢɜɚ, ɫɝɨɪɟɜɲɟɝɨ ɜ ɩɟɪɜɨɣ ɮɚɡɟ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ
Ɋɢɫ. 3. Ƚɪɚɮɢɤ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ
ɬɨɱɤɟ ɋ ɧɚ ɤɪɢɜɨɣ 3. ȼɬɨɪɨɣ ɦɚɤɫɢɦɭɦ ɭɱɢɬɵɜɚɟɬ
ɫɝɨɪɚɧɢɟ ɢɫɩɚɪɢɜɲɢɯɫɹ ɤɚɩɟɥɶ ɬɨɩɥɢɜɚ ɜ ɤɚɦɟɪɟ
ɫɝɨɪɚɧɢɹ, ɝɞɟ ɫɤɨɪɨɫɬɶ ɤɢɧɟɬɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɫɤɨɪɨɫɬɶɸ ɞɢɮɮɭɡɢɢ ɪɟɚɝɢɪɭɸɳɢɯ ɜɟɳɟɫɬɜ. ɉɪɨɰɟɫɫ ɫɝɨɪɚɧɢɹ ɜ ɷɬɨɣ ɮɚɡɟ ɯɚɪɚɤɬɟɪɟɧ ɬɟɦ, ɱɬɨ ɡɞɟɫɶ ɫɦɟɫɟɨɛɪɚɡɨɜɚɧɢɟ ɢɦɟɟɬ ɱɢɫɬɨ ɞɢɮɮɭɡɢɨɧɧɭɸ (ɢ ɬɭɪɛɭɥɟɧɬɧɭɸ) ɩɪɢɪɨɞɭ,
ɩɨɷɬɨɦɭ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ ɨɤɢɫɥɟɧɢɹ ɫɞɟɪɠɢɜɚɟɬɫɹ ɷɬɢɦ ɮɚɤɬɨɪɨɦ. Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɞɨɥɹ ɬɨɩɥɢɜɚ,
ɫɝɨɪɚɸɳɚɹ ɜ ɷɬɨɣ ɮɚɡɟ, ɫɨɫɬɚɜɥɹɟɬ ɜɟɥɢɱɢɧɭ 1 – ɏɋ (ɫɦ. ɪɢɫ. 3).
Ɉɩɢɫɚɧɢɟ ɫɤɨɪɨɫɬɢ ɫɝɨɪɚɧɢɹ ɤɚɤ ɩɟɪɜɨɝɨ, ɬɚɤ ɢ ɜɬɨɪɨɝɨ ɭɱɚɫɬɤɨɜ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ ɞɨɩɭɫɬɢɦɨ ɫ ɩɨɦɨɳɶɸ ɮɨɪɦɭɥɵ ȼɢɛɟ. Ɉɞɧɚɤɨ ɫɥɟɞɭɟɬ ɩɨɦɧɢɬɶ ɨ ɪɚɡɥɢɱɧɨɣ ɩɪɢɪɨɞɟ ɷɬɢɯ ɩɪɨɰɟɫɫɨɜ.
Ɋɟɡɭɥɶɬɢɪɭɸɳɭɸ ɤɪɢɜɭɸ ɫɤɨɪɨɫɬɢ ɜɵɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ ɫɭɦɦɭ ɞɜɭɯ
ɞɨ
, ɞɚɥɟɟ ɨɧɚ ɮɢɤɬɢɜɧɚ.
ɂ ɧɚɨɛɨɪɨɬ, ɤɪɢɜɚɹ 2 ɜ ɨɛɨɡɧɚɱɟɧɧɵɯ ɩɪɟɞɟɥɚɯ ɮɢɤɬɢɜɧɚ ɢ, ɧɚɱɢɧɚɹ ɨɬ
, ɞɟɣɫɬɜɢɬɟɥɶɧɚ.
ɤɪɢɜɵɯ 1 ɢ 2 (ɫɦ. ɪɢɫ. 3). Ʉɪɢɜɚɹ 1 ɮɢɡɢɱɟɫɤɢ ɢɦɟɟɬ ɦɟɫɬɨ ɨɬ
ɂɧɬɟɝɪɚɥ ɷɬɢɯ ɤɪɢɜɵɯ ɞɚɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ ɜ ɰɢɤɥɟ 3. ɉɟɪɟɫɬɪɨɢɦ ɟɟ ɜ ɥɨɝɚɪɢɮɦɢɱɟɫɤɭɸ ɚɧɚɦɨɪɮɨɡɭ, ɝɞɟ
; Y = lg ij.
Ʉɚɠɞɨɣ ɮɚɡɟ ɫɝɨɪɚɧɢɹ ɜ ɤɨɨɪɞɢɧɚɬɚɯ X–Y ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɜɨɹ ɩɪɹɦɚɹ (ɪɢɫ. 4).
Ɉɛɨɡɧɚɱɢɦ ɩɚɪɚɦɟɬɪɵ, ɨɬɧɨɫɹɳɢɟɫɹ ɤ ɩɟɪɜɨɦɭ ɭɱɚɫɬɤɭ, ɢɧɞɟɤɫɨɦ 1,
ɤɨ ɜɬɨɪɨɦɭ — ɢɧɞɟɤɫɨɦ 2:
,
(28)
Выпуск 2
.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ
ɜɨɡɦɨɠɧɵɦ ɜɵɱɢɫɥɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɝɨɪɚɧɢɹ:
68
,
(29)
Ɋɢɫ. 4. ɍɪɚɜɧɟɧɢɟ ɩɪɹɦɨɣ ɥɢɧɢɢ
ɞɥɹ I ɢ II ɮɚɡ ɫɝɨɪɚɧɢɹ
.
ɉɟɪɟɫɟɱɟɧɢɟ ɡɚɜɢɫɢɦɨɫɬɟɣ 1 ɢ 2 (ɫɦ. ɪɢɫ. 3) ɞɚɟɬ ɬɨɱɤɭ ɋ — ɝɪɚɧɢɰɭ ɪɚɡɞɟɥɚ I ɢ II ɮɚɡ ɫɝɨɪɚɧɢɹ, ɨɩɪɟɞɟɥɢɦ ɟɟ.
ȿɫɥɢ
(30)
ɬɨ ɜ ɨɛɳɟɣ ɬɨɱɤɟ ɋ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ 1 – ɏ1 = 1 – ɏ2.
Ɋɟɲɚɹ ɫɨɜɦɟɫɬɧɨ ɭɪɚɜɧɟɧɢɹ (30) ɨɬɧɨɫɢɬɟɥɶɧɨ ijɋ, ɩɨɥɭɱɢɦ
(31)
ɂɬɚɤ, ɩɨɥɭɱɟɧɚ ɜɨɡɦɨɠɧɨɫɬɶ, ɢɫɩɨɥɶɡɭɹ ɞɚɧɧɵɟ ɷɤɫɩɟɪɢɦɟɧɬɚ, ɨɩɢɫɚɬɶ ɩɪɨɰɟɫɫ ɜɵɞɟɥɟɧɢɹ
ɬɟɩɥɨɬɵ ɩɪɢ ɫɝɨɪɚɧɢɢ ɝɟɬɟɪɨɝɟɧɧɵɯ ɫɦɟɫɟɣ ɜ ɞɢɡɟɥɟ.
ɋɩɢɫɨɤ ɥɢɬɟɪɚɬɭɪɵ
1. ȼɢɛɟ ɂ. ɂ. Ɍɟɨɪɢɹ ɞɜɢɝɚɬɟɥɟɣ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ: ɤɨɧɫɩɟɤɬ ɥɟɤɰɢɣ / ɂ. ɂ. ȼɢɛɟ. — ɑɟɥɹɛɢɧɫɤ, 1974. — 252 ɫ.
2. Ⱦɶɹɱɟɧɤɨ ɇ. ɏ. Ɍɟɨɪɢɹ ɞɜɢɝɚɬɟɥɟɣ ɜɧɭɬɪɟɧɧɟɝɨ ɫɝɨɪɚɧɢɹ / ɇ. ɏ. Ⱦɶɹɱɟɧɤɨ. — Ʌ.: Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, 1974. — 552 ɫ.
3. ɉɟɬɪɢɱɟɧɤɨ Ɋ. Ɇ. Ʉɨɧɜɟɤɬɢɜɧɵɣ ɬɟɩɥɨɨɛɦɟɧ ɜ ɩɨɪɲɧɟɜɵɯ ɦɚɲɢɧɚɯ / Ɋ. Ɇ. ɉɟɬɪɢɱɟɧɤɨ,
Ɇ. Ɋ. ɉɟɬɪɢɱɟɧɤɨ. — Ʌ.: Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, 1979. — 233 ɫ.
4. ɋɜɢɪɢɞɨɜ ɘ. Ȼ. Ɍɨɩɥɢɜɨ ɢ ɬɨɩɥɢɜɨɩɨɞɚɱɚ ɚɜɬɨɬɪɚɤɬɨɪɧɵɯ ɞɢɡɟɥɟɣ / ɘ. Ȼ. ɋɜɢɪɢɞɨɜ
[ɢ ɞɪ.]. — Ʌ.: Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, 1979. — 248 ɫ.
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